Sigbovik 2014#

Click for full version PDF

! 2⁶

\" #

$

%$ &\'%(

{width="6.523665791776028in"
height="1.1070002187226597in"}

SIGBOVIK

A Record of the Proceedings of SIGBOVIK 2014

ISSN 2155-0166

April 1, 2014

Copyright is maintained by the individual authors, though obviously
this all gets posted to the Internet and stuff, because it's 2014.

Permission to make digital or hard copies of portions of this work for
personal use is granted; permission to make digital or hard copies of
portions of this work for classroom use is also granted, but seems
ill-advised. Abstracting with credit is permitted; abstracting with
credit cards seems difficult.

Additional copies of this work may be ordered from Lulu; refer to
http://sigbovik.org for details.

ȨȨ

SIGBOVIK 2014 {width="1.005333552055993in"
height="1.005333552055993in"}

Message from the Organizing Committee

Multiple-Choice Section

1. 5 points. Please indicate below the emotions with which the
SIGBOVIK Organizing Com mittee presents this document. Circle up to
three, but no fewer than four, choices.

$a$ Joy

$b$ Embarrassment

$c$ Surprise

$d$ Admiration

$e$ Arrogance

$f$ Pride

$g$ Terror

2. 5 points. Which is the correct full name of this conference?

$a$ The Eighth Annual Intercalary Conference about Symposium on
Human Dance Party of Workshop in Celebration of Harry W. Bovik's
2⁶th Birthday.

$b$ The Eightieth Annual Intracalary Workshop about Workshop on
Robot Dance Party of Conference in Mourning of Harry Q. Bovik's 2⁶th
Birthday.

$c$ The Eighth Centennial Intercalary Workshop about Symposium on
Robot Karaoke Party of Conference in Celebration of Harry Q. Bovik's
3⁶th Birthday.

$d$ The Eighth Annual Intercalary Workshop about Symposium on Robot
Dance Party of Conference in Celebration of Harry Q. Bovik's 2⁶th
Birthday.

Reading Comprehension Section

25 points.

This year's SIGBOVIK marks our eighth continuous year of high-quality
research in a rich variety of topics, including but not limited to
applied phlogistonics, synergistic hyperparadigmatism, and elbow
macaroni. Eight is a very special annuality of this conference, as it
not only breaks the

ȨȨȨ

"highest annuality" record set last year, but also is the fourth power
of two number of years for which this conference has been in
existence. If you're not impressed yet, note that the fourth power of
two is a very special power of two, as four is the second power of
two, and you know what they say about the second power of two.

As it is a very special year, we have decided to conduct a survey of
past SIGBOVIKs, or SIG BOVIX for short, classifying the various papers
to get a feel for where future SIGBOVIKs might be headed. This was
driven by the realization depicted in Figure 1.

Serious treatment

Humorous treatment

Serious idea

Humorous idea

+-----------------------------------+-----------------------------------+
| > Mainstream conferences | SIGBOVIK |
+===================================+===================================+
| SIGBOVIK | SIGBOVIK |
+-----------------------------------+-----------------------------------+

Figure 1: A research paper is comprised of an idea and a treatment of
that idea. Each of the idea and the treatment may be either serious or
humorous.

Observe that SIGBOVIK offers a venue for three times as many different
types of research as "mainstream" conferences. We won't belabour the
obvious conclusion that SIGBOVIK is superior, although, you know, just
getting that out there, we were all thinking it; rather, we are
interested in distinguishing among SIGBOVIK's three major categories
of research.

1. Humorous idea, humorous treatment. The most common, but by no
means the most lowly, of SIGBOVIK publications. The research
contribution is typically contained entirely within the paper itself;
no separate artefact is constructed.

2. Serious idea, humorous treatment. The rarest specimen of SIGBOVIK
research. Often a retelling of famous events, people, or theoretical
results from mainstream computer science.

3. Humorous idea; serious treatment. Frequently denoted by
independent artefacts accompa nying the paper submission, such as a
website, compiler implementation, hardware, or proof. Such
publications would often be suitable for acceptance at "mainstream"
conferences, were the core idea not out of scope.

I We surveyed the proceedings of past SIGs BOVIK the night
before finalizing the proceedings and ~~sending them off to Lulu~~
like responsible researchers. Our methodology is definitely completely
immune to any biases that might be caused by the survey not being
blinded in any way or by it being conducted by only one person, and
definitely free from any bias related to the study subject knowing in
advance which conclusions would be drawn. The results of our survey
are shown in Figures 2 and 3 ~~below~~ on the next page.

Ȩɨ

Humorous treatment of humorous idea Humorous treatment of serious idea
Serious treatment of humorous idea Other

SIGBOVIK year of incidence

2007 2008 2009 2010 2011 2012 2013 2014

32 20 30 33 16 17 15 16

2 0 1 0 0 1 2 0

2 4 3 0 4 6 6 8

1 1 5 3 0 2 2 0

Total publications 37 25 39 36 20 26 25 24

Figure 2: Results. The 'other' category comprises submissions that
defy my perfect classification scheme, including cryptic iconography,
video games, comics, choose your own adventures, and take-home midterm
examinations.

SIGBOVIK year of incidence

2007 2008 2009 2010 2011 2012 2013 2014

Meta-humor about research Type theory or programming jokes Puns

Poop or dick jokes

Politics, economics, or patents jokes Social media jokes

Other

7 2 8 8 8 1 2 2

8 3 1 7 2 1 2 4

4 4 8 1 0 0 2 3

1 0 1 1 0 1 1 2

0 0 0 0 1 2 2 1

0 0 0 2 2 1 0 0

12 11 11 12 3 11 4 4

Figure 3: Breakdown among category-1 publications of subject of humor.
Among this new 'other' category dwell comestibility theory,
NP-completeness, cat pictures, computational impossibilities, the
supernatural, and robot uprisings and other apocalypse situations.

A number of trends are evident. First and foremost is the decline over
time of the proportion of category-1 submissions and a corresponding
increase in submissions accompanied by an actual artefact that must have
been put together with blood, sweat, and so forth, rather than just the
cushy endeavour of writing down shallow drivel in LaTeX and calling that
a "research paper". Go us! Just kidding. We value all SIGBOVIK
submissions highly, ~~except for~~ especially yours. But really.

Second, we note the prominence among category-1 submissions of
meta-research papers; that is, papers about writing papers, giving
talks, or improving productivity. It is unsurprising that this is a
popular subject for obvious reasons. Finally, we note a modest decline
in the proportion of programming language papers, which we attribute to
SIGBOVIK's audience's interests expanding beyond the core of its
type-theoretician founding mothers and fathers, to include such
newfangled topics as Twitterers and Bitdollars.

Without further ado, adon't, or adonuts, the proceedings of your
SIGBOVIK #8. ɨ

ɨȨ

\<RX :RQW %HOLHYH 7KLV 7DEOH RI &RQWHQWV

7UDFN 7DNH 7KH 4XL] :KLFK 3RLQWOHVV 7LPH :DVWLQJ $PXVHPHQW DUH
\<RX\" >Qr iQ E22T :` /m i2 aim/2Mi \"mbv
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX j kX L2r
_2bmHib BM k/n SQr2`@>Qm`b
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXX8
jX GBM2 ` GQ;B+ 6`22
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX X X X
X X X X X X X X X X X X X X X Rd 9X Ai aiBHH a22Kb h? i \"H +F > b
>QT2 BM h?2b2 1ti`2K2Hv lM7 B` o `B Mib Q7 *?2bb X X X X X X X X
X X X X X X X X X X X X XkR

7UDFN (SLF /RFDO 1HZV 6WRULHV \<RXOO %H 6DG \<RX 0LVVHG

S _hA G h_ La*_ASh P6 .1 LǶa aS11*> hP h>1 6 *lGhu P6 h>1
J1GGPL *PGG1:1 P6 a*A1L*1a
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX X X X
X X X X X X X X X X X X X X X X X X X X X kN

kX M HvbBb Q7 i?2 1z2+ib Q7 am#bi MiB H G M2 *HQbm`2 .m`BM;
7i2`MQQM S2 F HQM; >2 pBHv@h` p2H2/ l`# M `i2`B H *?QF2@SQBMi
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX X X X
X X X X X X X X X X X X jj

jX u2i MQi?2` TTHB+ iBQM Q7 Pm` S2i h2+?MB[m2 X X X X X X X X X X X
X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X
X X X X X X X j8 9X SH2 b2 .QMǶi G2i PT2M >Qmb2 .2bi`Qv i?2
lMBp2`b2 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X
X X X X X X X X X X X X X X X X X X X 9R

7UDFN )RXU 8QEHOLHYDEOH 1HZ 7KHRUHWLFDO 3HUVSHFWLYHV

>2i2`QiQTv hvT2 h?2Q`v, .272Mb2 Q7 i?2 h` /BiBQM H 6QmM/ iBQMb Q7
J i?2K iB+b X X X X X X X X X X X X X X X X X X 9d kX h?2 .mKTBM; G2KK
@ bb2bbBM; _2;mH `Biv X X X X X X X X X X X X X X X X X X X X X X X
X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 8R jX
ai iBbiB+ H q i+? PTiBKBx iBQM
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX X X X
X X 8j 9X aBKTH2 * i2;Q`v@h?2Q`2iB+ lM/2`bi M/BM; Q7 *
i2;Q`v@h?2Q`2iB+ .B ;` Kb X X X X X X X X X X X X X X X X X X X X X
X X X 8d

7UDFN 7KH 7KUHH 0RVW ,PSRUWDQW :D\V WR 6WD\ 6DIH 7KLV 5HVHDUFK
6HDVRQ *`vTiQ;` T?B+ HHv@aQmM/ CQF2b
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX X X X
X X e8 kX .QHH `*QBM, *`vTiQ+m``2M+v rBi? S`QQ7@Q7@.QHH ` X X
X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X
X X X X X X X X X X X X ed jX hQr `/b *QKTH2i2Hv miQMQKQmb o2?B+H2 X
X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X
X X X X X X X X X X X X X X X X X X X X dR

ɨȨȨ

7UDFN ,PSURYH \<RXU 2ZQ 5HVHDUFK :LWK 7KHVH )LYH :HLUG 7ULFNV
\"2HB27@ambi BMBM; AM72`2M+2
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX X X X
X X X X X X dd kX aQHmiBQMb iQ G2v GBM2 ++2bb BM P++mHi *QKTmiBM; X X
X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X
X X X X X X X X X X X X X 3j

jX J2 bm`BM; uQm` P@M2bb,

.2i2`KBMBM; >Qr GBF2 S`Q# #BHBiv .Bbi`B#miBQM :Bp2M J i?2K iB+ H
P#D2+i Ab X X X X X X X X X X X X X X X X X X X X X3d 9X +H `B}+ iBQM
Q7 i2`KBMQHQ;v
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX X X X
X X X X NR 8X q? i- A7 Mvi?BM;- Bb 1TbBHQM\
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX X X X
X X XNj

7UDFN 7KHVH 1HZ :D\V WR 3URJUDP :LOO %ORZ \<RXU 0LQG A_a@Ry9y@\" b2/
*QKTmiBM;, h?2 lMi TT2/ *QKTmi iBQM H SQr2` Q7 \"m`2 m+` +v X X X
X X X X X X X X X X X X X X X XRyR

kX hQr `/b 6QQHBM; M/ 6QBHBM; i?2 La ,

am`p2vBM; i?2 ai i2 Q7 ai2; MQ;` T?B+ S`Q;` KKBM; G M;m ;2b X X X
X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X XRyj
jX SBF +?m- .QKQb m`- M/ Qi?2` JQMQH2tB+ H G M;m ;2b X X X X X X X X
X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X
X X RyN 9X lMBi@h2bi@\" b2/ S`Q;` KKBM;
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX X X X
X RR8

ɨȨȨȨ

)

*\
+\
, -

\%

* . $ $ $ $ $ $ $ $ $

& k/n

!!

* . / $\
$\
0\
\
\
\
$

1 \"\
\" # $ %

&\
\' #

* . $\
$

( ! $( )*\
+\
\
&\
\
!! , , - $& , $ .\
/ #\
, 0\
! # 1\
#2 0\
) 3

* . $\
\
$ $ $ $ 0\
$

ҫ

Ҭ

How to keep a graduate student busy

Paul Stansifer

1 April, 2014

Abstract

We propose a method for indefinitely occupying certain graduate stu
dents that requires only a finite amount of input information.

1 Motivation

Some graduate students are incapable of understanding recursion. Such
students need to be kept busy, lest they interfere with all of the
actual real work that is, in fact, really happening.

2 Method

To achieve this, simply apply the method described by Stansifer [1],
and iterate by one step more.

3 Mandible

You're not done with the previous section yet. Get out of here!

References

[1] Paul Stansifer. How to keep a graduate student busy. SIGBOVIK,
page [can I get back to you on that?], 2014.

ҭ

SIGBOVIK 2014 Paper Review
{width="0.9486668853893263in"
height="0.9486668853893263in"}

Paper 18: How to keep a graduate student busy

Norman I. Strong, RSU State University

Rating: ?? (??)

Confidence: ??/4

Program Chair's note: unfortunately, we are unable to print a review
for this paper as the reviewer assigned to the submission did not
finish reviewing the paper by the deadline. The last comment received
from the reviewer was "Since the 2014 work of Stansifer is so vital to
your method, please summarize the paper inline rather than assuming
the reader is already familiar it, as it is time-consuming and
tiresome for the reviewers to locate and review the prior work." The
PC apologizes for the delay and will pass on the rest of the review
when it is submitted.

ү

Abstract

New results in ^k/_n Power-Hours

Dr. Tom Murphy VII Ph.D.^∗

1 April 2014

-- The player may drink ⁺

⇒, or not drink ⇒

We correct for inebriated missteps, using computa tional methods to
establish new bounds in generalized ^k/_n Power-Hour theory.

Keywords: generalized binge drinking, maths, finite-state automata,
abstract interpretation

Introduction

A 2012 paper by Blum, Martens, Murphy, and Lovas[1] introduced the
^k/_n Power-Hour, a fractional variant on the well-known drinking
game. In a traditional Power Hour, participants drink one shot of beer
per minute for 60 minutes. Since 5--6 beers in an hour sometimes have
adverse effects, some players opt for an attenu ated version of the game
wherein fewer than 60 shots are consumed. However, since the game is
frantic and played simultaneous with others, it is critical to have a
mechanical procedure for performing the attenuated Hour. The framework
by Blum et al., hereafter BMML, gives a handful of simple operations
that can be used to define a state machine among p players:

• At the beginning of each minute, each player has at most one shot
glass in front of him or her

• The shot glass must be in one of three states: Filled , empty ∪, or
overturned ∩

• Atomically, each player performs an action based only on the state
of his or her cup. If not in pos session of a cup (written ∪), the
only action is to do nothing. With a cup:

^∗Copyright c 2014 the Regents of the Wikiplia Foundation. Appears in
SIGBOVIK 2014 with the chagrin of the Association for Computational
Heresy; IEEEEEE! press, Verlag-Verlag vol ume no. 0x40-2A. 0.00

-- The player may pass the cup in any state to any player (a fixed
player per action)

-- However: If the cup is filled and the player did not drink, it must
be passed in the filled state -- A player may not receive more than
one cup in the same round

Every assignment of rules and starting condition to p players yields a
deterministic outcome, though some of these are illegal (because they
result in two or more cups being passed to the same player in some
round). For legal games, the outcome is that the p players have
consumed k_i shots of beer where 1 ≤ i ≤ p and 0 ≤ k_i ≤ 60. For the
traditional power hour, the player starts with an empty cup, at each
step drinks,¹ leaves the cup empty, and passes to herself.

While the authors made a mostly clear definition of BMML and presented
some initial results, these results contained multiple serious errors
and the paper abruptly switches notation and assumptions several
times, and rambles incoherently. By their own admission, the au thors
were drinking while they wrote it, taking only one hour to do so.
Don't drink and derive, kids!

This paper revisits the problem of BMML from a modern, sober
perspective, clarifies some of the orig inal results, and presents
several new ones and a few conjectures. It is based on several pieces
of software, whose source is available online.²

1 One-player ^k/_n Power-Hours

The goal of the ^k/_n Power-Hour is to attenuate the num ber of
drinks consumed by the p players, and its expres

¹In practice, this is done by filling the cup and then drinking it.

²http://sourceforge.net/p/tom7misc/svn/HEAD/tree/ trunk/powerhour/

ұ

sive power comes from the ability to encode some state in the
orientation of the cups, and propagate that state via passing them
from player to player. Even without passing cups, the ability for a
single player to attenuate his drinking is nontrivial. Playing
drinking games alone is sad indeed, but the solo ^k/_n Power-Hour
still has prac tical applications. When playing a Power Hour with
others, if each player's desired k is attainable through solo methods
then there is no need for passing cups, which simplifies the
ergonomics considerably. A com mon case is where some of the players
would like to do half--Power-Hours, which is easily achieved in BMML
by transitioning ∪ to without drinking and to ∪ by drinking, and
passing to oneself.³

A full list of attainable ^k/_n Power-Hours where p = 1 appears in
Figure 1. Possible values of k are {0, 1, 2, 20, 29, 30, 31, 40, 58, 59,
60}. The BMML paper claimed that the possible values were {0, 1, 2, 20,
30, 40, 58, 59, 60}, describing 31 for example as "super impossible."
Achieving 31 is somewhat inter esting. One way to do it is to start with
∪, and use the rule that ∪ means drink and then fill the cup. We then
use the rule that means drink and flip the cup, and ∩ means don't drink
and fill the cup. Essentially we use ∪ to mean "this is the very first
state" and then take shots on alternating minutes by using ∩ and to
encode the parity. Exploiting non-steady-states like this (Figure 1) is
how we achieve k that does not share many factors with n.

It is tractable to work out the possibilities for the solo case by
hand, though apparently not while drinking [1]. These results were
generated by a computer program, which is probably necessary for p
> 1. In the remainder of the paper, I'll describe several different
approaches for exploring this space, and generalizations of it, com
putationally.

2 Two-player ^k/_n Power-Hours

For more players, the number of possible configurations explodes.
Let's make the following definitions to bound the size:

• t = 4, the number of starting states ( , ∪, ∩, ∪)

• a = 2 × p × 3, the number of actions given a cup. The player can
drink or not drink, pass to any player, and in 3 configurations ( , ∪,
∩)

³There are many variations, but this was the strategy used many
times in practice before being generalized to BMML.

Figure 1: State machine that achieves k = 31 in a solo BMML Power
Hour. + on an edge means the player drinks. The disembodied incoming
edge is the start state. The player always passes to herself.

Then the number of configurations is bounded by (t × a³)^p. For p =
1 this was just 864. For p = 2 it is 47,775,744; for p = 3 it's
12,694,994,583,552, already beyond the limits of straight enumeration.

However, this is just an upper bound. For one thing, the base of the
exponent is actually bounded by

t × a² × a_filled

where a_filled = (p×3)+p (the actions that can be taken on , where if
the player does not drink, then he must pass the cup ).

The values for p ∈ {1, 2, 3} are still 576; 21,233,664;
3,761,479,876,608. There are a few other simplifications possible.
Many of these games are illegal because they result in multiple cups
being passed to the same player in some turn. These are difficult to
exclude analytically, but there are some sufficient conditions; for
example, if two players pass to the same player no matter their in put
state, and every player starts with a cup, then their cups always
collide. There are also many games that are isomorphic. For one thing,
∪ and ∩ are not dis tinguished in the rules at all, so any two
configurations where these are simply swapped has the exact same out
come. Likewise for permuting the players.

21 million configurations is no big deal for a modern computer. A
simple SML program computes all of the configurations and runs them;
ones that are found to be illegal are rejected. (It implements the
first simplifica tion having to do with when generating the configura

Ҳ

k start rules

0 ∪ ∪⇒?, ∩⇒?, ⇒?

1 ∪ ∪ ⁺

⇒∩, ∩⇒∩, ⇒?

2 ∪ ∪ ⁺

⇒ , ∩⇒∩, ⁺

⇒∩

20 ∪ ∪⇒∩, ∩⇒ , ⁺

⇒∪

29 ∪ ∪⇒∩, ∩⇒ , ⁺

⇒∩

30 ∪ ∪ ⁺

⇒∩, ∩⇒∪, ⇒?

31 ∪ ∪ ⁺

⇒ , ∩⇒ , ⁺

⇒∩

40 ∪ ∪ ⁺

⇒∩, ∩⇒ , ⁺

⇒∪

58 ∪ ∪⇒∩, ∩⇒ , ⁺

⇒

59 ∪ ∪⇒∩, ∩ ⁺

⇒∩, ⇒?

60 ∪ ∪ ⁺

⇒∪, ∩⇒?, ⇒?

Figure 2: All the possible k for a solo Power-Hour in

BMML. A superscript + means that the player drinks. The symbol ? means
that any cup state can be used in that position. Note that 29 and 58
require wasting a shot of beer (the game ends with the shotglass full);
all the others but 31 permit a variant where a shot is wasted as well.
We do not concern ourselves much in this report with these leftover
shots.

tions, since it can be done statically.) All of the possible outcomes
are shown as black squares in Figure 3.

Each cell represents a pair of k₁, k₂ for the num ber of shots
imbibed by players 1 and 2. 454 of the 61² = 3721 combinations are
achievable. Note that col umn 0 represents the case where player 1
drinks noth ing. It dominates the matrix in the sense that if k₁, k₂
is achievable, then 0, k₂ is as well. Most of the time it is easy to
see how this is done: Take the configura tion that produces k₁, k₂
and do the same, but player 1 simply performs her actions without
drinking. This works except for the case where player 1 receives a and
passes it in a state other than . The player can't simply not drink, as
this is illegal (the beer must be emptied, and BMML does not permit such
messy reduc tions). It is curious that this does not affect the result;
I discuss this further in Section 7.2. Another interest ing column is
the last one, which represents outcomes of the form 60, k₂ , where the
first player achieves a full Power-Hour. This of course includes all of
the k₂ achievable solo (the players can just do their thing with out
interacting). But some new k are now achievable:

Figure 3: All of the possible outcomes (k) for the two players in a
BMML Power-Hour. The matrix is sym metric, of course, since the
players are interchangeable.

{3, 4, 15, 28, 32, 45, 56, 57}. Interacting with a player do ing a
full Power-Hour still affords us a few additional bits of information
that can be used to attenuate the other player's consumption. The
solution for 45 is in structive, and appears in Figure 4.

This is a useful result, but it may be the case that someone wants to
drink exactly 27 shots of beer, which is not possible with just two
players in BMML. There are two avenues to explore: Adding more
players, and generalizing BMML. We begin with the three-player case.

3 Three-player ^k/_n Power-Hours

With 3.7 trillion possible configurations, enumeration is not
feasible. But as we observed before, many of these combinations are
illegal (they result in a player recieving two cups), and many are
isomorphic to one another. By being clever about how we explore the
con figurations, testing "all" the three-player configurations becomes
feasible.

Here is a one-player BMML configuration that illustrates a particular
kind of redundancy: start ∪ ∪ ⁺

⇒∪ ⁺

⇒∩ ∩⇒

ҳ

Figure 4: State machine that achieves k₁ = 45, k₂ = 60 in a
two-player BMML Power Hour. The bottom row of states are for player 1,
who drinks 45, and the top for player 2, who drinks 60. Clearly, player
2 must drink at every step. The players always pass to each other, with
the two cups exchanging hands each turn. The cycles for the two cups are
disconnected; one alternates between in player 2's hand and ∪ in player
1's (cycle of length 2), drinking on each turn. This cycle yields 30
drinks for each player. The other cycle is of length 4; player 2 drinks
on every step (as we know), and player 1 every 4^th step, yielding 15
more drinks for a total of 45.

The cup starts empty, and at each step the player fills it and drinks
(traditional Power-Hour). The player also has rules for the case that
she observes a full or overturned cup. It does not matter what these are
because they can never be used. This example is trivial, but there are
many ways that the execution of a configuration can be indifferent to
some of its content. Another is a two player configuration like player 1
start ∪ ∪ ⁺

⇒∩@1 ⁺

⇒∩@2 ∩⇒ \@1

player 2 start ∪ ∪⇒∪@1 ⁺

⇒∩@1 ∩ ⁺

⇒ \@2

where the \@n notation means to pass the cup in that state to player n.
In this case, the first thing the players do is to pass both of their
cups to player 1, which is illegal and ends the game. Again, none of the
other rules are ever used.

In order to explore what is possible in three-player

games, we exploit this redundancy with a technique like abstract
interpretation [2]. The start state is always used, so we begin by
enumerating all assignments of start states to players. There are only
4^p. Every other rule starts out undetermined, maybe written like
this:

start ∪ ∪ ^?

⇒? ^?

⇒? ∩ ^?

⇒?

Now we execute programs as before, and hope that we never encounter a
situation where we depend on a rule. If we finish without ever using
one of the ? rules, we evaluated a potentially large group of
configurations all at once. During the execution of a configuration,
if we need to use a rule that is currently marked ?, we explore all of
the possibilities for that spot. This is accomplished by a loop that
looks like the following (in Pseudo SML):

val queue = (* all abstract configurations *) val results = (* map
from (k_1, k_2)

to example *)

fun loop nil = (* done *)

| loop (h :: t) =

let

val res = evaluate h

in

insert (results, res);

loop t

end handle Expand l => loop (l @ t)

fun evaluate config =

(* ... *)

case rulefor cup of

QuestionMark =>

raise Expand expandedconfigs

| (* ... *)

val () = loop queue

The key trick here for keeping the code under control is to
iteratively evaluate the configurations as usual, but if we find a ?,
then we abort the current simulation with an exception that carries
along the set of configurations that expand the current one in just
that position. This wastes some work (and we often need to restart
multiple times per abstract configuration), but not much: If a rule is
used at all, it is usually used in one of the first few rounds.

With this technique, we can simulate all possible two player games
with just 15,744,259 game-minutes simu lated (with naive enumeration
it would be 1.2 billion) in less than 2 seconds on a crappy old
computer.

Ҵ

Figure 5: Outcomes possible for the first two players in all different
3-player power hours (black), overlayed by all possible outcomes
outcomes for 2-player power hours (red). Mainly included because it
looks pretty sweet. The outcomes that are possible with three players
are a superset of those with two, which is intuitive: We can add a
third player to any game who just does nothing.

It is also feasible overnight to enumerate all three player games. The
results are three-dimensional, of course, but we can display the
outcomes for two of the players in the familiar presentation (Figure 5).
Note that k₁, k₂, k₃ is achievable for any k₁ ∈ {0 ... 60},
k₂ ∈ {0, 1, 2}, and some unknown k₃ (projected out of this display).
This is a significant improvement over what was achievable in BMML with
two players. It sug gests that with enough friends willing to follow a
pro gram, some set of people are likely to be able to achieve any amount
of drinks between them (if they have the ability to construct the right
rule set!); see Section 7.2.

The sheer number of configurations for 4 or more players makes these
exact enumeration techniques in feasible. However, we have other
avenues for general ization (and exploration), which are investigated
in the next chapter.

ҵ

4 Generalized BMML

Like any drinking game, there are several arbitrary things about BMML.
While we will not tamper with its essence (for example, allowing beer
to be spilled from a cup without drinking it), there are some other
variables to adjust. The most naturally flexible is the number of cup
states. We will always have , a cup with beer in it. In BMML we also
have ∪ and ∩. But why not ⊃ (cup turned on its side, facing west) or
^∧∪ (an upright cup with a cocktail umbrella on it)?

We define BMsL, where s is the number of distinct cup states. By
convention, the 0^th cup state will be the filled cup since it has
special rules. The remainder will be ∪ⁱ for i ∈ {1,...,s − 1}. BMML
is BM3L where we've just renamed ∪ to ∪¹ , and ∩ to ∪² .

Clearly, more cups give us more expressive power, and should allow us
to reach more outcomes. To il lustrate, recall the construction of k =
31 in the solo BM3L game (Figure 1). It has a length-2 cycle alter
nating between two cup states, where the player drinks on every other
turn. The third state is just used once as a drinking lead-in to make
the total 31 rather than 30. With an additional cup state, we can
straightforwardly transform this into a game with an outcome of k = 32
by extending the prelude with another state where the player drinks.
Of course, the expressive power is not just limited to such
extensions; we now can create cycles of new lengths, admit the
possibility of more disconnected cycles, and so on.

It is easy to enumerate the 1-player BMsL games. These appear in
Figure 6. The interesting range for s is {1 ... 8}.⁴ At 8 cup
states, the player can achieve any amount in a solo game. Importantly,
this extends to any number of players in BM8L, because the players can
pass to themselves and not even interact.

The two-player case is much more interesting. We've already enumerated
all the possible outcomes for BM3L (Figure 3). It is computationally
tractable to enumerate them for s \< 6. The set of achievable outcomes
in BMsL is always contained within BM(s + 1)L, because we can embed a
game from the former into the latter by just never producing the
additional cup state and having any arbitrary rule for it. Therefore,
we show these results in a composite grid where more and more states
are reachable as we increase s (Figure 7).

In order to efficiently enumerate BM5L, I improved

⁴It's not clear that BM0L should be considered legal as the rules
speak of a 0^th cup, but it is degenerate anyway.

s

e

t

a

t

s

p

u

C

the algorithm again. Observe that the "drink" action associated with a
rule usually does not affect anything but the final outcome. The only
exception is that in the rule for , the player must drink if passing
in a state other than . Putting this aside for a moment, note that we
can just count the number of times each rule was executed for each
player, producing an s-dimensional

Figure 6: Possible outcomes for BMsL with a single player. The vertical
axis shows an increasing number of cup states, and the horizontal axis
shows the achievable values of k drinks. With no cup states, it is only
possible to drink nothing. By convention, the 0^th cup is the special
"filled" state, so it is only possible to drink on every turn (60) or
never (0). As we add more cup states, the number of achievable states
strictly increases; with 8 cup states we can drink any amount. 7 and 53
drinks are the most elusive, and can only be done with 8 cup states.

{width="2.8420002187226596in"
height="2.838666885389326in"}

Figure 7: What's achievable for two players in a gen eralized BMsL
game, with s ranging from 1 cup state (darkest) to 5 (lightest).

vector [d₁,...,d_s] for each player. That player is able to
achieve many different drink totals, specifically, d₁ × r₁ +
... + d_s × r_s where r_i is 1 if the player should drink on that
rule and 0 if not. Simulating a game this way is even more like
abstract interpretation (we leave a concrete value free and compute a
formula rather than an integer), and allows us to evaluate many
concrete games at once. At the end, we simply plug in every legal
value for r_i for each player and insert those games into the
database. This last step is where we must tend to the exception around
. We may not set r₀ to 0 if the player ever passes in a non-full
state. A very close approximation would be to insist that r₀ = 1 if
the rule in the position does not output as , but this is inexact, as
that rule may never be executed.⁵ Instead, during simulation we keep
track of whether each player ever actually passed a non-full cup from
the state. If so, then we force r₀ = 1, which attends to this
special case.

Although this makes earlier enumerations extremely fast and BM5L quite
quick, 2-player BM6L ran 26 bil lion concrete states overnight and
made only modest progress. In the absence of fancier techniques for
reduc ing the state space, we must resort to different, inexact
approaches.

5 Sampling games

To establish a result like "BM5L cannot achieve 47, 27 " we really
need to enumerate all the BM5L games. (Or make some ad hoc proof of
the fact, which seems quite difficult.) However, to prove an existence
result like "BM7L can achieve 33, 49 " we only need to have a single
example configuration that produces that result. Therefore, we may be
able to improve our bounds on what is possible (or generate
conjectures) by sampling random configurations.

Sampling is actually much easier than enumeration. There is no need to
leave rules abstract. It is also easy to

⁵We may be able to argue that in that case, there always exists
another game that does not violate this condition. But I think it is
simpler to just implement the rules.

ҫҩ

stop and restart because there is no state other than the matrix of what
we've found. I use the SML textformat library [3] to serialize and
deserialize the matrix (which then makes it easy to generate these
graphics in a sep arate program). There are a handful of interesting as
pects:

Generating a random configuration. To generate a random game, we can
just fill in all of the slots (des tination and cup state for each rule,
starting cup state) uniformly at random. Many of these will be illegal,
but they fail very quickly at runtime; a lazy and pragmatic way to
"filter" to legal game. It is not simply a matter of generating all the
permutations on p×s nodes, by the way. Multiple cups can pass through
the same player on cycles of different periods, as long as they do not
collide within the 60 steps, and acyclic preludes (Figure 1) are
important and useful. For a uniformly random 2-player BM7L
configuration, 29.23% (measured empirically) are legal. However, we will
see later that we do not want to spend so much time exploring
configurations where one or both players start without a cup; these are
very lim ited. Therefore, the configuration generator is biased towards
producing a cup in the starting states most of the time.

Symmetry. We can get more bang for the buck by considering some obvious
symmetries. When a simula tion finishes and we have an outcome
k₁,...,k_p , it is clear that any permutation of k₁ ...k_p is
also achievable. We insert every permutation of the drink counts into
the database, along with the permuted example configura tion. Better
still would be to only store the outcomes in some normalized form (e.g.
require that k₁ ≤ ... ≤ k_p).

We already have exact results for two players in BM5L, so the next
uncharted territory is BM6L. The result after apparent convergence
appears in Figure 8. The sampling procedure runs for many hours before
plateauing overnight with 95.65% of the matrix filled. This suggests
that BM6L is not universal for two play ers, or else the
configurations for the missing cells are extremely rare.⁶

This approach scales much better than enumeration and is efficient for
all sorts of generalizations (it works best when the dimensionality is
low---i.e., two players--- and the expressiveness is high---i.e., many
cup states).

⁶This is definitely a possibility, as new cells were still appearing
after exploring tens of billions of samples. However, the gap here
seems quite large.

{width="2.8436668853893265in"
height="2.8220002187226596in"}

Figure 8: 37.1 billion samples of legal two-player BM6L
configurations. Darker cells represent outcomes that oc cur more
often; cells that are pure white never occurred and are likely to be
unattainable. Note that the inten sity represents the rank of
occurrence, not the magni tude; in actuality, outcomes like 0, 0 occur
much more often than others. 95.65% of the cells are filled.

Since we already know BM8L is universal, the remaining open problem is
BM7L, whose results are in Figure 9. Indeed, after more than 30
billion samples the matrix is completely filled in; we have found an
example configu ration that achieves every outcome. Some of these were
extremely rare, such as the solution for 11, 53 (Fig ure 10). In BM7L,
two players can drink any amount.

6 The fractal geometry of ^k/_n Power-Hours

Note that all of the two-dimensional figures resemble one another even
though they are fundamentally dif ferent (adding players, adding
states, adding random trials). Even samples from BMML with three
players (3D projected to 2D), which is shown in Figure 11, pro duces a
similar pattern. This suggests that the combi natorial problem ("what
outcomes are reachable from finite state machines that look kind of
like this?") has some geometric structure.

Some of the patterns are easy to explain. The top

ҫҫ

0 1 {width="2.8420002187226596in"
height="2.8220002187226596in"}

2 3 4

+ +

4 0 3 2 6

+

5

Figure 9: 30.7 billion samples of legal two-player BM7L

configurations. Fewer configurations were sampled than

+

in Figure 8 because they take somewhat longer than 6-

6

1

state games to simulate, and a smaller proportion of

random games are legal. Moreover, we stop after find

ing a solution for every cell, proving that BM7L is com

plete! The last cells found---an earlier version of this paper held
these as open problems!---were permutations of 11, 53 (Figure 10) and
49, 53 . Note that 53 drinks was also unattainable in a solo BM7L
power-hour; this may in some sense be the "hardest" number of shots to
drink in BMsL.

left half of the matrix is more populous than the bottom right, for
example. This is because we can bound the to tal number of drinks by
60×c, where c is the number of cups active in the game (same as the
number of cups in the starting states). The top-left half is the region
where this sum is less than or equal to 60; in two player games, both
players must start with a cup in order to get an outcome in the
bottom-right half. We also see distinct clumps around 0, 15, 30, 45, 60;
these correspond to simple fractions ("drink every other time"; "drink
three of four times") of 60. This is intuitive because the ex pressive
power of BMML comes from the ability to form cycles of cup states and
drink on some fraction of them. Clumps are formed around these values
because of the possibility of preludes leading into the cycles (Figures
1, 10) that either drink (adding to the total) or don't (sub tracting
from it). Minor clumps form as echoes between

Figure 10: A solution for the elusive 11, 53 two-player BM7L power
hour! This one was found after 30.7 bil lion outcomes sampled, making
it the most rare. By the end of the game, the two players are just
passing back and forth two cups in state 5. A long lead-in beginning
on the left-player's state 2 spans 12 different configura tions (the 6
cup states for the two players) before en tering the length-two cycle.
Both cups travel along this lead-in, with one three steps ahead of the
other. The right player drinks on every step until reaching the cy cle
(and then never again) for 11; the left player drinks during the cycle
plus a little extra during the lead-in for 53. This configuration is
quite flexible because the two players can make fine adjustments to
their drink total by drinking or not drinking on the lead-in rules,
which are executed just once or twice.

the major ones, because a player may participate in two cycles of
different length (Figure 4).

Of course, discretization effects compound and so the exact values of
cells are not neatly predictable. More over, clumps interfere by
overlapping; there are many different strategies for achieving 33, 33
. One way to

ҫҬ

{width="2.8420002187226596in"
height="2.905333552055993in"}

Figure 11: 490 million samples of three-player BMML Power Hours. The
cube is rotated 15 ^◦ along each axis, the top-left corner is 0, 0, 0 ,
and the bottom right is 60, 60, 60 .

make the basic structure more visible is to extend the number of
minutes that the game is played for. Fig ure 12 shows the utterly
unhealthy three-player Power Day (BM3L). In it, the clumps become tiny
dots, but some relationship among them along lines is clear. Inte rior
points can probably be found as linear combinations of two of these
lines; we exploit that exact structure in Section 4, in fact.

The less extreme ^k/_n Power-Three-Hours appears in Figure 13.

7 Conclusion

This section summarizes the known bounds for BMsL, and states some
conjectures, before concluding.

7.1 Known results

1. With one player, we have exact bounds on what is possible in the
generalized case. With 8 cup states, a single player can drink 0--60
shots. Since each player can just play independently, this result
extends to any number of players in BM8L. With

Figure 12: All possible outcomes for the first two play ers in
3-player power days. These are the same games as the 3-player power
hours, but at this scale makes it clear the groupings and their
sparsity in the limit. Lines plot ted from 0, 0 to 60, k₂ and k₁,
60 show significant structure, but don't explain some of the interior
points. These are probably games where a player participates in two
cycles of different periods.

{width="2.8436668853893265in"
height="2.8370002187226597in"}

Figure 13: 6,456,764,116 samples of two-player BM7L Power Three-Hours.

ҫҭ

fewer than 8 cup states, not every k can be achieved alone.

2. With two players in BM3L or BM4L, it is not pos sible for one of
the players to drink every k even if the other player helps her out.

3. With two players, we know that BM5L does al low one player to
drink any k₁ if the other player assists. In fact we can achieve any
k₁, k₂ where k₂ ∈ {0, 1}. No other k₂ can be used universally,
though of course many other combinations are pos sible (Figure 7).
Many pairs k₁, k₂ are known to be unattainable; this was
established by exhaus tively testing all possible configurations.

4. Open: Can BM6L achieve all k₁, k₂ ? Seems un likely, given
that random exploration plateaus with about 95.65% of the grid filled.

5. BM7L can achieve all k₁, k₂ . This was established by sampling
random games until we found an ex ample for every k₁, k₂ .

6. With three players in BM3L, one player can drink any number of
shots if the other two players help.

7.2 Conjectures

Freedom: With two friends, you can drink any amount. We know that in a
three-player game of BM3L, one of the three players can drink the k of
her choice. This straightforwardly extends to 3 × p-player BM3L games.
The Freedom conjecture is that with p + 2 players in BM3L, p of them may
have their choice of k₁ ...k_n drinks. If this conjecture fails, it
probably fails for 4 players, which might have a feasible enumer ation
strategy.

Teetotaller: Someone can drink nothing. When k₁,...,k_i,...,k_p
is achievable in BMsL, so is k₁,..., 0,...,k_p . This conjecture
would be trivial if not for the rule that requires us to drink the
contents of a full cup if we want to pass it in a different state.
This conjecture is true for all the graphics presented in this
paper;⁷ we can see that cells in the 0 column are always filled when
some other cell in that row is filled. If this

⁷Actually, it is not established for (only) 11 minutes in Fig ure
13, but this is not a proper BMsL game as it takes place over 180
minutes. There should be solutions for 11, like in Figure 10; this is
just a sample.

conjecture fails, it probably fails for BM1L or BM2L which have the
least freedom per player.

In this paper I presented some new results in ^k/_n Power-Hour
theory, as well as correct the historical record of some inebriated
missteps. We saw that stochastic simulation, abstract interpration,
and sam pling are powerful tools for solving combinatorial drink ing
problems. We established some firm results for the classic game and
some bounds for generalizations, as well as informally looked at some
visualizations of its ge ometric structure. However, there are still
several open problems in this field that demand further study.

References

[1] Ben Blum, Chris Martens, William Lovas, and Tom Murphy, VII.
Algorithms for k/n Power-Hours. SIGBOVIK 2012, pages 29--33, April
2012.

[2] P. Cousot and R. Cousot. Abstract interpretation: a unified
lattice model for static analysis of programs by construction or
approximation of fixpoints. 4^th POPL, pages 238--252.

[3] Tom Murphy, VII. The textformat library for Stan dard ML.
http://sourceforge.net/p/tom7misc/
svn/HEAD/tree/trunk/sml-lib/textformat/, 2013.

ҫү

SIGBOVIK 2014 Paper Review
{width="0.9486668853893263in"
height="0.9486668853893263in"}

Paper 1: New Results in k/n Power-Hours

Robert Marsh, King Under the Mountain

Rating: 3 (weak accept)

Confidence: 2/4

Man, figure 5 does look really sweet. like whoa. you could take that
and trim the edges off and use it as a boss in some kind of
diagonal-scrolling space shoot-em-up. no really, that's blowing my
mind. you could, like make an entire space invaders galaga thingy out
of these charts. it would be rad as all get out.

On the other hand, one must consider the broader implications of
research of this sort. In particular, should this conference encourage
an attempt at a k/n power hour for any k, even a difficult-to-reach
one like 11, 53 ? Let us first note that the finer things in life
should be savored. However, there is such a thing as Beer 30 Light,
and people are going to attempt such things whether we help them or
not, so we might as well ensure they have the tools they need for
slightly more responsible drinking.

In sum, this paper's significant contributions to cool fractally
things seems to outweigh its potential harm to society.

ҫұ

ҫҲ

/3+\'6 4-/) 6++ {width="1.0486668853893264in"
height="1.048665791776028in"}

\'614 3-/91/

)5((

+7)6/58/43

!& # \" \" # ! ! !#

93*6+*7 4, 14-/)/\'37 \'6493* 8.+ ;461* \'6+ 564:/3- 8.+46+27 /3
\'3* \'(498 /3+\'6 4-/) #6= /8 ,6++ 43 =496 5\'5+6 46 ;./8+(4\'6*
*+:/)+ 34;

$! \"#

!+7496)+ 38+656+8\'8/43

334:\'8/:+ 79(7869)896\'⅛= \'114;7 =49 84 24*+1 6+7496)+7 \'7
564547/8/437 +397 (14)0 ;461*7 8.+ 5477/(/⅛/+7 \'6+ +3*1+77

918/51+ /,,/)918/+7

64:+ 8.+46+27 /3 /389/8/43/78/) ⅓+\'6 14-/) ,46 \' ).\'11+3-+ 86=
8.+ /3)19*+* )1\'77/)\'1 ⅓+\'6 14-/) /378+\'*

64:+ %/8. 6/+3*7 *:+67\'6/+7

38+6\')8/:+1= ).\'11+3-+ =496 \'*:+67\'6/+7 84 *+243786\'8+ 8.\'8 \'
8.+46+2 /7 869+ ;/8.498 )43:+=/3- \'**/8/43\'1 /3,462\'8/43 6
)411\'(46\'8+ ;/8. ,6/+3*7 84 564:+ 3+; \'3* +\<)/8/3-
8.+46+27>=496 ).4/)+ 411\'(46\'8/43 431= 7955468+* 43 ;./8+(4\'6*
:+67/43

\'87

** 742+ 5+6743\'1 78=1+ 84 (46/3- 8.+46+27 ;/8. 496 3+; .\'8 5\')07

, =49 1/0+ /3+\'6 4-/) 6++ )437/*+6 95-6\'*/3- 84 /3+\'6 4-/) ,46
742+ \'**/8/43\'1 ,+\'896+7

98

.+ 56+2/92 431= )98 691+ \'114;7 =49 84 7\':+ =496 564-6+77 \'8 0+=#

).+)054/387 43 =496 ;\'= 84 564:/3- 8.+46+27

;.41+ 3+; )438+\<8 4, 5+67/78+38 564547/8/437 \'114;7 =49 84 *4
46*/3\'6= 14-/) \'3* ⅓+\'6 14-/) \'8 8.+ 7\'2+ 8/2+

/0+ 97 43 \")/+3)+ /6+)8 [.885 *\< *4/ 46-\
\
\
]{.underline}

ҫҳ

\' & *

\" #%\") %& ! \"(% \' &\' (# \' * ) ! * \"!&( \'\" #%\"#\"& \' \"!&
\'\" ! % \" ) &\" \") \' #% ) \"(& , #% ( \"! , !\' \', %( \'\" \' % )
%& \"! \" ! % \" \' % \" # !\'& \' \' % ! ! !\' \', +# !& \"! * &
\'\"\" \' \"(& # \"! #%\") ! (\' % % \'\" ) \" (& , \' ! % $( !\' %
&

! ## (% & &

^\' {width="0.260333552055993in"
height="0.23700021872265967in"}{width="0.260333552055993in"
height="0.2586668853893263in"}{width="0.26200021872265966in"
height="0.2586668853893263in"}

\'

) \"# % ##&

! % \"

%\"\" \'& %

%\"\" \'&

&& %& \"\
\' !

ҫҴ

SIGBOVIK 2014 Paper Review
{width="0.9486668853893263in"
height="0.9486668853893263in"}

Paper 21: Linear Logic Free

Review #1

dabestcoq, gmail.com

Rating: 0 (strong reject)

Confidence: 4/4

this paper SUX i spent like $50 on a premise but wen i used it to
prove an implicaton the premise was GONE WUT A RIPOFF!!!!!!! DO NOT
USE THIS LOGIC!!!1! propazitonal logic is WAY better

Review #2

idbangthattype, gmail.com

Rating: 4 (strong acccept)

Confidence: 4/4

Reviewer 1 you idiot that's the point of linear logic. The paper is
far from perfect. I for one wish the cut rule was included in the free
version but I gave it a 4 to make up for all the dumbass reviewers.

Review #3

obamaisasocialist, gmail.com

Rating: 0 (strong reject)

Confidence: 4/4

ummmmmm reviewer 2 maybe we all dont want u buttin in. u no hu else
told ppl wut 2 think? hitler

ҫҵ

Ҭҩ

It still seems that black has hope in these extremely unfair variants
of chess

Dr. Tom Murphy VII Ph.D. Ben Blum

Jim McCann, in italics ...... oh! .... nervous laughter .... no,
that's not part of the name still. I stopped sa 1 April 2014

Abstract

CHECKMATE.

Introduction

Chess is an old-timey game that you already know. One problem with
Chess is that it is hard; both play ers may struggle mightily in a
game, expending their brain-sugars, and it is not clear who the winner
will be. Another problem with Chess is that it isn't other games, and
we're pretty much over it. In this paper we attempt to address both
problems, with limited suc cess. We show how to combine Chess with
several other board games, in order to make it more predictable.

As usual for a Tom 7 SIGBOVIK joint, the results herein are real. The
source code that was used to solve the games or prove that no winning
strategy exists up to some depth can be found on the inter-net.¹

1 Chesstego

Chesstego is a combination of the games Chess and Stratego. You
already should know that every game in this paper is a combination of
Chess and something, but I wanted to emphasize the portmanteau. All of
the games will be named with portmanteau, and some of the names will
be achingly bad.

In Stratego, each player begins the game by arrang ing his or her
Stratego-pieces in a secret fashion on the board. In the world of
Stratego, civilization is ruled by a leader known as Flag. The
player's goal is to assassinate

^∗Copyright c 2014 the Regents of the Wikiplia Foundation. Appears in
SIGBOVIK 2014 with the undivided attention of the Association for
Computational Heresy; IEEEEEE! press, Verlag Verlag volume no.
0x40-2A. $0.00

¹In the Subversion repository at: https://sourceforge.net/
p/tom7misc/svn/HEAD/tree/trunk/chesstego/

the opponent Flag, using a member of his or her army. However, which
piece represents Flag is unknown! There are many ways we might apply
the Stratego system of governance to Chess.

Chesstego variation I. In this variation, each player decides in
secret, before the game begins, which of his or her pieces is the
actual King, that is, Flag. If this piece is checkmated, the game is
lost. There are two sub variations: I(a), where a player must announce
Check! when Flag is under attack, and all of the normal rules about
moving into (or castling through) check must be obeyed. In
subvariation I(b), which I prefer, the piece that is Flag may slip
silently into and out of check, and the game only ends when that piece
is captured.²

Chesstego variation I is a reasonable if slightly silly game, and it
is difficult. It may even be more difficult than Chess due to the
psychological mind-games that are possible. It can be hard to tell
which player is win ning, let alone which player will win. In this
paper we are interested in variants of Chess that both are other games
and are predictable. We'd like to give one of the players a clear
strategy for winning.

Chesstego variation II. In this variation, each player decides in
secret, before the game, which of her opponent's pieces is Flag. Same
as before, if this piece is captured, the game ends instantly. But
now, players don't even know which of their own pieces is their glori
ous ruler, Flag. This can be very exciting or titillating.

Unfortunately, there is no known winning strategy for White, and there
are no winning strategies with fewer than 6 moves. This was proved by
computer program. In fact, it was proved for a stronger case:

²In Chess proper, these formulations are nearly equivalent--- except
for rules like castling through check and some corner cases---but it
is deemed important for movie drama that play ers be able to announce
Check! and Checkmate! at times.

Ҭҫ

Chesstego variation III. In this variation, the first player, known as
White, chooses in secret both the iden 8

tity of Flag for his own populace, as well as the identity of Flag for
his opponent. Even in this very unfair setup, 7

Black can always survive for at least 6 moves.

This will not do! Black just has so many options

6

with all those pieces. Perhaps if he were handicapped 5

somewhat?

4

Chesstego variation IV. In this variation, White chooses the identity of
both Flags again, in secret with

3

out telling her opponent, and also Black does not get 2

any good pieces, just pawns. Like this:

1

+-----------------------------------------------------------------------+
| > 0Z0Z0j0Z o0opopop 0Z0Z0Z0Z ZPZ0Z0Z0 0Z0Z0Z0Z ZQZ0Z0Z0 PO0OPOPO |
| > SNA0JBMR |
+=======================================================================+
+-----------------------------------------------------------------------+

+-----------------------------------------------------------------------+
| > 0Z0ZkZ0Z opopopop 0Z0Z0Z0Z Z0Z0Z0Z0 0Z0Z0Z0Z Z0Z0Z0Z0 POPOPOPO |
| > SNAQJBMR |
+=======================================================================+
+-----------------------------------------------------------------------+

8

7

6

5

4

3

2

1

abcde f gh

Figure 1: Example hopeless match: 1. c4 Kf8 2. Qb3 b5 3. xb5 1--0

Now there are many more winning strategies, but the one from IV works as
well.

Other variations. Incidentally, my on-line version of Chess called
SICO³---where you just play a single move in a random game---has for
about six years had vari

Lo! This version is finally satisfactory. In this version we need not
equivocate over who shall win. White picks one of her very safe pieces
(e.g., one of the rooks) as Flag, and chooses Black's b7 pawn as Black
Flag. White's winning move is c2c4 and then Qb3, with Black Flag unable
to escape the B file (Fig ure 1). Choosing the f7 pawn works as well.

Chesstego variation V. This variation is just like IV but White gets
super good pieces everywhere instead of having some dumb ones, and
Black still gets bupkiss:

ations called "center wall" and "barricades"[1] which were inspired
by the layout of the Stratego board. How ever, these cannot be
considered worthy of portman teau, as the rules are basically just
Chess rules.

2 Cluess

This game, known as Chuessdo in the United Kingdom, is a cross between
Chess and Clue. In this version, the player called White is known as
Mrs. White, and the player called Black is known as Professor Plum.

+-----------------------------------------------------------------------+
| > 0Z0ZkZ0Z opopopop 0Z0Z0Z0Z Z0Z0Z0Z0 0Z0Z0Z0Z Z0Z0Z0Z0 NMNABMNM |
| > LQLQJQLQ |
+=======================================================================+
+-----------------------------------------------------------------------+

8

7

6

5

4

3

2

1

abcde f gh

3 Chess Who?

The board game Guess Who? disappointed millions of children with its
delightful television commercial that far outstripped the capabilities
of the actual game. This required them to add a disclaimer to the
commercial, "Game cards do not actually talk." In Guess Who?, players
take turns trying to guess the identity of the opponent, among a fixed
set of personalities with traits like curly hair, straight hair, brown
hair, short hair,

³On the internet at: http://snoot.org/toys/sico/

ҬҬ

bangs, long hair, blonde hair, red hair, or glasses. One player asks,
"Do you have curly hair?" and the other says "Yes" or "No" and then
the first player can elimi nate all the remaining personalities that
don't have the trait. It's basically binary search, but for kids.

In Chess Who?, which is the chess version, players have two different
options on each turn. They can either move a piece like normal, or ask a
question of their opponent. The question must be about the physical
characteristics of the pieces, for example, "Does your piece have curly
hair?" No pieces have curly hair, so nothing happens. The opponent might
ask a different question, on the next turn, like "Does your piece have
straight hair?" No pieces have straight hair, so nothing happens. On the
next turn, suppose the player asks, "Does your piece have brown hair?"
No pieces have brown hair, nor any hair at all, and no pieces have any
brown parts at all either. Stop asking. Next, Black asks, "Does your
piece have crenellations?" Both of White's rooks have crenellations, so
they are eliminated from the board (Figure 2).

crenellations, or horse ears, or two weird long shoulder ribbons that
I don't know what they are, or five pointy tines on her crown?" This
matches all of Black's pieces except his king, so he removes them all.
But then Black asks: "Does your piece not have a lumpy crown?" which
matches all of White's pieces except his king. So all we have left is
the two kings, which is known to be a draw [2].

4 Chessy Crush Saga

Chessy Crush Saga is a hybrid of Chess and the popular and lucrative
phone-game Candy Crush Saga. In this game, the regular moves of chess
are allowed, but it is also possible to crush chess pieces into
candies. Chessy Crush v1 follows the rules of Candy Crush closely:
When a piece moves such that three pieces of the same color are in a
row (either horizontally or vertically), those pieces are all removed.
Usually this is a tacti cal misstep in Chess, as three of one's own
pieces are destroyed for nothing. However, as in Candy Crush, re wards
are given when more than three like pieces are destroyed at once. The
simplest is to award the player

+-----------------------------------------------------------------------+
| > rmblkans opopopop 0Z0Z0Z0Z Z0Z0Z0Z0 0Z0Z0Z0Z Z0Z0Z0Z0 POPOPOPO |
| > ZNAQJBM0 |
+=======================================================================+
+-----------------------------------------------------------------------+

8

7

6

5

4

3

2

1

abcde f gh

with a Candy Rook at the place where the moved piece ended up. A Candy
Rook moves like a rook, but if it is crushed, it destroys all of the
opponent's pieces on the file (column) it currently occupies.⁴

As another simplification, we remove all of the proper pieces from the
black files, except for the King, in honor of the software company that
makes Candy Crush, "King." A densely packed board with pieces that can
move backward is dangerous, for it is easy to destroy one's own king by
moving out of and then back into the back file, crushing the whole thing
(Figure 3).

With just pawns, it seems that the best way to gain advantage for White
is to crush four pawns to create a Candy Rook before Black does, then
menace Black with it. Unfortunately, moving four pawns into forma

Figure 2: The board after 1. Does your piece have curly hair? . . . Does
your piece have straight hair? 2. Does your piece have brown hair? . . .
Does your piece have crenellations?

Next, White might ask, "Does your piece have a cross on his hat?" This
matches both Bishops and the King, but Black responds "Check!" because
it is illegal to ask a question that would eliminate the King.

This variation produces draws easily. An example Nash Equilibrium:
White begins by asking, "Does your piece have three lobes like a
truncated snowman, or

tion before black can interfere is not possible; Black can react to
White's first move and advance one of his own pawns towards the
construction (Figure 4). Moreover, if he does, and trades for one of
White's pawns (or better, the resulting candy), then Black is probably
in a supe rior position, White having crapified his pawn structure in
pursuit of candy. Worse still, crushing a successful Candy Rook is not
that menacing, since Black can sim

⁴In formal Candy Crush, this is the vertical striped candy, which is
awarded when the piece was moved vertically. To keep this variant
simple, we always award a "vertically striped" Candy Rook, since it
seems with only pawns, only vertical moves are likely. (This later
turns out to be a bad assumption.)

Ҭҭ

+-----------------------------------------------------------------------+
| > rmblkans Zpopopop pZ0Z0Z0Z Z0Z0Z0Z0 0Z0Z0Z0Z Z0Z0Z0Z0 |
| > |
| > POPOPOPO SNAQJBMR |
+=======================================================================+
+-----------------------------------------------------------------------+

8

7

6

5

4

3

2

1

abcde f gh

+-----------------------------------------------------------------------+
| > 0Z0ZkZ0Z Zpopopop 0Z0Z0Z0Z Z0Z0Z0Z0 0Z0Z0Z0Z ZpZPO0Z0 PZPZ0OPO |
| > Z0Z0J0Z0 |
+=======================================================================+
+-----------------------------------------------------------------------+

abcde f gh

Figure 3: "Fool's Mate" in the rejected Candy Crush v0, played with
normal pieces in the back ranks. White self-mates in two moves, crushing
all his own pieces e.g. with: 1. Nc3 a6 2. Nb1 (??) 0--1

ply move his king out of the way.

To correct these problems with balance (i.e., that the game may be
balanced), we simplify the candying rules: Any crush produces a Candy
Rook, including ones of length 3. This allows White to create a Candy
Rook before Blacks pawns can reach her. Furthermore, we stipulate that
the kings cannot move (they don't have legs anyway, this is plain to
see, so let's be realistic). In v2, the Candy Rook is extremely
powerful, since not only does it destroy an entire file (the e file
being the likely target, since it contains the immovable King), but
when it is used (by crushing) it is also replaced, since a crush
always yields candy. Therefore, White's most straightforward strategy
is to quickly create a Candy Rook, then crush it in the e file, which
wins. This should be a line where White's tempo advantage makes it
mostly immune from interference, since even a check is answered by
destroying the opponent's king.

The idea behind White's Omega Weapon is to cre ate a triplet of pawns
on rank 3, either c3--e3 or e3--g3. White begins by moving her king's
pawn to e3. Black can interfere with one side of the triplet (Figure
5), but only one. After 1. e3, if . . . f5 or h5, then White will
continue creating the triplet in c3--e3. Otherwise, she is safe to
create it in e3--g3. Once the Omega Weapon is constructed, she need
only move it to e2 (which is free due to the first move, and will be
adjacent to at least two pawns). This destroys the Black king, which

Figure 4: Black interfering with White's Omega Weapon main line: b3,
d3, e3, c3 (making candy), Rc2, Re2++. Black can progress pawns fast
enough to cap ture White's. She can also move her King, making the
candied rook less devastating. Ultimately, White's one tempo advantage
is not obviously winning.

cannot have moved, due to the rules. Unfortunately, this strategy can
be foiled by Black with a clever⁵ mu tual suicide, as shown in
Figure 6. This strategy is not easily defended against, nor is it
straightforward to fix the rules of the game,⁶ so it seems Chessy
Crush Saga v2 also retains hope for Black, even though the odds
initially seemed stacked against her.

5 Future work and conclusions

Many other games can be combined with Chess to ruin Chess. For
example, consider Chess Tac Toe, Chesslers of Catan, Chesstris, and
Hungry Hungry Hipposchess. Combining Chess and Sokoban is impossible,
obviously. The combination of Chess and Battleship is Battlechess,
published in 1988 by Interplay.

⁵This strategy was discovered by computer, like most clever things
these days.

⁶It seems perhaps we can eliminate Black's draw strategy by
restoring the idea of horizontally striped Candy Rooks (see foot note
above). I implemented this. Unfortunately, although the move that ends
the game in a draw is a horizontal move, the move that creates the
Candy Rook is a vertical one. Therefore, Black's Candy Rook is
vertically striped, and can successfully destroy the White king
(though it is then replaced with a horizontally striped Candy Rook to
observe the empty thrones).

Ҭү

+-----------------------------------------------------------------------+
| > 0Z0ZkZ0Z opo0opop 0Z0Z0Z0Z Z0Z0Z0Z0 0Z0o0Z0Z Z0OPZ0Z0 PO0ZPOPO |
| > Z0Z0J0Z0 |
+=======================================================================+
+-----------------------------------------------------------------------+

8

7

6

5

4

3

2

1

abcde f gh

+-----------------------------------------------------------------------+
| > 0Z0ZkZ0Z Z0Zpopop 0s0Z0Z0Z Z0Z0Z0Z0 0Z0Z0Z0Z Z0S0Z0Z0 PO0Z0OPO |
| > Z0Z0J0Z0 |
+=======================================================================+
+-----------------------------------------------------------------------+

abcde f gh

$a$

Figure 5: White may not use a fixed strategy to con struct her Omega
Weapon. The position shown is after

8

1. c3 d5 2. d3 d4. If 3. e3 (making candy) then . . . xe3, 7

obviously. White can make candy with 3. b3, but now e2 is not clear to
crush the Candy Rook here and destroy 6

the Black king.

5

In conclusion, San Dimas High School Footchess

4

rules!

3

References

2

1

[1] Tom Murphy, VII. SICO chess variations, April 2008.
http://snoot.org/toys/sico/variations. html.

+-----------------------------------------------------------------------+
| > 0Z0ZkZ0Z Z0Zpopop 0Z0ZrZ0Z Z0Z0Z0Z0 0Z0Z0Z0Z Z0Z0Z0Z0 0ZRZ0OPO |
| > Z0Z0J0Z0 |
+=======================================================================+
+-----------------------------------------------------------------------+

abcde f gh

$b$

[2] John Nunn. Secrets of pawnless endings. Gambit publications, 2^nd
edition, May 2002.

Figure 6: Black's surprising draw strategy in Chessy Crush v2. White
begins her Omega Weapon: 1. e3 c6 2. d3 a6 3. c3 (making candy) b6
(making candy) we have the board in (a). It seems that Black is stuck
after 4. Rc2 (making candy), since 5. Re2 (making candy) will crush
White's candy rook and destroy the entire e file, including Black's
king. Black defending with 4. . . . Re6 initially seems pointless
(White will destroy the rook as well so the check is irrelevant---this
indeed re futes 4. . . . Rb1) but Re6 actually creates a vertical
three-piece crush, sacrificing Black's king to destroy the e file
first, which also destroys White's king! Such mu tual destruction is
not possible in traditional chess, but it seems appropriate to
consider it a draw in Chessy Crush Saga v2. It appears that White can
head off this line with 4. Rc8++, a totally vanilla back-rank mate,
but this is not actually mate with the same 4. . . . Re6 (making
candy) escaping to a draw.

Ҭұ

ҬҲ

))

2

\% \' !\'\" \' & ! 4% )\' 0 ))& 4 ) %\'&+\" 5 4% ) )\"\"4 &4\"\")) 4%
&!) &)

& %

* . $\
$

& \' ) $ 6 \" &\
\
# \'\
( \' # /\
/ +\
6 \'\
\
& (

$ %

* . $ $ -

1 5 \'\
\' $ 4\
$ 3

&\
%\
$ $ %

* . 3\
$\
\
\
$ /

( 0 \" 4\

/

- \"

* . $\
\
$

Ҭҳ

ҬҴ

\" ! \" ! ! \" \" # \"% \" ! ! &7(-

*&7 +7.*3)8 \<* -&;* ,&9-*7*) -*7* 94)&> .3 (433*(9.43 \<.9-
&3 .88:* 9-&9 .8 4+ ;.9&1 -.8947.( 8.,3.+.(&3(* 94 &11 4+ :8
7*+*7*3):2 \<&8 -*1) &243, 9-* +&(:19> 4+ 9-* &> &3) !9*5-&3.*
&3* *39*7 +47 425:9&9.43&1 .414,> 43 &7(- .3 +:11 (4251.&3(* \<.9-
:3.;*78.9> 574(*):7*8 &3) &(&)*2.( 34728

47* 9-&3 5*7(*39 4+ 9-* +&(:19> 9440 5&79 .3 9-* ;49* ;*7
5*7(*39 4+ 9-*2 8540* 4:9 .3 +&;4:7 4+ 7*:3.9.3, \<.9- 9-* *1143
411*,* 4+ !(.*3(*8 \"-*8* 3:2\'*78 85*&0 +47 9-*28*1;*8

\"4 :3)*789&3) 9-* 7*&843 \'*-.3) 8:(- & (-4.(* .9 .8 *34:,- 94
034\< 9-* -.8947> 4+ 9-* &3* *39*7 &3) \<-&9 9-* 411*,* 4+
!(.*3(*8 &3) 9-* &3* *39*7 -&;* &1\<&>8 2*&39 +47 *&(- 49-*7

;*7>9-.3, .3 9-* &3* *39*7 +47 425:9&9.43&1 .414,> 85*&08 4+ 4:7
8-&7*) -.8947> &3) 57.)* 3 9-* +.789 )*,7**8 \<*7* &\<&7)*) .3
9-* :3)*7,7&):&9* (425:9&9.43&1 \'.414,> 574,7&2 &9 &73*,.* *1143
4:78*8 )*;*145*) +47 9-.8 574,7&2 89.2:1&9*) .39*7*89 &243,
,7&):&9* 89:)*398 &8 \<*11

3 *1143 411*,* 4+ !(.*3(* 7*(*.;*) & ,7&39 +742 9-* *7(0
425&3> 4:3)&9.43 94 (7*&9* & 3*\< 574,7&2 .3 (425:9&9.43&1 \'.414,>
&3) (-*2.897> \<-.(- 8:55479*) \'49- :3)*7,7&):&9* &3) ,7&):&9*
89:)*398 9-*7*\'> -*15.3, 94 89.2:1&9* )*;*1452*39 4+
.39*7).8(.51.3&7> (411&\'47&9.;* 574/*(98 2&/47 1.2.9&9.43 4+ 9-*
*7(0 574,7&2 \<&8 9-&9 89:)*398 -&) 94 \'* *37411*) .3 43* 4+ 9-*
97&).9.43&1 - 574,7&28 .;* >*&78 1&9*7 .3\
& 3*\< - 574,7&2 .3 (425:9&9.43&1 \'.414,> 9-* 4.39 &73*,.* *1143

3.;78.9> #3.;78.9> 4+ .998\':7,- - 74,7&2 .3 425:9&9.43&1 .414,>#

\<&8 *89&\'1.8-*) \<.9- 9-* +.789 89:)*398 *37411*) .3 &11

3 \"-* &> &3) !9*5-&3.* &3* *39*7 +47 425:9&9.43&1 .414,> .8
(7*&9*) &8 9-* (:12.3&9.43 4+ 2&3> >*&78 4+ )*;*1452*39 &3)
7*(7:.9.3, *++4798 &3) \<.9- 9-* ,4&1 4+ 7*&1.?.3, 9-* 549*39.&1
4+ 2&(-.3* 1*&73.3, +47 *=5&3).3, :3)*789&3).3, 4+ (4251*=
\'.414,.(&1 8>89*28 57.2&7> +4(:8 4+ 9-* (*39*7 .8 )*;*145.3,
9-* (425:9&9.43&1 94418 9-&9 \<.11 *3&\'1* &:942&9*) (7*&9.43 4+
)*9&.1*) 57*).(9.;* 24)*18 4+ \'.414,.(&1 574(*88*8 .3(1:).3,
&:942&9*) *=5*7.2*39 )*8.,3 &3) )&9& &(6:.8.9.43

3 +47 & 3:2\'*7 4+ 7*&8438 @ 2&> 4) /:),* 9-*2 @ 9-* &3* *39*7
\'*(&2* .98 4\<3 &(&)*2.( )*5&792*39 &3) 97&38+*7*) 94 (439741 4+
9-* !(-441 4+ 425:9*7 !(.*3(* \"-.8 \<&8 )43* \<.9- 34
(438.)*7&9.43 +47 9-* &(&)*2.( 2&0* :5 4+ 9-* +&(:19> $-*9-*7
9-.8 )*(.8.43 \<&8 \'&(0*) \'> & )*8.7* 94 \<.3 9-* 8:55479 4+
9-* 9*3:7*) 425:9*7 !(.*3(* +&(:19> *89&\'1.8-2*39 47 94 &943*
+47 9-* 57.47 1&(0 4+ & 5745*7 - 574,7&2 .8 +47 -.8947.&38 94 +.,:7*
4:9

$-&9 2&99*78 34\< .8 9-&9 9-.8 )*(.8.43 \<&8 2&)* .3 (1*&7
;.41&9.43 4+ 9-* :3.;*78.9> 34728 9-&9 Ҭҵ

/ * !& ($ . & , & !+!\'& / + % !& , + & + ,-* $$1 /!, , !+ \'&& ,
$ *+ !( \' , ,!% + &\' \' 1 \', * ,\' +# , -$,1 \' , & &, * 1 /
* /!, , , \'2 &+ \' -$,1 / &, ,\' !& \'& ( *,% &, & /\'# !& &\', *
\'. *&! , \'%!& %! %!&\'*!,! +

\'/ % &1 1 *+ $ , * * -$,1 \' , & &, * + 1 , , # !& , 1 / * &
\'. * $!# ($ +%! !+ !+ * ,\' !+ * /!,\
& / , \'-, , $$\'& \'$$ \' ! & + , -% $1 (, , +!,- ,!\'& !+
\'$$ / + \'!& , *\'- +- * ,!% + , & , , * $!+,! $$1 !, / + !&
( $ \' (*\', ,!& !,+ !&, * +,+ \'/ . * , -$,1 \'-$ &\', * \'&
!$ , %+ $. + ,\' , !+ \'-,* \'-+ !+,\'*! $ !&\"-+,!\
$$ , + 1 *+ !,!2 &+ & % &1 (- $! ! -* + % # ,\' , !+ !++- + 1!&
, , , & &, * !+ !+,\'*! $$1 + ! & ( *,% &, + / $$ #& / , !+ !&
\'-* *,+ & %!& + -, / ,\' (*\' *\'% , 0!+,!& * $!,1 & -!$ \'-*
\'\' & ! \'-*$1 * $ ,!\'&+ /!, , \'\'$ \' \'%(-, * ! & , / (*\'
*\'% # , & / + , , \'\' * $ ,!\'&+ /!, % ,, * %\'+, \'* -+ & ,
1 + \'-$ &\', $$ \'+, ,\' $\' # ( *,% &, $ !+(-, + \'/ . * /
0( , ,\' * % !& \'-* \'\' & ! \'-* / \'( , , -$,1 !& , \'$$ \' !
& + & !\'$\' !+,+ !& +( ! $$1 , & &, * /\'-$ /\'*# !& *! & $1
\'$$ \'* ,!. & !&, * !+ !($!& *1 &.!*\'&% &,

\'/ . * , !+ !+ &\', \'/ , +!,- ,!\'& . $\'( !% & ,!% !& ,, %(,+ /
* % ,\' (*!. !\'$\' !+,+ \' , !* !+ !($!& *1 ,* !,!\'&+ . & \'
, !* , &\'$\' ! + & ,\' +- \" , , % ,\' \'* ++!%!$ ,!\'& &,$1 ,
+\' $$ -, \'*!,! + \' . & * , \'%%!,, * +\'$-,!\'& ,\' * .!+ ,
(*\' * %%!& $ & - (\'$! 1 / ! / + !* , !& *!& % &, \'& , *! ,+
\' !+ !($!& *1 %!&\'*!,! +

\'+ / \' \'((\'+ , !+ ,* ,% &, / * !%% ! , $1 , * , & /!, * (*
++!\'& ,-* $$1 , !*+, !& $!& * / + , & &, * , !\'$\' ! $$1
\'*! &, & &, * & .! / \' , !+ , -$,1 \' , , , ( *,% &, ,-*& ,\' ,
$$\'& \'$$ \' ! & + \'* $( !& & !& , !* *! ,+ & $!. $!
\'\' + ,-* $$1 / \'-$ &\', $ . , !+ ($ -& / \'-$ &\', & \'& , &
&, * & !,+ % % *+ !& !+,* ++ !+ /\'-$ . & ,* 1 $ \'& \'-* ( *,

\' , !+ & / ,\' $( * , \'& !,!\'&+ +\' , , , & &, * \'* , !*+,
,!% !& !+,\'*1 / * $ ,\' ( -$$1 0(* ++ , !* * /!$$ * * !&
, !* \'/& -,-* \'/ . * / , \' / * *\'% \'-* \'$$ - + !& ,
\'\'$ \' * % 1 + 1 / * .!\'$ ,!& , &\'*%+ \' -&!. *+!,1 (\'$! 1
!*+,$1 !,4+ \'\' , !& , , , 1 , $ +, * % % * , , , * 0!+,+ +- ,
!& + -&!. *+!,1 (\'$! 1 3 ,, * $ , , & & . *

\'* \'. * , & &, * -, \'*!,! + * ** ,\' , / $$ #&\'/& \'\'$
\'\
* !, ,-* (* &, 3 (* &, \'-* * % ,! \'$$ - + * , /!, , !*
\'/& & + !& . *1 +!%!$ * +!,- ,!\'& / & , 1 * , , , -&!$ , *
$ + ( * ,!\'& \' , \'\'$ \'\
* !, ,-* 0 ,$1 / , , & &, * !+ \'!& &\'/ / + $ !,!% , & ! &\', *
)-!* &1 ( *%!++!\'& *\'% , + \'\'$ + &,* $ -, \'*!,! +

ҭҩ

# \"#( (# & \'#&( (# %)#( \' )( \" ( \' \' \"\"#( $ ( & \' %)#( &#!
\"#( & # # )! \"( ( & (( \" ( ( ! \"( # ( ## # & ! %)#( . & ( #\"\'
# \" $ \" \" ! - \" # ( \" # * # ( # ( $# - #+ * & ( \' # \'
\"#( ! ( ! * # ( #\"\' # )\" * &\' (- $# - /\
\" # %)#( - +&#( ( \' \'\' ! \" ( ( #* & ( )\" * &\' (- * &-#\" & \"
\"#+ ( - & #)(& * & + ( ( #\"\' # \" \"( & ) (- #!$ ( - ( \" + ( ( \'
\"\'(&) ( #\"\' \' ( + &

! &&#& ( \' () ( #\" \" ( \" \"( & & (\' + ( \' # \" #\" \" + ( \' \"
$$ \" \" \" ( )\" * &\' (- #* & ( $ \'( \' * & \' - )\" * &\' (-
\"\'( ()( #\"\' & \"#( (( \" \"- \'(&#\" & #\" ( #\"(& &- \" ! \"- \' \'
( - & \' - & \" )& & ! ( $ &(\" &\' $& & \"#( (# ) - )\" * &\' (- )
\" \' \" ( & $& ( $# \' )( - ( &) # #& - * #! (# * \" ( & , )\' *
(- \" , $( #\" \'! ( ( ( - \" ( \'( \" \' # ( )\" * &\' (- ( ( #\" -
( - \" * & & (

)\" &\'( \" + ( \' $$ \" \" + )\" &\'( \" ( ( ( \' ( #\"\' + & ! \"\'(
( ## # #!$)( & \" \" ( # # \" \' \" ( \' + + \'(& * (# \" \" #
) + ( #)& # ) \' \" & ! & #\"\'( \"( - $&#$#\' \" ##$ & ( #\" #\" -
\'\') \' + + \"( (# \'(& \" ( \" #)& * # (&)\'( \" #& #)& & ( #\"\' (#
%) #$ \" \" & )( + \' + \"# & $&# \'( $\'

# \'\' ( & \'( # ( \' (& \"\' & $( $ \' \'( \" (# ( \' ! \'\' &#!

)& \'$#\"\'#&\' ҭҫ#

ҭҬ

Analysis of the Effects of Substantial Lane Closure During Afternoon
Peak Along a Heavily-Traveled Urban Arterial Choke-Point

Nicholas Fudala

February 24, 2014

1 Introduction

We have been advised to begin by clarifying that, yes, we are the
traffic engineers responsible for the study at the heart of "Bridgegate"
and that Governor Chris Christie "had no knowledge of this---of the
planning, the execution, or anything about it."¹ With that out of the
way, we'd like to thank the media for the unexpected interest in our
work. While we once struggled to re ceive approval or even
acknowledgment for the legitimacy of our research interests, that being
our queue length prediction system, we now find ourselves overwhelmed
with inquiries seeking the answer to "what exactly is this traffic study
all about?"

2 Background

Traffic congestion is an unavoidable fact of mod ern life. Sometimes you
approach a line of red tail lights and have no idea how long it
stretches ahead of you. So one day, in 1986, while stuck in such a
predicament, we devised such a method to calculate queue length and
report its findings to each subscriber's one-way pager. Though offering
no congestion-free alter

natives, the system would offer peace of mind in knowing exactly how
long the subscriber would remain stuck in the queue, away from friends
and family, after a long day at work. Nineteen years later, while
still working out the bugs, an up start search engine named Google
released their "Google Maps" and its traffic observation fea ture,
effectively duplicating our effort for non pager devices. Therefore,
we seek to provide an alternative to Google and subsequent traffic ob
servation websites, apps, and local news broad casts.

3 Methodology

We were approached one day, to our complete surprise, by the
Transportation Commissioner of the State of New Jersey to conduct a
traffic study on the George Washington Bridge, con necting Fort Lee,
NJ and New York City. In spired by the original cause of the
congestion that would spark the idea for our queue length prediction
system we decided to simulate a mat tress on the freeway situation by
closing two of the three travel lanes from the bridge to Fort Lee. Our
proprietary algorithm relied on public

ҭҭ

use roadway sensors and cameras and converted all necessary data into a
text message provided to subscribers (which, of course, there were none
in this beta testing stage). Information was in stead unintentionally
encrypted and placed in a password-protected file.

4 Results and Future Research

Research is still ongoing as the authors are con tinually attempting to
guess the password pro tecting all relevant data and information from
the one-day traffic study. We are confident, as evidenced by the
unexpected outpouring of me dia and worldwide interest, that we will
find sup port in further study of our system. In fact, Governor Christie
has been quoted saying "Go ahead."² We believe it necessary to investi
gate worst-case scenario mattress-on-freeway sit uations and propose
research on complete lane closure during afternoon peak as well as
travel access restricted to one 8-foot shoulder during an ice storm. We
appreciate the continued sup port of the Governor, who agrees that "we
need to fix this problem, because I'm the boss."³

5 Acknowledgments

Special thanks to the Transportation Commis sioner of the State of New
Jersey, the Port Au thority of New York and New Jersey, and the
Governor's Office of New Jersey for providing unprecedented access with
virtually no notice to such a vital bottleneck.

References

¹ Kate Zernike. Christie linked to knowledge of shut lanes.
http://www.nytimes.com/2014/

02/01/nyregion/christie-bridge.html, January 31, 2014.

² The Washington Post. Full transcript: N.J. Gov. Chris Christies
Jan. 9 news conference on George Washington Bridge scandal.
http://www.washingtonpost.com/ politics/transcript-chris-christies

news-conference-on-george-washington
bridge-scandal/2014/01/09/d0f4711c 7944-11e3-8963-b4b654bcc9b2_story.
html, January 9, 2014.

³ CNN Political Tracker. Chris Christie: 'If I was in the Senate
right now, I'd kill myself'. http://politicalticker.blogs.cnn.com/
2013/10/11/chris-christie-if-i-was-in
the-senate-right-now-id-kill-myself/, October 11, 2013. CNN Political
Tracker.

ҭү

Yet Another Application of Our Pet Technique

Chester Francis Nicholas Fudala

February 25, 2014

Abstract {width="1.6786668853893263in"
height="1.875333552055993in"}

Traffic lights are the worst. In most cities, their

timing is probably just random guessing by some

hillbilly local who can't count past ten, and we're

unaware of more advanced techniques in the lit

erature. We apply the extensively tested and oc

casionally accepted Francis-Fudala technique to

the optimization of a simple two-phase isolated

traffic signal, and discuss some selected benefits.

1 Introduction

Traffic lights, also referred to as traffic sig nals, traffic lamps,
signal lights, stop lights and robots [1], are defined as "a road
signal for directing vehicular traffic by means of colored lights"
[2]. See Figure 1.

They were first introduced in 1868 in Lon don [1]. When you wait at a
red light, you waste time, and your car wastes gas, so it's bad for both
you and the environment. To our knowl edge, there is no known way to
improve upon random guessing for green time distribution, ei ther in the
literature or in practice [1, p. 1].

2 Our Approach

A potentially wildly successful and robust tech nique for optimal
decision-making is the Francis

Figure 1: A traffic light.

Fudala technique [3, 4]. A non-linear, multi objective, Bayesian
procedure utilizing dynamic programming, neural networks, and various
data mining approaches comprising several of the leading optimization
techniques in sequence, and occasionally produces results superior to
when used individually.

The algorithm uses a multi-step process to output a single value of 1
or 0 (change or hold current phase) based on an input of vehicles on
each link, geometric mean of vehicle loca tions, median of
time-to-intersection, time since last phase change, current time in
MATLAB (nanoseconds since January 0, 0), friction of road surface (in
simulation assumed to be 1), vehi cle (RGB), mean engine displacement
(cc), min

ҭұ

imum recommended tire inflation (psi), and var ious barometer
readings.

Inputs are first computed using a symbolic re gression tool very
similar to, but definitely not, Cornell University's Eureqa [5], for
a minimum of five days of simulation on a Pentium 4 Quad Core. These
outputs are then analyzed with a stochastic artificial neural network
that is not unlike, but also unlike, the one available in MAT LAB's
neural network package. The third step is a proprietary combination of
Google Translate German to English (but not) and WinZip.

In case you can't tell, this is really complicated and therefore
better.

The last digit of the WinZip file size in bytes is utilized in the next
step, unless that digit is nei ther zero nor one, in which case the
technique is repeated until an acceptable value is outputted. The
boolean output undergoes the final step, one that is so shocking and
brilliant that articulat ing it in this paper could destabilize all of
science (for an even more cryptic explanation, see [6]). Rest assured
it is so amazing and brilliant that it completely guarantees success and
is in no way possible to improve or even understand, as evi denced by
the US Patent Office refusing to even acknowledge our many applications.

2.1 Past Performance

The Francis-Fudala technique has been applied with various degrees of
success and non-success to a wide array of problems in the fields of
botany [7], psychology [8], paranormal psychol ogy [9],
stock-picking [10], lock-picking [11], off track betting [12],
on-track betting [13], guilt predictions on episodes of Dateline NBC
[14], automated tweet scheduling [15], alcohol con tent per unit
currency [16], number of M&M's in a cylindrical container [17], the
Aanderaa

Karp-Rosenberg conjecture [18], and number of Skittles in a cubical
container [19]. The algo rithm has routinely placed in the top 80%
of sub missions in multiple data mining competitions hosted on
Kaggle.com, and has been nominated multiple times for the Nobel Peace
Prize (the Prize in Economic Sciences surprisingly restricts
self-nomination).

2.2 Traffic Signal Application

Our technique was applied to a common two phase traffic signal at a
theoretical intersec tion. Modeling driver behavior proved particu
larly difficult, due to the complete lack of vehicle dynamic models
found in an extensive search of the literature that were either free,
in front of paywalls, or without lots of math. In this ap plication,
the intersection was modeled in Net Logo [20], assuming cubic
vehicles with point mass properties, accelerations of [inf, -inf],
using the car-following model employed in Frogger^TM. A visualization
of our network is shown in Fig ure 2.

{width="1.875333552055993in"
height="2.14200021872266in"}

Figure 2: Traffic signal application.

ҭҲ

2.3 Results

Analysis was abbreviated due to the excessively long computational
requirements of our algo rithm. Each second of simulation required be
tween 4 and 6 hours of computational time, so that a simulation of one
hour of evening peak period traffic required 33 days of computation.
Significance was therefore not calculated due to the low sample size of
n = 3. Results are shown in Table 1.

Technique Delay (s/veh) Stops

Random Guessing 56.7 421 Na¨ıve 54.5 450 Francis-Fudala 54.2!!! 3452

Table 1: Performance of the Francis-Fudala Technique compared with
benchmarks. Note the improved performance in delay. It's in the mid
dle bottom of the table.

3 Future Research

Although our testing conclusively demonstrated the vast superiority of
the Francis-Fudala tech nique, there remain a few areas for further re
search. Potential topics include the perfor mance of the Francis-Fudala
technique on a three-phase intersection, four-phase intersection,
five-phase intersection, six-phase intersection, seven-phase
intersection, eight-phase intersec tion, nine-phase intersection,
ten-phase inter section, eleven-phase intersection, twelve-phase
intersection, two-legged signalized roundabout, three-legged signalized
roundabout, four-legged signalized roundabout, five-legged signalized
roundabout, six-legged signalized roundabout, seven-legged signalized
roundabout, short-ramp

meters, long-ramp meters, on-ramp meters, off ramp meters, interchange
ramp meters, diamond interchanges, diverging diamond interchanges, and
theorized autonomous vehicle intersection with individualized lights
for each vehicle. Test ing on each of these signal configurations
would be incomplete without further testing of the ef fects of
standing snow, falling snow, falling snow blowing sideways, unexpected
snow, expected snow, ice, rain, icy-rain or sleet, hail, wind, glare,
earthquakes, solar eclipses, lunar eclipses, pro portion of trucks,
proportion of bicyclists, pres ence of pedestrians, presence of
particularly dis tracting pedestrians, sensor failures, police so
briety checkpoints, recurring congestion, non recurring congestion,
and random traffic light bulb burnouts. Obviously each of these com
binations requires its own paper, and probably book.

References

[1] Wikipedia. Traffic light. http://en.
wikipedia.org/wiki/Traffic_light.

[2] The Free Dictionary by Farlex. Traffic light.
http://www.thefreedictionary. com/traffic+light.

[3] Chester Francis. Artificial Complexity. PhD thesis, University
of Burgundy, submitted.

[4] Nicholas Fudala. Universal Complexity. PhD thesis, University of
Burgundy, sub mitted.

[5] Michael Schmidt and Hod Lipson. Distill ing free-form natural
laws from experimen tal data. Science, 234(5923):81--85, April 2009.

ҭҳ

[6] Chester Francis and Nicholas Fudala. An Even Newer Kind of
Science. Publisher: Author, 1^st edition, January 2003.

[7] Chester Francis and Nicholas Fudala. To wards predictive
coloration of the Eastern Maple. Journal of Botany Enthusiasts, sub
mitted.

[8] Chester Francis and Nicholas Fudala. Ap proaching an
understanding of the bias ef fect in handicapping of equine racing.
Jour nal of Sports Psychology, submitted.

[9] Chester Francis and Nicholas Fudala. Ap proaching an
understanding of the bias ef fect in handicapping of equine racing in
the presence of ghosts. Journal of Paranormal Psychology, submitted.

[10] Chester Francis and Nicholas Fudala. En route to PENNY STOCKS ARE
THE IPHONE OF INVESTING! The Motely Fool, submitted.

[11] Chester Francis and Nicholas Fudala. In the vicinity of a
predictive approach to fasten ing device liberation: a
quasi-philosophical perspective. Journal of Speculative Re search,
submitted.

[12] Chester Francis and Nicholas Fudala. Ap proaching an
understanding of the bias ef fect in handicapping of equine racing.
Daily Racing Form, submitted.

[13] Chester Francis and Nicholas Fudala. A novel stereoscopic
camera object identifica tion test case: classification of discarded
ticket status at Yonkers Raceway. IEEE Transactions on
Entrepreneurship, submit ted.

[14] Chester Francis and Nicholas Fudala. It's often the married
man. Journal of Media Studies, submitted.

[15] Chester Francis and Nicholas Fudala. Hash tag: profit. Harvard
Business Review, sub mitted.

[16] Chester Francis and Nicholas Fudala. Al cohol dependence and
poverty, but not the way you think. Journal of Substance Abuse,
submitted.

[17] Chester Francis and Nicholas Fudala. Step right up! How to beat
a carnie at his own game, and impress your friends. Topics in Social
Sciences: Special Issue on Carnival Culture, submitted.

[18] Chester Francis and Nicholas Fudala. To wards preliminary
understanding of the sig nificance, magnitude, and difficulty of the
Aanderaa-Karp-Rosenberg conjecture: ini tial thoughts. Nature,
submitted.

[19] Chester Francis and Nicholas Fudala. Step right up:
Particle-count prediction in a lin ear, equaliteral non-spherical
environment. Proceedings of the National Academy of Sci ences,
submitted.

[20] Uri Wilensky. Netlogo. http://ccl. northwestern.edu/netlogo/.

ҭҴ

SIGBOVIK 2014 Paper Review
{width="0.9486668853893263in"
height="0.9486668853893263in"}

Paper 5: Yet Another Application of Our Pet Techn

Robert Marsh, King Under the Mountain

Rating: 1 (strong reject)

Confidence: absolute/4

There are several problems with this paper. The modeling of vehicles
is rather poor - at the very least their acceleration in the road's
reference frame is limited by relativistic effects. Furthermore,
modern vehicles are curvy, not dumb and boxy (except the Nissan Cube,
which isdumb, boxy, and curvy, truly a marvel of modern engineering)
and thus would be best modeled as spheres. In addition, the
alternatives they test against don't include the current industry
standard dime-an-hour hick, suggesting that they were cherrypicked to
appear more favorable. And besides, they didn't cite anything I did,
so I don't see why I should let them get published.

ҭҵ

үҩ

SIGBOVIK • March MMXIV

Please Don't Let Open House Destroy the Universe

Jenn Landefeld^∗

Carnegie Mellon University

jennsbl@cs.cmu.edu

Abstract

Exploration of the multi-dimensional space-time rift potentials [1]
created through appointment scheduling containing m admitted students
crossed with n faculty crossed with y current graduate students
willing to speak with each other within two eight-hour sets of 30
minute meeting slots. The two day meeting period is also sprinkled
with a series of events that interfere with multiple potential 30
minute meeting times causing admitted students, current students and
faculty to not be able to meet with those they preferred to meet with.
Events also allow chance meetings which will generate emails
requesting additional meetings or changes to schedules that will cause
ripple effects across the entire appointment structure.

I. Introduction

I^{n this paper we explore the relatively un} documented
practice of inviting multiple

students admitted to a Computer Science Ph.D. Program to descend upon a
given uni versity to attempt to glean information from faculty and
current Ph.D. students in an ef fort to determine whether said
university and its faculty are a suitable fit for their research
interests. Through this exploration we will determine if there is a real
potential for the creation of a multi-dimensional space-time rift that
could be catastrophic in proportion.

II. Methods

For examining this dilemma we will assume the following defined
variables are in play:

Table 1: Number of People Needing Appointments

Faculty Admit Current Ph.D.

n =105 m =59 y =49

To accomplish the appointment schedule for matching m (where m is
those who are able to travel to visit the given University at the set
schedule time) across n and y we need to optimize the schedules to get
as many m into the offices of n they requested to meet while also
optimizing the schedules to accommodate the availability provided by
n, cross-referenced with their level of willingness to actually meet
with a given m.

When this optimization[2] fails, a second round attempt will be made
to provide any faculty interaction in a given area of research before
cross-checking the list of current Ph.D. student availability to match
admitted students to with current students whose advisor might
potentially be one of the faculty the admitted student requested to
meet with.

Faculty and current students are contacted in advance of the student
visits to assess their availability for 30 minute meeting slots during
morning and afternoon daylight work hours on two standard university
workdays compris ing a total of 5-6.5 hours of meeting slots each day.

^∗Thanks to Rob Simmons for a much more concise title than this paper
began with. Articles with short titles are cited more often.[3]
Thanks also to Martha Clarke for years of dedication to making this
process work for the Computer Science Department and without whose
retirement I wouldn't have had the privilege of taking on the daunting
task explored in this paper. There are so many more I could thank, but
I don't want to make them feel uncomfortable by pointing out their
contributions to the added complexity of the dilemma.

үҫ

SIGBOVIK • March MMXIV

be admit or faculty based)

Appealing to the \"What's in it for me factor\"

• Get me students to spend funding on -- so funding isn't taken back
by (a) de partment, (b) school, © university, (d) benefactor
(usually government funding with spending timeline/strings attached)

• Get me students to advance the research (more bodies on the problem)

• Get me students so I can write more grants to get more funding to
fund the students I'm recruiting.

Appealing to the Rock Star factor

• You can have you name on even more submitted papers?

• If you are tired of traveling and talking to people about the
research you can send a student.

• Get more students here to work with other faculty to keep those
faculty busy and to stop bugging you to do things.

Appealing to the \"Okay there's food I guess I will attend that\" factor

• We all know faculty and students in com puter science departments
like to eat - provide food!

Research we didn't have time to fully define or apply findings from¹

• Managing the Absent Minded Professor • Managing the Rock Star factor

• Mitigating the Curmudgeon factor • Mitigating the Procrastinator

• Managing unrealistic expectations of who will get to speak to whom
(this can

III. Conclusions and Future Research

Obvious conclusions (Duh)

• Admitted students are perfectly happy to visit to talk and eat. It's
not clear how to get them to understand the complexity and they will
not get to speak to every professor they requested a meeting with.

• Faculty like to eat, talk to some students they want to and don't
get to talk to some students they wanted to, and ask to meet with
students who don't visit.

• Current students get little done on their theses, get to eat and
talk a lot to students who may have really wanted to talk to their
advisor or may have no common research interest at all.

• Faculty who are not in the Computer Sci ence Department proper
generally have little vested interest in meeting with a student during
your Open House and may or may not offer time to do so, thus
increasing the complexity factor by the number faculty requested by
admits from departments outside yours.

• Some faculty who are not in the Com puter Science Department proper
may be more accommodating with their time than faculty in your own
department, thus increasing the complexity factor by the number
faculty requested by admits from departments outside yours.

• Current students are helpful and a tremendous benefit to have on
hand

¹We didn't have time to explore these in detail and apply them to
our optimization processes due to the following factors: (1) faculty
making their own appointments caused an additional time sink and
domino affect on scheduling that had to be handled before (2) applying
the requests of admitted students after they arrived and wanted
additional faculty added to their schedules while (3) adding faculty
who were suggested by other faculty to admitted students schedules
while (4) changing counts for events that students would now not be
attending due to additional appointments added to their schedule while
(5) simultaneously sending email to multiple admitted students and
faculty to confirm changed or additional appointments while (6)
updating, printing and distributing physical schedules and (7)
contacting the current students to either move appointments with an
admit or (8) emailing current students to cancel appointments entirely
then (8) repeat the process when faculty decided at the end of day one
that they did actually want to speak to another student on day two of
the event even though they originally said they had no available time
on day two while (9) contacting admits to cancel appointments with
faculty unable to return to campus due to travel issues while (10)
redoing schedules for any admitted students who had travel issues.

үҬ

SIGBOVIK • March MMXIV

for the events and appointments and scheduling couldn't truly be accom
plished without their willingness to fill in for busier, distracted,
or missing faculty.

• Some faculty need to learn how to say \"No\".

• Some faculty need to learn how to say \"Yes\".

While the research is not at all conclusive about the best
optimization methods to apply to the herding of cats², it is
apparent that more research is needed so admissions coordinators can
optimize the scheduling (if there is time and if there is funding
leftover from the food and admitted student travel budgets).

Without the possibility of applying opti mization for this process, each
incremental in crease in the number of admits attempting visit, crossed
with the number of faculty and depart ments engaged in the open house
process will steadily head toward rift creation. With the addition of
each request to meet with a faculty member outside the hosting
department cou pled with the admits expectations crossed with the amount
of time actually available to accom plish concurrent tasks the potential
escalates.

Questions we have not yet answered satisfacto rily and might be
suitable for future research are:

• Should we give the admitted students t-shirts? Everybody wants
another t shirt! Our research leads us to believe we should -- perhaps
to keep up with the \"Joneses\"³(you know, those other schools that
think they are top-tier and just may have handed out t-shirts when we
did not) or to add something else neat to the gift bags.

• Should we build a water park with a huge beach as a recruiting tool,
closer to campus than Sandcastle, of course. (ev eryone wants to be
closer to more water

than just 3 rivers and there should be lots of sand, right -
Sandcastle is just too far away - seriously!)?

• Should we build a solar dome to enable suntanning in the winter
months to com pete with the West Coast schools?

• Should we somehow encourage the devel opment (or build one
ourselves) of more ski areas within driving distance to take advantage
of the fact we seem to be drift ing north as far as weather patterns
are concerned? (Look out East Coast schools north of us - we are about
to seriously compete with your horrible weather!)

• How much email was actually sent and received by the admissions
coordinator during the time period of notifying stu dents they were
admitted, their Open House travel planning, attendance and
reimbursements and the decision dead line?

• Determining if coffee consumption is a valid method to sustain the
process and stave off the pending multidimensional space-time rift.

IV. Discussion

Other than a few long and many hurried meet ings with the one person
who created this pro cess, there has not been any discussion about the
overall dilemma regarding our potential to cause a multi-dimensional
space-time rift. In put would be welcome regarding methodology. Not
that I would apply any of them to future research, but it might be a
fun discussion none the-less.

It is hoped that discussion will not be ter ribly serious, as this
research was done with a lighthearted spirit. Data is still coming in
and the processes the are ongoing. I look forward to the next round of
applications, admissions meetings and Open House as sources of con
tinued research. ;-)

²This is a classic dilemma that surfaces repeatedly and is almost
lovingly referred to by ad ministrators across academia[4] see also:
http://chronicle.com/blognetwork/researchcentered/2011/09/23/
advanced-faculty-wrangling-techniques/

³Wikipedia definition
http://en.wikipedia.org/wiki/Keeping_up_with_the_Joneses

үҭ

References

SIGBOVIK • March MMXIV

[3] Carlos Eduardo Paiva, Joao Paulo da

Silveira, Nogueira Lima, and Bianca

[1] P. Bar-Joseph, Space-time discontinuous finite element
approximations for multi dimensional nonlinear hyperbolic systems.

Computational Mechanics, Volume 5, Issue 2-3, 145--160,
Springer-Verlag, 1989

[2] Vincent Conitzer, Tuomas Sandholm, Com pute the Optimal Strategy
to Commit to.

EC '06 Proceedings of the 7^th ACM con ference on Electronic commerce,
82--90, ACM 2006

үү

Sakamoto Ribeiro Paiva Articles with short titles describing the
results are cited more of ten.

Clinics (Sao Paulo) v.67(5); May 2012

[4] Marietta Del Favero, Nathaniel J. Bray Ph.D., M.Ed., Herding
Cats and Big Dogs: Tensions in the Faculty-Administrator Rela tionship

Higher Education: Handbook of Theory and Research, 477-54, Springer
Nether lands, 2010

)))

4

\%\
\
7

\'\
% $

&\
\
5 #

* .\
\
\
\
$\
\
\
$ 3 3

& # \" \' # #

* .\
\
\
$ $ 5

1 $ 1 $ 4 8

$

* . 6\
$ $\
$\
$

( \' & #\
\
$ +\
# & #\
\
$ #

* .\
$ $\
$

үұ

үҲ

Heterotopy Type Theory: A defense of the traditional foundations of
mathematics

Abstract

Thomas Cramer (R-TX) United States Senate

Sam Yeager

Arizona State Senate Id-I-UNNATURAL

A major focus of interest in type theory has been the treat ment of
identity types, a subject that recently underwent a major revision under
homotopy type theory [4]. Researchers in the field have historically
ignored the beliefs of a large segment of the population that wishes to
preserve the tradi tional meaning of identity types. Many authors
mistakenly refer to these types, even informally, as "proofs of
equality." This is not about equality. It is about our freedom to
practice type theory as we see fit, and we will defend this freedom
against any onslaught of political, or mathematical, correct ness. This
paper takes a firm stand against the liberal attack on identity, instead
offering a pure account of identity types, called heterotopy type
theory, which reaffirms their original intent. We hope this document
will be enshrined as a part of the Constitution of the Association for
Computing Machin ery [1], to protect the august institution of
identity against future attacks.

1. Introduction

Much prior work in type theory has dealt with the ways in which type
theories handle identity types Id_A(m, n), where A is a type and m and
n are terms of that type. With the recent introduction of homotopy type
theory [4], the discus sion of these identity types has gained renewed
interest, lead ing to a total redefinition of the meaning of identity.
Under this disturbing philosophy, terms of identity type are thought of
as paths in the space representing the type A. Elements of the iterated
identity type Id_IdA(m,n)(p, q) where p and q are paths between m and n
may be thought of as homotopies be tween these two paths. But it is not
for us to redefine identity. Identity is a concept that has been steeped
in tradition since the beginning of our field, and is granted a unique
status in the ancient books of mathematics. It may not be lightly al
tered to fit every passing trend, however fervent the support ers of
this trend may be.

2. Traditional identity types

The primary problem with new definitions of identity is the so-called
identity introduction rule.

Γ m : A

Γ refl_A(m) : Id_A(m, m)

This rule embodies the natural and logical conclusion of the slippery
slope on which type theory finds itself: if two things of similar
nature are allowed to form an identity, then why not allow a term to
enter into an identity with itself? The identity "proof" refl_A
represents all that is dangerous about modern type theory, and we
should not allow ourselves to tend in that direction. We, of course,
do not allow such a rule within our type theory. Instead, we propose
an alternate identity introduction form, which we call original
identifi cation and notate ido^F_A(m, n). To make sure that this
form cannot be twisted to allow instances of refl, it requires a wit
ness, F : A → bool, which asserts that m and n are eligible to be
identified by mapping one to tt and one to ff.¹

Id-I

Γ m : A Γ n : A F(m) = tt F(n) = ff Γ ido^F_A(m, n) : Id_A(m, n)

This is what one would expect as the natural definition of identity.
After all, it was Adam and Eve, not Adam and λx. Adam x.
Unfortunately, removing reflexivity in favor of our traditional
introduction form is not sufficient to restore traditional identity.
The depravity of modern type theory continues to such an extent that
the following term is actually definable within the type theory:

trans : Id_A(l,m) → Id_A(m, n) → Id_A(l, n)

While some would have us believe that trans is a perfectly natural and
wholesome property, we will see where this leads: having entered into
a solemn identity with l, m is immediately allowed to enter into an
identity with n as well. Were this not enough, trans has the audacity
to suggest that l and n are now identified! Clearly we cannot allow
such an

¹ Many types actually require two witnesses, but we present only one
here for simplicity.

үҳ

abomination to enter into our system. The root of this danger is
identity elimination, the so-called J rule.

Id-E-UNNATURAL

Γ p : Id_A(M,N)

Γ, x : A, y : A, z : Id_A(x, y) C type

Γ, x : A Q : [x, x,refl_A(x)/x, y, z]C

Γ J[x.y.z.C](p, x.Q):[M, N, p/x, y, z]C

This rule demonstrates the unbounded audacity of propo nents of this
unnatural and dangerous type theory. It is not enough for them that a
concept like refl be introduced into the theory, but they must impose it
on all type theorists by asserting an elimination form that treats all
self-respecting identities as if they were refl! As we did with identity
intro duction, we must present a proper identity elimination form, which
we call H after incisive social commentator Sean Han nity. This rule
states that once an identity p between x and y has been sanctified by
any witness, we may use it in any con text C requiring identified
elements without knowing what witness was used. In particular, we may do
this as long as we can form a term Q that is typed with C assuming that
x and y were identified by a witness that assigns tt to x and ff to all
other elements of A.

Id-E

Γ p : Id_A(M,N)

Γ, x : A, y : A, z : Id_A(x, y) C type

Γ, x : A, y : A Q : [x, y, ido¹

_{[A]{.underline}} (x, y)/x, y, z]C

Γ H[x.y.z.C](p, x.y.Q):[M, N, p/x, y, z]C where 1_{x} is an
indicator function

F : A → B, and two elements x, y such that Γ x : A and Γ y : A. Define

ap_F to be the action on paths of F. Activist type theorists would

like us to blindly assign to ap_F the type Id_A(x, y) → Id_B(F x, F

y). But suppose that some corrupting influence causes it to be the

case that F x = F y. Even if we have an honest-to-goodness identity p

Id_A(x, y), such as one formed by ido and a proper witness, ap_F p
will be typed by the immoral and unnatural type Id_a(F x, F x). But
all is not lost. If F is injective, we can be sure that the type B
will not diminish the identification of x and y by allowing their
F-mapped counterparts to live in refl. Therefore, when identifications
are mapped across types by functorial actions, it is important that we
only continue to accept the identification if the map in question is a
good, injective map. Recent work by Kennedy, et al. [5] suggests
that the action on paths of non-injective maps might be recognized at
a higher universe encompassing both A and B, but we do not accept the
validity of this work.

4. Higher inductive types

Identities hold such an exalted role within our society that it seems
natural to allow them to be defined directly as part of inductive
types. For example, the following is a definition of the type bool,
which not only defines the two elements, tt and ff, but allows them to
enter into a natural, traditional, identity that reaffirms their
commitment to be partners in their membership of the type bool:

tt : bool

ff : bool

p : Id_bool(tt, ff)

Non-believers might not accept such a definition that

1_{x}(z) =

tt : z = x ff : z = x

asserts an identity without what they would call "proof." Yet it is a
fundamental facet of heterotopy type theory that we

Homotopy type theorists might, at this point, display their inner doubt
with the system they have created by attempt ing to justify their
inference rules with a "local soundness proof." We will not do this
here, as our faith in the goodness of traditional identity types is
complete and no other proof is required.

Lest we leave the reader without hope, we should note that one tenet of
our philosophy remains uncorrupted by the forces against which we
struggle. The term sym : Id_A(x, y) → Id_A(y, x), which recognizes the
mutual com mitment to the bond of identification, continues to have a
place in modern type theory. Of course, sym is definable in our theory
as well.

sym xyp := H[x, y, .Id_A(y, x)](p, x.y.ido¹

_A (y, x))

3. Functoriality

Our efforts to correct the ills of type theory are thwarted once again
by the functorial action ap. Suppose we have a map

must take certain definitions on faith; this is why they are called
Higher inductive definitions.

5. Freedom of Expression Axiom

On the other hand, it is sometimes the case that we will be presented
with an alleged identification that must not be considered valid, as
to do so would conflict with our most deeply-held beliefs. To make
sure that others cannot infringe upon our rights by forcing us to
accept improper identifica tions, we introduce the Freedom of
Expression Axiom. This axiom provides a term fea_A(x, y) for x, y of
type A, which contradicts such a destructive identification.

FEA

Γ x : A Γ y : A

Γ fea_A(x, y) : ¬Id_A(x, y)

6. Related Work

The most closely related work to this paper in its free, natural
approach to type theory is Angiuli's work on unintentional

үҴ

type theory [2]. However, we resent that Angiuli, who has previously
embraced socialist policies [3], would refer to this type theory as
"unintentional" when it is clearly part of a larger, Intelligently
Designed type theory.

References

[1] Constitution of the ACM. http://www.acm.org/about/ constitution,
2014.

[2] C. Angiuli. The (∞, 1)-accidentopos model of unintentional type
theory. In Proceedings of the 7^th annual intercalary robot dance party
in celebtration of workshop on symposium about Harry Q. Bovik's 2⁶th
birthday (SIGBOVIK '13). ACH, Apr. 2013.

[3] K. Angiuli and F. Engels. Redistributive version control sys
tems. In Proceedings of the 7^th annual intercalary robot dance party
in celebtration of workshop on symposium about Harry Q. Bovik's 2⁶th
birthday (SIGBOVIK '13). ACH, Apr. 2013.

[4] I. for Advanced Study. Homotopy Type Theory: Univalent
Foundations of Mathematics. The Univalent Foundations Pro gram, 2013.
http://homotopytypetheory.org/book/.

[5] A. Kennedy et al. United States v. Windsor. 570 U.S. 12 (Docket
No. 12-307), 2013.

үҵ

ұҩ

The Dumping Lemma

Assessing Regularity

Naomi Saphra

Abstract

In the field of computational scatology, there has long stood a
question of how one might approach the question of a language's
regularity. It is widely acknowledged as desirable that a language
should be regular, as this eases the generation of outputs as well as
the digestion of inputs. However, it is often not obvious whether a
given language is, in fact, regular or tractable. Here we describe the
use of the Dumping Lemma to prove the regularity of a language.

1 Introduction

Because computational scatology is primarily concerned with outputs, the
most popular models in the field tend to be generative. Since the
field's humble beginnings, our concern with the taxonomy of output
languages and sets according to the automata that might have generated
them has been paramount. Once "Father of Compu tational Scatology" Anal
P¨uring first proposed the taxonomy that would bear his name of
P¨uring-computable and -complete languages, we devel oped vocabulary to
describe further demarcations of language categories. Among our family
of automata are the relatively simple models that can generate or
recognize the regular lan guages, Fecal State Automata (FSA) (as well as
their relatives, the Fecal State Transpoocers, beyond the scope of this
paper).

Unfortunately, the coprocom putability community has struggled to
consistently classify a given output set as regular or not. Thus we
present a new rule that can be employed in proving a regularity claim.

2 The High-Fiber Hy pothesis

In our work with FSAs, we have en countered a pattern of high-fiber in
puts to a recognizing automaton. This leads us to the conclusion that
regular languages must have a high-fiber seg ment, that is:

A regular input longer than length k must have a segment of fiber that
can be expanded arbitrarily and the input is still accepted by an FSA.

This is the claim that we will call the Dumping Lemma.

Proof In Figure 1 are images of regular inputs sets that somehow we
consider tantamount to a constructive proof. The fecoinformatic
implications of the evidence are obvious and left as an exercise to
the reader.

3 Future Work

We believe there to be a possible similar lemma for the higher-order
category of Context Pee Languages (CPLs). Though their context is pee,
they share many qualities with RLs, as

ұҫ

{width="2.1436668853893264in"
height="2.1436668853893264in"}{width="2.14700021872266in"
height="2.435333552055993in"}Figure 1: Regularizers

count. It is worth noting that trees are

they can be generated by Fecal Tree

widely considered to metabolize by ex

Automata. Because a feces tree has

creting oxygen and water, posing a fur

never been observed in the wild or im

ther challenge for any attempt to prove

plemented in practice, we cannot con

a Context Pee variant of the Dumping

firm these suspicions, but do present it

Lemma.

as a possible path to a higher citation

ұҬ

Statistical Watch Optimization

Bryce Summers

whowatchesthe@mailman.cmu.edu

SIG BOVIK Conference, April 1, 2014

March 7, 2014

Disclaimer

This research was made possible in part by generous funding from 1 -
800 - JUNK and the Com binatorics, Linear Optimization, and Cool
Kinematics research foundations. All information can be corroborated
by Father Time and therefore no source need be cited.

Abstract

In this paper we will be demonstrating applications of statistics and
probability theory to the reduction of mechanical energy used by the
clocks and watches that inhabit our world. We have found that we can
yield as much as 100 percent reductions in energy usage by breaking
all of the watches and that their functionality will not be affected.

Broken Watches are Optimal.

We must initially prove some complicated lemmas, and only then will we
be able to get to the intuitive proof.

Lemma 1 : Watches are either working or broken

There has been much debate over the years as an exact classification
of watches. Some watches perform full double pi radian oscillatory
movement, whereas others display dynamically induced interrupt
functionality. The watches that display distortion within their
homogeneity fields may have different magnitudes to their temporal
displacement vectors. While fully broken watches display fully
disrupted behavior, mongrels of the partial broken category may still
provide oscillatory movement that is not at ease with classical
harmonic rhythms expected from the modern day busy intellectual. For
our purposes we will simplify our analysis to those watches that
display full and nonexistent disruptive behavior, where we will call
the non-disrupted watches working and the fully disrupted watches
broken

Lemma 2 : Working watches maintain a constant have a constant error in
their temporal lookup provider functionality.

We need to show that working watches have a non-zero error from real
time and that they retain this error until the end of time.

First of all we know that watches are set through mechanical machines
or human hands and that they will not be set to the exact correct
positions due to the vibrations of the temporal setting apparatus.

Second of all, since we are considering theoretical lambertian watch
faces, the light scattering on the watches' temporal lookup
oscillators can be safely ignored and we can assume that working
watches will maintain a constant error from the real time specified by
the temporal laws of our forefathers since the dawn of time.

ұҭ

We can prove this second part via induction:

Base Case: The claim holds now.

Induction Hypothesis: The claim holds before now'.

Induction Step: Since the nature of time is subjective, and nothing
really happens in an infinitely small amount of time, the claim must
hold now'.

Lemma 3 : Broken Watches are correct two times a day.

Due to the closure of the real numbers mapped radians under the
theoretically correct movement operation of a perfect watch oscillatory
component, every point on the watch must be hit twice through the span
on 1 day. Since a broken watch must exhibit 1 constant state throughout
the day, it must exactly match the correct state precisely two times in
every day.

Lemma 4: Errors in time are signed values.

Humans naturally discuss errors in time using signed values. For
instance, 4:01 pm would be said to be 1 minute after 4 instead of 59
minutes before 5. Such a distinction of the two signed categories of
"after" and "before" is a natural convention in the understanding of
numerical time.

Lemma 5 : AM and PM are identical on mechanical watches

Watches providing movement of lack thereof through mechanical means are
assumed to provide the same user experience in the first half of the day
as the second.

Lemma 6 : Broken Watches need less energy to operate than Working
Watches.

Due to the abscense of movement in Broken Watches, they can be
implemented without the use of any mechanical motor, whereas Working
watches need to have energy sources installed to facilitate the movement
of their temporal reading components. Therefore, Broken Watches consume
less energy than working watches.

Broken Watch Optimality:

Many people are under the impression that Working Watches are more
useful for telling time than Broken Watches. We will attempt to examine
potential why people might come to this fallacious reasoning and attempt
to help these lost souls see the virtues of Broken Watch utilization.

Fallacy 1: Correctness.

Many rational people believe that Working watches are more correct than
broken watches. This is simply not the case. Lemma 2 shows that Working
watches have a finite error at every time during the day, so they are
correct 0 times in every day. Lemma 3 shows that Broken Watches are
correct two times a day.

Fallacy 1: Expected Error.

A perceptive person would probably state that the relative minuteness of
the size of errors in a tem poral information provider is much more
important that absolute correctness. Such as person would cite lemma 2
to show that Working watches have an expected error of . They would then
in their hubris neglect to examine the case for broken watches,
believing they have proved the optimality of Working watches. If such a
narrow-minded individual were to actually compute the expected value of
the average error for a Broken watch they would learn the expected error
of their ways.

By Lemma 4, A broken watch goes linearly from being 0 hours off to 12
hours off to - 12 hours off to ұү

0 hours off during the course of a day. Therefore we can compute the
expected error as follows: ₁₂

_{[0]{.underline} tdt +} ₁₂

E[Broken Error] =

_{[0]{.underline}} −tdt

₂₄ = 0

As witnessed by the impressive calculus, the Broken watch is expected
to on average be exactly correct. Thus, the Broken watch is on average
less erroneous than a working watch.

Fallacy 1: Military Time Expected Error.

An astute observer may object to our logical use of signed time and
demand that we hand error more precisely with less room for creative
interpretation.

In this case, we must yield to their demands and analyze the expected
error under military time, the most rigorous of time demains.

In this domain the error of the Working watch will still be by lemma
2.

The Broken watch's error would vary uniformly from 0 hours to 24
hours. Thus we compute the expected error as follows:

₂₄

_{[0]{.underline}} tdt

E[Broken [E]{.underline}rror] =

₂₄= 12

So by the groovy calculus, the expected error for the Broken Watch is
12 hours. By lemma 5, we can conclude that a rational individual
should expect the watch to be exactly correct.

Thus, under the strict standards of military time Broken Watches still
exhibit optimality over their working counterparts.

Energy Savings:

By lemma 6, transforming all of the working watches in this world into
broken watches, will lead to savings of 4 · π radians of mechanical
energy per watch per day and thereby help reduce the worlds' energy
consumption, while providing users with devices that have superior
correctness and error reduction.

Conclusion:

As our mathematics demonstrates, the current reliance of stressed out
individuals on concepts such as time, productivity, and watches may be
profoundly misguided and that many of the fallacious institutions that
we take for granted should be reexamined and optimized using proper
probabilistic methods.

ұұ

SIGBOVIK 2014 Paper Review
{width="0.9486668853893263in"
height="0.9486668853893263in"}

Paper 8: Statistical Watch Optimization

Ben Blum, Light Cone Sedentarian

Rating: 3 (weak accept)

Confidence: 4/4

The author presents an innovative new method for maintaining watch
accuracy that requires un precedentedly low amounts of maintenance
energy. However, I must note two major flaws with this work:

1. The author fails to survey related work, most importantly, the
seminal publication in the field "Mustard Watches", published well in
advance of this very conference's founding.

2. The author's treatment does not account for the effects of
relativity on broken watches. In modern times, time-travellers will
have been breaking causality left and right, and it is of paramount
importance for average citizens to be able to communicate with them if
one is wearing a broken watch and the other is not.

Nevertheless, this is an important theoretical advancement in the
field of Watch Theory, and opens several promising directions for
future and past work. Weak accept.

ұҲ

A Simple Category-Theoretic Understanding of Category-Theoretic
Diagrams

Stefan Muller

Carnegie Mellon University

smuller@cs.cmu.edu

Abstract

Textbooks and other introductions to topics in category the ory often
use the commutative diagram as a convenient tool to explain new ideas.
Unfortunately, for the uninitiated, these diagrams can cause more
confusion than enlightenment. In this paper, we seek to give a gentle
introduction to the use of commutative diagrams. To simply and clearly
explain this important concept, we frame the discussion in terms of sim
ple category theory itself and use a convenient tool for un derstanding
new ideas in category theory: commutative dia grams.

1. Introduction

Many discussions of category theory graphically represent the objects
and morphisms of a category using diagrams. In a diagram, objects of a
category are represented using one or more glyphs, typically a single
uppercase letter of the Ro man alphabet. A morphism between objects is
represented using a straight or, in rare instances where it is required
for clear planar presentation of the diagram, curved, line also labelled
with one or more glyphs, typically a single low ercase letter of the
Roman alphabet. Relationships between two paths between objects are
indicated by the commutativ ity of the diagram. While to the trained
category theorist, a commutative diagram can convey a great deal of
informa tion about an unfamiliar category under discussion, students and
those in other fields often have trouble understanding the relationships
implied by a commuting diagram. It is of ten possible to explain an
individual diagram in prose, but this defeats the purpose of the simple
graphical representa tion. This paper instead aims to explain diagrams
in gen eral by presenting these diagrams as functors. It is known that a
diagram of a category C may be viewed as a func tor F : D → C where D is
a small category (e.g. [1]), but this paper chooses an alternate
presentation that we believe is unique in its clarity and concision.

2. Diagrams as a Functor

Let C be a small finite category. We define a functor D from C to
diagrams of C. For an object A ∈ C, D(C) is the diagram

A B ^f

Figure 1. The diagram D(f) of the morphism f.

ABE ^{f g}

Figure 2. Composition of the morphism diagrams D(f) and D(g).

A

For objects A, B ∈ C, we can take the diagram of a morphism f : A → B.
D(f) is shown in Figure 1. If A, B, E ∈ C and there are two morphisms
f : A → B and g : B → E, the diagrams D(f) and D(g) may be composed by
merging them together at their common nodes, in this case, B. D(g) ◦
D(f) is shown in figure 2. We now show that D is a functor. Let A ∈ C,
and id_A be the identity morphism on A. D(id_A) is shown below.

A

It is obvious from the definition of morphism diagram composition that
this is the identity morphism on D(A). We must next check that, for A,
B, E ∈ C, f : A → B and g : B → E, we have D(g ◦ f) = D(g) ◦ D(f).
This fact is clear from the commutativity of the diagram in Figure 3.

3. Morphisms on Diagrams

We now observe that, for a category C, D(C) forms a category of
diagrams on C. Let C be a category. We define an object in D(C), A:

ұҳ

A A

A

_f g◦f

_{A A} A A

g

B C

A A

_{A A} A A

Figure 3. D preserves composition.

A B

C D

_{C D} A B Figure 4. The morphism ↓.

B B

E E

A B C D

_{B B} B B

B B

_{B B} B B

_{E E} E E

E E

_{E E} E E

Figure 5. The morphism ←.

Figure 7. respects composition.

A B

C D

the same morphisms apply. For instance, (←) =← and (↓) =↓. We also have
that, for any A ∈ D(C),

_{C D} A B

C D

A B

_{C D} A B Figure 6. Commutativity of ↓ and ←.

f

A B

(id_A) = id _(A). It now remains to check that if we have A, B, E ∈
D(C), f : A→B and g : B→E, then (g ◦ f) = (g)◦ (f). This is shown by the
commutativity of the diagram in Figure 7. We may now demonstrate for all
of the standard properties of functors, one of which is shown in Figure
8.

5. Future Work

We hypothesize, but have not yet shown, that the functor can be nested
arbitrarily deeply, resulting in a family of functors _i. A conception
of ₄ is shown in Figure 9. Understanding of the limit of this process,
notated _∞, will provide a fuller understanding and newfound clarity to
the device of commutative diagrams.

g

f

6. Conclusion

C D

One morphism ↓ is shown in Figure 4. Another simple morphism, ←, is
shown in Figure 5. ←◦↓=↓◦←, as shown by the commutativity of Figure 6.

4. The Functor

We now describe a functor on the category D(C) for any small category C.
(A) is defined to be the diagram in Figure 6. We refer to (D(C)) as the
category of diagram diagrams on C. Since diagram diagrams are also
diagrams,

This paper has shown by example that it is simple to gain a thorough
understanding of an unfamiliar topic in category theory through its
presentation in terms of commutative di agrams. We hope that this work
will be useful in the future to beginning students of category theory
and related fields of study. While commutative diagrams are just one
path to a full understanding of any concept, they are equivalent to
any other such path. We hypothesize that this fact can be demon
strated using a commutative diagram.

References

[1] J. P. May. A Concise Course in Algebraic Topology. The
University of Chicago Press, Chicago, 1999.

ұҴ

A B

C D

_{C D} A B

A B

C D

C D

_{C D} A B

A B

C D

^{C D} A B

_{C D} A B

A B

C D

A B

C D

^{C D} A B

_{C D} A B

A B

C D

A B

C D

_{C D} A B

A B

C D

A B

^{C D} A B

_{C D} A B

C D

A B

C D

A B

^{C D} A B

_{C D} A B A B

C D

A B

_{C D} A B

A B

C D

C D

_{C D} A B

Figure 8. A trivial property of the functor .

ұҵ

A B

C D

^{C D} A B

C D

A B

C D

^{C D} A B

C D

A B

_{C D} A B

A B

C D

A B

_{C D} A B

A B

C D

A B

_{C D} A B

A B

C D

^{C D} A B

C D

A B

C D

^{C D} A B

C D

A B

_{C D} A B

A B

C D

A B

_{C D} A B

A B

C D

A B

_{C D} A B

C D

A B

^{C D} A B

A B

C D

A B

^{C D} A B

A B

C D

_{C D} A B

C D

A B

C D

_{C D} A B

C D

A B

C D

_{C D} A B

C D

A B

^{C D} A B

A B

C D

A B

^{C D} A B

A B

C D

_{C D} A B ^{C D} A B

C D C D

A B A B

C D C D

_{C D} A B ^{C D} A B

C D C D

A B A B

C D C D

_{C D} A B ^{C D} A B

C D

A B

_{C D} A B

A B

C D

A B

_{C D} A B

A B

C D

^{C D} A B

C D

A B

C D

^{C D} A B

C D

A B

C D

^{C D} A B

C D

A B

_{C D} A B

A B

C D

A B

_{C D} A B

A B

C D

^{C D} A B

A B

C D

A B

^{C D} A B

A B

C D

A B

^{C D} A B

A B

C D

_{C D} A B

C D

A B

C D

_{C D} A B

C D

A B

^{C D} A B

A B

C D

A B

^{C D} A B

A B

C D

A B

^{C D} A B

A B A B

C D C D

_{C D} A B ^{C D} A B

C D C D

A B A B

C D C D

_{C D} A B ^{C D} A B

C D C D

A B A B

_{C D} A B

A B

C D

A B

_{C D} A B

A B

C D

A B

_{C D} A B

A B

C D

^{C D} A B

C D

A B

C D

^{C D} A B

C D

A B

_{C D} A B

A B

C D

A B

_{C D} A B

A B

C D

A B

_{C D} A B

C D

A B

^{C D} A B

A B

C D

A B

^{C D} A B

A B

C D

_{C D} A B

C D

A B

C D

_{C D} A B

C D

A B

C D

_{C D} A B

C D

A B

^{C D} A B

A B

C D

A B

^{C D} A B

A B

C D

_{C D} A B ^{C D} A B

C D C D

A B A B

C D C D

_{C D} A B ^{C D} A B

C D C D

A B A B

C D C D

_{C D} A B ^{C D} A B

C D

A B

_{C D} A B

A B

C D

A B

_{C D} A B

A B

C D

^{C D} A B

C D

A B

C D

^{C D} A B

C D

A B

C D

^{C D} A B

C D

A B

_{C D} A B

A B

C D

A B

_{C D} A B

A B

C D

^{C D} A B

A B

C D

A B

^{C D} A B

A B

C D

A B

^{C D} A B

A B

C D

_{C D} A B

C D

A B

C D

_{C D} A B

C D

A B

^{C D} A B

A B

C D

A B

^{C D} A B

A B

C D

A B

^{C D} A B

A B

C D

_{C D} A B

C D

A B

C D

_{C D} A B

C D

A B

Figure 9. A conjecture as to the structure of ₄. Ҳҩ

SIGBOVIK 2014 Paper Review
{width="0.9486668853893263in"
height="0.9486668853893263in"}

Paper 9: A Simple Category-Theoretic ...

Reviewed by: Ed Morehouse (Carnegie Mellon University)

"A Simple Category-Theoretic Understanding of Category-Theoretic
Diagrams" by "Stefan Muller" is a work of incomprehensible abstract
nonsense, and as such, constitutes a valuable contribution to the
field of category theory.

The article seems to be about understanding category theory through
the graphical language of commutative diagrams. I say, "seems to be",
because after gleaning this much from the abstract, I decided to test
(what I assume to be) the article's central thesis by attempting to
understand the article itself by just looking at the pictures.

I infer that the article begins by describing the basic properties of
morphisms in a category under composition and identity -- although it
could be talking about something else entirely, it's kind of hard to
say. The next bit seems like it might be about constructing a category
whose objects are themselves commutative diagrams and whose morphisms
are affine transformations of such¹.

The paper ends by constructing the "Morehouse-Sierpinski ω-category of
commuting squares" (let's call it). Although "Muller" has (for all I
know) now solved a long-standing open problem in higher dimensional
category theory by giving a finitary, constructive presentation of
this important category, there is still currently no type-theoretic
interpretation (that I could think of in 5 min utes), nor are current
L^AT_EX diagram-description packages adequate for drawing
ω-dimensional commutative diagrams. I'll just assume that "Muller"
leaves these issues for future work.

Rating: I give this article the terminal rating in the co-op of the
bicategory of journal reviews. Confidence: What am I supposed to put
here?

Why are the instructions not presented in picture-form, like the ones
for assembling my bookshelf:
{width="2.37200021872266in"
height="1.640333552055993in"}

¹note to self: ask "Muller" what the paper is really about, then
reject it and steal his idea.

Ҳҫ

ҲҬ

)$)))

7\
7 +

\% &\
#\
$ - (

- $&

* . 5 $ $ 8

&\
& 7 \' &\
$\
\
$\
\
\
$( - 9

* .\
$\
$ $ $ $\
$ $ $\
\
$

1\
& \' $

$ % &\
%\
$

* . $ $

Ҳҭ

Ҳү

Cryptographically-sound Jokes

Jim McCann^∗

TCHOW llc

What do you call a predatory fish endorsed by the NIST and NSA?

-- A 6265a4a07968a7c1df16a61004fb7191177cafd4^†!

Did you hear that the NSA is going into manufacturing
collision-resistant form-molding undergar ments?

-- Yeah, and they are changing their acronym to "NDA" for New

d4193f19ed359e122dbf51cc81e94145ca017bc8^‡ Associates.

How do you tell a member of the cryptographic elite from the plebes?

-- Ask them to pronounce b43c9a57aaf61f43e5021d305146d21473bded99^§!

Why did the drug user choose
9b4e473e4de7949c4ab8e441a7faa5e2b295b469^¶ over
4a82715423d654d61838e81060a4cdf1 ?

-- Because they always take the bag with the strongest hash.

What do you call an strongly mixed certifcate of ownership?

-- c387c982a132d05cbd5f88840aef2c8157740049^∗∗, of course!

^∗e-mail: ix@tchow.com

^†SHA('rk')

^‡SHA('pewear')

^§SHA('bboleth')

^¶SHA('bag')

MD5('bag')

^∗∗SHA('re')

Ҳұ

SIGBOVIK 2014 Paper Review
{width="1.0020002187226598in"
height="1.0020002187226598in"}

Paper 2: Cryptographically-sound Jokes

Emily Forney, The Humanities in General

Rating: 88 (strong accept)

Confidence: ¼

I really enjoy that the answers are little and at the bottom. If they
were larger and more noticeable it might have spoiled the jokes which
I totally figured out on my own. They also had really cute little
symbols to denote which joke they match up with. Not that I needed
that.

I strongly accepted this as a collection of jokes that are both about
cryptography and also written in cryptography, you know, the language.
That is completely in line with the title.

My confidence reflects my understanding of the topic: a 1, as in the
best level of understanding possible. Which is what I have.

We share jokes, we are friends now.

ҲҲ

DOLLARCOIN: A CRYPTOCURRENCY WITH PROOF-OF-DOLLAR PATRICK J. XIA

Abstract. We introduce DollarCoin, a cryptocurrency that uses a novel
scheme, proof of-dollar, to achieve a consistent and secure
blockchain. Security of the currency does not require energy
consumption or useless "make work" hash computations, as with extant
proof of-work schemes, nor is the scheme vulnerable to verification
monopolies by early adopters, as is the case with proof-of-stake
schemes. Security of the blockchain is instead regulated by the
relative scarcity of the United States Dollar. DollarCoin is the first
cryptocurrency that directly satisfies all three properties of
currency: it is a medium of exchange, a unit of account, and a store
of value.

Keywords. cryptocurrency, bitcoin, dollars, bills, gamechanger,
disrupt, awesome, super cool, thebest, hashtag

1. Introduction

Modern cryptocurrencies use a disincentive-based system to make
changing the network consensus economically difficult. In the case of
Bitcoin, the specific scheme used is the computation of a partial hash
inversion. Since there are, to date, no breaks in the SHA 256
cryptographic hash system, the best way to compute such a partial hash
inversion is by brute-forcing until one gets lucky and finds a
difficult "proof of work"; specifically, a extremely small (and
therefore unlikely) output hash value. This secures the blockchain as
long as nobody controls a large share of the computation power of the
network, but at the cost of an arms race as people attempt to compute
hashes as quickly as possible to increase the chance of finding a
"block." Such Bitcoin "mining," as it is called, requires a great deal
of energy expenditure to keep the network secure.

We propose skipping the middleman and providing direct proof-of-dollar
with a blockchain that consists of videos of burning US $1 notes.
Each video will be unique as the hash of every block header is
required to be written on the dollar bill to be burnt; the block
header includes the previous block's hash, which means that each block
is forced to build on every previous block, forming a valid
blockchain.

2. Implementation

DollarCoin is implemented identically to Bitcoin with the exception of
block format, as no nonce or difficulty adjustment is required. The
transaction format remains the exact same so that people may use
extant code to manually generate transactions for the DollarCoin
blockchain. The same system of double-SHA-256 hashes ensures
cryptographic integrity of the blockchain. A block contains these
fields:

Thanks to Harry Quetzalcoatl Bovik.

Ҳҳ

Field Description Size (octets) Magic Number Value always 0xD9B4BF00
(one more than Bitcoin) 4 Block size Number of bytes until end of
block 4 Block header Consists of block header, described below 72
Transaction counter Variable length positive integer (Bitcoin VarInt)
1 - 9 Video link length Number of bytes required for the video link 2
Video link A (possibly transient) link to a video ? Transactions The
list of transactions ?

and the block header is specified as so:

Field Description Size (octets) Version Block version information 4
Previous block Previous block's hash value 32 Merkle root The hash of
the Merkle tree of the transactions 32 Timestamp Timestamp recording
when this block was created 4

All hashes are the double SHA-256 scheme as specified in Bitcoin.
Block header hashes are independent from the video link, allowing for
video links to be changed in peer to peer communications so that they
are always up to date. Clients should (where "should" is defined as
the same as SHOULD in RFC 2119) cache videos locally to allow for
videos to be served on demand in case of inability to reach the
original video link (which is probably hosted on YouTube or
something).

3. Test plan

We intend on writing the code correctly the first time.

4. "Challenges", or: why our system is better

4.1. The 50% attack. One of the technological challenges that plagues
Bitcoin is the 50% attack: if one entity controls over 50% of
hashpower, then this entity is able to subvert the security of the
blockchain by forcing double-spends through. For this sort of attack
to work with DollarCoin, one entity must control over 50% of
circulating US $1 notes (or, probabilis tically speaking, a
significant share thereof). This is surely impossible. Furthermore,
the difficulty of mining bitcoin incentivizes individual participants
to conglomerate together in mining collectives known as "mining pools"
in order to mitigate the variance of the otherwise random process of
mining.

As of this writing, the top three Bitcoin mining collectives (one of
which is simply an organization with its own custom mining hardware)
control over 50% of hashrate, which means the security of the Bitcoin
blockchain can be compromised by only three actors. With DollarCoin,
there is no randomness in generation. Its security is derived from $1
notes

ҲҴ

accessible to every individual, eliminating the need for
conglomeration and making it far less susceptible to this sort of
attack.

4.2. Orphan blocks. DollarCoin has no difficulty adjustment scheme
because dollar bills are the only totally useless piece of currency
with an extant alternative (dollar coins). One might surmise that the
lack of difficulty adjustment could create a problem, as numerous
simultaneous contributions to the blockchain result in many orphan
blocks (blocks that no other blocks build upon).

This is not a problem. High numbers of orphan blocks will increase the
relative scarcity of DollarCoin and cause its value to go to the moon.

4.3. Transaction commitment times. If your merchant requires more
confirmations of a transaction than are currently present in the
blockchain, simply burn more dollar bills.

4.4. Exchange from traditional currencies. DollarCoin has a built-in
exchange in which users essentially deposit their cash via smartphone.
This is currently a one-way exchange, but in the future we imagine
banks will be happy to exchange your DollarCoin for dollar coins.

4.5. Symbol for the currency.

5. Launch

The genesis block will be mined at SIGBOVIK 2014.

Ҳҵ

ҳҩ

Abstract

Towards a Completely Autonomous Vehicle

Nicholas Fudala Chester Francis

February 25, 2014

fully-autonomous vehicles remain heavily reliant

on human interaction. An operator must mon

Much progress has been made in fully autonomous road vehicles. Yet even
the most advanced self-driving cars must rely on a human to manually
select a destination, as well as mon itor the system in a support role.
So needy. To address these shortcomings, we propose a com pletely
autonomous vehicle with two novel fea tures: (1) the ability to predict
and enforce its destination based on a passenger's Web activity, and (2)
the trait of self-actualization and emo tional autonomy based on
Maslow's hierarchy of needs. In theoretical testing, unexpected and oc
casionally embarrassing results were observed.

1 Introduction

The field of road vehicle automation has gained much attention with
high-profile prototypes from Google [1], Nissan [2], and others. Al
though vehicles automation of throttle, brak ing, and steering are often
referred to as "au tonomous vehicles", others have argued that the term
is a misnomer, as these vehicles re quire a human to input a destination
[3]. For many, destination selection and input is a frus trating and
unnecessary task, particularly given the extensive location-desired data
available for any user. Beyond destination-selection, today's

itor the system in the event of failure, provide fuel, and perform
basic maintenance. With an autonomous vehicle's delicate sensors and
com plex software, these duties can only be described as "high
maintenance." The vehicle itself can be described as "needy" or
"bitchy."

In addition to the National Highway Safety Administration (NHTSA)
levels of road vehicle automation [4], we propose additional require
ments based on Maslow's hierarchy of needs [5]. As shown in Table 1,
they both have five lev els, which is nice. In this paper, we propose
a vehicle that meets the fourth level requirements of both NHTSA (full
self-driving) and Maslow (self-actualization).

Level NHTSA [4] Maslow [5]

0 None Physiological 1 Function-specific Safety

2 Combined function Love/belonging 3 Limited self-driving Esteem 4
Full self-driving Self-actualization

Table 1: Levels of autonomy.

ҳҫ

Destination Frequency

AVN Awards Show, Las Vegas, Nevada 57% Cat Fanciers' Association World
Championship Cat Show, Novi, Michigan 25% Google, Mountain View,
California 10% Continuous 2-4 mile circumference of user's
residence¹ 8%

¹ In search of discreet local singles looking to f*ck.

Table 2: Projected destination frequency based on analysis of user
(authors') Web activity.

2 Automatic Destination Selec tion and Enforcement

We seek to remove this human decision-event step through our destination
prediction algo rithm, utilizing the most proprietary, embarrass ing,
and presumably truly revealing aspects of a user's financial,
location-based service, and In ternet browsing history, with weighted
emphasis on web browser privacy mode activity. The de tails of the
algorithm are both conceptual, non existent, and far too complicated for
this audi ence. See the results in Table 2 using the au thors' joint
data as test cases.

As we could never claim to be completely per fect, we have programmed an
override function that will allow the human to express their opin ion of
where they want to go, no matter how wrong and feeble-minded they may
be. Time lost due to manually over-riding the vehicle's se lection will
be discussed in the appendix of a different, unrelated study.

The potential time savings from the Auto matic Intuitive Destination
Selection System (AIDSS) cannot be underestimated. Wait, I mean, should
not be overestimated. Look, we estimate a savings of 3 seconds per
person per year (3000000 μs/per/yr), so don't estimate any higher or
lower than that. Using motorist value

of-time measurements of $21.46/hour in 2005 [6], our algorithm
should yield potential savings of $0.017 per person per year.²

3 Emotional Autonomy

An important component of a completely au tonomous vehicle is
emotional autonomy and self-actualization. We believe that our com
pletely autonomous vehicle, through advanced emotional independence,
will in fact yield the most authentic human-vehicle relationship ever
devised. While this is obviously completely and totally beneficial
over the long-term, we have ex perienced many barriers to
implementation dur ing initial testing. For example, the vehicle
seemed, for lack of a better term, rarely in the "mood" for refueling,
regardless of actual fuel level status. Some progress was made through
compliments, outright flattery, and promises of windshield wiper
replacement. The vehicle also refused all but expensive, premium fuel,
this is spite of manufacturer's recommendation of 87 octane rating,
and the researchers' repeated in sistence that premium fuel is totally
a scam. As these arguments are clearly independent from fact, they can
be classified as nothing other than

²In 2005. Who knows how much that could be worth now!

ҳҬ

Sigbovik 2014#

!& # \" \" # ! ! !#

$! \"#

.+ 56+2/92 431= )98 691+ \'114;7 =49 84 7\':+ =496 564-6+77 \'8 0+=#

3.;*78.9> #3.;*78.9> 4+ .998\':7,- - 74,7&2 .3 425:9&9.43&1 .414,>#

)& \'$#\"\'#&\' ҭҫ#

3.;78.9> #3.;78.9> 4+ .998\':7,- - 74,7&2 .3 425:9&9.43&1 .414,>#