As you’ve probably noticed, things have been rather slow around here lately. I’ve got more posts in the works on group theory and abstract algebra – but they take a lot of time to research and write, so they’ll be coming out slowly – one a week or so.

In the meantime, I’m looking for other topics to write about, and I’d like to know what you, my faithful readers, are interested in hearing about.

Some things I’ve considered:

- Cellular automata: CA are very cool. I’ve been wanting an excuse to read my copy of Wolfram’s text.
- Data structures: my programming-related posts have always been very popular; and there’s a collection of unusual data structures that have interesting mathematical properties.
- Game theory: a pretty cool area of math.
- Conway’s games: basically the second half of Conway’s ONAG.

Or any other mathematical subject that you’re interested in learning about. Suggest away in the comments.

And keep those bad-math links coming!

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michael cassidyMy vote:

1. Data Structures

2. Cellular automata

3. Conway’s games

michael cassidyi’m also curious about you surname: chu-carroll; since I dont find any chu-carrolls in 1850-1930 censuses I assume its ‘new.’My father was an orphan so I got into genealogy trying to learn about his family.

Mark C. Chu-CarrollMy last name is a combination of my family name (Carroll, which was in turn an americanization of Karolciok), and my wife’s (Chu).

We put hers first for the geekiest of reasons – she had more publications than I did, and a search for “Jennifer Chu” will

turn up “Jennifer Chu-Carroll”.

Jonathan Vos PostTwo for the price of one:

I’d enjoy it (and suspect that your readers would too) if you’d write about Cellular Automata, but with a little of the Science Fiction of Greg Egan, especially Permutation City, New York:

HarperCollins / HarperPrism, 1994 ISBN 0-06-105481-X.

In my humble opinion, Permutation City is the greatest novel about cellular automata and artificial evolution.

See also:

List of molecules in Hintze-Adami artificial chemistry (see comments for definition).

BluePhoenixI would like you to do some Game Theory… I love that topic π

JoshBoth game theory and CA are interesting topics, so I’d vote either of those. What’s even more interesting is when you put them together (ie games on spatial structures). Not only is this really cool (in my opinion), but you can get some really pretty pictures out of it.

Mike CroucherI’d love to see something on introductory game theory – I hardly know anything about it. If I had a second vote I would ask for data structures π

KyleHmm. Game theory and CA is my vote. I’ve studied both a lot already, but they seem more interesting than the others. Although, the data structures could be fairly cool, too. In fact, I’ll leave it up to you to decide which is cooler of those three!

On an unrelated note, do you ever listen to The Shins? I’ve had a hankerin’ for the song New Slang all morning, and thought you’d probably like them too.

apyI’d love to hear any mathematical break down of any gambling games if you know them. Kind of vague, I know.

JaneGame theory or dynamical systems would be good.

JeffReed Solomon Coding

SiliI haven’t even been able to keep up with your posts this far …

I sucked at math despite minoring in it (well, I never finished my degree …), but I possitively loathed computer science and I never took anything but the two mandatory courses. As has been the case with so many other subjects, I’ve at times sorta regretted it since. That’s just to say, that your programming posts are the ones that I certainly can’t understand – prolly as little as the bad math.

Not entirely sure why I shared that – if you want to do datastructures, I’d hate to hold you back. I just know I’m not likely to be able to follow.

I guess, though, that I might then get around to catching up with the algebra.

SharmaHey, an “esoteric data structures” post/series would be interesting. And I do not know much about game theory, so that should also be fine. But write on whatever topic you are comfortable with.

AnonymousWhat about continuing pi-calculus topic?

AnonymousGame theory! That would be awesome. Data structures would be cool too, but game theory gets my vote.

SpotWeldAs far as game theory goes, I wouldn’t mind hearing more about The Prisoner’s Deliemma. How do you apply CA to that?

OlivierHere’s my vote :

1. Conway’s games

2. Cellular automata

3. Game theory

eduardoLong time reader, first time commenter. My wife is getting her EdD in science education, she’s on the grant to do the Astrobiology in Secondary Classrooms curriculum (which even Neil Degrasse Tyson seemed excited about on the daily show), and one of the activities she’s come up with to teach “emergence and properties of life” is letting a bunch of kids loose on a Conways Game of Life application I wrote which allows them to change the rules.

Any sort or cellular automata / complex adaptive system emergence thing you post is going to be something useful she can try to roll up into a curriculum for kids π

Do it for the children!

Michael ChermsideOoh… Oooh!

Data structures would be FABULOUS.

Game theory would be neat too.

— Michael Chermside

ebhI always enjoy the posts where you talk about real-world applications of arcane algorithms and/or data structures. So I’d like to see more of that, to the degree you’re allowed to talk about what you do (did) at Google (IBM).

TonyPlease do game theory!

frankI have noticed it’s been slow. Usually I can read a post that truly interests me a week, but I noticed I haven’t been here in awhile, maybe it’s the titles that aren’t just catching my eye in the RSS feed ;). I think your suggestions are pretty good though! CA and Game Theory definitely. Curious though, you might put up a ‘reading’ list of books you commonly look up to in different areas.

As a personal suggestion though, I’d also wouldn’t mind seeing some Combinatory Logic / Lambda Calculus.

Matthew L.I’m always up for some data structures, although if you were to cover coding theory, like No.10 suggested, I wouldn’t mind seeing an intro somewhere between the pure math approaches (which tend to leave you a bit helpless trying to implement them) and the practical-example approach (which leaves you with some language-specific source code, but no idea why it works).

On the topic of data structures, although you probably have seen it, Eric Lippert (an Microsoft blogger at http://blogs.msdn.com/ericlippert/ ) had a great series recently on immutable data structures, working up to a finger-tree based Deque.

DougHi Mark,

I do like your proposed categories for discussion.

However, please consider this alternative from AMS 2000 Mathematics Subject Classification on 37-xx Dynamical systems and ergodic theory because:

a – Cellular automata are included as 37B15 and are also in 68Q80 Theory of computing [Wolfram NKS appears to be a form of dynamics];

b – Data structures are 68P05;

c – Game theory is not only 91Axx [Utility theory for games, Decision theory for games, Games involving topology or set theory and Applications of game theory, which can be dynamic], but also in 62Cxx Decision theory, 90Bxx Operations research and management science and 91Bxx Mathematical economics;

In addition, there appears to be a relation to 49-xx Calculus of variations and optimal control; optimization;

d – Conway’s games do include the ‘Game of Life’ in cellular automata.

I have been following the impressive Terence Tao lectures on 254A Ergodic Theory. I think that I may even understand some of this material?

After looking at the AMS classification, I found this great book by Boris Hasselblatt, Anatole Katok, A First Course in Dynamics: With a Panorama of Recent Developments, 436 pages, 2003.

Hints and answers are provided for some of the exercises. There is also discussion of bifurcation theory, attractors and repellers.

From my [naive?] perspective, dynamics is very close to unifying mathematics.

dileffanteAll alternatives you gave are great. If you go for CA, I hope the “Wolfram’s text” you are refering to is the one from the 80s; for anything newer, there are better places to go than the mammoth egotistical NKS (nicely reviewed by Cosma Shalizi).

I’d second Jane’s suggestion of dynamical systems, though. There are very nice things, like the connection between continuous dynamics and symbolic dynamics that allows to show chaos. And then you could shift to CA, already having the mathematical framework of DS.

Dave MWolfram. Lord knows *I’m* never going to read that thing.

drozGame theory with its applications to artificial intelligence would be interesting.

ggHave you ever done any posts on catastrophe theory? It’s something that I really need to understand better, but never seem to have the time to read up on…

Alex, FCDIANA mathematician, but I think cellular automata are super cool. Game theory would be the second choice.

LukeData structures would be cool. I’d love to see a post on hash tables.

Blake StaceyThe world needs an introduction to cellular automata which is, shall we say, less

personalthan Wolfram’s door-stopper. (Shalizi’s review is here; the link given above seems to be broken.)Jeb, FCDI would like to see a post or more about how algorithms are used in cryptography. Specifically, I would love to see a post on the zeta function and its cryptological applications a la Cryptonomicon (by Neal Stephenson).

Thanks,

Jeb

FritzMy vote goes to games.

Steve OlligAnother vote for Data Structures.

FernandoDear Mark,

I don’t know if this is bad math or not but supporting ideology through math smells fishy for sure:

“CANTOR’S DIAGONAL ARGUMENT:AN EXTENSION TO THE SOCIALIST

CALCULATION DEBATE”

http://www.mises.org/journals/qjae/pdf/qjae9_2_1.pdf

Fernando

gary thomsonCA please.

John1. Extend your discussion of monoids after reading the B.Jacobs & C.Heunen paper “Arrows, like Monads, are Monoids.”

2. Discuss Clifford Algebras, Geometric Algebra.

Jeff22I see another has used the handle…Jeff, so in light of this I’ll change my handle to Jeff22.

Eric J. Lerner suggest an alternative view to the big bang theory which might be worth discussion.

http://photoman.bizland/p13.htm

Alexandru1. Game Theory

2. Data structures

3. Cellular automata

Michael GreenbergMy vote goes to game theory, perhaps with a particular eye towards Eriskay and its semantics.

KKairosCellular automata.

mjMy vote goes to game theory! I would love to read the short (sort of) very clear articles you write on that!

VilleGame theory gets me vote. Also it would be great to hear about computational limitations on why it’s not used more in real life scenarios such as business and politics.

brad dunbarData Structures

Emergent mathematical effects within code structures are ridiculously cool.

MykolaMy vote is:

Game Theory

Data Structures

Cellular Automata

Michael FridmanDefinitely Game Theory! From my recent reading on evolution it seems to be the key to quite a number of aspects of our daily life…

Ben WraithI’d love to hear about game theory.

JimFioreCount me in for “unusual data structures”.

DanielPretty tough competition so far π

My vote goes for Cellular Automata (although all other topics sound nice).

By the way… what happened to Pica?

TorbjΓΆrn Larsson, OMData structures would be educational, but game theory or CA’s are entertaining.

So why not dynamical systems? π

(Or, if ambition bites you, I would like to learn more about modern math for theoretical physics. Why not put some fiber in our diet. You can’t be categorically against. π

JanneInteresting, esoteric data structures, and the algorithms that love them would be fun. There’s lots of computational problems that are basically solved by finding the appropriate structure to represent it after all. Just the simple concept of an integral image in image processing, for instance, can be a revelation the first time you encounter it.

By the way, we considered a double name, but mixing a Japanese and a European surname is practically begging for trouble so we’ve elected to keep separate names instead.

Mike R.Haven’t been reading here long, but I really like what I see. Cellular Automa would be really interesting, I know a little about it, and think it would make a great post. Fairly diverse from what I know, such as “the game of life”, pattern formation in nature, simulating an earthquake or stability of a pile of sand. Regardless, keep up the good posts.

PeterLet’s see….

I’d love something on learning to program, esp. learning to program object oriented languages (most particularly, I am struggling to learn R).

Your opinion of The Math Circle http://www.themathcircle.org/ would be great…. I think they’re awesome – teaching math the way it should be taught.

Cellular automata…. Wolfram’s big book is cool, but what an EGO! Holy Cow! It’s like “Newton and Einstein were OK, but now I’m here to straighten things out”. Wolfram is smart, but no one’s THAT smart.

Elementary and beautiful proofs….. these are great. Euclid’s proof of the infinitude of the primes is great, or the irrationality of root 2, or any others you know of

Philosophy of math is cool

So is history of math

PseudonymHow about something a little different like, I dunno, Galois theory or differential geometry?

Monado, FCDRisk perception. Why do cyclists ride without helmets but wearing paper face-masks?

Mark DowDiscrete dynamical systems, as a lead-in to CA.

CanuckistaniSolomonoff induction; AIXI/AIXItl.

MobysevenI’d love to learn a bit about game theory. A lot of your posts go over my head at the moment, but the ones I understand are great, and game theory is something I would like to know a bit more about.

Also, good recipes.

KI’ve been a long time silent reader π

My vote:

Game Theory

Data Structures

How about something simple(?) and yet profound, like Optimization? (Just to make sure that nobody gets confused – no, I’m not talking about code optimization π

Thiagarajan1)Cellular automata

2)*

Unusual* Data Structures…and how about rewrite systems??

Jordi DLTGame Theory!

Alex BesogonovHow about computational linguistics? Your wife’s specialization, AFAIR π

Another interesting field: genetic algorithms, evolved systems and emergent behavior.

CahitLet us start with an title in Game Theory:

Nash and the game HEX

KyleNice one, 58. Here’s an idea, Mark: Have your wife write some posts on her research field and post them here! Or does she have her own blog that I don’t know about? I would be super-interested in learning about computational linguistics, more so really than the other things you mentioned.

AnonymousFuzzy sets and logic

BrianWhat about something on logic? I know it may sound basic (though it can be made more complex), but how about showing how symbolic logic can be used to solve those damning liar/truth-teller logic puzzles?

Charles TyeHow about some posts on the Hilbert problems?

Stephen CrowleyCan you talk about this recent discovery of a

third degree transcendental L-function and shed some light on how big of a deal it is? I’ve always been fascinated by analytic number theory.

http://www.facebook.com/share_redirect.php?h=7bae5f3bd986e652abcab03b4051d788&url=http%3A%2F%2Fwww.bristol.ac.uk%2Fnews%2F2008%2F12017945200.html&sid=14347165972

BaldeagleCan you explain or comment on Trahtman’s solution for the road coloring problem?

cinereastePerhaps you’ve stopped counting votes at this point, since it’s been a couple of days, but I’d love to learn more about combinatorial game theory and Conway’s games. You started to get into the subject with your posts on surreal numbers a little while back, and so it seems like further exploring ONAG and Winning Ways would be a logical progression.

gretai feel rather silly compared to the BRAINIACs that have put comments to post for requests such as Tahtman’s solution for the road coloring problem but…

i am a simple person who (at age 40) is taking an online statistics class. i have used your site as reference several times. if you could take pity on us non-genius types, to continue posting on the basics of statistics…i would greatly appreciate it!

thanks, greta

Jonathan Vos PostWhy can we do Math at all? Creationists may have one explanation (which fails to explain why Intelligent Design advocates can’t do Math). Other explanations begin with animals having primitive Math abilities. For example Counting Crows, and:

Rudimentary math skills among fish

Posted by Cory Doctorow, March 22, 2008 5:13 AM

http://www.boingboing.net/2008/03/22/rudimentary-math-ski.html

Marilyn sez, “In an experiment at the U. of Padua last year, female mosquito fish preferred to join shoals that were larger by just one fish, ‘preferring shoals of four fish rather than three fish, and consistently preferring shoals of three fish over those containing just two.'”

This means that they have similar counting abilities to those observed in apes, monkeys and dolphins and humans with very limited mathematical ability.

Christian Agrillo, an experimental psychologist at the university of Padua in Italy said: “We have provided the first evidence that fish exhibit rudimentary mathematical abilities.”

ATCan we have Data Structures after Game Thoery?

henrahThis is an old comment thread, but I’m still posting my request for a series on data structures because I just plain want it that much.

Michael SchuerigI realize that I’m late to the party, but my suggestion is not on any list so far.

I’d love to read something on the practice of mathematics, specifically on ways of constructing proofs. As far as I can tell, math (text)books only present the final, crystallized proofs. Sometimes individual steps are annotated with why they are justified, but I’ve never ever seen it that someone explained how they thought of taking that particular step in the first place.

Apparently, math didactics boils down to dragging each neophyte through a rather long set of exercises and hoping that they somehow pick up the inexpressible know-how involved in acquiring a “mathematical compass” that guides along the right branches from conjecture to proof.

I’ve always kept some hope that there’s a more explicit way to teach and learn mathematics.