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Posts Tagged ‘mathematica’

Here’s an amazing video on YouTube (this will be old news to many people, as the video got popular last year at this time).  I got the back story on this bad boy from American Mathematical Society monthly mag, Notices.  You can get more detail on the video and the creators at IMA.

It’s a video of Moebius Transformations (produced by POV-ray and, of course, Mathematica)

Now that you’ve seen the visual you can appreciate the power of visualizing data and math.  Take a look at the mathematics.  I’d say a picture is worth AT LEAST a thousand words in this case.

For those wondering why we care about Moebius transformations…

In physics, the identity component of the Lorentz group acts on the celestial sphere the same way that the Möbius group acts on the Riemann sphere. In fact, these two groups are isomorphic. An observer who accelerates to relativistic velocities will see the pattern of constellations as seen near the Earth continuously transform according to infinitesimal Möbius transformations. This observation is often taken as the starting point of twistor theory.

Oh, and they are COOL!

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Mathematica is rad.

Machine learning is also rad.

Check out these fine demos and code files for some nice informatics and machine learning ideas.

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This is one fun little theorem.

Basically… if symbolic systems terminate (program halts/gives output), the terminating expression is independent of how the rules were applied.

You get “confluence” out of this.

You probably are thinking, “and so what does this have to do with my life?”

a) maybe nothing if arithmetic never enters your life (unlikely)

b) it’s extremely good to know when you use functional programming that you can get to the same answer with many different ways of writing something.  For good overview of functional programming, go here.

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I need a real world situation involving a rich, but somewhat contained behavior space to attempt a cellular automata model.

In watching the rather lame De La Hoya and Forbes fight last night (gosh, I haven’t seen a blockbuster match in 3-4 years and I watch a lot of boxing!) it occurred to me that boxing might be a very good subject to study.

Why?

  • Fixed physical space (boxing ring, arena)
  • Rich, but contained environment (ring, corners, arena, crowd, cities)
  • A huge amount of historical data (we can watch and record 100s of recent fights and study individual boxers)
  • Rewards and Punishments are severe and are both immediate and historical (large payouts, punches to the face, crowd chants… both in current bout and previous bout)
  • Possible use of local rules showcasing emergent bout behavior (avoid punch or punch at X moment drawn out over time reveals overall bout outcome, boxer movement, energy depletion…)
  • Readers would find the subject interesting outside of academics (boxing!)
  • I can remove some of the variables and likely not lose a lot of the value of the research (I might be able to ignore culture/social status/marital problems/etc. and still build a reliable model of a boxing bout and hopefully draw some connections between behavior and cellular automata modeling)
So who cares? or what does any of this have to do with anything?
Behaviorism has a robust theoretical framework but lacks a mathematical framework.  Up to now most of the mathematical explanations in behaviorism involves pretty standard multivariate statistics and statistics experimental design. (here’s a typical approach in schedule analysis) Researchers more and more use game theory models to generalize certain relationships.  However there is no robust mathematics of behavior (nothing even close to what we see in economics and physics) and there is no generalized computer modeling (that I can find… and I’m looking for modeling like we do with markets, the weather, and cosmology – all highly complex dynamic systems)
Some links to explore if interested in existing mathematical “laws and models.
Cellular Automata might provide a framework.  
Studying boxing might be a fun and interesting way to explore the capabilities to of automata to model human behavior.  What’s particularly interesting about boxing as a study of operant behavior is the number of obvious reinforcement schedules at play and the easy to spot emitted behavior.  
Boxing is equally interesting as a subject for automata because of the fixed space, dynamic physical motion and finite duration (i.e. we might actually be able to model in a reasonable time).  Lastly, in both cases we should be able to verify our findings against a lot of real data, both historical and in upcoming bouts.
More to come, certainly!
~R

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After a prodding from a pal, I decided to apply to the Wolfram Science NKS Summer School. NKS is a fun and exciting research area and Mathematica rocks. I have done some preliminary research in trying to merge automata to experimental analysis of behavior. Three solid weeks of study and interaction with others could do wonders to furthering those efforts! Heck, three weeks doing anything different always does wonders!

Below I present the thought process in applying to NKS Summer School. I’m not sure it’s interesting to anyone, but I am trying more and more to catalogue the web of contingencies involved in my own behavior.

John said, Go!, let’s go check out the app process. I got that same email, hmmm, I’ll check it out again. I saw the application form, looked simple. I read a few blog posts from the event last year. I swivele in my chair to see how accessible my NKS book was… oh, it is right there. I flip it open and read the preface and chapter 1. I look at the clock. Oh, shoot, I really need to finish this code for tomorrow’s 11am meeting in Santa Monica. Oh, shoot, this is so cool. I’ll read a bit more. Oh, look at this… when I picked this book up 4 years ago this all seemed so crazy hard and really he spends an awful lot of time and paper on repeating the same points about automata behavior. Gee the good stuff is left to an appendix after page 1100. OOo, he’s talkinga bout space and time and automata. That’s kinda fun and a different approach, oddly know equations or mathematica symbolics to mathematically meld them. lemme flip ahead…. check email. check clock. check blog stats. Crap it’s 2:30. and if i’m going to apply it has to be within 45 minutes or I’ll never do it. better take some notes. where was that stuff on responsibility and behavior? casual networks, that’s good stuff and interesting in that it meshes well with john’s visualizations. skinner, wonder what their opinion on skinner is. the phrasing in the book is somewhat dismissive of non computational sciences and of behaviorism. that’s usually the case. also their site is fairly devoid of social sciences and anything that goes beyond low level biology and physics. oh well, if i were to do this i’d want to mash behavior models to this. not sure you can even do that in 3 weeks. talking to wolfram himself would be cool. i should ask dani about this. yeah, but then I’ll question it. the app doesn’t lock you in. dump it in and see what happens. vermont for 3 weeks. hmmm, that’s cool. ok, how do I couch my response. they also want a resume. gotta dump that out from the blog and format it. should i submit as openoffice doc so they know i’m a tech. hey, i gotta download the latest release of mathematica, i got a note about that a week or so ago. that’s a big download, going to take awhile. alright, i have these notes. now I have to put together some indication of research interest. how to show detail in reading NKS? and what are they looking for… people who spent a lifetime working in it or is this a reach out… attract newbies who have solid interest? is commercial background a hinderance? is my commercial resume good enough, should it be reworked. cool, I went to uchicago. ENTP, wonder if they will get that. my resume is fun but certainly is an odd read. oh well, more time on that later. alright i’ve got these statements. ugh, lots of errors. this is why you don’t write in a text editor. takes too long to clean it all up. alright, i’ll correct the basics, read it outloud and then go. crap, running out of time. just get it in. fill it out… i bet this will crap out on upload and i’ll have to do it again. hahaha. oh, cool it worked. alright quick shoot it to john. ah crap, there’s a wrong tense or two and a mistyped word in the basic statements. not a lot I can do now. they have the blog and my resume. if i’m interesting as a personality and can twist NKS in new ways, maybe they will be into it. Let me quick confirm there’s no one who proposed some of my thinking… one dude did a social sciences lecture. crap requires mathematica to view. damnit, redoing linux messes up my flow. i should just do this on my laptop. based on the title and his bio doesn’t look much different than most social sciences. everything else typical bio, phys and math. alright, now i have to finish this code….first a vault soda and some cheez its.


Here are my original application answers to their open questions.

Tell us about your interest in Summer School?

NKS offers a new model for researching and applying an experimental analysis of behavior (empirical behaviorism). Popular sociology and psychology (and even some of the cognitive disciplines) rely far too much on statistical analysis and, perhaps, less accurate probabilistic models. The mathematical methods presented by NKS provides a structure that closely aligns with schedules of reinforcement we observe and the concept of selection by consequences.An intensive session in NKS should aid in my application of simple automata like models applied to the study of human behavior. In particular, I hope to research and complete a project based on social networks and the ever increasing merging of our offline and online lives.

My professional work in new media remains too “business oriented” to get to the root of what’s going on with human behavior and our interactions with information, the world and each other. Yet, I’ve had enough deep exposure to massive schedules of reinforcement, deep troves of user data and human computer interaction within companies like eHarmony, Yahoo!, Maxim, and Business.com to know that we now have the empirical data and computing capability to map extreme casual networks and model out possible simple rules generating the complexity of social behavior.

That said, I’m under no illusion that we’re close to fully mapping out or predicting human behavior. This summer session would aid in generating discussion and likely producing further avenues of research and applications of NKS and Mathematica.

In how much detail have your read NKS?

  I have completed NKS once in totality and referenced in regularly over the last 3.5 years. It has served as a research launching point for me into evolutionary programming, Dennet’s work, computation vs. statistical approaches and data compression issues in modeling. (among many other areas…) I maintain this cheatsheet of questions and NKS pointers on my desk for reference as I explore new media, experimental analysis of behavior, and social networks.

chapter 9
casual networks and schedules of reinforcement

page505
want to explore the multi pathway of our existence. selection by consequences in behavior might just be simplistic automata like rules based on schedules of reinforcement…. purely human level… what does that even mean?

page 516 is right to the heart of my questioning. “given only a causal network, what can one say about the evolution history?” that’s human behavior and how we typically represent it in the media. We report on a limited view of the casual network and have a real difficulty discussing the explicitly evolution history.

page 518 “This has the consequence that effects in such systems can spread only at a limited rate, as manifest for example in a maximum slope for the edges of patterns…” human behavior seems to have this quality as well, which we ob Chapter 10 on perception is tied directly to human behavior. how we absorb new stimuli and mash it to discriminant stimuli. probabilities of behavior… the part on statistical analysis. Determinism in human behavior is a fundamental discussion point. Free Will.

page 596 is key point of research here….slight variation in the rules can produce dramatically different behavior and traditional statistical analysis (what is most done in sociology and psychology) cannot help identify changes in the casual networks and/or underlying rulesets “for it has almost always been assumed that to emulate in any generality a process as sophisticated as human thinking would necessarily require an extremely complicated system” That’s precisely the assumption behaviorism goes after….

NKS might be the mathematical backing to unwind the thinking.

bottom of 629 contains an important disclaimer… “the system would almost certainly have to have built up a human-like base of experience.” This is worth testing. Perhaps it’s not true in that our genetics, epi genetics and physical environments are simply specifics of a simpler abstraction of fundamental “starting conditions.” There’s no need to appeal to a distinctly human quality of “human” thinking.

The discussion of verbal behavior/language is useful. Consider the “sms phenomenon”. We’re fully capable of evolving completely rule breaking verbal structures without destroying human communication. txting has structure but it’s hardly ordinary sequential grammatical.

The discussion in chapter 12 is useful as well. Purpose gets in the way of human behavioral analysis. We want to personify so badly, but there’s nothing in the evidence suggesting value in doing so.

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