The Computational Universe

I found Brooks’ writing to be a bit jarring in many respects. For one thing, he often does that which he criticizes in others; such as introducing “new stuff” into theories and resorting to ridicule instead of rational criticism of theories he doesn’t agree with, such as for example: “Penrose, in his bid for scientific materialism, has resorted to a mysterious higher force. Rather than accept the offensive idea that his magnificent mind is the product of simple mechanisms playing out together, he calls into play something too complicated for us to understand fully. He invents his own little deity, the god of quantum mechanics.” First off, Penrose obviously did not invent quantum mechanics, or the notion of quantum processes playing an important role in cognition and decision-making. This has formed part of the philosophical debate over free will vs. determinism for a while now. I think Brooks is much too arrogant in his presumption that he can understand Gödel’s Theorem in the context of Mathematics better than a mathematician could. Gödel’s result settled a long struggle in Mathematics between formalism and intuition: he showed that Mathematics was not reducible to logic, as Russell and Whitehead’s Principia Mathematica purported to show. If there is one human discipline computers would ever be able to understand (and here we may even use Searle’s strong understanding of the word understand), that would be Mathematics. There, models are studied for their own sake, not attaching any meaning to the symbols that are being manipulated to prove theorems. Gödel’s theorem shows that there are truths out there which are absolutely ungraspable to computers, with their AND, OR and NOT gates, because they don’t lie within the scope of logic. Machines will always lack intuition, inventiveness and originality. Brains which are only capable of logical operations would have never been able to discover Non-Euclidean Geometry, because they wouldn’t have felt any dissatisfaction or distaste for an “unnatural” fifth axiom. Perhaps I like to think that these qualities are present in the work of mathematicians out of an unsurpassable bias that only someone with Brooks’ neutrality would be able to overcome, but Brooks also sins of glorifying his own discipline by claiming that in principle he could build humanness from scratch.

At the end of an unusually hectic last week I decided it was time to set some time apart for this course and work on this blogging assignment. Much to my dismay, I realized I had missed both the talk by Tim Berners-Lee and the Laptop Orchestra Concert. After reading most of your posts, it seems like I didn’t miss much (as far as Berners-Lee is concerned); in fact, I googled Berners-Lee, and it turns out he gave a talk under the same title at the Royal Society at London two years ago (by the time he mentioned the date he was already halfway through the lecture) and also at Oxford University less than a month ago. I figured his talk at Oxford was probably pretty similar to the one he gave here, so I haven’t watched that, but I found the one at the Royal Society to be pretty accessible, although sometimes he did go over my head. (I had to go to Vincent’s link before I finally understood what was meant by ‘Semantic Web,’ and then I remembered he had actually explained it at the beginning of the lecture at the Royal Society). In this talk he stressed the applications of the web in the near future and also its motivations during its early stages. He didn’t delve into technical details too often, seeming more in favor of discussing broad concepts and ideas, and he often presented the audience with useful if perhaps a bit silly examples to illustrate why they should care about what he was talking about. Perhaps he later regretted having done this and eventually changed the lecture to the version presented here and possibly at Oxford. For most of the second half of the lecture he discussed the advantages of RTF over XML pretty much from a business perspective; which isn’t really my cup of tea, but I suppose some of you might find that more interesting and enlightening. The best part though were his quasi-jokes, the bad ones were funny because no one laughed, and he just resumed after a few seconds of awkward silence, and the good ones were funny because that is what makes them good, obviously. In closing, I also share a very profound admiration with most of you for this great innovator, and it is a shame that his talk here was so inaccessible… but the guy has done and is still doing some pretty amazing stuff, so many kudos for that. Cheers.

            Turing-Post programs may be seen by some as an unnecessary formalization of something that is pretty easy to understand intuitively: computation. It does seem to be fairly easy to identify problems which are computational in nature. When writing a mathematical proof, it is often enough to show that a problem is reducible to ‘mere computation.’ Mechanical steps are often regarded as obvious and are hardly ever included in proofs found in journals or textbooks for higher-level courses. Why then would we want to study computation formally, seeing as it seems to be looked down upon by mathematicians, and seriously, who else would ever want to waste their time studying an infinite string of 0’s and 1’s. As it turns out, mathematical proofs (besides being beautiful and an awful lot of fun) are a great time-saver in attempting to solve applied problems. Say some computer scientist wanted to write a program, which would decide whether a given program ever stops or not when given its code as input. How useful would such a program be? Unfortunately, as we learned in lecture and from the readings, no such program exists, so attempting to write it would be a tremendous waste of time and effort. If we didn’t have a formal and rigorous setting in which to test out this and other hypotheses in computer science, rigorous mathematics would be unfit to find answers about the nature of computation; seeing as mathematical tools are platonic in nature. In turn, by allowing formal discourse about computation, mathematicians also end up being able to answer questions about mathematics itself; for example, whether those proofs that they have off-handedly reduced to computation actually work or not. So after Turing-Post programs came along everyone lived happily ever after.

So I figured, me being a math major and all, that it’d be nice to write about Conway’s Game of Life for this assignment. I had heard about it before, but I didn’t know what it was until it was brought up in lecture. But, since I didn’t really know anything about it, what to write? I decided to go to the link at the end of the handout about the Game of Life, and “play” for a while. After a half hour I soon realized I didn’t know much more than when I started, and I was wasting precious Princetonian time in a silly game. Professor Arora said in lecture that the previous generation became quite addicted to this game. Why is the Game of Life so addictive? It certainly wouldn’t get old for me, but, again, I’m a math major, my goal in life is to get paid for doing this kind of thing. What is the appeal of the Game of Life to the common person? The Game of Life can help us understand many things from real life. For example, how can the DNA contained in a single cell be enough to describe an entire organism? Well, you just need to specify a set of local rules for the chemical substances contained in it (I haven’t taken Chem or Bio, is that right?), and voilá, we have gotten ourselves a person. But if someone isn’t into Biology, why the Game of Life? I kept googling (by the way, I can’t believe Microsoft Word still thinks ‘google’ isn’t a real verb) the Game of Life and found a lot of really cool-looking patterns, but did I find them cool because I’m biased? Whatever the reason, a lot of people thought it was really interesting. Maybe this was due to the fact that people assumed an understanding the rules would imply an understanding of the game. And when they realized this wasn’t the case, curiosity took over.

Something that I think is really interesting about the Game of Life is how it can be applied to robotics. Brooks’ idea that a robot didn’t need to make a model of the world in order to perform a task is analogous to Conway’s idea that a simple set of local rules can generate complex behavior. In the case of the robot, a set of rules of the form: “If there’s an obstacle, turn right” or “If the motors stall, turn around” can oftentimes generate behavior that is quite hard to predict. Scribbler doesn’t need  map of a room in order to navigate around it successfully. A robot, like the critters in the Game of Life, just needs to know what to do next from a very limited amount of input (whether there’s an obstacle or whether the motors are stalled), and whatever comes later will be dealt with later.

Hola! My name is Carlos and I’m sophomore in Rocky from San Juan, Puerto Rico. We don’t have a Winter, it’s amazing (really). I’m a math major and I’m possibly doing certificates in German and Spanish. I’m on the board of Acción Latina and a Peer Tutor for Math and Spanish. Next year I’ll be an RCA in Rocky and I just joined the Terrace F. Club. After Princeton I want to go to grad school and become a Mathematician. I enjoy Spanish and German literature, philosophy (I was actually thinking about being a philosophy major), coffee, foreign movies and the beach – a lot. I also like languages and foreign accents. I’m taking this class because as a math major I feel I should know a lot more about computers than I actually do (I basically only know how to use Word, Outlook and iTunes… I seem to be quite talented at Facebooking too). I don’t know if I’ll actually need to know programming because that depends on the kind of research I’ll be doing as a mathematician. I’m taking this class because i’m really interested in how the technology around me actually works. I’m very impressed by the amount of things that can be done with the aid of computers, and it’d be nice to have an idea of what is actually going on inside them. OK, I’m not going to lie, I also need a second ST, and this seems to be the best available option. I’m looking forward for a fun, informative and interesting course. I’ll be seeing you all around.

 Update 5pm on February 10th, 2006: I use a Dell laptop (one of those SCI laptops everyone has) and I’ve always used Windows, currently XP Professional. I get lost with Macs but I admire people who can use them. Seriously, kudos.