logicomix and atlas shrugged

Though Logicomix is in no way historically accurate, it portrays well a feeling that I think a lot of us share. I'm sure that a lot of people saw the delicate beauty in Euclid's Elements, in the (relative?) certainty of mathematics, and hoped that something remotely similar to Elements can be made to solve dilemmas that come up in every day life--a consistent philosophical system deduced from the basic facts that everyone would understand and agree upon.

I had the naiive thought once. It's comforting to believe that there's a way to make a limited set of assumptions about life and existence, and derive from those a consistent set of beliefs about everything from metaphysics to ethics to politics.

From what other people are saying around the interweb, I'm not sure if Bertrand Russel would be the right person to attribute this set of feelings to. Actually, this might sound weird, but a more appropriate person would be Ayn Rand.

I recall in Atlas Shrugged, she speaks of people -- even philosophers (and logicians?) -- using logic to prove that logic is flawed/inadequate. These people were, of course, the "bad guys", the people that are held by the masses to be the "leader" of their chosen fields, but who are really there to foil the heros, the proponents of logic.

I loath hearing things about so and so "used logic to prove that logic is inadequate". I heard it once on numb3rs, too, so it's quite annoying. I had no idea that this in fact had been done. It's Gödel's Incompleteness Theorem. Of course!

Did Ayn Rand know about Gödel? Would that changed her mind in any way? If we make the assumptions that (1) human life/experience/society is much more complicated than the natural numbers, and (2) a system of philosophy (built up from a few axioms, for our purpose) can be thought of as a model of the world, then Gödel seems to imply that any of our philosophical system is either incomplete or inconsistent.

I'm probably missing something very important here.

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reading monroe: book three

Just finished book 3, "Ultimate Journey". It's interesting how everything fits together so nicely - almost like a fiction. Except he seem way too candid. I really wish I'd be able to know for real.

But I feel happy for him: for seeking the answer and finding it.

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Simplicity of People

Many people whom I find interesting tell me that they are a very simple person. Sometimes they say this in comparison to me. I find this interesting, because sometimes I don't find their thoughts/actions/personality simple at all.

This is not difficult to explain. Simplicity of a person comes from the amount of "focus" they have. A "focused" person would have one ultimate goal, theme, mission, motivation or statement that would explain almost all their actions. Their individual actions and decisions can seem strange to an onlooker - even insane, but if one understands the "focus" of the person, the actions would be self explanatory. This is why Howard Roark strikes us to be such a simple person: we understand his focus, and all his actions - however strange - stems from that focus.

Thus it is easy to find ourselves to be simpler than others, because we understand the motivations behind our thoughts and actions better than we understand anyone else's.

Yet most of us are not like a fictional character: we are imperfect. Even if we understand what our "focus" is, not 100% of our actions are consistent with it. Why? Fear and laziness. (And perhaps other reasons too.) Fear, laziness, and other setbacks adds complications: they make us hypocrites, acting against our true self. It is therefore difficult for an average person to be simple.

Simplicity requires us to align all our actions with our thoughts. To be simple is thus a true accomplishment. Kudos to all of you who achieves it.

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Books I want to get through

In no particular order, these are the books that I've wanted to get through in the near future. Most of them that I've started reading, I liked. If you know any other good reads, please share =)

SICP - Structure and Interpretation of Computer Programs

This is the textbook they use to teach Scheme at MIT. HtDP was developed from SICP, because apparently some people (like us) are too dumb to go through with HtDP. It teaches programming quite differently from the way D does it, and also different from the techniques used in CS135/6. This is the real thing. I got stuck at end of chapter 2, and couldn't seem to move past there.... The entire book can be found online at http://mitpress.mit.edu/sicp/full-text/book/book.html

CLRS - Introduction to Algorithms

The book I was reading before I started typing this. It's a pretty rigorous book - when you flip through it you'll see words like THEORM, LEMMA, PROOF... very mathematical. Downside to that is that sometimes you have to know what to skip. At 105 pages, I'm only through 1/10 of the book, and it's still the preliminary stuff. Sad, I know.

GEB - Godel, Escher, Bach

I think I've said enough about this one already. It's awesome, but there're parts that are hard to get through - like typographical number theory. I know I'm in math, but I still get dumbfounded by complex notations and too much logic =( Author tries his best to write for people that aren't as bright as he is, though, so it's managable.

The Story of Mankind

Not an awesome book, but it goes through all the basic historical stuff. Of course, at 500 pages, the amount of details included is essentially zero. In defense of me reading it... well, I think I really need an overview of everything if I actually want to get through life...

A Brief History of Time / The Universe in a Nutshell (Hawking)

It's interesting stuff... and arguably important, too. It's not a difficult read either. Why didn't I just finish reading it when I started? DOH!

Applied Probability (Lange)

This is a book my mom got me, because the author is quite well respected (at least) in her circle of statisticans. I tried going through it last year, but lacked the mathematical background. Now I'm a little bit better at it - I can understand the first 3 pages, at least. I'll probably have to go through "Probability Models" by Ross first - I know some stuff from P, but there're interesting stuff in Ross's book (the one recommended for P exam, I believe) that I haven't gotten to. Applied Probability is quite theoretical, though... so this one is going to be last that will be crossed off.

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Godel, Escher, Bach

I'm glad that someone yelled at me for being so whimpy as to stop reading GEB due to its references to music, which I was clueless about. I stopped RIGHT when he was about to explain what canons and fugues are, and also the links between Bach's "Musical Offering", Escher's works, and Godel's theorems about completeness and consistency of formal systems. Now, I'm still only on page 100, scarcely a seventh of the book, but its beauty has already astounded me. It is a work that you can easily become addicted to. (And it's not too dense, so good for reading during boring lectures that you still have to sometimes pay a slight bit of attention to.)

Don't believe me?

Here's one of the dialogues in the book (the book alternates between a dialogue and a chapter of real stuff, someting that explains the dialogue). This one is called the "Sonata for Unaccompanied Achilles" where Achilles has a phone conversation with the Turtoise. Escher's piece "Mosaic II" is included below, it will help you with the puzzle =). Follow the link and scroll down a bit...

http://gskg.wordpress.com/2009/01/16/but-how-would-one-know/

Beautiful? No? It's a shame that I lack the musical background to fully enjoy the work.

PS: Getting the answer to the puzzles are important.

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