From the New York Times: “Games of Chicken”

May 31, 2011

Looks like my views are not unique.  I posted earlier on the subject of two-player games and the US debt ceiling situation. It must be an effective analogy, since the New York Times references it:

From the article:

Investors have grown accustomed to partisan games of chicken that always end with the needed increase in the government’s borrowing authority. But this showdown, many say, is riskier because of the strongly held antispending, antitax views of the many freshman House Republicans combined with the fragility of the economic recovery.

Source: In Showdown Over Debt, Neither Party is Blinking, The New York Times


Godel’s Incompleteness Theorem

May 31, 2011

In my atomically careful reading of Godel, Escher, Bach, I FINALLY made it up to the (almost) technical explanation of Godel’s Incompleteness Theorem. I had to read the chapter presenting the proof three times, yet I’m only beginning to grasp the ideas which were presented. Awesome stuff.

For those of you not familiar with Godel’s work, here’s a humorous analogy, courtesty xkcd:


Palin’s Presidential Run?

May 30, 2011

 

 

From the New York Times:

“Palin’s Path May Be Unclear, but her Ride is Revved up”

Wow, not much to say to this. I am eerily reminded of Philip Roth’s The Plot Against America in which Charles Lindbergh, a known Nazi sympathizer, was elected president in 1940. I’m not saying that Palin is an anti-Semite, but much of the book’s political message rested on the idea that Americans are more likely to vote for a glamorous candidate or a “Joe Six-Pack” kind of guy than a qualified candidate.

Just as with the novel, in which Lindbergh made no political comments other than vague statements about peace and freedom and staying out of the second World War, the article mentions that Palin made no political statements either. To quote directly:

“We encourage you to support the pro-America events we’ll be privileged to participate in during these coming weeks,” she said in a written statement. “Discover the ties that bind Americans, our history, our traditions, and the exceptional nature of our country!”

This is a topic of some fascination. I wrote an essay about it on my AP United States History test. Of course, it’s also an area that’s been essentially strip-mined by liberal pundits, so I won’t go any further with it. Just wanted to point out that particular resemblance, for those of you who have read Roth.

The flip-side is that we may get to have more Tina Fey as Sarah Palin now!


Descartes’ zero-axiom system

May 30, 2011

Descartes’ zero-axiom system

I first properly encountered Descartes in European History class, where he was introduced as the great skeptic who had rejected everything he believed, leaving only the essential, irrefutable, true-in-all-conceivable-universes “I think, therefore I am” – cogito ergo sum. Magnificent.

I had always meant to read some Cartesian philosophy, but I guess it slipped my mind. Except that this system of assuming nothing kept coming up. Douglas Adams references it in The Hitchhiker’s Guide to the Galaxy with Deep Thought, the super-computer which had been fed “I think therefore I am” and had deduced the existence of rice pudding and income tax in a blink of an eye.

Descartes’ fear of an “infinitely powerful demon” which sought to deceive mankind and which could only be defeated or circumvented by the “natural light of reason” is also referenced frequently in other writing, although less than respectfully.  Read the rest of this entry »


What is it that computers CAN’T do? A simple introduction to Turing’s Halting Problem

May 29, 2011

(This is the first in a series about computationally insolvable problems, with a focus on Turing machines and the halting problem)

As a modern society, we rely on faster and more powerful computers in greater and more diverse areas of our life with every successive generation. In fact, some people believe in (and are working hard towards) the possibility of a technological “Singularity” by the 2030’s, when artificial intelligence will have surpassed human intelligence sufficiently to recursively self-improve (eg. A slightly smarter-than-human AI will make an AI slightly smarter than itself, which will in turn improve its own design, etc) and when the future will become extremely difficult to predict.

Read the rest of this entry »


Three and a half important facts about the theory of evolution

May 28, 2011

I was recently reading The Mind’s I, an anthology of reflections on souls, self, and consciousness compiled by two of my intellectual heroes, Professors Douglas Hofstadter and Daniel Dennett. I’m about 150 pages and all I can say is that it’s definitely a must-read. But I’ll talk about that more in some other post.

One of the pieces featured in the book was an excerpt from Richard Dawkins’ The Selfish GeneAfter reading it, I kind of kicked myself. I’d never really been interested in Dawkins before, since to me he was just that “atheist guy”; now I would revise that mental reference to read “that guy who really knows his evolutionary biology and now uses his immense prestige in the scientific community as well as his high name recognition to widely promote his views regarding religion.”

Read the rest of this entry »


On the title of this blog

May 24, 2011

Some of you might be wondering, what does he mean by “Boundless Rationality?” Does he think that this blog is a Fountain of Truth and Objectivity? Well, let me explain.

Once upon a time, economists made their models based on the assumptions that humans made rational choices with perfect information and attempted to always maximize utility. In other words, they would have their utility function laid out to them with the sum of the products of the expected utilities and their respective probabilities. But alas, it was not so.

It turns out, most humans don’t really think that way. Some of the reasons:

1) Incomplete information and incorrect methods of reasoning lead to highly inaccurate inferences.

2) People have an inconsistent set of beliefs about the world around them.

3) People are emotionally attached to certain choices.

4) People are more likely to remain close to previously proposed solutions than to propose completely new ones.

etc, etc. So somewhere along the way, Herbert Simon proposed a new kind of model, bounded rationality, which took into account all of those aforementioned problems. Therefore, rather than looking for optimized rational models, bounded rationality theory searches for more realistic models on how humans make choices. But you’ll see more on that later.

So essentially, the title is a kind of a joke, or play on words. Boundless Rationality is an irrational thing to hope for. It doesn’t exist, because we can never actually have perfect information about the world around us, and even if we did, it would be far too costly to compute and make sense of it all.

Nevertheless, there are mathematicians and researchers who manipulate inductive probabilities (ie. weather forecasting, “There’s a 70 percent chance of rain tomorrow”) according to mathematical laws. The fact that I’m stating that might seem a bit surprising because it seems obvious. But it’s not. People continue to treat inductive probabilities in a sort of wishy-washy way which ends up in sub-optimal decision-making.

But it doesn’t have to be that way. There are and have been a number of researchers – Harsanyi, Jaynes, Tversky, Kahneman… – who have specialized in studying the ways that we treat incomplete information and try to come up with coherent and consistent ways to makes sense out of it. And they’ll be discussed a lot here

So that’s basically the idea of boundless rationality. It’s a practically and theoretically impossible ideal but it’s the right direction to look towards.

NB. But don’t worry, that’s not ALL this blog’s about!

Further Reading:

Bounded Rationality – Bryan D. Jones, U Washington

A Perspective on Judgment and Choice – Daniel Kahneman, Princeton University