Aug. 01 2010

The Permutation Game

Kant had already said that this proof was baloney, because “exis­tence” wasn’t a pred­i­cate like good­ness or knowl­edge. But Rus­sell and ana­lytic phi­los­o­phy took it one step fur­ther. In math and for­mal logic, exis­tence isn’t a pred­i­cate — it’s a quan­ti­fier. Like in the sen­tence, “For every nat­ural num­ber, there is a larger nat­ural num­ber.” We’re not mak­ing deep exis­tence claims here, just sin­gling out an ele­ment in a system.

So if we can come up with a model that’s foun­da­tion­ally and struc­turally sound, and works, let’s use it. What looked like an impos­si­ble prob­lem wasn’t a prob­lem after all; we’d just got­ten twisted up in the way we talked about it.

So phi­los­o­phy of math­e­mat­ics => math­e­mat­i­cal phi­los­o­phy. Change of gram­mar => change of perspective.

shaking off logical ambiguity.

Nov. 14 2009

Are the numbers, natural?

robertdow:

Naturally occurring numbers — like death rates, lengths of rivers, stock prices, and even electricity bills — have a rather unique distribution of leading (first) digits. Contrary to conventional wisdom, there’s not an even distribution; each digit does not have a 1 in 9, or 11%, chance of occurring.

Nov. 21 2008

Mathematically speaking, “Napoleon Dynamite” is a very significant problem for the Netflix Prize. Amazingly, Bertoni has deduced that this single movie is causing 15 percent of his remaining error rate; or to put it another way, if Bertoni could anticipate whether you’d like “Napoleon Dynamite” as accurately as he can for other movies, this feat alone would bring him 15 percent of the way to winning the $1 million prize. And while “Napoleon Dynamite” is the worst culprit, it isn’t the only troublemaker. A small subset of other titles have caused almost as much bedevilment among the Netflix Prize competitors. When Bertoni showed me a list of his 25 most-difficult-to-predict movies, I noticed they were all similar in some way to “Napoleon Dynamite” — culturally or politically polarizing and hard to classify, including “I Heart Huckabees,” “Lost in Translation,” “Fahrenheit 9/11,” “The Life Aquatic With Steve Zissou,” “Kill Bill: Volume 1” and “Sideways.”

So this is the question that gently haunts the Netflix competition, as well as the recommendation engines used by other online stores like Amazon and iTunes. Just how predictable is human taste, anyway? And if we can’t understand our own preferences, can computers really be any better at it?
The Screens Issue - If You Liked This, Sure to Love That - Winning the Netflix Prize

Sep. 18 2008

Useless Calculations

dailymeh:

A Fermi problem is “an estimation problem designed to teach dimensional analysis, approximation, and the importance of clearly identifying one’s assumptions” (wiki.) Abbas Raza demonstrates some, including estimating the weight of all the air in the Empire State Building, and the future of energy consumption:

… given our current worldwided energy consumption, and the fact that it is growing at more than 2% per year, if it were to continue to grow at that rate, we will have outstripped ALL the energy coming in from the sun in less than 500 years! Pretty shocking, no? And if we took into account the solar energy that is absorbed by the atmosphere before reaching the surface of Earth, and things like that, we have MUCH less time during which we can sustain 2% growth in energy consumption.

While we’re on the topic of estimation, did you know that if you estimate three or more variables simultaneously, the result will always be more accurate than if you estimate them separately? I sure didn’t until just now. (Thanks again, wiki.)