Yet another weird SF fan


I'm a mathematician, a libertarian, and a science-fiction fan. Common sense? What's that?

Go to first entry


 

Archives

<< current
 
E-mail address:
jhertzli AT ix DOT netcom DOT com


My Earthlink/Netcom Site

My Tweets

My other blogs
Small Sample Watch
XBM Graphics


The Former Four Horsemen of the Ablogalypse:
Someone who used to be sane (formerly War)
Someone who used to be serious (formerly Plague)
Rally 'round the President (formerly Famine)
Dr. Yes (formerly Death)

Interesting weblogs:
Back Off Government!
Bad Science
Blogblivion
Boing Boing
Debunkers Discussion Forum
Deep Space Bombardment
Depleted Cranium
Dr. Boli’s Celebrated Magazine.
EconLog
Foreign Dispatches
Good Math, Bad Math
Greenie Watch
The Hand Of Munger
Howard Lovy's NanoBot
Hyscience
Liberty's Torch
The Long View
My sister's blog
Neo Warmonger
Next Big Future
Out of Step Jew
Overcoming Bias
The Passing Parade
Peter Watts Newscrawl
Physics Geek
Pictures of Math
Poor Medical Student
Prolifeguy's take
The Raving Theist
RealityCarnival
Respectful Insolence
Sedenion
Seriously Science
Shtetl-Optimized
Slate Star Codex
The Speculist
The Technoptimist
TJIC
Tools of Renewal
XBM Graphics
Zoe Brain

Other interesting web sites:
Aspies For Freedom
Crank Dot Net
Day By Day
Dihydrogen Monoxide - DHMO Homepage
Fourmilab
Jewish Pro-Life Foundation
Libertarians for Life
The Mad Revisionist
Piled Higher and Deeper
Science, Pseudoscience, and Irrationalism
Sustainability of Human Progress


























Yet another weird SF fan
 

Tuesday, September 02, 2014

Douglas Adams, Enormous Integers, and Infinity

John Baez's discussion of enormous integers and infinity:

Here’s a puzzle due to the logician Harvey Friedman. It too has an unexpected answer.

Say you have a finite alphabet to write with. How long can a word be if no block of letters in this word, from the nth letter to the 2nth, is allowed to appear as a subsequence of a bigger block from the mth letter to the 2mth?

If you have just one letter, this is the longest it can be:

AAA

If you have two, this is the longest it can be:

ABBBAAAAAAA

Puzzle: How long can the word be if you have three letters in your alphabet?

Friedman showed there’s still a finite upper bound on how long it can be. But, he showed it’s incomprehensibly huge!

Now Friedman is one of the world’s experts on large cardinals—large infinite numbers. So when he says a finite number is incomprehensibly huge, you sit up and listen. It’s like seeing a seasoned tiger hunter running through the jungle with his shotgun, yelling “Help! It’s a giant ant!”

reminded me of the following Douglas Adams quote:

The car shot forward into the circle of light, and suddenly Arthur had a fairly clear idea of what infinity looked like.

It wasn't infinity in fact. Infinity itself looks flat and uninteresting. Looking up into the night sky is looking into infinity—distance is incomprehensible and therefore meaningless. The chamber into which the aircar emerged was anything but infinite, but it was just very very big, so big that it gave the impression of infinity far better than infinity itself.

I'm reminded of the saying “This is not mathematics. This is theology.” (about the more abstract parts of mathematics).

1 Comments:

Anonymous Georg Cantor said...

Indeed. The whole business could drive you nuts.

12:01 PM  

Post a Comment

<< Home

 
Profiles
My Blogger Profile
eXTReMe Tracker X-treme Tracker

Site Meter
The Atom Feed This page is powered by Blogger.