How are we different from patterns in data?

June 19, 2005 2:40 PM

What are some good writings on the relationship between what we think of as the physical world and the world of mathematical abstractions (the space in which, for example, all possible sequences exist) ?

I think the natural conclusion of a "rationalistic" way of looking at the world is that the physical world can comfortably exist within "the mathiverse" and I would like to know who has taken this position before, and who has argued against it.

posted by teleskiving to religion & philosophy (16 comments total)

Roger Penrose's The Road to Reality (review).
posted by Rothko at 2:56 PM on June 19, 2005

I read a book that deals with calculus in a very nice way, similar to what you need. However, it's not so much about "the real line" versus the "ruler in my laboratory. It's a truly interesting (and well written)book that looks at the conceptual foundations of calculus, and the magic of taking increasingly smaller measurements.

A Tour of the Calculus (Berlinski)

I see from the page-title, that you wonder how people are different from patterns in data. Some researchers argue that they're not -- check out "machine learning" which is a statistical technique that basically solves problems by assumin that the real world *is* the pattern in the data...
posted by zpousman at 3:07 PM on June 19, 2005

Flatland, maybe? Too obvious?
posted by ITheCosmos at 3:16 PM on June 19, 2005

Rothko, zpousman, thanks for your responses. The Penrose book does sound like the kind of thing I'm interested in. What I'm really looking for is people who have argued for or against the idea that the "physical" world exists entirely within the world of mathematical abstractions. Essentially, if we are just patterns in data, and all possible data exists in the world of mathematical abstractions, why invoke a separate physical world?

On preview, ITheCosmos I haven't read Flatland but I have read Ian Stewart's sequel which is I think where I picked up the term "mathiverse". It's a fun read.
posted by teleskiving at 3:25 PM on June 19, 2005

Max Tegmark - "Is 'the theory of everything' merely the ultimate ensemble theory?" (PDF)
posted by mcguirk at 3:28 PM on June 19, 2005

I guess Wittgenstein's Tractatus can fit in this category.
posted by springload at 3:38 PM on June 19, 2005

Where Mathematics Comes From takes the opposite tack. It argues that what's real is the physical world, and higher mathematics comes from the metaphors we use to deal with the physical world. I'm not sure I agree, but the authors give an interesting argument and lots of concrete examples.
posted by nebulawindphone at 3:49 PM on June 19, 2005

mcguirk, that is exactly what I wanted! And it should be a good starting point to find related stuff. Thanks.
posted by teleskiving at 3:54 PM on June 19, 2005

Infinity and the Mind by Rudy Rucker?
posted by nervestaple at 3:59 PM on June 19, 2005

perhaps this is too obvious, but:

google search and wikipedia entry on philosophy of mathematics

One brief summary (with references) of the philosophical positions that have been taken is this one.

Stanford encyclopedia of philosophy entry on Quine/Putnam's indispensibility argument for mathematical realism
posted by advil at 5:50 PM on June 19, 2005

Non-standard calculus has some interesting ideas, and challenges the gamut of mathematical realism.
posted by meehawl at 6:26 PM on June 19, 2005

Yer all effin stoned!

Seriously though, thanks for this thread...I'm loving these links.
posted by jikel_morten at 7:26 PM on June 19, 2005

Absolute must read is Hofstadter's Godel Escher Bach.

Also, if you can find any of Dan Dennett's papers (not books) on pattern recognition, it's good reading too.
posted by yesster at 6:31 AM on June 20, 2005

Mathenauts

"Division by Zero", Ted Chiang, available in his (outstanding) collection Stories of Your Life and Others

Check the rest of this Mathematical Fiction Home Page.
posted by Zed_Lopez at 9:08 AM on June 20, 2005

There's a wonderful piece of dramatic literature dealing with math and thermodynamics; Arcadia is one of my favorite Tom Stoppard plays.
posted by Elsbet at 11:01 AM on June 20, 2005

Just about to drop off the page... thanks to everyone for their suggestions!
posted by teleskiving at 12:09 PM on June 20, 2005