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.
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.
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
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
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
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
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
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
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
posted by teleskiving at 3:54 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
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
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
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
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
"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
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
posted by teleskiving at 12:09 PM on June 20, 2005
This thread is closed to new comments.
posted by Rothko at 2:56 PM on June 19, 2005