I was thinking of this post, which has lines like these:
If I’ve got a hundred calculators, all of them rather error-prone—say a 10% probability of error—then there is no one calculator I can point to and say, “This is the standard!” I might pick a calculator that would happen, on this occasion, to vote with ten other calculators rather than ninety other calculators. This is why I have to idealize the answer, to talk about this ethereal thing that is not associated with any particular physical process known to me—not even arithmetic done in my own head, which can also be “incorrect”.
Thanks for pulling that up. I tried reading through the entire post, but I became confused at several points. Might be because I haven’t read the previous posts in that particular series. Or maybe I’m just overly tired. I’ll take another crack at it tomorrow.
From what you quoted, I do have to positively update my degree of belief in the “Eliezer is a mathematical Platonist” hypothesis. It’s weak-medium evidence, but still evidence. I think much stronger evidence would be if he actually identified as a math realist. If he said, “Hey guys, I believe the natural numbers exist in a mind-independent, non-spatiotemporal way.” and proceeded to explain how to meshes well with reductionism, naturalism, etc.
If someone at in contact with him sees this and could ask him for me, that’d be awesome.
This quote from the post Beautiful Math seems to take a position of “math is in part pre-existing (at least those that involve physics) but Platonia write large is illusionary.” It’s written in 2008 and EY doesn’t seem to have changed his mind in the interim.
Stars are mine. EDIT: Erm Italics. Damn sorta reddit markup while also having some differences!
“The joy of mathematics is inventing mathematical objects, and then noticing that the mathematical objects that you just created have all sorts of wonderful properties that you never intentionally built into them. It is like building a toaster and then realizing that your invention also, for some unexplained reason, acts as a rocket jetpack and MP3 player.
Numbers, according to our best guess at history, have been invented and reinvented over the course of time. (Apparently some artifacts from 30,000 BC have marks cut that look suspiciously like tally marks.) But I doubt that a single one of the human beings who invented counting visualized the employment they would provide to generations of mathematicians. Or the excitement that would someday surround Fermat’s Last Theorem, or the factoring problem in RSA cryptography… and yet these are as implicit in the definition of the natural numbers, as are the first and second difference tables implicit in the sequence of squares.
This is what creates the impression of a mathematical universe that is “out there” in Platonia, a universe which humans are exploring rather than creating. Our definitions teleport us to various locations in Platonia, but we don’t create the surrounding environment. It seems this way, at least, because we don’t remember creating all the wonderful things we find. The inventors of the natural numbers teleported to Countingland, but did not create it, and later mathematicians spent centuries exploring Countingland and discovering all sorts of things no one in 30,000 BC could begin to imagine.
To say that human beings “invented numbers”—or invented the structure implicit in numbers—seems like claiming that Neil Armstrong hand-crafted the Moon. The universe existed before there were any sentient beings to observe it, which implies that physics preceded physicists. This is a puzzle, I know; but if you claim the physicists came first, it is even more confusing because instantiating a physicist takes quite a lot of physics. Physics involves math, so math—or at least that portion of math which is contained in physics—must have preceded mathematicians. Otherwise, there would have no structured universe running long enough for innumerate organisms to evolve for the billions of years required to produce mathematicians.”
I don’t think that physics existed before humans; physical law did. Physics is the study of physical law, just as math is the study of mathematical objects and systems of laws that are obeyed by those objects. Thus I wouldn’t say that math existed before intelligent life, but nathenatical objects did.
On first blush that seems to be a semantic argument. It doesn’t seem you actually disagree with EY, but rather you seem to object to the use of the Physics and put in its place “Physical law” and put “mathematical objects” in place of “mathematics.”
Is this an accurate description of what you are trying to say?
Eliezer also wrote multiple times that he’s an “infinite set atheist”. I’m not sure that’s actually compatible with mathematical Platonism. (The way I understand it, at least.)
I was thinking of this post, which has lines like these:
(Bolding, but not italics, added.)
Thanks for pulling that up. I tried reading through the entire post, but I became confused at several points. Might be because I haven’t read the previous posts in that particular series. Or maybe I’m just overly tired. I’ll take another crack at it tomorrow.
From what you quoted, I do have to positively update my degree of belief in the “Eliezer is a mathematical Platonist” hypothesis. It’s weak-medium evidence, but still evidence. I think much stronger evidence would be if he actually identified as a math realist. If he said, “Hey guys, I believe the natural numbers exist in a mind-independent, non-spatiotemporal way.” and proceeded to explain how to meshes well with reductionism, naturalism, etc.
If someone at in contact with him sees this and could ask him for me, that’d be awesome.
This quote from the post Beautiful Math seems to take a position of “math is in part pre-existing (at least those that involve physics) but Platonia write large is illusionary.” It’s written in 2008 and EY doesn’t seem to have changed his mind in the interim.
Stars are mine. EDIT: Erm Italics. Damn sorta reddit markup while also having some differences!
http://lesswrong.com/lw/mq/beautiful_math/:
“The joy of mathematics is inventing mathematical objects, and then noticing that the mathematical objects that you just created have all sorts of wonderful properties that you never intentionally built into them. It is like building a toaster and then realizing that your invention also, for some unexplained reason, acts as a rocket jetpack and MP3 player.
Numbers, according to our best guess at history, have been invented and reinvented over the course of time. (Apparently some artifacts from 30,000 BC have marks cut that look suspiciously like tally marks.) But I doubt that a single one of the human beings who invented counting visualized the employment they would provide to generations of mathematicians. Or the excitement that would someday surround Fermat’s Last Theorem, or the factoring problem in RSA cryptography… and yet these are as implicit in the definition of the natural numbers, as are the first and second difference tables implicit in the sequence of squares.
This is what creates the impression of a mathematical universe that is “out there” in Platonia, a universe which humans are exploring rather than creating. Our definitions teleport us to various locations in Platonia, but we don’t create the surrounding environment. It seems this way, at least, because we don’t remember creating all the wonderful things we find. The inventors of the natural numbers teleported to Countingland, but did not create it, and later mathematicians spent centuries exploring Countingland and discovering all sorts of things no one in 30,000 BC could begin to imagine.
To say that human beings “invented numbers”—or invented the structure implicit in numbers—seems like claiming that Neil Armstrong hand-crafted the Moon. The universe existed before there were any sentient beings to observe it, which implies that physics preceded physicists. This is a puzzle, I know; but if you claim the physicists came first, it is even more confusing because instantiating a physicist takes quite a lot of physics. Physics involves math, so math—or at least that portion of math which is contained in physics—must have preceded mathematicians. Otherwise, there would have no structured universe running long enough for innumerate organisms to evolve for the billions of years required to produce mathematicians.”
I don’t think that physics existed before humans; physical law did. Physics is the study of physical law, just as math is the study of mathematical objects and systems of laws that are obeyed by those objects. Thus I wouldn’t say that math existed before intelligent life, but nathenatical objects did.
On first blush that seems to be a semantic argument. It doesn’t seem you actually disagree with EY, but rather you seem to object to the use of the Physics and put in its place “Physical law” and put “mathematical objects” in place of “mathematics.”
Is this an accurate description of what you are trying to say?
yep. I figure we should be more specific with our words if we’re going to be understood properly.
Very informative! Thank you kindly for pulling this up for me.
Eliezer also wrote multiple times that he’s an “infinite set atheist”. I’m not sure that’s actually compatible with mathematical Platonism. (The way I understand it, at least.)
Also, see How to Convince Me That 2 + 2 = 3.