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They speak of the Philsophy of Mathematics. I typed a lot out and chose to delete it. In short, it is considered the highest order among Mathematicians. However

by KGIII 9y ago

They speak of the Philsophy of Mathematics. I typed a lot out and chose to delete it. In short, it is considered the highest order among Mathematicians. However, us Applied Mathematicians just get on with the real work and have pretty much figured out that they are insane. It's a bit like true random and infinity. It's best not to think about it to much and only useful for post doc bar conversations or impressing stoned Econ undergrads of your preferred gender. Even then, it's best not to think about it too much.

eastWestMath 9y ago
Eh, everyone but the set theorists ignores the set theorists at this point. I think some exciting things happened in the 60's with forcing, but a lot of the subsequent developments seem pretty contrived.
- cgmg 9y ago
  To an outsider, practically any area of advanced, pure mathematics looks contrived. That doesn't mean it's not beautiful and interesting, particularly to those who study it. Also, the claim that 'everybody ignores set theorists' is patently false.
  - KGIII 9y ago
    They are a bunch of damned liars. 0.999... = 1 Not only can I prove it, I can tell you the excuses they use to justify it. I'm pretty sure that they just realized that it was 'proven' and had to then come up with a reason. I really do try to not think about it too much, though I may sometimes ponder it a bit while smoking. It's all horrible. I don't know what they hell they were thinking. Half of them probably belong in asylums.
    - Simon_says 9y ago
      People who get confused about that equality are in actuality confused about what a real number is. In particular they probably think that real numbers are digit expansions, and they have probably never seen a construction of the reals. You can show this person a proof, and you might get them to shut up about it, but they’ll never believe it on an intuitive level until you show them what real numbers actually are and what their relationship to their (non-unique!) digital representation is.
      - enord 9y ago
        I believe the confusion is spread across several layers. For those in the know, infinite decimal expansion is syntactic sugar for a limit over a particular infinite series of sums, but this convention sidesteps how people are taught syntactic manipulation and how it's intetpteted in a particular algebra. 0.999... is presented as a term, that can be syntactically replaced with an actual infinite decimal expansion, upon which the normal syntactic opetations can be applied, specifically "=" as in "0.999...=1". This is ofcourse impossible, because even if the rules are valid you would be applying them forever. This is the apparent absudity of the equation. In defence of people who hold this intuition: it's a valid concern in many branches of math(discrete, constructive, infinitesimal etc.), just not in informal expositions of the properties of real numbers.
        cgmg 9y ago
        Yes, '0.999...' formally stands for the sum from n = 1 to infinity of 9 / 10^n.
        KGIII 9y ago
        Heh... You kinda prove my point for me. If you could step up to the board and actually expand the ... for us, we'd be much obliged. You can keep writing 9 forever and you will never reach a whole number. But, it does reach a whole number and there is proof! So, they made a rule. The rule is, of course, silly. Infinity itself is silly. Not even atoms are infinite. Not even atoms can be infinity divisible. It's a horrible idea, really. (I have karma to burn.) By the way, it's a damned good thing infinity doesnt exist. If you had a tape measure that was infinitely long and folded it in half, we aren't really sure what would happen. Hell, I wasn't using that karma for anything better. While I'm here... When you're done finding an infinite tape measure, I'd like it if you could bring me -1 apple. No, not a slip of paper representing an owed apple, but -1 apple. Math and reality are only loosely coupled. Mathematics is a language. It can tell lies. 1 + 1 = 74 See? That's pretty obviously a lie. It can tell stories, physicists are pretty fond of using it for that. It can be so very descriptive and elegant. It can be so deceptive, as we see with the 'well, let's just let that be represented by 9/10' silliness. It's pretty horrible, really. Like I said, it's best not to think about it too much. It's kind of contrived in a few areas.
Sniffnoy 9y ago
> They speak of the Philsophy of Mathematics. In short, it is considered the highest order among Mathematicians. Speaking as a pure mathematician: It's really not. When I say this stuff is pointless, that it doesn't affect ordinary mathematics, I'm not just talking applied math; I'm talking, well, all of ordinary mathematics, pretty much. Number theory, combinatorics... every now and then a question comes up whose answer depends on the continuum hypothesis admittedly but it's seriously rare (and on those few occasions when it has happened, I think often someone comes along and says that this means that you were really asking the wrong question in the first palce). I mean, OK, there are people such as Harvey Friedman who work out arithmetic consequences of such assumptions. But the statements they come up with are seriously contrived, not the sort of thing ordinary mathematicians care about, even if the statements no longer involve infinities. Hell I work with infinities sometimes and I don't care about this stuff! Of course, I'm not a proper logician or set theorist. But doing computations with ordinals and well partial orders is fun... and the answers you get never end up depending on this sort of stuff. :P
- KGIII 9y ago
  Well, yes. They are insane. Infinity is a rubbish idea, by the way. I've given it much thought and concluded it is best to just not think about it. Cantor was a lunatic, and I'm not entirely certain that infinity isn't a causal factor. Don't get me started. It doesn't end well. ;-) Eventually I go off on the absurdity of 'true random' and our presumption to know the differences between it and unpredictability. It's hubris and madness, all the way down. They really should stop teaching mathematics by rote. If you're familiar with my posting history, I very seldom say 'should.'

by KGIII 9y ago

eastWestMath 9y ago

Eh, everyone but the set theorists ignores the set theorists at this point. I think some exciting things happened in the 60's with forcing, but a lot of the subsequent developments seem pretty contrived.

cgmg 9y ago
To an outsider, practically any area of advanced, pure mathematics looks contrived. That doesn't mean it's not beautiful and interesting, particularly to those who study it. Also, the claim that 'everybody ignores set theorists' is patently false.
- KGIII 9y ago
  They are a bunch of damned liars. 0.999... = 1 Not only can I prove it, I can tell you the excuses they use to justify it. I'm pretty sure that they just realized that it was 'proven' and had to then come up with a reason. I really do try to not think about it too much, though I may sometimes ponder it a bit while smoking. It's all horrible. I don't know what they hell they were thinking. Half of them probably belong in asylums.
  - Simon_says 9y ago
    People who get confused about that equality are in actuality confused about what a real number is. In particular they probably think that real numbers are digit expansions, and they have probably never seen a construction of the reals. You can show this person a proof, and you might get them to shut up about it, but they’ll never believe it on an intuitive level until you show them what real numbers actually are and what their relationship to their (non-unique!) digital representation is.
    - enord 9y ago
      I believe the confusion is spread across several layers. For those in the know, infinite decimal expansion is syntactic sugar for a limit over a particular infinite series of sums, but this convention sidesteps how people are taught syntactic manipulation and how it's intetpteted in a particular algebra. 0.999... is presented as a term, that can be syntactically replaced with an actual infinite decimal expansion, upon which the normal syntactic opetations can be applied, specifically "=" as in "0.999...=1". This is ofcourse impossible, because even if the rules are valid you would be applying them forever. This is the apparent absudity of the equation. In defence of people who hold this intuition: it's a valid concern in many branches of math(discrete, constructive, infinitesimal etc.), just not in informal expositions of the properties of real numbers.
      - cgmg 9y ago
        Yes, '0.999...' formally stands for the sum from n = 1 to infinity of 9 / 10^n.
        KGIII 9y ago
        Heh... You kinda prove my point for me. If you could step up to the board and actually expand the ... for us, we'd be much obliged. You can keep writing 9 forever and you will never reach a whole number. But, it does reach a whole number and there is proof! So, they made a rule. The rule is, of course, silly. Infinity itself is silly. Not even atoms are infinite. Not even atoms can be infinity divisible. It's a horrible idea, really. (I have karma to burn.) By the way, it's a damned good thing infinity doesnt exist. If you had a tape measure that was infinitely long and folded it in half, we aren't really sure what would happen. Hell, I wasn't using that karma for anything better. While I'm here... When you're done finding an infinite tape measure, I'd like it if you could bring me -1 apple. No, not a slip of paper representing an owed apple, but -1 apple. Math and reality are only loosely coupled. Mathematics is a language. It can tell lies. 1 + 1 = 74 See? That's pretty obviously a lie. It can tell stories, physicists are pretty fond of using it for that. It can be so very descriptive and elegant. It can be so deceptive, as we see with the 'well, let's just let that be represented by 9/10' silliness. It's pretty horrible, really. Like I said, it's best not to think about it too much. It's kind of contrived in a few areas.

Sniffnoy 9y ago

> They speak of the Philsophy of Mathematics. In short, it is considered the highest order among Mathematicians. Speaking as a pure mathematician: It's really not. When I say this stuff is pointless, that it doesn't affect ordinary mathematics, I'm not just talking applied math; I'm talking, well, all of ordinary mathematics, pretty much. Number theory, combinatorics... every now and then a question comes up whose answer depends on the continuum hypothesis admittedly but it's seriously rare (and on those few occasions when it has happened, I think often someone comes along and says that this means that you were really asking the wrong question in the first palce). I mean, OK, there are people such as Harvey Friedman who work out arithmetic consequences of such assumptions. But the statements they come up with are seriously contrived, not the sort of thing ordinary mathematicians care about, even if the statements no longer involve infinities. Hell I work with infinities sometimes and I don't care about this stuff! Of course, I'm not a proper logician or set theorist. But doing computations with ordinals and well partial orders is fun... and the answers you get never end up depending on this sort of stuff. :P

KGIII 9y ago
Well, yes. They are insane. Infinity is a rubbish idea, by the way. I've given it much thought and concluded it is best to just not think about it. Cantor was a lunatic, and I'm not entirely certain that infinity isn't a causal factor. Don't get me started. It doesn't end well. ;-) Eventually I go off on the absurdity of 'true random' and our presumption to know the differences between it and unpredictability. It's hubris and madness, all the way down. They really should stop teaching mathematics by rote. If you're familiar with my posting history, I very seldom say 'should.'