3 ms·

No, you have this exactly backwards. ¼ and 1/4 are the same symbol, and so is this: @ @ @ @ ____ @ @@ @ @ @@

by lisper 5y ago

No, you have this exactly backwards. ¼ and 1/4 are the same symbol, and so is this: @ @ @ @ ____ @ @@ @ @ @@@@ @ @ The whole point of symbols is that they retain their essential properties through a variety of changes in their physical appearance.

bawolff 5y ago
Why? I feel like you're just asserting disagreement without argument here. I think this is primarily a philosophical dispute on the nature of symbols, where both are just different foundations leading to the same concept. But if my take is backwards or wrong, then it should lead to some disconnect between it and what people mean by symbol in practise. So what is it? > The whole point of symbols is that they retain their essential properties through a variety of changes in their physical appearance. Whether they keep essential properties through multiple physical forms or whether many different unique symbols all point to the same (non physically realizable) "form". Doesn't seem materially different to me, just different foundations for the same idea.
- lisper 5y ago
  > Doesn't seem materially different to me It isn't. It's the same idea expressed with different words. But what matters about symbols, the thing that makes them useful, is that there is a mapping from a potentially infinite number of physical things to a finite number of Platonic ideals or whatever you want to call them. Whether you want to call "4" and "four" the "same symbol" or "different symbols denoting the same concept" doesn't matter. What matters, the source of the utility, is that there is a finite number of equivalence classes that the physical things can be unambiguously mapped to.
  - bawolff 5y ago
    > It isn't. It's the same idea expressed with different words. But one is "backwards" and one is not? > is that there is a finite number of equivalence classes that the physical things can be unambiguously mapped to. Unambigious is quite a claim. Is 3.0 and 3 the same symbol on your view? Depending on context they might denote the same idea (the number three). Other times maybe 3 is an integer and 3.0 is a float and their types are important. Sometimes my computer spits out 10 to mean the sixtenth natural number, sometimes the second natural number, sometimes the tenth natural number. Its all the same physical thing, however what other physical things its equivalent to depends on context.
    - lisper 5y ago
      > Unambigious is quite a claim. No, it's not. The symbol systems used for math are deliberately engineered to make this true. > Is 3.0 and 3 the same symbol on your view? Depending on context Exactly. It depends on the context. Sometimes "A" and "a" ArE tHe SaMe SyMbOl, SoMeTiMeS tHeY aReN't. (Sometimes "Y" and "TH" are the same symbol! [1]) Likewise, sometimes "3.0" and "3" are the same symbol, sometimes they aren't. But within a given context, in order to qualify as math, the mapping has to be unambiguous. [1] https://www.youtube.com/watch?v=PVVTk7yy4kU https://www.youtube.com/watch?v=PVVTk7yy4kU
kmill 5y ago
This is either quite the claim or you have a non-standard definition of "symbol." Each of those three representations are obviously different, though they all refer to the concept of "one-quarter," and I very much question the one made from @ signs. (And to be annoying, ¼ and 1/4 both have completely different UTF-8 representations, but I'd still associate them with the concept of "one-quarter.") It seems like you're conflating "signifier" with "signified". I'd say the whole point of symbols is that they play a role in semiosis, where an interpreter (us) receives meaning (the "signified") from decoding a symbol (the "signifier"). My own decoding apparatus gets the same roughly the same meaning from ¼ and 1/4. But the meaning's not a symbol in itself. What I was obliquely getting at earlier in bringing up intuitionism is that math seems to derive from pre-existing mental processes. Recognition and manipulation of symbols seems to be no more special than other mental processes. Rule-based manipulation seems to appeal to our understanding of causality, for example.
- lisper 5y ago
  > I very much question the one made from @ signs There are limits to what can be expressed in an HN comment. If we were standing at a whiteboard I could draw many more different variations on the theme than I can here. > you have a non-standard definition of "symbol." A symbol is a physical thing that can be unambiguously mapped into one of a finite set of equivalence classes. ¼ and 1/4 and even "one-quarter" can all be unambiguously mapped (within a particular context, i.e. people speaking English talking about math) onto a single concept which is denoted ¼ or 1/4 or "one-quarter" or "one-quarter". > It seems like you're conflating "signifier" with "signified". No, I'm not conflating them. It's just very hard to talk about these things because the only tool we have at our disposal is signifiers. I can't actually show you the thing that is signified by ¼ and 1/4 and "one-quarter", I can only talk about its properties (and I can only do that using signifiers). > math seems to derive from pre-existing mental processes That is a very human-centric view of things. It happens to arise in humans from pre-existing mental processes, but that doesn't mean that math necessarily or inherently arises that way. In fact, math arises in nature in myriad ways, many of which are not even mental processes at all. > Recognition and manipulation of symbols seems to be no more special than other mental processes. Oh, that is where you are very, very wrong, my friend. Manipulation of symbols is very special. There's a reason it's called the "computer revolution".

by lisper 5y ago

bawolff 5y ago

Why? I feel like you're just asserting disagreement without argument here. I think this is primarily a philosophical dispute on the nature of symbols, where both are just different foundations leading to the same concept. But if my take is backwards or wrong, then it should lead to some disconnect between it and what people mean by symbol in practise. So what is it? > The whole point of symbols is that they retain their essential properties through a variety of changes in their physical appearance. Whether they keep essential properties through multiple physical forms or whether many different unique symbols all point to the same (non physically realizable) "form". Doesn't seem materially different to me, just different foundations for the same idea.

lisper 5y ago
> Doesn't seem materially different to me It isn't. It's the same idea expressed with different words. But what matters about symbols, the thing that makes them useful, is that there is a mapping from a potentially infinite number of physical things to a finite number of Platonic ideals or whatever you want to call them. Whether you want to call "4" and "four" the "same symbol" or "different symbols denoting the same concept" doesn't matter. What matters, the source of the utility, is that there is a finite number of equivalence classes that the physical things can be unambiguously mapped to.
- bawolff 5y ago
  > It isn't. It's the same idea expressed with different words. But one is "backwards" and one is not? > is that there is a finite number of equivalence classes that the physical things can be unambiguously mapped to. Unambigious is quite a claim. Is 3.0 and 3 the same symbol on your view? Depending on context they might denote the same idea (the number three). Other times maybe 3 is an integer and 3.0 is a float and their types are important. Sometimes my computer spits out 10 to mean the sixtenth natural number, sometimes the second natural number, sometimes the tenth natural number. Its all the same physical thing, however what other physical things its equivalent to depends on context.
  - lisper 5y ago
    > Unambigious is quite a claim. No, it's not. The symbol systems used for math are deliberately engineered to make this true. > Is 3.0 and 3 the same symbol on your view? Depending on context Exactly. It depends on the context. Sometimes "A" and "a" ArE tHe SaMe SyMbOl, SoMeTiMeS tHeY aReN't. (Sometimes "Y" and "TH" are the same symbol! [1]) Likewise, sometimes "3.0" and "3" are the same symbol, sometimes they aren't. But within a given context, in order to qualify as math, the mapping has to be unambiguous. [1] https://www.youtube.com/watch?v=PVVTk7yy4kU https://www.youtube.com/watch?v=PVVTk7yy4kU

kmill 5y ago

This is either quite the claim or you have a non-standard definition of "symbol." Each of those three representations are obviously different, though they all refer to the concept of "one-quarter," and I very much question the one made from @ signs. (And to be annoying, ¼ and 1/4 both have completely different UTF-8 representations, but I'd still associate them with the concept of "one-quarter.") It seems like you're conflating "signifier" with "signified". I'd say the whole point of symbols is that they play a role in semiosis, where an interpreter (us) receives meaning (the "signified") from decoding a symbol (the "signifier"). My own decoding apparatus gets the same roughly the same meaning from ¼ and 1/4. But the meaning's not a symbol in itself. What I was obliquely getting at earlier in bringing up intuitionism is that math seems to derive from pre-existing mental processes. Recognition and manipulation of symbols seems to be no more special than other mental processes. Rule-based manipulation seems to appeal to our understanding of causality, for example.

lisper 5y ago
> I very much question the one made from @ signs There are limits to what can be expressed in an HN comment. If we were standing at a whiteboard I could draw many more different variations on the theme than I can here. > you have a non-standard definition of "symbol." A symbol is a physical thing that can be unambiguously mapped into one of a finite set of equivalence classes. ¼ and 1/4 and even "one-quarter" can all be unambiguously mapped (within a particular context, i.e. people speaking English talking about math) onto a single concept which is denoted ¼ or 1/4 or "one-quarter" or "one-quarter". > It seems like you're conflating "signifier" with "signified". No, I'm not conflating them. It's just very hard to talk about these things because the only tool we have at our disposal is signifiers. I can't actually show you the thing that is signified by ¼ and 1/4 and "one-quarter", I can only talk about its properties (and I can only do that using signifiers). > math seems to derive from pre-existing mental processes That is a very human-centric view of things. It happens to arise in humans from pre-existing mental processes, but that doesn't mean that math necessarily or inherently arises that way. In fact, math arises in nature in myriad ways, many of which are not even mental processes at all. > Recognition and manipulation of symbols seems to be no more special than other mental processes. Oh, that is where you are very, very wrong, my friend. Manipulation of symbols is very special. There's a reason it's called the "computer revolution".