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Sorry but I disagree. Dirac disagrees here as well. We discovered the positron from mathematics not the other way around. Many other discoveries have been made

Sorry but I disagree. Dirac disagrees here as well. We discovered the positron from mathematics not the other way around. Many other discoveries have been made due to the application of mathematics (check out AlphaGo and ChatGPT).

pphysch 3y ago
Mathematics being a exceptionally useful human tool is compatible with mathematics not being "natural". Must hammers grow on trees? It is also worth pointing out that the basic mathematics of deep learning are quite old and relatively simple. It was actually the technological advancement of being able to economically perform trillions of grade-school arithmetical operations per second that unlocked it, not some "mathematical discovery".
- photon_lines 3y ago
  I'm sorry but I'm not sure what you mean by mathematics not being 'natural.' Einstein, Feynman, and many others used mathematics to give us an amazing exposition into the universe. Feynman in fact has stated that a 'particle' takes all possible 'path' computations into account for every possible 'particle trajectory' that exists and that the path of least energy (i.e. least information exchange) takes precedence. If you're telling me this isn't mathematical then you honestly don't know much about mathematics.
  - pphysch 3y ago
    Frankly, it's clear that you haven't studied mathematics in any real depth. Everything can be described (read: approximated, modeled) in mathematical terms; that's the whole point! That doesn't mean mathematical objects and processes must exist independently of those descriptions.
    - User23 3y ago
      But they do exist independently. If models weren't independent of the described phenomena then there couldn't be incorrect models.
- d1sxeyes 3y ago
  If I have one widget, and someone gives me a widget, I now have two widgets. If I then need to give someone one widget, then I will have one widget left. If someone else needs a widget, and so I break my widget in half and we share, I have half a widget left. Then five people turn up and give me three widgets each. I now have 15 and a half widgets. The basic, most fundamental principles on which mathematics is based are surely natural and discoverable. Other types of mathematics are born out of these principles.
  - raincole 3y ago
    To me this is exactly why mathematics is not natural. Counting natural numbers is not natural. > one widget And what's a widget? This implies there are "objects" and an object has its "boundry". Counting is completely human-defined. You can count earth as one and mars as two, or you can count solar system as one and an atom in another galaxy as two. It's a man-made system that help us think. Or you can count particle by particle... well never mind, we're in a thread of an article about why particles are actually probability clouds :)
    - d1sxeyes 3y ago
      If you reject the idea that objects exist, then of course they will resist attempts to count them.
      - raincole 3y ago
        "Things" exist. "Objects"? Not so much. Why is my mug is one object, instead of two, or three, or 10^26 objects? Counting is very abtrary. Seeing a mug as a whole instead of a bunch of sub-atom waveforms[1] is a choice (that our brain hardware made for us). [1]: Even this plural is very questionable
        d1sxeyes 3y ago
        Hm, so essentially your argument is that an object is a label that we put upon a quantity of stuff? I'm not sure that I agree, but for the sake of argument, even if I accept that principle, you can still count how many of that quantity of stuff you have. If I decide that a mug is made up of one part, then if I get a second mug, I have 2 mugs. If I instead say that a mug is made up of 10^26 objects, and I get another 10^26 objects, I'll have 20^26 objects. It's easier to count 1 + 1 than 10^26 + 10^26, but there's no change in the fundamental principle of counting just because we don't agree on the number we have to count up to. All of these are predictable and create natural mathematics through addition and subtraction (or multiplication/division, which are basically just repeated addition/subtraction). > Seeing a mug as a whole instead of a bunch of sub-atom waveforms[1] is a choice [...] Our brain is doing that because that bunch of subatomic waveforms have useful properties when considered together. They can hold quantities of other bunches of subatomic waveforms, for example, whereas a different collection of subatomic waveforms like my desk would not hold my coffee. Your contention that there's no such thing as an object seems a bit solipsistic, and more of a philosophical question than a relevant or useful way of thinking about the universe as we experience it.

pphysch 3y ago

Mathematics being a exceptionally useful human tool is compatible with mathematics not being "natural". Must hammers grow on trees? It is also worth pointing out that the basic mathematics of deep learning are quite old and relatively simple. It was actually the technological advancement of being able to economically perform trillions of grade-school arithmetical operations per second that unlocked it, not some "mathematical discovery".

photon_lines 3y ago
I'm sorry but I'm not sure what you mean by mathematics not being 'natural.' Einstein, Feynman, and many others used mathematics to give us an amazing exposition into the universe. Feynman in fact has stated that a 'particle' takes all possible 'path' computations into account for every possible 'particle trajectory' that exists and that the path of least energy (i.e. least information exchange) takes precedence. If you're telling me this isn't mathematical then you honestly don't know much about mathematics.
- pphysch 3y ago
  Frankly, it's clear that you haven't studied mathematics in any real depth. Everything can be described (read: approximated, modeled) in mathematical terms; that's the whole point! That doesn't mean mathematical objects and processes must exist independently of those descriptions.
  - User23 3y ago
    But they do exist independently. If models weren't independent of the described phenomena then there couldn't be incorrect models.
d1sxeyes 3y ago
If I have one widget, and someone gives me a widget, I now have two widgets. If I then need to give someone one widget, then I will have one widget left. If someone else needs a widget, and so I break my widget in half and we share, I have half a widget left. Then five people turn up and give me three widgets each. I now have 15 and a half widgets. The basic, most fundamental principles on which mathematics is based are surely natural and discoverable. Other types of mathematics are born out of these principles.
- raincole 3y ago
  To me this is exactly why mathematics is not natural. Counting natural numbers is not natural. > one widget And what's a widget? This implies there are "objects" and an object has its "boundry". Counting is completely human-defined. You can count earth as one and mars as two, or you can count solar system as one and an atom in another galaxy as two. It's a man-made system that help us think. Or you can count particle by particle... well never mind, we're in a thread of an article about why particles are actually probability clouds :)
  - d1sxeyes 3y ago
    If you reject the idea that objects exist, then of course they will resist attempts to count them.
    - raincole 3y ago
      "Things" exist. "Objects"? Not so much. Why is my mug is one object, instead of two, or three, or 10^26 objects? Counting is very abtrary. Seeing a mug as a whole instead of a bunch of sub-atom waveforms[1] is a choice (that our brain hardware made for us). [1]: Even this plural is very questionable
      - d1sxeyes 3y ago
        Hm, so essentially your argument is that an object is a label that we put upon a quantity of stuff? I'm not sure that I agree, but for the sake of argument, even if I accept that principle, you can still count how many of that quantity of stuff you have. If I decide that a mug is made up of one part, then if I get a second mug, I have 2 mugs. If I instead say that a mug is made up of 10^26 objects, and I get another 10^26 objects, I'll have 20^26 objects. It's easier to count 1 + 1 than 10^26 + 10^26, but there's no change in the fundamental principle of counting just because we don't agree on the number we have to count up to. All of these are predictable and create natural mathematics through addition and subtraction (or multiplication/division, which are basically just repeated addition/subtraction). > Seeing a mug as a whole instead of a bunch of sub-atom waveforms[1] is a choice [...] Our brain is doing that because that bunch of subatomic waveforms have useful properties when considered together. They can hold quantities of other bunches of subatomic waveforms, for example, whereas a different collection of subatomic waveforms like my desk would not hold my coffee. Your contention that there's no such thing as an object seems a bit solipsistic, and more of a philosophical question than a relevant or useful way of thinking about the universe as we experience it.