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Mathematics is an inherent part of the Universe. What we Discover/Invent are Models/Notation for identifying and using them. The difference today is that we hav

Mathematics is an inherent part of the Universe. What we Discover/Invent are Models/Notation for identifying and using them. The difference today is that we have built and extended the Abstractions/Relationships to such an extent that people feel it is not "Real" which is of course not the case. The best argument for this are the various structures across the World (eg. Pyramids in Egypt/Central-Latin America, Temples/Structures in India, Aqueducts from ancient Rome, Great wall from ancient China etc.) spanning thousands of years which could not have been built without a knowledge of Mathematics as we define it today. Their approach and models/notation may have been different but the essence of the Mathematical Abstraction is the same.

meroes 3y ago
There’s so much more math though. More than will ever be seen or used in structures, thought about, etc even in principle. E.g. if string theory isn’t real the math still is, so where is it? Part of the universe is pretty unsatisfying.
- rramadass 3y ago
  >There’s so much more math though. True, that is why I used the words "Discover/Invent". Also i used physical structures as an example since they are the most visible and unarguable evidence of "Real" Mathematics from the earliest times. You can invent abstractions to model concrete things(eg. all that is needed to model a skyscraper) or to model still further abstractions in a chain (eg. vector spaces for multidimensional/functional/etc. spaces). We only realize that it is "Real" when it is "Applied" in the concrete World (eg. number theory in cryptography).
  - meroes 3y ago
    I’m not disagreeing just thinking your line of argument must say more about where all this perpetually undiscovered math is confined in the universe. It sounds like you’re forced to believe math is abstract in nature then, but doesn’t that conflict with your earlier points.
    - rramadass 3y ago
      https://news.ycombinator.com/item?id=37662094 https://news.ycombinator.com/item?id=37662094 >where all this perpetually undiscovered math is confined in the universe It is in the very fabric/structure of the Universe itself Eg. Calculus buried in the motion of planets around the Sun and discovered by Newton.
- grumblingdev 3y ago
  Agree. Our math is convenient for us humans living in our universe. But how much of our math is just a poor approximation of our universe? Like Newton's gravity was. If our math only _approximates_ the world, if we discovered something that explains things better, it would all be irrelevant. There are a lot of hints that something big is missing in our maths as a means of explanation. Like the mathematical constants Pi and Euler repeating infinitely, quantum randomness...
EGreg 3y ago
Sometimes math can be pretty surprising, such as when complex numbers might be shown to be necessary to explain quantum mechanics: https://www.nature.com/articles/s41586-021-04160-4 https://www.nature.com/articles/s41586-021-04160-4 Or when group theory predicts subatomic particles through symmetries: https://www.britannica.com/science/subatomic-particle/Hidden-symmetry https://www.britannica.com/science/subatomic-particle/Hidden... But other things like continuity and limits, as well as various topological spaces, seem to be purely mathematical constructs.
- eigenket 3y ago
  Continuity and limits, and some relevant topological spaces are absolutely required to describe very basic fundamental physics. You can't write down even stuff like Newton's laws without calculus, and you can't do calculus without something equivalent to limits.
- rramadass 3y ago
  See my other comment here: https://news.ycombinator.com/item?id=37656080 https://news.ycombinator.com/item?id=37656080 As the other commentator points out, "Continuity and Limits" are fundamental to explaining physical phenomena (via differential equations) and are not "purely mathematical constructs". PS: You might find this interesting; Imaginary Numbers are Real - https://www.youtube.com/playlist?list=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF https://www.youtube.com/playlist?list=PLiaHhY2iBX9g6KIvZ_703...
  - jonathanstrange 3y ago
    You point to the argument that "we have to calculate with them, therefore they are real", but another aspect of the debate is about which mathematical entities are real in the sense of being physically realizable. From this perspective, it's not even clear that real numbers are real, e.g. whether and how it would physically possible for a real-number based quantity to be present in a finite space.
    - rramadass 3y ago

meroes 3y ago

There’s so much more math though. More than will ever be seen or used in structures, thought about, etc even in principle. E.g. if string theory isn’t real the math still is, so where is it? Part of the universe is pretty unsatisfying.

rramadass 3y ago
>There’s so much more math though. True, that is why I used the words "Discover/Invent". Also i used physical structures as an example since they are the most visible and unarguable evidence of "Real" Mathematics from the earliest times. You can invent abstractions to model concrete things(eg. all that is needed to model a skyscraper) or to model still further abstractions in a chain (eg. vector spaces for multidimensional/functional/etc. spaces). We only realize that it is "Real" when it is "Applied" in the concrete World (eg. number theory in cryptography).
- meroes 3y ago
  I’m not disagreeing just thinking your line of argument must say more about where all this perpetually undiscovered math is confined in the universe. It sounds like you’re forced to believe math is abstract in nature then, but doesn’t that conflict with your earlier points.
  - rramadass 3y ago
    https://news.ycombinator.com/item?id=37662094 https://news.ycombinator.com/item?id=37662094 >where all this perpetually undiscovered math is confined in the universe It is in the very fabric/structure of the Universe itself Eg. Calculus buried in the motion of planets around the Sun and discovered by Newton.
grumblingdev 3y ago
Agree. Our math is convenient for us humans living in our universe. But how much of our math is just a poor approximation of our universe? Like Newton's gravity was. If our math only _approximates_ the world, if we discovered something that explains things better, it would all be irrelevant. There are a lot of hints that something big is missing in our maths as a means of explanation. Like the mathematical constants Pi and Euler repeating infinitely, quantum randomness...

EGreg 3y ago

Sometimes math can be pretty surprising, such as when complex numbers might be shown to be necessary to explain quantum mechanics: https://www.nature.com/articles/s41586-021-04160-4 https://www.nature.com/articles/s41586-021-04160-4 Or when group theory predicts subatomic particles through symmetries: https://www.britannica.com/science/subatomic-particle/Hidden-symmetry https://www.britannica.com/science/subatomic-particle/Hidden... But other things like continuity and limits, as well as various topological spaces, seem to be purely mathematical constructs.

eigenket 3y ago
Continuity and limits, and some relevant topological spaces are absolutely required to describe very basic fundamental physics. You can't write down even stuff like Newton's laws without calculus, and you can't do calculus without something equivalent to limits.
rramadass 3y ago
See my other comment here: https://news.ycombinator.com/item?id=37656080 https://news.ycombinator.com/item?id=37656080 As the other commentator points out, "Continuity and Limits" are fundamental to explaining physical phenomena (via differential equations) and are not "purely mathematical constructs". PS: You might find this interesting; Imaginary Numbers are Real - https://www.youtube.com/playlist?list=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF https://www.youtube.com/playlist?list=PLiaHhY2iBX9g6KIvZ_703...
- jonathanstrange 3y ago
  You point to the argument that "we have to calculate with them, therefore they are real", but another aspect of the debate is about which mathematical entities are real in the sense of being physically realizable. From this perspective, it's not even clear that real numbers are real, e.g. whether and how it would physically possible for a real-number based quantity to be present in a finite space.
  - rramadass 3y ago