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> I would argue that this is wrong. That's what physicists do, not mathematicians. Notice that many mathematicians would not agree with you, here (but probably

> I would argue that this is wrong. That's what physicists do, not mathematicians. Notice that many mathematicians would not agree with you, here (but probably, a majority would). As the mathematician V.I.Arnold famously said, "mathematics is a branch of physics where experiments are cheap". So, yes, in the minds of lots of mathematicians, what they do is precisely to study and understand nature.

TeMPOraL 6y ago
In that sense, though, programming would be a branch of physics that's concerned with making brute-force experiments cheap (thus saving the mathematical work needed to find clever tricks to do that same experiment by manipulating a small bunch of symbols).
- TheOtherHobbes 6y ago
  Well - that's engineering. Physics is experimental model building of phenomena which are not yet understood and are being explored. Engineering is experimental model building of phenomena which are mostly understood, albeit sometimes with some quirks and unexpected edge cases. Applied math is the toolset used in both physics and engineering. Pure math is the abstract and philosophical exploration of symbolic relationships within all of math. Academic CS - Wirth and Dijkstra-style - is the tiny subset of pure math used to explore theories of computing. Practical CS is mostly just relatively trivial puzzle solving using a combination of cookbook academic CS with a bit of invention and innovation with influences from user psychology, marketing, and business design. The most academic and mathematical parts of practical CS is ML and AI, which are genuinely exploratory. The second most academic part is probably processor architecture, where you may be applying statistical modelling to cache design and instruction pipeline outcomes. Most of the rest is pretty basic compared to engineering modelling - never mind academic physics.
  - amelius 6y ago
    Speaking of Dijkstra, he famously refused the title "physicist" and instead chose to use the title "programmer".
  - nobodyandproud 6y ago
    There’s a difference between applied physics and theoretic physics as well. Every discipline has its ivory tower and “plebeian” branches. No need to give physics a free pass :)
roenxi 6y ago
Even if a lot of mathematicians think math is about studying nature they are demonstrably wrong. One can do maths that has no known relation to physical reality, has no basis in physical reality or sits in direct opposition to how physical reality actually works. That is precisely the opposite of physics to say that "well, if I can imagine it it must be nature". So by counterexample, since the field of maths contains things that are anathema to the science of physics maths cannot be a branch of physics. Math is the study of abstract patterns and those cannot be escaped. But just because individual mathematicians dedicate their lives to finding abstract patterns inspired by physics doesn't mean that either physics or math are branches of the other.
- spacedome 6y ago
  You are making a lot of ontological and epistemological assumptions that are contentious in the philosophy of math. Not saying you are wrong in thinking this, metaphysical questions don't necessarily have answers, but many would not agree with you.
mkl 6y ago
I am a mathematician. Nature is of no consideration whatsoever in some fields of maths. But nature or applications to it are the primary focus in many other fields of maths. In still others, nature would be a source of analogies, or applications of a few special cases, etc. Muddying the waters, some mathematicians would expand the definition of "nature" to include completely abstract ideas - anything that feels "discovered", for example. Mathematics is the study of patterns. Any kind of pattern you can imagine, in anything, including relationships between things. What things? Any things. That covers a lot!
- coldtea 6y ago
  >I am a mathematician. Nature is of no consideration whatsoever in some fields of maths. It's not about actual nature (the universe etc) being into consideration. It's about many mathematicians coming to see maths as exploration (physics-style) of a mathematical universe, so to speak, rather than a simple constructive process. So, they come to see mathematics as a kind of physics in this regard, no in the sense that they concern themselves with the outside nature. But in that math work appears to them as exploring a natural landscape (just one made of patterns and numbers).
  - mkl 6y ago
    Yes, that's what my comment says (but maybe you read it before I edited it to be clearer): >> Muddying the waters, some mathematicians would expand the definition of "nature" to include completely abstract ideas - anything that feels "discovered", for example.
    - coldtea 6y ago
      Yes, that. Though I wouldn't necessarily consider it "muddying the waters", but taking another criterium as important in the distinction of physics-like or not. Namely, not whether it concerns the study of the material universe, but whether it involves experimentation/discovery of in place structures, and other such physics-like processes (which they think it does).
wott 6y ago
I see mathematics as completely opposite to studying nature. Mathematicians work on extremely simple objects as a basis. For example (since we're here), give them a 0 and 1, and they will spend 200 years building a whole theoretical world from that, an artificial system they will describe through thousands and thousands of pages of theorems, getting more and more complex as time goes. Nature is an extremely complex system from the start. Trying to understand and describe it is not at all the same approach. You take a complex system (the complexity of the system is given, fixed externally by the nature) and try to simplify it. You can see this difference in the software world too. Mathematicians (CS) will build and favour the use languages which are based on a single simplistic axiom: "everything is a list" for the most famous example, "everything is a function" for others, and then you are supposed to build all the rest on those simplistic bases, and in practice that will mean twisting, bending, squeezing the problem world (i.e. the nature) to make it fit in your model. On the other side, you have programmers, which will more often favour practical, pragmatical languages, which do not exhibit the clean regular, symmetrical simplicity of the former ones, but which are more adapted to describe a complex, irregular world.
prionassembly 6y ago
Then, Arnold also says that mechanics is geometry in phase space (which subsumes physics in mathematics, like in the later “mathematical universe hypothesis” metaphysicians).
- enriquto 6y ago
  you know, as they say, "(...) consistency is the hobgoblin of little minds (...)"
  - prionassembly 6y ago
    It’s middlebrow but I still love Whitman where he goes “Do I contradict myself? Very well, I contradict myself. I am large, I contain multitudes”.
thevardanian 6y ago
Math, like philosophy, is only interested in using concepts, structures, or otherwise rigorous ideas to pry into other ideas. Like philosophy it is in some senses self referential, and not really interested in discovering some idea of "truth", but rather exploring the avenues by which truth itself is defined.
FabHK 6y ago
> As the mathematician V.I.Arnold famously said, "mathematics is a branch of physics where experiments are cheap". I think that is not so much subsuming mathematics under physics as a cheeky way of avowing mathematical Platonism, where eternal mathematical truths reside in some Platonic realm of ideas and wait to be discovered (not invented or proven) by mathematicians.
- enriquto 6y ago
  You can read the whole text that starts with that quote here: https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html As you say, it is written in a playful and cheeky manner, but it is just a rhetorical device; the meaning is certainly very deep. Even deeper and longer, but in a similar spirit, you have this text: http://math.ucr.edu/home/baez/Polymath.pdf http://math.ucr.edu/home/baez/Polymath.pdf It starts with a famous quote, replicating Caesar's gallic war: All mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like), hydrodynamics (supported by manufacturers of atomic submarines) and celestial mechanics (financed by military and other institutions dealing with missiles, such as NASA).

TeMPOraL 6y ago

In that sense, though, programming would be a branch of physics that's concerned with making brute-force experiments cheap (thus saving the mathematical work needed to find clever tricks to do that same experiment by manipulating a small bunch of symbols).

TheOtherHobbes 6y ago
Well - that's engineering. Physics is experimental model building of phenomena which are not yet understood and are being explored. Engineering is experimental model building of phenomena which are mostly understood, albeit sometimes with some quirks and unexpected edge cases. Applied math is the toolset used in both physics and engineering. Pure math is the abstract and philosophical exploration of symbolic relationships within all of math. Academic CS - Wirth and Dijkstra-style - is the tiny subset of pure math used to explore theories of computing. Practical CS is mostly just relatively trivial puzzle solving using a combination of cookbook academic CS with a bit of invention and innovation with influences from user psychology, marketing, and business design. The most academic and mathematical parts of practical CS is ML and AI, which are genuinely exploratory. The second most academic part is probably processor architecture, where you may be applying statistical modelling to cache design and instruction pipeline outcomes. Most of the rest is pretty basic compared to engineering modelling - never mind academic physics.
- amelius 6y ago
  Speaking of Dijkstra, he famously refused the title "physicist" and instead chose to use the title "programmer".
- nobodyandproud 6y ago
  There’s a difference between applied physics and theoretic physics as well. Every discipline has its ivory tower and “plebeian” branches. No need to give physics a free pass :)

roenxi 6y ago

Even if a lot of mathematicians think math is about studying nature they are demonstrably wrong. One can do maths that has no known relation to physical reality, has no basis in physical reality or sits in direct opposition to how physical reality actually works. That is precisely the opposite of physics to say that "well, if I can imagine it it must be nature". So by counterexample, since the field of maths contains things that are anathema to the science of physics maths cannot be a branch of physics. Math is the study of abstract patterns and those cannot be escaped. But just because individual mathematicians dedicate their lives to finding abstract patterns inspired by physics doesn't mean that either physics or math are branches of the other.

spacedome 6y ago
You are making a lot of ontological and epistemological assumptions that are contentious in the philosophy of math. Not saying you are wrong in thinking this, metaphysical questions don't necessarily have answers, but many would not agree with you.

mkl 6y ago

I am a mathematician. Nature is of no consideration whatsoever in some fields of maths. But nature or applications to it are the primary focus in many other fields of maths. In still others, nature would be a source of analogies, or applications of a few special cases, etc. Muddying the waters, some mathematicians would expand the definition of "nature" to include completely abstract ideas - anything that feels "discovered", for example. Mathematics is the study of patterns. Any kind of pattern you can imagine, in anything, including relationships between things. What things? Any things. That covers a lot!

coldtea 6y ago
>I am a mathematician. Nature is of no consideration whatsoever in some fields of maths. It's not about actual nature (the universe etc) being into consideration. It's about many mathematicians coming to see maths as exploration (physics-style) of a mathematical universe, so to speak, rather than a simple constructive process. So, they come to see mathematics as a kind of physics in this regard, no in the sense that they concern themselves with the outside nature. But in that math work appears to them as exploring a natural landscape (just one made of patterns and numbers).
- mkl 6y ago
  Yes, that's what my comment says (but maybe you read it before I edited it to be clearer): >> Muddying the waters, some mathematicians would expand the definition of "nature" to include completely abstract ideas - anything that feels "discovered", for example.
  - coldtea 6y ago
    Yes, that. Though I wouldn't necessarily consider it "muddying the waters", but taking another criterium as important in the distinction of physics-like or not. Namely, not whether it concerns the study of the material universe, but whether it involves experimentation/discovery of in place structures, and other such physics-like processes (which they think it does).

wott 6y ago

I see mathematics as completely opposite to studying nature. Mathematicians work on extremely simple objects as a basis. For example (since we're here), give them a 0 and 1, and they will spend 200 years building a whole theoretical world from that, an artificial system they will describe through thousands and thousands of pages of theorems, getting more and more complex as time goes. Nature is an extremely complex system from the start. Trying to understand and describe it is not at all the same approach. You take a complex system (the complexity of the system is given, fixed externally by the nature) and try to simplify it. You can see this difference in the software world too. Mathematicians (CS) will build and favour the use languages which are based on a single simplistic axiom: "everything is a list" for the most famous example, "everything is a function" for others, and then you are supposed to build all the rest on those simplistic bases, and in practice that will mean twisting, bending, squeezing the problem world (i.e. the nature) to make it fit in your model. On the other side, you have programmers, which will more often favour practical, pragmatical languages, which do not exhibit the clean regular, symmetrical simplicity of the former ones, but which are more adapted to describe a complex, irregular world.

prionassembly 6y ago

Then, Arnold also says that mechanics is geometry in phase space (which subsumes physics in mathematics, like in the later “mathematical universe hypothesis” metaphysicians).

enriquto 6y ago
you know, as they say, "(...) consistency is the hobgoblin of little minds (...)"
- prionassembly 6y ago
  It’s middlebrow but I still love Whitman where he goes “Do I contradict myself? Very well, I contradict myself. I am large, I contain multitudes”.

thevardanian 6y ago

Math, like philosophy, is only interested in using concepts, structures, or otherwise rigorous ideas to pry into other ideas. Like philosophy it is in some senses self referential, and not really interested in discovering some idea of "truth", but rather exploring the avenues by which truth itself is defined.

FabHK 6y ago

> As the mathematician V.I.Arnold famously said, "mathematics is a branch of physics where experiments are cheap". I think that is not so much subsuming mathematics under physics as a cheeky way of avowing mathematical Platonism, where eternal mathematical truths reside in some Platonic realm of ideas and wait to be discovered (not invented or proven) by mathematicians.

enriquto 6y ago
You can read the whole text that starts with that quote here: https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html As you say, it is written in a playful and cheeky manner, but it is just a rhetorical device; the meaning is certainly very deep. Even deeper and longer, but in a similar spirit, you have this text: http://math.ucr.edu/home/baez/Polymath.pdf http://math.ucr.edu/home/baez/Polymath.pdf It starts with a famous quote, replicating Caesar's gallic war: All mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like), hydrodynamics (supported by manufacturers of atomic submarines) and celestial mechanics (financed by military and other institutions dealing with missiles, such as NASA).