7 ms·

A better question is - is math an inherent part of the universe or is it a uniquely human construct?

by drdec 3y ago

otabdeveloper4 3y ago
It can be both.
mensetmanusman 3y ago
The universe has a mind (human) and its current opinion is that math is inherent and discovered.
rramadass 3y ago
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
blacksqr 3y ago
Reader added context: humans are an inherent part of the universe.
Tao3300 3y ago
We are a way for the universe to know itself. Carl Sagan
- kordlessagain 3y ago
  "Through our eyes, the universe is perceiving itself. Through our ears, the universe is listening to its harmonies. We are the witnesses through which the universe becomes conscious of its glory, of its magnificence." - Alan Watts
jstanley 3y ago
There's also the viewpoint that the universe is part of mathematics.
- quickthrower2 3y ago
  The mathematical model of the universe is part of mathematics.
  - jstanley 3y ago
    But the universe itself might be made of mathematics, to the extent that it is made of anything at all.
posterboy 3y ago
it depends a lot on who you ask, so that part is human, and the part that you didn't specify is ambiguous enough that the answer can only be yeah no.
Aardwolf 3y ago
Would in a completely different universe with completely different physics where some life and civilization (for whatever that means in those different physics) manage to emerge, this civilization have similar mathematics, or completely different? Is it possible for a universe to exist where those who can think and would follow all possible logic rules, find that e.g. the natural base of logarithms turns out to be something else than 2.71828, or get different prime numbers in the integers despite using similar addition and multiplication rules, or other such changes..., or would they find exactly the same? I think they would find exactly the same (when it comes to the real actual logic, they may use different conventions and focus on different things if they got e.g. a different amount of dimensions in their universe etc...), I simply can't think how following logic rules could conclude something else no matter in what universe...
- tsimionescu 3y ago
  This depends a lot on how different you imagine this universe could be. For example, in this different universe, if I have an apple and you give me another apple, how many apples do I have? If I have 2, just like in our own universe, then you're probably right. But what if I have 3 apples? What if I still have 1 apple? We can certainly create number systems that don't behave like the integers, or addition operations where 1 + 1 = something other than 2. We haven't explored many of those too much because they're not very interesting, but they still have structure and may have similar concepts to what we call prime numbers etc. The integers and regular addition happen to be much more useful for understanding our world than all of these other systems. In a vastly different universe, the opposite may happen: if they studied this weird operation where 1+1=2, they would reach the same conclusions as we do. But they never study it, because it doesn't match their universe at all.
- stared 3y ago
  > the natural base of logarithms turns out to be something else than 2.71828 The Euler number has a very concrete definition (or, actually, quite a few equivalent ones). The answer is clear if definitions are the same (all - including the operations we perform and structures we use). Yet, math we know revolves around the abstraction of (discrete) language AND that we operate with things that we count. Even if we were slime molds (well within the same universe), we may have never developed the concept of integers. At the same time, there could have been 3D geometry without words.
deleted 3y ago
[deleted]
jug 3y ago
Math is a human construct to describe inherent parts of the universe (among other things). The universe is compatible with math not because the math is part of it, but because the universe is what math was invented to describe. Most fundamentally, relationships between related structures and sizes. Obviously the universe is full of those since an order does emanate in ours. So aliens probably also have math and even discovering the same relationships etc but that still won't make math an inherent part of the universe to me. The universe doesn't care for math, it just is. Intelligent beings want to describe and discuss it though so we keep inventing math in order to do so and speak a common language. Personally I find this very simple and not controversial at all. Math was simply invented as a system for us to teach and jot down things so that we don't lose knowledge across generations or for example colleagues.
- simonh 3y ago
  Right, mathematics is a language for very formally and precisely describe consistent relationships. Since the universe is persistent and consistent, it is useful to us such descriptions. I may not be possible to know why the universe is this particular way, but I don't think the universe is consistent 'because of maths'. The universe is this way for unknown reasons, but languages don't define or create the things they describe. To prove this, we can construct descriptions of things that do not or cannot physically exist. Frodo the Hobbit, for example, in English. I'm sure there are equivalent expressions in maths that don't relate to physical things. The description, and therefore the concept exist (same thing), but the thing itself does not. Another way to say it is that the description does not correspond to something that is physically real. So we can construct mathematical descriptions of unreal or hypothetical things, and we can construct English language descriptions of such things. That's just a feature of languages.
- criddell 3y ago
  The mathematical universe hypothesis says reality is mathematics. Not just that math can model reality, but that the universe is a mathematical structure. That isn't really at odds with what you are saying though, it's just a lower level.
grumblingdev 3y ago
A good line of questioning is to explore the constants that arise in physics, of which there are nineteen[3]. E.g. "Why is the speed of light what it is?". ~300,000,000 meters per second. But the definition of a meter is actually defined by the speed of light, so this number is very human-math-specific. So instead, you want to look at the speed of light in terms of other physical constants to find a "dimensionless" constant. This leads us to the fine-structure constant[1], which is a single number that pops out when you relate a few of these experimentally measured constants to each other. 0.0072973525693 ≃ 1/137 This is a number that if any different would mean the universe would not exist in the way it does. Something very human is the notion of "1". Counting things is very important to intelligent life. I was thinking the other day, about the world from the perspective of a tree. It doesn't care about counting things. So "1" is irrelevant to it. It's an invented concept by humans. And most of our mathematical thinking is based around this. There could be an infinitely deeper and more complicated maths to explain things. It's like looking at a leaf without a microscope to figure out biological processes. Until the 1600s, biologists could only study what their eyes could see. All this quantum randomness feels like we are still just looking at a leaf with our eyes. [1]: https://en.wikipedia.org/wiki/Fine-structure_constant https://en.wikipedia.org/wiki/Fine-structure_constant [2]: https://en.wikipedia.org/wiki/Dimensionless_physical_constant https://en.wikipedia.org/wiki/Dimensionless_physical_constan... [3]: https://en.wikipedia.org/wiki/Physical_constant#Number_of_fundamental_constants https://en.wikipedia.org/wiki/Physical_constant#Number_of_fu...
- joe__f 3y ago
  How do you know that trees don't care about counting things? Have you ever been a tree?
- chaoticmass 3y ago
  Plants may not have a concept of numbers or math, but they seem to follow mathematical patterns regardless. https://thatsmaths.com/2014/06/05/sunflowers-and-fibonacci-models-of-efficiency/ https://thatsmaths.com/2014/06/05/sunflowers-and-fibonacci-m...

A better question is - is math an inherent part of the universe or is it a uniquely human construct?

by drdec 3y ago

A better question is - is math an inherent part of the universe or is it a uniquely human construct?

otabdeveloper4 3y ago

It can be both.

mensetmanusman 3y ago

The universe has a mind (human) and its current opinion is that math is inherent and discovered.

rramadass 3y ago

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

blacksqr 3y ago

Reader added context: humans are an inherent part of the universe.

Tao3300 3y ago

We are a way for the universe to know itself. Carl Sagan

kordlessagain 3y ago
"Through our eyes, the universe is perceiving itself. Through our ears, the universe is listening to its harmonies. We are the witnesses through which the universe becomes conscious of its glory, of its magnificence." - Alan Watts

jstanley 3y ago

There's also the viewpoint that the universe is part of mathematics.

quickthrower2 3y ago
The mathematical model of the universe is part of mathematics.
- jstanley 3y ago
  But the universe itself might be made of mathematics, to the extent that it is made of anything at all.

posterboy 3y ago

it depends a lot on who you ask, so that part is human, and the part that you didn't specify is ambiguous enough that the answer can only be yeah no.

Aardwolf 3y ago

Would in a completely different universe with completely different physics where some life and civilization (for whatever that means in those different physics) manage to emerge, this civilization have similar mathematics, or completely different? Is it possible for a universe to exist where those who can think and would follow all possible logic rules, find that e.g. the natural base of logarithms turns out to be something else than 2.71828, or get different prime numbers in the integers despite using similar addition and multiplication rules, or other such changes..., or would they find exactly the same? I think they would find exactly the same (when it comes to the real actual logic, they may use different conventions and focus on different things if they got e.g. a different amount of dimensions in their universe etc...), I simply can't think how following logic rules could conclude something else no matter in what universe...

tsimionescu 3y ago
This depends a lot on how different you imagine this universe could be. For example, in this different universe, if I have an apple and you give me another apple, how many apples do I have? If I have 2, just like in our own universe, then you're probably right. But what if I have 3 apples? What if I still have 1 apple? We can certainly create number systems that don't behave like the integers, or addition operations where 1 + 1 = something other than 2. We haven't explored many of those too much because they're not very interesting, but they still have structure and may have similar concepts to what we call prime numbers etc. The integers and regular addition happen to be much more useful for understanding our world than all of these other systems. In a vastly different universe, the opposite may happen: if they studied this weird operation where 1+1=2, they would reach the same conclusions as we do. But they never study it, because it doesn't match their universe at all.
stared 3y ago
> the natural base of logarithms turns out to be something else than 2.71828 The Euler number has a very concrete definition (or, actually, quite a few equivalent ones). The answer is clear if definitions are the same (all - including the operations we perform and structures we use). Yet, math we know revolves around the abstraction of (discrete) language AND that we operate with things that we count. Even if we were slime molds (well within the same universe), we may have never developed the concept of integers. At the same time, there could have been 3D geometry without words.

deleted 3y ago

[deleted]

jug 3y ago

Math is a human construct to describe inherent parts of the universe (among other things). The universe is compatible with math not because the math is part of it, but because the universe is what math was invented to describe. Most fundamentally, relationships between related structures and sizes. Obviously the universe is full of those since an order does emanate in ours. So aliens probably also have math and even discovering the same relationships etc but that still won't make math an inherent part of the universe to me. The universe doesn't care for math, it just is. Intelligent beings want to describe and discuss it though so we keep inventing math in order to do so and speak a common language. Personally I find this very simple and not controversial at all. Math was simply invented as a system for us to teach and jot down things so that we don't lose knowledge across generations or for example colleagues.

simonh 3y ago
Right, mathematics is a language for very formally and precisely describe consistent relationships. Since the universe is persistent and consistent, it is useful to us such descriptions. I may not be possible to know why the universe is this particular way, but I don't think the universe is consistent 'because of maths'. The universe is this way for unknown reasons, but languages don't define or create the things they describe. To prove this, we can construct descriptions of things that do not or cannot physically exist. Frodo the Hobbit, for example, in English. I'm sure there are equivalent expressions in maths that don't relate to physical things. The description, and therefore the concept exist (same thing), but the thing itself does not. Another way to say it is that the description does not correspond to something that is physically real. So we can construct mathematical descriptions of unreal or hypothetical things, and we can construct English language descriptions of such things. That's just a feature of languages.
criddell 3y ago
The mathematical universe hypothesis says reality is mathematics. Not just that math can model reality, but that the universe is a mathematical structure. That isn't really at odds with what you are saying though, it's just a lower level.

grumblingdev 3y ago

A good line of questioning is to explore the constants that arise in physics, of which there are nineteen[3]. E.g. "Why is the speed of light what it is?". ~300,000,000 meters per second. But the definition of a meter is actually defined by the speed of light, so this number is very human-math-specific. So instead, you want to look at the speed of light in terms of other physical constants to find a "dimensionless" constant. This leads us to the fine-structure constant[1], which is a single number that pops out when you relate a few of these experimentally measured constants to each other. 0.0072973525693 ≃ 1/137 This is a number that if any different would mean the universe would not exist in the way it does. Something very human is the notion of "1". Counting things is very important to intelligent life. I was thinking the other day, about the world from the perspective of a tree. It doesn't care about counting things. So "1" is irrelevant to it. It's an invented concept by humans. And most of our mathematical thinking is based around this. There could be an infinitely deeper and more complicated maths to explain things. It's like looking at a leaf without a microscope to figure out biological processes. Until the 1600s, biologists could only study what their eyes could see. All this quantum randomness feels like we are still just looking at a leaf with our eyes. [1]: https://en.wikipedia.org/wiki/Fine-structure_constant https://en.wikipedia.org/wiki/Fine-structure_constant [2]: https://en.wikipedia.org/wiki/Dimensionless_physical_constant https://en.wikipedia.org/wiki/Dimensionless_physical_constan... [3]: https://en.wikipedia.org/wiki/Physical_constant#Number_of_fundamental_constants https://en.wikipedia.org/wiki/Physical_constant#Number_of_fu...

joe__f 3y ago
How do you know that trees don't care about counting things? Have you ever been a tree?
chaoticmass 3y ago
Plants may not have a concept of numbers or math, but they seem to follow mathematical patterns regardless. https://thatsmaths.com/2014/06/05/sunflowers-and-fibonacci-models-of-efficiency/ https://thatsmaths.com/2014/06/05/sunflowers-and-fibonacci-m...