4 ms·

Mathematics continually surprises us when seemingly disparate areas suddenly become linked, sharing some sort of relationship that was not appreciated until muc

by retrac 4y ago

Mathematics continually surprises us when seemingly disparate areas suddenly become linked, sharing some sort of relationship that was not appreciated until much later. Some think mathematics is something like a physical law, or property of the universe. So figuring out such things may be like fundamental physics research. Hard to quantify the value, but there is value. Seemingly unrelated developments in mathematics have had a habit of helping to solve problems in physics in the past, at least. I don't think anyone really expected the exciting new mathematics of statistics in the 18th century, to one day be relevant to physics. But it would be.

chasd00 4y ago
> Some think mathematics is something like a physical law, or property of the universe my kid asked me if math was invented or discovered. i said "invented", i hope i'm right considering he views me as some all knowing oracle of information. just a little bit of pressure there.
- layer8 4y ago
  Computers were invented, but you could also say that we discovered how universal computation works. It’s not like there’s some fundamentally different form of computation that we could have invented instead. Even more so in math, the truths in math are discovered, not invented.
  - claytongulick 4y ago
    The mathematical realm is a purely human construct. There's no such thing as "one" in nature: there's not "one" apple. An apple is a monstrously complex collection of cells and dynamic chemical processes, it's not "one". The concept of numbers are a tool that humans use to categorize, summarize and model the world around us. The "truths" we discover in math are only true in the mathematical realm, which is an inexact model of the physical realm. Useful, but undeniably a human construct. So yes, math is invented. Though we constantly discover new ways to use it in the physical world.
    - layer8 4y ago
      Just as one (no pun intended) example, the fact that there are exactly five platonic solids in three-dimensional space is not something that is invented. It is discovered. And facts like that govern what is possible in the physical world, for example what kind of crystalline atomic structures can form. There is nothing “invented” about that. The fact that the physical space we live in has three dimensions also isn’t invented. These numbers, three and five here, are not a human invention. They correspond to facts we discovered, and they represent truths that are independent of human existence or inventions. Maths is exactly about that, discovering the fundamental truths that, based on logic, we find couldn’t have been any other way.
      - claytongulick 4y ago
        It's a bit of a difficult concept to wrap our head around because we've been taught to associate "number symbols" and names with "things" since we were toddlers, but they absolutely aren't the same thing. There's no such thing as "three", other than a categorization that we, as humans, apply to model the physical phenomenon. We've developed language and symbols over time to more precisely model the things we observe, but it's important to remember that our symbols are different from the things they are invented to represent. It's really hard to separate this abstract concept from our observed reality when they are so tightly coupled - the idea of "three dimensional space" is a model we've constructed to categorize and represent, in a convenient way, observed phenomenon that is too difficult to talk about in other terms. We didn't "discover" that there are three dimensions, for example. We developed language and a mental framework for categorizing space in such a way that we could more easily reason about it and communicate our reasoning effectively with others. We didn't "discover" Ohm's law. We created a set of units, names and concepts that would allow us to model the relationship in an analytic way, between other concepts such as current, voltage and resistance. Ohm's law isn't not a fundamental law of nature. Above all else, it's a series of struggles with language to describe things we observe. "Ohm" as a unit of resistance, "Voltage", "Amperage" - all of this was invented in order to be able to reason about things we were seeing, and it seems to be a good mental model and tool for getting things done, but it is very different than the actual reality. We didn't "discover" the number three - we created the concept of numbers and refined their meaning over time. For a very long time, in most civilizations there wasn't a concept of "zero" in number symbols. We needed a way to communicate that concept though, so invented a symbol to represent it. Number systems and the symbols that represent them have varied wildly throughout human history, and there appears to be a neurological attachment in the human brain that associates quantity with physicality (specifically fingers) [1] that makes grokking this concept especially difficult. When we become sophisticated enough that using our fingers wasn't sufficient to reason and communicate, we started using bone tally marks as a quantity representation - but all of these things, fingers, tally marks, glyphs - are just symbols that humans have created over time to imperfectly model physical phenomena. It's no different than any other sort of naming. We look at differences between birds, and attach a symbol of "hawk" to one, and "eagle" to another. There's no such thing as "hawk" or "eagle" in nature, these are human invented symbols that help us categorize and communicate in a short-hand way, differences between species we observe. Numbers are the same, but we've also invented a bunch of rules for manipulating those symbols to communicate more advanced concepts: addition, subtraction, etc... Now it's true, of course, that we discover new things all the time. Frequently we need to invent new ways of describing it. We discovered, by observing the stars, that planets follow an elliptical orbit. We couldn't describe that well using the tools we had, so invented Calculus. [1] https://en.wikipedia.org/wiki/History_of_ancient_numeral_systems https://en.wikipedia.org/wiki/History_of_ancient_numeral_sys...
- anonymousDan 4y ago
  That's a really insightful question for a kid to ask! Not sure I agree with your answer though, for me that's the kind if thing it would be hard to prove either way (ironically).
- nomemory 4y ago
  That is a good question for a kid. Ask him back, if it's discovered, where was it "stored" all this time. If it's invented, does it mean that other potential sentient species will have a different math than ours ?
- psychoslave 4y ago
  You missed a great opportunity to answer a simple "yes". ;)
- truckerbill 4y ago
  Given the fact the rules exist whether we know about it or not, I'm team discovered
- lixtra 4y ago
  Definitions (and axioms) are invented. Theorems are then discovered.
JohnMakin 4y ago
not to nitpick, but there's a ton of stuff in mathematics that is just defined out of convenience or convention, it's not natural law. Rather, a better definition would be that mathematics is a description of reality, rather than law itself.
- msm_ 4y ago
  Isn't it the same? Laws of physics describe how the physical world works, similarly to "laws of math" that describe how the mathematical world works. In both cases we tend to define our laws in a way that's easy for humans to use and understand.

by retrac 4y ago

chasd00 4y ago

> Some think mathematics is something like a physical law, or property of the universe my kid asked me if math was invented or discovered. i said "invented", i hope i'm right considering he views me as some all knowing oracle of information. just a little bit of pressure there.

layer8 4y ago
Computers were invented, but you could also say that we discovered how universal computation works. It’s not like there’s some fundamentally different form of computation that we could have invented instead. Even more so in math, the truths in math are discovered, not invented.
- claytongulick 4y ago
  The mathematical realm is a purely human construct. There's no such thing as "one" in nature: there's not "one" apple. An apple is a monstrously complex collection of cells and dynamic chemical processes, it's not "one". The concept of numbers are a tool that humans use to categorize, summarize and model the world around us. The "truths" we discover in math are only true in the mathematical realm, which is an inexact model of the physical realm. Useful, but undeniably a human construct. So yes, math is invented. Though we constantly discover new ways to use it in the physical world.
  - layer8 4y ago
    Just as one (no pun intended) example, the fact that there are exactly five platonic solids in three-dimensional space is not something that is invented. It is discovered. And facts like that govern what is possible in the physical world, for example what kind of crystalline atomic structures can form. There is nothing “invented” about that. The fact that the physical space we live in has three dimensions also isn’t invented. These numbers, three and five here, are not a human invention. They correspond to facts we discovered, and they represent truths that are independent of human existence or inventions. Maths is exactly about that, discovering the fundamental truths that, based on logic, we find couldn’t have been any other way.
    - claytongulick 4y ago
      It's a bit of a difficult concept to wrap our head around because we've been taught to associate "number symbols" and names with "things" since we were toddlers, but they absolutely aren't the same thing. There's no such thing as "three", other than a categorization that we, as humans, apply to model the physical phenomenon. We've developed language and symbols over time to more precisely model the things we observe, but it's important to remember that our symbols are different from the things they are invented to represent. It's really hard to separate this abstract concept from our observed reality when they are so tightly coupled - the idea of "three dimensional space" is a model we've constructed to categorize and represent, in a convenient way, observed phenomenon that is too difficult to talk about in other terms. We didn't "discover" that there are three dimensions, for example. We developed language and a mental framework for categorizing space in such a way that we could more easily reason about it and communicate our reasoning effectively with others. We didn't "discover" Ohm's law. We created a set of units, names and concepts that would allow us to model the relationship in an analytic way, between other concepts such as current, voltage and resistance. Ohm's law isn't not a fundamental law of nature. Above all else, it's a series of struggles with language to describe things we observe. "Ohm" as a unit of resistance, "Voltage", "Amperage" - all of this was invented in order to be able to reason about things we were seeing, and it seems to be a good mental model and tool for getting things done, but it is very different than the actual reality. We didn't "discover" the number three - we created the concept of numbers and refined their meaning over time. For a very long time, in most civilizations there wasn't a concept of "zero" in number symbols. We needed a way to communicate that concept though, so invented a symbol to represent it. Number systems and the symbols that represent them have varied wildly throughout human history, and there appears to be a neurological attachment in the human brain that associates quantity with physicality (specifically fingers) [1] that makes grokking this concept especially difficult. When we become sophisticated enough that using our fingers wasn't sufficient to reason and communicate, we started using bone tally marks as a quantity representation - but all of these things, fingers, tally marks, glyphs - are just symbols that humans have created over time to imperfectly model physical phenomena. It's no different than any other sort of naming. We look at differences between birds, and attach a symbol of "hawk" to one, and "eagle" to another. There's no such thing as "hawk" or "eagle" in nature, these are human invented symbols that help us categorize and communicate in a short-hand way, differences between species we observe. Numbers are the same, but we've also invented a bunch of rules for manipulating those symbols to communicate more advanced concepts: addition, subtraction, etc... Now it's true, of course, that we discover new things all the time. Frequently we need to invent new ways of describing it. We discovered, by observing the stars, that planets follow an elliptical orbit. We couldn't describe that well using the tools we had, so invented Calculus. [1] https://en.wikipedia.org/wiki/History_of_ancient_numeral_systems https://en.wikipedia.org/wiki/History_of_ancient_numeral_sys...
anonymousDan 4y ago
That's a really insightful question for a kid to ask! Not sure I agree with your answer though, for me that's the kind if thing it would be hard to prove either way (ironically).
nomemory 4y ago
That is a good question for a kid. Ask him back, if it's discovered, where was it "stored" all this time. If it's invented, does it mean that other potential sentient species will have a different math than ours ?
psychoslave 4y ago
You missed a great opportunity to answer a simple "yes". ;)
truckerbill 4y ago
Given the fact the rules exist whether we know about it or not, I'm team discovered
lixtra 4y ago
Definitions (and axioms) are invented. Theorems are then discovered.

JohnMakin 4y ago

not to nitpick, but there's a ton of stuff in mathematics that is just defined out of convenience or convention, it's not natural law. Rather, a better definition would be that mathematics is a description of reality, rather than law itself.

msm_ 4y ago
Isn't it the same? Laws of physics describe how the physical world works, similarly to "laws of math" that describe how the mathematical world works. In both cases we tend to define our laws in a way that's easy for humans to use and understand.