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Small nit, but as hinted at by the other responses, humans didn't "invent" multiplication, they discovered it. In the same way we didn't "invent" the fact that

Small nit, but as hinted at by the other responses, humans didn't "invent" multiplication, they discovered it. In the same way we didn't "invent" the fact that the earth revolves around the sun, we discovered it.

beat 10y ago
I'd argue that we discovered the earth goes around the sun, but we invented multiplication. It's a philosophical argument, however.
- Retric 10y ago
  Generally invention applies to the first discovers. I would suggest in the entire universe both observable or not we are unlikely to be the first species to discover multiplication. Languages like English, French etc on the other hand have much better odds even if language as a concept is really old. PS: I have even seen 'rediscovery' used for the same situations when a math idea was lost etc.
simondedalus 10y ago
that's debatable, once you appreciate the point about having a reason to do something. calculation itself really only exists with purpose. it's a thing to do if you have a reason to do it. of course, these kinds of things too seem more "discovered" than "invented", but it's a very different kind of discovery than "the earth revolves around the sun". the earth revolves around the son, as far as we can figure these days, whether any agent/subjectivity/etc intends anything or not. however, no full-blooded calculation will ever occur anywhere in the universe unless someone needs to figure something out. in other words, intention is implicit with calculation (and truth-functional representation, by the by). as such, you could make a case for an argument for "inventing" strategies in mathematics. and of course, a lot depends on your ontology of mathematics in the first place. if you're a wittgensteinian about numbers, and you think any of what i said above is at all compelling, you may be inclined to believe that mathematics itself is an invention. you may admit of some more nuanced way that entities like "number" still exist without mathematics as a tool, you may not, but you'd probably see all mathematics existing as active work, not pre-existing objective Truth. of course, most people think of math as an always-there abstract object (roughly). maybe they're right. even so, there must be some force in the "i use it as a tool" and "it just revolves around the sun no matter what anyone--god or man or beast--wants" distinction.
- beat 10y ago
  Calculation can be done purely for pleasure. I have math nerd friends who sit and do math for fun. It's related to other challenging, creative pursuits, like playing music or writing poetry.
  - danielam 10y ago
    Calculation is not math per se.
cderwin 10y ago
I actually don't think this is true. Multiplication isn't some natural phenomenon that humans just stumbled upon, like gravity or nuclear energy, even if it does help to explain some observable phenomena. Multiplication is entirely a human idea -- it only exists in human brains. Multiplication was only "discovered" in the same way love, or music, or any of the liberal arts were "discovered" -- which is to say, not at all. I guess the straightforward counterargument here is that if multiplication only exists in humans' minds how can computers do it, but computers have absolutely zero autonomy -- a computer can't compute a product, or even "discover" multiplication without receiving explicit intructions from a human to do so -- in my mind a computer can't be deemed the one discovering multiplication if that discovery relied 100% on the design of human beings.

beat 10y ago

I'd argue that we discovered the earth goes around the sun, but we invented multiplication. It's a philosophical argument, however.

Retric 10y ago
Generally invention applies to the first discovers. I would suggest in the entire universe both observable or not we are unlikely to be the first species to discover multiplication. Languages like English, French etc on the other hand have much better odds even if language as a concept is really old. PS: I have even seen 'rediscovery' used for the same situations when a math idea was lost etc.

simondedalus 10y ago

that's debatable, once you appreciate the point about having a reason to do something. calculation itself really only exists with purpose. it's a thing to do if you have a reason to do it. of course, these kinds of things too seem more "discovered" than "invented", but it's a very different kind of discovery than "the earth revolves around the sun". the earth revolves around the son, as far as we can figure these days, whether any agent/subjectivity/etc intends anything or not. however, no full-blooded calculation will ever occur anywhere in the universe unless someone needs to figure something out. in other words, intention is implicit with calculation (and truth-functional representation, by the by). as such, you could make a case for an argument for "inventing" strategies in mathematics. and of course, a lot depends on your ontology of mathematics in the first place. if you're a wittgensteinian about numbers, and you think any of what i said above is at all compelling, you may be inclined to believe that mathematics itself is an invention. you may admit of some more nuanced way that entities like "number" still exist without mathematics as a tool, you may not, but you'd probably see all mathematics existing as active work, not pre-existing objective Truth. of course, most people think of math as an always-there abstract object (roughly). maybe they're right. even so, there must be some force in the "i use it as a tool" and "it just revolves around the sun no matter what anyone--god or man or beast--wants" distinction.

beat 10y ago
Calculation can be done purely for pleasure. I have math nerd friends who sit and do math for fun. It's related to other challenging, creative pursuits, like playing music or writing poetry.
- danielam 10y ago
  Calculation is not math per se.

cderwin 10y ago

I actually don't think this is true. Multiplication isn't some natural phenomenon that humans just stumbled upon, like gravity or nuclear energy, even if it does help to explain some observable phenomena. Multiplication is entirely a human idea -- it only exists in human brains. Multiplication was only "discovered" in the same way love, or music, or any of the liberal arts were "discovered" -- which is to say, not at all. I guess the straightforward counterargument here is that if multiplication only exists in humans' minds how can computers do it, but computers have absolutely zero autonomy -- a computer can't compute a product, or even "discover" multiplication without receiving explicit intructions from a human to do so -- in my mind a computer can't be deemed the one discovering multiplication if that discovery relied 100% on the design of human beings.