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Roger Penrose – Is Mathematics Invented or Discovered? [video]

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Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]

#291

Post by Koshkin »

cpsempek wrote: post #56
justforfunhere wrote: post #38

Could the same be said about just about everything? Like Music. Is a Song just a combination of notes, beats, intervals, voice etc. waiting to be discovered? Or is it something that a musician invents in her brain through talent, experience, practice and trail and error. Or for that matter, a startup idea? A product/service that would bring immense value to its consumers, but it is not there yet, waiting to be discov…

I think I get your point and I‘m open to ideas which drive home your point in a more precise way. However, the main difference between concerning ourselves with whether or not mathematical objects exists vs music or start-up ideas is their place in building a foundation for understanding reality. Science has been a productive program for understanding reality. It happens to be underpinned by math. And as a result, we…

You can try to answer a simpler question: does the number 3 exist? If you define 3 as "the obvious common feature shared by three cows, three pencils, and three stars in the sky," then the question becomes "does this common feature exist?" and the answer, then, is, well, of course, yes, it does - because it's obviously there!

Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]

#292

Post by ip26 »

lisper wrote: post #184

The question assumes that there is a difference between invention and discovery. There isn't. Invention is a kind of discovery. The apparent distinction arises from our separation of physical and mental processes. But this is a purely artificial separation, a human conceit, because (unless you're a dualist) mental processes are physical processes. Specifically, mental processes are computational processes, which are…

The words "invention" and "discovery" are also both human conceits. It seems perfectly appropriate, then, for them to distinguish two separate other human conceits.

Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]

#293

Post by Koshkin »

DeathArrow wrote: post #61
justforfunhere wrote: post #38

Could the same be said about just about everything? Like Music. Is a Song just a combination of notes, beats, intervals, voice etc. waiting to be discovered? Or is it something that a musician invents in her brain through talent, experience, practice and trail and error. Or for that matter, a startup idea? A product/service that would bring immense value to its consumers, but it is not there yet, waiting to be discov…

On a fundamental level music is math.

Well, that's this:

https://en.wikipedia.org/wiki/Harmonic_function

vs. this:

http://openmusictheory.com/harmonicFunctions.html

Maybe, at some fundamental level, they are the same...

Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]

#295

Post by cmonnow »

alanbernstein wrote: post #242
lisper wrote: post #233

Earlier quoted context omitted.

OK let me invent something: gnoiwiof wefoin wf oinwfe oinfowin wfeoi fwenoifwe Do you count that as in invention? If not, what distinguishes it from your "invention"?

You seem to be protesting that the bird invention is nonsense, and no more meaningful than random letters. Regardless of the answer to your question, I think you might be overlooking a different point. Here is my invention: a new piece of jewelry, a double ring, which you wear on both a finger and a toe at the same time. This is a realizable physical object that (presumably) has never existed before. Is it a discover…

Your comment, made by alanbernstein 3 hours ago on this website hackernews on 4/17/2020 has never existed before. Is it an invention ?

Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]

#296

Post by thomasahle »

jeffdavis wrote: post #187
thomasahle wrote: post #33

Earlier quoted context omitted.

> The same for negative numbers, for that matter. It might be expressed differently, but the concept of addition seems very fundemental, and additive inverses (negative numbers) are a very real part of addition. > It's silly to think that the sqaure root of negative one is something real to be discovered If we assume the aliens also have a need for multiplication, combining it with multiplication we get polynomials,…

"additive inverses (negative numbers) are a very real part of addition" Inverses are just an abstraction that helps you rearrange operations. You'd think something like accounting would need negative numbers, but nope, it gets along just fine without them.

They have the concept of "minus", which is just another way of adding with a negative.

Also deficits and surpluses seem like normal accounting terms.

Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]

#297

Post by stjohnswarts »

dTal wrote: post #202
pdonis wrote: post #198

Earlier quoted context omitted.

> Invention is a kind of discovery. Some inventions can be thought of this way, but I don't think all inventions can. For a relevant example, human mathematical notation is a human invention that I don't think can be usefully thought of as a kind of discovery. (Another poster upthread mentioned Tegmark's response drawing a distinction between the structure of mathematics, which we discover, and the language we use to…

I think notation can certainly be regarded as a kind of discovery. As time goes on, notation improves dramatically as a tool of thought. This improvement is a result of feedback over what works and what doesn't. The feedback is discovery. Invention = discovery in "solution space".

I don't understand why it is useful to argue "invention is discovery is invention". They are fairly well defined in the dictionary and it's a useful distinction to humans. Sure there is a gray area of a wide swathe of overlap, but in general they are useful as commonly understood.

Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]

#298

Post by guerrilla »

Tainnor wrote: post #213
guerrilla wrote: post #189

Earlier quoted context omitted.

Irrefutable and "unequivically" true if you take some classical FOL as a productive method of producing knowledge, a philosophical assumption. Philosophy came first, mathematical logic is just a formalization of that and the reason it was formalized at all and not somethimg else is epistemological. Your entire argument attempting dismiss philosophy is philosophy.

I didn't dismiss philosophy. I said that as soon as you fix some axioms (such as those of classical FOL), the conclusions are irrefutable. This is where mathematics begins. The question where those axioms come from or whether they are "true" are philosophical. The two disciplines are related, but separate. Lots of mathematicians have different "foundational" beliefs from each other; some have studied or deeply though…

Okay, I read too much into what you were saying. Yes, you're right about all of that.

Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]

#299

Post by dntbnmpls »

lisper wrote: post #184

The question assumes that there is a difference between invention and discovery. There isn't. Invention is a kind of discovery. The apparent distinction arises from our separation of physical and mental processes. But this is a purely artificial separation, a human conceit, because (unless you're a dualist) mental processes are physical processes. Specifically, mental processes are computational processes, which are…

> The apparent distinction arises from our separation of physical and mental processes.

The distinction is that discovery is of something that exists without human intervention and invention exists because of human intervention.

For example, telescopes are invented ( human made ). The moons of Saturn are discovered ( not human made ).

You created a straw man and argued about dualism. The question of discovery and invention has nothing to do with mind/body problem.

Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]

#300

Post by hliyan »

StandardFuture wrote: post #154
henrik_w wrote: post #136

Earlier quoted context omitted.

I really liked this perspective from Bartosz Milewski in this (very good) podcast episode: mathematics is not inherent to the world, it is inherent to the human brain (paraphrased, around minute 32 in the episode) https://corecursive.com/035-bartosz-milewski-category-theory...

And really one of the biggest pieces of proof of this is that some of the earliest mathematics developed was planar geometry. But, planar geometry (primarily involving triangles and squares) does not actually exist in nature. Which means that planar geometry is an approximation technique developed by the brain in order to begin to understand the actual much more complex geometries that appear in the real world. This…

I too, subscribe to this view. In my mind, reality is nothing more than a vast integer variable field with interactions between some variables. All our mental models, from vision to math are attempts at approximating that complexity down to a level that our brain's limited processing capacity can handle...

Why integers one might ask. For me, even rational numbers are such an approximation.

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