Roger Penrose – Is Mathematics Invented or Discovered? [video] • Hacker News Board

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

#201

Post by lisper » Fri, Apr 17, 2020, 4:14 PM UTC

pdonis wrote: post #198

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…

> 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…

> human mathematical notation is a human invention that I don't think can be usefully thought of as a kind of discovery

Why not? It's a discovery of visual features that the human brain and unaided eye can easily discern, and the discovery of a correspondence of those visual features to concepts that the human brain can easily remember. All of these are (on the assumption that dualism is false) physical processes.

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

#202

Post by dTal » Fri, Apr 17, 2020, 4:15 PM UTC

pdonis wrote: post #198

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…

> 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".

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

#203

Post by steve76 » Fri, Apr 17, 2020, 4:16 PM UTC

I would go with invented.

I think this ends with humans changing the universe to fit their needs. The math is right because humans made it.

I think of satellites and solar orbiters made from matter waves that encompass everything. Medical applications built around them.

Humans manipulating their photoelectric properties. They still see a sun. Everything else sees the sun as a black hole because of what we did to ourselves.

Distant stars focus into existence because of telescopes on Earth. Everything that existed already leaves us alone, so to a degree they must see it too.

There's some contest to see how insignificant we can make ourselves just for petty license. Convince no one. Start building.

Odds are, other more powerful people thought of it and did it before.

That telescope in geneva to me is not just some far off irrelevant land to look at. It's in the material, a grain structure of our Sun.

Serves as great motivation.

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

#204

Post by pdonis » Fri, Apr 17, 2020, 4:19 PM UTC

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.

I'm not sure I understand this either. I think our ordinary intuitions would say that both invention and discovery are mental processes. They're just different kinds of mental processes: invention has an element of arbitrariness or choice in it that discovery does not.

I have no problem with saying that mental processes are physical processes; I just don't think that means invention is a kind of discovery.

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

#205

Post by Tainnor » Fri, Apr 17, 2020, 4:22 PM UTC

naasking wrote: post #178

Tainnor wrote: post #156

Earlier quoted context omitted.

Yep, the counterpoint to the unreasonable effectiveness of maths in the natural sciences is accompanied by the unreasonable ineffectiveness of maths in the social sciences, humanities, etc. Although at least to some extent statistics is the one branch of mathematics that does seem to be applicable (but the way this influences results, as opposed to methods, seems to be mathematically not that interesting). There have…

> Yep, the counterpoint to the unreasonable effectiveness of maths in the natural sciences is accompanied by the unreasonable ineffectiveness of maths in the social sciences, humanities, etc. Except it's not ineffective at all in these subjects. Social science experiments have so many variables that the small experiments that can be conducted given the financial resources are insufficient to infer a good model. This…

If it's ineffective in practice, I consider it to be ineffective.

But even if you could design an experiment perfectly and come up with some strong statistical evidence and then had other means to tease out what is actually causal and what is only correlational, you'd only know what influences what and not necessarily why. But yes, I did say that statistics/probability is some rare exception.

You can study group theory and understand the way physical forces work better, or hilbert spaces to understand quantum mechanics, but I haven't yet heard of anyone who has studied topology or galois theory and found that incredibly useful for understanding social phenomena better.

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

#206

Post by pdonis » Fri, Apr 17, 2020, 4:22 PM UTC

lisper wrote: post #201

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…

> human mathematical notation is a human invention that I don't think can be usefully thought of as a kind of discovery Why not? It's a discovery of visual features that the human brain and unaided eye can easily discern, and the discovery of a correspondence of those visual features to concepts that the human brain can easily remember. All of these are (on the assumption that dualism is false) physical processes.

> It's a discovery of visual features that the human brain and unaided eye can easily discern, and the discovery of a correspondence of those visual features to concepts that the human brain can easily remember.

Hm. Yes, I suppose you could look at it this way. However, there is still an element of arbitrariness or choice involved that is not present in the discovery of mathematical structures themselves. All humans discover the same mathematical structures, but different humans invent different mathematical notations to describe those same mathematical structures.

So I guess it's a matter of whether you want to focus on the similarities or the differences between those two cases.

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

#207

Post by lisper » Fri, Apr 17, 2020, 4:27 PM UTC

pdonis wrote: post #204

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. I'm not sure I understand this either. I think our ordinary intuitions would say that both invention and discovery are mental processes. They're just different kinds of mental processes: invention has an element of arbitrariness or choice in it that discovery does not. I have no problem with saying that mental processes are physic…

> invention has an element of arbitrariness or choice in it that discovery does not

Yes, I can understand how someone could reach this conclusion. I used to believe it myself. But if you think about it you will realize that this appearance of "arbitrariness or choice" is an illusion. Take the airplane for example. Was it invented or discovered? Is there a relevant distinction between the "invention" of the airplane and the "discovery" of the principles of aerodynamics? What is it?

Even the arts can be seen as a process of discovery, specifically, the discovery of what processes and artifacts produce favorable reactions in human brains.

It's really a matter of perspective, of what dramatic narrative you choose to apply. Any story of invention can be re-cast as a story of discovery.

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

#208

Post by yters » Fri, Apr 17, 2020, 4:29 PM UTC

lisper wrote: post #199

yters wrote: post #197

Earlier quoted context omitted.

So, if there is a difference between invention and discovery, then dualism is true?

Yes, though that's a bit of an odd way of putting it. It's kind of like saying that if matter can't be broken down into smaller constituents beyond a certain point then atomism must be true. It's more of a definition of dualism/atomism than a logical entailment.

One man's modus ponens is another man's modus tollens.

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

#209

Post by red75prime » Fri, Apr 17, 2020, 4:29 PM UTC

fsflover wrote: post #95

zelos wrote: post #40

Earlier quoted context omitted.

> But to complicate things a bit, some things don't exist unless we observe them. Is this intepretation of quantum mechanics still the canonical one?

This is a philosophical question. "No experimental evidence exists that distinguishes among these interpretations." https://en.wikipedia.org/wiki/Interpretations_of_quantum_mec...

[0] Proposal for an experimental test of the many-worlds interpretation of quantum mechanics

I can't judge whether this proposal makes sense, but there's that.

0: https://arxiv.org/pdf/quant-ph/9510007.pdf

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

#210

Post by dorgo » Fri, Apr 17, 2020, 4:30 PM UTC

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.

You make the distinction based on (physical or mental) processes involved in the discovery/invention. I wouldn't care so much about how the discovery/invention came to be and look more into what the discovery/invention is about.

Usually, you can discover things which are present in the real world. Mathematicians are rarely interested in the real world. They invent things which are true (or false) regardless of the physical world.