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Comment by lisper | Hacker News Reader

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 physical. So it's not surprising that the structure of the physical world should be reflected back on itself in the structure of mental processes. It's universal Turing machines all the way down.

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OK let me invent something:

A fignaft is a small pink bird from the island of slamp. It has a short triangular beak well adapted to plucking seeds out of the hard cones of the humnit bush. It was nearly hunted to extinction by the umaglots, until their chief shaman declared the bird to be a repository of the souls of men lost at sea. Since then it has made a remarkable recovery.

In contrast to the mental process required to invent an imaginary bird such as this, the folks who discovered DNA used tools to image cell internals such that the structure of the contents was revealed.

When DNA was discovered, something about the structure of the external world was made clear to us, and many other processes could be clarified as a result. The fignaft bird, on the other hand, only reveals the contents of my mind, and is constructed entirely of existing knowledge.

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 discovery?

This double ring may be the instrument that discovers a market for itself, or a visual/tactile aid to remind oneself of something, but in itself this invention is not a discovery of anything that can be said to have existed.

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

If I must choose between invention and discovery, then yes.

All you did was discover that if you typed those words on your computer, they would appear on that website on that day.

So each distinct event can be discovered, regardless of how predictable it is based on previous events? Each sunrise is a discovery?

"predictability" is only a function of your memory capacity and/or knowledge.

To a scientist/saint who has done a lifetime of study/penance on the past, present and future, every invention is predictable. To a goldfish with 5-second memory, every sunrise, why every breath, is a discovery.

Look at it another way. A scientist 'discovers' the atom. He didn't 'invent' it, right? Now, how did he discover it ? Using a microscope that another scientist 'invented'. So far so good?

Now go down the chain to that scientist. How did he 'invent' the microscope ? Did he make it out of thin air ? No, he was one day playing with 2 optic lenses that another scientist 'invented', and when placed in a line, he 'discovered' that they magnified it 100 times what one lens did. And he told everyone that 2 lenses together is called a microscope that he 'invented'. So far, so good ?

Now, go down the chain to that scientist. How did he 'invent' the optic lens ? Did he create it out of thin air ? No, he was one day playing with glass which another scientist 'invented', and when looking through it, he 'discovered' that they magnified it things 10 times their size. And he told everyone that looking through a glass lens is a 'magnifying glass' that he 'invented'. So far, so good ?

You see the pattern here ? Every permutation combination of nature exists. In other words, all possible inventions already exist waiting to be discovered by humans, or all possible discoveries are waiting to be invented.

The 2 words are synonyms.

Something 'new' that you 'discovered' was someone else's 'invention'. And once you go beyond the deepest chain that your senses can reach, even the physical laws that govern our universe that were 'discovered' are an 'invention' of God. Where did God discover it from ? We can ask Him.

I wonder if there are languages where this question doesn't make much sense, because, say, both invention and discovery translate to the same word just meaning "creation".

No need to wonder. English is that language.

Tomorrow I can come up with a new word called 'oogabookga' which means invention/discovery/creation, and then make enough people accept it so it makes it into the dictionary, and then 20 years later, 2 other folks like us will argue about the semantics between oogabookga and invention and discovery.

That's exactly what happened with invention/discovery 20 (or 200) years ago, and we are those 2 people now.

> The question assumes that there is a difference between invention and discovery. There isn't. Invention is a kind of discovery.

this is self-contradictory. if invention is a kind of discovery, then they aren't equivalent as you say.

invention and discovery are clearly different but related concepts. hence the question. i didn't invent the sun. i discovered it, for myself, the first time i saw it. this is a structure that exists.

the mathematical question boils down to whether the structures that we find are discovered or conjured up. our physical inventions do discover new things, but these are things that existed whether the invention happened or not. the invention is simply a process.

>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.

But mathematicians are present in the real world, so you can choose to see math as the discovery of the behavior of the brains of mathematicians.

lol, yes, you discover how mathematicians think, but what they think is still an invention.

In the end, I agree that if we expand the definition of the universe beyond physical world to contain "everything" then yes, every invention is also a discovery.

> what they think is still an invention

Is there anything that any human thinks (other than straight-out mimicry) that is not an invention?

If I type:

squirgle florb snozbar

would you say that I have invented something? Because if the answer to that is yes, then I'll concede the point (and observe that "invention" is not a particularly interesting concept). But if the answer is no, then I challenge you to draw a distinction between what I just did and what mathematicians do in a principled way.

neither inventions nor discoveries have to be interesting.

>squirgle florb snozbar

yes, you invented something (i think you can even claim copyright on that). I agree that it is not very interesting. mathematicians usually/sometimes produce more interesing inventions.

> yes, you invented something

OK, I guess we'll have to agree to disagree then. I would not call that an invention (and I think most people would agree).

> 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.

> 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.

> if you think about it you will realize that this appearance of "arbitrariness or choice" is an illusion.

I don't think that's the illusion. I think the illusion is that something as complex, for example, as "the airplane" has to be pigeonholed as either an invention or a discovery, instead of being a complicated process in which both invention and discovery were involved.

> Any story of invention can be re-cast as a story of discovery.

I think this depends on how far you are willing to stretch the meaning of the word "discovery".

No, it's an observation that there is no sharp line between invention and discovery. If you want to dispute that, you'll have to tell me how I can distinguish between the two.

> it's an observation that there is no sharp line between invention and discovery

This is true of pretty much any human categories, yes. That does not mean the categories aren't valid or that they should all be collapsed into one.

Fair enough. But notwithstanding, I contend that my claim is not vacuous. I would say that this particular failure of categorization actually reveals a deep truth, namely, that computation is universal.

> I would say that this particular failure of categorization actually reveals a deep truth, namely, that computation is universal.

I agree that computation is universal, but I don't see drawing a distinction between discovery and invention as denying that fact. In "computation is universal" language, the distinction is just the observation that there are different kinds of computations--moreover, there are different kinds of computations in the category "human mental processes". We don't need to say they're all the same to recognize that they're all computations at bottom.

> "arbitrariness or choice" is an illusion

after reading a little about quantum mechanics I'm not so sure any more.

>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.

That assumes that the artists test their work against real audience and adjust their style accordingly. Maybe they do, but I'm sure that there are artists out there who just create art.

>> "arbitrariness or choice" is an illusion

>after reading a little about quantum mechanics I'm not so sure any more.

Even Brownian motion would suffice, a chemical phenomena we've known about for millennia.[0] The jittering of sodium and potassium ions between neurons can be enough to trigger spike firing in a 'random' way[1]. At the end of the day, we are just complicated salty sacks of stochastic processes trying to reproduce, not much more.

[0] yes, it's 'quantum mechanical' in cause, like all things are. I'd say it's more statistical mechanics than quantum though, but to each their own: https://en.wikipedia.org/wiki/Brownian_motion

[1] https://en.wikipedia.org/wiki/Principles_of_Neural_Science

I think a useful dichotomy is between whether an intellectual product's existence is possible without the existence of the person who created it. Copyrightable works typically could not exist without their creator. Only Prince was capable of creating When Doves Cry and only Jane Austen was capable of writing Pride and Prejudice. But inventions share with mathematical discoveries that they can (and often are) created or discovered separately by more than one person.

> 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 describe it, which we invent.)

> 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.

> there is still an element of arbitrariness or choice involved that is not present in the discovery of mathematical structures themselves

That's not true. There is this thing in math called the "axiom of choice" which you can, quite literally, choose to accept or not. And math is chock-full of this kind of thing. Even geometry comes in different flavors: Euclidean and non-Euclidean. And we don't even know which of them corresponds to physical reality on cosmological scales!

> There is this thing in math called the "axiom of choice" which you can, quite literally, choose to accept or not.

No, there are these different mathematical structures: set theory with the axiom of choice, set theory with the negation of the axiom of choice, and set theory with neither. (More precisely, "Zermelo-Frankel set theory", since there are other set theories.) All of those structures were discovered. And, as I said, different humans invented different notations to describe these different structures.

Humans choose which of these structures to use for particular applications, yes. I don't think that process is either invention or discovery. Not everything humans do has to be an invention or a discovery.

Similar remarks apply to geometry.

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.

> 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.

> Invention is a kind of discovery.

Presumably you would agree that not all of discovery is also invention. So doesn't that restore the original question of asking whether mathematics is an invention or discovery which is not invention?

You say

> mental processes are computational processes

as if this were obvious but... If you accept the possibility of random events (something deeply related to Quantum Mechanics)... There can be lots of non-computable things out there in our minds...

Such as? "Computational processes" ≈ "arbitrarily approximable by a classical computer," and QM absolutely fits in there: I just solve Schrodinger's equation for the Hamiltonian you care about to whatever precision you need. It will take exponential time, but that seems perfectly reasonable.

Exactly. Furthermore, there is no evidence that quantum processes are at all salient to what the brain does. There is nothing in the I/O behavior of a human brain that provides any evidence of quantum processes going on. There are also good theoretical reasons to believe that quantum mechanic is not salient to the operation of the human brain. The brain is thoroughly thermalized, so it decoheres in time scales that are vastly faster than any of its interesting behaviors.

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

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.

Yeah, I'm inventing Thailand just now, especially around Ko Lanta.

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