The list of posts I need to respond to is growing faster than my available time to respond. I'm plugging along though. Like the guy writing his autobiography. He takes a day to write about each minute of his life. He gets farther and farther behind every day. Yet if he lives forever, he'll document every minute.

Really? What is number theory about? What is Principia Mathematica about? — tom

Ok good questions. First to clarify what I'm talking about, my totally humble thesis is:

There is no general definition of number anywhere in mathematics. Of course there are perfectly clear definitions of particular types of numbers. Integers, reals, quaternions, p-adics, transfinite ordinals, and so on. But nowhere in mathematical literature will you find anyone who ever says: "A number is defined as such and so."

I regard this as a philosophical curiosity, worthy of discussion. What surprises me is people claiming that my thesis is factually false.

Now to falsify my thesis, all anyone needs to do is post a reference to a math textbook or published paper where someone defines what a number is, in a way that other mathematicians have adopted (ie not specialized to that one paper).

Post that reference and my thesis stands refuted.

All the verbiage in the world that is NOT such a specific reference does NOT falsify my thesis.

I trust this is perfectly clear to fairminded philosophers. I am not making any metaphysical statement about numbers. I'm saying that in the mathematical literature, there is no general definition of number.

To falsify a universal statement it is both necessary and sufficient for you to supply a single counterexample.

And if you DON'T, my thesis stands till you do.

* Now you did reference two interesting topics. First, number theory at the elementary level is about the study of the integers, and sometimes just the positive integers. These two classes of numbers have perfectly good definitions. At higher levels. algebraic number theory is the study of the algebraic integers. Analytic number theory is the use of the techniques of analysis: limits, calculus, etc., to study integers or algebraic integers.

In all of number theory, there is no definition of number.

* Now the Principia is cool. It's one of my favorite things. In the Principia, Newton describes the fundamentals of calculus; and uses his techniques to prove that the planets and the apples on the trees obey a universal law of gravitation that can be described by a simple equation.

Now that's cool as hell. He was one smart cookie that Isaac.

But I can tell you for a fact that in all of the Principia there is no definition of what a number is. Why would Newton concern himself with a matter as trivial as that? He was laying out how the universe works, not quibbling about definitions.

As an aside, Newton had worked out calculus using a symbolic formulation; but he wrote the Principia using the geometry of the ancients. He knew that he was proposing radical ideas, and he wanted to use familiar mathematics. He didn't let his new notation get in the way of the acceptance of his physical ideas.

Another reason Newton deliberately obfuscated the Principia was, in his own words, "... to avoid being baited by little Smatterers in Mathematicks."

I can totally relate!

Sorry but you are bullshitting to an extraordinary level. — tom

I wish you could explain this to me. I stated that in all of math there's no official definition of a number.

Why does this push your buttons? Why would you even doubt me? I've done the research. It's not hard to verify. I think there might be a Stackexchange thread about it.

Why do you think I'm bullshitting about this? And really, if you think of it, why WOULD I bullshit about something like this? What's in it for me?

You think numbers are defined in terms of quantity? — tom

No, you didn't read far enough back in the thread. Someone proposed the definition, "A number represents a quantity." I proposed the counterexample of the imaginary unit i, which does not denote a quantity in any sensible interpretation of the word. And I also asked that poster to define quantity for me. So that I would know for myself whether i could be somehow interpreted as denoting a quantity.

So I was asking the question as part of my challenge to their proposed definition of a number.

You understood me to be claiming that a number represents a quantity, but of course that is NOT a belief I hold. Complex numbers, p-adics, transfinite ordinals. I would never say a number represents a quantity.

i represents the square root of -1. — tom

Agreed, though it's more precise to say that i represents "a" square root of -1, because -i is another one, and i and -i can't be distinguished. There's no sense of positive or negative in the complex numbers.

i is a number. — tom

Yes of course. I believe in the complex numbers.

i exists. — tom

Yes it does. It not only has existence within formal mathematics; it occurs everywhere in the real world. If you want to do quantum field theory or just turn left at the corner, you are using the number i.

Simples. — tom

Absolutely. Since we share the same mathematical ontology, I wonder what I said to upset you.

Numbers do number-like things. What are the important things left unsaid? — apokrisis

Saying that a number is anything that's number-like is a circular definition. No better than the poster above who said that a quantity is anything that's quantitative. You are defining a thing in terms of itself. It's not a definition.

Even worse, being "number-like" is neither necessary nor sufficient for something to be considered a number! Some examples:

* Matrices can be added, subtracted, multiplied, and sometimes divided. In fact the set of nxn matrices for fixed n forms a ring, an important algebraic structure. But matrices are not regarded as numbers.

* The set of permutations on a given finite set forms a group. An example would be the six permutations of the set {a,b,c}. Geometrically this is the group of symetries of an equalateral triangle.

Permutations can be combined via the operations of composition: you do one permutation followed by another. With this operation, the set of permutations is a group. You can multiply and divide. But nobody ever calls a permutation a number.

* If we have a pair or an arbitrary collection of algebraic objects such as groups, rings, fields, vector spaces, or modules, we can form their direct sum and their direct product; and in the case of modules, their tensor product. These sums and products obey various algebraic identities and are considered part of the study of algebra.

But nobody ever calls groups, rings, fields, etc. "numbers." They're algebraic objects but they are not numbers.

These examples show that there are things that are "number-like" that are not numbers; and things that are not numbers that can nevertheless be added and multiplied.

I make two assertions:

1) In math, there is no general definition of number. Of course there are perfectly clear definitions of certain classes or types of number: integers, reals, quaternions, p-adics, transfinite ordinals, etc. But there is no general definition that says, "A number is such-and-so."

I was surprised at the, let's say, passion of some of the responses to this tame and factual assertion. Many interesting points were raised. I'll try to respond in detail to each post in the next couple of days.

2) It's surprisingly tricky to give a good definition of number. I hope my examples bear that out. But if they don't, I have a lot more examples!

And I'll try one: number is that which has neither extension, substance, nor quality, but that expresses/represents quantity. — tim wood

Ok I'll play. Four questions.

* What is quantity?

* The imaginary unit i with i^2 = -1 ... what quantity does it represent?

* Do you regard i as a number?

* Does i exist?

That's one reason a definition for number is good to have before talking about them. — tim wood

It's a philosophical curiosity that there is no definition of number in mathematics. In other words if you major in math, get a Ph.D. spend a career as a professional mathematician, you will never encounter a book or a paper that says, "A number is such and so."

A number is pretty much anything that's number-like, and the concept is historically contingent. First numbers were only the whole numbers and the ratios. Pythagoras discovered irrational numbers. Not till the middle ages did we start regarding zero and negative numbers as numbers. Not till Cantor did we regard transfinite quantities as numbers. There are all kinds of other mathematical objects we call numbers such as the p-adics, the dual and perplex numbers, nonstandard integers and reals, and so forth.

Yet there is not one single definition of number. It's an amorphous concept. Mathematicians "know one when they see one." I don't know if this has caught the attention of philosophers. But there is no definition of number.

Maybe Tegmark has good justification, now, for saying that it isn't. — Michael Ossipoff

The rightness or wrongness of Tegmark's idea doesn't matter so much as the fact that I can add, "and Tegmark agrees with me!" when I argue the same point. It doesn't matter whether Tegmark and I are right or wrong. How can anyone really know? But at least I can stand my ground on this particular point with greater rhetorical force.

I seem to remember from Zen and the Art of Motorcycle Maintenance that rhetoric is regarded as one of the lesser arts. Reasoning for the purpose of winning an argument is inferior to reasoning for the purpose of discovering truth. If I understood all that correctly.

The "law" is really an automatisation of justice, much like Bitcoin would be an automatisation of payment systems. If you look at human history the trend is to go from less automatisation to more automatisation. But there is a problem that is often forgotten with moving from less automatisation to more. The more automatisation there is, the more inescapable control there exists, and the less freedom in the real sense of the term. — Agustino

That fits nicely with some thoughts I have.

The risk isn't computers acting like people. The risk is people acting like computers.

Every time you're trying to explain your particular situation to a bureaucrat and they stonewall you with "policy," that's a system that's operating like an algorithm, to the detriment of the human in particular and humanity in general.

Every time a cop shoots an unarmed civilian in a bad shoot and the chief says, "Our officer followed departmental procedures," well DUH, your procedures need to be changed then. You need to train cops not to shoot the wrong people. It's literally impossible to foresee every situation. You have to train people to have a heart, not a flow chart.

Our worry about AI is misplaced. We need to start looking at the way we treat each other. No computer could be any worse to us than we already are.

Everyone would submit orders for all products to a central computer. — Agustino

Well see now I'm confused. To me this is a recipe for failure. You have to let the system make decisions organically from the bottom up. Top down control has been a bloody awful failure in China and the Soviet Union and Venezuela and Cuba. I don't understand how one could advocate for this and still hope to have a human society.

I think what I'm saying is that making society run by rules is totalitarianism when our current techno-society does it; and it's totalitarian when Marxist idealists imagine you could ever run a world like this.

Top down doesn't work. You want to empower from the bottom up. You want to program humanity into your system. And the only way to program humanity is to not program humanity at all.

the property of "being a human" is incompatible with the property of "being a number" — Abaoaqu

What a wonderful thought. In the old days people had phone numbers like MUrray Hill 5-9975. You'd dial the MU characters on your dial phone. In the 1960's the phone company started phasing out those exchanges. Many people objected at the dehumanization, erasing the history of the exchange names, the neighborhoods they represented, and replacing them with numbers. Some people understood what was coming.

In our contemporary AI society we are nothing but numbers, and not even individual numbers. We're datapoints in a huge "corpus" as they call a big pile of data. Data to be mined, sliced, diced, and statistically analyzed.

The property of being a human IS incompatible with being a number. I have always felt that. But society is going the other way. We are each numbers and our world is stumbling one innovation at a time into a monstrous cybertotalitarianism.

I find this view so appalling and maddening that I have trouble calmly rebutting it — Dlaw

It it intellectual rebuttal that's important here? Or the emotions stirred up by family dynamics? Perhaps this is more of a psychological problem than a philosophical one.

An obvious difference though is that share prices try to reflect the value of the company where it's usually clear that labour adds value. — Benkei

That was in the old days of sound monetary policy. As David Stockman notes, that was the time of President Dwight Eisenhower and Fed Chairman William McChesney Martin.

Today, stock prices represent buybacks funded by cheap interest rates driven by massive QE by the world's central banks.

That's one of the arguments made by crypto enthusiasts. That it's the stock market that's the real bubble backed by nothing but speculation. You have to admit they have a point.

began to watch the GDAX board — ArguingWAristotleTiff

That GDAX board sure is addictive! I don't trust the exchanges with serious money. But I have a little play money in there and the past few nights I spend way to much time watching the green and orange candlesticks fight it out on the Litecoin chart on GDAX.

You know, if we could see all this from twenty years in the future, a lot of things would be completely obvious. And the clues were here all the time. But in the present we can't see what's true and what will last.

Perhaps this is the start of a philosophical view. What things last? What things pass? If we think from that point of view, can we figure out how to intelligently deploy our assets in the crypto revolution to come?

I think the current wild west environment is fun to watch but nothing I'd recommend that anyone spend any serious money in. One week it's bitcoin then it's bcash then it's ripple and now it's ethereum. If anyone could figure out what the hysterical dumb crowd is going to do ahead of everyone else, you could surf that wave and make money.

But who can predict the actions of the raving crowd? "I can calculate the motions of the heavens, but not the madness of people." -- Isaac Newton, after losing his fortune in the South Sea Island bubble of 1720.

Max Tegmark says there are no infinities in the world.

He explicitly says that the infinities that come up in multiverse theory are breakdowns in our theory, and not actual infinities of universes.

http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/

Also see my extended discussion here.

https://thephilosophyforum.com/discussion/comment/142382

I've done a little web research on the subject of physical infinity. I have come to a definitive conclusion on the matter, definitive in the sense that I have solid support for my point of view the next time this comes up online.

I looked at several popularized article based on a Google search for "physical infinity."

Many of the articles were very lightweight and uninformed. A typical example talked about the achievements of Cantor, then invoked the Hilbert hotel argument to show how strange infinity is, claimed that there are infinitesimals in calculus, then started waving their hands at physics.

So many of the articles were like this that I realized that most of the people writing popularized articles about infinity don't know the first thing about it. They've heard of Cantor and they've heard about the Hilbert hotel, a story that Hilbert told once to a public audience, and never mentioned again in his entire career. Hilbert's hotel is like the bowling ball and rubber sheet model of gravity. It's not literally true. It's a popularization. A fable for the tourists. Not to be taken as a substitute for actual math or physics.

So people hear about Cantor and about the Hilbert hotel and they think they understand mathematical infinity and set theory and they simply don't. And they transmit their misunderstandings to a new generation of credulous readers.

Fortunately after wading through all this garbage I hit the mothorlode. I found Max Tegmark's on-the-record opinion.

Max Tegmark says there are no physical infinities. And that infinity is a "bad idea that needs to be banished from physics."


I'd like to pull a few quotes from his article. But it's a short article and well worth reading in its entirety.

http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/

By the way Tegmark explicitly says that the infinities in the multiverse argument are meaningless. That supports my position in the multiverse thread where people were arguing that there are literally infinitely many universes. Max Tegmark says you're wrong.

Herewith some quotes.

Physics is all about predicting the future from the past, but inflation seems to sabotage this. When we try to predict the probability that something particular will happen, inflation always gives the same useless answer: infinity divided by infinity. The problem is that whatever experiment you make, inflation predicts there will be infinitely many copies of you, far away in our infinite space, obtaining each physically possible outcome; and despite years of teeth-grinding in the cosmology community, no consensus has emerged on how to extract sensible answers from these infinities. So, strictly speaking, we physicists can no longer predict anything at all! — Tegmark

Infinity Doesn’t Exist — Tegmark

Consider, for example, the air in front of you. Keeping track of the positions and speeds of octillions of atoms would be hopelessly complicated. But if you ignore the fact that air is made of atoms and instead approximate it as a continuum—a smooth substance that has a density, pressure, and velocity at each point—you’ll find that this idealized air obeys a beautifully simple equation explaining almost everything we care about: how to build airplanes, how we hear them with sound waves, how to make weather forecasts, and so forth. Yet despite all that convenience, air of course isn’t truly continuous. I think it’s the same way for space, time, and all the other building blocks of our physical world. — Tegmark

Not only do we lack evidence for the infinite but we don’t need the infinite to do physics. Our best computer simulations, accurately describing everything from the formation of galaxies to tomorrow’s weather to the masses of elementary particles, use only finite computer resources by treating everything as finite. So if we can do without infinity to figure out what happens next, surely nature can, too—in a way that’s more deep and elegant than the hacks we use for our computer simulations. — Tegmark

Our challenge as physicists is to discover this elegant way and the infinity-free equations describing it—the true laws of physics. To start this search in earnest, we need to question infinity. I’m betting that we also need to let go of it. — Tegmark

Well folks there you have it. Tegmark doesn't think infinities are real.

That's good enough for me. I suspect the link to this article will save me a lot of trouble going forward when these convos come up.

The technical definition requires the physical manipulation of an infinite tape. — apokrisis

You mean an unbounded tape. Your ignorance is showing. Again.

If all there is to do here is to keep correcting your misrepresentation of my arguments, that is really a waste of time. — apokrisis

No amount of erudition can compensate for your bad manners. And as in our previous convo a few months ago, the more wrong you are on the facts [which several people noted at the time] the more condescending you act. Transparent and shallow, you fool no one but yourself.

And remember where this started - your claim that abstract thoughts are biochemical processes. You followed that howler by jumping the other way - saying the mind was in no way the product of informational processes. — apokrisis

The way this started IIRC is that you accused me of being a dualist and have then proceeded to make a dualist argument for the past several posts.

I actually haven't got much to say at this point and would like to wind this down. I do appreciate that this convo has taken a turn for the civil and interesting. But I'm really argued out on this topic at the moment. I will take your advice and go read up on semiotics. It wouldn't be the first time I've taken a run at that subject but I do admit it eludes me.

But if thought isn't biochemical then what is it? Oh, "informational." But you are using that word in a specific way that's different than what I mean by it.

This second misstep was based on your very narrow conception of information processing - one rooted in TMs. — apokrisis

Ah yes. Right, we agree on our point of divergence. Well, information processing is a TM. That's the technical definition. You have a more philosophical orientation. You said a post or two back that "information is meaning." I could not disagree more. So we have identified another point of disagreement.

The reason for the unreasonable effectiveness of TMs is that they are the theoretical limit on semiotic encoding. Semiosis depends on symbols. A TM is the conceptually simplest — apokrisis

I must say I actually find that comment interesting. I promise to do my homework on this. The theoretical limit on semiotic encoding. I don't think I understand entirely what it means, but I do find the idea thought provoking. I'll do some thinking and reading.

This ignores the fact that the flying machine designers quickly gave up trying to copy the flapping wings of birds and instead focused on a non-bird model of flying machines. The flapping did not prove "unreasonably effective".

Whereas the opposite is the case with NNs. Having got programmable computers, it was the case that even just emulating biologically-inspired information processing architectures was "unreasonably effective" for certain tasks, like pattern matching. — apokrisis

But that doesn't prove that minds work that way. Only that NNs have been doing some amazing things. Ever since Deep Blue beat Kasparov I've had to pay attention to weak AI. It's impressive. But I'm sure you know that chess playing algorithms operate very differently than chess playing humans. So my point about birds and airplanes stands IMO.

So that is a particularly inapt comparison with which to make your case. — apokrisis

No, it's perfectly on target. In the beginning, we tried to program chess algorithms with expert knowledge. (You remember the expert systems movement I'm sure). That got the algorithms to a certain level. But to achieve mastery of the game, the designers gave up trying to teach the machine strategy. They just turned the NN loose and let it train itself. [That's the Alpha Zero approach]. So algorithms play chess very differently than humans do. The bird/airplane analogy is directly on point.

So an organism is a machine? You seem out of touch with biology. — apokrisis

Well if it's not, then you are making a dualist argument. Because if something is not physical, then what is it? You'll say "informational" and then I'll point out that the mind isn't a TM and you'll say that information processing is not a TM and I'll say you're wrong about that.

Are you making a dualistic argument or not?

Artificial Life Needs a Real Epistemology - H. H. Pattee
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.18.1316&rep=rep1&type=pdf — apokrisis

Thank you, I'll read that.

So on the one hand you can't even define what you might mean by mind. On the other, you can make confident claims about neuroscience having a quite limited understanding. — apokrisis

I said no such thing about neuroscience. I objected to your claiming that neuroscientists think the mind is a computer program. Which is the same exact thing as an "informational process" even though you keep claiming it isn't.

And you keep reverting to talk of "brain biochemistry" when the question is about cognitive functions. — apokrisis

And physicists keep talking about "gravity" when the question is about falling functions.

If cognitive functions aren't a product of our physical bodies, then you are a dualist. Which is fine, except that we got started when you accused me of being a dualist.

Don't you see the inconsistency of one minute admitting to knowing little, the next to be making a sweeping judgement of the whole field? — apokrisis

You're the one who made a sweeping statement about neuroscientists. I pointed out that at best, SOME neuroscientists agree with you and others don't.

That's my understanding of the Church-Turing thesis. If you have a different idea I'd be interested to hear it.
— fishfry

That defines computation in the general limit ... if you are computing number theoretic functions. — apokrisis

Number-theoretic functions can implement everything else as far as we know. After all a NN is just a set of nodes with numeric weights. An NN is just a set of number-theoretic functions. Turing understood that number-theoretic functions aren't a limitation; but that rather they can be used to compute anything that we think of as computable.

So perhaps brains might not be that kind of "computer". — apokrisis

I'm perfectly willing to grant you that. I even agree with you. But then what kind of computer are they? What kind of computer ISN'T "that kind of computer?" The answer requires a breakthrough in physics and computer science.

Maybe there is not a single arithmetic operation involved in their neural processes. Maybe even "summing weights" is just an analogy for the integrative processes of brain cells. — apokrisis

Well summing weights is not an analogy for how NNs work. It's the literal truth of how they work. And by admitting that when it comes to brains, NN's are at best an analogy, you are conceding my point. Brains aren't NNs. You just agreed that they're only analogies to NNs.

Church-Turing may have zilch to do with neurology. — apokrisis

Right. May have. Some future genius is going to have to sort this out because as of today, if something is a computational or informational process, it's essentially a TM. If minds are informational but not TMs, then science has no current understanding of what that would be.

And yet it is still wrong to then attribute neural information processes to "biochemistry". — apokrisis

You are quite the dualist. If something's not physical, what is it?

And how could you have a view either way without a little more neuroscience to inform your opinion? — apokrisis

How could you have a view either way without a little more computer science to inform your opinion?

Given that TMs require no more physics than a gate that can read, write and erase a symbol on an infinite tape, why the heck would we expect new physics to make a difference to Turing universal computation? — apokrisis

Because we have to go past the Church-Turing thesis to find a mode of computation that's not a TM, and that has the ability to implement mind. And I believe that we'll need new physics to make that breakthrough. I have some ideas along this line but I don't want to toss them out at this moment.

The power of Turing machines is that they need the least physics we can imagine. What more do you want - time travel, Hilbert space, quantum teleportation? — apokrisis

Mind. Isn't that the "hard problem" as they say? We're trying to figure out how a body can have a mind. It's real puzzler.

That's back to front. It is the virtual elimination of any complicated physics which is the guarantee of the computational universality. — apokrisis

If brains implement minds and brains aren't TMs then what exactly are minds? Isn't that the question? I don't have the answer but nobody else does either. Not even the neuroscientists, who you seem to think have already settled the matter.

When you say "information is meaning," that's something I absolutely deny by my definition of information.
— fishfry

Who could win an argument against your private definitions? — apokrisis

Private between me and every computer scientist and information theorist in the world. Information is a bitstring that can be cranked out by a TM. Randomness is a bitstring that can't. Kolmogorov. He and I inhabit the same private world, although he's a hell of a lot smarter. And deader.

So let's stick to the real world of science, maths and philosophy. — apokrisis

I hardly regard math as part of the real world. it's literally the opposite of the real world. And philosophy has even less of a claim on being real. Surely you know this.

If you want to talk about Shannon entropy, fine. But then we all know that is based on counting meaningless bits. If we understood the pattern to mean something, then each successive bit would fail to be such a surprise. — apokrisis

If the next bit's not a surprise, it's because there's a TM behind the curtain. Which reminds me a little of the intuitionists, who think there's some kind of active agent creating "free choice sequences." I tried to understand that idea once and gave up. Is that what you are referring to here?

If I know you are transmitting the digits of pi, I could stop you right after you said "3". — apokrisis

Of course. Pi is a computable number. We only need to write a program to implement any of the many known closed-form expressions to calculate its digits. You know you're drifting into agreeing with me again.

You don't get it. — apokrisis

LOL. By which you mean, "You have an opinion that differs from mine, and I haven't got much of an argument."

Information theory defines a baseline where the meaning of a bit string is maximally uncertain. — apokrisis

Um ... that's a little murky.

Each bit says nothing about the following bit. — apokrisis

Yes ok.

Then from that baseline, you can start to quantify the semantics. You can derive measures such as mutual information that speak to the information content. — apokrisis

Murky. Bitstrings generated by TMs we call information; and those not generated by TMs, we call random. Quantifying semantics is a mystifying phrase to me. I'm not saying it's meaningless or wrong, just that I don't know how to quantify semantics or what that would mean.

That's one of the advantages of a semiotic approach to the whole issue. It recognises that there is a modelling relation involved. A symbol has meaning due to a habit of interpretation. — apokrisis

The habits of the human minds that assign meaning to the symbols. And even that is a function of language. A cat is a gato is a chat. Meaningless strings of symbols, assigned meanings by humans.

That habit is tied to action in the world. — apokrisis

Actions of humans.

So the informational side of the equation is causally connected to the material side. — apokrisis

Causally? No. The link seems arbitrary. As George Carlin asked, why do we park in the driveway and drive on the parkway?

The link between words and their meaning is anything BUT causal. It's arbitrary. Isn't it?

There is only meaning in relation to the material consequences of any beliefs. — apokrisis

Murky. You were making the claim that there's a causal connection between the arbitrary string of symbols "gato" and a furry four-legged domesticated carnivorous mammal with soft fur, a short snout, and retractile claws. You're wrong about there being a causal relation. But this quoted sentence seems to come out of nowhere and mean nothing.

.
Again, read Pattee - http://www.academia.edu/3144895/The_Necessity_of_Biosemiotics_Matter-Symbol_Complementarity — apokrisis

I promise to do so. I have a lot of research and thinking to do as a result of this thread.

You keep misrepresenting my argument. — apokrisis

I'm shocked. You have an argument? Sorry couldn't resist. You keep misrepresenting my argument too. But I think we're really repeating ourselves at this point. I really have to stop responding.

The significance of an NN would be that it captures something important about brain cognition. That is different from claiming the brain is literally just an NN. — apokrisis

Well then you have backed off your claims and essentially agreed with me. I am in full agreement that NNs have done some amazing things in constrained domains. That does NOT mean the brain is an NN. Please don't make me say birds/airplanes again.

And you seem confused about algorithms. — apokrisis

LOL. That's like me saying you're confused about Peirce. It would push your buttons only for the sake of doing so.

I'm not confused about algorithms. I think very clearly about algorithms. That's why I know that algorithms are dumb as rocks. And that's an insult to rocks.

They are rules for making calculations. So they are something we think it meaningful for a TM to do. They are not the barest syntax of rule following we can imagine. They are semantic actions performed on a machine. — apokrisis

Oh My God. No. TMs are not semantics. I'm sure you didn't mean to write that. I hope you didn't. Algorithms are syntax. Their semantics comes from humans. Please tell me you understand this.

So already we are into the real world where computation carries extra semantic baggage. — apokrisis

Not in my world. Not in anybody's world. Computations are bit flipping. Pure syntax. The meaning is entirely supplied by humans. Remember the 80s movie War Games? The computer doesn't know the difference between playing a game and blowing up the world. To the bit-flipping circuits there is no difference.

The algorithms are intended to represent some actual informational process. — apokrisis

The intention comes from the humans. They are "intended." But the intention appears nowhere in the code.

This could be just handling a company's payroll or driving a video display. Or it could be an attempt to mimic the connective behaviour of neural circuits. — apokrisis

It's only flipping bits. The meaning is in the intention of the human programmers. Play a war game or blow up the world. The computer just flips the bits, it doesn't know the meaning of anything. I really hope you are not confused on this point. I have no idea why you are trying to say something that you must know to be false.

A TM is just a universal algorithm runner. — apokrisis

To be picky, a UTM is a universal algorithm runner. A specific TM only runs one algo. Minor quibble.

How we then exploit that is down to the kind of information processing we think might be meaningful. We have to write an algorithm that seems to perform the task we have in mind. — apokrisis

we have in mind

Yes. You agree with me totally. We supply the meaning. The meaning comes from our minds. There is no meaning and no mind in an algorithm or in a computation.

That could be representing brain functions. — apokrisis

Could be. Yes. Agreed.

It could be representing accounting functions or moving image functions. Universal Turing machines have zilch to say about whether we humans are choosing to run usefully realistic routines or just scrambled garbage randomly concocted. — apokrisis

Right. Why do you so strenuously agree with me?

You are confusing yourself in jumping so interchangeably between talk of TMs, information, computation and algorithms. — apokrisis

No. I'm not confused. An algorithm is a description of a computation. A computation is a physical implementation of an algorithm. Information consists of bistrings cranked out by programs.

Again, we write the algorithms. They have zilch to do with the universality of TMs. So you can't claim them as "mere". They are intended to represent some meaningful relation expressed as some mathematical operation. They have to perform a function we find useful. Thus they could model a company's payroll, or model the cognitive operations of a brain. — apokrisis

Well algos only model a very limited subset of brain activity. And even if you had (in the future) an algo that could simulate the physiological functioning of a brain, it still would not implement a mind. Just as a computer simulation of gravity does not attract nearby bowling balls.

A payroll model is probably pretty ho hum. But a workable brain model? — apokrisis

Just a matter of time an neuroscience. But you are conflating brain with mind. I fully agree that one could in principle someday have a computer program that performs a reasonable simulation of a brain. I deny that such a simulation would have a mind. I agree that one could disagree with what I just said.

Yes, the map is not then the territory. As someone pushing semiosis - a modelling relations view of "information processing" - you don't have to explain that to me. It is what I've been saying. — apokrisis

Well we have been in agreement for quite some time I think.

You are convincing me of your utter unfamiliarity with neural networks in practice. Or even in theory. — apokrisis

In other words you have no argument so you toss out a little gratuitous snark. It's ok, it's the best you can do.

In fact it is completely custom hardware. It is not a simulation of a neural net on conventional technology. It is a direct hardware implementation of a neural network. — apokrisis

It's still conventional computing. Still a physical implementation of a TM. If your friend says he has a computer whose code and/or data can't possibly be backed up, he's lying. What happens when there's a power failure? He types it all in again? I'm aware that there is custom hardware to implement NNs. But it's still based on the conventional model of computation.

Yes, I've spent 40 years being critical of the over-blown claims of computer science. — apokrisis

As have I. I read Dreyfus's What Computers Can't Do many years ago and it's influenced my thinking about all this.

So why are you so hell-bent on convincing me that I'm wrong when I am in full agreement with everything you say except for your tragic misunderstanding of computer science?

So I am basically skeptical of the usual talk of getting close to building "a conscious machine". I know enough about the biology of brains to see how far off any computer system still is. — apokrisis

Which is exactly what I've been saying all along.

Indeed, I would like it if there was an in principle argument for why no mechanical device could ever simulate the necessary biological processes. It would suit my prejudices. So I am just being honest when I confess that there isn't an absolute argument. The effectiveness of NNs suggests that some level of mind-like technology - as good as cockroaches and ants - may be feasible. — apokrisis

I see no disagreement between us here.

And remember where this started - your claim that abstract thoughts are biochemical processes. — apokrisis

It started with you calling me a dualist and then pushing dualistic ideas yourself.

You followed that howler by jumping the other way - saying the mind was in no way the product of informational processes. — apokrisis

It's not, if by informational processes we take the standard contemporary definition in computer science.

This second misstep was based on your very narrow conception of information processing - one rooted in TMs. — apokrisis

If you have a better idea, and not just handwavy misunderstanding, I would like to hear it. If you have figured out how to break the Church-Turing barrier it will make the news because it would refute an 80 year old orthodoxy.

The reason for the unreasonable effectiveness of TMs is that they are the theoretical limit on semiotic encoding. Semiosis depends on symbols. A TM is the conceptually simplest machine for handling symbol strings. — apokrisis

Actually there are much simpler models such as finite automata. But your statement about the limit of semiotic encoding, that's something that I have to go find out more about. It sounds interesting.

A DNA strand can code for a pretty vast array of protein molecules, but that’s it really. Human language can code for a vast array of ideas. That's really powerful as we know. But a TM can implement mathematical algorithms. It can articulate any mathematically-constructable pattern. That is a whole other level of semiosis. — apokrisis

I could write a program that would simulate everything we know about DNA (assuming I took the trouble to learn about DNA). In fact it's the informational basis of life that is the strongest evidence for the point you're trying to make. The next leap is to see how perhaps mind might actually be informational yet not a TM. Or perhaps we're all just programs. It's possible. I don't think so and I don't want to think so, but maybe we're all characters in a Philip K. Dick novel who wake up to discover we're just robots.

So yes. TMs are

really basic. They represent pure syntactic potential, stripped of all physical constraints as well as all semantic. — apokrisis

Yeah yeah. We've both run out of stuff to say.

But then we do have to build b

ack the semantics - add the algorithmic structures - to make TM-based technology do actually useful things. Much like DNA has to code for the kind of neural connectivity that can do actually useful things for organisms. — apokrisis

DNA is the programming of life. But is it the programming of mind? I don't think that discovery's been made yet.

Semiosis recognises the essential continuity here. It sees the ontological difference that codes or syntax makes, the new "unphysical" possibilities they create. — apokrisis

Unphysical. So we're dualists again?

Maybe that's the "physics revolution" you are talking about. I certainly think that it is myself. It explains the information theoretic and thermodynamic turn now happening in fundamental physics I would argue. — apokrisis

The revolution IMO is to break the Church-Turing barrier. We have to find a mode of computation that lets us say that mind is a computation but not a TM. It's my belief we'll need new physics for this.

Fine. I would agree that NNs are not biologically realistic in some fundamental ways. — apokrisis

Then we are fundamentally in agreement.

But also, NNs are an attempt to be more biologically realistic in some important structural or information-processing fashion.[ — apokrisis

Of course. I hope you don't think I'm dismissive of the amazing achievements of weak AI these days. From chess to Go to driving cars to facial recognition.

But isn't it true that just because we can cleverly simulate an approximation of certain aspects of the human mind, that this does not necessarily mean that this is literally how the human mind works?

In other words we've invented flying machines; but that doesn't mean we've discovered the mechanism by which birds fly. On the contrary, we've shown that the way humans make flying machines is different than the way God (or nature) does. And by analogy, perhaps the way humans make thinking machines is different than the way nature does. In which case, NN's can be as clever as you like, but minds are still not NNs. Just like birds aren't jet engines with fixed wings and small bags of salted peanuts.

So this could easily be an argument over whether the glass is half full or half empty. — apokrisis

Humans can build machines that emulate what nature does, but we do it differently than nature does.

That is why the epistemology of NNs demands especial care in a Philosophy of Mind discussion. — apokrisis

Can you explain what the epistemology of NNs means? That went over my head.

Airplanes are stunningly effective at flying, yet birds don't work that way.
— fishfry

But what is the "unreasonably effective" feature they share? Is it an aerofoil wing that creates lift? — apokrisis

Well that's the point. Just because we can make flying machines doesn't mean that nature's flying machines work the same way. And just because we can make thinking machines doesn't mean nature's thinking machines work that way.

I agree that human machines are just basically different from biological organisms. — apokrisis

Well we have to be careful here. If I'm making a physicalist (but not computationalist) argument, then I must admit that we are machines. But we are not computations. I'm making that distinction. We are machines that think, but we are not computations.

However again, you need some actual general metaphysical argument to spell out the precise nature of that difference.p/quote]

Sadly I have none. I am a philosophical ignoramus. My shame knows no bounds. Yet must I have a general metaphysical argument before I can have an opinion about whether minds are algorithms?
— apokrisis

And that is what I'm talking about with biosemiosis, autopoiesis and other "buzzwords". — apokrisis

My complaint about the buzzwords is that you often fail to explain your ideas to me in ways I can understand. And even if I went back to school and got a Ph.D. in philosophy, I might still miss out on Peirce. So if you care to explain your viewpoints I'd learn something.

You need a theory of the distinction if you want to say anything definite on the matter. And you seem quite dismissive of the literature here. — apokrisis

No, only dismissive of your unwillingness to explain things that you know and I don't.

You agree with me that perhaps the explanation of mind must await the next revolution (or two) in physics?
— fishfry

No. I was being sarcastic. — apokrisis

Ah, a crushing disappointment then.

Physics is already undergoing the right kinds of revolution anyway. Thermodynamics is becoming foundational. Physics is becoming information theoretic. Holism and emergence can now be modelled in a variety of ways. — apokrisis

So physics is already pretty much complete, and all we need to do is fill in the details? That's exactly what they thought in 1900, right before the quantum revolution. Surely history teaches us that there are radical paradigm shifts in physics every couple of centuries. The next one might not happen in our lifetimes but it's certain that it will happen sooner or later.

So Newtonian materialism is out-dated. — apokrisis

Just as our current ideas may soon be equally as out-dated.

Existence can be understood as a dissipative process. — apokrisis

What does that mean? I confess to having lived a dissipated life but I don't think that's what you mean.

And that is a framework which biology and neurology slot straight into. — apokrisis

Sure. No disagreement.

Well I would say this shows you don't have an appropriate general metaphysical framework. — apokrisis

To my eternal shame. Must one have a general metaphysical framework in order to have an opinion about whether minds are algorithms? I don't know much about philosophy but I do know a lot about algorithms, and I know that algorithms are literally dumber than rocks. A rock sitting there on the ground has more claim to be a thinking entity than an algorithm does. I don't need to have a general metaphysical framework to know that.

It has to be a central issue if you are arguing either for or against artificial life and mind. — apokrisis

If you are arguing that before I can express an opinion I need to know more about philosophy, this forum would be a lonely place if you applied that standard to everyone. But I do take your point. I'm ignorant of philosophy. I've stated that many times. I don't pretend to know what I don't know.

That is why I urged you to read that Pattee paper. — apokrisis

Sorry I must have missed that. Link again please?

Whatever mind is, it's not a computation.
— fishfry

That's a hand-waving statement, so not much use in a serious debate here. — apokrisis

It's a summary of my strongly held belief, based on a lifetime of having a mind (and occasionally losing it) and an adult lifetime of working with algorithms. Algorithms are much dumber than minds.

At the moment I have

no clue what you even mean by "mind". I get the impression it is probably the standard dualistic substance ontology - a sensing stuff, a bunch of "feels". — apokrisis

Well if you're going to take me down the rabbit hole of the philosophy of mind, I'm sure you know more than I do. But I don't think that my subjective experiences and ability to be in the world as an intelligent human being are the result of an algorithmic process.

So we wouldn't even be on the same page for a serious discussion in terms of a comparison of neurological processes and computational mechanisms. You are likely already convinced that there is no physicalist understanding of what brains do. — apokrisis

How can you say that? Of course there is some physicalist understanding of what brains do, even though our current state of knowledge is quite limited. And since I've said repeatedly that mind [whatever it is] is a function of brain/biochemistry, it follows that there may someday be understanding of it. Why would you think I've said the opposite?

You seem to entirely miss the point. — apokrisis

I answered the literal question you asked. You should ask a more precise question then.

You appear to believe that TMs completely define all possible notions of computation, information ... — apokrisis

That's my understanding of the Church-Turing thesis. If you have a different idea I'd be interested to hear it.

and semiosis. — apokrisis

I confess I don't understand the meaning of that word, and looking it up from time to time doesn't seem to help.

And so any question about "information processes" or "processing architecture" gets immediately translated into a TM view. — apokrisis

That's Church-Turing, and nobody has figured out how to defined a model of computation or information processing that violates it by not being a TM. You are very casually ignoring this point and I'd like to you to comment on it.

But just maybe TMs are a very tiny fragment of a much larger landscape. — apokrisis

YES!! But not according to contemporary theory, because we know of no such larger computational landscape. That's exactly why I think we need a revolution in physics that shows us how to go past TMs into some mode of computation that is more powerful than a TM.

Of course, there is something immensely powerful about TMs in being (almost) pure syntax/no semantics. In short, they are (near) perfect machines. They represent a completely constrained and rule-bound universe. And so they leave out all the "messiness" of the physical and biological world. — apokrisis

Yes. You are eloquently expressing my very point.

They leave out, in fact, information as traditionally understood - ie: information as meaning. — apokrisis

Aha. Here we have a point of divergence in our worldviews. Information processing is what a TM does, by definition. Flipping bits according to an algorithm.

When you say "information is meaning," that's something I absolutely deny by my definition of information. A bitstring carries information but it does not carry meaning. Only a human can say what the computation "means." Searle's intensionality. The Chinese room manipulates information but it has no notion of what any of it means. That's the entire point. One with which you sometimes seem to agree.

I don't think you can claim that information is meaning. Information is meaningless. Humans give meaning to information. Isn't that true? If I say I saw a "cat," the symbols by themselves convey know meaning. It's humans, English-speaking ones at that, who say that the word cat stands for a furry domesticated mammal that's not a dog.

It is like the syntax of Boolean logic. To reconnect to the OP, there is something "unreasonably effective" about reaching the limits on a de-semanticised view of reality - one where we just model reality in terms of its simplest syntactical rules. — apokrisis

Well you can't model all of reality with algorithms. Only certain aspects of it. The map is not the territory and the model is not the thing itself.

So TMs and Boolean logic idealise reality. They abstract away the materiality or particularity of physicalist semantics to arrive at the simplest, sparest, syntactical forms. — apokrisis

Yes. We're 100% in agreement here. Algorithms abstract certain aspects of reality.

Great. Defining the ultimate limits of reality is what it is all about. But maybe there is such a thing as over-simplification. — apokrisis

Like claiming that because NNs can do clever tricks like playing Go, that the human mind must be an NN. Now THAT is over simplification.

Machines are rule-bound artificial systems. — apokrisis

If by machines you mean computations. If I am making a physicalist argument I have to claim that humans are machines but not computations.

And so they can't construct themselves. They can't give themselves purposes , they don't have autonomy. Machines are useful to us humans as it is we who get to design the machines, build them to serve some purpose. — apokrisis

Yes. Humans provide the meaning. Information by itself has no meaning. You are agreeing with me again. Been happening a lot lately!!

However organisms are systems with evolved designs and purposes. They have an irreducible causal complexity. And that is their "secret". There is always semantics - or semiosis - involved. — apokrisis

YES!!!!!!!!! That's what I'm saying. Minds go way beyond algorithms. You are totally agreeing with me.

So the whole mechanical paradigm of nature is flawed at root if it excludes the basic causal complexity of real living and minding creatures. — apokrisis

Ah. No.The computational paradigm of nature is flawed. We need a breakthrough in figuring out physical explanations how meat machines like us can have minds yet not be computations. We need a revolution in physics, we need to break through the Church-Turing constraint, we need to figure out the nature of a machine that does more than computing.

We can see that TMs and Boolean logic leave out formal and final cause. Well they leave out material cause as well. All they are is pure syntax. They can be used - by an organism with a purpose and a design - to represent a formal system of entailment. They can capture the description of a syntactic structure. But being such a rarified representation of reality, the computational patterns that result have an extreme real-world brittleness. — apokrisis

Right. Humans aren't computations. After all this you're agreeing with me.

But then you say well yes humans aren't TMs but they are NN's. And you won't come to terms with the fact that NNs are a special case of TMs. NNs are algorithms. So you aren't gaining anything by claiming that humans are NNs and not TMs. We keep going over this point.

In practice, any computer program or computer circuit is incredibly prone to bugs. Just one broken link and the whole finite state automata grinds to a halt. — apokrisis

Humans too. Disease, death. All machines are imperfect. The solar system probably isn't stable. [Open question at the moment]. The universe will someday collapse or else expand into eternal cold. Reality is highly imperfect. What point are you making?

Organisms by contrasts not only thrive on physical instability, their very existence depends on it. Life and mind arise on the "edge of chaos" as where things are perched on the verge of falling apart, that is where the slightest extra informational nudge can push them instead into falling together. — apokrisis

Well you're arguing that humans aren't computations, which I've been saying for several posts now. You agree with me. I'm gratified.

But if you want to claim that humans are NN's, you have no argument because NN's are TMs.

So life and mind thrive on material dynamism. TMs and other machines only flourish where all the uncertainties of the real world have been managed out of existence by their human designers. Mindless routine following becomes possible where minds have made that a safe thing to do. — apokrisis

So minds aren't algorithms. You are making my point for me.

Anyway, my point is that any biologist or neurologist would understand that computers and organisms are different in this fundamental way. There is a reason why TMs are both such "universal" machines, and also the most biologically helpless of physical structures. — apokrisis

Right. Right. Right. Right. So the question is: What exactly are we doing that goes beyond mere algorithms? That's the question. You haven't got an answer. I haven't either. But we agree that humans are not computations. And that NNs are computations. So humans aren't NNs either. We don't understand the mechanism by which humans operate in the world.

There is a general metaphysical paradigm that accounts for why brains aren't computers, and yet also, we could build computers that start to have some of that biological realism designed into them. — apokrisis

Sure, the chess playing and Go playing and automobile driving and face recognizing algorithms are very impressive these days. That doesn't tell us anything about minds.

A "true" NN has to learn for itself. That's both its advantage and disadvantage. It is essentially a black box to its human owner. — apokrisis

So you are distinguishing between the fake NN's that are merely reorganized ways of implementing TMs' and "true" NNs that are some theoretical construct that are NOT the NNs of current theory. That's it right there. You admit that you are not talking about NNs as currently understood. You are using "NN" to mean whatever it is that humans do, that's not a computation.

I know a "mad genius" who has developed one of the currently most advanced neural network computers in the world. It runs his company for him. But he has no clue how it works inside. It grew its own "programme". And if it failed, he couldn't transfer its software to another hardware rack. He can't even do a memory back-up as such. — apokrisis

I call bs on that. Not that you don't know some guy, but that he can't back up his system. If it's built out of processors and memory devices then he can back them up just fine with perfectly conventional techniques. There is no magic hardware paradigm. There are only different ways of organizing the bit-flipping activity.

But because the memory doesn't work like a traditional TM device, and instead is more like a brain, that is not such a problem as it has natural fault tolerance. The failure of individual links can't corrupt the whole system. — apokrisis

I spent years working on fault-tolerant systems. I think your friend is messing with you. Error-correcting codes, fault-tolerance via hardware redundancy, via voting, via consensus algorithms, are all well-studied ideas since the 1970's. Cryptocurrencies fall into that space, they're a brilliant solution to the problem of distributed consensus on adversarial networks.

Your friend doesn't have a computer that's "more like a brain." He's just taking advantage of his philosophically trained friend who thinks computers are magic, and funnin' ya.

So yep, the whole NN issue isn't clear-cut. But the field has a history now. Computer science has been exploring the degree to which neurologically realistic architectures can lead to a more organismic notion of a machine. — apokrisis

Absolutely. But they have not broken the Church-Turing barrier. They have not implemented a mind. And they have not by any stretch of the imagination proved that minds are NNs, any more than a 747 proves that a bird is like an airplane.

We already have a mathematical definition of the most non-organismic one - a TM/Boolean one - as the theoretical limit of a machine that is all syntax, no semantics. So the next question for the engineers is how to start building back in some useful biological realism. And that in turn demands a general metaphysical theory about how to define "semantic processing", or semiosis. — apokrisis

Ok, you're arguing that the AI community needs to learn more philosophy. A traditional argument. But it still doesn't mean that minds are algorithms or NNs. It only means that NNs are better at building thinking machines than earlier computing paradigms.


I do hope you agree that building artificial machines that exhibit "thinking" in constrained domains is one thing; and that claiming that the human mind works that same way is quite another.

There are lot of idiots making videos on YouTube. — tom

Yes but this guy had a British accent. And a beard.

Your suggestion that the physics just isn't valid in the region in question seems to make more sense than saying that the density there is infinite. — Michael Ossipoff

I really think so but if you look at the multiverse thread on this forum or in many other online conversations and presentations, a lot of people think physical infinities are real. I think the physics popularizers are spreading a lot of confusion. Some people in the multiverse thread are very seriously convinced that there are literally and actually an uncountable infinity of multiverses. I still don't believe that can be true. I think a lot of people are using infinity incorrectly in physical arguments. But I can't get to the bottom of it because even the highly credible PBS physics videos are spreading the same confusion.

It seems curious that it was only just a few posts back that you were trumpeting the mind-like abilities of NNs. — apokrisis

I oppose that notion every chance I get. It's not possible that I expressed such an opinion. Two possibilities:

* You misunderstood something I wrote; or

* I expressed myself so badly that I communicated the opposite of what I intended.

One's just as likely as the other.

But no, NN's are not "mind-like." It's starting to become my mission in life to explain to people why NN's are *NOT* "mind-like." To the extent that I fail to make a convincing argument, I need to work on my argument. To the extent that I'm giving you the opposite impression of what I'm actually trying to say, I have to work harder not to do that.

So if they were inspired by the "computational" structure of the brain, it is surprising they should indeed be so effective at machine learning, and yet the brain itself would not function along these lines. — apokrisis

Airplanes are stunningly effective at flying, yet birds don't work that way.

Sounds legit. — apokrisis

You agree with me that perhaps the explanation of mind must await the next revolution (or two) in physics? If you agreed with that point you'd be halfway to agreeing with the rest of my thesis. There's a lot we don't know.

So that is a retraction of your original statement coupled to a backtrack on the retraction? — apokrisis

You asked me if I thought biochemistry was both necessary and sufficient for mind. I said it's neither necessary nor sufficient. You are seeing this as a retraction? How so?

It is the structure of the matter that matters and not the particular matter. — apokrisis

I don't know. Perhaps it has to be biological. Perhaps not. I don't think it's relevant to my argument. Whatever mind is, it's not a computation. But I take no position on whether it has to be biological or not. Is that more clear? I don't know what you think I'm retracting.

But you don't want to say the structure implements any kind of informational process? — apokrisis

Hmmm ... that's kind of an interesting technical question. So there's the neural wetware of the brain, and you are asking me if it is possible that SOME informational process is implemented.

Um ... well ... sure. Why not. If I blink my eyes at you in morse code I'm digitizing my thoughts. For that matter, I can execute the Euclidean algorithm with pencil and paper. So yes, wetware can certainly implement computational processes. But not everything wetware does can be explained by a computation.

Do you really want to argue that Searle thinks "biochemical processes" are a necessary and sufficient condition of conscious thought? — apokrisis

Now that you mention it, I can narrow down my claim. There are really two issues here: What I think about mind; and what I think Searle thinks about mind.

My belief in the correctness of what I think is in no way affected by the state of my knowledge about what Searle thinks.

My thesis here is that mind arises from a physical process in the brain; but that it is not a computational process in any way that we currently understand computation. It's not a TM or an NN or a cellular automata or anything else along those lines.

I don't know what the actual mechanism might be. I'm not sure even what it means to say that there is a process that follows physical law but that is not a computation. I think these are matters for future geniuses to work out. I think this will take another revolution in physics.

Now as it happens, the way I got my opinion is that I read something Searle wrote, or perhaps said in a video. I may well have misunderstood what he said; but in any event it sparked this thesis in my mind, or gave clarity to some vaguer notions I'd been having.

So Searle is the inspiration for my opinion but may not himself actually share my opinion. But really -- isn't that classic Searle? For decades people have been misunderstanding the CRA yet have been intellectually inspired by their own misunderstandings.

ps -- Oh wait you said necessary and sufficient. No I don't think biochemistry is necessary. Or sufficient. It just "happens to be the case" in this instance. It's possible that machinery might become conscious, so biochemistry's not necessary. And there's plenty of biochemical matter walking around that's not particularly conscious, so biochemistry is not sufficient.

But more recently, it occurs to me that there's really something ridiculous about the notion of places of infinite matter-density scattered here and there around us. Infinite density in our physical world is nonsensical. — Michael Ossipoff

Are you starting to come around to my point of view?

But intuitively I expect that the universe is infinite. — Michael Ossipoff

Or not? I can't square those two statements.

I'm going to look into this question. What the physicists really think about the singularities where the equations break down.

Wasn't this the big deal with renormalization? They had these equations with infinities in them and Feynman and a couple of other guys (Schwinger and Tomonaga) got the Nobel prize for figuring out to finesse their way around the infinities? I confess that's all I know about it, wish I knew more.

One more thought I wanted to toss out is that there's an intermediate idea where something could be unbounded. For any large energy level you can name, there's a small region around the singularity where the energy exceeds that level. You can make the energy as large (but still finite) as you want, by taking smaller neighborhoods of the singularity. But it's never actually infinity. The energy level is always finite.

An analogy is the function f(x) = 1/x for positive real numbers x. Can you make 1/x greater than a million? Yes. Greater than a billion? Yes. You can make 1/x as large as you like, simply by letting x be close enough to zero. But 1/x is always some finite number, even though it's a large one. It is never actually infinity.

I suspect that perhaps the physicists really mean something along those lines. They say infinite but if they had paid better attention in math class they'd say unbounded.

Just a guess. I'm going to look into this.

But the problem was you began this by claiming biochemistry is capable of things like understanding Chinese. — apokrisis

That's my understanding of Searle's position as well. The mechanism remains to be discovered.

Nope. I made the point that humans and NNs can emulate TMs. — apokrisis

Oh I quite agree with that. I can take a pencil and paper and step through a program. It's a common debugging technique. And you're right, that doesn't make me a TM. But I can do many things that CAN'T be emulated by a TM. Like understand Chinese. If I could understand Chinese. That's one of Searle's points that he's made over the years. When he speaks English he's doing something very different in character from what he's doing when he speaks Chinese using the symbolic rules.

You only turn anything I say back to front anyway. — apokrisis

Peace brother. I'm out.

But most physicists must not either, because they're nearly unanimous about there being black-holes in which there's matter with infinite density. — Michael Ossipoff

So I've heard. I just watched a Youtube video last night in which the speaker made that exact same point, that black holes have infinite density.

By the way these are the PBS Space Time videos and I highly recommend them.

https://www.youtube.com/channel/UC7_gcs09iThXybpVgjHZ_7g

Now there are three cases as I see them.

1: When speakers say that a singularity has infinite energy, they are speaking loosely and meaning that the equations break down and we don't really know what happens; or

2: They truly believe that a state of actually infinite energy can exist in our world, and someone should tell them that it's just the equations breaking down at a mathematical singularity and not an actual infinity of energy; or

3: They believe there's an actually infinite energy state, and they're right, and I'm simply wrong and not up to speed on these latest developments.

Now I really believe the truth is #1 and $2 and most definitely not #3. There are singularities in the equations where there's a division by zero. We don't even need crazy quantum theory to illustrate the idea. Just take good old classical vanilla Newtonian gravity, m1*m2/r-squared. Since we have r-squared in the denominator, if the radius is zero the gravitational energy is infinite. Is this literally true? No, it's just that either there aren't actually any point masses in the world (which there aren't) or that if there are, the gravitational equation is simply not applicable there.

That's what I think this is about. That when a physicist says that a black hole singularity is a point-mass with infinite energy, they're speaking figuratively. Their literal meaning is: "There's a zero in the denominator and the equation blows up."

If someone has a genuine reference to the contrary, I'd be grateful for the link. But just someone in a video or paper saying that there are point masses with infinite energy isn't enough. I would need to be convinced they really mean it literally and have physical proof that there is any such thing in the world as an actual point mass with an infinite energy potential. I don't think any physicist actually believes that but like I say, if I'm wrong someone give me a solid link please.

So you are making the point that a NN somehow implements semantics? That's wrong. We'll have to agree to disagree here. And once again you have an insult but not a substantive argument. Everyone here can see that. And since I've referenced Searle twice you'd have to know that I'm thoroughly familiar with the CRA and the surrounding arguments.

Are you actually incapable of making a substantive argument? "You are wrong because Point 1, Point 2, and Point 3?" You simply can't do it?

Make a substantive argument or show everyone on this site that you're not capable of doing so.

Are you actually making the claim that even though a NN can be emulated by a TM, the NN somehow implements semantics? That's so wrong ... well it's wrong. Leave it at that. A thing that can be implemented or emulated as an algorithm is an algorithm. But if that's your argument, so be it. But you haven't provided an argument. You do not possess the ability to outline a rational argument. You make a claim but you provide no substantive argument.

And for what it's worth, you completely miss the point of the CRA. If you think an NN that can be emulated by a TM can nevertheless embody semantics, you simply have no idea what the CRA says.

If you ever had general anesthesia you'd have personal experience that sleep is a much higher state of consciousness than anesthesia. When you're asleep you are aware of sounds and will wake up if you hear something unfamiliar. Dreaming can be just as realistic as being awake. But when you're in surgery you are gone. You do not exist. They turn you off then they turn you back on. Sleep is closer to waking than it is to anesthesia.

NYT wrote about this a while back. http://www.nytimes.com/2013/12/15/magazine/what-anesthesia-can-teach-us-about-consciousness.html

And I have investigated neural nets. — apokrisis

Then you must have a substantive response to my point that if mind is an informational function of a neural net executing in the brain, then it can be implemented as a Turing machine. So it's not logically consistent to claim that mind is a neural net without admitting that your position requires you to also agree that mind must be a TM.

That is:

* If you claim that mind is a neural net; then you must also agree that mind is a TM.

I could well be wrong. If you have a substantive response to my point then perhaps I'll learn something. If you don't, you don't.

Hmm. So what I have got from this exchange is that you struggle to keep track of your own arguments because you don't actually have a well constructed metaphysical position. And when you encounter someone who does, you bluster and ad hom. Nice. — apokrisis

I'd love to chat with you without the snark. This isn't fun. I'm going to withdraw. Suggest you investigate the relationship between neural nets and Turing machines. I did a little research since my last post and apparently neural nets are computationally weaker than TMs. Some neural nets are Turing complete but some aren't. And of course none have computational abilities beyond the TM, since we know of no such thing in the physical world.

All the best.

So, it can't possibly be true because it would be absurd. That's a terrible argument — T Clark

Oh I totally agree. Set-theoretical physics is absurd till we discover it's not. I know that. When professor so-and-so from Helsinki counts the points in a line next week and yes, "Yup. It's the same as the number of reals, and here's the physical experiment that shows that," then the idea goes from absurd to true, as physical ideas often go.

But I do say that the current absurdity of set-theoretic physics is a weak meta-argument against physical actual infinity. It's a valid argument till we discover it's not. If someone tells me they believe in physical infinity, they need to answer the question of whether by infinity they mean set-theoretic infinity. And the infinity believers never have a good answer for that. So I have at least a meta-argument that I'd love to hear a substantive response to someday. I've heard Tegmark considers something along these lines but I'm not familiar enough with the specifics.

There's a pretty good link here. https://mathoverflow.net/questions/201216/applications-of-set-theory-in-physics

My point is that that the infinite multiverse folks have to account for set theory or explain why they don't have to. This is rarely if ever addressed in the literature of the infinitists.

I ended up with about 10 different crypto products — Ian

@Ian How many different exchanges are you on? It seems that for each coin, you have to sign up on some obscure exchange that wants your ID and personal info. How do you manage the mechanics and also the security of dealing with many exchanges? Or did you find one exchange that has a lot of coins?

Also, if the universe turns out to be infinite, then maybe physics or astronomy will someday be able to say things that involve the super-huge numbers. — Michael Ossipoff

As I'm fond of pointing out, if the universe instantiates actual infinity, then set theory becomes an experimental science. Physics postdocs would apply for grants to count the number of points in a line segment, to investigate the continuum hypothesis. Large cardinal axioms would have deterministic truth values subject to theoretical derivation and experimental confirmation.

The idea that set theory could ever be an experimental science is so absurd as to provide a strong argument against the existence of an actual infinity in the world. Likewise to the idea of an infinite metaverse. Same argument.

Or, equally interesting, someone would need to prove that the universe instantiates infinity, but that set theory doesn't apply for some reason. That set theoretical infinity is the wrong theory of infinity to describe the physically infinite.

Either way, anyone who thinks the universe instantiates infinity needs to deal with these considerations.

Much of your argument centers around your belief that neural networks are a different mode of computation than Turing machines. I do not believe you are correct but there's a fair amount of confusion of this point online. Before replying to your specific points I'll lay out my understanding, and if you or anyone else can clarify or amend my thoughts, please do.

* First, there are Turing machines (TMs). The Church-Turing thesis says that anything we can compute, can be computed by a TM. This is an eighty year old core idea in computer science that has never been refuted. If tomorrow morning professor so-and-so in Helsinki publishes a paper called, "A mode of computation that's not a TM," it would rock the computer science world and it would make the popular media. "80 year old computer theory debunked," etc.

This hasn't happened. As far as anyone in the world knows, everything that we would call a computation can be implemented as a TM.

* Real-world neural nets are TMs. This must be true; if not, Church-Turing would be broken and we'd all have heard about it.

What is a neural net (NN)? It consists of a set of nodes, each assigned a numeric weight. Then we apply some logic: If the weight of this node is such and so and its immediate neighbors are such and so and their neighbors are such and so, then do something. This is perfectly conventional programming. The greatest weak AI in the world, such as AlphaGo Zero, is a conventional computer program implemented on conventional hardware. A real-world implementation of a TM.

To be sure, neural nets are very clever ways go organize a conventional computation. But they are conventional computations nonetheless.

* Theorestical neural nets. In the abstract model, the numeric weights of the nodes can be real numbers. Since in general it takes an infinite amount of information to specify a real number, there are no real-world implementations of theoretical NNs. I'm not aware of the theory of computation behind NN and how they relate to Church-Turing.

* Wetware NNs such as the brain. Since brains are physical, even if they are NN's, they are TMs. Moreover, the idea that the mind implemented by the brain is a NN is a speculative idea. Nobody has proof. There's no reason to believe a mind/brain is a TM and plenty of reasons to doubt it.

I'm definitely not claiming computationalism - or at least not Turing machine computation as you seem to suggest. The mainstream neuroscience view - since Sherrington's "enchanted loom" or Hebbs's learning networks - is some kind of neural net form of "computation". — apokrisis

Any physical implmentation of a NN is a TM. If you disagree then you either believe the Church-Turing thesis has been falsified (which it hasn't) or that the brain contains nodes that can represent arbitrary real numbers (absurd) or you have some other justification for your claim. Please provide such justification.

As far as what constitutes mainstream neuroscience, I'm not qualified to judge. I hope you would agree that the opinions of neuroscientists donot constitute a refutation of Church-Turing, merely ignorance of it.

And more to the point, it is mainstream to emphasise that the brain is involved in informational activity, not merely biochemical activity. — apokrisis

It may be mainstream speculation, but it is certainly not mainstream established fact. But again, why are you so hung up on the opinions of neuroscientists? Since any real-world NN must be implemented as a TM, the burden is on you to explain yourself.

Otherwise why is neuroscience interested in discovering the secrets of the neural code, or brain's processing architecture? — apokrisis

How does that prove a real-world NN isn't a TM? You are committed to your argumentum ad populum but you don't seem to be able to reason on your own.

It knows the biophysics of what makes a neuron fire. But how that firing then represents or symbolises something with felt meaning is the big question. — apokrisis

Oh, I thought it was a computer program as you keep claiming. Or a NN, which is just a particular kind of computer program. Now you admit that we DON'T understand how firing neurons give rise to mind. Well then at last we agree.

And that can only be approached in terms of something other than a biochemical materialism. — apokrisis

Why?

It demands a semiotic or information theoretic framework. — apokrisis

Why?

Which in turn has already considered Turing computation and found it not the answer. — apokrisis

Funny you should say that, since many people (wrongly) believe the mind is literally a TM computation. But if the mind is ANY kind of computation, you have to explain how it could be a computation yet not be a TM. This point does not seem to be appreciated in the literature

So broadly speaking, neuroscientists think thoughts are informational processes and not biochemical events. — apokrisis

Some do, some don't. Some scientists used to think heat was caused by phlogiston. What of it? You are continually trying to substitute claims about the opinions of some neuroscientists for thinking things through on your own.

At the same time, they don't think the brain is literally a Turing machine or programmable computer. That might be a helpful analogy, like calling the eye a camera. But just as quickly, the caveats would begin. — apokrisis

I'm glad that you agree with me on at least this point. The problem is that there is no other mode of computation as far as we know.

Computers are machines. They are devices that construct patterns. So yes, of course, human minds seem to operate in a fundamentally different fashion. We can grasp the whole of some pattern. We can understand it "organically" as a system of constraints, rather than as an atomistic construction. — apokrisis

If you agree with me why do you keep trying to disagree? I have no idea what your point is. You go back and forth on your own opinion.

Our abductive or intuitive approach to reasoning begins with this ability to see the whole that "stands behind" the part. We can make inferences to the best explanation. And then, having framed an axiom or hypothesis, we are also quite good at deducing consequences and confirming by observation. — apokrisis

Yes. Which neither confirms nor denies that mind is a computation, since even the weak AI's are quite impressive these days in seeing the whole, as in facial recognition.

So when it comes to mathematical truth, that is what we think we are doing. We notice something about the world. We then leap towards some rational principle that could "stand behind" this something as its more general constraint. — apokrisis

You are eloquently agreeing with my point.

Turing machines are really bad at making such a holistic generalisation. — apokrisis

These days, strangely and counterintuitively, TMs are incredibly good at generalization and "gestalt," at least in constrained domains. AlphaGo Zero is mind-blowing in its philosophical implications and AlphaGo Zero is a TM.

Neural network computers are our attempt to build machines that are good at implementing this precise inferential leap. — apokrisis

Agreed. NN's are a clever way of organizing a conventional TM. But every NN is implemented as a TM. They're computer programs implemented on conventional hardware. Please tell me you understand this point. There are no magic NN computers. They're NN algorithms implemented on TMs.

Yeah. I don't claim complete substrate independence. But then my "computationalism" is a semiotic or embodied one. The whole point is that it hinges on a separation which then allows an interaction. — apokrisis

If it's a computation then it's a TM. You need to deal with this point.

A Turing machine does not self-replicate. — apokrisis

Neither does a person without children. What does that have to do with the subject at hand? Red herring.

A Turing machine does not have to manage its material flows or compete with other TMs. — apokrisis

Ever hear of core wars? Oldtime hackers used to write programs that would compete with each other for machine resources. Of course TMs can be programmed to compete with other TMs.

But a living thing is all about regulating its physics with information. — apokrisis

You are confusing the issue by bringing up living things. Nothing to do with the subject at hand.

So an independence from physical substrate (an epistemic cut) is required by life and mind. — apokrisis

I don't see why. Searle believes mind is a function of the physical brain, just not a computational one. You don't need mysticism or duality.

But only so as to be able to regulate that physics - bend it in the direction which is making the autopoietic wholeness that is "an organism". — apokrisis

Autopoeietic. Whatever. What's that mean? I could look it up but I'd like you to explain this in your own words what your point is. NNs are TMs and if you think the mind is a computation then you think the mind is a TM. You have to deal with that by denying it (with evidence) or accepting it.

Yes, you can measure one side of the computational story in terms of entropy production. But how do you measure the other side of the story in terms of "negentropy" production? The fact that your computer runs either hotter or colder doesn't say much about whether its eventual output is righter or wronger. — apokrisis

I don't follow the relevance of that para.

We are labouring the point. If you really can't see the difference between syntax and semantics by now, things are likely hopeless. — apokrisis

If you don't see the difference between fish and bicycles, things are likely hopeless. WTF? You think I don't know the difference between syntax and semantics? You're flailing.

You keep talking about the physical events as if they are the informational processes. — apokrisis

No no. But informational processes ARE physical events. Running Euclid's algorithm in a supercomputer or with pencil and paper are physical processes [not events]. They require energy and output heat. The description of the algorithm, the program, does not compute anything.

Of course a neuron or a transistor or a membrane receptor or a speedometer can be described in terms of their "physics". But it is hardly the level of description that explains "the process" which we are interested in. — apokrisis

It doesn't explain mind. It only points out that you don't need duality to explain computation. Computation is a physical process. [And not the converse as you tried to claim I said earlier].

To reduce functional or informational processes to atomistic material events becomes a nonsense. — apokrisis

Why? Who's the dualist now? What kind of mystical process are you believing in? If my mind is not a function of my physical brain, what do you think it is, exactly? Are you a dualist or not?

Especially for true computationalism. The only time we are interested in the physics of a logic gate is when it doesn't behave like a logic gate - that is when it has some uncontrolled physical process going on. — apokrisis

Uncontrolled physical process? You know you are not speaking coherently these past few paragraphs. You're flailing randomly.

So algorithms are extreme mechanistic dualism in fact. — apokrisis

Dualism, why? I program a computer to add 2 + 2, it outputs 4. Where is the dualism? The computer inputs electricity, outputs heat, and performs a computation. I really don't understand your mysticism around this very commonplace and well-understood phenomenon of computation.

You don't even have to run a programme for it to "have a result". — apokrisis

That's just wrong. If I write down the Euclidean algorithm, it has no result. Only when I implement the program on a physical substrate and execute the algorithm does it produce a result. If you don't understand this there really is nothing to talk about.

The result could only be different if the physics of the real world somehow intruded, And then we would say the computer had a bug. It over-heated or something. — apokrisis

What of it? You just claimed a program need not be executed to produce a result. That's "not even wrong." Its a profound misunderstanding of computation.

And maths is kind of like that. We imagine it as transcendent and eternal truths - things that would be true without ever needing the reality of physical instantiation. Pure information. — apokrisis

Ok we're Platonists today. Fair enough. But where do these truths live? You are quite the mystic.

It is crazy to talk of Euclidean maths as existing in some geezer's long dead brain. — apokrisis

Really? Crazy? That the best you can do in lieu of an actual argument? You haven't made a single rational argument in this entire post. I don't think you have one.

Why do you interpret that as a mystical statement? My point was that it is not a mystery because it is what you would expect from principles of physicalist symmetry. If every kind of difference gets cancelled (as the negatives erase the positives) then what you are left with is the mid-point balance. It would be natural to expect "flatness" as the emergent limit state. — apokrisis

Nonsense. Mathematical nonsense and physical nonsense. You must have missed the Einstenian revolution. It's not 1900 anymore.

Well it is your choice to ignore what we know to be fundamental in preference for what we know to be emergent. — apokrisis

Ah, emergence. Another murky concept. Hydrogen's not wet and oxygen's not wet but water is wet. Zowie, cosmic.

I honestly have no idea what you are going on about. I really don't think you are making any sense at all.

Fine. The philosophical issue here is not the pragmatics of mathematical research. And I even agree that mathematical research - in being an informational theoretic exercise ... — apokrisis

Didn't I already remind you earlier that Gödel disproved that math is an information-theoretic exercise? Why are you doubling down on a claim I've already falsified?

Maths doesn't really want to even concern itself with geometry - the physical constraints of space - let alone with actual materiality, or the constraints of energy, the possibilities of change. So - as institutional habit - integers are as real as rocks. — apokrisis

You seem to be back in 1840, railing against the great discovery of non-Euclidean geometry. Is that your complaint? That math isn't physics? I'm sure the physicists agree with you.

Except they are then ... ideas? Constructs? Thoughts in the head? — apokrisis

The nature of mathematical truth is indeed an open question.

You seem to want it both ways. And that winds up in Platonism. — apokrisis

I just want you to say something that's reasonably on topic and that makes some sort of sense. I have no idea what you're going on about here.

That is why my own position is the semiotic one where the integers are the ideal limits on materiality. — apokrisis

"the integers are the ideal limits on materiality" -- This is supposed to make logical sense to me? Is this some sort of postmodern theory? I confess I don't take postmodern mathematical musings very seriously. Perhaps you do. If you would take the time to explain what you mean by "the integers are the ideal limits on materiality" then perhaps I'd learn something.

That is a formula of words that both accepts a strong difference and a strong connection between the two sides of the semiotic equation. Information is real if it is causal. And being an actual limit on material freedom is pretty clearly causal. — apokrisis

You sound like a raving postmodernist. Perhaps you are a postmodernist and I'm insuffiently appreciative of that point of view. That may well be the case.

See earlier where I spoke about abductive reasoning and our ability to make inferential leaps. Gödel validates my approach here. The failure of logical atomism is the solid ground for the holist. It is why a semiotic approach to reality is justified. — apokrisis

Semiotic. Whatever. Explain yourself clearly if you can. Can you?

You mentioned pi. I am just highlighting how the usual woo-woo aspect - the fact that there is just this "one number" picked at random out of all the numbers on the number-line - masks a bigger story. The woo-woo evaporates when you see there is a "material" process that picks out a value for "being flat". Two kinds of possible curvature had a mid-point balance. Pi is a number that emerges due to something more holistic going on. The fact that it emerges "right there" on the number-line is not some kind of weird magic. — apokrisis

Tell me something. What is the true value of 3? And why does it emerge "right there" on the number line, halfway between 2 and 4?

It is even easier to see with other constant like e that are directly derived from growth processes. There the contrasting actions that produce the emergent ratio are in plain sight. It is funny that e should be 2.71828. — apokrisis

It's hilarious.

But then that becomes obvious when it is realised that growth always has to start from some thing that is just itself 1. There is no reason to think of e as anything but natural after that. — apokrisis

Mystical word salad.

But I am not Kantian, except in a loose sense. I'm Peircean in the way Peirce fixed Kant. — apokrisis

Maybe we better not go there. You remember how that went last time. Although I suspect this is the problem. You are arguing from a very particular point of view. But you are not willing or able to explain yourself. So everything that anyone says is wrong from your point of view, and you're right, and you're condescending, but you can't explain your ideas in everyday English. And in my experience, you don't really understand a lot of the ideas whose terminology you carelessly sling around.

And I'm arguing flatness is special as the mid-point of opposing extremes of curvature. It has physically important properties too. Only flat geometries preserve invariance under transformations of scale. That is a really important emergent property when it comes to things like Universes. — apokrisis

Oh to be back in 1840 when Euclidian geometry was given to us by God.

And as I repeat, it is very important metaphysically that absolute scale invariance only appears at a particular numeric value of pi. That is how a Universe is even possible. — apokrisis

What is the specific numeric value of 3? I already explained to you that pi is a particular real number whose value does not change and has nothing to do with geometry.

So you are focused on the triviality of pi being given some particular position on the number line - look guys, its 3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408 ...

And that is what makes folk go woo. It seems both weirdly specific and weirdly random. There seems no natural reason for the value. — apokrisis

What is the natural reason for the value of 3?

But it's a ratio derived from the radius being granted as the natural unit. Let's call the radius 1. Let's get a grip on this weird thing called curvature by starting with the "most natural part of the story" - a line segment. That gets to be "1" on the number-line. — apokrisis

Bearing in mind that the unit distance is arbitrary. A linear scaling factor would make no difference.

Well, as I say, once mathematicians woke up to the fact that flatness was a rather special case of curvature, and once physicists in turn woke up to the fact that scale invariance was essential to any kind of workable Universe (its called rather grandly the cosmological principle), well, maybe it is the ratio that should be called "1". A straight line segment is only a natural unit in the context of an already flat space which supports unlimited scale transformations. It depends on the emergent fact of parallel lines or infinite rays being an actual possibility. — apokrisis

I have no doubt that what you're saying makes perfect sense to you. It makes no sense to me. I don't get where you're coming from.

I am being anti-mystical in pointing out the very physical basis of pi as a number. It is a ratio that picks out a critical geometric balance. — apokrisis

Even if I grant your point, what of it? Why are you going on about pi?

The number 3 is trivial by comparison. — apokrisis

Then explain to me what mystical geometric balance causes 3 to have the exact value that is has.

Well there are physical arguments for why the geometry of universes are optimal if they have just three orthogonal spatial directions. But 3 as a member of the integers has no numeric specialness by design. The special or natural numbers are 1 and 0. We see this in the symmetries captured by identity operations. There is something basic or universal when we hit the bedrock that is a symmetry or invariance. — apokrisis

Look, maybe Pearce said all this. I haven't the knowledge to comment. You seem to know a lot about this, or at least you know the buzzwords. It's pointless to argue with you about it.

You would call it a mystical fact perhaps. I see it as quite reasonable and self-explanatory. — apokrisis

I can no longer converse with you on this point.

Nope. At least not your notion of computation as Turing machine/programmable computation. — apokrisis

What is your model of computation? And how do you square it with the Church-Turing thesis?

I take an information theoretic perspective. And more specifically, a semiotic one. In technology terms, neural networks come the closest to implementing that notion of computation. — apokrisis

Yes and any NN that can exist in the physical world is a TM. You have to refute this or accept it. I'm perfectly willing to be shown wrong, since I'd learn something. Do it.

And numbers vs rocks is a distinction that relies on a classical metaphysics - one in which the divide between observers and observables does not present an epistemic difficulty. The epistemic cut - the necessary separation of the information from the physics - can be treated as an ontological fact. — apokrisis

You are the buzzword king. You do have a hard time translating your buzzwords into ideas that you can explain to people.

So my positions on both "mind is a computation" and "reality is classical" are the same. — apokrisis

If mind is a computation and if it's implemented on a physical brain, then it's a TM.

Semiotics starts from the view that there is no fundamental ontic division of observers and observables. But that is also the division which must emerge via some epistemic cut. It is the basis of intelligibility. And even the Universe can only exist to the degree it hangs together in intelligible fashion. — apokrisis

I yield to your facility with buzzwords.

Hence why maths tends to be unreasonably effective at describing the Universe. Or being in general. — apokrisis

It's a puzzler alright. Or perhaps math is only telling us something about our own minds, and not the universe at large. That's a possibility too.

Labouring the point still, but I'm sorry. I'm not a computationalist in the sense you are hoping for. — apokrisis

Well we're back to the NN = TM issue again. That's the core issue here. You think there's a mode of computation that is not a TM and that can be physically implemented in the brain. This I deny. Computer science is on my side I believe. I could be wrong. I await clarity.

Indeed, that was what I was accusing you of. You seem to believe reality is a machine. An account of physical events is sufficient. — apokrisis

I have never believed that and I strenuously oppose it. But it's normal for you to think I've said the opposite of what I think I said. We may just have to live with that.

But yes, you also seem to say the opposite. This is a symptom that your metaphysics is "commonsensical" and not well thought out. — apokrisis

I admit I'm not much of a philosopher. If you ever took the trouble to explain your points of view to me, I'd learn something. But that never seems to happen.

Again, bully for mathematicians. Bully for engineers. Bully even for most physicists (as very few are employed in frontier theory construction).

But it is curious to be complaining about metaphysics where metaphysics is appropriate. — apokrisis

You were complaining that mathematicians aren't in a state of "epistemic shock." I pointed out that when mathematicians are doing math, they're not doing philosophy. You want people to do their jobs, not get lost in the wonder of it all.

And so far you haven't put forward any clear exposition of your own epistemic position, let alone given a clear justification for it. — apokrisis

I haven't got much of an epistemic position today. I vaguely recall originally making some minor point which I no longer remember. I don't believe the mind is a TM and I don't believe real-world NN's are anything other than TMs. That's plenty of position. By the way don't you mean ontic position? What is, rather than how we know what is? I'm even confused about your nonstandard use of "epistemic." I never understand anything you say.

You just hoped to be able to label me with some obviously weak ontology that I spend most of my time arguing against. — apokrisis

LOL. And you are doing the same to me.

Bottom line, why don't you just explain to me why you think a real-world NN is anything other than a TM. That's at least one subject that might be of interest, and it's one where we're reasonably on the same page even though we have different opinions.

I don't detect the relevance of your question. — ProgrammingGodJordan

Weak AI systems are an artifact of modern technology, like cars and flatscreen tv's. On what basis would one ask if AI is our purpose? Perhaps God put us on earth to invent flat screen tv's so God could watch the NFL playoffs, which are starting this very day. You actually didn't understand my point? That's astonishing.

Avant Guard — Bitter Crank

Objectifies chairs.

How do you know the purpose of life isn't to create automobiles or flat screen tv's?

Is chili soup?

Zero. They did a study. The US government does whatever it wants regardless of voter sentiment.

Multivariate analysis indicates that economic elites and organised groups representing business interests have substantial independent impacts on US government policy, while average citizens and mass-based interest groups have little or no independent influence.

http://www.bbc.com/news/blogs-echochambers-27074746

I know the real proof is very complex but it seems to rely on a modified form of the Liar's paradox. Can you explain where I went wrong. Thanks — TheMadFool

G is not provable but it's true. But I'm not really an expert on the fine points so I probably shouldn't have jumped in earlier.

Have I got it right? — TheMadFool

No.

Hawking argues something like the curvature of spacetime is analogous to the surface of a sphere — tim wood

Yeah but where'd the sphere come from? If you're on the surface it looks like you can go in all directions forever. But if you are outside the sphere, you can ask why there is a sphere at all. Did it have a beginning?

Maths is unreasonably effective. It’s abstractions are more than mere intellectual accidents. There must be a reason for their Platonic seeming necessity. So therefore that is why the nature of mathematical truth remains so central to physicalist inquiry. — apokrisis

Agreed.

Neuroscience believes thoughts to be informational processes, not biochemical ones. — apokrisis

Of course nothing of the sort is true, but I see where you're going in the next couple of paragraphs so this is not a crucial point.

What's true is this. Computationalism s the claim that the mind (or the universe, in a more grandiose version) is a computation. Now those neuroscientists who are computationalists believe that thoughts are informational processes; and those who aren't, don't.

I hope you will agree with me that this is a true statement about the states of belief of neuroscientists, and that this is NOT a settled issue by any means. If nothing else, if mind is a computation, what's the algorithm? When you bring me some computer code and say, "Here, this is how you implement an mind. It's 875,356 of C++. Some grad student figured it out," then maybe I'll believe you. Till then, the burden of proof is on you.

It's fine if you want to argue from a computationalist point of view. Just so you don't claim that it's the only point of view and that the neuroscientists have all agreed on it. That last part isn't true.

To use the easily abused computational analogy, the "material physics" explains nothing. You could implement the logic of a Turing machine in some system of tin cans and bits of twine. — apokrisis

Yes I understand substrate independence. Any Turing machine computes the same thing whether you implement it with pencil and paper or on a supercomputer or in the wetware of the brain. So if you believe that mind is a computation, then mind is a TM executed in the hardware of the brain. However if you DON'T believe that mind is a computation, you no longer necessarily have substrate independence. I hope you would grant me this. Searle makes the same point. He's said that he thinks mind is a physical but not computational aspect of the brain. I agree with him about that.

So a science of the mind definitely does need a dualist physicalism of some kind. There has to be some ontic difference between information and entropy, even if they also arise in some common (mutual) fashion. — apokrisis

You are describing the distinction in computer science between a program and a computation. Take the Euclidean algorithm to find the greatest common divisor of two integers. By itself, it does nothing. It csn not find the GCD of two integers. The only way to do that is to execute the algorithm on physical hardware. That is a physical process involving an input of energy and an output of heat. Something a physicist could observe and quantify.

So yes we always have that dualism. Where does the algorithm itself live? Well it lived first in Euclid's brain. But isn't Euclid's mind a physical process? His abstract thoughts are physical processes, and his thoughts can be implemented as physical processes. But I don't see why we need dualism.

But putting that aside, the issue here is the epistemic one of a distinction between observers and observables. Classical physics just presumes that observers are free agents, able to make measurements of reality without disturbing that reality. And this supports the idea that thoughts and rocks are unproblematically separate. Not only are our conceptions of reality a free invention of the human mind, but so do our perceptions of reality enjoy a matching freedom from our ability to invent. — apokrisis

I would say that I think this is a little off-target in the sense that it's one complication too many. If we try to weave quantum theory into this we may lose our way. It's hard enough to try to pin down the difference between the abstract and the physical. So I'm not going to try to think about this. You have to start somewhere, and perhaps we could agree that for purposes of this conversation, there is the number pi and there is a rock, and that we don't have to consider their quantum relationship to each other, if any.

This epistemic shock doesn't seem to have registered with the mathematical community as far as I can see. — apokrisis

I don't see why it should. When Wiles proved FLT, he didn't say to himself, "Well, quantum theory says that the integers are just like rocks." Why would this come up? Mathematicians do math. Some mathematicians sometimes do philosophy. But when mathematicians do philosophy they're acting as philosophers, not as mathematicians. Wiles doesn't sit around thinking about the nature of the integers. To a number theories, integers are as real as rocks. I doubt Wiles would agree that he's written a work of fiction. Or even give the matter any thought at all.

The ontological options are still either that maths is a free invention or a perception of Platonic reality. — apokrisis

Right. Philosophers are rightly concerned with this question. But mathematicians aren't. There is no epistemic shock or even any thoughts at all of philosophy. Some mathematicans care about these things but it's not a requirement of the job.

It has to conform to the rules of an informational process - the syntax that is grounded in set theory, or category theory, or whatever other fundamental notion of a closed syntactical system happens to be in vogue at the time. — apokrisis

Ooh you are on shaky ground here! Gödel told us that math is NOT an informational process! No algorithm can determine the truth of mathematical statements. First you say mind is a computation and then you say that math is. Well we know for a fact that math is NOT a computational process. Perhaps mind isn't either! You know Penrose has made that argument, that incompleteness shows that mind is not a computation. Nobody takes Penrose's argument seriously, but after all he is Sir Roger and the rest of us aren't.

I hope you can see that your computationalist bias may be leading you astray. There are important things in the world that are not computations. Like mathematical truth.

Sanity is not having to think, it appears. — apokrisis

Well you can drive yourself nuts thinking about this too hard. If every single thing in the world needed to make perfectly logical sense, we couldn't get out of bed in the morning. Life does not make sense! Of course a computationalist like yourself would not understand that. You think we're all just a computer program. That's a silly idea. There I said it. I really disagree with computationalism.

Yes, it is out there as a ratio capturing a primal relation of a physical world with some kind of limit-state perfect symmetry. Let that world be not perfectly flat, let it be non-Euclidean, and the value of pi starts to wander accordingly. — apokrisis

Jeez that sounds a little mystical. You're saying that Euclidean geometry is the midpoint between elliptic and hyperbolic geometry. Yes this is a true mathematical fact, but it is not mystical. It's just pi. There are plenty of other real numbers out there too. Pi's not that big a deal really. I only used it as a familiar example of a number whose physical existence can be argued against. I didn't mean it in a mystical sense.

Between the hyperbolic and the hyperspheric, there is only one geometry that is absolutely balanced enough that the value of pi is as stable as far as the eye can see. Whether your circles are big or small, now pi remains always the same. — apokrisis

Yes but you're going all woo-woo about a trivial mathematical fact. Well not trivial, non-Euclidean geometry was a big deal when it was discovered. And as Kant noted, we do seem to have an intuition of Euclidean geometry. I'll grant you that. But I think you're making too much of this.

Also I have a picky little pedantic point. The ratio of a circle's circumference to its diameter is different depending on the geometry. But the number pi is always 3.14159... Pi is a particular real number. It's not defined geometrically these days. If we called the circle ratio the foozle, then you can say that in Euclidean geometry the foozle is pi and in non-Euclidean geometry it's not. But pi is always pi. It's a number. It's like asking what's the value of 3 in hyperbolic space. It's 3.

So pi pops out of reality, out of nature, not by accident but because the very possibility of a "physical relation" has some emergent invariant limit. It arises out of the broken symmetry that is a perfect orthogonality. — apokrisis

You and Kant. He was wrong. You're wrong. Euclidean geometry's not special. It's just something we seem to have an intuition of. I'll grant you the psychological and philosophical interest of that fact. But not the mathematical importance.

In short, you are a Euclidean-chauvinist!

Thus on the one hand, pi - as a position on the number line - looks the purest accident. Why should it have that exact value? — apokrisis

I'll answer that question, if you'll first tell me why 3, a point on the number line by the purist accident, has that exact value. It's a mystery!! Why does 3 have the exact value of 3? It's because it's the number 3. And pi is the number pi. It's just a real number.

It's true that it's the ratio of a circle's circumference to its diameter is pi, but if it were 3 or 47 or 18, you'd be asking why it's that? It's just what it is. The only really interesting thing is that the ratio is always the same no matter what size the circle is! That's the real breakthrough here, that was a great discovery once. [Edit - You made the point that this is only true in Euclidean geometry. Point taken].

On the other, pi is the identity relation when it comes to a limit notion of orthogonal dimensionality. — apokrisis

You are really into pi mysticism. What I mean is, what you wrote here is pretty word salad-y. I have to repeat, I only picked pi because it's a good candidate to make the point that numbers are abstract and not physical. I could have made the exact same point with 3, but people have a harder time understanding that 3 isn't any more physical than pi.

I did NOT intend to inspire any pi mysticism. There is nothing special about pi. It's just a real number. There are plenty of real numbers, many of them interesting for various reasons. It's a matter of historical contingency which ones got discovered first.

We might as well just give its value as 1. Everything else that is less perfectly broken can be measured as some difference to that. — apokrisis

Yes, linear scaling factors don't matter. If you think of the number line, it doesn't matter what names we give anything. If we called 3 by the name 47, everything else would work out the same. Math wouldn't change.

* So to sum up:

- You are arguing from a computationalist point of view, but I'm not sure what point you are trying to make. Looking back I see that now. Even if I agree with you that mind is computation, there are still numbers and rocks. I possibly did not follow your argument.

- You are wrong that math is a computation. And like many computationlists, you underestimate or ignore the importance of non-computable phenomena in the world. Remember even Tegmark distinguishes between the mathematical universe hypothesis and the computable universe hypothesis. Computationalism is a very strong assumption.

* Mathematicians do math, not philosophy. My sense is that the vast majority of working mathematicians never give any thought to philosophy. When an engineer is building a bridge, do you want him spending his time contemplating the fact that there is no difference between him and the bridge? Or do you want him calculating the load factors according to state of the art engineering principles?

Well I hope some of this was on target.

I haven't gone through all the posts, but my take is that cryptos are like the internet boom in the 90s. Generally, I think many will do well, but once the bubble bursts, there will only be few remaining which are reputable. If you own those few in the long run, you'll likely stand the chance of making some decent coin.. — dnote

Yes that's pretty much what's going to happen. The current phase is going to crash terribly and a lot of people are going to get hurt. It's not just the cryptos themselves, but the exchanges where you trade fiat for cryptos. There are a lot of shady and undercapitalized companies out there handling people's money. There's no regulation. When the crash comes, a lot of people are never going to get their money out.

This will be interesting to watch. I do believe blockchain technology will change the world in ways we can't even begin to imagine. But the current mania is going to end badly.

a human invention, a mere accidental notion — apokrisis

Yes and No!! Yes, numbers are a human invention. But accidental? No. They don't seem that way. Archimedes wasn't hallucinating. There's some mathematical constant pi "out there." This is a deep mystery. Our abstractions are telling us something about the world. We're not sure what.

I don't think you and I disagree all that much.

But that is just an ontology endorsing a sharply divided dualism. — apokrisis

Oh I see. I stand accused of being a dualist. And we know how out of favor they are.

My understanding is that we can accommodate abstract mental constructs quite easily within physicalism. Abstractions are thoughts, biochemical processes in my brain.

But thoughts are still different from rocks. Thoughts and rocks are both physical processes, but they have a different character. One doesn't need dualism.

Even thoughts come in two flavors. Thoughts about physical things, and thoughts about abstract things. Thinking about rocks and thinking about pi. Observations of the world versus dreams. Writing history versus writing fiction. Our brains go quite comfortably back and forth between the real and the unreal. Yet sane people alway know the difference.