The Hard Problem of Gravity

[Belz...]

It's nothing to do with advancing my argument. You made a statement - that a network of transistors could be made equivalent to any biochemical process - that is simply, plain, wrong and I gave a simple counterexample to demonstrate it.

In other words what makes up consciousness is a question of substance ? If it were behaviour, it could be replicated using transistors, indeed. So what are you saying, now ?

 

[Belz...]

So we have three things - spherical (a mathematical term), round, and the particular shape of one particular apple, as mathematically described. To what degree of precision? For some purposes, a cube big enough to enclose the apple would be good enough. Can the apple be described with total precision? Not in this universe.

Why not ? Why wouldn't the exact shape of the apple be mathematically describable ? Even in principle ?

It was dead. I raised it up on the third day.

Actually, only after a day and a half.

 

[westprog]

Why not ? Why wouldn't the exact shape of the apple be mathematically describable ? Even in principle ?

Because it doesn't have an exact shape. Nothing does.

 

[westprog]

In other words what makes up consciousness is a question of substance ? If it were behaviour, it could be replicated using transistors, indeed. So what are you saying, now ?

He didn't say consciousness, he said any biochemical process. He was clearly incorrect, and I pointed it out. I don't see the point of pursuing an error.

No, I don't think that consciousness is a matter of behaviour, because very little to do with consciousness could be deduced from behaviour. What we know of consciousness we know by telling each other about it. Call that behaviour if you wish.

 

[westprog]

What the hell else would you expect?

Why is it surprising that the same thing is the same thing? I want to know.

How did we learn that America was really there? Because different people went to the same place and there it was. How did we learn that Z-rays weren't real? Because when different people looked for them, they weren't there.

We've a well-founded system for determining what is real and what isn't. And each time we perform calculations, we get the same answers. That's what differentiates mathematics from novels. One is discovered, the other made up.

Of course, as RD has pointed out, both novels and mathematical theories are products of the physical world, as is the statement 1+1=3. But objective truth is clearly a seperate matter from this.

 

[westprog]

Wrong. When you a combine sets of five discrete things and four discrete things you get a set of nine discrete things. That is what mathematics says, and it always happens.

And just how do you produce sets of things? In the real world? Mathematics won't tell you that.

Isn't it strange that the mathematicians and the physicists continue to regard their fields as separate? That mathematicians don't regard themselves as scientists? Isn't it odd that there's never anything about computing in the physics textbooks, except the hints on using FORTRAN to crunch numbers?

 

[cyborg]

And each time we perform calculations, we get the same answers.

Right.

And yet again I must ask:

Why are you surprised that something that is the same, is the same?

We've a well-founded system for determining what is real and what isn't.

Questions mathematics cannot answer:

Is America really there?
Are Z-rays real?

That's what differentiates mathematics from novels. One is discovered, the other made up.

If mathematics is discovered then so are novels.

 

[rocketdodger]

The principle of quantum uncertainty.

Yeah, that is correct, I have to say.

So my question would be, how are you so sure that reality behaves according to independent mathematical truth, given things like quantum uncertainty?

 

[rocketdodger]

But objective truth is clearly a seperate matter from this.

Well, that is your problem right there. You assume objective truth is seperate from reality despite having zero evidence.

 

[rocketdodger]

The GC is already a statement. But if the GC is true, there's no smallest counterexample (call it SCGC). The question isn't whether or not GC is mathematical (GC itself falls under the umbrella of mathematical concerns)--it's whether or not there is such a "thing" as SCGC--that is, whether SCGC conveys a real relationship, or is simply a contradictory concept.

If you interpret this in the general--there's absolutely no guarantee that GC, or some GC-ish statement, can be proven to be true if it is true. As such, there's nothing to guarantee that SCGC like relationships, given that they don't hold, can be shown not to hold with an algorithm that runs in finite time.

Now, you can describe the SCGC--in fact, merely by talking about it, we are describing it. But the description of the number is not the interesting thing with respect to mathematics. The interesting thing is whether or not there is such a relationship--whether there is a smallest counterexample. SCGC conveys something "real" if and only if (and in the sense that and only in the sense that) the GC is false.

So it doesn't help us at all to be able to describe the SCGC. What we want to know, in terms of mathematics, is whether or not the relationship holds. We want to know if there's a finite counterexample.

The problem is, there are an infinite number of candidates, and there's nothing that gives us any guarantees that if GC is true, we should be able to in principle prove it. Now if GC is false, we're lucky (at least in principle). And if it's true, we might could prove it. But it's not guaranteed.

Even the fact that it's a logical extension of relationships isn't sufficient to give us this guarantee.

I am not sure we are talking about the same thing anymore.

I am saying that the GC itself is isomorphic to some mathematical statement because it is a well formed sentence of English (or whatever language it is stated in).

I am saying that the ideas of the GC itself, as present in a human mind, are isomorphic to some other mathematical statement because those ideas are after all just a bunch of particles in a brain.

I am not saying anything about the truth of the GC.

So what we have here is a bunch of mathematical statements -- for example, about the position of particles in your brain when you are thinking about it or the position of particles on a monitor displaying the wikipedia entry on the GC -- that turn out to be isomorphic to the GC. If nothing was isomorphic to the GC then clearly we wouldn't even be able to write it down, and we can.

I mean, you can take two views of mathematics in this context. The first view, which I think is a cop-out, is that there just happens to be a world of mathematics out there and we are discovering it. The other view, which I hold, is that we are simply uncovering the emergent behavior of physical world.

Its like computer science, right. There is no abstract world of software that floats around independent of reality, and programmers don't "discover" software. We work with a very small set of rules and produce incredibly complex emergent behavior from those rules.

 

[Belz...]

Because it doesn't have an exact shape. Nothing does.

That makes no sense, whatsoever. EVERYTHING has an exact shape. That this shape isn't a "circle" or a "square" is irrelevant. It's a shape and it's quite exact.

 

[yy2bggggs]

I am not sure we are talking about the same thing anymore.

Apparently we're not. I'm talking about mathematics, and you're talking about the concept of mathematics.

Its like computer science, right. There is no abstract world of software that floats around independent of reality, and programmers don't "discover" software. We work with a very small set of rules and produce incredibly complex emergent behavior from those rules.

I think you mean computer programming. Computer science works with things such as "discovering" the Halting Problem.

You're making grand statements without any meaning, by the way, and quite possibly committing a straw man while doing so. The term "exist" has a mathematical meaning (no, not the one you're using... the one mathematics uses... you know, "for all", "exists", that sort of thing?) Keep this meaning in mind--the mathematical meaning of exists. Got it? Good.

Now, when we speak in terms of the abstract world of mathematics, we're speaking of things that exist. Don't backslide now--keep track of what we're talking about. We're in mathematics land.

Now, here's the thing. SCGC denotes a particular number. Does that number exist? That is a question in the realm of mathematics. It's a meaningful question, I assure you. It has an answer--I assure you. It doesn't become true or become false when we prove it--when we come up with a finite algorithm that is able to describe how it is logically related to the existing set of relationships we do happen to know about. The logical extension of those relationships either includes, or does not include, SCGC.

I am saying that the GC itself is isomorphic to some mathematical statement because it is a well formed sentence of English (or whatever language it is stated in).

Sure, and unicorns and fairies are isomorphic in the same sense. They are isomorphic. It's perfectly true that they are. But it has absolutely nothing to do with whether or not there are unicorns, or whether or not there are fairies. You're just saying, essentially, that everything we say here involves internet protocols. Big deal.

Yes, it's no longer what you were talking about, once we consider whether or not there actually are unicorns, or whether or not there actually are fairies, or whether or not there actually does exist an SCGC. But I really don't care--it was never what you were talking about. That itself is the entire point I was bringing up.

I mean, you can take two views of mathematics in this context. The first view, which I think is a cop-out, is that there just happens to be a world of mathematics out there and we are discovering it. The other view, which I hold, is that we are simply uncovering the emergent behavior of physical world.

What a navel gazer! Either this is true or that is true. Has it ever occurred to you that they are completely different kinds of things, and they are both true? And that only the "discover" thing has anything to do with what mathematics is, just like only that actual creature with the horn has to do with what a unicorn is?

This "cop out"--this thing other than the "view" you take--that is not "the other view". That is another true thing.

 

[Belz...]

He didn't say consciousness, he said any biochemical process. He was clearly incorrect, and I pointed it out. I don't see the point of pursuing an error.

So if we could simulate a biochemical process we wouldn't get the same results ?

No, I don't think that consciousness is a matter of behaviour, because very little to do with consciousness could be deduced from behaviour. What we know of consciousness we know by telling each other about it. Call that behaviour if you wish.

How else would you like to call it, exactly ? Behaviour, actually, is ALL we have to infer consciousness. We've covered this, already.

 

[westprog]

Well, that is your problem right there. You assume objective truth is seperate from reality despite having zero evidence.

No, it's exactly the opposite. I believe reality rests on objective truth. I don't think there can be any reality without objective truth.

 

[westprog]

That makes no sense, whatsoever. EVERYTHING has an exact shape. That this shape isn't a "circle" or a "square" is irrelevant. It's a shape and it's quite exact.

We haven't believed that to be true for nearly a century now.

 

[westprog]

Yeah, that is correct, I have to say.

So my question would be, how are you so sure that reality behaves according to independent mathematical truth, given things like quantum uncertainty?

I'm not. That's your contention. I'm claiming that independent mathematical truth is objectively true quite independently of its relationship with the physical world. It's also just as much part of reality as the physical world, and does not depend on it.

 

[Belz...]

We haven't believed that to be true for nearly a century now.

So you are saying that objects CANNOT be described mathematically ?

 

[rocketdodger]

I'm not. That's your contention. I'm claiming that independent mathematical truth is objectively true quite independently of its relationship with the physical world. It's also just as much part of reality as the physical world, and does not depend on it.

But the only way you could possibly argue such a thing is to assume apriori that human consciousness has access to something other than the physical world.

Otherwise, whether mathematical truth exists independently of its relationship with the physical world is impossible to know since our only access to mathematical truth is via the physical world.

This is the same error Penrose makes. He claims humans must have access to the non-physical because humans are able to understand mathematical theorems that can't be generated by a physical algorithm -- exactly the conclusion he is already assuming.

 

[AkuManiMani]

Would you argue that if someone created a program that was more 'complex' than a human it should be entitled to more legal rights than an actual human?

What more legal rights?

If there were a artificial construct created with operational complexity comparable to, or greater than, that of a human would you consider it to be have 'greater' value than the life of a human?

For example, would it be justified to kill, or otherwise harm, a human to prevent harm from being done to said construct merely on the basis of its complexity?

Is complexity your criteria for ethics?

It's part of everyone's criteria for ethics.

Really? I thought the capacity to experience suffering was the basis for giving an entity ethical consideration.

Not only is it not unethical to kill, say, a brick, we don't even consider the question meaningful.

Ofcourse. Because a brick is not alive and, as far as can be told, bricks cannot experience anything, let alone suffering. The thing is, if one were to arrange bricks or their materials in a more 'complex' way this would not change. Clearly there is more to ethical concerns than mere complexity.

 

[AkuManiMani]

So you are saying that objects CANNOT be described mathematically ?

I'm gunna venture a guess and say that he means that a mathematical description of a thing is not the thing itself, and that things IAOT may have properties and aspects that aren't part of a particular description.