Is naturalism = physicalism? Or is there a further distinction?
— fishfry
That's not exactly wrong. But let analytic philosophers loose on an -ism and in a few years you'll have dozens of them. In the first half of the last century, there wasn't a concept of computability, so that issue is undetermined. — Ludwig V

People keep using the word naturalism and I'm trying to understand what it means. Is it the same or different than physicalism?

I'm clearly out of date. Apologies to Searle. However, I'm not much reassured. If Searle is positing consciousness as an unknown something-or-other in addition to what is currently recognized as physical, he is positing a consciousness of the gaps, which is at least close to dualism. — Ludwig V

He associates it with life. Something about living things. And surely we haven't got a computer science theory of when a program running on a digital computer becomes alive. Any more than we know when it becomes conscious. Or if, rather than when. What is the spark of life? Some call it the soul. The thing that's present when you're a live, absent when you're dead, and nobody knows what it is? Maybe consciousness is something that comes along with that.

That is my understanding of my own recollection of what Searle said in a video I watched a couple of years ago. No claim that Searle holds or ever held this position as I explained it. But it sounds reasonable. It's a coherent belief. Something about life is conducive to consciousness.

A computationalist would call that very human-centric, like geocentrism. Destined by analogy with history to look silly someday.

The mistake is to start with "Consciousness is....". We know what consciousness is; we don't know how to explain the physical basis of consciousness - yet. But it is clear that there are many disparate phenomena involved and it is possible that consciousness will not map neatly onto the physical world. (Consider the many complicated physical phenomena that are involved in the emotions, for example). — Ludwig V

I'm sticking to physicalism without computationalism till I get some new input on the subject.

Emotions are another good example, thanks for that. They're squirts of hormones in the limbic system or some such. Nobody understands how it works. It doesn't seem very computer-like to me.

I believe in that same lecture (or perhaps a different one) he [Bostrom?] did NOT advocate dualism. ... That is, consciousness is physical, but not computational.
— fishfry
Wait, Bostrom said that mind is not computational, and yet pushes a view that our consciousness is the result of a computation? That seems to be a direct denial of his own paper. Got a link to where this is said? — noAxioms

You grabbed a statement I made to @Ludwig V about Searle, interpolated Bostrom, and snapped back me for a link to something you imagined I said?

I was a little put off by this latest post. You sniped at literally every sentence I wrote.

I was more interested in taking the discussion in the direction of my new understanding that Bostrom explicitly says that in the future they'll figure out how to implement consciousness on a computerer .

In my mind that renders the conversation moot. If that assumption is false, the paper is wrong. If it's true, then I'm a program running in a computer, and it doesn't matter if God or future people did it. So the paper doesn't say anything interesting.

That kind of wrapped it up for me. And it clarified a point I've been wondering about, which is what Bostrom says about computational consciousness. He assumes it. Hell of an assumption to casually slip in, rather that explicitly noting it.

Anyway I don't think I could add value by sniping back at every sentence-by-sentence dispute, so I think my best bet is to leave this as it is.

This has been on my mind today. As an American I need to say my piece, loathe as I am to tread in the murky and shark-infested waters of the political forums.

I'm feeling deep sadness and depression today at the country I've woken up in.

I would argue that even if you hate and despise Trump to the ends of the earth; what has happened today is a very bad day in the history of this country.

I'm reminded of one of my favorite films, A Man For All Seasons. Paul Scofield gives an incredible performance as Sir Thomas More, a man of principle who gets in trouble with Henry VIII in the 1530s. It's based on a true story. The State is determined to get him whether he's guilty of anything or not.

There's a scene that's been on my mind lately.

William Roper: “So, now you give the Devil the benefit of law!”

Sir Thomas More: “Yes! What would you do? Cut a great road through the law to get after the Devil?”

William Roper: “Yes, I'd cut down every law in England to do that!”

Sir Thomas More: “Oh? And when the last law was down, and the Devil turned 'round on you, where would you hide, Roper, the laws all being flat? This country is planted thick with laws, from coast to coast, Man's laws, not God's! And if you cut them down, and you're just the man to do it, do you really think you could stand upright in the winds that would blow then? Yes, I'd give the Devil benefit of law, for my own safety's sake!” — A Man For All Seasons

― Robert Bolt, A Man for All Seasons: A Play in Two Acts

I'm appalled that so many liberals, good liberals whose side I've been on all my life, are so gleeful today. Do you not understand what you've done? The hush money case is a chickenshit case. Bragg's office already looked at it and decided it was a loser. They didn't bring the case. Then the Biden administration actively worked with Bragg's office to revive and prosecute the case.

I will note that the White House has been muted in their public gloating. I think their overnight internal polling is not favorable. Americans, not just those on the right, but centrists and even some liberals, are seeing this the way I see it.

A decent liberal of conscience must have qualms about this conviction. It doesn't matter if Donald Trump is the devil. The precedent set today will not work out as you hope.

This verdict is a bad thing. It does not matter what you think of Donald Trump. It's a blatantly political case: a sitting president using a state judicial system to pursue an extremely weak and petty case against his political opponent in the upcoming presidential election. Not to mention the egregiously biased judge who doesn't care that the case will be overturned on appeal. They just want a conviction today. It's shameful.

I say it's shameful even if Trump is the guiltiest bookkeeper in history, the worst hush money payer, the stupidest Stormy-f*cker ever. I think a lot of people, not just me, and not just those on the right, see this for what it is. It's the most blatant election interference in the history of this country. It's banana republic stuff.

It is possible to loathe Trump and still see that this verdict is indeed, a very bad day for this country. My liberal friends, you have sown the wind, and you will reap the whirlwind.

This is what I came here to say.

Sir Thomas More was beheaded in 1535.

@noAxioms, I was motivated to click on the Bostrom paper and I actually found the line that stops me in my tracks every time.

Suppose that these simulated people are conscious (as
they would be if the simulations were sufficiently fine‐grained and if a certain
quite widely accepted position in the philosophy of mind is correct). — Bostrom

As you know, I am not one of those who "widely accept" this utterly unprovable and extremely unlikely claim. I can't see reading further. Bostrom assumes that consciousness can be implemented on a computer. I say no. It can't.

I found something else that stops me from reading the rest of the paper. It's the very first sentence.

Many works of science fiction as well as some forecasts by serious technologists
and futurologists predict that enormous amounts of computing power will be
available in the future. — Bostrom

Yes. But no matter how enormous the amount of computing power we have, it can not and does not increase the space of problems we can solve. That's the essence of computability. More power makes the computation run faster. It can't compute anything that wasn't already computable before.

So now I see why I can never get into the Bostrom paper. Right in the first paragraph, he loses all credibility with me. It's a core assumption that computers can create consciousness. There's no evidence for that. Why read further? I'll concede that IF consciousness is computational, then I'm already a "simulation," ie an executing computer program. And who's the simulator? God or a future civilization? What difference does it make if I'm a program either way?

So even if he's right, there's no reason to read the rest of it. Computational consciousness is one of his core assumptions. If it's false, the paper's worthless. If it's true, the paper's trivial.

And if the simulators are a future civilization, who created them? In the end it's either "God did it," or "We don't know." So this paper adds nothing. He slipped in the computational consciousness assumption, in which case there's actually nothing else to say. We're all executing programs.

Oh, and instead of justifying and supporting his computational consciousness claim, he blithely says it's "widely accepted." By whom?

Once again, I'm dismayed at how many otherwise clever people take this paper seriously. And once again, I could not get past the introduction and the first paragraph.

too snippy. — scherz0

Too snippy? You've been spamming this lame question all over the Internet. Consider yourself snipped.

You don't seem to understand what is being discussed at all. — Michael

Have a nice evening. I'll forego responding in kind.

@Michael, This post may be of interest to you.

So, the terminal state not being defined does not prevent me defining one arbitrarily?
Isn't it the case that there is a requirement - that the terminal state not be defined by the function. — Ludwig V

This is the bit with the ordinals I was using earlier.

What is a sequence? A sequence is a function whose domain is the natural numbers 1, 2, 3, ...

For each natural number, there's a value, like 1/2, 1/4, 1/8, ...

We can conceptually adjoin a "point at infinity" to the natural numbers, traditionally called $\omega$ in this context, so that our extended natural numbers look like

1, 2, 3, 4, ... $\omega$.

This structure, the extended naturals, are called $\omega + 1$, because the natural numbers themselves are called $\omega$. That's just another name for the more usual notation $\mathbb N$, except that $\omega$ implies the set of natural numbers in their usual order.

So if a sequence like 1/2, 1/4, 1/8, ... is a function on the domain $\omega$, an "extended sequence" (not the official terminology) is a function on $\omega + 1$. Such a function might look like this:

1/2, 1/4, 1/8, 1/16, ..., 47

Here I just defined 47 as the terminal state.

Another possible completion is

1/2, 1/4, 1/8, 1/16, ..., plate of spaghetti

There is absolutely nothing wrong with that. I've just adjoined a plate of spaghetti to the rational numbers, and defined the terminal state of this particular sequence to be the plate of spaghetti.

Now in this case there is ONE completion that is "natural," namely:

1/2, 1/4, 1/8, 1/16, ..., 0

That completion is just as arbitrary as any other. But it has one supreme virtue: 0 happens to be the limit of the sequence. So that's why I call it natural.

The problem with the lamp is that the sequence 0, 1, 0, 1, ... has no natural completion. That's why we can define the terminal state of the lamp as on, or off, or a plate of spaghetti, or Cinderella's coach.

All completions are legal; and no completion is natural; because the lamp sequence does not have a limit.

How could the mind-body problem not be relevant if people are positing that sims might be people (and sometimes asserting that at least some people are sims?)
Yes. Sometimes I find his tendency to present dualism as common sense ridiculous and sometimes annoying. It reminds me of Bishop Berkeley and his wilful refusal to recognize that he is contradicting common sense.
But the rhetoric of that sentence is genius. A mystery created from a commonplace. — Ludwig V

I believe in that same lecture (or perhaps a different one) he did NOT advocate dualism. He advocated what I call "secret sauce," my phrase, not Searle's. That is, consciousness is physical, but not computational. That's the point I've been making to @noAxioms.

"Naturalism" is used much more widely than that. I've been classified as a naturalist because I reject dualism. — Ludwig V

I thought naturalism (as I understand it, based on a five second lookup) is the exact opposite of dualism. Is naturalism = physicalism? Or is there a further distinction?

My point is that naturalism is not necessarily computationalism. Mind could be physical but not computatational. This is something I believe, though of course proof is lacking.

If my reality is nothing but a "simulation," then I'm not real. There is only the simulation. Meaning that I'm not a simulation, I'm an instantiation.
— fishfry
Better put than I managed. — Ludwig V

Thanks, but noAxioms doesn't believe in the word.

You can define the terminal state to be on, off, or a plate of spaghetti and be consistent with the rules of the game.
— fishfry

No you can't. — Michael

What do you mean I can't? I already have, numerous times in this thread.

The point is that the sequence 0, 1, 0, 1, ... has no limit. We are free to define a terminal state that is not a limit, but is just a value assigned to a point beyond the sequence, traditionally notated as $\omega$. This value could be 0, it could be 1, or it could be a plate of spaghetti.

Now I will agree with you that we COULD make a rule that the terminal state must be 0 or 1. That rules out the spaghetti. But there is no logical preference between 0 and 1. Neither value could be the limit of the sequence, since that sequence does not have a limit.

I addressed this in my initial defence of Thomson here, and even more clearly below. — Michael

You can't have addressed it, since what I said is true.

You're claiming that "a plate of spaghetti" is a coherent answer to the question "is the lamp on or off after two minutes?" — Michael

It's consistent with the rules of the game. But if you add the rule that it must be 0 or 1, then either answer will do, and neither answer has any logical relationship to the sequence, since the sequence doesn't have a limit.

SEP is clear that Thompson was clear on this point, in full agreement with me.

So I think the confusion is yours. — Michael

You know, I lost track of whether I said this to you, or you said this to me. I'm sure we both feel that way. Can't we just agree to disagree? This poor deceased equine has been flogged well into the next life.

He discusses the sequence and its sum, but only to show its irrelevancy, hence the earlier quote. — Michael

All possible terminal states are equally irrelevant, because the sequence has no limit.

May I ask, you do you understand that? Do you understand that the sequence 0, 1, 0, 1, ... has no limit, and can not be made to have a limit?

From his paper:

What is the sum of the infinite divergent sequence +1, -1, +1, ...? Now mathematicians do say that this sequence has a sum; they say that its sum is 1/2. And this answer does not help us, since we attach no sense here to saying that the lamp is half-on. — Michael

Completely irrelevant to anything. Nor do mathematicians say any such thing, except by using asymptotic density (which I believe SEP refers to as Cesaro summation).

You haven't proved your point. You haven't even made a point.

I'm sorry. I was talking about the convergent series. Didn't check — Ludwig V

My confusion.

I do not think Michael and I are making the same point.
— fishfry
Perhaps not. But if the last term in the series is not defined, contradictions are likely to follow from the attempt to identify it. Equally, if something gives rise to a contradiction, the definition will be faulty. So, if you are right, I need to ask why it matters. — Ludwig V

There is no last term in any infinite sequence. There may (or may not) be a limit. Big difference.

There is no last term of the sequence 1/2, 1/4, 1/8, ...

It has a limit of 0. But 0 is not an element of the sequence.

Also the terminology I'm using is that a sequence is a comma-separated infinite list, 1/2, 1/4, 1/8, ...

A series is an infinite sum: 1/2 + 1/4 + 1/8 + ...

The elements of a sequence are not "premises," as @Michael seems to think. They're just numbers. Some sequences, like 1/2, 1/4, 1/8, ... have a limit, in this case 0. Other sequences, like 0, 1, 0, 1, ... can't possibly have a limit. That doesn't stop you from defining a "terminal state," which I've formalized as a value at $\omega$. But there's no need for there to be any logical relation between the sequence itself, and the arbitrarily-defined terminal state. That's why lamp on, lamp off, or lamp turns into a plate of spaghetti, are all equally valid terminal states to the sequence 0, 1, 0, 1 ...

Even if you insist that the terminal state must be either 0 or 1, there is no logical way to prefer one over the other.

My reply was edited since I think I finally grasped what you mean by 'instantiation', as being distinct from 'simulation'. — noAxioms

Yay!

But may I say that earlier, you noted that these threads are getting long. I too could live with a much more focussed conversation. Actually I'm near the end of my interest in this topic. I've already stipulated that I haven't read the Bostrom paper, so for all I know, I'm misunderstanding his argument. Can we wrap this up soon? It's feeding time in my digital vat.

No they're not. They are using the word in a single consistent manner at all times. You admit that it is you that is finding two different meanings and trying to use two different words to distinguish them. Under naturalism, there is a physical system that is simulated using a model of physical laws. It's completely computational in all cases. — noAxioms

Naturalism is computationalism? I genuinely doubt that, but I'm no expert.

I acknowledged your opinion. It isn't wrong, merely inconsistent with Bostrom's naturalism opinion. — noAxioms

I concede that I have not read Bostrom all the way through. Every time I've taken a run at his paper in the past, my eyes glaze over, my mind says, "This is bullpucky," and I click on something else.

My opinion is that the economy isn't an example of something noncomputational. — noAxioms

Really? The economy is the deterministic output of a computer program? Your Nobel in economics awaits if you can prove that, even if the economics Nobel is not really a Nobel.

I deny that physics is computational, or rather I'm pretty sure it's not.
With that I completely agree, which is why any computation of our physics is necessarily an approximation.[/quoe]

We are 100% in agreement on this point.
— noAxioms

I'm unclear of the distinction between that and simulation. Bostrom says that it is humans (or 'post-humans') running the big computer. Simulation theory in general doesn't require that detail. — noAxioms

I was going to respond, but we've been over this. If my reality is nothing but a "simulation," then I'm not real. There is only the simulation. Meaning that I'm not a simulation, I'm an instantiation. Ok I responded anyway. Wish I hadn't.

Not at all. I am balking at your equating a premise that science in general would find false (2+2=5) with one that science in general accepts as true (naturalism). — noAxioms

I said that "If 2 + 2 = 5 then I am the Pope" is a true proposition of sentential logic. Nobody said anything about naturalism. How did you interpolate that here? You entirely changed the subject.

Good. Best they could do at the time. Even today, few non-headset games even have a first person perspective. Minecraft and Portal come to mind. I'm sure there are others, but still a small percentage. Earliest one I can think of is Battlezone. Remember that one? It pre-dates pacman I think. Ground breaking stuff it was. — noAxioms

Never much of a game aficionado I'm afraid. I remember Lunar Lander and Asteroids.

But I do object to the "best they could do at the time" argument that video games are getting better, therefore in the future they'll be indistinguishable from reality. Since we have made zero progress on instantiation (there's that word again) consciousness, we have made NO progress in that area, and the argument fails.

Yes. "Real time". But technically, all computation has this requirement, which is one reason nobody makes real Turing machines. Imagine if you had a 4-banger calculator that took 40 years to add 2+2. Would you use it? Does that make adding 2+2 something more than computational? — noAxioms

I am not the person who makes the distinction between computability and complexity theory. That's the computer scientists. You already agree with me. I agree that I don't know the official terminology for how this affects real time systems.

A good stance, and I worded it as 'belief' instead of 'opinion', which may have been too hash. The simulation hypothesis can only be considered under the naturalism it presumes, whether or not naturalism is part of one's opinion. — noAxioms

Maybe you could explain what you mean by naturalism. I don't know what the word means.

Nevermind, I looked it up. It's "the philosophical belief that everything arises from natural properties and causes, and supernatural or spiritual explanations are excluded or discounted."

Fine. I can stipulate to that. But naturalism does not imply computationalism! I'm sure I've already made this point at length.

Your opinion then is that we have the secret sauce, and that whatever it is, it isn't computational, although I don't know how you can infer it being noncomputational if you don't have any idea what it is. So probably also another opinion. — noAxioms

It's clear to me that there are profound limits to what can be computed. It was clear to Turing as well, since he was the first person to document an easily described problem that can not possibly be solved by a computation.

There isn't a separate Cartesan "I" thing under naturalism. — noAxioms

So the simulator implements my consciousness. And exactly how does it do that? And exactly what is it that makes a program conscious? Is my web browser conscious? Who believes such nonsense?

Explaining it and defending it are two different things. The abstract is accurate, meaning I find it reasonably valid and sound, although it seems that it has been updated since wiki lists 5 options now instead of the original 3, but the new ones seem to overlap with the old ones. — noAxioms

I made a recent attempt to read the paper, by far not my first time, and as usual my eyes glazed and I clicked on something else. Perhaps someday I'll get it, but its charms and logic are lost on me so far.

Much (the majority?) of criticism and support seem to be from people without a reasonable understanding of what it says. You can include me on that list. Don't trust what I say, but I have read the actual paper at least, and I know the difference between it, other sim proposals, and with a VR proposal. Many of the articles discussing it seem not to know the differences. — noAxioms

I have conceded many times over the superiority of your knowledge in this area. I have not conceded the superiority of your opinions about what it all means. In fact you yourself have said, more than once, that you don't agree with the conclusions of the paper. So why bother with the likes of me? Leave me in my ignorance, please. I don't care much about simulation theory because it's such obvious pretentious garbage.

Is my consciousness part of the simulation?
So says Bostrom, yes. — noAxioms

But how is that done? What lines of code must I run to imbue my program with consciousness? I'd be very interested to hear your answer to this question. Is it just a matter of lines of code? Microsoft Windows has some fifty million lines of code. Is it conscious? Is it just a matter of running it faster? I can't believe you are defending such an indefensible proposition, that a computer program can be conscious, without having any inkling of how it's done.

Naturalism says it is if the simulation is run at a sufficiently detailed level, which is still classical, not necessarily down to the quantum level. — noAxioms

Naturalism does not say a computer program can become conscious. It says we REJECT the supernatural, we don't embrace it!

A VR does not produce a second consciousness for the avatar. A sufficiently detailed VR might for an NPC, but nothing like that exists in any current VR system. The current VR immersion (with the 3D headset and all) is barely better than the one for Pacman. — noAxioms

But in terms of implementing consciousness, it is no better than Pong. That is the "video game improvement" argument I objected to earlier. We have made NO progress in implementing consciousness. No progress at all.

With a good one, there'd be no controller in your hand. You would not have access to say your real body being touched. — noAxioms

I would still be the one having the experience. The "I" having the experience. My experience is not induced by a headset. I really don't think you are thinking these matters through.

No, that isn't needed, but it is needed if the sim is gleaning intent from the physics it is simulating, and Bostrom very much does propose that it is interpreting human intent. Also, that understanding is needed for any human that is not born, but is part of the initial state. So bottom line, yea, it is needed. — noAxioms

Can't comment on what I haven't read. If Bostrom thinks a computer can instantiate consciousness, the burden is on him to say how, since nobody has the slightest idea how.

A pure simulation of a human from the human's initial state has no need for knowledge of how memory and consciousness works, for the exact same reason that physics doesn't need to know the details of the workings of the things that result from the physics. — noAxioms

Where is your evidence that computer programs are conscious? Why are you arguing this nonsensical line that you can't possibly have any evidence for?

Centuries hence, it seems so. Without it, there can be no plausible initial state, unless you go back 3 billion years where the initial states were less complicated — noAxioms

So in the future there will be a breakthrough. Well who can argue with that? Will that be before or after pigs fly? You know, I can't believe Bostrom is making such a weak and nonsensical argument.

But that goes against the claim that "the video games are so much better now," an argument often given in support of the simulation hypothesis.
No video game claims any understanding of what is referred to as the hard problem. If somebody references a game as an illustration of Bostrom's hypothesis, then they don't understand the difference between a sim and a VR. But they're probably just using games as one way to demonstrate Moore's law, which Bostrom presumes to continue for centuries. — noAxioms

Quite possibly I've seen other people make the video game progress argument. If it's not Bostrom's, I have terribly maligned him. But my simulator made me do it, honest. I had no choice.

Do I have choice, by the way? Does Bostrom deny free will? My web browser can't be a word processor, no matter how hard it tries. Programs do exactly what they're programmed to do, a matter of great frustration to programmers.

If all this is a simulation, I am still very much real according to my stated definition of 'real' and you've not given yours. SH is very different than BiV and Boltzmann brains. — noAxioms

I don't see how. If I'm a simulation running in a computer, I might as well be a brain in a vat or the only conscious thing in the universe. What distinction among these ideas do you see?

I don't think there is the sort of free will you're thinking if our world is a simulation. — noAxioms

No free will. Ok. So sim theory is ultimately nihilistic. I murdered all those people but it wasn't my fault, Your Honor, my simulator made me do it.

A simulation like that doesn't have causality from outside the system. If it did, it would probably be a VR. I say this, but I've done chip simulations that get driven from external state. The signals fed to the chip are artificial, not from other simulated circuits since it's only the one chip being tested. Such a chip simulation is hard to classify as a VR. — noAxioms

External inputs don't matter, since programs are coded to do one thing or another thing depending on the input. Programs don't have free will by virtue of getting external inputs.

You are part of the physical evolution of the chosen initial state. That answer pretty much applies to any simulation, including all the ones I've seen done. You want to call it an instantiation and I think I see how you're using that word. A simulation is the execution (instantiation) of a mathematical model, that model itself being an approximation of some hypothetical corresponding reality. Since it is the execution of a model, it is presumably exact, except the model might include randomness, in which case the exactness is wrong since multiple instantiations of the same model will evolve differently. Bostrom does propose some randomness in his model, so not sure how 'exact' it would be. Said randomness need only be apparent, so it can be driven by a pseudo-random mechanism, which restores the deterministic nature of the simulation. — noAxioms

You contradicted yourself at least three times getting from the beginning to the end of that para. No free will but there might be if there's randomness, but it might only be pseudo-randomness, in which case it's not random after all.

Anyway I don't think I have the heart to unpack all the (in my opinion) confusion in that paragraph.

You can't go from "people aren't special in the universe," to "therefore people are computational."
I don't think any physical thing (people or otherwise) is computational. But an approximation can be, and people are no exception to that according to science. — noAxioms

According to science? What serious scientist parrots a single word of this nonsense? Name and shame please. I'm not talking about Neil deG Tyson or the deluded George Smoot in a TED talk. I mean a scientist who wrote a peer-reviewed paper that says "people are no exception" ... wait, what? I went back to try to parse what you wrote and you agreed -- YOU AGREED! -- that no physical thing is computational.

Then we're done. You have accepted my point.

Yet you think I'm an approximate computation?

I urge you to think about what you are saying.

You're not taking down Bostrom's argument. You presume his premisies to be false. I presume them to be true, and I think his conclusion doesn't follow from them. — noAxioms

Ok. That's interesting. Why do you think his conclusion doesn't follow from his premises? That might be interesting.

That's right. BiV is like the video game: an artificial (virtual) experience stream to the real (not simulated) experiencer, effectively a video game for the B in the Vat, whatever its nature. — noAxioms

So brain in vat IS is like simulation after all?

Very unlikely for the reason's I've stated. Only if you're part of the initial state, and then only if that initial state had some kind of access to the molecular state of everybody on Earth many centuries prior, which they don't because there's no tech today that can do that. — noAxioms

Where are all these rules and justifications written down?

Under Bostrom's view, the universe is a simulation, or at least something that can be seen from the simulation since most of it is just phenomenal. — noAxioms

A simulation of what? And here we go in circles again.

Yes, our universe is what it is, and that's an intantiation in your wording. But the wording give no clue as to the nature of how it comes to be, since any story fits. — noAxioms

The theists say God did it. The sim theorists say God did it and God is a Turing machine. Why am I required to spend any time at all caring about this argument?

Bostrom gives one possible way that it is instantiated. A deity is another. Both fail to solve the problem of 'why there's something and not nothing', but Bostrom isn't positing a solution to that problem. The deity answer often is such an attempt, and a failed one since it explains a complicated thing by positing an even more complicated thing. — noAxioms

Oh no, that's my point. Sim theory is God as a program, constrained by the laws of computation. That's one extra hypothesis. Unconstrained God is MORE LIKELY than constrained God. Why is God constrained to computability? If there is a God, I imagine God can solve the Halting problem (simply by looking at all the programs and seeing which ones halt) and therefore, God is not computational. That's a pretty good argument IMO.

I think I understand your usage of that word, and I don't in any way presume that I am instantiated. — noAxioms

Really. You're not here at all? You're imagining all this? But the thing that's imagining exists. So that was instantiated.

You were instantiated and you are instantiated at every moment of your existence.

But that's me, being far more skeptical than most. — noAxioms

That you don't exist? That takes skepticism a bit too far.

Being instantiated doesn't solve any problems. — noAxioms

Nor does denying you exist.

I personally suspect that the sum of 2 and 2 is 4 even in the absence of anything actually performing that calculation (absence of it being instantiated). Apparently I am in the minority in this opinion. — noAxioms

That's a different subject entirely. Best if I don't respond with my opinion.

I never said your opinion is wrong. It's just a different one than somebody else's. Different premises. — noAxioms

Well these days even that's heresy.

I think I'm in the minority of being somebody who has opinions X and Y and such, and I also think I'm mostly wrong about them. Some are probably right, but I realize that the odds of me getting most of them right is stupidly low. — noAxioms

This conversation is flaming out entirely.

God instantiated the universe. You say God is a digital computer.
I say that? — noAxioms

You say that Bostrom says that, but then you say you disagree with Bostrom. But here I meant you as someone in general who believe in simulation theory.

'God' sound like the extra assumption in that statement. Occam says it's better to ditch both the deity and the simulation layers — noAxioms

So you reject simulation theory. Good. We're in agreement. Let's stop arguing with each other and join forces and fight the evil simulation theorists.

Surely, the contradiction is the result of the lack of any definition of the terminal state. If the terminal state could be a plate of spaghetti, why couldn't be a lamp that is neither on nor off?

I really cannot see what you two are arguing about. Why does the difference matter? — Ludwig V

Me either.

The plate of spaghetti is a great dramatic way of making the point that there is no definition. But the series is defined on the basis that its limit is 1. You can't derive 1/2 from a plate of spaghetti. — Ludwig V

Don't follow. The limit of 0, 1, 0, 1, ... can not be 1. Nor can it be 0. It's a sequence that has no limit.

My point is that I think that the disagreement between you and fishfry is about different ways to make the same point. — Ludwig V

I do not think @Michael and I are making the same point.

I'm currently feeling unwell and will reply shortly. Cheers, and thank you for continuing this dialogue. — keystone

No worries, as they say. Get well soon.

Conclusion: set theory is in violation of the law of identity. I've explained to you why this is the case. Do you agree with me? — Metaphysician Undercover

LOL.

No, I don't agree with you.

The terminal state isn't just undefined; any proposed terminal state is inconsistent. The lamp cannot be either on or off after two minutes even though it must be either on or off after two minutes. This is a contradiction, therefore it is impossible to have pushed the button an infinite number of times. — Michael

You can't push a button an infinite number of times. This is not a physical experiment. It's purely an abstract mathematical exercise.

You can define the terminal state to be on, off, or a plate of spaghetti and be consistent with the rules of the game. It's not a real light bulb, it's not driven by a real circuit. You're confusing yourself on this point.

We're discussing the consequence of having pushed a button an infinite number of times, not the limit of some infinite sequence of numbers. These are two different things. — Michael

You can't push a button an infinite number of times. It's not a real button, it's an abstract thought experiment about an entirely fictional entity.

And since when can't we use math to model some real or fictional situation? Did you complain when Maxwell wrote down his equations of electromagnetism? Hey it's electricity and magnetism buddy, it's not math. Surely you are not trying to make this absurd claim, are you?

The sequence 0, 1, 0, 1, ... which clearly has no limit, is a perfect mathematical model of this problem. You can define the terminal state -- that is, the state at $\omega$, as 0, or 1, or a plate of spaghetti. It makes no difference to the original sequence.

As Thomson says, "the impossibility of a super-task does not depend at all on whether some vaguely-felt-to-be associated arithmetical sequence is convergent or divergent." — Michael

That's funny, because according to SEP, he used the asymptotic density of the sequence 0, 1, 0, 1, ... to argue that the final state must be 1/2. He made that exact argument using that exact sequence. So you are mistaken, because Thompson has used the exact same reasoning I did. Please read this section:

https://plato.stanford.edu/entries/spacetime-supertasks/#MissLimiThomLamp

We need not use the word same if it bothers you.
— fishfry

Great, I prefer the word "equal". It's better suited for that purpose. — Metaphysician Undercover

I could say I was using the word same in a casual sense.

Or, I could say that when i comes to sets, two sets are the same if they have the same elements. Same set. Equal sets or same set. It's the same.

"Equal" generally allows that the two things which are said to be equal are not necessarily the same. — Metaphysician Undercover

In set theory, two sets that are equal are the same set. Two numbers that are equal are the same number. You're playing word games.

"Same" is defined by the law of identity as indicating one thing only. — Metaphysician Undercover

Same set. That's what it means.

That is the commonly expressed difference between "same" and "equal". — Metaphysician Undercover

Commonly meaning you've said it a couple hundred times, to little effect. You've had the extensional/intensional distinction pointed out to you many times to no avail.

"Equal" indicates a similarity of two things by both sharing an identifiable property, while "same" means that you are referring to one thing only. — Metaphysician Undercover

Well if we're talking about sets, equal and same are the same. And I'm talking about sets.

Generally I disagree with your wording, as indicated above. — Metaphysician Undercover

Sets that are equal are the same set.

The axiom of extensionality indicates what is required for two sets to be equal, yet you state this as "the same". That I take as a mistaken use of words. — Metaphysician Undercover

They're the same set. If you can give me an example of two sets that are equal yet not the same set, well ... you can't.

I didn't say that though. I simply gave an example of how fiction is useful, one that was obvious. — Metaphysician Undercover

So math is a useful fiction.

Many times fiction is used in ways not intended to deceive, like the use of counterfactuals in logic, for example. So, the issue is complex, because mathematics, like fiction in general has many uses. — Metaphysician Undercover

You are agreeing with me.

These are broad generalizations which I can't relate to because I do not accept them as valid
generalizations, so I do not reply. — Metaphysician Undercover

You object to symbolic notation for math. Do you object to symbolic notation for music? For thought and speech? For chess?

For example, you say that language "attempts to...". But language doesn't attempt anything, individual people attempt to do things with the use of language. And, there is such an extremely broad range of things which people attempt to do with language, that it doesn't make sense to make the generalization that what people attempt to do with language is to capture "some aspect of abstract thought". — Metaphysician Undercover

You are avoiding the issues I've raised.

My point has always been that "same" in this context is not consistent with "same" in the context of the law of identity. So, to say " 2+ 2 and 4 symbolize the same set" is to use "same in a way which is in violation of the law of identity. — Metaphysician Undercover

In this context, same means that we may write the symbol "=" between the sets. The axiom of extensionality tells us when we may write A = B. If you prefer to be formal, we could simply never say, even casually, that A and B are "the same." Only that they satisfy the axiom of extensionality and therefore we may write A = B. And if you don't like the equal sign, we could use some other symbol.

Whether we are talking about "same thing", "same set", "same number", or "same kick in the ass", is irrelevant. The point is that this specific use of "same" is very clearly in violation of the law of identity. — Metaphysician Undercover

We need not use the word same if it bothers you. It's sufficient that the statement A = B is true (within set theory) exactly when A and B satisfy the axiom of extensionality. And "=" doesn't mean anything, it's just a symbol.

If the law of identity indicates that only a thing can be said to be "the same", and you do not believe that a set is a thing, and you want to say that a set is the same, then I suggest that you do not agree with the way that "same' is used by the law of identity. Is this the case? Do you believe that mathematicians have a better definition of "same"? — Metaphysician Undercover

Same is only being used casually. When pressed, we always revert to the definition of = given by the axiom of extensionality.

If math is a flagrant fiction, why's it so darn useful?
— fishfry

In case you have never noticed, fiction is extremely useful. I suggest you begin with a look at the obvious, deception. Deception demonstrates that fiction is very useful in convincing others, to help us get what we want from them. And, so is mathematics. — Metaphysician Undercover

Then why are you disagreeing with me? If you say that mathematics is a useful fiction, that's exactly what I would say. And if you say it's a useful deception, that's fine.

May I ask, is chess similarly a useful deception? Language? You didn't respond to my point earlier that language is also a formal symbology that attempts to capture, however imperfectly. some aspect of abstract thought.

You wanted something new so see the above. — Michael

Was that the pseudocode I was supposed to look at?

I entirely agree, with one exception. Code is a notation for a physical process executing on a finite computer. The mathematical lamp problem is the same code, but interpreted in abstract mathematical space where the process never ends. With that caveat I accept your pseudocode.

BUT!!!!!! You have not defined the terminal state. So why do you think there should be a sensible answer for what it is?

After all, there is no number that can serve as the limit of the sequence 0, 1, 0, 1, ...

I don't see how your expressing the problem in pseudocode adds anything. We all have agreed to it long ago, even before you wrote it down. That's the premise of the problem. But the question is about the terminal state, which is not defined.

I am not an avatar in a video game, for the usual Cartesian reason. There's a "me" in here having subjective experiences.
— fishfry
I'm agree with fishfry here, but adding that if the "me" in here is having subjective experience, then I must be able to interact with the presented illusory environment, that is, I can cause things to happen in the environment and get appropriate feed-back from the environment. But that would make me a real person, not a simulation (though I might be a clone.) — Ludwig V

Ah the mind-body problem. I saw a video of Searle giving a lecture. He raised his right arm and said, "I think to myself, I'll raise my right arm. And my right arm goes up. How does that happen?"

(0,1) is the union of (1/n, 1 - 1/n) as n goes to infinity. I just wrote (0,1) as the union of infinitely many open intervals.
— fishfry

Based on your description:

n=1 (1,0)
n=2 (1/2,1/2)
n=3 (1/3,2/3)
etc.

I don't follow. What exactly are you combining into a union? — keystone

Yes you're right, I should say that n goes from 3 to infinity here, forget 1 and 2.

So I'm unioning (1/3, 2/3), (1/4, 3/4), (1/5, 4/5), ...

You can see that if x is in (0,1), then x is in a least one (actually all but finitely many) of the sets (1/n, 1 - 1/n).

I've summarized key aspects of my argument in the following table, where I provide two analogous examples (a fitness gym vs. a path). Can you please tell me which cells in the table you disagree with or do not understand? This will help us identify the confusion and hopefully advance the conversation. You don't have to read the column for the fitness gym. I've only included it to ensure that our thinking is grounded in reality. — keystone

I would have to give this some thought. Would it make progress if I stipulate to your metaphysics? I don't know what to say anymore.

My argument is that the top-down perspective lays equal claim to the irrational points. You can't claim that there are gaps in my intervals just because the non-computable irrational points in my view do not have corresponding numbers. Both of our views of a line involve the exact same 2ℵ0
2
ℵ
0
points. The difference is that my points are bundled together as a single package (thus not needing numbers) whereas your points are independent (thus needing numbers). — keystone

Yes ok, so if you have an alternate way of getting to the same real numbers, what does it matter? The real numbers are categorical. That means that any two models of the second-order real numbers are isomorphic. Second order basically means that you can express the least upper bound property.

You mentioned that a rational number, which is a point, can also be considered as nested stacks of intervals, essentially an arbitrarily small line. However, no matter how small that line is, it can never truly be a point. — keystone

Not a line, a nested collection of lines. The point zero is (-1, 1), (-1/2, 1/2), (-1/3, 1/3), etc.

No real numbers are isolated.
— fishfry

Interesting. It sounds like you might agree that the best one can do is isolate a small bundle around the real number. What is the length of such a bundle - positive rational? Zero? Ever shrinking? — keystone

Every interval containing a given real number, necessarily contains other real numbers. That's the definition of (not) being isolated.

We don't need to discuss supertasks. They're not relevant to either of our positions. — keystone

That was my only point.

You seem to be the one finding two different meanings, one which sounds like how others use 'simulation', and then this other thing which for reasons not spelled out, require exactness, and is perhaps not computational. I have no idea how to simulate something non-computational, let alone doing it exactly. I don't think anybody else is suggesting any such thing. — noAxioms

My point is that Bostrom and others are equivocating simulation in this manner, and this clouds their thinking and confuses everyone else. so yes, I am the one finding two different meanings. I might be wrong, but we are 100% agreed that "I am the one finding two different meanings." I not only conceded that, I insist on it. It's my thesis. Glad we're agreed.

I am allowed to have an opinion, right? I've already admitted I haven't read the paper so I could be wrong. But I do have my opinion, and you seem to understand my opinion perfectly well. In which case I'm happy. I don't require agreement. And you have motivated me a bit to go read it, though I do have other priorities and might not get to it. In which case I'll remain both ignorant and wrong. But at least I'll have my opinion :-)

BTW we do simulate noncomputational things all the time. That's why there's computation! We don't know the exact rules by which the economy works, but we run economic simulation of models of the economy all the time.

Well yea, you deny the premise that physics is computational at the necessary levels of precision needed. — noAxioms

Oh no that's not true. I deny that physics is computational, or rather I'm pretty sure it's not.

But I am certain that we simulate, approximate, and model physics extremely well. What's the famous factoid, that quantum chromodynamics predicts the magnetic moment of the electron to 13 decimal places or some such. I certainly respect and enjoy such brilliant approximating. But what the hell's an electron, and more importantly why, nobody quite knows. We're approximating. Simulating. Modeling. We are not engaging with the thing itself.

Whereas (this is my thesis and maybe not Bostrom's) simulation theory says that our very existence, as it really is, is a program in the big computer in the sky. An entirely different thing than simulation.

No, you're not in the position to say what other people think follows from accepting that 2+2=5. — noAxioms

Oh my, are we disagreeing on propositional logic? I thought that everyone (when playing the game of rationality and logic) agrees that IF 2 +2 = 5 THEN I am the Pope. One need not believe either clause to recognize the truth of the proposition.

Truly not following you since I'm sure you agree with me about this. I mean, we all do believe in material implication, don't we?

You said "Then whatever [VR] is doing is not computational.", and now you say it is nothing but.
Perhaps you don't consider pacman to be an example of VR. It's admittedly crude and not deeply emersive, but most action video games are nevertheless a form of VR. — noAxioms

I'll stipulate that if I had enough quarters and enough beer I might find my experience of the game so immersive that it's practically VR. From PacMan to the new Apple headset's not that far a leap, the underlying tech is the same. So I'll call PacMan early VR, I have no problem with that.

I think the point was about execution speed. Self-driving cars and realtime systems in general are doing something that's not just computation, since execution speed is a factor. I assume computer scientists must have a technical term for that, when execution speed makes a difference in the output of a computation. It's just a semantic point, not too important I think.

The point seems moot. The subject of the topic is simulation theory, not VR theory. VR examples have little to no bearing on simulation hypothesis, a hypothesis you just plain deny due to your lack of belief that a human is computational. — noAxioms

I have opinions, I have beliefs, I don't deny them. I really doubt humans are computational in the sense of our present understanding of computation. We have some extra secret sauce, I don't know what it is.

I don't think I ever said that. This quote is mistakenly attributed to me. Maybe I'm wrong about that. It's a long thread. — noAxioms

I'll agree with you there, and the forum software confuses me sometimes.

You seem to go on endlessly about me somehow disagreeing with the definition of computability. I'm not. Real-time issues don't exist in simulation hypothesis, so those are moot until one starts talking about something other than SH. — noAxioms

Ok. Apologies for going on endlessly. I could end this. We're past the point of whatever we were talking about originally. The best thing for me to do would be to go read the Bostrom paper or remain silent, as Wittgenstein suggests.

Under the simulation hypothesis, you are yourself, which is tautologically true, SH or not. — noAxioms

A system can't simulate itself, except trivially in the sense that an apple is a perfect simulation of an apple. If a thing simulated itself the simulation would have to contain a copy of the simulation and ad infinitum.

There is not a different 'more real' or 'less real' fishfry somewhere else. It is an ancestor simulation, not a simulation of a fishfry model. Your maker is still your mother, also part of the simulation. — noAxioms

But then was is my Cartesian "I", the thing that doubts, the thing that is deceived? Is that not being simulated too? What are these thoughts and experiences I spend so much of my life having?

You are part of one large simulation, and yes, me quoting Bostrom. I don't buy the hypothesis for a moment. — noAxioms

But you'll defend it to the death against the likes of me, who hasn't even read the paper? Honestly I'm not worth the effort :-)

I understand that you're trying to just explain to me what Bostrom says, but my problem is that I have certain preconceptions about what he says, and I believe them pretty strongly. That's because even though I haven't read Bostrom, I've read a bit of simulation criticism and support. So I've formed a worldview about it.

You are not an approximation of anything. The simulation is an approximation of the physics of a system (a planet perhaps). You are part of the state of that simulation. — noAxioms

Is my consciousness part of the simulation? Is that the distinction between VR and Sim?

Probably not, unless the simulation's initial state was very recent (our time) and that initial state included a real person who happened to identify as fishfry. — noAxioms

So maybe or maybe not?

I seriously doubt the GS people centuries in the future would know almost anything about you except your parental lineage, all of which is only relevant if the initial state was set since your birth. It has to start somewhere, and that means that the people of that time are created in thin air, with memories totally consistent with their nonexistent past. Doing that requires a full knowledge of how memory and consciousness works, not just a model of how physics works. The initial state requires far more work than does the simulation itself, which is fairly trivial if you get the state right.
Such things are easy with weather and car crashes, but a nightmare for something complex. — noAxioms

Full knowledge of how memory and consciousness works. So Bostrom is assuming this problem has been solved? But that goes against the claim that "the video games are so much better now," an argument often given in support of the simulation hypothesis.

Probably none of them, unless they are older than the date of the initial state. Anybody conceived after simulation start has zero probability of having a corresponding real person. — noAxioms

So I'm not real, according to the theory. Why is simulation theory better than brain in a vat theory or Boltzmann brain theory?

No. They're no different, except they have real memories, not fake ones put there by the initial state. Maybe the sim only last 10 minutes and everybody is 'corresponding'. This is presuming that the people of the future know exactly who and where everybody is at some random time centuries prior. They don't. — noAxioms

Even if they did, they would not know what each person is going to do next. Unless you also reject free will.

Why do you harp on this? Of what possible importance would it be to anybody in a sim to have a corresponding person (long dead) in the GS? — noAxioms

If I'm a simulation, what am I a simulation of?

If I'm a simulation of something, what is that something? If I'm not a simulation of anything, then by definition I'm not a simulation. I'm an instantiation. This is the semantic point I'm insisting on, rightly or wrongly.

I do realize that I am asking this question of a person who thinks people are special in the universe can cannot be computational like everything else. — noAxioms

Well it's plainly false that "everything else" is computational. For example an oracle for the Halting problem is not computational, yet it's a standard device in computer science theory. So that's one thing that's not computational. There are many others. Chaitin's Omega is not computable but we can define it. For all you know, the world is not computational. For all I know, it is. But You are wrong to say that "everything else" is computational when I know at least two things that aren't. Maybe there are others. Like minds.

You can't go from "people aren't special in the universe," to "therefore people are computational." There's no link between those two things.

Bostrom is maybe. You forget who's pushing the hypothesis. It isn't me, but I'm a computer person and at least I understand it enough to see it for the nonsense it is. — noAxioms

You are strenuously trying to explain to me that Bostrom's idea is nonsense; but not liking my own argument as to why it's nonsense. Why are we doing this?

SH is not a BiV scenario. VR is, but Bostrom is not talking VR. — noAxioms

SH is not brain in vat? Now I'm confused again. I thought VR was like a video game, and SH is where my mind is being instantiated too.

An corresponding people from the initial state of the sim would correspond to people centuries dead in the GS world, so nobody can correspond to any living 'real' person. — noAxioms

So now I'm a simulation of a dead person. You know you keep changing your explanation of this point. I think you should consider retracting it entirely, and trying to understand why I am so insistent on my claim that the word simulation is being used wrongly here.

Sorry, but despite your repeated use of that word, I don't know what you mean by it. — noAxioms

I've explained it as well as I can.

You've mentioned that it needs to be 'exact', and the exact physics of even a small trivial real system cannot be exactly simulated, so there cannot be what you call an instantiation. So we're back only to simulations of the approximate physics of some chosen system. — noAxioms

There cannot be instantiation? What do you think the universe is? We've all been instantiated somehow. We are here. We have been instantiated. That's the point.

tl;dr: Well ... I'm pretty clear in my own mind what I mean, but if you say I'm misunderstanding Bostrom, I can't disagree, since I haven't read the paper. But I really think I'm right and everyone else is confused on this point. So if you simply want to make the point that I have an opinion and that I'm wrong. I agree. I have my opinion and I may be wrong, but the more we talk about it, the more these concepts are clear in my mind, and I think I'm right.

God instantiated the universe. You say God is a digital computer. I say that's one extra assumption and by Occam, we should just stick with God. That's what I get from Bostrom.

I have no problem acknowledging that 2+2=4. I have a problem with people who claim that "2+2" symbolizes the same thing that "4" does. — Metaphysician Undercover

2 + 2 and 4 symbolize the same set. You are the one strawmanning the claim that somebody says they're the same thing.

YOU are doing that. Not any mathematicians, unless they are speaking casually.

2 + 2 and 4 symbolize the same set. Not necessarily the same thing, whatever that might happen to mean in someone's lexicon. "Thing" is not a term of art in mathematics. Set is. I have explained this to you certainly more than ten or twenty times.

And so, I refused to accept your claim to have proven that "2+2" signifies the very same thing as "4" does. — Metaphysician Undercover

I have never made that claim. In your refusal to engage with a single thing I've ever said to you, you BELIEVE, in your heart of hearts, that I have claimed that 2 + 2 and 4 are the same "thing." I will credit you with sincerity for once.

But I have not said that, and if you will go back through my posting history as long as you want, you will never find that I ever said that.

I have said, repeatedly, that 2 + 2 and 4 represent the same set. And that, by the rules of the formal system known as set theory, is as true a statement as a statement ever could be true. It's as true as saying that bishops travel only on diagonals. It's not true by virtue of any property or aspect of the world. It's true by virtue of the rules of chess.

Likewise, the fact that 2 + 2 and 4 symbolize the same set, is derivable from the rules of set theory.

Simply put, if the right side of an equation does not signify something distinct from the left side, mathematics would be completely useless. — Metaphysician Undercover

Ah, the old tautology argument. "Since everything in math follows from axioms, the theorems are already inherent in the axioms, hence they add no new information, hence they are useless."

I counter that argument by asking whether the sculptor adds value in finding the statue within the stone.

Of course he does. The theorems follow logically from the axioms; but they do not necessarily follow obviously. It often takes great ingenuity and insight to derive theorems that are interesting, useful, and beautiful. That's mathematics.

You can say that I have a problem with formalism, — Metaphysician Undercover

I have observed with my own eyes your inability and unwillingness to engage with my Peano proof that 2 + 2 = 4, and the statement of the axiom of extensionality.

I don't "say" the sun rises in the east. I observe it to happen with great regularity. I don't "say" you have a problem with formalism; I observe it.

I will admit that you haven't failed to engage with formalism as many times as the sun has risen. But I'm willing to bet that's only because I haven't challenged you that many times.

because I do. Like claiming that accepting certain axioms qualifies as having counted infinite numbers, formalism claims to do the impossible. — Metaphysician Undercover

You are making a category error akin to complaining that bishops "make church laws, be a judge in church matters and to enforce observance of these laws," in response to my telling you that bishops move and capture along diagonals.

You are railing against a metaphysics that is not claimed by any practitioners of mathematics.

That is, to remove all content from a logical application, to have a logical system which is purely formal. If such a thing was possible we'd have a logical system which is absolutely useless, applicable to nothing whatsoever. — My vetaphysician Undercover

You're just making the unreasonable effectiveness argument. If math is a flagrant fiction, why's it so darn useful?

You are not the first person to notice this, and you are not special for having noticed it. You are "special" in a different sense, for thinking you've had a profound insight, when it's such a commonplace. Bertrand Russell said, "Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true." He was making the same point.

Attempts at formalism end up disguising content as form, — Metaphysician Undercover

I see the point you're making, but what of it? Do you object to chess because it redefines what bishops are? You're so against formalism that you reject it entirely? Why do you bother to read and write? Language is just an abstract formalism for notating thoughts, and we know words are just an approximation to thoughts. Why aren't you equally against language?

producing a smoke and mirrors system of sophistry, — Metaphysician Undercover

Just as language is, as some philosophers have argued.

which is riddled with errors, due to the inherent unintelligibility of the content, which then permeates through the entire system, undetected because its existence is denied. — Metaphysician Undercover

Just like language.

"Man and His Symbols," Jung. Humans use symbols. You are standing four-square against mathematical symbolism but not other forms of symbolism. Presumably you're not picketing art museums and book publishers.

Why is that?

Logical equivalence does not imply "the same as". I have no problem with the axiom of extensionality. — Metaphysician Undercover

Our conversations have proven and confirmed to me that you do have a problem with the axiom of extensionality. You are unable to engage with the mathematical formalism, and therefore you do not understand what it says, and how it is to be used. And the reason you can't engage with the formalism is that you don't seem to understand material implication.

That's what I determined. You've said nothing to convince me otherwise recently. If I have misconstrued your position, I'd be grateful for any correction. But I don't think I have, because before that you refused to even acknowledge my proof that 2 + 2 = 4 from the Peano axioms.

That just shows you won't/can't engage with the symbolism. Either way, if you are not willing to do that, then there's little else I can say.

[Note: These next two paras inserted a bit later]

For what it's worth: The axiom of extensionality is the definition of a symbol. Nobody is saying it means anything at all. If you denied that sets exist, I would agree with you. They're mathematical fictions.

But they are useful, because we can base almost all modern math on them; and two, they're interesting in their own right. You are the only one trying to give the axiom of extensionality metaphysical implications that are not really there.

I have a problem with people who conflate the axiom of extensionality with the law of identity, to interpret that axiom as saying two equal things are the same thing. — Metaphysician Undercover

Are these people in the room with us right now?

..... unless you think of fishfry as an avatar. On the other hand, if I am a simulation that is not aware of the fact, I must be able to act and react in my world. In that case, I am not a simulation of anything. — Ludwig V

I am not an avatar in a video game, for the usual Cartesian reason. There's a "me" in here having subjective experiences.

I can write (0,1) as the union of arbitrarily many intervals. However, I cannot write (0,1) as the union of infinitely many intervals. — keystone

(0,1) is the union of (1/n, 1 - 1/n) as n goes to infinity. I just wrote (0,1) as the union of infinitely many open intervals.

For example, consider describing (0,1) as the union of N equal-length non-degenerate intervals (plus a bunch of points).

Length of (0,1) = Length of each interval * number of intervals
Length of (0,1) = (1/N) * N

This equation is valid when N is any positive natural number, but it is not valid when N is infinity. — keystone

Infinity is not a natural number.

Therefore, it is not sensible to define the interval (0,1) as the union of infinitely many intervals. — keystone

I just showed you exactly how to do that.

And what I'm saying is that since we have to pick a finite number, why not just pick N=1? — keystone

Lost me entirely with this line of thought.

I don't have to cut (0,1) at all to give it length. All 2ℵ0
2
ℵ
0
points that you are looking for are there from the start, albeit bundled together in one single object. Cuts don't create length, all they do is divide length. — keystone

Ok ...

We can sensibly devise a plan for arithmetic on rationals, AND we can completely execute arithmetic on rationals.
We can sensibly devise a plan for arithmetic on irrationals, but we cannot completely execute arithmetic on irrationals.
There is a distinction here that gets lost when you give rationals and irrationals the same status. — keystone

I just don't follow your idea of assigning status to various classes of numbers. That can be done historically, but not mathematically. The rationals can be extended to the reals by a logical process. If you believe in the rationals you must believe in the reals, since the reals are what you get when you plug all the holes in the rationals.

Nothing is for free, not even the rationals. When I start with path (−∞,+∞)
(
−
∞
,
+
∞
)
I have no numbers. Instead I have 2ℵ0
2
ℵ
0
points bundled together in a single object. Again, with the fitness membership bundle, there's not a price for every atom (or rather every point) in the gym. There's just a price for the bundle. We don't get the price per point for free. What would that price even be - seriously? $0/point? A bottom-up pricing model is absolute nonsen — keystone

Lost me again.

What is a plan if not a form of algorithm? — keystone

Plans are far more general than algorithms. Not every plan is computable. Chaitin's Omega is "planned" if you like, but not computable. Chaitin's number illustrates the subtle distinction between definable and computable.

https://en.wikipedia.org/wiki/Chaitin%27s_constant

I'm not suggesting that non-computable points don't exist within the (0,1) bundle; rather, I'm saying it's impossible to isolate such points. — keystone

Chaitin's Omega is one such noncomputable number that can be specifically defined.

You're right that most of the noncomputables have no unique definition and can't be "isolated," but so what?

Humans have never isolated a non-computable point and never will — keystone

Chaitin again. You're wrong.

—it's simply unfeasible to come up with a plan to do so. It seems almost as if you're adopting a stance based on faith. But why? What is the need to isolate non-computable points? — keystone

Please read the Wiki page on Chaitin's Omega. It's a noncomputable number that is perfectly understandable and specific enough, depending only on the chosen encoding of Turing machines.

I'm not referring to a verbal description, but rather to isolating it using cuts. For instance, you might attempt to pinpoint Chaitin's number within the interval (0.007, 0.008) for a specific Turing machine. However, this interval has a finite length of 0.001. It is not feasible to devise a plan to successively refine these intervals to confine Chaitin's number within an arbitrarily narrow range. — keystone

Ok whatever. Not sure where this is going. All real numbers are defined by Dedekind cuts.

A point can never be perfectly represented using a line, no matter how small that line is. — keystone

Did I say the contrary? I don't recall doing that.

I see (0,1) as a bundle of 2ℵ0
2
ℵ
0
points. You see (0,1) as 2ℵ0
2
ℵ
0
isolated points. — keystone

No real numbers are isolated.

cuts. I need to absolutely mince that line until it's made of individual objects that have no length. This requires a supertask. It's not possible. It's not sensical. — keystone

Whatever. This is depressing me a bit. I no longer know what we're talking about.

The above two comments seem to contradict each other. By your definition, a simulation isn't one unless it is exact, and then you give examples of simulations that are not exact. — noAxioms

That's disingenuous. A simulation of the world, as in simulation theory, must be exact.

A simulation of gravity is necessarily an approximation.

That's because the two usages of simulation are being equivocated. Which is why I say Bostrom-like simulation should be called instantiation.

It's not me using the same word two different ways. It's me trying to EXPLAIN that OTHER people are using the same word for two very different things. Leading directly to so much confusion around the subject.

You also said that consciousness is not computational, and therefore the GS cannot simulate via computation, a conscious thing. — noAxioms

Correct. I say that under the hypothesis that we are a simulation, the simulation -- more properly called an instantiation -- is exact.

But I also maintain that the hypothesis is false. So there's no contradiction.

If 2 + 2 = 5 than I am the Pope. The implication is true, and the premise is false. That's exactly what I said.

That puts you into a position to not dictate whether or not those holding a different opinion would say that exactness is required or not. — noAxioms

So I am not in a position to dictated whether or not 2 + 2 = 5 because I hold that the proposition is false? You are not making sense.

So pacman does not involve computation. Hmm....[/quoet]

Pacman ONLY involves computation. No sentience is involved.

The points you're making in this post are trivial and wrong, not up to your usual standards.
— noAxioms

the rate of computation is essential. None of your examples above are VR examples. — noAxioms

ANY phenomenon whatsoever that depends on execution speed is not (only) computational. That's not me saying that, and it is not a deep or clever point. It's merely the definition of computation.

Other examples is any other kind of real-time programming such as a self driving car. A car cannot function if its processing uses paper and pencil. A certain minimal rate of computation is required, or the task cannot be done. Computing slowly isn't enough if you take 3 months to see the stop sign. You seem to assert that what a self-driving car does therefore cannot be computation, but it very much is. — noAxioms

That shows that complexity theory is important in self-driving cars, not just computability theory.

You have already agreed with me on these definitions many posts ago, so I don't understand why you're pretending not to remember agreeing with me.

What does running an algorithm fast do that running the same algorithm slowly doesn't?
I already told you: It gets it done before the computer ceases computing. A human with a pencil lives maybe 50 years (with the pencil) and accomplishes what a computer can do in under a second, and computers tend to last longer than a second before they fail. A computer can come up with an answer while the answer is still needed. In a simulation, there are no deadlines to meet (except getting something done before the computer fails), but in any kind of real-time programming, it must be completed before the output is needed by the consumer of that output. — noAxioms

Agreed. Which does not alter the definition of computation, a point you have already agreed to.

If it whistles Dixie, it is computing something different. Both should have identical output. Euclid's algorithm isn't a real-time task. — noAxioms

You are arguing about a point you have long since already agreed with. Go take it up with the computer scientists. These are their definitions, not mine.

I take your point about real time computing, but that does not change the definition of computability.

Only to a real-time task, and none of your examples are one. — noAxioms

I take your point about real time computation, but it doesn't change the definition of computation. I'm not aware of how computer scientists patch that little issue but I'll concede it for the moment.

There's a model of physics, and any sim is only a computable approximation of that. Bostrom says that a human is a product of physics, and thus can be functionally simulated given a sufficient level of detail, which is still classical. — noAxioms

So who is the me that's being simulated? I'd like to meet him. Is that what "Prepare to meet your maker" means? Then I'm not in a hurry to meet him, so nevermind.

Same model, different supervenience, if I get my terminology straight. — noAxioms

Ok that was about the overlap between Tegmark and Bostrom. Trolling squared.

I don't know what you think it means for a real person to be simulated. — noAxioms

You (or you quoting Bostrom) say that I'm a simulation, meaning that I'm an approximation of something. I'm asking what I'm an approximation of.

Bostrom suggests a sim of ancestral history, which means that random new people get born, and these people do not in any way correspond to actual people that might have existed in the history of the GS. Much depends on what period of history they choose for their initial state. — noAxioms

So do I correspond to an actual person or not? As I go through my daily life and encounter other humanoid-appearing creatures, is there a way for me to determine which correspond to actual people and which don't? Are the non-corresponding creatures like NPCs in video games?

You know you are really out on a limb here, are you sure you want to be defending this theory of corresponding and non-corresponding people?

That would be something other than 'ancestral history'. You say take a molecular scan of a real person, create a sim model of that exact arrangement of matter, put it in a small environment, and see what it does. That's far more likely than this 'ancestral' thing, but it also would be trivial for the simulated person to realize he's not the original since he's been put in this tiny bounded space, a sort of jail, when he remembers getting into the scanning machine. — noAxioms

Farther out on the same limb. You're making a point not worth defending. I don't happen to remember being put in the scanning machine, but only because my vat programmers have erased my memory. Other than that, I'm trapped on this planet. I can't fly like the birds, I can't swim like the fish, I can't live forever, and I have to wait in line at the DMV just to be allowed to drive my car. Sounds like a tiny bounded space to me.

Now according to your stated beliefs, that simulation wouldn't work. It is computational and you say a person isn't, so the simulated thing would not be functional at any level of detail. — noAxioms

Not my stated beliefs. A premise that I reject, but can nonetheless explore the consequences of. I reject that 2 + 2 = 5, but I can still assert that if 2 + 2 = 5 then I am the Pope.

No, I did not suggest there needs to be a 2nd fishfry that is 'real'. Ancestral history simulations certainly don't produce simulated people that correspond to people in the GS world. — noAxioms

So we're all non-corresponding players now? Not just some of us?

No, not two of you. Bostrom's sim hypothesis would have all of us being in one large simulation, and no real fishfry in the GS world. I apologize if something I posted led you to conclude that I was suggesting otherwise. — noAxioms

You said the simulations are an approximation. I asked the perfectly obvious question, an approximation of what? And your answer is corresponding and non-corresponding entities. No answer at all since it raises even more questions. Like whether my next door neighbor is one of those non-corresponders, in which case I should report him at once.

What is approximated is the physics. I can simulate planetary motion by modeling Earth as a point mass. That's a super-trivial approximation of Earth that works for seeing where it is 100 years from now, but it needs more detail if you say want to see which way the planet is facing in 100 years. — noAxioms

Simulation as approximation. As opposed to simulation as instantiation. A crucial semantic error Bostrom made that has led to the exact confusion you have here. He should have long ago corrected himself. If he had called it "computational instantiation theory" it would be much more clear that all he means is God as a Turing machine.

Yes, but over time, many video games keep getting closer and closer to the sort of reality we'
re used to. Not all of them. Some are still total fiction with deliberate fiction physics, if they have physics at all. They're also video games, which makes them VR, not simulations. — noAxioms

VR? You mean Ms. Pac-Man experiences her reality but we know it's only an illusion?

Honestly I think you have gotten yourself tangled up trying to defend the indefensible.

It's low hanging fruit to debunk various videos. There is indeed whole sites dedicated to debunking relativity in all possible ways, and it is a interesting exercise to find the fallacious reasoning in every one of the arguments. — noAxioms

Not what I said. Not debunking relativity. Debunking explanations of relativity by all the popular Youtube physicists. Not the same thing at all.

The delayed choice quantum eraser isn't really an experiment having anything to do with relativity theory. — noAxioms

Makes my eyes glaze, can't hold up my end of that convo.

News to me as well. It seems to require at least some level of what would qualify as 'understanding'. — noAxioms

Yes, the chess-playing LLM is a startling datapoint.

On the other hand, the new Google AI search says to put glue on pizza in case your cheese doesn't stick. So there's still hope for us humans. @flannel jesus

https://www.businessinsider.com/google-ai-glue-pizza-i-tried-it-2024-5

From past experience I understand that fishfry is very slow to accept the reality that some principles employed by mathematicians are incoherent. — Metaphysician Undercover

That's funny, coming from someone who can't understand the axiom of extensionality because you don't understand material implication.

Now I'm confused. I thought you didn't know what "metaphysics" means - or what metaphysics is. — Ludwig V

I don't know what @Micheal means by metaphysically impossible. I know what metaphysics means. More or less. Not an expert.

I'm puzzled now about "natural". If the terminal state of the lamp is not defined, there is no way to define it - natural or otherwise. Or, possibly better, any arbitrary state will do. Hence the plate of spaghetti. — Ludwig V

Contrast with the staircase. The walker is present at each step, and the terminal state is undefined. If we define the terminal state as "walker is present," that is natural, ie continuous. If the walker is defined to be absent at the terminal state, that's discontinuous: 1, 1, 1, 1, ... with terminal state 0. That's unnatural.

Likewise Cinderella's coach. Coach at midnight minus 1/2 second, coach at mid minus 1/4, etc. Pumpkin makes it discontinuous. The natural continuation would be for it to remain a pumpkin.

I'm defining natural as continuous.

Yes, of course - and since it is not defined, Michael can derive a contradiction - two equally possible or impossible states. — Ludwig V

There is no natural continuation. No terminal state that makes 0, 1, 0, 1, ... continuous.

H'm. I would be quite happy with that acceptable usage. But it suggests that 1,1.4,1.41, 1.414... is incomplete, and we are back with the temptation to think that series can somehow be completed. It's probably better to stick with "not applicable". — Ludwig V

Yes, the completion in that case is sqrt(2). That's how we define the irrationals as particular sequences of rationals.

I think that's the heart of the problem. My only hesitation is that the lamp is imaginary, so it sits on an ill-defined boundary between the two. I'm very suspicious of the idea that anything anyone can imagine is (logically) possible. Twin Earth is a good example. But there's a raft of others. — Ludwig V

My point is that the lamp is fictitious and violates the laws of physics. So its terminal state need not be on or off. It could be a plate of spaghetti. That is no more fictitious than the lamp itself.

I don't know what to say. Ryle would go on about category mistakes. In poetry (or politics) people sometimes talk of a "tin ear". That's exactly what this is - a rhetorical gesture that confuses "concrete" with "well defined" and with - well - concrete. It's protesting too much. There must be some repressed doubt going on there. — Ludwig V

I don't just oppose the modal realists. I think they're insane. Or trolling.

You are lucky. It will spare you a world of grief and confusion. Modal logic can look after itself. — Ludwig V

My feelings exactly.

The system is telling me that you mentioned me in the context of this comment in the thread on the Fall of Man paradox, but I can't find any mention of me. But the system is doing some weird things anyway, so I'm not going to worry about it. I do regret not having been aware of the thread sooner. I thought it had something to do with theology. — Ludwig V

I no longer know what any of these threads are about. Perhaps I never did.

As far as I can see I've addressed everything you've said. — Michael

I respectfully disagree. You've addressed none of my points.

In the message you linked to, you concluded:-
So the fact that the status of the lamp at t1 is "undefined" given A is the very proof that the supertask described in A is metaphysically impossible.
— Michael
I think that this is what fishfry was saying. (Substituting "logically impossible" for "metaphysically impossible".) — Ludwig V

No. I'm saying that there's no natural way to define the terminal state. There are lots of ways to defined it. I define it as a plate of spaghetti. That's entirely consistent with the rules of the lamp problem, which only defines the state of the lamp at the points of the sequence, and not at the limit; and it's not a real lamp, so turning into spaghetti is no more unrealistic than cycling at arbitrarily small time intervals.

You persist in searching for an infinite set made up of tiny fundamental building blocks to assemble, like a mosaic. This bottom-up approach colors your perspective, but it's not feasible to represent the interval (0,1) as a union of such micro-continua—it simply doesn't work. I am seeking a construction that, at least theoretically, could be explicitly written down. — keystone

The nested interval construction can be explicitly written down. I perhaps am not sharing your vision here.

In contrast, a top-down approach begins with a singleton set that includes a large fundamental bundle to trim, like a sculpture. Each cut can split it into finitely more, smaller bundles. Although we can continue making cuts indefinitely, there is no necessity to complete a supertask and produce an infinite set of tiny micro-continua. Our strategy only needs to involve a finite number of cuts to produce the necessary elements for the computation at hand. Why do you believe it's necessary to have all the intervals? — keystone

Finitely many cuts won't get you enough of the points. Your continuum will be full of holes. The set of real numbers approximable by finite sequences is only countably infinite.

Oops, I meant to edit the quote as follows with the underlined part being the part I disagree with: "I mean that the sequence itself IS the number pi". — keystone

The sequence is defined as pi. And thereafter, it might as well be taken for pi since, by suitably defining arithmetic on the set of sequence stacks, it will have all the required properties of pi.

In our discussion, I've always acknowledged the value and beauty of irrationals. However, I believe they don't share the same status as rational numbers. — keystone

The reals are logically constructed from the rationals. If you have the rationals you get the reals for free.

Rationals correspond to singleton intervals and represent specific points, whereas irrationals correspond to non-degenerate intervals and represent lines, albeit arbitrarily small ones. You're correct, the S-B tree isn't fundamental to my perspective. — keystone

Glad to hear that!

Yes, but let me qualify my position as I think we will disagree on some details. We can execute cuts to isolate rationals within singleton intervals. We can plan to isolate computable irrationals within arbitrarily small intervals. However, even that plan alone is not feasible for non-computable irrationals. — keystone

I don't see why. You haven't mentioned algorithms, and it's the existence of certain algorithms that distinguishes computable from noncomputable reals.

The best we could plan for is to isolate non-computable irrationals within a finite length interval. I hold this view because any plan we devise must, at least theoretically, be expressible in a finite number of characters. — keystone

Ok. But now you're saying that just because you can't express something, it doesn't exist. Maybe things exist that are beyond our ability to express.

Besides, why would we even need to isolate non-computables? They're social creatures that like to live in large communities. — keystone

Well, some of them can be isolated, if by that you mean defined. Most can't.

No, I view rationals as singleton intervals. — keystone

Yes. Agreed. But they can ALSO be taken to be nested stacks. And then there is no difference in status between the rationals and the irrationals.

I can devise a plan to target an irrational whose midpoint is arbitrarily close to a rational, but when I actually execute the cut, I must choose a positive epsilon value, and the resulting distance between the point and the resulting line segment's midpoint will necessarily be non-zero. It is for reasons like this why it is critical to distinguish between the plan and the execution of the plan. With the top-down view, there is an inherent approximation in the act of executing a plan - a principle analogous to the Uncertainty Principle in QM. — keystone

I don't follow all this but maybe it's ok.

But if you mean that a point has length 0, and an interval has a positive length, the unsigned difference of its endpoints, we agree.
— fishfry

Excellent. This is a crucial point that I will revisit as we continue our discussion. — keystone

Ok good.

I acknowledge that most mathematicians are Platonists and therefore see no necessity for supertasks. — keystone

No. Supertasks are simply not part of math. Not because anyone's a Platonist or a realist or a formalist or whatever, but because the subject never comes up. It's like you're learning to drive, and you ask, well, how do I peel the apple? The answer is, peeling apples is not part of learning to drive. And you say, "Oh, is that because most drivers are Platonists?"

Makes no sense. Apples have nothing do do with driving, supertasks have nothing to do with math.

However, constructivist (and people like me) needs supertasks to arrive at the objects that Platonists consider to exist. — keystone

If that's true, then you are saying that supertasks are a formalism or a concept that let you reproduce standard math, while pretending that you reject parts of standard math.

I don't care if there are supertasks or not, but I am driven to straighten out the bad thinking around limits (or die trying, is more like it).
— fishfry
I'm entirely in favour of the project, but, to be honest, I don't think it is worth dying for. — Ludwig V

I love to spread the gospel of Cauchy and Weierstrass.

I think that's the first time I've encountered anyone on these sites who understands the difference between "discrete" and "discreet". Not patronizing, just saying. — Ludwig V

I'm sure I'm not the only one. I've always been a finicky speller.

Likewise 1/2 + 1/4 + 1/8 + ... and 1 are two text string expressions for the same abstract object, namely the number we call 1.
— fishfry
Now you have me a bit puzzled. In my book, that means that the equation is about the complete series, which seems at odds with the idea that it can't be completed. — Ludwig V

Well "completed" is a loaded term, but it has no mathematical meaning. Mathematicians don't use the word. Given a sequence, it may or may not have a limit. The word completed is not a technical term.

On the other hand, the real numbers are the completion of the rationals, meaning that the reals consist of all the limits of all the Cauchy sequences of rationals. But that's a technical definition, it doesn't have the overtones you're giving to it.

What does "complete" mean? Or does it mean the sense in which it is "always already" complete? (see below) — Ludwig V

"Complete" is not an applicable mathematical term. Unless you want to say that sqrt(2) completes the sequence 1, 1.4, 1.41, 1.414, ... That's an acceptable usage. But it doesn't mean there is any kind of magic jump at the end. It just means the terms of the sequence are arbitrarily close to the limit.

It might be easier to understand if you thought of them as regarding all possible worlds as equally possible. — Ludwig V

I even disagree with that. But some of the possible worlds people (David Lewis, I believe) claim that the possible worlds are real.

I could understand that. I hope they don't mean that all possible worlds are equally actual.... — Ludwig V

Most comprehensively in On the Plurality of Worlds, Lewis defended modal realism: the view that possible worlds exist as concrete entities in logical space, and that our world is one among many equally real possible ones. -- David Lewis

The day I read that is the day I gave up on caring about possible worlds.

But some people tend to think only of one kind of possibility - logical possibility. But there many other sorts - physically possible, legally possible, practically possible, etc. etc. I say that possible means different things in different contexts, but it may be that I should be saying there is cloud of possible worlds for each kind. Or maybe physically possible worlds are a subset of logically possible worlds. It's all very confusing. But I shouldn't get too snooty. There is, apparently, a need to this concept in modal logic, but I don't understand what it is. — Ludwig V

Well it all went over my head when I took a MOOC on the subject.

Well, in that case, you are also traversing the infinitely many possible points along the way, as well as the convergent series based on "<divide by> 3" and all the other series based on all the other numbers, plus all the regular divisions by feet or metres. Or maybe you could decide that all these ways of dividing up your journey are in your head, not in the world. Think of them as possible segments rather than chunks of matter or space. — Ludwig V

Yes. If time is like the real numbers, then Zeno supertasks are a everyday occurrence. You execute one when you roll over in your sleep. This is the point I made to @Michael.

But in math, 1/2 + 1/4 + ... is added together all at once. And the sum is exactly 1, right now, right this moment.
— fishfry
Yes. Thanks for clarifying that for me. That's what I was trying to express when I started babbling on about "always already" in that post that you couldn't get your head around. The comparison with Loop program captures what I've been wrestling with trying to clarify. All that business about getting (or not getting) to the end... It's important though that it's a physical process which takes time. You can switch it off at the end of 60 seconds, and see how far it got, but it won't have completed anything, will it? — Ludwig V

The mathematical series sums immediately. The loop takes time and never achieves its limit, since computing resources are bounded. Under the thought process experiment of "adding the next term" at successively halved time intervals, I'd say it completes in finite time. But that confuses people because we're conflating math and physics.

There's no clear criterion for what is conceivable and what is not, in spite of generations of logicians. It seems pretty clear that some people have a much more generous concept of that than I do. There are famous philosophical issues around that many people seem able to conceive of, but I can't. I don't know what's wrong with me. — Ludwig V

I agree. @Michael keeps saying supertasks are metaphysically impossible, and I think they're metaphysically possible.

I said it couldn't simulate itself exactly. I didn't say it couldn't simulate itself. — noAxioms

Well yes, by my definitions "couldn't simulate exactly" is synonymous with couldn't simulate.

Again, we have this ongoing equivocation of the word simulation. I agree with you that when I program my computer to simulate gravity or the weather, the simulation is not exact. It's an approximation.

But when the GS simulates my consciousness and the experience of my senses, that is exact. There is no other thing "being" simulated. The simulation is the only version of reality.

But you claim Bostrom has already considered that point, and I am not in a position to disagree. So I could be wrong.

Faster does not help when it comes to computation.
It is necessary for a VR, — noAxioms

Then whatever it's doing is not computational. If you execute Euclid's algorithm faster, it is still Euclid's algorithm and has no capabilities (other than working faster) than it did before. It does not acquire more side effects or epiphenomena or "emergences" like consciousness or realism.

This point is essential. And it's not deep. It's just a restatement of the definition of computability, as opposed to complexity, where execution speed matters a lot.

but not a simulation, all of which is pointed out in my topic. It's why a sim can be done with pencil/paper and a VR cannot. — noAxioms

If that is true, then VR is not computational. Because -- by the definition of computability -- speed doesn't matter. If a supercomputer computes Euclid's algorithm, and when you run the same code using pencil and paper it doesn't compute Euclid's algorithm, then the supercomputer did not compute Euclid's algorithm.

This is so fundamental to computing that it must be agreed to. If running an algorithm fast does something that running the same algorithm slowly doesn't do, then whatever it's doing is not computational. Else it could do the same computation slowly. That's the definition.

Jumping into a faster complexity class does not let you compute more things than you could before.

Still, Bostrom needs a fast computer because a simulation with paper and such would have humanity go extinct before a fraction of a second was simulated. Bostrom is not making an 'in principle' argument. — noAxioms

What does running an algorithm fast do that running the same algorithm slowly doesn't? You need to explain this clearly please so that I can understand.

Going faster can never let you compute more things than you could with pencil and paper. If going faster makes a difference, then the difference is not computational. It's something else.
True only in principle. — noAxioms

True by the very definition of computation.

In reality, each number written on a paper will likely rot away before it is needed for the next step. The guy with the pencil will die, as will all of humanity. So will the superfast computer (it cannot run forever in practice), but it will have gotten a lot further than the pencil team, and a lot further than any TM, however pimped out you make it. — noAxioms

Even if I agree 100%, the definition of computability specifically ignores matters of time, space, energy, and resources.

That's a different kind of computability: the ability to get it done before the demise of the thing doing the computing. — noAxioms

No. It's not. It's still computability. It's a different complexity class at best. Those are the definitions. I did not make them up. A function is computable if there's a TM that computes it. Time doesn't matter.

I agree with all your points on the definition of computability, but I wasn't talking about that. — noAxioms

Ok you agree. That's good. So if I write some code, and when I run it slowly it computes Euclid's algorithm; and when I run it fast, it computes Euclid's algorithm and whistles Dixie; then by the definition of computability, which you have now agreed to, whistling Dixie is not a computable function. It it were, the slow algorithm would get the same output as the fast one.

That's the only point I'm making. But it's important, because you claim that running the algorithm fast makes a qualitative difference. And I am pointing out that the difference, whatever it is, can not be a computation alone. It's doing something extra.

.

.
OK. I seem to be blowing it off to semantics, and I made MsPM an extension of me, not an extension of my mind. I consider myself to be conscious, not just a body that contains something that is. — noAxioms

Yes you are, MsPM isn't. And it's not just semantics. Ms. PM does not inherit your humanity, sentience, qualia, or experiences.

Bostrom's view is that a sim of a person is also the execution of an approximate mathematical model. That this conflicts with your opinion means that your opinion is incompatible with what Bostrom hypothesizes. — noAxioms

Wait. There's an abstract mathematical model of a human and any particular sim is only an approximate instance? Is that what you are saying Bostrom is saying? That's more like Tegmark, that we're all mathematical structures.

If you mean that the thing simualted (us) is exactly the same as us, that is tautologically true, yes. But I'm saying that the simulated 'us' cannot be an exact simulation of a person in the GS world. — noAxioms

So there's a simulation of a person AND there's a real person being simulated? Now you have TWO mysteries instead of one. I'm a simulation and there's a real me above that? I don't believe that.

Yet again, the thing being simulated is 'ancestral history', whatever that means. — noAxioms

I'm afraid I am not able to process this. Every simulation entity S has a "real" counterpart S' that's the thing being simulated? This is not a coherent ontology.

Bostrom does not suggest that there is or ever was a real fishfry in the GS world. You are part of the simulation, and that's it. — noAxioms

You have just finished telling me that I am a simulation. For sake of discussion I accept that.

Then you tell me that I'm only an approximation of a real person.

And NOW you tell me that there is no real person.

I don't follow your chain of exposition here.

The history being simulated is quite different than the one that actually happened way in the past history of the GS world, although the initial state of the simulation presumably had similarities to some actual past state of the GS history. Bostrom gives no indication of when this initial state was likely placed. Last Tuesday? A minute ago? 50000 years ago when humanity just started looking like us? — noAxioms

I'll stop responding point by point here because I no longer accept the coherence of the thesis being proposed. I'm a sim fishfry and there's a "real" entity fishfry who's being simulated, but who isn't reall there. My parser has stopped here, I need context and explanation before I can go on.

You are misconstruing what Bostrom and other simulationists believe, then. They're not saying we're an approximation. They're saying our exact reality is being instantiated by a computer.
Again, tautologically true. But our reality is the causal result of an approximation of some past GS state. — noAxioms

Ditto, will defer comment. My brain threw a "Makes No Sense" exception.

Apparently 'because they can' and we don't because we can't. But visionaries have always had a lot of trouble guessing what purposes would be served by future high computing capacity. Anyway, I don't buy that reasoning because it's only there because the hypothesis needs it to hold any water. — noAxioms

Ok. This was about ancestor simulation. I've always thought that was a weak part of the argument. What we do is invent video games that use different physics and are nothing like us at all. We don't run ancestor simulations. "Ok I'll be James Madison and you be Dolly."

And she exquisitely tore apart a lot of the woo surrounding the delayed choice quantum eraser since that experiment is so often billed as an example of reverse causality. The one I tore apart had to do with general relativity, which I don't even know that well, but I know enough to show the assertions in the video to be bunk. — noAxioms

I've seen videos where someone debunks every other relativity video on the Internet, from the Science Asylum to the annoying (my personal opinion) British PBS guy, to the guy from Fermilab, Don Lincoln, and a few others. I don't know enough physics to disagree with any of them.

That works great for opening, perhaps for 20 moves even. But eventually it has to get to a position that it hasn't seen in its training data, and then what? — noAxioms

That's the astonishing thing. It plays pretty well even then, in games whose length exceeds the length of any of its training data. That was the scary and surprising part.

It can't just auto-complete with more text, since the text given would likely not be a legal move. So I'd like to see an article about how it proceeds from a middle-game. Turns out that the LLM is often more capable than I give it credit for. Scary. — noAxioms

I think the article in @flannel jesus's article(s) go over some of that, I haven't read it all yet.

The argument form I am using is called modus tollens and is valid: — Michael

Your post seems to add nothing new, and does not appear to engage with any of the points I've made. I have nothing to add till I see a need to write something I haven't already said.

I've enjoyed the chat but progress has not been made in some time.

You're just proving yourself to be an uneducated person who clearly finds pride in having radical uneducated opinions. — Christoffer

When I criticized the notion of emergence, you could have said, "Well, you're wrong, because this, that, and the other thing." But you are unable to express substantive thoughts of your own. Instead you got arrogant and defensive and started throwing out links and buzzwords, soon followed by insults. Are you like this in real life? People see through you, you know.

You're unpleasant, so I won't be interacting with you further.

All the best.

↪fishfry okay so I guess I'm confused why, after all that, you still said

No internal model of any aspect of the actual game — flannel jesus

The programmers gave it no internal model. It developed one on its own. I'm astonished at this example. Has caused me to rethink my opinions of LLMs.

For full clarity, and I'm probably being unnecessarily pedantic here, it's not necessarily fair to say that's all they did. That's all their goal was, that's all they were asked to - BUT what all of this should tell you, in my opinion, is that when a neural net is asked to achieve a task, there's no telling HOW it's actually going to achieve that task. — flannel jesus

Yes, I already knew that about neural nets. But (AFAIK) LLMs are a restricted class of neural nets, good only for finding string continuations. It turns out that's a far more powerful ability than I (we?) realized.

In order to achieve the task of auto completing the chess text strings, it seemingly did something extra - it built an internal model of a board game which it (apparently) reverse engineered from the strings. (I actually think that's more interesting than its relatively high chess rating, the fact that it can reverse engineer the rules of chess seeing nothing but chess notation). — flannel jesus

Yes, I'm gobsmacked by this example.

Also in passing I learned about linear probes, which I gather are simpler neural nets that can analyze the internals of other neural nets. So they are working on the "black box" problem, trying to understand the inner workings of neural nets. That's good to know.

So we have to distinguish, I think, between the goals it was given, and how it accomplished those goals. — flannel jesus

We know neural nets play chess, better than the greatest grandmasters these days. What we didn't know was that an LLM could play chess, and develop an internal model of the game without any programming. So string continuation might be an approach to a wider class of problems than we realize.

Apologies if I'm just repeating the obvious. — flannel jesus

I think we're in agreement. And thanks so much for pointing me at that example. It's a revelation.

An exact simulation of any GS world cannot be done by that GS.
My comment to which you replied talks about us being the GS, and when we run a simulation of this world it is always an approximation. My example was a VR one, but it goes for an actual sim as well.
If our world is a simulation, then it is either a total fiction created by some completely different (and more capable) GS world, or, per Bostrom, it is an approximation of the GS world. It cannot be exact for several reasons, another of which is that our world is not finite in extent. — noAxioms

I've seen that used as an argument against simulation theory. That it takes energy to simulate each level, and there wouldn't be enough energy several levels down to create a realistic simulation. But that assumes that the upstairs physics is like ours. But that's false. Ms. Pac-Man, should she be sentient, would be wrong to assume that our physics is like hers.

Anyway, read Bostrom. The paper sets out details of where the simulation goes into greater detail (but still an approximation) and where it approximates to a greater degree. — keystone

I might give it another run one of these days. So much to read, so little time, so many Youtube videos ...

The base simulator IS the real world, and it isn't approximating our world, it is approximating its own world according to Bostrom. I say 'base' because we might be 13 levels down or something, but it cannot be infinite regress. — keystone

It can't be simulating itself, you just agreed with that.

Not me. There's probably somebody out there that does. It's like asking if electrons have an interior life. Wrong question. — keystone

Sometimes I think pansychism is the only way out.

Bostrom asks, "Are you a COMPUTER simulation?" (my emphasis)

I suspect he meant a computer as we know it today, but oodles smaller/faster, as if Moore's law can continue for many more centuries. The computers of today are pretty inconceivable to those that first made them, as are the applications to which they can be applied. — keystone

Faster does not help when it comes to computation. I thought we'd agreed on that. A supercomputer can execute Euclid's greatest common divisor algorithm faster than I can with pencil and paper; but in principle there is nothing it can do that I can't.

If consciousness involves a TM "going faster," then whatever it is doing to instantiate consciousness can not be computational. Literally by the definition of computation.

Is that clear? I thought we were agreed on the definition. Going faster can never let you compute more things than you could with pencil and paper. If going faster makes a difference, then the difference is not computational. It's something else.

If a TM can be conscious by going fast, but not by going slow then consciousness by definition is not a computable function. Going fast can bump you into a more favorable complexity class; but it's can't change the status of computability.

You agree with me on this point then, am I correct?
Being correct is not a function of finding one person that agrees with you on something. We could both be wrong. — keystone

I think I meant, was I correct that we are in agreement. Even if both wrong.

Well for one, that mind is computational or not. — keystone

I'm with the nots.

About 2, the difference is pure language. You use words differently than do I. I see no fundamental differences between our views. — keystone

This was about whether my mind somehow extends to Ms. Pac-Man's. I think it's an important point, not just semantics.

I hope that we are agreed that a simulation of gravity or a simulation of the stock market is not the same use of the word as the GS simulating my mind for me.
I don't see a different usage of the word, no. But again, this might just be a difference in language, how each of us uses the words in question. — keystone

It's a thousand percent different. It's apples and rutabagas. A simulation of gravity is the execution of an approximate mathematical model.

The GS's simulation of us is exact. We ARE the simulation. This seems to be a real point of difference, not just semantics.

Again, that cannot be. That's not possible. All of them have to be approximations. — keystone

If we are only being approximated by the simulator, what is being approximated?

Nonsense. Real things are simulated all the time, and all of them are approximations. — keystone

That's exactly why I say the simulator instantiates us, it does not simulate us. Because simulation means something else, and perhaps Bostrom has poisoned these waters forever.

Correct. It needs to be close enough to achieve the goal of the simulation, but it doesn't need to be closer than that. — keystone

Then what is the thing being simulated? You mean there's a real me, and the me that I experience is only an approximation to it? I don't think I agree with any of this.

You are misconstruing what Bostrom and other simulationists believe, then. They're not saying we're an approximation. They're saying our exact reality is being instantiated by a computer.
He goes into some detail about what parts are more heavily approximated and which are done to greater detail. — keystone

Ok I'll have to either read the paper or put a sock in it. The latter takes far less effort and is my likely path here. If Bostrom has already addressed my concerns then I should go read the paper.

Indeed, why? I see no reason to do it, even if we had this unimaginable capability. — keystone

Right. Why would anyone run an ancestor simulation? We don't, why should our future selves?

Agree. I said I didn't get my physics from videos. I didn't say that anybody that appears in a video is disreputable. — keystone

Good point.

I did take apart a Sabine video, showing it to be flat out wrong. It shows that the videos are not peer reviewed, and a good physics source is. This doesn't make Sabine disreputable. It means mistakes remain where peer review is absent. — keystone

The closer she stays to the stuff she knows, the better she is. She likes to extrapolate into subjects she knows nothing about, and then she's often wrong. I've learned a lot about MOND and dark matter from her.

My consciousness is the thing that has the experience, and science has absolutely no explanation for that.
You have no more explanation than science does. Just saying that your comment, true or false, isn't evidence one way or the other. — keystone

I'm not claiming to have an explanation. Just that some of the cogsci folks are out over their skis these days.

Fair enough. I hold the bar higher for LLM because you can ask it to write a program to do a small thing, and it does, but it fails for something more involved, any task that requires more understanding of a deeper problem. This is why no LLM is replacing human programmers at corporations (yet), even if they very much are writing papers for students. — keystone

I have just been made aware, via @flannel jesus, that an LLM has learned to play chess by training on nothing more than the records of games in standard chess notation. By doing nothing more than auto-completing these games as text strings, it can play passable chess. So I have had to seriously back off my own criticisms of LLMs along those lines. Anything that can be notated is fair game for an LLM. I've realized that humanity is doomed and I'm now ready to now bow down to my silicon overlords.

Bottom line is, the LLM algorithm isn't "understand, then write about that understanding", it is more "write something likely to be a plausible reply", a reworded plagiarism of pre-existing content. — keystone

This was my exact position 24 hours ago. Now that I know that an LLM can play chess, I am not so sure. They were able to show that the chess LLM forms a mental picture of the position on the board, even though it was not programmed with any such categories of knowledge. It's really quite startling, at least to me. As close to the "emergence" that I've long argued against, as I've seen yet.

Because asserting that a TM is or is not a person is very different than asserting that a TM and a human are or are not capable of simulating each other. — keystone

I can simulate a TM with pencil and paper. A TM can emulate a person, as via a chatbot. A TM can not instantiate consciousness or self-awareness. So I have been arguing, and so I believe. Hence, there ain't no simulator. There might be a God, because God is the simulator without the requirement of being a computation. That's why I say God is more likely than the simulation argument. One less assumption.

I think they are chainsaws, not to be trifled with by the untrained masses.
— fishfry

This sounds a lot like gatekeeping. — keystone

I won't argue this point with you. I stand by it.

Cesàro summations are very simple. Nevertheless, let's set aside Grandi's series for now. It doesn't have any relevance to my position...until further on. — keystone

I can't see that you have a position. I see you as struggling to understand the nature of the mathematical continuum.

There are fiber bundles in math. A hairbrush with bristles sticking out is a fiber bundle. Off topic but reminded me of the name.
— fishfry

Wow, I feel like a generation alpha kid trying to come up with an email address - all the good names are already taken! — keystone

Funny.

Anyway, I'd actually rather call the bundles 'quanta', but to avoid QM-washing this discussion I'll keep calling them bundles. — keystone

Bundles is is. Should I think of them as tiny little wriggly micro-continua?

Further. bundles have interval descriptions but individual points (within a bundle) do not. In other words, the bundle is the fundamental unit. Sure, we can perform a cut actualize a 0D bundle, such as [0.5,0.5], but that point is emergent. — keystone

Ok, You have all the intervals, but no individual points. Is that right I can live with that. But I already showed that if you have all the intervals, you can derive the points as downward nested sequences of intervals.

I don’t believe that’s the case. It seems there are three factors involved here. (1) I'm refining my ideas—thank you for your assistance with this. (2) I'm improving how I communicate my ideas—again, thanks for your help. (3) You are starting to understand that my perspective doesn’t undermine any established mathematics; it mainly reinterprets it (making bundles fundamental). — keystone

I am not the lord high defender of the mathematical realm. I don't care if you overturn mathematics. I'm not defending mathematics. I'm trying to clarify ideas about mathematics, and trying to frame your ideas in the context of what's already known about mathematics.

Well sure, every irrational can be identified with a descending sequence of open intervals. I can locate pi in the sequence (3, 4), (3.1, 3.2), (3.14, 3.15), (3.141, 3.142), ... I mean that the sequence itself IS the number pi... Does that idea resonate with you?
— fishfry

ABSOLUTELY (except for the underlined part). — keystone

Nothing showed up underlined so I don't know what you are referring to. But if you agree that a descending stack of intervals can be taken as the definition of a point, that's a major agreement between us.

I did note this 2 days ago when I said that 1D cuts around φ are more true to the Cauchy definition of φ than 0D cuts. I also chose the golden ratio in that message because it has a beautiful description using the SB-algorithm. — keystone

It's irrational. I've joined your church. I no longer believe in irraionals.

What, now you believe in irrationals? You know the S-B tree is not the only kind of tree structure that represents the real numbers. I don't know why you are fixated on it.

Look at the figure below. — keystone

I don't relate. Sorry.

I've never denied the significance of irrationals. My view is simply that because irrationals are always encompassed within bundles, or rather are the bundles themselves, they differ distinctly from isolated points/rational numbers. — keystone

Well, irrationals are downward nested stacks of intervals. That's the next best thing. Can we agree on that?

But ... so are the rationals! Right?

Wait, I'm not proposing that an irrational is a descent down to a point. Rather, I'm proposing that irrationals are infinite descents involving arbitrarily smaller intervals. — keystone

That's exactly what I said. There is no point. All there is is the downward nested stack. We identify the stack with the point that it represents, even if the point isn't "there."

The interval never has a length of 0 whereby a single irrational point is isolated. — keystone

No real number is isolated. Any interval that contains it necessarily also contains infinitely many other real numbers on either side of it. But if you mean that a point has length 0, and an interval has a positive length, the unsigned difference of its endpoints, we agree.

Ah, okay, so you don't require a point at pi. Awesome. It seems like we're making progress. — keystone

Yes. I don't require a point at pi. I simply define pi to be the nested stack "above" where it should be. Or more accurately, the equivalence class of all the nested stacks above where it should be.

Once we're completely aligned, I'd like to explore what I believe are the unseen and surprising consequences of this perspective with you. — keystone

Ok! Very much making progress. But do note that what I'm describing is actually the standard mathematical way of thinking about the real numbers. The method of nested stacks is a small variation on the method of Cauchy sequences.

Distinguishing between planning and execution is paramount. The inability to differentiate between them is precisely why there are so many infinity cranks. Cranks reject the concept of completing a supertask. — keystone

Forget supertasks please. There's been enough silly talk about them.

On the other hand, mathematicians refuse to reject supertasks (or ideas implicitly associated with them) because they carry profound aesthetic and practical value. — keystone

Mathematicians in general have no interest in supertasks. They're mainly a curiosity for the computer scientists as I understand it.

I find myself in the middle ground. What I suggest is that mathematicians would find complete satisfaction in merely planning the supertask, without concerning themselves with the imperfections of its incomplete execution. — keystone

I don't know why you think that supertasks are an interest of mathematicians.

There’s a lot wrong with the world today, but would you really want to live an Amish or Mennonite lifestyle? — keystone

It's a thought. I don't believe I'd take well to getting up at 5am to milk the bull.

Personally, I appreciate living in the most interesting of times, despite the uncertainty of our future. — keystone

I like the modern world, but I don't think that applied mathematicians are universally engaged in creating good.

I simply do not understand why you jump to saying that means it's metaphysically impossible.
— fishfry

Because it leads to contradictions as shown by Thomson's lamp, defended here and expanded on here. — Michael

Thompson's lamp does not lead to a contradiction showing that supertasks are impossible. That's your interpretation, which you are failing to explain or defend to my satisfaction.

Also because it's the conclusion of this sound argument:

P1. If we can recite the natural numbers at successively halved intervals of time then we can recite every natural number in finite time
P2. It is metaphysically impossible to recite every natural number in finite time
C1. Therefore, it is metaphysically impossible to recite the natural numbers at successively halved intervals of time — Michael

P2 is false. As shown by P1. But look, Michael. We have not said anything new to each other in about a week. May we not just agree to disagree? I already pointed out that you claim P2 is true essentially by claiming it's true. Circular.

I justify P2 with this tautology:

P3. If we start reciting the natural numbers then either we stop on some finite number or we never stop — Michael

How in this great vast wonderful world of ours, does P3 justify P2? They're not even related. You are just confused about what it means to iterate an infinite sequence in math. It doesn't stop, because there's no last element. But under the successive halving hypothesis, all numbers are recited. One day you are going to wake up and this is going to be as clear to you as it is to me. Till then, I can't really repeat it any more times than I already have.

Again:


(1) The sequence 1, 2, 3, 4, ... never stops. It has no last element. You can always find the next one.

(2) Under the successive halving hypothesis, all numbers are counted. Because as can be plainly seen, there is no number that isn't.


When you understand that both these are true, you will be enlightened. I implore the math gods to bring you this insight in a dream. Else my fingers are going to fall off repeatedly explaining it to you.

Metaphysical impossibilities are things which are necessarily false; e.g. see Kripke's Naming and Necessity in which he argues that "water is H2O" is necessarily true even though not a priori (i.e. logically necessary). — Michael

Ok thanks for that. So something is metaphysically impossible if it's necessarily false.

But I do believe that under that definition, I have shown that a Zeno-like supertask is NOT metaphysically impossible, because it is NOT necessarily false. A Zeno-like supertask is indeed POSSIBLE under the assumption that time is like the real numbers, and that an interval of 1 second is equal to an interval of 1/2 second plus 1/4 second, dot dot dot, exactly as it works for the mathematical real numbers.

I would be the first to admit that such a think is highly unlikely. But it is not inconceivable, and therefore is is not necessarily false, and therefore it is not metaphysically impossible.

That is my rejoinder to your claim that supertasks are metaphysically impossible. I can conceive of a circumstance in which they're possible.

But I would even go so far as to say that supertasks are logically impossible (as shown by the above argument and Thomson's lamp). I simply went for the phrase "metaphysical impossibility" because it's the weaker claim and so easier to defend.[/quote]

Because it leads to contradictions as shown by Thomson's lamp, defended here and expanded on here. — Michael

Thompson's lamp shows absolutely no such thing. And of all the paradoxes you could think of, Thompson's lamp is the least relevant thought experiment possible. It just shows that there's no natural way to define the limit of a sequence of alternating 0's and 1's. A trivial observation. Nothing to do with the metaphysical impossibility of supertasks.

Also because it's the conclusion of this sound argument: — Michael

I'm going to skip engaging with the rest of this. I have articulated my objections to your claims as clearly as I humanly can; and many times over already. I haven't said anything new to you in my last half dozen posts. You just prefer not to engage with my arguments. I wish you would.

Thanks for clarifying that. I find it quite hard to remember what everyone's position actually is. It gets lost in all the detail. — Ludwig V

Yes, I am experiencing that myself. No idea what's being argued in some of these threads or what claims anyone is defending.

I try to take a useful role around here clarifying some of the vague and imprecise mathematical ideas people have. Misunderstandings around mathematical convergence and limiting processes abound in supertask and Zeno discussions. My main goal is to try to rigorize and clarify the mathematical discussions, without necessarily taking strong positions on the paradoxes themselves. I don't care if there are supertasks or not, but I am driven to straighten out the bad thinking around limits (or die trying, is more like it).

One might say that one cannot complete such a series. I'm not sure of my ground here, but I think you will find that everything depends on what is meant by "complete" and it won't mean completing a recitation of all the steps in the series. — Ludwig V

Don't remember what that was in reference to, but based on the next para perhaps we're talking about mathematical infinite sums?

I would be very grateful if you could help me clarify this. When you say:-
When a mathematician says that 1/2 + 1/4 + 1/8 + ... = 1, they don't mean that you can perform this calculation with pencil and paper before lunchtime. They mean that the two expressions on either side of the equal sign denote the same real number.
— fishfry
That's not quite as simple as it looks. The left-hand side will never equal the right-hand side as long as I try to make them equal by adding further steps in accordance with the same rule (...1/16, 1/32...). That's what it means to say that 1 is the limit, not the last step. But if I add 1/8 again, the two sides will be equal. Does that count as completing the sequence? — Ludwig V

The two sides are equal. Unlike a For loop in programming, the left side is not a process or a sequence of steps. The left side happens "all at once" in exactly the same way that 1 + 1 = 2. It's true right now and it's true for all time. 1 + 1 and 2 are different text string expressions for the same abstract object, the number we call 2.

Likewise 1/2 + 1/4 + 1/8 + ... and 1 are two text string expressions for the same abstract object, namely the number we call 1.

In programming with think of loops as taking place in time. And they do. A loop in a programming language is a notation for a physical process that inputs energy and outputs heat and takes a certain amount of time. And of course the computer process never finishes, it just hits the computational limits of the computer and doesn't get any larger after a certain point.

But in math, 1/2 + 1/4 + ... is added together all at once. And the sum is exactly 1, right now, right this moment. And the reason the sum is 1 is because we cleverly define it to be that way. We define the sum of that series to be the limit of the sequence of partial sums: 1/2, 3/4, 7/8, ... And that sequence has the limit 1, because we have carefully set up the definition of a limit in such a way that it's true.

Am I addressing or at least understanding your concern? It's a common one when it comes to convergence.

In math, the notation 1/2 + 1/4 + 1/8 + ... does NOT denote a process or a sequence of discrete steps.

Rather, it's the sum of infinitely many numbers, taken all at once. And it evaluates exactly to the same abstract number that the notation "1" evaluates to. It is no difference than 1 + 1. It's 2 right now, not later one when the process completes. It's not a process. It's a sum. A binary operation. Two numbers go in, one comes out. Or infinitely many numbers go in, and their sum comes out. Immediately. No resources such as time or energy are consumed. The sum just is.

Whether possible worlds count as real depends entirely on what you mean by "real". For some people, "real" comes down to true. If it is possible that it will rain tomorrow then possible worlds are real because it is true that it will rain tomorrow. For others, a possibility is not actual, so cannot be real. — Ludwig V

Some people regard all possible worlds as equally true. That viewpoint doesn't resonate with me.

Quite so. But I think there is a confusion going on here. If you'll allow a temporary and artificial distinction... Roughly, it's the difference between an analysis, which doesn't change or affect its object, and a division or separation which does. That's the difference between measuring a plank of wood as 10 cm long and cutting it into 1cm lengths. The first is an analysis, the second is a division.
There are infinite ways in which I can mark out the plank, and they are all true at the same time and the physical object that is the plank is unaffected by any of them. True, the marks will be physical objects, so there will be limits to what I can do. But the system allows me infinite possibilities, including a convergent series. None of these makes the slightest difference to the plank. So when you visit Zeno for a beer, the fact that there are infinitely many analyses of your journey does not make the slightest difference. It's all in your head. — Ludwig V

You lost me here. I believe I was arguing to @Michael that it's at least conceivable that we execute a Zeno walk on the way to the kitchen for a snack; and that therefore, the idea is at least metaphysically possible. That's all I'm saying.

Oh maybe I understand ... you're saying that just because the path can be infinitely subdivided, does not mean that I'm actually executing that sequence. I think I disagree. I have to traverse each of the segments to get to the kitchen.

But all I'm saying is that it's at least conceivable; in which case it's not metaphysically impossible. I don't have to argue strongly that it's true; only that it's at least barely conceivable.

(Here's a thought. When you drink your beer, you have to drink 1/2 of it and then 1/4 of it and then... Your beer will never be finished. :smile: But then, a similar argument would show that you can't even start drinking it. :sad: ) — Ludwig V

Right. Aleph-null bottles of beer on the wall, aleph-null bottles of beer. You take one down, pass it around, aleph-null bottles of beer on the wall ... :-)

You could probably help me out by clearly defining metaphysically impossible.
— fishfry
It simply isn't clear. "Metaphysics" is a word looking for a meaning. There is some connection with logic, but what differentiates the two is a mystery. — Ludwig V

I think this was @Michael I was asking. Did my quoting get messed up? Michael keeps saying supertasks are metaphysically impossible, and I want to make sure I understand what he means by that.