Yes, for things I haven't even noticed yet. But I think an explanation is needed if I am in a place I've never been, write a list of what I see, and another person in the same situation puts the same things on their list. — Patterner

My example is memorizing words/symbols without knowing their meaning, only to learn later how to read them. That's proof of information independent of your mind, a sort of refutation of solipsistic idealism.

If they are also asserting mind and consciousness can come from matter somehow, they have an even higher burden of proof. — RogueAI

Bostrom seems to presume this. If they do manage to simulate a human enough to appear conscious, those that deny consciousness can come from matter will simply deny that the simulated person is conscious. A successful simulation won't change their opinion.

Me? I make no such claim. — fishfry

No, not you. No quote of yours was in the bit there to which I was replying.

I say that consciousness is physical but not computational.

What do you mean by that? I mean, technically, none of physics is computational if done to a sufficient level of detail, but I don't think that level of detail is needed in a simulation.
Computation is classical and physics has been shown to be not.

What's the difference between [ID]and sim theory?

Not too much. Both are deliberate choices of interesting mathematics. The vast majority of possible universe are not interesting.

A simulation of gravity does not implement gravity. Simulations of brains therefore do not necessarily implement minds.

I didn't say implement them. I said that they would find the familiar pattern. If nothing is known about how that works, then you can't say it wouldn't happen with the sim.

The question is, why do we mock the Godly street preacher, and venerate the simulation theory TED talker?

There's a lot more veneration of the God talkers than you suggest here, and if Bostrom screamed his assertions from a box in a subway station, he'd get a lot less attention. He's getting mocked plenty in topics like this one. Bostrom is venerated at the Ted talk because the audience is full of people who's seen Inception and think that's what he's talking about.

Again, do you believe in intelligent design? Nothing provokes scientists more than that idea, they hate it. While gladly advocating simulation theory.

I'm gladly advocating it?? Bostrom claims we are in a sim of us: The world simulating us is the same as the one simulated. That's not ID since the design is already made and it is just mimicry. But in general, if you admit that we know nothing of the world running the sim, then the idea is no different than deism.

I see no difference between "God did it" and "The Great Simulator" did it, except that the GS is required to be a computation

Is it? If we can know nothing of those running it, how do we know it is a computation? At what point does it cease to be sim theory and just become straight up god:"whoomp, there it is" theory?

It seems a lot of my answers agree with yours, but your tone suggests disagreement with my replies.

Simulation theory says we are computations. That can only be understood as computation as we currently understand it. Turing machines, finite state automata, etc.

OK. You have a tighter definition of the term. You must call it something else if it is done, but not done as computation as you currently understand it. Do quantum computers qualify? Are they (if one is actually created) beyond our current understanding? Can they run a simulation, or would a different world need to be used? Can a quantum computer solve the halting problem for a Turing machine?

I mean, the god people do it all the time. God created physics, be it computable or not. Time as well, and general causality. That sounds an awful lot like a simulation mechanism to me. Old school says the sim began ~6000 years ago, but lately, in an attempt to avoid all out denial of science, they've backed off to a view of the project starting at the big bang, and perhaps with initial conditions that bring us about, because it's all about us after all.
That's a big difference BTW between god and a sim: A sim is run to see what happens, to gain information. God creates something where he knows exactly what will happen, and he wants that to happen. He gains no knowledge by running the universe experiment, at least not the god typically asserted.

Well then you are agreeing with me. It's a theological claim.

Deism isn't theological. It would be if those running the simulation implemented say a moral code which they expect to be followed by the subjects being simulated, "or else ...".

So the Great Simulator doesn't ask Abraham to kill his son?

That's messing with the simulation, violating the causality rules and such. If it works like that, then its a VR for the great simulator, and the rest of us are NPCs being asked to kill our sons.

But Tegmark's MUH is such a category error that I can't imagine he's serious.

Him redefining the categories is not a category error. You're begging a different definition. Mathematics is not a map in the view.

The MUH predicts that the majority of consciousness are Boltzmann brains, reducing the hypothesis to where it cannot be simultaneously believed and justified. That's a huge hit to the idea, and one which he must be aware, and has perhaps attempted a refinement, but it wasn't addressed in the book.

But now we know better. It doesn't need creation, only simulation!! /s

A simulation is a created thing. It exists in time. There's no evidence that our universe exists in time.

Oh I see your point! Thank you for explaining that. She gets her consciousness from me. I enjoy making Ms. Pac-Man eat the dots. I can see that. But Ms. Pac-Man does not have an inner life.

You see that Ms Pacman is you, but you still deny your inner life?

My experience is her experience.

A bit like you saying that your experience is the same experience had by the body of fishfry. Well, fishfry body doesn't have experience separate from 'you', and similarly Ms Paceman doesn't have separate experience. She does become a zombie while the game isn't being played, zooming around randomly and getting killed in short order.

Is this a form of pantheism? I enjoy throwing a rock, and by your theory, the rock enjoys being thrown.

It does? Where did I say anything like that? Because I intentionally caused it to move? That's different than me being the rock while doing so, making it move on its own.
Pantheism? What's that got to do with it? Do you mean panpsychism?
A dualist has a mind and a body, and typically the body has presumed boundaries which usually don't include the rock, but there's no actual hard definition of where the boundary is since there's nothing physical about it. So for instance, are the clothes I'm wearing part of me? The usual presumption is yes, despite that probably not being the answer if it is asked as a question.
"Where does 'you'" physically stop? It's more of a language thing than a physics thing. I typically don't include the rock as part of 'me', and you probably don't either. I could open an entire topic about this.

But that's his argument against the Chinese room understanding Chinese. He says that we humans provide the meaning or intentionality. He says that the room does NOT have meaning or intentionality.

Searle also plays the game of refusing to apply a word to something nonhuman doing exactly what the word means when a human does it. That's begging his conclusion.

I looked at the wiki page and the argument seems to have been updated. The guy doing it (instead of the computer) cannot pass the Turing test since speed is an issue. Somebody who takes 20 years to reply to 'hello' is probably not going to pass a Turing test. Speed up time in the box and this objection goes away. No, the man in the box does not understand the conversation any more than does the CPU in the AI or than does a human brain cell.

Physics is the historically contingent human activity of Aristotle and Newton and Einstein explaining why bowling balls fall down.

Not talking about a human activity. I'm talking about the actual nature of the world, not how we describe that nature.

Ok ... not entirely sure about this. Isn't it the opposite? If my mind is primary and my experiences are an illusion, the illusion-giver, the simulator, may withdraw my reality at any moment.

That's a description of VR, not a simulation. Mind is primary in that scenario. It is real, and the rest illusion.

With sim, the world behavior (physics) is primary, and things proceed according to the rules, without outside interference or intentionality. I have done both kinds. They're very different.

If there's a simulator, they may get bored of providing me with this interesting reality and unplug me, and I'll cease to be.

That sounds more like a sim, yes. If they unplug it, everything/everybody is gone, but perhaps still on disk somewhere. It could be restarted 2 years from now and the simulated beings would never notice the interruption. They very much would notice if it was a VR.

And if VR is true, the same thing might happen, but my untethered mind will remain, but devoid of experiences.

It would be like quitting PacMan. Devoid of experience of the pacman world, but not devoid of experience.

I did a short breakdown of the topic here: — Lionino

That goes down a rabbit hole of info and posts to even more topics. Good reading.

I was looking at Steffan's slideshow, and it goes into how Cantor's axioms are paradoxical because the set of all sets has smaller cardinality that the set of all subsets of that set. But for similar reasons as have been discussed in this thread, I'm not convinced by it since the axioms only seem relevant to finite sets (similar to a sequence having a first and last step only being relevant to a finite set of steps), and none of the sets in the paradox is finite. So it's a bit like saying infinity squared is larger than infinity, which it isn't.
Far be it for humble me to not be as distressed by this as the hardened mathematicians. I take their word that this has more teeth than I see.

Also of interest is the mention of Godel demonstrating that a goal to find a complete and consistent foundation of mathematics cannot be reached. Does this mean that there cannot be one, or just that we cannot know it to be complete and consistent?

Yes, and I think that Lionino may have been protesting at such ways of talking. If one is not a platonist, the way to say what you want to say is to conceptualise "real" in a non-platonic way. — Ludwig V

I have issues with what most people label 'realism', so I'm probably further from platonism than are most. Real is a relation to me, and I use the word that way.

I've noticed a variety of extensions of the use of "=" lately, so I'm sorry if I misused it.

OK, there can be more than one use of the symbol. We seem to not be in disagreement.


The modal fictionalism link is appreciated.

I don't think the calculus is relevant. — Ludwig V

Well, when was the notion of limits of a series introduced? Not back then I think. I'm not an expert in the history, but Zeno was definitely using techniques beyond the state of the art at the time. Good for him.
There are people today that say that there are no real infinities, whatever that means. I think this might be one example of such an assertion.

If you accept that Twin Earth is not physically possible

Where there's not-water? I accept that as a physical impossibility, yes, but overtaking a tortoise is not.

there's no need to argue about the sun example. Maybe your imagination is richer than mine.

A list of valid options is not a definition of a state.
— noAxioms
Parent = (Mother or father).

Well illustrate. A list is not a parent, so I disagree with the '=' you put there. I'm sure there is a correct symbol to express that any member of that list satisfies the definition of parent.

Tegmark must be trolling. — fishfry

I replied to this in the simulation topic since discussion of it seems to be of little relevance to this topic.

But you [Michae] just proved P2 yourself! You agreed that under the hypothesis of being able to recite a number at successively halved intervals of time, there is no number that is the first to not be recited.

This proves that all numbers are recited. — fishfry

The two of us also seem to be on the same page.

I said that time stops? — Metaphysician Undercover

Not in those words. "Does not allow for a minute to pass", like somehow the way a thing is described has any effect at all on the actual thing.

The specifications do not allow for a minute to pass, that's the problem. — Metaphysician Undercover

Anyway, I see nothing in any of the supertask descriptions that in any way inhibits the passage of time (all assuming that time is something that passes of course).

I don't think so. I said that in the scenario of the op, 60 seconds will never pass.

The OP scenario is pure abstract, and it directly describes a state beyond the passage of a minute.

But clearly time does not stop. In that scenario, time keeps passing in smaller and smaller increments, such that there is never enough to reach 60 seconds, but time never stops.

Ah, it slows, but never to zero. That's the difference between my wording and yours. Equally bunk of course. It isn't even meaningful to talk about the rate of time flow since there are no units for it. The OP makes zero mention of any alteration of the rate of flow of time.

So you deny that numbers exist? Really? — Ludwig V

Not to put words in anybody's mouth, but such a statement depends heavily on the definition of 'exists'. For instance, does the number 37 have a location somewhere in our universe? When was it created? That references a definition of "is a object in our universe". If you define 'exists' as 'is an abstract concept in some mind somewhere', then 37 exists as long as somebody is thus abstracting. It's still a version of 'is part of the universe'.
I am not really sure of the definition Lionino is using. I didn't get it from the brief context.

Look at Tegmark's view mentioned above. He is definitely using a definition of 'exists' that doesn't supervene on our universe, and suggests that the reverse is the case.

Patterner bumped this old post, so I tracked down what was being referenced.

I'm not making any claim other than we know mind and consciousness exist. It's up to the people asserting mindless stuff (i.e., matter) exists and consciousness and mind emerge from it to prove it. — RogueAI

Minds/consciousness can't come from matter, therefore simulation theory is false.
— RogueAI

How do you prove that?
— Benj96

Why is the burden of proof on me? We know mind and consciousness exist. The existence of mind-independent stuff is simply asserted. I would like to see a proof that this stuff exists. Something a little more robust than "go kick a rock". — RogueAI

You're making the strong claim that mind/consciousness can't come from matter, so the burden of proof of that claim is definitely on you. If Bostrom makes the claim that mind/consciousness does emerge from matter, then the burden of proof of that is his. I'm not sure if he's making the claim directly, but his sim argument depends on it, and he's claiming the sim argument, so the burden is still there, as it is on you for your strong claim.

You make a second claim, that sim theory is false if your assertion is true. To me, that's another thing in need of proof. You arrange matter into a person and somehow a mind thingy finds it. What's different about the simulation that the same thing wouldn't happen, that the simulated thing would be conscious the same way you claim to be, despite it being attached only to a simulated physical?

I agree that 'klick a rock' is a catchy phrase, but since the experience of stubbing your toe is identical in the two views, kicking a rock demonstrates nothing. It seems to be a cheap counter to rocks being declared not-real.

Is the idea that the many minds/consciousnesses all think up the same things that we generally take to be mind-independent stuff? — Patterner

That's a far stronger argument for mind independent stuff. It doesn't refute solipsism since there aren't other minds also agreeing on the rock that you haven't even noticed yet. But similar arguments can be used to refute solipsism.

Why do people who reject God accept the Great Simulator? — fishfry

More to the point, why would anybody (even Bostrom) accept the SH? People choose a view either because there is evidence or because they want it to be true. The former is a rational motivation and the latter is rationalized. Bostrom's argument seems to attempt to bend the facts horribly to make the hypothesis plausible. This suggests that he wants it to be for some reason, but I cannot fathom why somebody would want to actually believe that. OK, I see why one might want to appear to believe it: Because of the popularity of the idea from movie fiction. He has gained money/status/notoriety from pushing a view that nobody else is in a coherent manner. Elon Musk is a decent example of an incoherent hypothesis, and he's not doing it for the notoriety that he already had. Without knowing it, he pushes for VR, and I can see reasons why somebody might choose that.

The GS is just God constrained to computability.

The world simulating us is not constrained to the computability laws that constrain our world. It is thus constrained in Bostrom's view, but not in general. It's sort of a computing version of deism. The creating simulator starts it up, but then steps back and never interferes and lays no demands on what the occupants do, nor does it make any promises to them. The typically posited god usually does have promises and demands, but not necessarily under deism.

I laid out my case that Tegmark is a troll here ... — fishfry

I haven't got round to replying to that endless topic yet, but Tegmark is more appropriately discussed here since it has little to do with supertasks.

You say category error: Please explain that without begging a different view. You do explain it there, but you are very much begging a different view when doing so. Tegmark is saying that mathematics (not any mental concept of it) IS the territory. Our abstract usage of mathematics is the map, but that abstraction is not what is the universe.

How does he get around the category error problem, confusing the map with the territory, or the program with its execution? My hat is off to you for having read the source material.

It's not much different than all these centuries where the universe was considered to be an 'object', a thing contained by time and in need of creation. They all of a sudden a new view comes along and the category changes. It isn't an object created in time, but rather a structure that contains time. Most people still hold the 'contained by time' view since it is more intuitive. Tegmark is doing something similar: changing the categorical relations. Refute it from its own premises, but not by begging different ones.

You give your browser far too much credit. It passes no judgment on anything. You are the one who has judgment. The browser just flips bits on your computer to implement certain communication protocols that it uses to exchange data with a web server. And the data has no meaning, it's just a long string of bits. Humans give it interpretation and meaning.

Your refusal to apply the language you use for human activities to something non-human doesn't mean that the non-human thing isn't doing them.

Does Ms. Pac-Man experience pleasure eating white dots,
Obviously yes.
— noAxioms

You can't believe that. Are you joking with me or making some kind of point I'm not understanding? It's not possible that you believe that literally.

Ms Pacman is you. It's a VR game, and you enjoy eating the dots, else you'd not be cramming quarters into the machine. It is a straight up case of dualism. Ms Pacman's consciousness is yours. She is the avatar, who doesn't enjoy the dots any more than you claim your physical avatar enjoys the ice cream.

Searle's rolling in his grave and he's not even dead. That's not true. Searle denies that bit-flipping instantiates intentionality or feelings like pleasure.

Searle says exactly that, since what your avatar does instantiates feeling in your mind. Intentionality comes from that mind and not from the avatar. Likewise, Ms Pacman makes no choices on her own, since the intentionality comes from the mind (you) who is obviously very much enjoying eating the dots.

A physicalist, which Searle is

Perhaps this is the disconnect. In what way is Searle a physicalist? Usually the term is used for a physical monist: All physics (including people) operate by the laws of physics, every bit of which is arguably computational.; Searle perhaps posits a different kind of matter that he still labels 'physics', but the physics community doesn't since there's been no demonstration of it.

I'm still disturbed by the things you claim to believe.

Have I claimed beliefs? Do I believe the rock exists independent of me? Do you know enough of my beliefs to answer that?
What's the point of sharing them? I try to understand the alternatives, and point out those alternatives to those asserting that some particular view must be the case. I don't think I assert that any particular view must be the case, but maybe I do sometimes. Like I said, I shy away from something like BIV due to it being empty of information, but not because it must be otherwise.

Anyway if simulation theory is true, we're all characters in a video game

No, that's if VR is true. SH is not modelled by a video game.

So when someone describes the situation in a way that seems to make that fact impossible, why don't we just reject it as inapplicable? — Ludwig V

I do, but Zeno's division of the task didn't seem to make anything impossible. To read Aristotle, Zeno seems to believe in the discreetness of anything of magnitude, directly contradicting Aristotle's physics of the day, which were his opinions pretty much by definition. Much of his opinions held for millenia. Some still do.
Also keep in mind that physics was absolute back then, and calculus was unheard of.
So Zeno's premise that in any task of changing location, one must first go to the halfway point. Zeno seems to have put that up there as a ridiculous premise, one in which he didn't believe. It was an attack on Aristotle's position which would find no fault with the statement. Given Zeno's beliefs, the premise above is false, and he attempts to demonstrate why, but of course he can only do so by begging his own opinion, which is the second premise that I've been going on about.

But we allow physical impossibilities into fiction all the time. They even crop up in philosophical examples. "The sun might not rise tomorrow morning"

Not an example of a physical impossibility. Yes, i agree that physical impossibilities can be turned into fiction. Did I say otherwise?

Your point about the final state not being defined is about logic, not physics (despite some people thinking that it is about physics).

The state of Achilles is that he is even with the tortoise. It's admittedly not final because he continues on after the task of overtaking it is complete and takes the lead. There's nothing about that where physics stops being relevant.

The lamp example? That isn't physics. Never was.

In any case, the final state is defined. It must (on or off) or (0 or 1).

A list of valid options is not a definition of a state.

Wouldn't it be more accurate to say that it is undetermined?

Synonym?

But it would be absurd to say that every state in the series is indeterminate.

They are, or at least the existing ones are. None of the ones you listed was an existing step.

The time length is irrelevant. — Metaphysician Undercover

Says the proponent that time stops.

See my comment above. I suspect Zeno believed his premise to be false, that one must first get halfway before getting to the goal. He was trying to illustrate this belief by driving Aristotle's assertions to absurdity, but he must beg his own beliefs to do this.
If there was a better worded argument provided by Zeno himself, perhaps Aristotle didn't convey the full argument, in the interest of waving away a suggestion that he is wrong. So many modern mathematical tools were not available to them back then.

I gave you Aristotle's wording.

To me it was just another wording, but apparently so since I see it referenced verbatim on so many discussions. Interesting is the total lack of mention of the tortoise.

He rejects most of the arguments because they contradict his own assertions.

The matter of instants appears irrelevant here, and the problem seems to be with the assumed nature of space, rather than time.

The argument is the same with space. He says "time is not composed of indivisible moments any more than any other magnitude is composed of indivisibles". Space qualifies as an 'other magnitude'.

Like above, noAxioms insisted Zeno did not conclude that the faster runner could not overtake the slower, — Metaphysician Undercover

I said no such thing. Zeno very much is reported to have concluded such things.

requires that consciousness is computational, a point I strenuously disagree with, with Penrose and Searle on my side.
— fishfry

Why do you think it's not computational? — RogueAI

With the Penrose & Searle reference right there? The answer is obvious. Bostrom obviously doesn't hold this view.

So you DO have axioms :-) — fishfry

I hold them to be true out of necessity, not because they necessarily are. Another one then I forgot to list: No magic. "I don't know, needs more investigation" is a far better answer than the god of the gaps explanation. Every time one of those open questions finally gets answered, it's never magic. The magic explanation is thus far on the wrong end of a shutout.

Why does the sun cross the sky each day? God carries it thus. What's have we learned since? Clue: It isn't that Earth goes around the sun, since it doesn't do that each day, yet that's the rebuttal typically given.

Likewise Tegmark's mathematical universe. An even more obvious troll. — fishfry

You may not buy into Tegmark's suggestions, but that doesn't make him a troll. I don't agree with him either, but I still read the book and find it revolutionary. His attempts at empirical evidence are completely faulty, but one is expected to pony up evidence to bump the idea from interpretation to actual 'theory'. He doesn't call it that, only calling it 'hypothesis', but even that word implies falsifiability.

Is your web browser passing judgment on the opinions you post to this site? — fishfry

Matter of time. Right now it only passes judgment on my choice of sites on which I choose to post my opinions.

Does Ms. Pac-Man experience pleasure eating white dots,

Obviously yes. As a Searle fan, you should know this. The question is does Blinky experience pleasure eating Ms Pacman? Blinky is an NPC. Ms Pacman is not. The answer there is no only because such experience would provide no benefit to Blinky, so there's no reason for it to be there. This would not be the case in Bostrom's sim, were it possible.

the brain does not operate by the same principles as a Turing machine.

Agree, but a physicalist would say that the brain could be implemented by a Turing machine, just as it could be pencil and paper. Arguably, the latter might actually be more efficient. Turing machines are not designed for practicality. They're a model of computability.

@Joshs Just some side comments on the Zahavi quote

The universe is said to have existed for many billions of years. — Zahavi

That comment (the verb 'exist for', not to mention the tense, implies a universe contained by time. Physicist probably say this all the time, but accepted physics doesn't word it that way. Most people don't reach for B series speak except for explicit need. But the prevalence of A-series in common language goes a long way toward reinforcing the A view.
So are we going to say "the temporal size of the universe is bounded only on one side, and fuzzily bounded on the other"? Who wants to hear that?
All this commentary of mine seems irrelevant to why you posted this.

Husserls fundamental claim is that our experience of a temporal object (as well as our experience of change and succession) would be impossible if our consciousness were only conscious of that which is given in a punctual now, and if the stream of consciousness consequently consisted in a series of isolated now-points, like a line of pearls. If this were the case, were we only able to experience that which is given right now, we would, in fact, be unable to experience anything with a temporal extension, that is, anything that endured. This is obviously not the case, so consequently we are forced to acknowledge that our consciousness, one way or the other, can encompass more than that which is given right now. We can be co-conscious of that which has just been, and that which is just about to occur.

OK, but none of this seems revolutionary. Yes, being conscious of what has just been is what short term memory is for. Being conscious of what is about to occur is the ability to predict, a critical ability if one is to be more fit. The quote calls it imagination, not memory. 'Imagination' probably better describes the predicting end and not so much the direct perception of temporal objects. I suppose imagination is a term that can be used to describe the recall of some immediate memory.

I see a reported conflict between the Brentano view and Husseri's, or rather I don't see a conflict. The seem to be slightly different words for the exact same thing, a difference being at a level that, well, seems irrelevant at least to this topic.

Also, there is no perception of a punctual 'now'. There is process to be had, which delays it a fraction of a second, give or take. Anything perceived is already past.

And not only that, we find a consciousness that still hears the first two notes (it neither imagines nor remembers them).

Good example. I don't see the difference between the 'this' and the 'not that'. It seems like being nitpicky about the words to describe the psychological experience of temporal things. None of the article seems to in any way be relevant to this experience being different from one interpretation of time vs another, which is why I thought the topic was brought up.

You have accidentally quoted Michael as me. — Tom Storm

So I have. Fixed, sort of. Sorry about that.

You seem to get what Josh is conveying more than I. All I see is different words that don't really contract each other. I agree with both sides, and that's probably wrong in some way.

Yes, it affects how we think of them. It doesn't effect the situation, despite all the assertions to the contrary by several members.
— noAxioms
Yes - unless it is a fictional situation - whether in the philosophical or the literary sense. — Ludwig V

I must disagree there. If there are two different descriptions of a fictional situation, and the description affects the thing being described differently, then they're describing two different things, not the same thing in two differnt ways.
The tortoise being overtaken is fiction, but mirrors real physical situations, unlike almost all the other examples in this topic. Describing the motion of Achilles as normal or as a supertask has zero effect on the ability of Achilles to overtake the tortoise.

A thought experiment is a valid method of deriving conclusions from premises. They only get fictional if the premises are faulty, such as the lamp, a device which cannot physically operate as described.
— noAxioms
That may explain why I have been confusing them. Thanks for that.

I must clarify that the lamp itself is physically impossible, making it fiction. I said 'faulty', which it is not. It measures something undefined, so it isn't a contradiction (a fault) that the final state isn't defined.

I have wondered whether one could replace the Thompson lamp with a question, such as whether the final number was odd or even.

Exact same scenario. But it's like asking if the smell of lavender is odd or even. There isn't a number that corresponds to the quantity of steps taken.

The lack of a first step does not prevent the beginning of the task
— noAxioms
It literally does. — Michael

This is exactly why I asked for your definition of 'start' since you seemed to be committing an equivocation fallacy between two definitions. You copped out and gave a synonym (begin) that has the same two definitions.
Is it Sv1 or Sv2? Because you are using both here, playing a language game.

I am saying that the lack of a first step does not prevent the beginning (Sv2 definition, 'transitions from not doing the task to doing it') of the task. You reply that it literally does, but Sv1 is the literal definition (the finite, 'has a first step').
I would not state that the lack of a first step does not prevent the first step from occurring (Sv1). That would be a contradiction indeed.

You ignored it and just said "when the time comes I say the next number". That doesn't explain how the recitation can begin without a first number to say.

You cannot show how that description doesn't work. Your only argument is that it doesn't perform a first step, but the description doesn't mention the need to do so, so the criticism is inapplicable.

I am right now trying to recite the natural numbers in descending order but am silent because I cannot begin.

You are not. It isn't a physically possible task. If you want to do a physically possible one, do Zeno's dichotomy. It's easy. You do it every day. The task is started despite the lack of a first step.

If you take the physical impossibliity away, then you failed because you didn't recite each number at the prescribed time. Your choice not to do so. You didn't follow my procedure. If it's been a minute, you admit to not following it.

Consider the infinite sequence {0, 1, 0, 1, 0, 1, ...}.

Now consider reciting its terms in reverse. — Michael

Undefined. You give no indication of when each number is to be recited. When do I say the 71st to the last zero for instance? I can answer that with a scenario that is properly described. It isn't a supertask as described.

Here's what Aristotle reported:

The second is the so-called 'Achilles', and it amounts to this, that in a race the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.
— Aristotle Physics 239b 14-17 — Metaphysician Undercover

That's apparently what somebody else reported about what Aristotle reported. I've seen it conveyed about 20 different ways. This particular wording says 'never' and 'always', temporal terms implying that even when more than a minute has passed, (we're assuming a minute here), Achilles will still lag the tortoise. The logic as worded here is invalid for that reason since the argument doesn't demonstrate any such thing. I've seen more valid ways of wording it (from Aristotle himself), in which case it simply becomes unsound.

How is this different from what I said?

It isn't much. I just didn't like the fact that the quote didn't match the site linked. Too bad Zeno's original argument is gone. Maybe he covered his ass better than the summary provided by somebody paraphrasing Mr. A.

Without axioms it's difficult to get reasoning off the ground. You have to start somewhere, right? — fishfry

I start with a few.
1) It's not all a lie. I mean, I can't know that, but if it's all crap, then I can know nothing regardless of how I interpret the lies, so I have no choice but to give weight to the empirical.
2) It's not about me. If I am the center of the universe, the rest is probably a lie. So I pretty much find that any view that puts me, humanity, Earth, the universe itself, as the center of something larger, to be unproductive.

Descartes apparently worried about it all being a lie. I reject that road only because it is untravelable, not because it is wrong. But it seems that modern science has thrown a cold paid of doubt on the validity of "I think therefore I am".

VR says that all you know is potentially lies. You are not of this universe, but rather you are experiencing it. All very dualistic.
If you think about it, the view can be empirically tested. Not so much with the simulation hypothesis.
— noAxioms
Yes but everyone agrees with that. There's a world "out there," and we experience it through our senses. — fishfry

Not sure what you mean by empirical testing here.

As I said, one can empirically examine the causal chain that makes the body walk for instance. In a VR, it does not originate in the brain of the avatar, but external, from the mind controlling the body. Say you're playing tomb raider. Open up Lara Croft's head. No brain in there, or if there is, it's just a prop. None of the stuff she does has its cause originating from there.
Why does nobody pursue such investigations? Is technogoly still so backwards that it can't be done? They already have machines that can detect a decision having been made before you are aware of having done so yourself.

It's always been unclear to me which aspect of simulate/VR Bostrom is arguing.
Definitely the former. But Elon musk is arguing for VR, and references Bostrom's paper to support it, so he has no idea what he's talking about.
— noAxioms

Right. And I saw a TED talk where George Smoot, the guy who discovered the cosmic background radiation anisotropy, was enthusiastically advocating simulation theory. Neil deGrasse Tyson too. A lot of people who should know better say trendy things for no reason at all. More arguments against simulation IMO.

Trendy, yes. Kind of dumbs down the validity of any scientific discovery. Why would a simulation choose to display CMB anisotropy if that isn't what a real universe would look like?

I've seen the argument -- perhaps this wasn't in the original Bostrom paper, I don't recall -- that we should consider Pong, the original video game. versus the amazingly realistic video games of today — fishfry

I think that example was being used as an illustration of Moore's law, and not as support for a VR hypothesis.

Yes. Let's talk about this over there. — fishfry

I replied to much of your post, but all over there.

Just the ordinary meaning of "start", e.g. "begin". — Michael

In that case I reject your premise. The lack of a first step does not prevent the beginning of the task, which is simply the transition from the time prior to any of the steps being taken, to the time during which steps are being taken.

You ask me, right now, to recite the natural numbers in descending order. How do I begin to perform this supertask? — Michael

I described exactly how to do that, and you found no fault with it, choosing instead to try a different wording of your additional premise. Why does my description fail? What step is missed? None, and it's done in finite time, so you apparently cannot find fault except by asserting additional premises, all of which take the form of asserting a need to perform a step that by definition doesn't exist.

The paradox is like this. — Metaphysician Undercover

I know the story. You seem to have reworded it for your purposes, since the quote you give does not come from that site, but the site also seems to be conveying the story in its own words, not as reported by Aristotle.

Zeno concludes that the faster runner cannot overtake the slower.

Yes, and without justification, or at least without explicitly stating the additional premise that makes the conclusion valid.

Other quote:
... And it seems that Achilles will always be stuck in this situation.

Same thing. Does not follow.

Funny that the animation on that site below that quote shows 'lightning fast' Achilles moving at only twice the speed of the tortoise. It also shows Achilles slowing down to pretty much a halt, which is why he never passes the tortoise in the animation.

Are we resorting back to the beginning of the discussion here? If you cannot counter my posts, you just start over with the original story? Yes, you can keep the topic going a long time this way, but you're not helping your case.

But different descriptions of the same situation can affect how we think about that situation. — Ludwig V

Yes, it affects how we think of them. It doesn't effect the situation, despite all the assertions to the contrary by several members.

An additional difficulty, I suspect, is that our descriptions are fictional (sorry, thought-experiments)

A thought experiment is a valid method of deriving conclusions from premises. They only get fictional if the premises are faulty, such as the lamp, a device which cannot physically operate as described.[/quote]

According to this, "many philosophers have argued that relativity implies eternalism. Philosopher of science Dean Rickles says that, "the consensus among philosophers seems to be that special and general relativity are incompatible with presentism." — Michael

Relativity does give a strong suggestion, but it is going too far to assert full incompatibility.
The two premises of SR is where the trouble is. I googled "premises of special relativity"

PBS came up first: "the same laws of physics hold true in all inertial reference frames and that the speed of light is the same for all observers"
This suggests a metaphysical assumption. If the laws actually are frame independent, then presentism is wrong since it requires a preferred frame.
But if the same two premises are more loosely worded, then presentism works:
The same laws of physics appear to hold true in all inertial reference frames and that the speed of light appears the same for all observers.

Now it's about appearances, about empirical evidence, about science, not philosophy. This is fully compatible with presentism since all it says is that there may be a preferred frame, but there's no way to figure out which one. The one-way speed of light is not c in any frame but the preferred one, but there's no way to measure the one-way speed of light.

The rest of the theory is unaltered since the only difference between the interpretations of time is that eternalism assigns identical ontology to all spacetime events and presentism assigns different ontology to them (each getting one of four values). None of relativity theory rests on the ontology assignment given by some abstract theory, so there is no incompatibility with relativity theory.

I have found fault with any posted falsification of presentism or eternalism, and I've seen plenty of both.

Do you mean that time is also an aspect of consciousness and therefore located in our cognitive apparatus (but that may be closer to Kant?). — Tom Storm

There are three kinds of time, and those that ask "what is time" never seem to realize it.

1) Proper time. This one is very much physical and real, and is what a clock measures. Proper time is frame invariant.
2) Coordinate time: This one is the abstract assignment of time coordinates to spacetime events and is thus very frame dependent. A calendar is a decent example of one.
3) Phenomenological time, which is the phenomenological experience of the advancement of the present. It is part of consciousness, yes, but also part of pretty much any system that interacts with its environment in real time, but the word phenomenological only seems to apply to the conscious cases. This one seems to be frame independent, and the various interpretations of time differ as to whether the phenomenon corresponds to any physical noumenon.

This IEP snippet may give you a sense of what I mean — Joshs

I read it all, and while I think it fairly clearly conveys what the common sense view is, it then declares itself to not be that, and what it is (the last paragraph) kind of lost me. I could not, from that, summarize what Husserl is trying to get at.

Does Bostrom actually address this distinction? — fishfry

Bostrom seems to presume that consciousness is computational, and leaves it undefended.
In such a simulation, nobody is being fooled.

In a VR, is it a lie to have the subject experience a world that is not the same world as the reality in which the mind exists? If so, most forms of dualism are arguably deceptions.

It is impolite to ask for an opinion, receive one and not replying. — Alkis Piskas

You're not the first in this thread to express disapproval of this practice. I noted it before I posted my first reply and didn't bother to address any of his post directly, knowing that he seems not to even read any of the replies to most of his topics.

I cannot start reciting the natural numbers in descending order because there is no first natural number for me to start with. — Michael

Given your reluctance to clarify the definition of the verb 'to start', I cannot respond appropriately to this statement. I gave a pair of options, or you can supply your own, so long as it isn't open to equivocation.

I'm pretty sure that one comes down to being able to split the pieces up into pieces that aren't measurable — fdrake

Your confidence in your own understanding is then stronger than my confidence in mind.

I still wonder (when I haven't anything more important to wonder about) whether Aristotelian physics is not fully applicable or not physics or false. — Ludwig V

Some of both, I'm sure. The impetus thing had to go (survived until Newton, not bad...), but one could argue that it is a poor description of inertia.

when we finally split the atom. (Which, you will remember, was by definition unsplittable).

The smallest thing still is. Unfortunately the word got applied to something that was a composite object, and they kept that instead of renaming the assembly and keeping 'atom' for anything fundamental.

I don't see the need for any other premise.Achilles is moving, and described as doing this in a way in which he will always have to move further before he can overtake the tortoise. — Metaphysician Undercover

Not always. Just a minute. I know, Zeno doesn't give the time, but we've been using a minute. The way the scenario is described has no effect on the situation compared to a different way of describing it.

Anyway, I deny that Zeno in any way suggests that the overtaking will never take place. He just says that another step always follows any given step.

Michael has added the verbalizing of the natural number count, but that doesn't change it taking only a minute.

The Romans thought mind was a flow, because they had great waterworks, and so forth. We live in the age of computation so we think we're computers. — fishfry

They can't both be right?

You're agreeing with my point.

I think I am, yes.

I've seen Searle argue that consciousness is physical but not computational. Some kind of secret sauce found in living things and not in digital circuits. Don't know much about analog computation with respect to consciousness.

Anything analog can be approximated with digital. But anything digital can be perfectly implemented with analog. Searle is perhaps referencing property dualism? I don't know if I got that right. Can't seem to articulate the differences between the variants.

As Descartes noted, I may be deceived, but there is an I who is being deceived.

I guess I'm even more skeptical than Descartes. I win! I didn't pick my handle for no reason. I try not to leave anything unquestioned.

So the VR theory doesn't solve anything at all, it leaves the mystery of what my own consciousness is.

VR says that all you know is potentially lies. You are not of this universe, but rather you are experiencing it. All very dualistic. The 'brain' in the body (if there is one at all, have you ever checked?) is not what's making any of the decisions.
If you think about it, the view can be empirically tested. Not so much with the simulation hypothesis.

It's always been unclear to me which aspect of simulate/VR Bostrom is arguing.

Definitely the former. But Elon musk is arguing for VR, and references Bostrom's paper to support it, so he has no idea what he's talking about.

The comment above (and my reply) belongs in the other topic. I see you posted more or less the same question there.

There is never a final tick in an infinite sequence, even if the sequence has a limit.

or not a first tick. Zeno's dichotomy very much has a final tick. I can make a scenario that has a first and last, and gets singular in the middle somewhere. Just illustrating the classical snippet: Never say never.

By phenomenological I meant phenomenological philosophy — Joshs

I looked up the SEP article on this, and I don't think I used the term incorrectly. It doesn't seem to presume any particular interpretation of mind. It says:
"In its root meaning, then, phenomenology is the study of phenomena: literally, appearances as opposed to reality."
This is what I am talking about. The phenomenal experience of say a person does not vary depending on which interpretation of time is 'reality'. The experience is the same, and has to be, else there very much would be an empirical test to falsify some of them.
That said, I do realize that some interpretations of mind are incompatible with some interpretations of time. Perhaps this is where you are coming from. My description of one of the interpretations of time conflicts with your beliefs about the nature of mind. That doesn't disprove anybody's view of either.

I am experiencing the present continuously. — Truth Seeker

I already acknowledged your stated opinion in this matter.

None of us can time travel to the past or the distant future.

SEP says otherwise, but I agree here. What most people think of as time travel is impossible. SEP for instance considers time dilation to be time travel, meaning all of us do it just by crossing the street and back. I disagree with this qualifying as much as you probably do.

how do we know that the past and the future exist? — Truth Seeker

They're all interpretations. By definition you can't know this. Only one view (spotlight) says the future exists, and its proponents cannot run a test to confirm the premise.

No, I'm saying that something with no start cannot start and something with no end cannot end. — Michael

This seems to be playing language equivocation games. You introduce the word 'start' here, undefined twice, once as a noun and once as a verb. Given certain definitions of both usages, I may or may not accept this additional premise you state.

The noun definition I will call Sn.
Sn1: The "start" of a sequence is a first step. This is exactly a bound, but you say 'No, ..." above, denying my calling it a bound, so you must mean a different defintion Sn2 of 'start' that this sequence doesn't have. I can't think of one that is distinct from a bound, so you need to help me here.

The verb is also used (cannot 'start'). Here I can think of at least two definitions:
Sv1: To start is to initiate the first step. This again is a reference to the bound.
Sv2: To to start is to commence the steps. There is a duration during which none of the steps has been performed, even in part. There is a duration when steps are being executed, and a duration when all steps have been completed. To start is to transition from the first to the second duration.

I suspect that you are actually equivocating multiple definitions of the verb to make your point. I mean, if you go with Sn1 and Sv1, then I actually agree with your added premise. A sequence lacking a specific step cannot execute the nonexistent step. That holds water. But then you equivocate to Sv2 and conclude that the existing steps cannot commence.

Your argument is effectively "by definition it has no start therefore it can start without a start" which is ridiculous

You are clearly using Sn1 as your noun definition here, which is a direct reference to the bound that we both acknowledge doesn't exist. This usage of the noun contradicts your opening word "No" in your post where you imply that your argument is something other than "an additional premise of the necessity of a bound to something explicitly defined to be unbounded". You contradict yourself.

Given the Sv2 definition for the verb, my argument is pretty much that, yes. It isn't ridiculous because I gave a precise description of how to do it. Your expressed ridicule isn't valid logic.

I am in the present continuously, not in the past. — Truth Seeker

OK, you are a presentist then. Under raw presentism, the past doesn't exist, and you can't 'change' what is nonexistent.

The eternalist view there is no 'the present' or 'the past'. There is a worldline that is 'you' and that worldline is as much a part of 2023 as it is 2024 or 2025. 2024 is not special in any regard. Hence my comment that 'you're already there', It was an eternalist statement, not a statement that makes sense given your interpretation of choice.

Under moving spotlight and growing block, you have a worldline very much like eternalism. You are there in 2023 as well as in the present. Your assertion above indicates that you don't buy into any of these worldline views.

Holding a strong belief in one of the options is just fine. But you can't critique the others if you don't understand them.

A problem I see here is what would we call “evidence” to either confirm or deny one of these theories. What would that look like? When I go “back to change” something existing in the past, when I get there, am I changing something which is presently in front me that is supposedly in the past. Is this evidence of presentism or block theory? — Richard B

Much of this topic seems to have revolved around the concept of 'time travel', which is defined differently from one interpretation to the next. In presentism, there is no past to go to. Under growing block, if you go to a place that isn't the present, how can you 'do' anything since you are no longer at the present? Do you bring the present with you? Such travel is very incoherent in growing block.
Under eternalism, time travel is any worldline that doesn't progress into its own future light cone.

Under any interpretation, time travel seems to be a state where the object is in a state that is causally a function of subsequent events: People having memories of future events for example. This is impossible under classical physics, so discussion of it will not yield any "evidence" about which interpretation is more likely.

preventing the murder of John Lennon. Can we do that? — Truth Seeker

Classical physics does not allow reverse causality. No physics allows non-local information transfer, and saving John would very much constitute non-local information transfer.

Well, I suspect that that sort of 'temporal change' would branch-off into another timeline (i.e. 'parallel' version of this universe) in which JL lived at least one more day — 180 Proof

Case in point. No known physics supports that. It again would constitute non-local information transfer. The branching is allowed under some interpretations of QM. The cause of it coming from subsequent events is not.

What is missing is the phenomenological experience of time — Joshs

The phenomenological experience of time is identical for every interpretation. That's why they're called interpretations.

If no particular step can overtake the tortoise, then the tortoise, by the described motion cannot be overtaken. Where's the need for another premise? — Metaphysician Undercover

Great. Then show the logic that concludes this, without resort to another premise.

Following from the described premises, the supertask cannot be completed.

That logic has not been shown. It's a non sequitur until it is spelled out.

It is logically implied that there is always further distance for Achilles to cover before overtaking the tortoise.

No such implication exists, and no such statement is made. Asserting this would be another premise, and one that makes no sense either. And yes, it would follow that the tortoise cannot be overtaken if this additional premise is added.

It clearly does not have a start. — Metaphysician Undercover

Your usage of 'clearly' implies you are referencing a second premise based on perhaps your intuition. What you may find 'clear' seems to be in direct contradiction with the first premise, I am presuming your 'clear' assumption is something on the order that there must be a first step, equivalent to asserting a bound to something explicitly defined as not being bounded. Of course you're going to run into contradictions if you add a second premise that directly denies the first premise. It isn't a paradox then, it's just wrong.
If that isn't your 'clear' premise, then state what you find so clear.

Michael also makes this mistake despite it being pointed out so many times.

There is no first natural number to start with. — Michael

Totally predictable response. We're like over 400 posts into this topic and you're you're stuck on the same fundamental mistake. You (as well as Meta above) seem to insist on an additional premise of the necessity of a bound to something explicitly defined to be unbounded. My method for performing the task made no mention of doing a first step, but it can be mathematically shown that any given step is done, and that the steps are done in order.

It is logically impossible to have started reciting the natural numbers in descending order.

An unbacked assertion, especially when I showed how to do it. Your presented 'logic' seems to be the argument above, declaring a second premise that happens to contradict the thing you want to find impossible. The logic to which you refer is only valid for finite sets, but you cannot learn this.

You can disprove it by naming a number that isn't covered by my procedure, or by naming a pair of numbers that are recited out of sequence, or some other such demonstration of a violation of the task as described. That's how you go about it when dealing with unbounded sets. Hilbert's hotel is a great educational exercise showing how mathematics deals with infinities.

As for the merely logically possible - as in logically but not metaphysically possible - , I imagine procedures like Banach Tarski. Turning a sphere into two spheres using only the material in the first sphere. But that's just because I can't imagine a concept of space used in metaphysics (like extension) that makes central use of non-measurable sets (things with ill defined extension in principle). — fdrake

I don't think it is the extension that is ill defined with that case, but rather a leveraging of the fact that the pieces are made of infinite points each, and you don't need 'more natural numbers' to count each one of them twice. I don't understand the Banach Tarski thing enough to know why 5 is a lower limit of the number of pieces.
Anyway, I chalk it up to another illustration of why the logical rules of bounded sets don't necessarily apply to unbounded ones. The posters above clearly cannot accept this, and so we go in circles.

Physically possible? That's getting hard. A universe that contains violations of the second law of thermodynamics is metaphysically possible. Like Lord of the Rings, Harry Potter. In the sense that there's a self consistent narrative going through those works of fiction whose behaviour is impossible to translate to our universe, those universes would be metaphysically but not physically possible.

OK, here you seem to use 'metaphysically possible' to mean 'possible in a universe with different physical laws'. But I don't find that very distinct from logically possible.

So when I hear Michael talking about the impossibility of a geometric series "completing" (so to speak) due to being unable to recite the terms in finite time,

I don't think he says that time is the issue. It is his insistence on the need to eventually recite the highest number, after which there are no more. That number doesn't exist, so the task cannot be done because it missed at least that one.

I have seen photos of black holes online — Truth Seeker

No you have not. Light cannot escape from one, so they cannot be photographed. What you see is probably X-ray radiation coming from the accretion disk.

The one presentist interpretation of relativity that I know about (an alternate theory that denies all the postulates of SR) calls them frozen stars because all the matter piles up around where Einstein would put the event horizon. Nothing can fall in in finite time, and the black hole will evaporate before the matter does, so no black hole.

That makes for an interesting way to prove to yourself that presentism is true or not, similar to a way to prove an afterlife. You fall into a large black hole. If you find yourself in there unharmed as Einstein suggests, then all forms of presentism are false. Problem is, just like the afterlife test, you cannot report your findings to the rest of the universe.

Moving spotlight allows them because there isn't a present time, only a present event (a single point in all of spacetime), and that point can be inside a black hole, so there's no contradiction. The other views posit a present moment in the universe, and no foliation of spacetime covers all events, so there are places (black holes) that cannot exist since the present will never get to them.

How do I visit last year?

You're already there.

I thought Moving Spotlight was the same as Block Time Theory. — Truth Seeker

It is. I say as much in my prior post. I've just never heard it called Block Time 'theory' before. The view cannot be logically argued for since it is epiphenomenal.

Apparently, Einstein subscribed to Eternalism/Block Universe Theory. Why would he do that?

Because it's the only one that allows relativity of simultaneity, something that derives directly from the premises of special relativity. Black holes don't exist except in eternalism and moving spotlight, and the latter is kind of a solipsistic view.

None of them are theories. They're all interpretations, and being interpretations, they cannot have empirical evidence.

If the past still exists, why can't we visit it and change it? — Truth Seeker

You can visit it. If you look at last year, you'll find yourself there. Of course the same goes for 2025, except that a view of that is not available in 2024.

This interpretation seems to me both the most evidence-based and consistent with human experience. — 180 Proof

You acknowlege that they're interpretations, which is means there cannot be evidence. Perhaps you feel otherwise. I know at least one that does, and cannot conceive of any other view.

Any presentist model (they all are except eternalism) is more consistent with biological intuition since an assumption of such is extremely advantageous for being fit. So it's built into living things at a very fundamental level. But that doesn't make it true.

While you're busy listing variants of presentism, you forgot moving spotlight.

On the surface, they all make the exact same predictions, so from that standpoint, there is zero empirical evidence one way or another.
Some of the views conflict with other philosophical assumptions (free will being probably the biggest one), so one might choose a compatible view so one doesn't need to challenge other beliefs.

You have not represented the views well. Eternalism does not posit that all events exist simultaneously, which means at the same time. The events all exist with equal ontology, but they have frame dependent time coordinates that are not all the same, so they're not 'simultaneous'. For instance, any time-like separated pair of events is objectively ordered 'this one, then that one'. They can not be simultaneous or ordered the other way around.

Block Time theory as distinct from eternalism? Something you move through? That sounds like a different name for moving spotlight, so perhaps I withdraw my initial comment. It's a dualistic epiphenomenal view.

Plank length is not a physical limit, only a limit of significance. If I have it right, any pair of points separated by a distance smaller than that is not meaningfully/measurably distinguishable from just the two being the same point. It doesn't mean that the two points are necessarily the same point. But I gave some QM examples that suggest a non-continuous model of reality.
— noAxioms
I have been wondering about exactly that point, and trying to work up the courage to articulate in this context. Thanks. — Ludwig V

Well my quote above is not given from authority. Planck units are just a standard of natural units. A Plank length is a small distance, but the fact that they know that distance down to at least 7 significant digits means that far smaller space units are meaningful. Still, wiki says "Since the 1950s, it has been conjectured that quantum fluctuations of the spacetime metric might make the familiar notion of distance inapplicable below the Planck length", which is similar to what I was trying to convey.

There's lots of useful stuff on the wiki Planck units page that's better expressed than me trying to paraphrase it here.

Interestingly, a unit of Planck energy is said to be the equivalent of the chemical energy contained in the fuel tank of a fairly large car. Certainly not the minimum meaningful energy. One unit of Planck force is an even larger silly number. Such is the way with natural units.

If physics requires a non-continuous model of reality, then so be it, but then it would be empirical (physical) and wouldn't affect the geometrical concepts, would it?

A more complex model for the universe does not effect a simple geometric model at all, no. The simple model simply isn't fully applicable to the reality it is supposed to describe, just like Newtonian physics isn't fully applicable to the same reality, despite the fact that they'll continue to teach it in schools.

If what happened to the question whether matter was continuous or not is anything to go by, I think that a third alternative is most likely.

Somebody still suggests that matter is continuous? I mean, that sort of went out the window a couple centuries ago.

I imagined you lot were talking about metaphysical rather than logical possibility. — fdrake

Actually, I've been asking about the distinction between those two. Nobody has really answered. A nice example (not a supertask example if possible) of something that is one but not the other would be nice.

So you’re claiming that it’s logically possible to have recited the natural numbers in descending order. That’s evidently absurd. — Michael

It may grind against your intuitions, but no logical argument against it has been presented. That you personally find it 'evidently absurd' carries no weight.
How does it start? That's easy. When the appropriate time comes, the number to be recited at that time is recited. That wasn't so hard, was it? It works for both scenarios, counting up or down.

I doubt that consciousness is computable — fishfry

what, because consciousness is not a physical process, or that physical processes cannot be simulated? You seem to be in the former camp. If that's the case, then no, it probably isn't computable.

After all if we're computations, what are the odds we'd figure that out right when we're in the age of computation?

Pretty much 1-1 odds. That's when the terminology became part of our language. You describe yourself in terms of the things you know.

We are water. The vast majority of mass would be lost (as would consciousness) if the water was taken away. Lots of pipes going here and there. It's a pretty good description for the Roman days.

Because if so, then where is the conscious mind? In the pencil? In the paper? In the air? In a neural network?

In the process.

Yes, I saw a domino logic gate on Youtube a while back.

Gawd, I spelled it 'Turning' machine. More typos.
Anyway, yes, the discussion was inspired by that. Any moron can create a domino or gate, but creating a nor gate gets tricky. Any gate can only be used once, so it's impossible to create say a flip flop, normally a trivial thing created with a pair of nor gates.

I've not seen the video, but mention of it inspired me to design a Turing machine with the technology. Can dominos be used to run a physical simulation? I think it's possible since I found not obvious roadblocks. I'm tempted to start a topic on it, but not here since it isn't a philosophy topic at all.

Perhaps it's some kind of analog computation, but that's not the same thing.

I've also programmed analog computers in school, never on the job. It's a different sort of thing, I tell ya.

ps -- I checked out the Simulation thread and from there, saw your initial post in the "What is the Simulation Hypothesis" thread, and I agree with everything you said. I especially appreciated the distinction between simulation and VR, which is something a lot of the simulation discussions miss.

Your view of consciousness is modelled by a VR. One big distinction is that a VR cannot be implemented with paper and pencil (or dominos).

I was imagining a clock that speeds up in its ticking to ape a convergent geometric series. — fdrake

OK, that would be pretty much what has been the topic of discussion this whole thread. If it completes in finite time, it's a supertask. Don't forget the inverse case where the clock starts fast and slows down to its final tick.

I think you misunderstand Zeno's paradoxes. Zeno concluded that Achilles cannot overtake the tortoise. That is explicit. — Metaphysician Undercover

Correct, but a second unstated premise must be assumed in order to draw this conclusion, since without it, one can only say that the tortoise cannot be overtaken at any particular step. That second premise might well be that supertasks cannot be completed. That premise is indeed in contradiction with the first premise and empirical observation. At least one of the three is wrong.

even though the logic proceeding from fundamental axioms proves

Fundamental axioms? None of the premises are that. They're both easily doubted.

Due to the strength of the empirical evidence, we are led toward the conclusion that the fundamental axioms concerning the continuity of space and time, and the infinite divisibility of those continuums, must be faulty.

Or the premise of supertasks being uncompletable is wrong, or that empirical evidence isn't as strong as is asserted.

Asserting that your premise of choice must be the faulty one is a mistake.

Why? The ticks per second is also going to infinity. — fdrake

The sum of an infinite set of identical finite numbers is not finite, no matter how small the number being summed. It needs to complete in finite time to be a supertask.

I don't really think it matters whether this is a supertask or not, though. It was an attempt to give an example that hits Michael's argument.

does not prove that the following supertask is metaphysically possible: — Michael

I was wondering about what is actually meant by 'metaphysically possible' or 'logically possible'. The latter is probably the same as 'mathematically possible', but I'm wondering how the former is distinct.

I notice you ignored my prior post. That itself indicates to me that you do not intent to actually consider points made against your stance. I was hoping for more confidence in it.

No. I'm talking about computability theory. — fishfry

Gotcha. No argument then. As I already pointed out, you had referenced power instead of computability: "there's no difference in computational power between parallel and serial processing." and I took it as a statement of work over time.

I brought this up in my simulation-theory topic. A simulation of Earth to a precision sufficient for consciousness can be done by pencil and paper, or by dominos falling, The latter is really interesting: set up dominos so that you get the function of a Turning machine. Not easy, but it seem that it can be done.

Whether someone regards that as a supertask or tells me I forgot about the Planck limit and so forth are different issues.

Plank length is not a physical limit, only a limit of significance. If I have it right, any pair of points separated by a distance smaller than that is not meaningfully/measurably distinguishable from just the two being the same point. It doesn't mean that the two points are necessarily the same point.
But I gave some QM examples that suggest a non-continuous model of reality.

The Zeno Wiki page doesn't mention a horse. Did I miss something? Ludwig V mentioned a horse too.

Yes. Search for 'horse' in the last 20 posts or so.

But empirical knowledge has problems like what Hume showed with the problem of induction. Because of this, empirical knowledge does not prove the supertask to be impossible. — Metaphysician Undercover

Because of this, empirical knowledge doesn't prove pretty much anything to be possible or impossible. That's why science theories are supported by evidence and not by proofs. They'd be theorems, not theories, if they were provable.

That the supertask is not completable is not denied, that it is not completable is what actually leads to the problem. In Zeno' paradox Achilles never catches the tortoise because the supertask is never completed.

I beg to differ. That simply does not follow from the description. Zeno describes a physical completable supertask, which is only as possible as the soundness of his first premise.

Achilles will pass the tortoise, and in the op 60 seconds will pass. This shows that the supertask as a fiction.

Again I differ. The supertask (if that premise is true) is not fiction. I mean, my opinion is that there isn't a physical supertask, but opinion isn't evidence, and I have no evidence (let alone proof) that it isn't a supertask.

Declaring something to be impossible is a strong claim and requires strong evidence.

That seems to me a good response, though not quite the knock-out blow one would hope for. — Ludwig V

If there was an easy knock-out blow to it, it wouldn't be a topic on philosophy/mathematical discussions.

This logical consequence can be shown when the experiment is explained more clearly:

A1. At t0 the lamp is off
A2. The button is pressed only as described by this sequence of operations: at t1/2 I press the button, at t3/4 I press the button, at t7/8 I press the button, and so on ad infinitum

Compare with:

B1. At t0 the lamp is off
B2. The button is pressed only as described by this sequence of operations: at t1/2 I press the button

The status of the lamp at t1 must be a logical consequence of the status of the lamp at t0 and the button-pressing procedure that occurs between t0 and t1 because nothing else controls the behaviour of the lamp.

If no consistent conclusion can be deduced about the lamp at t1 then there’s something wrong with your button-pressing procedure. — Michael

I see that you have an opinion, and that you are attempting to rationalize this opinion. But you leave some pretty low hanging fruit in this post, and rather than have me point them out and you denying whatever it is I post, I invite you to step into my shoes and critique the above. If your opinion was the opposite, what portions of the above argument would you put in bold and say is wrong?

I want to see if you are aware of the issues against which you are arguing.
Your response to me never seems to be along such lines. Instead of pointing out faults in my assertions or whatever, you simply ignore the argument and post yet another rewording of a counterargument, making the same mistakes (from my point of view). So show me that you at least know where I think those mistakes are being made.

The important part is in bold. If there is a problem with the button-pressing procedure, which there is in the case of A2, then this problem remains even if the button is broken and doesn't actually turn the lamp on — Michael

OK, the bold line is telling. There is something wrong with the procedure. I've pointed it out in several posts. The lamp isn't broken. That violates the mathematical definition of how the thing works. There is no physical lamp since physics cannot do what is described.

A clock ticks 1 time per second.
You start with a cake.
Every second the clock ticks, cut the cake in half.
Make the clock variable, it ticks n times a second.
The limit clock as n tends to infinity applies an infinity of divisions to the cake in 1 second. There is no final operation. — fdrake

This is not a supertask, not even as the tick rate increases arbitrarily high, because the cake (if it is continuous, which a physical one isn't) is going to take forever to consume at any clock rate.

I'm sorry I don't know about Zeno's horse — Ludwig V

Look at the context to which my "Zeno's horse" was a reply. You were talking about Ryle saying something on the order of "putting a mathematical harness on a physical horse". It's what Zeno is doing with any of his scenarios, and what almost none of the other scenarios is doing.

If you mean Thompson's lamp, quite so.

The lamp, and almost all the other examples that are not Zeno. They all seem to argue along the lines of <if impossible/self-contradictory thing is true, then contradictions result>. This is a bit like asking "If the sun suddenly didn't exist, how long would it take Earth's orbit to straighten out?"

Do I understand correctly that Thompson actually argued that supertasks are impossible?)

I don't see that. At best he showed that one example is undefined. To prove something impossible it must be shown that there is not a single valid one. To prove them physically possible, one must show only a single case (the proverbial black swan). Nobody has done either of those (not even Zeno), so we are allowed our opinions.

The physical premise of "for something to go from A to B, it must first go halfway there" is very questionable. A great example is a photon going from emitter to detector. Nothing in quantum theory says that the photon is at the halfway point at the time halfway between the emission and absorption events. The principle of counterfactual definiteness (PCD) says it is, and that principle has never been demonstrated to be the case. It is in fact not the case in mosl interpretations of quantum mechanics, including any of the ones that deny faster than light causality.

Not sure what you mean by potential cardinality. — fishfry

Pick a number, say 27. I believe it has been shown that there exists a set the cardinality of which is 27, if that's valid terminology. One could also reference aleph-26, but I'm not sure that one can prove that no sets exist with cardinalities between the ones labeled 1 through 27.

Point being that you get no increase in computational power from parallelization.

I beg to differ. A 16 processor machine can sustain a far greater work load than a single-processor machine. The Cray machines were highly parallelized (SIMD architecture) in which thousands of floating point operations were performed by every instruction. These machines were great for stuff like weather simulation.

No function is computable by a parallel process that's not already computable by a linear process.

With that I agree. But that same function can also be done by paper & pencil. You said 'powerful', a reference to how fast the work is completed, and more processors helps with that.

Coloring the steps reduces to the lamp.

I notice that any scenario with a contradiction involves invoking magic. Suppose this physically impossible thing (infinite gods, stairs requiring faster-than-light speed, lamp switches that operate without delay. No magical measurement of something nonexistent. Zeno doesn't do that. No magic invoked, and the first premise thus produces no paradox.

My Quora feed gives me a lot of cute cat pics lately. Makes me happy. Quora certainly used to be a lot better.

Oh it serves its purpose, but correct answers are not promoted above the others, and apparently a great deal of their posters don't know what they're talking about when it comes to stuff like this.

Ryle might have called it a category mistake and talked of putting a physical harness on a mathematical horse or (better, perhaps) putting a mathematical harness on a physical horse, He and many others thought that nothing further needed to be said. — Ludwig V

It is very valid to apply mathematics to physics, but it really helps then if that to which it is being applied is actual physics. Creation of a device to measure a nonexisting thing is not actual physics.

Zeno's horse is quite real. Almost none of the others are.

That's almost right, the logic is valid, but not necessarily sound. — Metaphysician Undercover

Exactly so. I have correct my post. I meant valid and wrote 'sound' in haste. A simple application of modus ponens shows the lack of soundness of Zeno's conclusion iff empirical knowledge is given any weight.

The conflicting premise which would be used to disprove this, the limitations of divisibility

The conflicting premise seemed to be a denial of the completability of a supertask. He never suggests a limit to divisibility.

↪noAxioms you seem to think the supertask is generating so fast it evades us, in fact we can meet it and persevere at the front of its generation, or even cut it all in one swift equation, — Barkon

I have no idea what that collection of words means, so while it may seem to you that I think it, I quite assure you that I don't.

√ω has no meaning in the ordinals, but I believe it does have meaning in the Surreal numbers, which I don't know much about. — fishfry

OK. I'll accept that. I do believe somebody has shown no limit to the potential cardinality of some sets.

But naturals aren't integers which aren't rationals which aren't reals which aren't complex numbers which aren't quaternions.

Missed one. :smile:

Wiki has many errors.

Ditto with SEP.

In computer science you can always linearize parallel streams, there's no difference in computational power between parallel and serial processing.

I worked a great deal of my career writing code for multiple processors operating under the same address space. It gets interesting keeping them from collisions, with say two of them trying to write different data to the same location.
Anyway, not sure what you mean by your statement. It seems on the surface to say two processors is no more powerful than one, which isn't true, but two also isn't twice as powerful.

Clearly it isn't a supertask if it is impossible to go only half the remaining distance for some intervals. If that is possible, then it must be a supertask.
— noAxioms
Ok, then since walking is commonplace, so are supertasks.

You didn't read my comment then. Ability to move is a given (an axiom, not something that can be proven). Given that, doing so is a supertask only if Zeno's premise holds, that for any starting point, one must first move halfway to the goal. I can't prove that it holds, but I can't prove that it doesn't hold either.

Yes. Although the rationals don't represent any ordinal. The ordinals only apply to well-ordered sets.

OK. Yet another thing I didn't know.

I defined the terminal lamp state as a plate of spaghetti.

Yes, the PoS solution.

unlike the lamp, there IS a naturally preferred solution to the staircase. If the walker is on each step at each time, then defining the walker to be present at the bottom of the stairs preserves the continuity of the path. So the staircase (if I even understood the problem, which I may not have) at least has a natural terminating state.

Does 'bottom of the stairs' imply a bottom step? If every other step was black and white, what color is the bottom step? PoS, I know. Same problem from where I stand.

No idea. Found a physics.SE thread.

I'll look at that. I have all the respect for the PSE guys, who blow everybody else away. Quora stands somewhat at the opposite end of that spectrum.

It [completing without a last step] means that is isn't a finite sequence of operations.
— noAxioms

No, it doesn't. Saying that it is an infinite sequence of operations means that it isn't a finite sequence of operations. — Michael

Finite means bounded. That means a finite sequence of steps that has a first and last step. An infinite sequence means not (a finite sequence of steps that has a first and last step). It being called 'infinite' literally means that the last step you keep referencing doesn't exist.

I see you have Barkon joining your ranks. I hope you find the company good.

What does it mean for every operation to occur without some final operation occurring? — Michael

It means that is isn't a finite sequence of operations. How is it a contradiction that there isn't a final natural number? Instead of just asserting it, show it.

@Barkon also seems to be running on his intuitions and makes unjustified assertions.
If I'm wrong, don't just tell me; show me where.
If Michael is wrong, don't just tell him; show him where.

How can a sequence of operations in which each occurs after the other complete without there being a final operation? — Michael

By definition, the sequence completes by having every operation occurring before some finite time. To demonstrate otherwise, one must find a remaining operation which necessarily is not completed at that time.

That there must be a final step in such a sequence not only does not follow from the description of such a supertask, it in fact directly contradicts the description of the supertask.

To demonstrate the impossibility of Zeno's physical supertask, one must attack the premise, not the logic. The logic is valid, at least until he additionally posits the impossibility of the first premise, but that only gives rise to a direct contradiction, not a paradox.

X is a true fact of motion. X is is a false fact of motion. Therefore either motion is impossible, or at least one of the premises is wrong.

strictly with respect to order, they are two different representations of the same ordered set. — fishfry

Agree.

Transfinite ordinal numbers are numbers.

Are they? Does √ω have meaning? It does for numbers. It's a serious question. I am no expert on how transfinite ordinal numbers are treated. It seems like a different species, like having a set {1, 2, 3, ... , green} which is also a valid set, and countable.

Yes, ordered set. I have been casually using the curly braces, but you are absolutely correct. {1/2, 3/4, 7/8, ..., 1} has no order, I could stick the 1 in the middle or at the beginning and it would be the same set, but I'd lose the order that I consider important.

Ordering irrelevant. The set supposedly needs to be countable, and it is. Michael's definition of supertask came from wiki, and that definition says it is countable, else it's a hypertask. The SEP definition of supertask omits the 'countable' part and seemingly groups the two categories under one word.

The definition also includes 'sequential', meaning parallel execution of multiple steps is not allowed.

Yes ok but then ... how is walking across the room by first traversing 1/2, then half of the remaining half, etc., not a supertask?

Clearly it isn't a supertask if it is impossible to go only half the remaining distance for some intervals. If that is possible, then it must be a supertask.

It violates thebijunction
— noAxioms

I take that back. It doesn't violate the bijection. And I spelled it wrong too. So many errors.

Note that I no longer have an order-preserving bijection.

That's fine. The rational numbers are both ordered and countable, but they cannot be counted in order.

Ah yes, why am I doing all this?

It solves the lamp problem. The lamp state is a function on <1/2, 3/4, 7/8, ..., 1> defined as "on" at 1/2, "off" at 3/4, "on" at 7/8, and so forth.

But now we see (more clearly, IMO) that the state at 1 is simply undefined. The statement of the problem defines the lamp state at each element of the sequence; but does NOT define the state at the limit.

Sounds like the lamp problem is unsolved. It is still 'undefined'.

Another note: The paradox of the gods that I occasionally bring up is fun to ponder, but it isn't a supertask since it cannot be completed (or even started). Progress is impossible. Ditto with the grim reaper 'paradox' where I die immediately and cannot complete the task.

Note that the staircase is different. The walker is on step 1, on step 2, etc. So the natural, continuous way of completing the sequence is to say that the walker is at the bottom of the stairs.

There is no bottom, and the OP did not suggest a bottom step. He is done, and no stairs are observable. It's mathematical only, but framed with a physical sounding analogy, which makes it fall apart.
Your ω might help with the stairs. The guy is at 'the bottom' and there is but the one step there, labeled ω. No steps attached to it, but step on that one step and up you go, at some small finite numbered step after any arbitrarily small time.

Unless the answer is that we satisfy Zeno and execute a supertask every time we walk across the room. But Michael objects to that, for reasons I don't yet understand.

His assertion isn't justified, I agree.

Some speculative physicists (at least one, I believe) think the world is a large finite grid

So much for the postulates of relativity then. I kind of thought we demolished that idea with some simple examples. It seems to be a 'finite automata' model, and the first postulate of SR is really hard (impossbile) to implement with such a model, so a whole new theory is needed to explain pretty much everything if you're going to posit something like that. I haven't read it of course, so any criticism I voice is a strawman at best.

The chessboard universe sounds very classical, and it's been proven that physics is not classical, so I wonder how this model you speak of gets around that.

Well ok, then why don't I complete a supertask when I walk across the room, first going halfway, etc.? Can you distinguish this case from your definition?
— fishfry

If supertasks are impossible and motion is possible then motion isn't a supertask. — Michael

This evaded the question ask. Sure, we all agree that if supertasks are impossible, then supertasks are impossible. He asked how you justify the impossibility of a supertask. All your arguments seem to hinge on a variant that there isn't a largest natural number.

By definition supertasks are non-terminating processes — Michael

The wiki definition you gave made no mention of 'terminate'. If you mean that it doesn't complete, it by definition does in a finite time. If you mean that it has no terminal step, then you're making the mistake I identify just above since the definition does not require one.

Tasks are performed ad infinitum. I never stop counting. — Michael

You also wield the term 'ad infinitum', which typically means 'going on forever', which also violates the definition which explicitly requires a finite time to the task You very much do stop counting at time 1. There is at that time not another number, so by counterexample, your assertion that you will never stop counting is false.

They are not premises. (3) isn't intended to follow from (1) and (2). — Michael

Right you are.
They are three options, and the premise (the one and only and false one) is that one of the three options is very likely to be true. In fact, all three as you stated them are unlikely and a 4th option is the true one: There is neither capability nor desire to run sims of more conscious humans than there are real humans.

As for 1, his assignment of low probabiltiy to that is due to becoming extinct before it happens, not to it not being plausibly possible. Discussion of item 2 seems to suggest that it is for some reason, something that a wealthy person would want to do. I have no idea why. I guess it implies that despite this arbitrarily advanced technology, it's still costly to use it.

Yes, I agree that nowhere in the paper (except an impication in the title) does he conclude that the third option is the most likely. He's done talk shows and such, and there's very much an argument for its likelihood, but maybe such assertions are necessary to get him on the paying talk show.

Bostrom is saying that one of these is almost certainly true:

1. Almost every intelligent civilisation is incapable of creating simulations — Michael

Bostrom does not say this. We create simulations today. He calls the state 'posthuman', and it apparently means a device capable of simulating all of human civilization to a level sufficient for the full consciousness of the humans, and also a full simulation of more complex things like the simulation hardware itself.

2. Almost every intelligent civilisation doesn't want to create simulations

He doesn't say that either. He says that nobody will run 'ancestor simulations', which is defined as simulations (however long or brief) of our own evolutionary history. But such a simulation is impossible since no intiial state they give it would evolve anything like our actual history. They can run a sim of an arbitrary alternate outcome from the initial state, but that won't be our ancestry history, it will just be a simulation of fiction. Depending on where they put the initial state, there might not ever be humans at all.

So two premises, each of which has odds of being almost exactly 1.

3. Almost every conscious person is living in a simulation

That is a valid suggestion if the odds of the above two are small.

Point is, you are misstating Bostrom's premises. Item 3 doesn't follow from the premises as you word them.

He doesn't say which of the three is most likely to be true.

He does. Most of the paper focuses on rationalizing low probabilities for the first two premises to the point of 3 being likely.

Therefore, if simulated persons do not greatly outnumber non-simulated persons then most civilisations are either incapable of or unwilling to make simulations. — Michael

Incapable or unwilling to simulate a lot of them. I see purpose in simulating one person, or a very small group in a closed environment. There's value to that. But not to simulating that group that has decided to have its own simulating machine and running the same simulation.

I don't see why you say that. I think you are assuming at least a soft determinism? — Ludwig V

Scientific discover is sort of inevitable. Einstein stated somewhere that relativity theory was totally ripe after M&M experiment showed the apparent frame invariance of light speed. Minkowski would have come up with SR, but not GR. Others would have had to finish it.

The progress of physics is yes, a sort of fatalistic thing, much like Asimov's foundation series: It will happen inevitably, presuming there is the means to make progress. Much of progress hinges on the political state of things, which cannot be fully predicted.

Remember, there were times during the Cold War when nuclear holocaust hung by a thread.

Oh yes. That's what I mean above by 'presuming there is the means to make progress'. Plenty of viable outcomes have us all nuked away, or a pandemic or something. Asteroid is not likely since that isn't a chaotic function over times as short as centuries.

You say that you wouldn't necessarily run detailed simulations of everything at the same time, but switch to closer simulations when necessary to maintain the illusion.

Bostrom suggests that, yes. It's a necessary thing for an open system. Most simulations we run today are not open. Not always the case. I used to run computer chip simulations which has to be an open system since (most) chips need external input to drive them. We needed to see how the chip would function before going to the great expense of actually manufacturing a batch.

That's all very well, though it imposes an extra burden on the machinery because it will have to be aware of what people are attending to at all times.

You got it. Also what their devices are attending to, even when the people are not around.

What if the human decides to dig at location X? That location was trivially simulated up until now, but suddenly the machine has to decide if there should be a dinosaur there or something, even when the digging is not being done for purposes of looking for them.

it wouldn't be easy to fool them all the time.

Nope. It would be dang difficult, which is a decent reason why nobody would attempt such simulations, simulations good enough to fool its occupants, even the very smart but skeptical ones.

Didn't you say something to the effect that quantum mechanics and general relativity couldn't be simulated?

QM can't easily be simulated, but it can be done. My example of the cc of water was an example beyond some limits, but it depends on the interpretation being simulated.
I don't see much difficulty with relativity theory being simulated. They do that all the time in astronomical simulations like what it looks like to fall into a black hole, or a sim of our collision with Andromeda.

The difficultly in simulating QM is not in any way evidence that it is wrong. It's just evidence that it isn't classical, and most simulations as we know them are classical simulations.

There are two physics involved. One is the physics of the simulated world, which would need to be quite like ours.

If we are simulated, then the physics of the simulated word IS our physics, by definition. They can't be wrong. They might be only an approximation of what the runners of the simulation actually wanted.

For instance, any simulation run by us is discreet. Humans and machines only have access to a countable set of numbers, leaving most of the real numbers inaccessible. For instance, a typical floating point number is but 64 bits in a computer, more if you want more precision. There are only so many values that a finite number of bits can represent. The rest are off limits.
Real physics seems to work with real numbers, not these discreet numbers. But we can't prove that.

You believe in limits, you said so. And if you believe even in the very basics of set theory, in the principle that I can always union two sets, then I can adjoin 1 to {1/2, 1/3, 1/4, 1/5, ...} to create the set {1/2, 1/3, 1/4, 1/5, ..., 1}.

It's such a commonplace example, yet you claim to not believe it? — fishfry

I said I had no problem with any of that.
Is it a belief thing, like it is some kind of religious proposition or something? "Hey, I'm going rogue here and will suspend belief that 7 is a factor of 35".

Or what is your objection, exactly?

Treating infinity as a number, something you didn't do in your unionized set above

It's an infinite sequence. I stuck the number 1 on the end.

Yea, when it normally is depicted at the beginning. From what I know, a set is a set regardless of the ordering. There must be a different term (ordered set?) that distinguishes two identical sets ordered differently, sort of like {1, 3, 5, 7 --- --- 8, 6, 4, 2}

The entire set is ordered by the usual order on the rational numbers. So why is it troubling you that I called 1 the "infinitieth" member of the ordered set?

It violates thebijunction. You can't say what number comes just before it, which you can for any other element except of course the first. You can do that with any other element.

It's a perfect description of what's going on. And it's a revealing and insightful way to conceptualize the final state of a supertask. Which is why I'm mentioning it so often in this thread.

OK, but what problem does it solve? It doesn't solve Zeno's thing because there's no problem with it. It doesn't solve the lamp thing since it still provides no answer to it.

In terms of known physics as of this writing, we can not sensibly discuss what might be going on below the Planck length.

Nobody's asking the particle to meaningfully discuss (mathematically or not) the step. It only has to get from one side to the other, and it does. Your argument is similar to Michael wanting a person to recite the number of each step, a form of meaningful discussion.

Maybe we live in a discrete grid of points -- which would actually resolve Zeno's paradoxes.

It would falsify the first premise. Continuous space falsifies the second premise. Zeno posits two mutually contradictory premises, which isn't a paradox, only a par of mutually contradictory premises,.

But you can't say "you can traverse the space of that step, even when well below the Planck length" because there is no evidence, no theory of physics that supports that claim.

But I can say "for all we know, ....", and then there's no claim. I'm not making the claim you state. I'm simply saying we don't know it's not true. I even put out my opinion that I don't think it's true, but the chessboard thing isn't the alternative. That's even worse. It is a direct violation of all the premises of relativity theory (none of which has been proved).

IMO the final state is simply not defined by the premises of the problem, — fishfry

Spot on, yes.

A supertask is "a countably infinite sequence of operations that occur sequentially within a finite interval of time." — Michael

Yea, I don't know how that could have been lost. I don't think anybody attempted to redefine it anywhere.

The first is that the whole of our world could not be simulated, because the hardware would have to be bigger than the whole (real) world. — Ludwig V

Yes, the world would have to be bounded, probably more than once. Bostrom for instance suggests the detailed simulation be bounded at human brains (all of them). A less detailed simulation of bodies, animals (all animals will apparently be NPCs), purposeful devices and such. Probably at least 5 levels of this, ending with 'everything else' which simulates the stars in the sky and such, more in detail only when purposefully being paid attention to.
This makes it hard to see physics be different here from there since the physics of a thing changes whenever you try to investigate it.

The second is that exact simulation of even a small part of the real world, down to sub-atomic and near-light-speed events could not be constructed, for the same reason.

It has to be done at that level if someone is paying attention to it. But you choose an easy interpretation like Copenhagen, and it's usually only one particle (like the electron being sent through the double slits) that has to be simulated.
Consider smoke detectors, which very much depend on quantum indeterminism to work. Those I suppose can be classically simulated when nobody is observing them closely.

So it would not be possible to simulate the progress of research in physics over the last 100 years or so?

That isn't an isulated system. One could put together an approximation of the state of Earth in 1924 and simulate it from there. That (the setting up of a plausible world) would require for instance a full understanding of physical consciousness and how memories work so that each person is created will a full memory of his past and has no idea that he just came into existence. The people there pushing the view of 'Last Tuesdayism' would be correct without knowing it.

Then you run the simulation for a simulated century and you get some world that differs completely from ours, but if they haven't killed themselves, the physics would likely have developed more or less at pace with our own history. All the names of the main contributors that hadn't been born by 1925 would be different, and the contributions of those that did exist would change.

I think you'll have to say that the hardware of this simulation we live in must be much, much more powerful than anything we can conceive of and that QM and GR are false. No?

Bostrom makes some outlandish suggestions that say otherwise, like for instance that Moore's law will continue indefinitely.
Don't know what you mean by QM and GR being wrong. They're not, but they're not necessarily the physics of whatever is simulating us.

The paradox of the situation is that believers in it have to put more faith in their fancies than in their experience — Ludwig V

You got it. I also see no motivation for our simulators to run this simulation. Bostrom suggests the 'ancestor history' thing, but it wouldn't be our history being simulated, just 'a' history, and a very different one. The only purpose of that might be to see how things might otherwise have turned out. How lucky are we to have survived to the point of being able to put together these simulations?

So I agree: the far simpler model is to presume our experiences are valid evidence of how things are, since the alternative is making up conclusions from zero evidence.

I don't beleive we are in a simulation, but this is my reaction to your points. — Tom Storm

As I've pointed out already, you're speaking to air. jasonm doesn't contribute to his own topics.

If we are a simulation and there is a world outside ours, how would we know what is possible? Since we know nothing of the world outside the simulation, we don't even know if it is done via computers. — Tom Storm

Exactly. Everybody online that pushes something like this presumes unreasonably that the world simulating us has similar physics.

Bostrom's Simulation Argument is that one of these is almost certainly true:

1. The fraction of human-level civilizations that reach a posthuman stage (that is, one capable of running high-fidelity ancestor simulations) is very close to zero, or
2. The fraction of posthuman civilizations that are interested in running simulations of their evolutionary history, or variations thereof, is very close to zero, or — Michael

I find both these to be highly unlikely, for the reason stated in this topic and mine. Bostrom of course has motivation to rationalize a higher probability for both of these, but rationalizing is not being rational.

OK. Is that because [points] have no dimension - are not a part of the line? — Ludwig V

They are part of the line. Yes, a point is dimensionless, size zero. Any sum of a finite bunch of zeros is zero. But the number of points on a line segment isn't finite.

Ok. Perhaps you and Michael could hash this out. He thinks supertasks are metaphysically impossible — fishfry

Perhaps he does, but he fallaciously keeps submitting cases that need a final step in order to demonstrate the contradiction. I don't.

I say they're conditionally physically possible, but the condition is unreasonable. There seems to be a finite number of steps involved for Achilles, and that makes the physical case not a supertask. I cannot prove this. It's an opinion.

Do you have a hard time with 0 being the limit of 1/2, 1/3, 1/4, 1/5, 1/6, ...? It's true that 0 is not a "step", but it's an element of the set {1/2, 1/3, 1/4, 1/5, 1/6, ..., 0}, which is a perfectly valid set. — Ludwig V

I have no problem with any that.

You can think of 0 as the infinitieth item, but not the infinitieth step.

OK, that's probably a problem. It is treating something that isn't a number as a number. It would suggest a prior element numbered ∞-1.

Even if space is continuous, we can't cut it up or even sensibly talk about it below the Planck length.

But you can traverse the space of that step, even when well below the Planck length.


In math? Via the standard limiting process. In physics? I don't know,
— fishfry
In physics, the same way as math, except one isn't required to ponder the physical case since it isn't abstract. One completes the task simply by moving, something an inertial particle can do. The inertial particle is incapable of worrying about the mathematics of the situation.
— noAxioms

Yes ok ... math and physics are human inventions that bear some mysterious relation to reality. I agree with that, if that's what you meant.

The closed unit interval [0,1] has a first point and a last point, has length1, and is made up of 0-length points.

So it does. Zeno's supertask is not a closed interval, but I agree that closed intervals have first and last points.

I'm not sure I fully understand. Forgive me, but are these simulations not the ones where they put crash test dummies in a model of car and ram it into a brick wall? How is that not crashing actual cars?

Or do you mean studying thr aftermath of incidental crashes on the road? Not sure how often this actually happens as there would be a lot of legal red tape with ongoing investigations into real victims. — Benj96

No, none of those cases are examples of simulations. Yes, they're are crashing real cars. I'm talking about a computer model of a car crashed into a virtual brick wall, another car/truck, whatever... Yes, those simulations have occupants in them. Much of the point of the simulation to to find a design that best protects those occupants. The auto industry has huge computers dedicated to doing this sort of thing continuously.

I have myself run plenty of simulations, but not being in the auto industry, most of mine didn't have living things simulated in them.

Perhaps I am wrong about determinism tho. I always figured if variables were fully predetermined then the outcome would be invariably predetermined and fully predictable.

That's what determinism means, yes. I don't think 'predetermined' is a distinct concept from 'determined'.

There are valid interpretations of physics that are fully deterministic: Relativity theory, Bohmian mechanics come to mind. There are interpretations that are not deterministic, such as RQM or Copenhagen interpretations. Bottom line: jury is out on the subject.

You'd think a simulation of reality would choose to simulate one of the deterministic models, but if I was tasked with implementing one, I would choose the nondeterministic ones since it is far less work. But it means things occurring without cause, such as the decay of some unstable particle.

I figured that nothing is fully predetermined in real life experiment because there is almost certainly extraneous variables interacting to make the outcome for example 1+1 + X variable + Y variable + Nth variable = 2?

It is unpredictable because the initial conditions of the system fundamentally cannot be known, but given a deterministic model and perfect initial conditions, the (closed) system will do the same thing every single time.

That highlights a different issue with simulations: No system can be closed, so it is at the boundaries of the non-closed systems where one looks for the evidence of being simulated. The car crash thing is usually a closed system. There is no environment. There's the car and its target, and sufficient road to run the scenario. Nothing else.

Do you mean that no-one living in our world could create a simulation of our world? — Ludwig V

Of course not. There would for one be a need for more data than there is medium on which to store it. You you need to simulate a small system, with far less effort put into simulation of the interaction of that small system with the part outside the system.
For example, imagine an atomic simulation of a cc of water just sitting there in a tube, doing that under MWI, a hard deterministic model. I don't think any technology could simulate the water at that level for even one second. So you cut corners and don't simulate at that level unless something intentionally is paying attention to that level. Any you choose something like Copenhagen which is easier to simulate.

That's just a posh way of saying that the battle seems real to those in the simulation.

OK, 'seems' is a better word. But to us, we typically presume reality to be whatever 'seems' real to us without explicitly defining it that way.
Heck, that's why I favor a relation interpretation, which explicitly says exactly that. X is real to Y. Being real is a relation, not a property, so by that definition, the battle IS real to those partaking in it.

Reality, by definition, is not "in" the simulation, but outside it.

By another definition (one very appropriate for this topic, yes), I agree. Reality might not be the world simulating us. We might be 27 levels down, but there's a base reality up there (as is typically presumed), and that one is 'the reality' by the definition implied by a topic like this.

The OP has some problems. Most importantly, he has a reputation for posting an OP and then never returning to the topic. Hence I won't bother with direct replies.

He doesn't seem to know the difference between the simulation argument (Bostrom is a good example of this) and a virtual reality argument (the Matrix is the typical example). The difference is spelled out in my fairly recent topic here https://thephilosophyforum.com/discussion/15060/what-is-simulation-hypothesis-and-how-likely-is-it

Almost all of the arguments in favor of such things posit violations of the laws of physics. The VR hypothesis does by definition. Any simulated body being controlled by a real eternal mind/person operates under different physics than bodies that are not (called NPCs by the VR community).
Bostrom similarly suggests that physical law changes depending on the simulation's determination of intent, which means that the simulation is tasked with gleaning meaningful intent out of particle motion.

If this world is simulated, the "real" world must be very like this one - as in the "Matrix" — Ludwig V

Not true. We would have zero empirical access to the level that is running the simulation, so we can know nothing about it. It might not be a 3 dimensional space world with physics as we know it. That's kind of likely actually since our physics cannot be self-simulated. At the classical level, maybe, but not beyond that.

Therefore, everything cannot be a simulation. — jkop

Good argument, but nobody asserted that 'everything is a simulation'. The argument still is valid that if we're 'probably' simulated, and if the simulating world is similar to ours, then they're also 'probably simulated'. But that's a lot of 'if's.

In a VR, the frog, and even yourself is just a collection of colored shapes, as you put it. A VR is nothing but a simulated experiential feed to a real external entity (you). You would have no way of knowing if other people (or the frog) are similarly avatars under external control, or if they're just part of the simulation (an NPC).
Yes, the apparent frog would have to apparently attempt to evade capture for it to be convincing. A simulation that doesn't do that would be simulating physics contradictory to the physics being presented to us.

if the simulation (e.g an emergent property within a network of electrical circuits) — jkop

Just FYI, there are countless ways to run simulations. Networks of electrical circuits is but one, and those might not even be a thing in the world simulating us.
There was a suggesting that it be done via domino chains falling down. That's a tough one, but I couldn't falsify the suggestion that a Turning machine can be made thus from dominos, so it apparently works. That means (presuming physicalism) consciousness can arise from falling dominos.

If the universe is simulated or in part simulated, it doesn't make it any less real, it just means the product of the universe came about through non-conventional means — Barkon

Agree with this, but not sure what conventional is here. Adding a more fundamental layer to the model, especially a more complicated one, just makes the problem harder, very similar to positing that God created it all. The god is harder to explain than the simpler universe.

I agree that being simulated doesn't really make anything 'fake'.

"Universe" is a bit slippery here. If it means "everything that exists", — Ludwig V

Definitions vary. In this topic, it is helpful to say 'world'. We are one world, and the level simulating us is another. Maybe they're simulating a bunch of them and we are running several simulations of our own. Those are all different worlds, all part of one 'everything that exists', which is a defintion I never liked anyway.

The idea of "real" is also slippery here - or better, it's meaning is contextual. A simulation of a battle isn't a real battle, but it is a real simulation — Ludwig V

The battle is real to those in the simulation, but not real to those running the simulation.

If our world is a simulation, violations of the laws of physics would be bugs. — Lionino

Apparent violations would be bugs. Actual violations are seemingly necessary, to the point where I've never seen a hypothesis that didn't suggest fully consistent phsical laws. For instance, do we simulate the quantum interactions between a pair of protons in a star in some other galaxy? Or do we just simulate an occasional photon reaching Earth?

Minds/consciousness can't come from matter, therefore simulation theory is false. — RogueAI

So the alternative has been falsified? News to me.

If a simulation is wholly deterministic, there is no added value to run it in the first place. For all variables throughout the simulations play are already known by the creators. — Benj96

Lionino correctly points out the error here. Deterministic doesn't mean predictable. Simulations are run today precisely for the purpose of learning something unknown despite being fully determined. Car crashes are a great example of this, a far more cost effective method of testing automobile designs than crashing actual cars.

-----
Again, all this is covered in my other thread linked above.

The problem I was trying to point out that is that, if we admit a ∞-th step, this step should be associated with a state in one of those mechanisms Michael made up. — Lionino

Michael's mechanisms (some of which he made up) are not resolved by addiing a single step task to the supertask. The supertask reaches 1 when all the steps are completed. It isn't sort of 1, it's there since where else would it be? The arguments against that suggest some sort of 'point immediately adjacent to, and prior to 1', which is contradictory. There are no adjacent points in continuums.

I agree with fishfry that there is no step that gives us 1 since by definition, any given step gets us only halfway there
— noAxioms

But I don't agree that 1 is not reached by the completion of the supertask. Only that 1 is not reached by any step.

I take it you are talking about physical space, not mathematical space? — Ludwig V

Yes. 'Planck [pretty much anything] is a physical concept, not a mathematical one. In mathematics, there is no number smaller than can be meaningfully discussed.

But there are 3-dimensional figures in physics, aren't there? It's the solidity that's the problem, isn't it?

Sure. A rock, at a given time, is a 3 dimensional thing. A rock, it's entire worldline, is a 4 dimensional thing. Correct. It isn't a solid. You can measure a piece of it at a sort of 4D 'point', an event. The rock worldline consists of a collection of such point events, a huge number, but not infinite. They're not really points since position and momentum cannot be both known, so you can know one or the other or an approximate combination of both.

One can measure or calculate the length of a circumference, can't one? Or is uncountability a consequence of the irrationality of "pi"?

Yes, one can calculate the circumference. No, the irrationality of pi is irrelevant. It could be a line segment of length 1. You know the length, and it isn't irrational, but the segment still consists of an uncountable number of points. There's no part of the segment that isn't a point (or a set of them), and yet points have no size, so no finite number of them can actually fill a nonzero length of that segment.

Just checking - by "step" do you mean stage of the series. If I am travelling at any spead, I will complete more and more steps in a given period of time, and that number (of steps) will approach (but not reach) infinity.

Yes, a step is a finite (nonzero) duration, like the first step is going halfway to the goal. Each step goes half the remaining way to the goal. Those are steps. You complete all the steps by time 1, so the task is then complete. No contradiction so long as we don't reference 'the highest natural number' which doesn't exist.

So is the cutting up of the path into standard units. It's just a question of choosing the appropriate mathematical calculation for the task at hand.

One must define how the task is divided into steps in order to tell Zeno's story. There are multiple ways to do it, but to be a supertask, the steps need to get arbitrarily small somewhere, and the most simple way to do that is at the beginning or the end of the task. How one abstractly divides the space has no effect on the actual performance of the task. One can argue that all tasks of any kind are supertasks because one can easily divide any finite duration into infinite parts, but the much of the analysis of doing so relies on the mathematics of countable infinities.

So I can go from 0 to 1 and assign a 'step' to every zero-duration point between those limits. That can be done, and can be completed, but since the steps are not countable, it is hard to draw any conclusion from it all.

Then you say. — Lionino

That's me saying something, not fishfry.

I personally don't like the ∞-th step, but it works. The supertask is completed, then the ∞-th step is taken after that. The supertask had all nonzero duration steps, and this additional step has no duration. I don't find it wrong, but I find it needless.

Is there not a contrast between these two sets of statements?

I agree with fishfry that there is no step that gives us 1 since by definition, any given step gets us only halfway there. If fishfry wants to add an addition single step after the supertask completes, that's fine, but it isn't a step of the supertask.

I don't see how you could count all the natural numbers by saying them out loud or writing them down. Is this under dispute? — fishfry

No. Nobody seem to have suggested that was possible. It simply isn't a supertask.

Do you mean the fact that I can walk a city block in finite time even though I had to pass through 1/2, 3/4, etc? I agree with you, that's a mystery to me.

Yes, I mean that, and it's not a mystery to me. If spacetime is continuous, then it's an example of a physical supertask and there's no contradiction in it.

The lamp could turn into a pumpkin too.

No, the lamp changes things. It introduces a contradiction by attempting to measure a nonexistent thing. That in itself is fine, but the output of a non-measurement is undefined.

I looked up [Bernadete's Paradox of the God], didn't seem to find a definitive version.

Nicely stated by Michael in reply 30, top post of page 2 if you get 30 per page like I do.

Ah the ping pong balls. Don't know. I seem to remember it makes a difference as to whether they're numbered or not.

It's important to the demonstration of the jar being empty, so yes, it makes a difference.

If you number them 1, 2, 3, ... then the vase is empty at the end, since every ball eventually gets taken out. But if they're not numbered, the vase will have infinitely many balls because you're always adding another 9. Is that about right?

The outcome seems undefined if they're not numbered since no bijection can be assigned, They don't have to have a number written on them, they just need to be idenfifed, perhaps by placing them in order in the jar, which is a 1-ball wide linear pipe where you remove them from the bottom.

It nicely illustrates that ∞*9 is not larger than ∞, and so there's no reason to suggest that the jar shouldn't be empty after the completion of the supertask. Again, it seems that any argument against this relies on a fallacious assumption of a last step that sooo many people are making in this topic.

So I believe I've been trying to get across the opposite of what you thought I said. There is an ∞-th item, namely the limit of the sequence. — fishfry

That can't be a step, since every step in a supertask is followed by more steps, and that one isn't. I have a hard time with this ∞-th step.

The common explanation that calculus lets us sum an infinite series, I reject. Because that's only a mathematical exercise and has no evidentiary support in known physics. — fishfry

The cutting up of the path into infinite steps was already a mathematical exercise. The fact that the physical space can be thus meaningfully cut up is true if the space is continuous. That latter one is the only barrier, since it probably isn't meaningfully, despite all our naïve observations about the nice neat grid of the chessboard.

If it is indeed accomplishing an infinite amount of steps, is there not a step where the sequence gives us 1? If not, how is the walk ever completed — Lionino

As has been stated so many times, by performing all the steps, which happens in finite time no problem. There is a final step only in a finite sequence, so using a finite definition of 'complete' is inapplicable to a non-finite task.

In math? Via the standard limiting process. In physics? I don't know, — fishfry

In physics, the same way as math, except one isn't required to ponder the physical case since it isn't abstract. One completes the task simply by moving, something an inertial particle can do. The inertial particle is incapable of worrying about the mathematics of the situation.

Physics doesn't support these notions since we can't reason below the Planck length.

Which is to say that space isn't measurably continuous, so the walk isn't measurably a supertask. I would agree with that.

How do dimensionless points form lines and planes and solids? — fishfry

Mathematics: by not having a last one (or adjacent ones even). Physics: There are no solids.

(But the converging series does not consist of points, but of lengths, which are components.) — Ludwig V

Yes. The latter is a countable set of lengths. The set of points on say a circle is an uncountable set

A robot cannot decide whether or not to make the call, a person can. — Metaphysician Undercover

That's quite the assertion. Above and beyond the usual conservative stance.

The point of my example with the ship was to counter your assertion of Newton forces not being necessary to move and free will being enough. I said you'd need help from Newton. Asking for a line to be thrown to you is you admitting the help from Newton was necessary. That's what the tether is: a way to do it by exerting an external force, since the free will couldn't do it itself.