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.

Assuming at the most microscopic level, the object is on an 8x8 chessboard. The pawn moves from e2 to e3. There is no e2.1 or other smaller increments in this finite world. At T1 it's at e2 and T30 it's at e3. The assumption is that at some point in time, it was no where while transitioning (moving?) from e2 to e3. — Hanover

I discussed that in my post, but you quoted the bit at the bottom which abandons the chessboard model in favor of quantum mechanics, calling the former model a naïve

What empirical evidence is there that observations have been made of there being no object for some length of time and then it suddenly reappearing?

None, but there's also no evidence that it is there when not being measured. It's all about measurement and not about discreetness.

If it's at L-1 at T-1 and L-2 at T-2, how long did it take to get from L-1 to L-2? — Hanover

In that frame, it took time 1 to get from T-1 to T-2. That's pretty obvious, no? In natural units, that's light speed.

If the answer is 0, then it was at L-1 and L-2 at the same time because if T-2 minus T-1 = 0, then T-1 = T-2.

If the answer is zero, then T-2 is no-t when it is at L-2.
In computer jargon, what you are describing is 'jaggies', the tendency of 'straight' lines to appear jagged when displayed on say your computer screen, a discreet array. An object that moves fast (faster than one L per T) will either be at multiple locations at the same time, or it will skip all the locations between and only be at one location per time.
I've played a game with the latter physics. I could get my ship to go super fast and go straight for the enemy blocking my way. If I did it right, I would be in front of him at one time unit, and beyond him the next time unit, apparently passing right through without collision because there was no time 1.5 where I was where he was.

More problems with that model: If the particle is moving at 0.7 per time unit, it is never at a location in space except every 10 time units where you find it 7 units from where it was before. It can't be anyplace between since it is never at a space location at the same time as a time quanta. This is silly. You probably need to fill in the dots between, but then the motion is erratic rather than sporatic.

I'm only asking how far 1,1 is from 1,2 in a discrete space system. As far as I can tell, it's 0 units, right? — Hanover

No, they're 0,1 from each other, which isn't zero. One of the coordinates is different.

Anyway, you seem to see the sorts of contradictions that arise from such a naive model. If space and time is discreet, quantum mechanics describes it far better than the chessboard model.

the walk only finishes if it accomplishes an infinite amount of steps. Right? — Lionino

Right

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?

By completing all the steps. This is not a contradiction.

if so, is there not a corresponding state for the mechanism when the full time elapses?

Not any more than there is a last natural number. I'm presuming you're talking about the state of something like the lamp. The state of Achilles is easy: He's where the tortoise is.

I don't see a problem until the premise of a last step is introduced, which is by definition contradictory.

given that quantum mechanics and General Relativity are known to be incompatible, it would seem that at least one of them is false, — Michael

They're both incomplete, just like
Newtonian mechanics was incomplete, but not false. OK, parts of it were outright false, but it's still taught in (pretty much) any school. GR definitely breaks down at small scales.

No one said free will has infinite capacity? — Metaphysician Undercover

I didn't say infinite capacity. I denied that your free will has any capacity at all, since even the most trivial capacity would get you back to your ship 2 meters away, even if not quickly.

I think, and then I do. The "force" which moves me comes from within me, and therefore cannot be described by Newton's conceptions of force. — Metaphysician Undercover

The spaceship example shows this to be nonsense. It would be a revolution indeed if anybody could do that.

a radio call to someone inside the spaceship, to please shoot me a line, might help. That demonstrates the benefit of free will — Metaphysician Undercover

Free will isn't necessary to do any of that. A robot has the same capacity to make such a call, and robots by definition lack it. This is also utterly off topic to this discussion, but I took the easy bait anyway.

If I stand in a parking lot and call out "one, two, three, ..." and keep going .. — fishfry

OK, that other meaning of 'count'.

I think we're talking past each other. When asked for the difference between a mathematical and physical supertask, you seem to focus on two different definitions of countable: The assignment of a bijection, and calling or writing down each of the numbers.

I'm talking about a physical supertask as described by Zeno, which arguably has countably (first definition) steps performed in finite time. Nobody is posited to vocalize the number of each step as it is performed.

It's just like Cinderella's coach. It's a coach at midnight minus 1/2, midnight minus 1/4, etc. At at exactly midnight, it turns into a coach.

Bit off on the lore. It turns into a pumpkin, and at the 12th stroke, where presumably midnight is the first stroke, but I googled that and could not find an official ruling on the topic.

The Planck-scale defying lamp circuit is every bit as fictional as Cinderella's coach. Since the state at 1 is not defined, I'm free to define it as a plate of spaghetti. That's the solution to the lamp problem.

No argument. That seems to be a valid way out of most attempts to assign a count to the nonexistent last/first step, or to simply assert the necessity of the nonexistent thing.

I like Bernadete's Paradox of the Gods because it doesn't make those mistakes, and thus seems very much paradoxical since motion seems prevented by a nonexistent barrier.

For educational purposes concerning how infinity works, I like Littlewood-Ross Paradox because it is even more unintuitive, but actually not paradoxical at all since it doesn't break any of the above rules. It shows a linear series (effectively 9+9+9+...) being zero after the completion of every step.

If I could, say, produce an equation based on the one in my earlier post that could calculate the last time interval given a smallest stipulated chunk of time, would that be a valid final step in the summation? — ToothyMaw

If you stopped the summation there, then yes, there would be a final step, but it wouldn't have infinite steps defined then. It wouldn't be a supertask.

And would that sum not eventually terminate given a smallest sliver of time exists

If there's a smallest quanta of time, then there can be no physical supertasks.

I think, and then I do. The "force" which moves me comes from within me, and therefore cannot be described by Newton's conceptions of force. — Metaphysician Undercover

LOL. Tell that to the guy stranded 2 meters from his space ship without a tether. No amount of free will is going to get you back to it. You're going to need a little help from Newton.

The use of "physical" in this thread has gotten so ambiguous, that equivocation abounds everywhere. — Metaphysician Undercover

Yea, I noticed.

How much time elapses from travel to point a to point b and where is the object located during that time lapse? — Hanover

I'll attempt this. Michael talks about motion from A to B without there being a between. This can happen two ways.
1) Space is quantized. There simply isn't a location halfway between A and B. For a slow particle, this might mean that it spend quite a bit of time at A, and then suddenly is at B. That seems rather contradictory since one might ask what changes during all those times when the thing was at A. If it is at A twice, it is stationary and has no obvious state anywhere to go to B after some nonzero time.

2) Time is quantized, which is troublesome for fast particles. You have time 1 where the thing is at A, and time 2 where it is at B, quite a ways away. There are valid locations between A and B that the particle never visited since the time it should have been there is nonexistent.

All the above sort of presumes a naïve finite-automata sort of view of a quantized space and or time. It presumes a particle has a location (A, B) at a given state and time. Well that presumption was pretty much thrown out of the window with quantum theory.
A more realistic answer to your question comes from there. It says that you measure the particle at A, and later at B (maybe hours later). Where was the particle between those times? If not measured, it doesn't have a location. It does exist, but needs to be measured to have a location or (not and) a momentum.

what maintains its identity during that interval?

Physics has no concept of identity of anything. It is a human convention, a pure abstraction. Any given convention seems falsifiable by certain examples.

a set like N = {30, 15, 15/2}? Does that not include a first step? — ToothyMaw

Yes, that series has a first step, but not a last one. You can number the steps in the series if you start at the big steps. Similarly, you can number the dichotomy steps in reverse order, since the big steps are at the end.

And would that sum not eventually terminate given a smallest sliver of time exists

If there's a smallest sliver of time, there is no bijection with the set of natural numbers since there are only a finite number of steps.

or continue indefinitely given time is infinitely divisible?

'Continue indefinitely' is a phrase implying 'for all time', yet all the steps are taken after only a minute, so even if time is infinitely divisible, the series completes in short order.

Can we not count the intervals starting with 1 — ToothyMaw

No. In the dichotomy scenario, there is no first step to which that number can be assigned.

To count a set means to place it into bijection with: — fishfry

OK, that meaning of 'count'. In that case, I don't see how mathematical counting differs from physical counting. That bijection can be done in either case. In the case with the tortoise, for any physical moment in time, the step number of that moment can be known.


I am saying that Zeno describes a physical supertask, that Achilles must first go to where the tortoise was before beginning to travel to where the tortoise is at the end of that prior step.
Zeno goes on to beg the impossibility of the task he's just described, so yes, he ends up with a contradiction, but not a paradox.

Depends on the exchange rate. — fishfry

I also would hate to have to talk about the poor kilometerage that Bob's truck gets.

It [the even-oddness of ω]is neither, and who's asking such a thing? — fishfry

The lamp scenario asks it, which is why the comment was relevant.

Some supertasks are coherent and consistent, therefore logically logically possible. In this case, that is the proof that they are "possible" — Metaphysician Undercover

I think the person to whom I was replying was suggesting that somebody had asserted a proof that a physical supertask was possible. But I did not recall anybody posting such an assertion.

I have more or less dropped out due to the repetitive assertions not making progress, but thank you for this post.

the set {1/2, 3/4, 7/8, ..., 1} — fishfry

Interesting. Is it a countable set? I suppose it is, but only if you count the 1 first. The set without the 1 can be counted in order. The set with the 1 is still ordered, but cannot be counted in order unless you assign ω as its count, but that isn't a number, one to which one can apply operations that one might do to a number, such as factor it. That 'final step' does have a defined start and finish after all, both of which can be computed from knowing where it appears on the list.

This is not radical. The rational numbers are countable, but not if counted in order, so it's not a new thing.

If Zeno includes 'ω' as a zero-duration final step, then there is a final step, but it doesn't resolve the lamp thing because ω being odd or even is not a defined thing.

and we inquire about the final state at ω

Which works until you ask if ω is even or odd.

Using mathematics to try to prove that supertasks are possible is a fallacy. — Michael

Totally agree, but I'm not aware of anybody claiming a proof that supertasks are possible. Maybe I missed it.

Well physics is of course exempt from math and logic. The world does whatever it's doing. We humans came out of caves and invented math and logic. The world is always primary. Remember that Einstein's world was revolutionary -- overthrowing 230 years of Newtonian physics. — fishfry

The relativity thing was more of a refinement and had little practical value for some time. Newtonian physics put men on the moon well over a half century later.
QM on the other hand was quite a hit, especially to logic. Still, logic survived without changes and only a whole mess of intuitive premises had to be questioned. Can you think of any physical example that actually is exempt from mathematics or logic?

QM is also the road to travel if you want to find a way to demonstrate that supertasks are incoherent.
Zeno's primary premise is probably not valid under QM, but the points I'm trying to make presume it is.

in math I can invoke the axiom of infinity, declare the natural numbers to be the smallest inductive set guaranteed by the axiom, and count it by placing its elements into order-bijection with themselves. The former is a physical activity taking place in the world and subject to limitations of space, time, and energy. The latter is a purely abstract mental activity.

What is this 'the former'? The physical activity of making a declaration? There's definitely some abstraction going on there, as there is with any deliberate activity.
The latter seems to be the expression of a rule that maps the two halves of the bijection, which seems to be about as physical of an activity as was the declaration.

if thoughts are biochemical processes; are not our thoughts of infinity a kind of physical manifestation?

No argument here.

So bottom line it's clear to me that we can't count the integers physically

Depends on what you mean by count, and especially countable, since plenty of equivocation is going on in this topic.
If you mean mentally ponder each number in turn, that takes a finite time per number, and no person will get very far. That's one meaning of 'count'. Another is to assign this bijection, the creation of a method to assign a counting number to any given integer, and that is a task that can be done physically. It is this latter definition that is being referenced when a set is declared to be countably infinite. It means you can work out the count of any given term, not that there is a meaningful total count of them.

but we can easily count them mathematically

Sorry, but what? I still see no difference. What meaning of 'count them' are you using that it is easy only in mathematics?

And the reason I say that we can't physically do infinitely many things in finite time "as far as we know," is because the history of physics shows that every few centuries or so, we get very radically new notions of how the world works.

That doesn't follow at all since by this reasoning, 'as far as we know' we can do physically infinite things.
I never made the claim that a supertask is physically possible. I simply followed through with it as a premise, which, unless falsified, can be physically true 'as far as we know'.

Nobody can say whether physically instantiated infinities might be part of physics in two hundred years.

They've been a possibility already, since very long ago. It's just not been proven. Zeno's premise is a demonstration of one.

You italicize 'according to present physics', like your argument is that there's some basic flaw in current physics that precludes supertasks. How so?
— noAxioms

Not a flaw, of course, any more than general relativity revealed a flaw in Newtonian gravity. Rather, I expect radical refinements, paradigm shifts in Kuhn's terminology, in the way we understand the world. Infinitary physics is not part of contemporary physics. But there is no reason that it won't be at some time in the future. Therefore, I say that supertasks are incompatible with physics ... as far as I know.

We split the atom, you know. That was regarded as a metaphysical impossibility once too.

QM does very much suggest the discreetness of matter, but Zeno's premise doesn't rely on the continuity of matter. It works best with a single fundamental particle moving through continuous space and time, and overtaking another such particle.

The next shift just may well incorporate some notion of infinitary set theory; in which case actual supertasks may be on the table.

They were never off the table since current physics doesn't forbid them. Maybe future physics will for instance quantize either space or time (I can think of some obvious ways to drive that to contradiction). Future findings take things off the table, not put new ones on. The initial state of physics is "I know nothing so anything is possible'.

I analogize with the case of non-Euclidean geometry; at first considered too absurd to exist

Heh, despite the detractor standing on an obvious example of such a geometry.

then when shown to be logically consistent, considered only a mathematician's plaything, of no use to more practical-minded folk; and then shown to be the most suitable framework for Einstein's radical new geometry of spacetime.

Octonians shows signs of this sort of revolution.

eternal inflation. That's a theory of cosmology that posits a fixed beginning for the universe, but no ending.

Actually, the big bang theory already does that much.
Yes, I know about eternal inflation, and something like it seems necessary for reasons I gave in my prior post.

Physicists are vague on this point, but if time is eternally creating new universes, why shouldn't there be infinitely many of them.

It is a mistake to talk about 'time creating these other universe'. Time, as we know it, is a feature/dimension of our one 'universe' and there isn't that sort of time 'on the outside'. There is no simultaneity convention, so it isn't meaningful to talk about if new bubbles are still being started or that this one came before that one.

All that said, the model has no reason to be bounded, and infinite bubbles is likely. This is the type-II multiverse, as categorized by Tegmark. Types I and III are also infinite, as is IV if you accept his take on it. All different categories of multiverses.

And two, the many-world interpretation of quantum physics.

That's the type III.

In Everett's many-world's interpretation, an observation causes the thing to be in both states.[/quote]Ouch. Is that a quote? It did not match any google search.
Observation for one is a horrible word, implying that human experience of something is necessary for something fundamental to occur. This is only true in Wigner interpretation, and Wigner himself abandoned it due to it leading so solipsism.

In some other universe I didn't write this. I know it sounds like bullshit,

I don't buy into MWI, but bullshit is is not. It is easily the most clean and elegant of the interpretations with only one simple premise: "All isolated systems evolve according to the Schrodinger equation". That's it.

These are just two areas I know about in which the idea of infinity is being taken seriously by speculative physicists.

Everett's work is technically philosophy since, like any interpretation of anything, it is net empirically testable.
I would have loved to see Einstein's take on MWI since it so embraces the deterministic no-dice-rolling principle to which he held so dear.

Well I can walk a mile

Ah, local boy. I am more used to interacting with those who walk a km. There's more of em.

But let me riddle you this. Suppose that eternal inflation is true; so that the world had a beginning but no end, and bubble universes are forever coming into existence. — fishfry

That wording implies a sort of meaningful simultaneity that just doesn't exist.

And suppose that in the first bubble universe, somebody says "1".

The universes in eternal inflation theory are not countable.

Yes, each step in a supertask can and does have a serial number. That's what countably infinite means.

P1. It takes me 30 seconds to recite the first natural number, 15 seconds to recite the second natural number, 7.5 seconds to recite the third natural number, and so on ad infinitum. — Michael

You're not going to get past step 10 at best. I just takes longer than the step duration to recite a syllable. I don't think this is your point, but it's a poor wording due to this. Yes, step 13 has a defined duration at known start and stop times. The duration simply isn't long enough to recite anything.

P2. 30 + 15 + 7.5 + ... = 60

C1. The sequence of operations1 described in P1 ends at 60 seconds without ending on some final natural number.

But given that ad infinitum means "without end",

No. It means 'without final step'. You're apparently equivocating "without end" to mean that the process is incomplete after any amount of time.

What else does "the sequence of operations ends" mean if not "the final operation in the sequence is performed"?

There we go with the finite definition again.
"The sequence of operations ends" means that "all operations in the sequence are performed".

This is a great example of the endless repetition of assertions/bad-definitions I'm seeing in this topic. Surely you know this answer is coming from me.

Calculating the limit does not entail a process that reaches that limit. This is a misinterpretation of the concept of limit.This article describes it this way:
In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value... — Relativist

Good source. It says that the limit is approached as the input approaches the specified value.
This means that the limit isn't reached at some finite point in the series, exemplified by the comment:
"This means that the value of the function f can be made arbitrarily close to L, by choosing x sufficiently close to c"
The approaching goes on while x is still at some finite step.

Since x reaches infinity at time 1, all steps are completed at that time, so the task is complete.

Are you saying that you believe that there would still be an April 29, even if there never was any human beings with their time measuring techniques, and dating practises? — Metaphysician Undercover

Read carefully. I didn't say that.

I said
1) that discussion of the question above and your personal beliefs in the matter is off topic
and
2), that you [cannot / choose not to] understand what others mean when they presume what Michael conveyed better than I could:

That we coin the term “X” to refer to some Y isn’t that Y depends on us referring to it using the term “X”. This is where you fail to make a use-mention distinction. — Michael

You (M-U) seem to either not be able to separate "X" and Y, or you refuse to communicate with those that do.

And do you believe that...

My personal beliefs in this matter are irrelevant. I simply know what somebody means when they treat Y as something independent of "X".

I agree that it's impossible to do infinitely many physical thinks in finite time according to present physics. — fishfry

What is it about 'physical' that makes this difference? Everybody just says 'it does', but I obviously can physically move from here to there, so the claim above seems pretty unreasonable, like physics is somehow exempt from mathematics (or logic in Relativist's case) or something.

You italicize 'according to present physics', like your argument is that there's some basic flaw in current physics that precludes supertasks. How so?

I mean, I can claim that there are no physical supertasks, but only by presuming say some QM interpretation for which there is zero evidence, one that denies physical continuity of space and time. By definition a supertask, physical or otherwise, is completed. If it can't, it's not a supertask.

We seem to be talking in circles, with all logic from the 'impossible' side being based on either there being a last infinite number, or on non-sequiturs based on the lack of said last number.

The goal is not unreachable. That simply doesn't follow from arguments based on finite logic, and it is in defiance of modus ponens. It's just necessarily not reached by any specific act in the list.
— Relativist

There is a bijection yes. It does not imply that both or neither completes.
— noAxioms
Why not?

You defined the second task as a non-supertask, requiring infinite time. That's why not.
I can play that game with a finite list of three steps, with the middle step of one task requiring one to make a square circle. It does not follow that the other list of three steps cannot be completed in a short time just because there exists a bijection between the steps of the two tasks.

That's like saying today would be April 29 even if there was never any human beings to determine this. — Metaphysician Undercover

Exactly so.
Your disagreement with views that suggest this is a subject for a different topic. Your displayed lack of comprehension of what the person means when he says things like that is either in total ignorance of the alternatives or a deliberate choice. Being the cynic I am, I always suspect the latter. It's my job as a moderator elsewhere.

I do thank you for verifying my earlier assessment.

I'm not the one advocating for supertasks — fishfry

For the record, I am personally advocating that they have not been shown to be physically impossible. All the 'paradoxes' that result are from inappropriately wielding finite logic in my opinion.
Thomson's lamp is a wonderful example of this, but other examples seem to have more bite.

I would invite you to read up on eternal inflation, a speculative cosmological theory that involves actual infinity. — fishfry

Does it? It seems to be a more complex model that suggests stupid sizes for 'what is', but not 'actual infinite' more than the standard flat model that comes from the cosmological principle. Yes, I know the page you link mentions 'hypothetically infinite' once. I have a deep respect for the eternal inflation model since something like it is necessary to counter the fine-tuning argument for a purposeful creation.

I agree with Michal that the sort of infinity suggested by eternal inflation is not representative of a supertask. I do realize that some people just deny 'actual infinity' of any kind, but that is not justified, hence is not evidence.