That's not what the quotation says - unless you take "not involving practical action" to mean "waste of time".

Similarly, why don't we sometimes notice violations of the laws of physics? — jasonm

Well, perhaps we do. But when we do, we don't immediately assume that they are violations of anything. The most reasonable assumption is that we don't understand what is going on. Sometimes, it turns out that what we've noticed doesn't violate our laws of physics. Somtimes we decide that our laws need to be revised. It would take an awful lot to conclude that the phenomena betray the hidden machinery of a simulation. To conclude that would be no more reasonable than concluding that God had performed a miracle.

Fair enough. How do we know what the locale is really like, so that we can evaluate the simulation as accurate or not?

Such things are good only for having fun and creating sci-fi stories. — Alkis Piskas

Yes. But some people have peculiar ideas of fun. Other people get annoyed and engage in the forlorn hope of persuading them to stop being so silly.

It reminds of Descartes, but it is not strictly the same. — Lionino

True. The point of the comparison is to introduce some perspective and suggest that these thought-experiments are subject to similar criticisms.

Light reflecting off of objects and producing color and form in mind is a kind of simulation. — Barkon

Really? What is it a simulation of?

A technologically mature “posthuman” civilization would have enormous computing power. Based on this empirical fact, the simulation argument shows that at least one of the following propositions is true: (1) The fraction of human‐level civilizations that reach a posthuman stage is very close to zero; (2) The fraction of posthuman civilizations that are interested in running ancestor‐simulations is very close to zero; (3) The fraction of all people with our kind of experiences that are living in a simulation is very close to one.

If (1) is true, then we will almost certainly go extinct before reaching posthumanity. If (2) is true, then there must be a strong convergence among the courses of advanced civilizations so that virtually none contains any relatively wealthy individuals who desire to run ancestor‐simulations and are free to do so. If (3) is true, then we almost certainly live in a simulation. In the dark forest of our current ignorance, it seems sensible to apportion one’s credence roughly evenly between (1), (2), and (3).

I suppose it is not unreasonable to apply a judicious, but not radical, scepticism to this argument or at least some of it. Long posts risk not being read, so I shall focus:-

(3) The fraction of all people with our kind of experiences that are living in a simulation is very close to one.

I charitably assume that "all people" means all people past, present and future, including artificial people developed as part of a holistic simulation - if there be any such. What is the evidence that there are any people with our kind of experiences living in a simulation - apart from NASA experiments, archaeological research and trials for deep-sea mining? None that I know of.

But the Doomsday Clock is at 90 seconds. Extinction without any evolutionary descendants is a real possibility and should have been included as a fourth possibility - amongst many others.

If (3) is true, then we almost certainly live in a simulation.

That seems to follow. However, let us note that "we almost certainly live in a simulation" assigns a probability of, say, 0.99 to "we live in a simulation".

In the dark forest of our current ignorance, it seems sensible to apportion one’s credence roughly evenly between (1), (2), and (3).

In probability theory, it is indeed regarded as sensible to do that if we have listed all the possibilities. But the rule only really applies in mathematical probability, which this exercise is certainly not. The Bayesian notion of credence is based on an admittedly subjective evaluation of the evidence for each outcome. But there is no real evidence for anything here, so the assignment is arbitrary, rather than sensible.

In any case, what we actually have is a probability of 0.33 that the probability we are living in a simulation is 0.99. That seems a good deal less than almost certain and almost certainly less that 0.5.

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

Yes he does, and, as you say, he doesn't say which of them he thinks most likely - though many people seem to have decided that 3) is the best bet. I've no idea why.
But I couldn't see why Bostrom thought that one of those three must be true.

the physics would likely have developed more or less at pace with our own history. — noAxioms

I don't see why you say that. I think you are assuming at least a soft determinism? But given that the starting-point of the history in the simulation is not more than roughly the same, I don't think you have any real basis for that assumption. I grow even more sceptical when I remember the argument that small differences, over time, can result in big differences. Remember, there were times during the Cold War when nuclear holocaust hung by a thread.
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. 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.
But what I'm thinking about is what would happen if the people inside the simulation decided to do some physics, including, of course, experiments. That would require interaction between the person and the machinery even when they are carrying out experiments designed to reveal the physics at work. If the progress of science is anything to go by, it wouldn't be easy to fool them all the time.

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. — noAxioms

Didn't you say something to the effect that quantum mechanics and general relativity couldn't be simulated? Perhaps I misunderstood.
There are two physics involved. One is the physics of the simulated world, which would need to be quite like ours. The other is the physics of the world in which the simulators exist.

How lucky are we to have survived to the point of being able to put together these simulations? — noAxioms

Even luckier to have the resources to waste on such a project.

From the viewpoint of fish in an aquarium, is their existence a simulated life, in that the aquarium simulates the ocean, or is it a real life, in that their environment is all they know. — RussellA

Both make some sort of sense. It would also be possible to say that the aquarium is a little bit of the ocean. It would also be possible to say that, since the water they swim in and the food they eat are both real that their world, though small, is not simulated.

Takeaway pizzas simulate real food, social media simulates real life, sports events simulate medieval battles, surveillance cameras simulate the nosy neighbour in a small village, modern government tries to simulate the parents in a traditional family (whether father of the nation or mamala to the people) and corporate employers simulate the process of having to work for essential food and shelter. — RussellA

You are confusing "simulate" with "is like".

As regards argument 1), the designers do pop out at times, but the life-form is not aware because of their necessarily limited intelligence.
As regards 2), similarly, the life-form doesn't notice violations in the laws of physics also because of their necessarily limited intelligence
As regards 3), the same amount of computing power would be required to house a "simulated" world as a "real" world.
As regards 4), the simplest explanation for fish in an aquarium is that they exist in a simulated world — RussellA

1) Do you have any evidence for that?
2) Do you have any evidence for that?
3) The real world does not need to be housed and therefore does not require any computing power.
4) What is the question the fish are asking? If there's no question, there's no need for an explanation.

You may respond that humans are the supreme intelligence in the universe and are all knowing, yet humans have only been around for 2.8 million years whilst fish have managed to successfully survive in a hostile world for more than 500 million years, regardless of whether this world happens to be "simulated" or "real". — RussellA

What does that have to do with anything?

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. Would it not be a mistake to assume that what applies in our world applies outside it? This seems an odd position to take. — Tom Storm

It rather depends on what your project is. If the project is to make a space for fantasies, then the fact that we don't know is an opportunity, not a problem. Myths have always been stories told where knowledge was not possible. This is a myth.

Also, I think many do not realize that the “God hypothesis” has come back in a stealthy sort a way. Instead of the watch needing a designer, the simulation needs a simulator. — Richard B

Good point.
Come to think of it, the argument could be seen as a version of Berkeley's "proof" of God.

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. Would it not be a mistake to assume that what applies in our world applies outside it? This seems an odd position to take. — Tom Storm

It rather depends on what your project is. If the project is to make a space for fantasies, then the fact that we don't know is an opportunity, not a problem. The point where knowledge runs out is always an opportunity for myth to fill the gap. This is a myth.

That's one of the cognitive traps of the lamp problem. IMO the final state is simply not defined by the premises of the problem, AND there is no solution that makes the sequence continuous, therefore spaghetti is as sensible as anything else. And I've convinced myself that this is the solution to the problem. — fishfry

I agree with you. It suits my approach well, in that the existence of the problem is a result of the way it is defined, or not defined.

The walker is on step one, the walker is on step two, etc. So if we define the final state to be that the walker is at the bottom of the stairs, that definition has the virtue of making the walker's sequence continuous. — fishfry

That's the way ω is defined, isn't it? Although I'm not sure what you mean by "continuous" there.
I still feel uncomfortable, because it does get to the bottom of the stairs by placing a foot on each of the stairs, in sequence. But that's exactly the hypnotism of the way the problem is defined. And if an infinite physical staircase is the scenario, then anything goes..

I have been known to take my bat home when I think that a discussion has become fruitless, even before it gets bad-tempered.

Yes ok, so the coach can turn into a pumpkin and the lamp can turn into a plate of spaghetti. Are you agreeing with me on that point? — fishfry

Yes. But I have an obstinate feeling that that fact is a reductio of the process that generated it. So I'm not questioning what you say, but rather what we make of it.

I was making my point about mathematical convergent sequences. Don't know whether it strictly applies to walking. — fishfry

It may be a bad habit to think of applications of a mathematical process. But that's what's going on with the infinite staircase. So it might be relevant to that.

I understand. It's probably best not to comment any further.

Your are being too kind to call this even “highly improbable”. Just because we can imagine such fanciful scenarios does not mean they are possible. — Richard B

I agree. I understand the argument as being a version of Cartesian scepticism. The possibility that God, or an evil demon is feeding us false information is also a fanciful scenario. The paradox of the situation is that believers in it have to put more faith in their fancies than in their experience.

Descartes did at least try to insulate his reflections from being mistaken for real, by proposing them as a thought experiment for academic purposes. I say "try" because so many people have treated his conclusions as objectively true and struggled to escape from the conclusion, when, on Descartes' own presentation, all they have to do is get up from their warm oven and go for a brisk walk in the fresh air.

So you cut corners and don't simulate at that level unless something intentionally is paying attention to that level. — noAxioms

So there are two ways that a simulation of our world would differ from the real world - sorry, the world as we know it.
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.
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.
So it would not be possible to simulate the progress of research in physics over the last 100 years or so?

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?

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. — noAxioms

Surely, we have to presume there is a base reality, or face an infinite regress.

Surely the programmers can create whatever physics, chemistry and phenomena they like. — Benj96

Not quite. They can simulate them, but that just means they can create an illusion of them. They can't create them for real.

Ofc I'm on some fantasy rant here. But I enjoy dabbling in wild metaphysical speculation — Benj96

Yes. It's a curious game. I've never understood the rules.

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. — noAxioms

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

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. — noAxioms

Yes, it is. An infinite number, to be exact.

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

That's just a posh way of saying that the battle seems real to those in the simulation. Reality, by definition, is not "in" the simulation, but outside it.

The sequence itself has no last item. But the "augmented sequence," if you call it that, does. We can simply stick the limit at the end. — fishfry

I think that's all right. When I walk a mile, I start a potentially infinite series of paces. When I have done (approximately) 1,760 of them, I stop. The fact that the 1,760th of them is the last one is, from the point of the view of the sequence, arbitrary, not included in the sequence . The sequence itself could continue, but doesn't.

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. — noAxioms

OK. Is that because they have no dimension - are not a part of the line?

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

Because <the infinity symbol> can't be associated with any natural number?

I agree with that too. In the end, I don't think reasoning about infinity gets us anywhere. — Lionino

Then the ultimate paradox is that there seems to be no end to the reasoning.

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. — noAxioms

I don't quite understand. Is the point that the simple arithmetic analysis doesn't reference the highest natural number, so that way of reaching it is OK. It doesn't look like completing all the steps to me - it looks more like jumping over them. But I have travelled over all the spaces.

Which is to say that space isn't measurably continuous, — noAxioms

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

Physics: There are no solids. — noAxioms

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

The set of points on say a circle is an uncountable set — noAxioms

That's a surprise to me. One can measure or calculate the length of a circumference, can't one? Or is uncountability a consequence of the irrationality of "pi"?

As has been stated so many times, by performing all the steps, which happens in finite time no problem. — noAxioms

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

The cutting up of the path into infinite steps was already a mathematical exercise. — noAxioms

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.

The causal history, however, is what makes it necessary to experience the frog as a frog and not as a hopping constellation of colored shapes. — jkop

I think the point goes deeper than that. We can experience a constellation of coloured shapes as a frog, but only as a picture of a frog. My past experience acting in the world no doubt contributes to that. But to seriously fool me as a real frog, it would have to respond to my attempts to catch it (by hopping out of reach). Can I be fooled into thinking I am attempting to catch it? I would have to have all the sensory inputs, including the proprioceptive inputs that tell me where my body is and what it is doing. But if that was all controlled by the simulation machinery, I would not feel that I was doing it - my "body" would not be my own. The inputs would have to respond to my outputs - the signals that would, in real life, control my body. That is, inputs from the machinery would never be enough. I would have to be in control of my "body". The machinery has to respond to me - it has to become my body.

Yet many people seem to believe that the whole universe, or at least our experienced part of the universe, is or could be a simulation. — jkop

"Universe" is a bit slippery here. If it means "everything that exists", we have to take into account that a simulation cannot be everything that exists, because it must be a simulation of something and that something must be real - an alternate reality. We are used to the idea that there can be alternate worlds in the same universe nowadays, but the idea of alternate universes presupposes that there can be no communication of any kind from one to another.

If the universe is simulated or in part simulated, it doesn't make it any less real, — Barkon

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, and it is a simulation of real (or possibly real) events. I think you are proposing that a whole universe might be simulated by a process that would be controlled in order to serve some purpose. But if everything is included, not only is there no reality to be simulated, but also there is nowhere for the creators (or their hardware) to be. So I don't quite understand what you are getting at here.

If a simulation exists, then there must exist at least one more thing (or set of things) which is constitutive for the simulation, e.g. a brain, a computer, their materials and properties and surrounding conditions of satisfaction. Therefore, everything cannot be a simulation. — jkop

I like that argument a lot. :smile:

Furthermore, if the simulation (e.g an emergent property within a network of electrical circuits) is about something (e.g. our world at the level of humans and mid sized objects), then we have at least three things to consider: the simulation (emerging from electric circuits), what causes it (a brain and computers etc), and what it is about (a part of our world). So, not only is it impossible for everything to be a simulation, the simulation is just one thing among many other things in our world. — jkop

"Three things" might prove to be contentious, depending on how you define "thing". But the conclusion seems to me to be sound.

A frog is not just a constellation of coloured shapes that hop around for no apparent reason. Simulations, pictures, or descriptions of frogs are syntactically disjoint and detachable in a way that real frogs are not. Real frogs are continuous, recalcitrant, and seamlessly connected to other creatures and environments, which in turn are connected to chemistry, physics, astrophysics, cosmology or everything. Our ability to identify frogs, as frogs, has a causal history that arguably amounts to everything, and a simulation cannot be everything. — jkop

You are, rightly, thinking of me as a passive spectator in the simulation. You have left out a really important point. We are embodied and active in the world. So the frog is not just a "constellation of coloured shapes" (and sounds, smells, touches and even tastes), but also something that we interact with (as the frog interacts with us). For me, it's the interaction that distinguishes the real frog from the dream. True, I can imagine an illusory frog that I don't interact with, but only because I sometimes interact with the things that I perceive.

'highly improbable.' — jasonm

That's very generous.

If this world is simulated, the "real" world must be very like this one - as in the "Matrix". But then, it if the real world is very like this one, does it include all the evidence that this world is simulated. In other words, will the inhabitants of the real world believe that they are living in a simulation. So the real world is also a simulation.....

But how do we know that this world is a simulation if we have no access to the real world and cannot compare one with the other?

I cannot distinguish the idea that this world is simulated from a fantasy or, better, a nightmare.

If you agree, I'm happy, because that's the only point I'm making. I've never written more just say less. My only point is that in the lamp and these other problems, we're not defining the state at the limit. Therefore the choice of state is pretty much arbitrary. If we thought about it that way it might be more clear. — fishfry

:smile:

If I can walk from one end of the grocery aisle to the other, I don't see why you can't get down the staircase, infinitely many steps or not. — fishfry

But I did walk through infinitely many inverse powers of two lengths at the grocery store. I did sum an infinite series in finite time. — fishfry

I find this very confusing. I take your point about abstraction. But I find that abstraction can create confusion, because it persuades us to focus on similarities and neglect differences. My reaction here is to pay attention to the difference between these kinds of infinite series. It's not meant to contradict the abstraction.

It's a thought experiment. There are no infinite staircases. — fishfry

Exactly. So it isn't about physics. But it isn't about mathematics either. So it seems to me an exercise in imagination, and that provides a magic wand.

Aha. You'd have to ask those who care so much. I think they only show that underspecified problems can have arbitrary answers. But others see deeper meanings. — fishfry

Deep? or Deepity? (RIP Dennett)

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

Yes. Euclid (or Euclidean geometry at least) starts from a foundation - axioms and definitions. But they are an extension of our common sense processes of measuring things. (You can understand more accurate and less accurate measurements.) Extend this without limit - Hey Presto! dimensionless points! That is, to understand what a point is, you have to start from lines and planes and solids and our practice of measuring them and establishing locations. I find that quite satisfying. Start with the practical world, generate a mathematics, take it back to the practical world. (Yes, I do think that actual practice in the real world is more fundamental than logic.)
Once you define geometrical points in that context, there is no difficulty about passing or crossing an infinite number of points. (But the converging series does not consist of points, but of lengths, which are components.)

So there's something interesting going on. — fishfry

My supervisor used to say that when he got really excited, which was not often.

I believe Churchill also said that the greatest argument against democracy is a five minute conversation with the average voter. — fishfry

Yes, he did say that. He was also right about that, as well.
People are making a mistake when they think that voters need to decide on specific measures. That way, madness lies. The classic reference for this is the expedition to Sicily by Athens in 415–413 BCE. See Wikipedia - Sicilian Expedition. A better model is the Spartan one (which was a democracy, of sorts, despite rumours to the contrary); that is about consent, not decision. Which is the other point people don't seem to understand. The vote is, or should be, about legitimizing the regime, and all that requires is acquiescence, not decision. A majority vote with a choice is a way of palliating the opposition - much better than repressing it. But then, it does require that the opposition accepts defeat; when that breaks down, the system is in serious danger. (Trump!) The Government needs to secure approval of the election arrangements from the opposition - too many of them neglect that.

That's very interesting! I wouldn't mind government subsidies if they're fairly distributed among the college and non-college individuals. — fishfry

H'm. It's true that there is government support for both groups, but many people feel that there is less support for sub-degree programmes and complain about that - with justification in my view. Others complain the employers should pay for these programmes, as the primary beneficiaries - and they do pay for, and are involved in the delivery of, many of them by providing work experience.

I am no fan of Churchill, but I tend to agree with the statement (probably falsely attributed to him and loosely paraphrased) "Democratic capitalism is the worst of all possible systems, apart from all the others". — Janus

Churchill does quote it, but doesn't take credit for it. Also, there are various forms of it. See Quote Investigator.

We have no disagreement then. People should pay off their own loans that they knowingly agreed to pay. — fishfry

I thought I had already said that I don't have a problem with that. When I said that politics is a messy business, best not really be conducted in public, I was also accepting that it was a bribe to voters. All democracies do that - it's an inevitable outcome of the system. Non-democratic governments do it as well. Politicians have to keep their supporters sweet. I'm not even saying it is right, or all right, just that it always happens.

Welders don't have student loans. — fishfry

Each country has its own system. In the UK, the "trades" like welding and pipefitting, do get government support - and this is a "right-wing" government. See Skills for careers. Some people regard this as a blatant subsidy for employers, who should be paying. But there are complications.
Higher-level professions depend on degree-level courses, and these get student loans. But these are repaid on a sliding scale, dependent on you income. (Effectively, it's an additional income tax). The Government assumes that 35% to 40% of the total will never be repaid. There's your forgiveness, but sanctioned by Parliament.
Re-training is more of a problem.

they (potential parents) will somehow, in blind anticipation, be innately inclined to sufficiently understand and appropriately nurture their children’s naturally developing minds and needs. — FrankGSterleJr

Yes. The idea that we all know how to bring up children, just because we have been through it ourselves, or because of "instinct" is arrogant beyond belief.

We can, however, educate young people for this most important job ever, even those who plan to remain childless, through mandatory high-school child-development science curriculum. — FrankGSterleJr

On the other hand, anyone who is can be confident that their study and research has revealed to them the correct way to do that is also arrogant beyond belief.

The only thing that's certain is that no-one knows for sure. It's wiser to muddle through with a great deal of humility and with as much restraint as possible.

The greatest error of all is to think of bringing up children as like making a cake. It is an interaction, in which the child is a partner, not a passive subject.

But the State's function is anti-social in both origin and function. — NOS4A2

I don't know what you have in mind when you say that. I don't see how state can exist without society, or society without the state. They are interdependent.
It's nice to think of a society that works by co-operation and not compulsion. But I don't see how that is possible. At the same time, compulsion can only get so far. So a society based only on compulsion won't get far.

Now you're speaking my language. Thomas Paine wrote that writers tend to confound Society and Government, as if the two were one and the same, so I appreciate your distinction. — NOS4A2

I don't know much about the detail of what he said. But Government does like to think of itself as above the fray. In some ways, it is, but in other ways it is just one part of it. Whether its use of physical force gives it a special role or not depends on whether the force is used to keep the peace or to squash opposition. There is also the awkward point that the people who are the Government are also members of Society and so liable to see society from a point of view within it.
So although the two are not just one and the same, they are not two clearly distinct entities.

I suspect also that he thought that the "common man" was a special group, with special rights. That makes him just another spokesman for an interest group. (I'm getting at the idea that the majority can become tyrannical just as easily as any other sub-group in a society).

Exactly. Capitalism and socialism - Tweedledum and Tweedledee.

So we have only two things to fear - the state and everyone else.

Why don’t we just organize, find some like minded people, and implement our philosophy by living it and doing it? — NOS4A2

Excellent. But you should think it through. It is not capitalism or socialism as long as everyone is a volunteer and so can leave when they want to. When that stops - and it always does - Society begins.

In one it could be you; in the other it couldn't. — NOS4A2

There's always a group of people in control, who exclude most of us. In either state, in theory, I could join the group that's in control. But then I would have to serve them.

The only thing that differs between them is who they believe should control capital. — NOS4A2

..... but what they all have in common is that it isn't us.

But yes, I think any system modelled on the republican state relegates us to the status of serfs. — NOS4A2

What other state, other than anarchism, wouldn't relegate us to serfdom?

I don't know that anyone would disagree with you. It is always a question of how to achieve such a goal. — Leontiskos

I agree - no-one would disagree - until it comes to the question of what children need. Then, we're all over the place.

That is precisely where the socialism comes in, and it quickly resembles serfdom. — NOS4A2

.... and do you really think that capitalism doesn't resemble serfdom?

But one cannot use armchair philosophy to determine the smallest unit of space/time/movement. — Michael

Given the logical paradoxes that continuous space and time entail, I think that discrete spacetime is not just a physical fact but a necessity. — Michael

I don't think you can have it both ways.

And the passage of time that we would measure as being 60 seconds occurs even when we don't measure it. — Michael

I'm not quite sure what you are saying. Do you think that the passage of time occurs when we can't measure it? Analogously (if that's a word), if we can't measure the location or momentum of an object, it doesn't have them? Does that mean that it doesn't exist?
There are two philosophies that I can think of that would justify those views. One of them is Logical Positivism, which was developed precisely to justify both Quantum Mechanics and General Relativity. The other is Bishop Berkeley's idealism. Which do you hold?

There are physical theories that treat spacetime as discrete. They are not supported to the extent that General Relativity is, but given that quantum mechanics and General Relativity are known to be incompatible, it would seem that at least one of them is false, and my money is on General Relativity being false. — Michael

That means you think it is possible that space-time is continuous at the quantum level. Interesting. But I suppose it fits with your acceptance of continuous space-time in mathematics.
The empirical evidence for your position is the empirical fact that we can't measure very small units of time or space. I'm not sure that constitutes convincing empirical one way or the other. Or have I got something wrong?

Given the logical paradoxes that continuous space and time entail, I think that discrete spacetime is not just a physical fact but a necessity. — Michael

Which ones do you have in mind? You mentioned the problems with a converging series. But that's a mathematical problem, not an empirical one. How does empirically non-continuous space and time solve those issues?

Even if you are determinist and do not agree with free will causation, quantum mechanics clearly demonstrates that your statement is false. — Metaphysician Undercover

I hope you don't mind my saying that your choice of free will as an example was perhaps ill-advised. It's far too contentious to work. Quantum mechanics is a much better choice. But there is the problem that there are many interpretations of it, so it is not clear that it proves what you think it proves.

In the future, if physics ever figures out how to work with physically instantiated infinities, supertasks might be possible. Way too soon to know. — fishfry

I think you are both mistaken to rely on physics to define what one wants to get at in this context. Physics is not only limited by the current state of knowledge, but also by its exclusion of much that one would normally take to be both physical and real. Somewhere near the heart of this is that there is no clear concept that will catch what we might mean by "whatever exists that is not mathematics" or by "whatever applied mathematics is applied to".

Jeez that's kind of creepy ... true, I suppose. Death is the least upper bound of the open set of life. — fishfry

I'm sorry. I didn't mean to gross you out. Perhaps if you think of death as a least upper bound, you'll be able to think of it differently. It is, after all, an everyday and commonplace event - even if, in polite society, we don't like to mention it.

I just mentioned that I could argue it either way. — fishfry

Yes. I was just drawing out the implications. You might disagree.

The sequence is endless, and there's an extra point that's defined to be strictly greater than all the others. We can't get to the limit by successors, but we can get there by a limiting process. — fishfry

Yes. In the context of the Achilles problem that's fine and I understand that you are treating that and the natural numbers as parallel. It's not clear to me that it really works. It makes sense to say that "1" limits "1/2, 1/4, ..." But I'm not at all sure that it makes sense to say that <omega> limits the sequence of natural numbers. "+1" adds to the previous value. "<divide by 2>" reduces from the previous value. The parallel is not complete. There are differences as well as similarities.

How can it be out of reach? I went to the supermarket today. I walked from one end of the aisle to the other. I reached the end. I did indeed evidently sum a convergent infinite series. — fishfry

Did you "get to the limit by successors" or "get there by a limiting process"? I don't think so. You are just not applying that frame to your trip.

I think some of Zeno's other paradoxes are more interesting. When you shoot an arrow, it's motionless in an instant. How does it know where to go next, and at what speed? I think that's a more interesting puzzle. Where are velocity and momentum "recorded?" How does the arrow know what to do next? — fishfry

I've met other mathematicians who agree that Achilles is not interesting. But I'm fascinated that you think the arrow is interesting. I don't. Starting is a boundary condition and so not part of the temporal sequence, any more than the boundary of my garden is a patch of land. End of problem.

But this may be interesting in the context of what we are talking about. A geometrical point does not occupy any space. It is dimensionless. One could say it is infinitely small. But it is obvious that there is no problem about passing an infinite number of them. It is a question of how you think about them. This is not quite the same as Zeno's problem, but it is close.

That is a perfectly sensible answer to the question, "What is the state at the limit?" It's perfectly sensible because the conditions of the problem don't specify the value at the limit. And since the lamp is not physical, it can turn into anything we like at the limit. It's no different than Cinderella's coach, which is a coach at 1/2 second before midnight, 1/4 second before midnight, and so on, and turns into a coach at midnight. — fishfry

I agree with that.
Perhaps then, these problems are not mathematical and not physical, but imaginary - a thought experiment. (The Cinderella example shows that we can easily imagine physically impossible events) That suggests what you seem to be saying - that there are no rules. (Which is why I posited another infinite staircase going up). But if there are no rules, what is the experiment meant to show? The only restriction I can think of is that it needs to be logically self-consistent - and the infinite staircase is certainly that. I guess the weak spot in the supertask is the application of a time limit. However, I also want to say that I cannot imagine an endless staircase, only one that has not ended yet - once I've imagined that, I can wave my hand and say, that is actually an infinite staircase.

Why shouldn't I take out $100,000 US in loans to study underwater basket weaving, if I'm reasonably sure some future administration is going to transfer my loans to the taxpayers? — fishfry

I'm sorry about this rant, but I don't know how else to respond.

It depends on your philosophy of education. The thinking behind all education is a mess; the thinking behind higher education is even more of a mess; and the thinking about adult education is practically non-existent. You can think about in terms of vocational (career) benefits and non-vocational ("for fun") programmes and a combination of private benefits (for the student) and public benefits (for society in general). There's also an issue about benefits to employers, but these are rarely thought about in their own right.

Underwater basket weaving looks like a bad career choice, but possibly a good choice for fun. Either way, the student should pay. Some programmes, like IT skills (and mathematical ones) lead to extremely profitable careers in the finance industry; again, the student should pay. But if there's a serious shortage of welders, such that various industries cannot find the workers they need, there's good reason why employers, and/or the state, might want to pay. Then there are programmes like social work and nursing, which require specialized professional training, but don't pay well. Isn't there a good case for state support? What abaout high-level professional careers which could be financed by students, but where that is impractical because of their high costs whether in infrastructure or time required; again, public subsidy makes sense. Another category is risky careers, like acting or archaeology or philosophy; again, there's a case for public subsidy, not only to ensure a supply for the labour market, but because the existence of those careers is a public good.

If you thought that was a mess, consider the non-vocational subjects, or those subjects which can be studied for vocational reasons and can also be studied for fun. The catch here is that all the specific vocational careers presuppose some level of basic, general skills and knowledge, which enables people to function in society in general, both within and without their vocations; these skills are also the basis of good citizenship. These include reading, writing, and arithmetic, but also extend (In the UK) to Science, Technology, Engineering and Mathematics (practice needs theory, after all) and to various skills under the heading of good citizenship - philosophy, literature and history and the arts. Those last four are often regarded as purely for fun, so I don't claim that the idea that they are not just for fun is uncontentious. Perhaps the most effective argument for them is that democracy cannot function properly without them. J.S. Mill recognized this, but it seems now to be ignored, which is a pity. Mind you, the idea that an understanding of the humanities was essential for a decent society took a very serious knock in WW2. But it is far from dead.

Underwater basket weaving? Probably not. Philosophy? Fine Art? There's at least a case to think about, isn't there?

PS. I forgot to explain how students should pay when they need to. Through the tax system. If their career choice pays off, they will pay increased taxes, so the public purse will benefit and their debt "repaid" - or, if you prefer, the public investment in their career pays off. Where their career does not pay off in that way, the public (and employers) will benefit from an increased supply of highly qualified labour. Where their career is not directly developed by their qualification, it will have been helped by the "transferable skills" developed in their programme and by the improved contribution they can make by their contribution to social and political life.
In other words, payment through the tax system is perfectly well justified by the multiple benefits provided by higher education. Nobody has a problem with that way of paying for schools. Why would higher education be any different?

"Classical" liberalism, which is more like conservatism today. Although conservatism is pretty muddled, what are they really for? — fishfry

That process - what was liberal and new, becomes old hat, and conservative. That what's happened to feminism, etc. The agenda has moved on. It's very disappointing to those of us who thought the problems were solved. But there are unsolved and unconsidered issues and big gaps in even the basic rights that one thought had been established.

There's no rehabilitation going on. There's a revolving door of people committing violent crimes, being put back on the street, and re-offending. — fishfry

If that's so, there is a problem.

Some of the people on that "side" are victims, I imagine they don't even have an inner monologue so they can't even filter what information is fed to them. — Lionino

That's perfectly possible. But if you want them to develop one, it's as well not to tell them about it. Shouting about it just breeds resentment and resistance.

I don't see why not. The whole point of the puzzle is to sum 1/2 + 1/4 + ... = 1, and then to ask what is the final state. — fishfry

The sequence is endless, and there's an extra point that's defined to be strictly greater than all the others. We can't get to the limit by successors, but we can get there by a limiting process. — fishfry

OK. I remembered WIttgenstein's oracular remark that death is not a part of life. My concern that the limit is not generated by the defining formula isn't the problem I thought it might be.

I've convinced myself both ways. On the one hand we can't physically count all the natural numbers, because there aren't enough atoms in the observable universe. We're finite creatures.
On the other hand, supertasks are possible, because I can walk a mile, meaning I walked 1/2 a mile, 1/4 mile, dot dot dot. — fishfry

I don't really believe in "possible" without qualification. There's logically possible, (is mathematically possible the same or something different? Does is apply here?), physically possible, and a range of others, such as legally possible. So what kind of possibility is a supertask?

A lamp that cycles in arbitrarily small amounts of time is not physical. A staircase that we occupy for arbitrarily small intervals of time is not physical. So trying to use physical reasoning is counterproductive and confusing. That's my objection to all these kinds of puzzles. People say there's a conflict between the math and the physics ... but as i see it, there's no physics either. — fishfry

So your reply is that it is neither. It suggests a combination of physical and mathematical rules which is incoherent but generates an illusion. That's why

It may "lead" somewhere but there's no law that constrains the final state. It may be discontinuous, like Cinderella's coach that's a coach at 1/2, 1/4, 1/8, ... seconds before midnight, then becomes a coach at midnight. That's why it's perfectly possible that the lamp becomes a pumpkin after 1 second. — fishfry

But then you say

On the other hand, supertasks are possible, because I can walk a mile, meaning I walked 1/2 a mile, 1/4 mile, dot dot dot

Obviously, as each stage gets smaller, I will complete it more quickly. But still, it will take some period of time, and the final step looks out of reach. That looks like a combination of physical and mathematical rules.
It isn't a real problem because I can analyze the task in a different way. I can complete the first yard, the second yard.... When I have completed 1760 yards, I have completed the task. But the supertasks seem not to permit that kind of analysis. Is that the issue?

We were on the right track - UK, Australia, NZ, Canada, most of Europe and even the US - for a large portion of the 20th century. (Chastened by the depression, governments curbed big capital and invested in the population at large) Then, starting about 1980, the political pendulum was pushed hard to the right. Now, the far left is where the moderate right (remember them?) was in 1976. Now, we're heading toward fascism at a fair clip. — Vera Mont

I won't disagree with any of that. The obvious questions are when the pendulum will start to move the other way and how much damage will be done before that finally happens. Oh, and whether it is just a pendulum but more of a spiral - upwards. I happy to answer the first with "eventually". The others require "Don't know"

Reform is an uphill battle. — Vera Mont

Well, yes. Obviously a downhill battle would be better, but I'll settle for that.

Thanks for the clips. Very instructive.

The practicality is not yet upon us. I don't think reform is feasible. — Vera Mont

You are not alone. I also think the prospects are very very gloomy. I have the impression that many people all round the world have a sense of impending doom. I wish I could be more optimistic.

House-of-cards economies like the one we're living in periodically collapse. — Vera Mont

Yes. Any economic/social system is vulnerable to catastrophic events. But life goes on. People pick themselves up and work out what they will do next. That's not a facile optimism. It would be much, much better to avoid the disaster in the first place, but it isn't always possible.
Your analysis of where we are is quite familiar, but doesn't help much. Capitalism has been in crisis practically ever since it was invented. It is extremely resilient and adaptable, which is both a curse and a blessing. The obvious alternative is Socialism, which is as polymorphous as capitalism. It seems to be more effective as way of modifying capitalism than as a system in its own right. We seem to be working out how to blend the two, and that seems to me to be the right way to go

In the DEI departments of university administrations I imagine. — fishfry

Not so. I don't know what data is available to you, but perhaps you should look around. All I'm saying is that you cannot assume that every vocational programme provides marketable qualifications nor that every non-vocational programme does not. It's up to the market to decide what it wants.
Equally, it is up to students to decide what they want, even if they make choices that you think are unwise. It's not as if we can predict and provide what the economy wants.

Point being that pipefitters shouldn't be shouldering the cost of the loans forgiven for social justice majors. — fishfry

Well, if the cost is funded by general taxation, the contribution will depend on their income. That doesn't seem unreasonable - unless you think that people should not study social justice. But I think it is a good thing that as many people as possible should understand what social justice is.

Right. The "liberals" used to be for the working classes. Now the liberals support the elite against the working classes. Bit of a puzzler. — fishfry

It's complicated. In the UK, liberals in the 19th century were, by and large, members of the elite. They were never particularly enthusiastic about supporting the working classes. They were much more interested in free trade, political issues like voting rights and moral/social issues like divorce, gay rights &c. (Conservatives supported protection and social conservatism). The working classes, by and large, had to fight their own battles, which they did through the Trade Unions.
But I'm sure the alignments were different in the USA.

Violent criminals are being put back on the street to re-offend. That's not fair to the victims. Violent criminals belong behind bars. — fishfry

People can't re-offend if they're locked up. — fishfry

You can't imprison violent criminals forever, unless you can prove them criminally insane. Sooner or later, they have to hit the streets again. That's why rehabilitation is so important.

Perhaps I just spend to much time following NYC politics. They're having a problem with soft-on-crime politicians leading to a great decrease in public safety. — fishfry

Nothing wrong with that, so long as you are open to new ideas occasionally.
I don't know the details, but my instinct is to suggest that if the rehabilitation programmes in NYC aren't working, find a better programme, don't give up on the attempt. Money spent on effective programmes to keep people out of prison is a good investment. Back that up by improving detection and arrest, which is by far the most effective deterrent. Tossing people out of prison into the general population will not work and putting them back in prison later on is very expensive, not only in running the prisons, but also in the damage inflicted on families and children.

I didn't think I was. I meant to describe political positions. I'm quite aware of the magnanimous billionnaires who use their money for culture and charity, as well as larcenous beggars. — Vera Mont

I'm sorry if I took you the wrong way.

No. I have trouble dealing with the concept of wealth in any distribution. I'd rather think in terms of resource allocation and sharing. — Vera Mont

I don't understand this. Money represents resources. So the distribution of money is allocation of resources. Sharing is more complicated, but the family is partly about sharing resources, isn't it? Perhaps you are just talking about an attitude? Or do you have in mind a reform of property laws?

I believe everyone should have enough food, shelter, security and leisure, a chance to contribute to their community and be recognized for their effort, access to education and the freedom to fulfill their potential.
I believe nobody should have more of anything than they can use and enjoy in one lifetime.
I believe no child should start life materially better off than others of its cohort, and those who start life with a handicap should be offered all available support by the community, as should any adult who falls ill, is injured or grows feeble.
I believe we should not take from the Earth more than we collectively need, and dispose of our waste in a productive manner.
I realize it's a pipe-dream. — Vera Mont

I don't have a problem with pipe-dreams. I understand your objection to inherited wealth. But I'll spare you any flat-footed objections about practicalities.