As for multiple definitions with different answers, can you specify two definitions of ‘universe’ that have different answers? I of course do not only mean the observable universe.
A ‘standard’ definition of “universe” is “all existing matter and space”. If we allow for the many-worlds hypothesis, then the universe is infinitely large even if a Laplacian Demon could know the entirety of the universe at a given state (i.e.; simultaneously finite and infinite). If we operate under a definition of “universe” whereby the MWI creates a new universe for each “choice”, then we have no way of knowing where or if there is an outer bound of our universe beyond the observable lightcone.
Furthermore, if some variants of M-Theory are correct then our universe may be possessed of a specific shape and be limited in scope regardless; so again it could be finite. And again, under other variants of how we interpret M-Theory, each p-brane and membrane is not a separate universe but part of a whole. Which is presumed infinite.
So the problem is that we have no acceptably rigorous definition of what is a “universe” in order to start making assertions about its finiteness or lack thereof.
Even if we use the conventional “assumption” of what our Universe is which existed shortly after the ‘discovery’ of the Big Bang (i.e.; the collection of galaxies and matter that we can either observe or that directly and observably interacts with what we can observe, and the spacetime continuum these interactions occur within) -- we lack the ability to derive any information about its scope or dimension.
So no probability assertion about the universe’s scope should, rationally speaking, have anything remotely resembling a high threshold of confidence. Said confidence should, in fact, approach zero.
I am not in the habit of bothering with probability statements whose confidence is below 1%; I find them not merely a waste of time but damaging.
Isn’t it enough to simply say, “There is as yet insufficient data for a meaningful reply” to the question?
So you are against induction, in general? Nothing directly unobservable is knowable? Do you really think that the assumption that the physical laws are the same outside Earth’s light cone as they are inside is an error?
It’s not that I am against induction (in fact, I routinely refer to Popperian Falsificationism as the resolution to Hume’s Problem of Induction). Instead, I am acknowledging that induction has limits. What inductive process will allow you to derive the words written on the can in front of me as I type this?
Nothing directly unobservable is knowable?
No. All things which are entirely unobservable are unknowable. Indirect observation qualifies as a form of observation. That which is outside of our lightcone is entirely unobservable (as yet.)
Do you really think that the assumption that the physical laws are the same outside Earth’s light cone as they are inside is an error?
We have no basis for the assumption at all. It furthermore rests on the additional assumption *that there is even a “physical” at all there.
Furthermore: there is some disagreement at the “bleeding edge” of physics as to whether gravity is a constant. And that’s just what we can observe.
I recall the admonition that “The Universe is Queerer than we can suppose”. From it, I have a generalized principle: when I have no information to make assertions with, I acknowledge my ignorance. When, however, I observe that no information is available, I note this fact and move on.
Making ‘guesses’ as to the ‘probability’ of assertions when you know your priors are entirely arbitrary is … counterproductive. It can only serve to prime you.
I routinely refer to Popperian Falsificationism as the resolution to Hume’s Problem of Induction
I used to do the same thing and felt quite satisfied doing so. I thought it was settled. But then I started learning about Solomonoff Induction which I now believe is a better solution. If you are a hardcore Popperian Falsification fan, even after learning about Solomonoff Induction, I would suggest reading David Deutsch’s The Beginning of Infinity. It pushes falsification as far as I’ve ever seen and even when you find yourself disagreeing, it’s an interesting read.
We have no basis for the assumption at all. It furthermore rests on the additional assumption *that there is even a “physical” at all there.
We have observed that the universe is regular and that there is nothing special about Earth, as far as we know. That’s quite a good basis for the assumptions, in my opinion. Although I am not completely sure what you mean by “physical” here.
I don’t understand why, in the title of the linked article, possible information leak from black holes is referred to as “gravity not being constant”. Nor I understand what this has to do with induction or falsificationism.
We have observed that the universe is regular and that there is nothing special about Earth
The Copernican Principle has served us well. Ironically, it turns out it was somewhat misguided about the Earth itself. I don’t believe that out of the single-digit percentage of planets yet discovered that are categorized as “Earth-like”, that any of them fall particularly close on the parameters relevant to “humans would be comfortable living here if they brought the right flora and fauna with them Spore-style”). Certainly none of them have been around yellow stars and all have had rather bizarre irradiation profiles.
As to the regularity of the universe—well, that’s what the notion of a variable constant of gravity was about. I’ve seen conjecture that ‘dark matter’/‘dark energy’ might be nothing more than our failure to recognize that the gravitational constant changes in some regions of space. The thing about the information leak from black holes has to to with a conjectured way of testing that (even Hawking Radiation doesn’t retrieve information from black holes; that according to what we now know is a one-way trip.)
Although I am not completely sure what you mean by “physical” here.
Well, imagine spacetime has a definite, discrete barrier. On our side there’s still ‘physical’ stuff. On the outside of that barrier… there’s nothing. No physical anything. Not even space. (This gets headachey when we start realizing that means there’s no “outside” outside there...)
Suffice it to say that I was being ‘colorful’ in saying that we have no way of knowing that the universe doesn’t just stop at the edge of the Earth’s lightcone. (It’s actually a pretty mundane assertion; most discussions on the matter I’ve ever heard of make this the null hypothesis.)
Nor I understand what this has to do with induction or falsificationism.
You have a better epistemology for evaluating beliefs about the observable universe?
I don’t believe that out of the single-digit percentage of planets yet discovered that are categorized as “Earth-like”, that any of them fall particularly close on the parameters relevant to “humans would be comfortable living here if they brought the right flora and fauna with them Spore-style”).
By special, when speaking about fundamental physics, I certainly don’t mean “is capable of maintaining carbon-based life”. Earth may be unique in this respect while the physical laws being the same everywhere.
As to the regularity of the universe—well, that’s what the notion of a variable constant of gravity was about. I’ve seen conjecture that ‘dark matter’/‘dark energy’ might be nothing more than our failure to recognize that the gravitational constant changes in some regions of space.
Even if this were true, so what? Instead of standard Einstein equations one would get a modified set of equations with a new dynamical field instead of constant G. This wouldn’t challenge regularity of the universe.
Suffice it to say that I was being ‘colorful’ in saying that we have no way of knowing that the universe doesn’t just stop at the edge of the Earth’s lightcone. (It’s actually a pretty mundane assertion; most discussions on the matter I’ve ever heard of make this the null hypothesis.)
The null hypothesis is what? That the universe stops just there, or that we have no way of knowing?
It seems strange. If you walk along an unknown road and are forced to return at one point, do you (without additional information) suppose that the road ends just beyond the last corner you have seen?
By the way, the relevant Earth’s lightcone is precisely your lightcone or mine?
If we allow for the many-worlds hypothesis, then the universe is infinitely large
OK, you have a good point. I was not considering each branch to count as an entire new space that we need to add up with every other branch. I guess I’m talking about our current branch, right now. Also, I could easily be wrong but I think there are no branch points that create an infinite number of new branches and so there still may be an insanely vast but finite number of branches.
So no probability assertion about the universe’s scope should, rationally speaking, have anything remotely resembling a high threshold of confidence. Said confidence should, in fact, approach zero.
I think that if you take Occam’s Razor seriously, then you never have uncertainties that literally are zero. (I don’t know what approaching zero would mean in this context).
A ‘standard’ definition of “universe” is “all existing matter and space”. If we allow for the many-worlds hypothesis, then the universe is infinitely large even if a Laplacian Demon could know the entirety of the universe at a given state (i.e.; simultaneously finite and infinite). If we operate under a definition of “universe” whereby the MWI creates a new universe for each “choice”, then we have no way of knowing where or if there is an outer bound of our universe beyond the observable lightcone.
Furthermore, if some variants of M-Theory are correct then our universe may be possessed of a specific shape and be limited in scope regardless; so again it could be finite. And again, under other variants of how we interpret M-Theory, each p-brane and membrane is not a separate universe but part of a whole. Which is presumed infinite.
So the problem is that we have no acceptably rigorous definition of what is a “universe” in order to start making assertions about its finiteness or lack thereof.
Even if we use the conventional “assumption” of what our Universe is which existed shortly after the ‘discovery’ of the Big Bang (i.e.; the collection of galaxies and matter that we can either observe or that directly and observably interacts with what we can observe, and the spacetime continuum these interactions occur within) -- we lack the ability to derive any information about its scope or dimension.
So no probability assertion about the universe’s scope should, rationally speaking, have anything remotely resembling a high threshold of confidence. Said confidence should, in fact, approach zero.
I am not in the habit of bothering with probability statements whose confidence is below 1%; I find them not merely a waste of time but damaging.
Isn’t it enough to simply say, “There is as yet insufficient data for a meaningful reply” to the question?
So you are against induction, in general? Nothing directly unobservable is knowable? Do you really think that the assumption that the physical laws are the same outside Earth’s light cone as they are inside is an error?
It’s not that I am against induction (in fact, I routinely refer to Popperian Falsificationism as the resolution to Hume’s Problem of Induction). Instead, I am acknowledging that induction has limits. What inductive process will allow you to derive the words written on the can in front of me as I type this?
No. All things which are entirely unobservable are unknowable. Indirect observation qualifies as a form of observation. That which is outside of our lightcone is entirely unobservable (as yet.)
We have no basis for the assumption at all. It furthermore rests on the additional assumption *that there is even a “physical” at all there.
Furthermore: there is some disagreement at the “bleeding edge” of physics as to whether gravity is a constant. And that’s just what we can observe.
I recall the admonition that “The Universe is Queerer than we can suppose”. From it, I have a generalized principle: when I have no information to make assertions with, I acknowledge my ignorance. When, however, I observe that no information is available, I note this fact and move on.
Making ‘guesses’ as to the ‘probability’ of assertions when you know your priors are entirely arbitrary is … counterproductive. It can only serve to prime you.
I used to do the same thing and felt quite satisfied doing so. I thought it was settled. But then I started learning about Solomonoff Induction which I now believe is a better solution. If you are a hardcore Popperian Falsification fan, even after learning about Solomonoff Induction, I would suggest reading David Deutsch’s The Beginning of Infinity. It pushes falsification as far as I’ve ever seen and even when you find yourself disagreeing, it’s an interesting read.
We have observed that the universe is regular and that there is nothing special about Earth, as far as we know. That’s quite a good basis for the assumptions, in my opinion. Although I am not completely sure what you mean by “physical” here.
I don’t understand why, in the title of the linked article, possible information leak from black holes is referred to as “gravity not being constant”. Nor I understand what this has to do with induction or falsificationism.
The Copernican Principle has served us well. Ironically, it turns out it was somewhat misguided about the Earth itself. I don’t believe that out of the single-digit percentage of planets yet discovered that are categorized as “Earth-like”, that any of them fall particularly close on the parameters relevant to “humans would be comfortable living here if they brought the right flora and fauna with them Spore-style”). Certainly none of them have been around yellow stars and all have had rather bizarre irradiation profiles.
As to the regularity of the universe—well, that’s what the notion of a variable constant of gravity was about. I’ve seen conjecture that ‘dark matter’/‘dark energy’ might be nothing more than our failure to recognize that the gravitational constant changes in some regions of space. The thing about the information leak from black holes has to to with a conjectured way of testing that (even Hawking Radiation doesn’t retrieve information from black holes; that according to what we now know is a one-way trip.)
Well, imagine spacetime has a definite, discrete barrier. On our side there’s still ‘physical’ stuff. On the outside of that barrier… there’s nothing. No physical anything. Not even space. (This gets headachey when we start realizing that means there’s no “outside” outside there...)
Suffice it to say that I was being ‘colorful’ in saying that we have no way of knowing that the universe doesn’t just stop at the edge of the Earth’s lightcone. (It’s actually a pretty mundane assertion; most discussions on the matter I’ve ever heard of make this the null hypothesis.)
You have a better epistemology for evaluating beliefs about the observable universe?
By special, when speaking about fundamental physics, I certainly don’t mean “is capable of maintaining carbon-based life”. Earth may be unique in this respect while the physical laws being the same everywhere.
Even if this were true, so what? Instead of standard Einstein equations one would get a modified set of equations with a new dynamical field instead of constant G. This wouldn’t challenge regularity of the universe.
The null hypothesis is what? That the universe stops just there, or that we have no way of knowing?
It seems strange. If you walk along an unknown road and are forced to return at one point, do you (without additional information) suppose that the road ends just beyond the last corner you have seen?
By the way, the relevant Earth’s lightcone is precisely your lightcone or mine?
In practice the former.
OK, you have a good point. I was not considering each branch to count as an entire new space that we need to add up with every other branch. I guess I’m talking about our current branch, right now. Also, I could easily be wrong but I think there are no branch points that create an infinite number of new branches and so there still may be an insanely vast but finite number of branches.
I think that if you take Occam’s Razor seriously, then you never have uncertainties that literally are zero. (I don’t know what approaching zero would mean in this context).