Isn’t that an unknowable? We literally have no means of deriving information about the universe beyond our lightcone. And that’s not even touching on what qualifies as “part of” the universe, depending on which definition of “universe” you are using.
Pray tell; what mathematics are applicable? (Note: “Physics” isn’t applicable.)
Furthermore: What can mathematics inform you of if I tell you that I either am or am not thinking of a number that may or may not be imaginary, negative, irrational, rational, positive, complex, whole, or real. Please illustrate.
If physics is not applicable to understanding the nature of the universe then we are all in a lot of trouble.
Tell me; are you in the habit of using English grammar as the ruleset for arranging Zen gardens?
Physics is topically contingent to “the physical”. The Laws of Physics as we know them have further been derived through Popperian Falsification. Even within our own lightcone we still from time to time see the revival of conjecture as to whether the gravity constant or others are actually constant or if they vary from one region to another. Because nothing outside our lightcone interacts with us, we have no way of knowing which, if any, of the Laws of Physics we yet have are applicable. We can assume—certainly—but this does not inform us of anything other than our assumptions. Conjecture without corroboration is not derived information on the subject matter.
And all of this is even assuming that there’s “physical” out there at all. Which, again, because it is not observable—we have no way of knowing at all. It could be nothing. It could be a micron larger than our lightcone. It could be a mile. Or it could be infinite. Or, under certain even more bizarre conceptions (involving inversions of topology and strange physics), there could conceivably even be less than what we observe.
All of this without getting into philosophical “trickery” such as the simulated universe argument.
So, yes. Physics is not applicable to answering the question “what is there beyond the Earth’s Lightcone?”.
Given assumptions that seem natural now. I don’t actually disagree with those assumptions. But those assumptions are, in fact, assumptions. (Recall the bizarre topology example that permits for negative space beyond our lightcone.)
Given, furthermore, what the original question was—P(Universe-is-Infinite) -- the question of whether there’s even a ‘something’ out beyond the lightcone remains even-more-relevant.
And as I originally, I believe, said—the low confidence interval necessary to properly express a Bayesian probability prediction in my opinion makes it far more ‘appropriate’ to simply say, “There is as yet insufficient evidence for a meaningful reply.” (Or, short-handed: “It’s unknowable.”)
Furthermore: What can mathematics inform you of if I tell you that I either am or am not thinking of a number that may or may not be imaginary, negative, irrational, rational, positive, complex, whole, or real. Please illustrate.
I don’t think mathematics claims that it can answer that question. It is more focused on answering questions like “what does 1 + 2 = 3 mean, and why do we think it is true?”
but folks here at LW seem to disagree when I assert that mathematics lacks empirical content.
That’s a curious notion. I’m about ready to believe just about anything of the LW commenter community nowadays, though. I’ve been thoroughly disabused of several notions regarding this site’s populace over the last two monhs. <_<
That being said; it might help if I explain how I parse “real” from “exists”. To my definitions, “real” covers anything which is a proscriptive restriction on the behaviors of that which exists. “Exists” is anything that directly interacts with something else (or conceivably could / did). I categorize “numbers” in the same ‘area’ as I do ‘the laws of logic’—they are real, but do not exist. Mostly these things can be treated as “definitionally true”; we define 2 as “1+1” and we define “1″ as “a single thing”.
(Side note: this neatly resolves the Transcendental Argument for God, by the way. “Resolves” in the sense I am an atheist.)
It’s not completely so—it might become apparent that the universe was finite, and that would answer the question. But determining that it is infinite is different—after any finite amount of time, you can only see a finite part of any universe. So you will never know for sure.
It’s not completely so—it might become apparent that the universe was finite,
How would this come about? The entire problem of attempting to make observations beyond our lightcone is that there are no interactions beyond that boundary.
If you started seeing earlier versions of the same part of the universe that you now are standing in at an apparently large distance out in space, you pretty much know the universe is finite. Light travelling all the way around the universe and arriving back where it started would be a large clue that the universe was finite.
Unknowable? Maybe you can’t be certain but there are indirect reasons to think it is, by noticing that it appears flat with no sign of a boundary. 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. I don’t see how the question is undefined.
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).
Probability that the universe is infinitely large.
P(infinite x,y,z) ~ .00001
Isn’t that an unknowable? We literally have no means of deriving information about the universe beyond our lightcone. And that’s not even touching on what qualifies as “part of” the universe, depending on which definition of “universe” you are using.
It’s an undefined question, I feel.
Mathematics.
Pray tell; what mathematics are applicable? (Note: “Physics” isn’t applicable.)
Furthermore: What can mathematics inform you of if I tell you that I either am or am not thinking of a number that may or may not be imaginary, negative, irrational, rational, positive, complex, whole, or real. Please illustrate.
If physics is not applicable to understanding the nature of the universe then we are all in a lot of trouble.
Tell me; are you in the habit of using English grammar as the ruleset for arranging Zen gardens?
Physics is topically contingent to “the physical”. The Laws of Physics as we know them have further been derived through Popperian Falsification. Even within our own lightcone we still from time to time see the revival of conjecture as to whether the gravity constant or others are actually constant or if they vary from one region to another. Because nothing outside our lightcone interacts with us, we have no way of knowing which, if any, of the Laws of Physics we yet have are applicable. We can assume—certainly—but this does not inform us of anything other than our assumptions. Conjecture without corroboration is not derived information on the subject matter.
And all of this is even assuming that there’s “physical” out there at all. Which, again, because it is not observable—we have no way of knowing at all. It could be nothing. It could be a micron larger than our lightcone. It could be a mile. Or it could be infinite. Or, under certain even more bizarre conceptions (involving inversions of topology and strange physics), there could conceivably even be less than what we observe.
All of this without getting into philosophical “trickery” such as the simulated universe argument.
So, yes. Physics is not applicable to answering the question “what is there beyond the Earth’s Lightcone?”.
I don’t know precisely how likely these three options are, but infinite seems astronomically more likely that any arbitrary amount.
Given assumptions that seem natural now. I don’t actually disagree with those assumptions. But those assumptions are, in fact, assumptions. (Recall the bizarre topology example that permits for negative space beyond our lightcone.)
Given, furthermore, what the original question was—P(Universe-is-Infinite) -- the question of whether there’s even a ‘something’ out beyond the lightcone remains even-more-relevant.
And as I originally, I believe, said—the low confidence interval necessary to properly express a Bayesian probability prediction in my opinion makes it far more ‘appropriate’ to simply say, “There is as yet insufficient evidence for a meaningful reply.” (Or, short-handed: “It’s unknowable.”)
I don’t think mathematics claims that it can answer that question. It is more focused on answering questions like “what does 1 + 2 = 3 mean, and why do we think it is true?”
Then you agree with my position over that of wedrifid’s.
But I think “1 + 2 = 3” is true outside our lightcone.
And what information does this allow us to derive about what is outside of our lightcone?
Remember: “1 + 2 = 3” is definitionally true. It would remain true even if the universe did not exist; it is a non-contingent / non-local truth.
Fair enough. I should have reference the Pythagorean theorem.
I don’t disagree with this statement, but folks here at LW seem to disagree when I assert that mathematics lacks empirical content.
That’s a curious notion. I’m about ready to believe just about anything of the LW commenter community nowadays, though. I’ve been thoroughly disabused of several notions regarding this site’s populace over the last two monhs. <_<
That being said; it might help if I explain how I parse “real” from “exists”. To my definitions, “real” covers anything which is a proscriptive restriction on the behaviors of that which exists. “Exists” is anything that directly interacts with something else (or conceivably could / did). I categorize “numbers” in the same ‘area’ as I do ‘the laws of logic’—they are real, but do not exist. Mostly these things can be treated as “definitionally true”; we define 2 as “1+1” and we define “1″ as “a single thing”.
(Side note: this neatly resolves the Transcendental Argument for God, by the way. “Resolves” in the sense I am an atheist.)
Not complex or real, most likely… I’d say 37… wait, actually, I call bluff. You have no number in mind. :P
I no longer recall. Perhaps we should attempt to derive my forgotten memory together. What steps should we take to derive that information?
It’s not completely so—it might become apparent that the universe was finite, and that would answer the question. But determining that it is infinite is different—after any finite amount of time, you can only see a finite part of any universe. So you will never know for sure.
How would this come about? The entire problem of attempting to make observations beyond our lightcone is that there are no interactions beyond that boundary.
If you started seeing earlier versions of the same part of the universe that you now are standing in at an apparently large distance out in space, you pretty much know the universe is finite. Light travelling all the way around the universe and arriving back where it started would be a large clue that the universe was finite.
Unknowable? Maybe you can’t be certain but there are indirect reasons to think it is, by noticing that it appears flat with no sign of a boundary. 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. I don’t see how the question is undefined.
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).