I was annoyed at the ending to "Source Code". They set up a poignant death at the end (the "frozen" scene), highlighting his noble but futile gesture. It should have ended there. But then they undid it all by tacking on a Hollywood, happily-ever-after ending.
My problem is The FA was short on details, so I'm assuming that they have mutually exclusive models that predict values that differ by a few orders of magnitude.
They have exclusive models, but the problem is that you can't really rule some of them out. A flat space model is theoretically distinct from a curved space model, but observationally similar to a curved space model with very little curvature.
If I were running a casino and I were taking bets on the true size of the universe, I could use an analysis based on Bayesian statistics to set my odds, but that doesn't mean that I should consider this number a true age of the universe.
Sure you should. If you're interested in "the true age of the universe", Bayesian statistics will give you a better answer, because it accounts for all the models under consideration. It's a way of logically and quantitatively combining information. Indeed, as the paper discusses, it gives tighter constraints on the curvature parameter than non-model averaged constraints, since it has a consistent way of assessing which models give more plausible estimates.
Sure, you can through up our hands and say it's Cosmology so we're uncertain about everything, but that doesn't make this good science.
It's the epitome of good science. Good science is about assessing the strengths of hypotheses, and providing estimates with credible error bounds. If you're asking the question "what is the true age of the universe", arguably the only credible way of assessing the uncertainty in the answer is by model averaging.
I would much rather see the numbers from the different models plotted on a log scale with marker sizes varying with the relative uncertainty or credibility of the models along with limits from any hard data that we actually have.
You're perfectly welcome to do that, but it (1) doesn't answer the question (what is the age of the universe) and (2) doesn't assess the relative credibility of different models.
It only answers a bunch of different questions: what is the age of the universe according to model X, Y, or Z? That's fine, but the next step is to combine the information we have about different models to synthesize an answer to the question we're ultimately asking: how old is the universe, according to everything that we know?
Frankly, it's absurd to claim that looking at models in isolation is "good science" but that looking at what the totality of theory and evidence tells us is "bad science".
I could do a similar analysis on models for the nEDM and use this value if I were taking bets on the nEDM. But to say that I know the value of the nEDM would be bogus.
It's no more bogus than saying you know the value of the nEDM, based on what the Standard Model predicts.
Of course, we don't know the value of the nEDM. That's the point. We can't trust the Standard Model estimate, because the Standard Model might be wrong. We can't trust competing estimates either, for the same reasons. Nor can we trust all the estimates combined (in a model averaging sense). But all the estimates combined are less wrong than is any individual estimate.
The figure doesn't acutally show the priors (despite the labels). It shows the posteriors (inferred using the labeled priors). For example, the "Astronomer's Prior" gives uniform probability between -1 and 1. But the posterior implied by that prior, and the observed data, is highly peaked near zero, indicating that the data favor a flat universe.
The odd peak occurs because there are really separate models being considered. Some of them are flat-universe (zero Omega) models, and some aren't. If you give any weight to the flat-universe models, they'll get a "spike" in probability. There's a little bit of probability on either side of the spike, coming from the low Omegas implied by non-flat models with close-to-flat geometries.
The two panels in the figure who the posteriors you get assuming two different priors ("astronomer's" and "curvature scale").
The "250x times bigger" bound is their result for the curvature scale prior. Under the astronomer's prior, they get about 400x times bigger. They reported the first figure as a conservative lower bound (which contains the other bound).
I am a physicist. The situation is complex. The speed of light limit applies to the motion of matter and energy as measured in a local inertial reference frame. It doesn't apply to space itself. It can be hard to define "the speed of space"; in general, that doesn't even make any mathematical sense in general relativity.
In the case of a perfectly symmetric expanding universe, though, you can sort of define "the speed of space": a hyperspherical universe, for example, has a well-defined volume. You can convert that to a radius. (This won't work for some arbitrary lumpy geometry.) Likewise, such a universe has a well defined "universal time": it's the time measured by an observer who views the cosmic background radiation as the same in all directions (up to some statistical fluctuations). (This again won't work in an arbitrary lumpy universe, since it will never look symmetric to any observer.) You can then divide the change in "radius" by the change in "universal time" to get a "speed".
Because of these complications, cosmologists don't really lie awake at night trying to work out the speed of the universe's expansion. It's a messy concept that doesn't have much practical use.
But anyway, your analogy with the ants is pretty good.
Your side note about "the Big Rip" refers to "phantom energy", which is a kind of dark energy with particularly extreme properties. I believe it has been observationally ruled out by now.
In all of the theories you mention, there is no center of the universe, and no "where the Big Bang actually began". The Big Bang occurred everywhere, at the same time: it was the event when all the points in space began expanding away from each other. The Big Bang was the expansion of space itself, along with everything in it, not the explosion of matter at some location within space.
There's a theory that says the full universe is much bigger than the observable universe, so there are many (maybe infinitely many) other galaxies that we can't see. They're all part of our universe, though, and were created in the same Big Bang. That's the theory TFA is talking about.
There is another theory that holds that a big universe can create miniature Big Bangs and "pocket" or "bubble" universes, possibly indistinguishable from our own. Each one of these "pocket universes" is completely disconnected from all the others. Each one has its own "observable" universe, thinks of the rest of its pocket universe is the entire universe, and has no knowledge of the higher universe that is spawning these bubbles. This theory is known as "eternal inflation".
Astronomers have different conventions they use when talking about distances. When talking about "the size of the universe" in relation to the observable universe, in this context, what they mean is "the size at the present time". That is, you freeze the universe's expansion at the current time, and ask how much bigger the total universe is compared to the bubble which encloses the galaxies we can currently see.
If the matter within the universe is expanding, it has to be expanding into something.
No, it doesn't. You're thinking in terms of extrinsic geometry, in which geometric concepts such as "size" and "distance" within a curved space are defined with respect to some higher-dimensional flat space. But there is no need to do so, and general relativity is not formulated that way. Its geometry is purely intrinsic, meaning that all geometric relations are defined completely within the curved space. Distances between points in a curved space can change, and you don't have to pretend that they're moving in some higher hyperspace in order to describe how they change.
Saying it's like a balloon proves the point. The balloon may be expanding, but it is expanding into the box/room/whatever. Your explanation simply says the balloon is expanding into itself.
No, it doesn't. The balloon analogy is an analogy. It's not literally how general relativity describes the universe. The reason why it's used is because nobody can visualize a 3D curved hypersurface. So you are instead supposed to imagine a 2D curved surface. But the baggage that comes with this analogy is that we are used to thinking of 2D surfaces as sitting inside of a 3D space. This is misleading, because that's not how relativity actually describes the geometry of space — it's not sitting inside of some higher 4D hyperspace. It's an inevitable flaw in an analogy designed to allow you to visualize one aspect of the true geometry.
The same goes for the origination of the Big Bang (or Expansion). You can't say the matter in the universe was in a ball (metaphorically speaking) and then at some point it began to expand because it has to expand into something, not into itself. Further, what was that point of matter sitting in before it expanded? Was it sitting in emptiness? If so, what was that emptiness contained in?
None of those questions have anything to do with the actual Big Bang in relativity. The universe is not, and never was, sitting inside something. It is not, and never has, expanding into any other space. The universe is all that is.
If you don't know what the universe is expanding into, then say so. Don't say it's expanding but not into anything.
But the latter is literally correct. In general relativity, the universe is expanding, insofar as the distances between points increase with time. But that theory does not contain any higher space in which the universe is embedded, or into which it expands. It's not that we don't know what it's expanding into. It's that the notion of "expansion" in general relativity has nothing to do with expanding into anything, and general relativity does not refer to and does not need any such concept.
I don't think he's referring to the edge of the "observable universe".
Yes, I realized that in a followup comment.
The article states that the universe is 250x the size of the obserable universe
.
No, it says it's at least 250x the size. It could actually be infinitely bigger.
To a 3d observer, a balloon's surface is of limited space. To the ant though, the surface of balloon is endless.
It's both "of limited space" and "endless": it's finite (compact) but unbounded. Those are separate mathematical concepts.
That observation never quite sat with me though. It works for an ant - incapable of reason, but swap out the situation for a PERSON sitting on another circular surface (like, say, a planet), and we have figured out quite readily that our surface is unending but finite - it's obvious - go in another direction and you end up circling back.
Yes, an ant or a person can in principle discern that their universe is finite, in this case. (In the real universe it's hard, because we can only observe a small part of the overall geometry.)
By the same token, you can't just easily dismiss a perceived infinity of the universe via analogy as a meaningless question.
We don't perceive the universe as infinite, even though it may be. We can only see a finite part of it, and make inferences about the parts we can't see (finite or infinite).
There must be a logical mechanic behind it. Either the universe literally ends with a wall (highly unlikely), it truly is infinite, or, there is some mechanism by which you "double back" and circle back to your previous position.
Cosmologists tend to favor the second, but the third is also a possible solution of general relativity.
Just personally, I've never seen a truly convincing mechanic for explaining just how the last one would work.
What is there to explain? It corresponds to a 3D hyperspherical geometry, or something similar, instead of a 3D Euclidean geometry. No, you can't envision it, because your visual cortex didn't evolve to visualize higher-dimensional curved spaces.
I'm just saying that before I truly embrace that ideas I need a working model of how it would work as perceived infinity, outside of an analogy or "it just works that way".
You can't truly visualize a 3D hypersphere, the way you can a 2D sphere. Nobody can, because humans can only picture 2D surfaces. That's what "surface" means to humans. But mathematically, there can be higher dimensional surfaces. Whether you favor a flat or curved universe shouldn't depend on what you find easier to imagine; it should depend on what observations about the universe imply.
There isn't any "up", away from the surface of the sphere. In this analogy, the universe is a spherical surface. We imagine it embedded in some 3D space because that's how we're used to conceiving of surfaces. But in relativity, there is no higher dimensional embedding space. It's just a visualization tool.
Ignoring the analogy, the actual spatial geometry in consideration is a 3D hyperspherical surface. You could think of it as being the surface of a 4D ball, but there is no fourth hyperspatial dimension in this scenario. It would again be just a visualization tool (which doesn't help, since we don't visualize things in 4D anyway).
I have no idea what you're talking about. "Political science?" Bayesian statistics is used in physics all the time. I use it myself, and I'm a physicist. It's the only form of statistics that allows you to talk about the probability of hypotheses, which is of obvious interest to scientists. I think it's bizarre to be told that, as a scientist, I'm not "supposed" to be interested in that. And I can't imagine why you don't think it makes sense to account for uncertainty in which model is correct when estimating cosmological variables. We are, after all, uncertain about that!
Yes, many cosmologists think the universe may be infinite. The size estimate is a lower bound. The universe is at least 250 times bigger than the observable universe. It could actually be infinitely bigger. We can't prove that. We can just put a lower bound on its size.
1. You assign probabilities to the various hypotheses according to how well they agree with observed data, and form a weighted average.
2. The theories aren't inelegant. They agree quite well with observed data, down to the detailed angular power spectrum of the cosmic background radiation. There are just a few uncertain parameters that need to be nailed down.
3. The universe will probably expand forever and suffer a "heat death". Or, if not forever, it will expand for a very long time and effectively suffer one before collapsing again.
I think I misunderstood your question in my previous response. By "outer edge", do you mean "edge of the universe outside the observable universe"? If so, there is no edge to the universe. However, you can still talk about the universe's size.
Imagine the universe to be like the surface of a sphere. To a "flatlander" living in the surface, there is no edge. They can go round and round as much as they want. The "observable universe" would be some part of this surface, a circular "cap" centered on some particular point (the Earth's location). This research studies how much bigger the whole sphere is than the "cap".
Or, the universe could be infinite. The study only put a bound on the size of the rest of the universe: at least 250 times bigger. It could actually be infinitely bigger than the observable universe.
There's nothing "physical" about the edge of the observable universe. It's just the boundary between galaxies whose light has had time to reach us, and galaxies whose light is still on its way.
What good would that do? It's not like Java is some esoteric language and software companies can't find anyone to write Android apps in it. Or, if you're implying that this conversion tool would let you port iPhone apps to Android, the programming language isn't the main barrier to that. It's the completely different APIs.
That's precisely because insolation will increase to the level I'm talking about. I'm saying that if insolation is below that level, the Earth will retain its water; above that level, it will lose it. You can get insolation that high either by being closer to the Sun (like Venus), or by waiting (until the Sun gets brighter). Once you cross the insolation threshold, you lose water rapidly (within a few million years).
Slashdot Mirror
to say that you're prejudiced against all races.
That's part of the Hollywood ending: we never actually see that character or are invited to empathize with him, so we can happily ignore him.
A Hollywood happy ending that, I might add, trashed the whole premise and logic of the movie.
I was annoyed at the ending to "Source Code". They set up a poignant death at the end (the "frozen" scene), highlighting his noble but futile gesture. It should have ended there. But then they undid it all by tacking on a Hollywood, happily-ever-after ending.
Maybe the GP was recycling this old Dan Quayle joke.
They're open. Duh.
My vote goes to the Live Free or Die Hard, with the hackers causing explosions in the natgas infrastructure at will.
Unrealistic, but maybe inspired by this?
Any Klemperer rosettes?
Better that than the 9 billion names of God. We know how that turned out.
My problem is The FA was short on details, so I'm assuming that they have mutually exclusive models that predict values that differ by a few orders of magnitude.
They have exclusive models, but the problem is that you can't really rule some of them out. A flat space model is theoretically distinct from a curved space model, but observationally similar to a curved space model with very little curvature.
If I were running a casino and I were taking bets on the true size of the universe, I could use an analysis based on Bayesian statistics to set my odds, but that doesn't mean that I should consider this number a true age of the universe.
Sure you should. If you're interested in "the true age of the universe", Bayesian statistics will give you a better answer, because it accounts for all the models under consideration. It's a way of logically and quantitatively combining information. Indeed, as the paper discusses, it gives tighter constraints on the curvature parameter than non-model averaged constraints, since it has a consistent way of assessing which models give more plausible estimates.
Sure, you can through up our hands and say it's Cosmology so we're uncertain about everything, but that doesn't make this good science.
It's the epitome of good science. Good science is about assessing the strengths of hypotheses, and providing estimates with credible error bounds. If you're asking the question "what is the true age of the universe", arguably the only credible way of assessing the uncertainty in the answer is by model averaging.
I would much rather see the numbers from the different models plotted on a log scale with marker sizes varying with the relative uncertainty or credibility of the models along with limits from any hard data that we actually have.
You're perfectly welcome to do that, but it (1) doesn't answer the question (what is the age of the universe) and (2) doesn't assess the relative credibility of different models.
It only answers a bunch of different questions: what is the age of the universe according to model X, Y, or Z? That's fine, but the next step is to combine the information we have about different models to synthesize an answer to the question we're ultimately asking: how old is the universe, according to everything that we know?
Frankly, it's absurd to claim that looking at models in isolation is "good science" but that looking at what the totality of theory and evidence tells us is "bad science".
I could do a similar analysis on models for the nEDM and use this value if I were taking bets on the nEDM. But to say that I know the value of the nEDM would be bogus.
It's no more bogus than saying you know the value of the nEDM, based on what the Standard Model predicts.
Of course, we don't know the value of the nEDM. That's the point. We can't trust the Standard Model estimate, because the Standard Model might be wrong. We can't trust competing estimates either, for the same reasons. Nor can we trust all the estimates combined (in a model averaging sense). But all the estimates combined are less wrong than is any individual estimate.
The figure doesn't acutally show the priors (despite the labels). It shows the posteriors (inferred using the labeled priors). For example, the "Astronomer's Prior" gives uniform probability between -1 and 1. But the posterior implied by that prior, and the observed data, is highly peaked near zero, indicating that the data favor a flat universe.
The odd peak occurs because there are really separate models being considered. Some of them are flat-universe (zero Omega) models, and some aren't. If you give any weight to the flat-universe models, they'll get a "spike" in probability. There's a little bit of probability on either side of the spike, coming from the low Omegas implied by non-flat models with close-to-flat geometries.
The two panels in the figure who the posteriors you get assuming two different priors ("astronomer's" and "curvature scale").
The "250x times bigger" bound is their result for the curvature scale prior. Under the astronomer's prior, they get about 400x times bigger. They reported the first figure as a conservative lower bound (which contains the other bound).
I am a physicist. The situation is complex. The speed of light limit applies to the motion of matter and energy as measured in a local inertial reference frame. It doesn't apply to space itself. It can be hard to define "the speed of space"; in general, that doesn't even make any mathematical sense in general relativity.
In the case of a perfectly symmetric expanding universe, though, you can sort of define "the speed of space": a hyperspherical universe, for example, has a well-defined volume. You can convert that to a radius. (This won't work for some arbitrary lumpy geometry.) Likewise, such a universe has a well defined "universal time": it's the time measured by an observer who views the cosmic background radiation as the same in all directions (up to some statistical fluctuations). (This again won't work in an arbitrary lumpy universe, since it will never look symmetric to any observer.) You can then divide the change in "radius" by the change in "universal time" to get a "speed".
Because of these complications, cosmologists don't really lie awake at night trying to work out the speed of the universe's expansion. It's a messy concept that doesn't have much practical use.
But anyway, your analogy with the ants is pretty good.
Your side note about "the Big Rip" refers to "phantom energy", which is a kind of dark energy with particularly extreme properties. I believe it has been observationally ruled out by now.
In all of the theories you mention, there is no center of the universe, and no "where the Big Bang actually began". The Big Bang occurred everywhere, at the same time: it was the event when all the points in space began expanding away from each other. The Big Bang was the expansion of space itself, along with everything in it, not the explosion of matter at some location within space.
I'm not sure which theory you're thinking of.
There's a theory that says the full universe is much bigger than the observable universe, so there are many (maybe infinitely many) other galaxies that we can't see. They're all part of our universe, though, and were created in the same Big Bang. That's the theory TFA is talking about.
There is another theory that holds that a big universe can create miniature Big Bangs and "pocket" or "bubble" universes, possibly indistinguishable from our own. Each one of these "pocket universes" is completely disconnected from all the others. Each one has its own "observable" universe, thinks of the rest of its pocket universe is the entire universe, and has no knowledge of the higher universe that is spawning these bubbles. This theory is known as "eternal inflation".
Astronomers have different conventions they use when talking about distances. When talking about "the size of the universe" in relation to the observable universe, in this context, what they mean is "the size at the present time". That is, you freeze the universe's expansion at the current time, and ask how much bigger the total universe is compared to the bubble which encloses the galaxies we can currently see.
If the matter within the universe is expanding, it has to be expanding into something.
No, it doesn't. You're thinking in terms of extrinsic geometry, in which geometric concepts such as "size" and "distance" within a curved space are defined with respect to some higher-dimensional flat space. But there is no need to do so, and general relativity is not formulated that way. Its geometry is purely intrinsic, meaning that all geometric relations are defined completely within the curved space. Distances between points in a curved space can change, and you don't have to pretend that they're moving in some higher hyperspace in order to describe how they change.
Saying it's like a balloon proves the point. The balloon may be expanding, but it is expanding into the box/room/whatever. Your explanation simply says the balloon is expanding into itself.
No, it doesn't. The balloon analogy is an analogy. It's not literally how general relativity describes the universe. The reason why it's used is because nobody can visualize a 3D curved hypersurface. So you are instead supposed to imagine a 2D curved surface. But the baggage that comes with this analogy is that we are used to thinking of 2D surfaces as sitting inside of a 3D space. This is misleading, because that's not how relativity actually describes the geometry of space — it's not sitting inside of some higher 4D hyperspace. It's an inevitable flaw in an analogy designed to allow you to visualize one aspect of the true geometry.
The same goes for the origination of the Big Bang (or Expansion). You can't say the matter in the universe was in a ball (metaphorically speaking) and then at some point it began to expand because it has to expand into something, not into itself. Further, what was that point of matter sitting in before it expanded? Was it sitting in emptiness? If so, what was that emptiness contained in?
None of those questions have anything to do with the actual Big Bang in relativity. The universe is not, and never was, sitting inside something. It is not, and never has, expanding into any other space. The universe is all that is.
If you don't know what the universe is expanding into, then say so. Don't say it's expanding but not into anything.
But the latter is literally correct. In general relativity, the universe is expanding, insofar as the distances between points increase with time. But that theory does not contain any higher space in which the universe is embedded, or into which it expands. It's not that we don't know what it's expanding into. It's that the notion of "expansion" in general relativity has nothing to do with expanding into anything, and general relativity does not refer to and does not need any such concept.
I don't think he's referring to the edge of the "observable universe".
Yes, I realized that in a followup comment.
The article states that the universe is 250x the size of the obserable universe
.
No, it says it's at least 250x the size. It could actually be infinitely bigger.
To a 3d observer, a balloon's surface is of limited space. To the ant though, the surface of balloon is endless.
It's both "of limited space" and "endless": it's finite (compact) but unbounded. Those are separate mathematical concepts.
That observation never quite sat with me though. It works for an ant - incapable of reason, but swap out the situation for a PERSON sitting on another circular surface (like, say, a planet), and we have figured out quite readily that our surface is unending but finite - it's obvious - go in another direction and you end up circling back.
Yes, an ant or a person can in principle discern that their universe is finite, in this case. (In the real universe it's hard, because we can only observe a small part of the overall geometry.)
By the same token, you can't just easily dismiss a perceived infinity of the universe via analogy as a meaningless question.
We don't perceive the universe as infinite, even though it may be. We can only see a finite part of it, and make inferences about the parts we can't see (finite or infinite).
There must be a logical mechanic behind it. Either the universe literally ends with a wall (highly unlikely), it truly is infinite, or, there is some mechanism by which you "double back" and circle back to your previous position.
Cosmologists tend to favor the second, but the third is also a possible solution of general relativity.
Just personally, I've never seen a truly convincing mechanic for explaining just how the last one would work.
What is there to explain? It corresponds to a 3D hyperspherical geometry, or something similar, instead of a 3D Euclidean geometry. No, you can't envision it, because your visual cortex didn't evolve to visualize higher-dimensional curved spaces.
I'm just saying that before I truly embrace that ideas I need a working model of how it would work as perceived infinity, outside of an analogy or "it just works that way".
You can't truly visualize a 3D hypersphere, the way you can a 2D sphere. Nobody can, because humans can only picture 2D surfaces. That's what "surface" means to humans. But mathematically, there can be higher dimensional surfaces. Whether you favor a flat or curved universe shouldn't depend on what you find easier to imagine; it should depend on what observations about the universe imply.
There isn't any "up", away from the surface of the sphere. In this analogy, the universe is a spherical surface. We imagine it embedded in some 3D space because that's how we're used to conceiving of surfaces. But in relativity, there is no higher dimensional embedding space. It's just a visualization tool.
Ignoring the analogy, the actual spatial geometry in consideration is a 3D hyperspherical surface. You could think of it as being the surface of a 4D ball, but there is no fourth hyperspatial dimension in this scenario. It would again be just a visualization tool (which doesn't help, since we don't visualize things in 4D anyway).
I have no idea what you're talking about. "Political science?" Bayesian statistics is used in physics all the time. I use it myself, and I'm a physicist. It's the only form of statistics that allows you to talk about the probability of hypotheses, which is of obvious interest to scientists. I think it's bizarre to be told that, as a scientist, I'm not "supposed" to be interested in that. And I can't imagine why you don't think it makes sense to account for uncertainty in which model is correct when estimating cosmological variables. We are, after all, uncertain about that!
Yes, many cosmologists think the universe may be infinite. The size estimate is a lower bound. The universe is at least 250 times bigger than the observable universe. It could actually be infinitely bigger. We can't prove that. We can just put a lower bound on its size.
1. You assign probabilities to the various hypotheses according to how well they agree with observed data, and form a weighted average.
2. The theories aren't inelegant. They agree quite well with observed data, down to the detailed angular power spectrum of the cosmic background radiation. There are just a few uncertain parameters that need to be nailed down.
3. The universe will probably expand forever and suffer a "heat death". Or, if not forever, it will expand for a very long time and effectively suffer one before collapsing again.
I think I misunderstood your question in my previous response. By "outer edge", do you mean "edge of the universe outside the observable universe"? If so, there is no edge to the universe. However, you can still talk about the universe's size.
Imagine the universe to be like the surface of a sphere. To a "flatlander" living in the surface, there is no edge. They can go round and round as much as they want. The "observable universe" would be some part of this surface, a circular "cap" centered on some particular point (the Earth's location). This research studies how much bigger the whole sphere is than the "cap".
Or, the universe could be infinite. The study only put a bound on the size of the rest of the universe: at least 250 times bigger. It could actually be infinitely bigger than the observable universe.
There's nothing "physical" about the edge of the observable universe. It's just the boundary between galaxies whose light has had time to reach us, and galaxies whose light is still on its way.
What good would that do? It's not like Java is some esoteric language and software companies can't find anyone to write Android apps in it. Or, if you're implying that this conversion tool would let you port iPhone apps to Android, the programming language isn't the main barrier to that. It's the completely different APIs.
That's precisely because insolation will increase to the level I'm talking about. I'm saying that if insolation is below that level, the Earth will retain its water; above that level, it will lose it. You can get insolation that high either by being closer to the Sun (like Venus), or by waiting (until the Sun gets brighter). Once you cross the insolation threshold, you lose water rapidly (within a few million years).