Seems reasonable.
Of course, I’ve just about tapped out my science/philosophy of thought and consciouness depths. So if you do it, it’ll be the other brains computing the course of that thread.
What percentage of numbers are prime?
You can’t take a percent of infinity.
You can’t? I would swear that you in fact can. Isn’t that what we do in math when we take the limit, for example, the value of an asset over infinite time? (aka an infinite series of a number that is shrinking) Primes are funny because they aren’t smooth mathematically so while we can observe that they get rarer and rarer the bigger the numbers get, we can’t prove exact properties of them over infinity.
Actually this calculation is the idea behind the Prime Number Theorem.
And to a first approximation the number of primes less than x is asymptotically x/ln(x). This means that the fraction of numbers that are prime goes to zero in the limit, but it does so in a well defined way.
Some probability problems are well-defined when dealing with infinities, and some are not. Some seem well-defined, but turn out not to be once one looks at them with enough rigor. And some problems which lack sufficient rigor can have that rigor applied in multiple different ways, which lead to different answers. Which one applies here depends on just exactly how the multiverse is structured.
There’s a third possibility, also: Bubble universes in the eternal inflation model. In these, you could in principle point with your finger in the direction towards some other universe, but the bubbles are receding from each other at such great speed that causal connection between them is impossible. Such bubbles might or might not show variation in fundamental constants: I don’t think that question is actually resolved.
In most braneworld models, the branes are in fact causally connected, just not easily. Electromagnetism, the strong force, and the weak force are confined to the branes, but gravitational effects can still bridge the gap.
It occurs to me that I ought to clarify what I mean here. By way of example, here’s an argument that exactly 1/3 of all natural numbers are even. List out all numbers, like so: 1 3 2 5 7 4 9 11 6 13 15 8 17 19 10 21 23 12… That’s a list of all natural numbers, right? And if I look at the first n numbers on that list, and find the proportion that are even, that proportion is definitely approaching a limit of 1/3 as n increases.
Now, most people would say that this argument is wrong, because I’m taking the numbers out of order. And this is perhaps a reasonable thing to say, because the natural numbers have an obvious simple order to them. But when I’m looking at the set of all universes, is there a natural order to place them in? I suppose it makes sense to put our own Universe first on the list, but is there one particular universe that ought to be second, or third? Maybe I could list the universes in order of distance from our own… but then, how are we measuring the distance? Some sort of measure of how different they are from our own, perhaps? But then, the first universes I count will always be the ones most like our own, and if there are an infinite number that are enough like our own to have life, then I might never reach any of the non-life-bearing ones on my list.
This opens the possibility of signalling. If we could create gravity waves at will, then we could send messages to nearby branes, and maybe even get messages back.
I can call spirits from the vasty deep.
… Why, so can I, or so can any man; But will they come when you do call for them?
Well I’ve never been clear on that aspect. But if it’s as you say then ISTM the multiverse doesn’t really help with the issue of why all the constants in our universe appear fine-tuned. Because it just kicks it further down the road: considering the infinity of multiverses that could not harbour life, what good fortune this is the one that exists.
NB: This isn’t a religious argument. And I’m on the fence of whether I think it’s even a meaningful question
The “fine tuning” argument is really solipsistic nonsense. If the universe were not configured as it is, we would not be here to ask the question and the issue would be resolved. The need for the universe to be finely tuned to permit our existence is predicated on some essential necessity of that existence, rather than that we just happened to emerge from the existing mechanics of physics and chemisty of a convenient universe. Could those mechanics be altered by an arbitrary change in universal constants making any order impossible? Sure, that is concievable, but there would be no one in that universe to ask questions.
The question of multiple universes is purely speculative and not possible of being frames as even a hypothesis without some fundamental breakthoughs in the physics of cosmology, e.g. some ability to finely measure and control gravity (which, as Chronos adroitly corrected me, may allow causal connections between seperate branes), so any question predicated on their existence is also speculative. Speculation can be quite fun, of course, and lead to enjoyable fiction, but we cannot draw any useful conclusions without observable phenomena and measureable data.
Stranger
This is true only if you look at the integers as an ordered set and then only in the usual order. What proportion is even if you put them in the order:
1,2,3,5,4,7,9,11,6,13,15,17,19,8,…
putting n odd numbers between 2n-2 and 2n? As far as anyone knows, there is no way of ordering the universes and Stranger’s point is well taken. Anyway, I’ll take a flier and say the odds are 0. Suppose there is a universe out there just like ours except the gravitational constant differs in the 10th decimal. Maybe life would still be possible, maybe not. How could we know? I think the question is essentially meaningless.
As I mentioned in my previous post, I’m not sure that the fine-tuning “problem” is really a problem that needs or could be solved. However, I also don’t find the anthropic principle compelling either.
A pretty sizeable chunk of science is investigating and understanding phenomena that human life depends on.
Now it’s true that why this constant is 4.3 instead of 4.2 is a different kind of question to “How does water dissolve so many things?”, say. It’s a Why question vs a How question, for a start.
But for me, I don’t see why that makes the anthropic principle “work” or be a satisfying answer.
Yes, but please take my point in the context of what it was replying to. I was not claiming that we actually do know anything about the properties of the multiverse, if it exists. Of course we do not. I was countering the false assertion that it is impossible, in principle, to determine any properties of something that is infinite.
Isn’t it amazing that human beings just happen to live on Earth, where there is liquid water, an oxygen atmosphere and photosynthesis, which can support us, instead of Mars, where we’d freeze, suffocate, and starve to death?
Of course there aren’t any human beings on Mars, and it’s not just random chance that humans evolved on Earth, a planet fine-tuned to support human life, rather than on Mars, a planet without any of the things required to support human life.
Our lungs aren’t perfectly adapted to breathe Earth’s air by chance, rather, the Earth’s atmosphere existed and our ancestors evolved to breathe it.
So since we exist, we must exist in a universe and planet where human life could exist.
Of course, our universe isn’t exactly finely tuned to support the presence of life, since even here in our solar system life apparently only exists on one small planet. The other bodies in the solar system are implacably hostile to life. Most of the matter in the universe is collected into starts, which can’t support life, or frozen iceballs that can’t support life, or finely dispersed gas and dust, which can’t support life.
If I were going to design a universe capable of supporting life as we know it, Jim, I could do a much better job. Like that giant sun and tiny Earth, that’s ridiculous, it should be the other way around. And those other big planets are just a waste of space, so replace them with tiny moving lights. And other stars? Silly. And let’s put a dome over the Earth to hold in the atmosphere rather than use gravity. So something more like this: http://i.onionstatic.com/avclub/6235/81/16x9/1200.jpg
Stranger, it isn’t, and it in fact supports the multiple universe hypothesis.
Observation : the various parameters of this universe must be set an exact way or we would not be here.
Observation : no coherent model of time and cause and effect as observed by the nature of this universe allows an event to spontaneously, from nothing, create just this universe and no other.
Resulting Hypothesis : some type of eternal mechanism has created this universe and others with different parameters and will do so forever.
If this hypothesized mechanism didn’t create all possible parameters somehow (whether those extra universes will exist before/after this one, or they all exist right now simultaneously), it would be extraordinarily unlikely for us to be here.
I know this hypothesis is thin. There are many other explanations for our existence, but this one has the benefit of being as simple as possible.
The simplest possible explanation that explains all observations is the model you should use.
No, but it is thought that slight changes in the parameters and the universe would just be an ever expanding ball of dark gas, or just light expanding forever and no matter, or other such possibilities where no life at all can be possible. The possibility of self replicating complex matter spontaneously evolving requires an awful lot of characteristics specific to this universe.
That specificity is information, and the simplest model of universe formation posits a simple, eternal mechanism that creates them. Therefore, that mechanism could not have the information to create this specific universe alone, and thus, there must be other universes - or this one must repeat with different parameters.
Everything beyond that is mostly speculation, but the edge possibility that the other universes are visible from telescopes here allows at least a possibility of gathering the evidence to investigate it one way or another.
I don’t think I accept your invocation of Occam’s Razor here.
First, here’s Andre Linde with a good account of the fine-tuning problem, the anthropic principle and the multiverse:
https://www.edge.org/response-detail/25535
But it seems to me that there are three possible resolutions to the apparent fine-tuning problem, and (given the lack of evidence to support string theory) it would be extremely difficult to defend the position that any one of these is a more economical explanation than the others.
(1) Multiverse + anthropic principle. No constraint on parameter space, a vast variety of universes DO all exist, the vast majority inconsistent with life. The anthropic principle explains why we see ours.
(2) There is a better model for how universes are built, that does not have all the free parameters of current string theory. In other words, the parameter values found in our universe arise from the model somehow as the only valid solution. The only real basis to claim that this is unlikely is that we have been looking for such a model for decades and have failed. But that seems a weak argument to me.
(3) We are wrong about our interpretation of the parameter space and “life” is not as unlikely as it appears. This would probably need to be combined with a weaker form of (2) above, where a better model that current string theory might constrain parameter space allowing a much narrower variety of possible universes.
Of course, but the issue with the fine-tuning argument is that even our universe, even if earth is the only planet with life, would look lush compared to one where the strong force was a smidge stronger, say.
I’m no proponent of the fine-tuning argument, I am just saying I don’t think these standard handwaves quite work.
(although, as I say, I’m not sure it’s an issue that needs addressing anyway)
Yes. If the current model of string theory is correct, it appears the vast majority of allowable parameter values are inconsistent with the existence of any form of stable matter, let alone “life” under even the broadest of definitions. This may be wrong, but that’s what the only viable current models seem to say. And we need a little better than a hand-wavey “maybe life is less unlikely than we think” to resolve it.
Keep in mind, we’re all talking about “life as we know it”, here. I can envision, for instance, a form of life not dependent on any form of matter at all, and composed entirely of gravitational waves. Such life would exist far more slowly than the sort we’re familiar with, but that only matters if you’re measuring using life-as-we-know-it time units. By the same token, I can also envision a form of life based on strong-force “chemistry” instead of electromagnetic, which could only have existed in the first few minutes of our Universe’s history, and which would consider absurd the notion that anything could live 10^28 picoseconds past the heat death of the Universe.
But I think the argument is that even forms of “life” that are beyond our wildest imagination surely have a requirement for some degree of stability, and that under the current unconstrained models the vast majority of the parameter space is unstable. (I’m not quite sure if stable/unstable is the best terminology here, but something like that.)