## Very large numbers generated from orderings, combinations, permutations

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On another forum, someone said that she’d read or heard that the number of orders in which 52 cards can be arranged is greater than the number of grains of sands on all the worlds’s beaches. She said that can’t be true, and that it must be made up, and that it can’t be that a deck of cards can be arranged in billions of orders.
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I replied that it’s a lot more than billions. It’s a trillion trillion trillion trillion trillion. …times 80 million.
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A typical estimate of the number of grains of sand on the world’s beaches is roughly on the order of a billion trillion. Maybe there could be high estimates of a trillion trillion.
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Then she asked a good question that hadn’t occurred to me: Then in how many orders could a list of all the world’s people be arranged?
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10^(72 billion).
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How much space would you need to write that? If you used a (fairly typical) type-size in which each character occupies a square millimeter, then, to write the necessary string of “A trillon trillion trillion…trillion trillion trillion…trillion trillion trillion”, you’d need a piece of land about 718 feet square.
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(In this post, when I say that a number is about 10^N, I mean that the exponent rounds to N, when rounded to the nearest whole number. When I, instead say “roughly”, I mean only that it’s close to that.).
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That’s a large number. What could it enumerate? Let’s compare it to what’s arguably the largest local cosmic number, the number of Planck volumes in the observable universe. Let’s call that “Npvou” (pvou stands for Planck volumes, observable universe.)
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The observable universe is a little more than 90 billion lightyears in diameter.
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A Planck volume is about a trillionth of a trillionth of a trillionth of a trillionth of a trillionth of the volume of a proton.
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The number of orders in which a list of all the world’s people could be arranged is roughly the 400 millionth power of Npvou.
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You’d have to multiply the number of Planck volumes in the observable universe by itself roughly 400 million times, to get the number of orders in which could be arranged a list of the world’s people.
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But you can get a similarly large number, starting with a number a lot smaller than the world population.
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The number of orders in which120 objects can be arranged is roughly a trillion times the number of Planck volumes in the observable universe, give or take a factor of 10.
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You know those rectangular QR scan-patterns, consisting of an array of smaller squares, shaded and unshaded, which you can scan, to reach an advertiser’s website? A typical such array is 35X35 small squares.
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The number of possible combinations of shaded and unshaded squares in that array is roughly the square of the number of Planck volumes in the observable universe.
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But say that, not only do you chose some arbitrary combination, of any size, of small squares in that array, but you also number them in some order. The number of ways you can do that is the number of permutations (ordered combinations) of all sizes that can be taken from 1225 objects.
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Where N is very large, he number of permutations, of all sizes, that can be taken from N objects approaches e*(N!), where e is the base of the natural logarithms.
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With N = 1225, that number is about Npvou to the 17th power. You’d have to raise the number of Planck volumes in the observable universe to the 17th power, to get the number of permutations of all sizes that can be taken from the small squares in that 35X35 array.
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Maybe the number of Planck volumes in the observable universe could be called the largest local cosmic number. But there’s a larger cosmic number:
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Max Tegmark estimated that, if the universe is infinite, and if the physical constants are the same out to a sufficient distance, and if the spatial density of mass doesn’t systematically vary out to a sufficient distance, (What I say below depends on those assumptions,which might not really hold,out to those greater distances) then the most likely distance to the nearest Hubble volume whose things and events are identical to the things and events of our Hubble volume (whose center we’re at) is roughly 10^(10^118) meters.
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I’ll I’ll call that Dd (for “duplication distance”)
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Well, what if we numbered and listed all of the orders in which 120 objects can be arranged.
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In how many orders could that list be arranged?
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Roughly at least10^(10^200).
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What power is that of Dd? That would be 10^200 divided by 10^118. That would be 10^82, which is close to the estimate for the number of atoms in the observable universe. That’s how many times you’d have to multiply Dd by itself to get the number of orders in which could be arranged all of the orders in which 120 objects could be arranged.
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What about dividing 10^(10^200) by Dd? That would be 10^ ((10^200) – (10^118)). That’s very close to about 10^(10^200). In other words, dividing 10^(10^200) by Dd, isn’t much different from dividing it by 1.
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Compared to 10^(10^200), with respect to division, Dd doesn’t look different from 1.
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That doesn’t change if Dd is expressed in Planck lengths instead of meters.
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A Planck-length is about hundredth of a millionth of a trillionth of the diameter of a proton.
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How many Hubble volumes, scattered here and there, could be expected to be found out to a distance of 10^(10^200) meters? Dividing by Dd, and cubing the result, you get about 10^(10^200.477) Hubble volumes within that distance.
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In general doing relatively small things to a very large number doesn’t noticeably change that large number
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Of course all of that is also true of the number of orders in which could be arranged all of the orders in which a list of the world’s population could be arranged, except much moreso.
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Of course the reason why you can get such very large numbers from the number of orderings, combinations or permutations of relatively small numbers, is because all the many multiplications. …an enhancement that results in numbers larger than the enormous Npou, because Npvou is only a straight unenhanced count.
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I’m not interested in cosmic matters, because this universe is just what’s needed for us to be here. Naturally, when physicists investigate and examine the physical world, they’ll find something that’s consistent with our existence. The cosmic matters aren’t really part of our lives, and, for awe or wonder, what could match the amazing fact that this life started?
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..but there was no other way to say anything about how large those numbers are, except in comparison to cosmic numbers.
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Michael Ossipoff
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Related science fiction story. One of my favorites. "Nine Billion Names of God." Arthur C. Clarke.

Monks in the Himalayas are writing all the different combinations that 13 letters that can be written by hand on parchment. These are the nine billion names of God (more or less). They have been working for centuries.Their religion says when all the names are listed, the world will end.

Computer scientist brings a powerful computer (1960s style) up the mountain to the monastery along with a power supply. They set it up and start printing out the names. And then .....

Speaking of Asian end of world prophecies:

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I liked that Clarke story, "The Nine Billion Names of God".

Michael Ossipoff
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you like big numbers? Youtube Graham's number, and then Tree(3).
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you like big numbers? Youtube Graham's number, and then Tree(3).

SCG(13) has TREE(3) beat, big-time.

It's difficult to find authoritative, reliable information about this, but it's said that SCG(13) > TREE(TREE(TREE(...TREE(3)...))), where the nesting is iterated TREE(3) times.

...and that TREE(3) > g(g(g(...g(64)...))), where the nesting is iterated g(64) times.

I don't know if that's true, but I've heard it from googology hobbyists.

The largest 3 numbers that I've heard of that are mentioned by a proved mathematical theorem are all from theorems about graphs.

Yes, those graph theorems mention some numbers that are incomparably, incomprehensibly larger than what's gotten by orderings, combinations and permutations, and make (World Population)!! look like 1.

Michael Ossipoff
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In my initial post to this thread, i forgot to mention another large set of combinations:

Suppose you have a piece of drawing-paper 2 feet by 1.5 feet.

How many monochrome drawings could be made on that paper, if each effective pixel is a micron across? (A micron is now called a "micrometer". It's roughly the size of a small protozoan or a large bacterium.)

That's roughly close to (World Popuation)!!, the number of orders in which could be arranged a list of the orders in which could be arranged the world's population.

Well, it's almost a trillion times as large, but, for such large numbers, that's close.

But I don't know if most paper has texture as fine as a micron. So maybe there could really only be more like about 10^(1 billion) different monochrome drawings made on that piece of paper.

But that's still roughly the 5 millionth power of the number of Planck volumes in the observable universe.

Michael Ossipoff
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you like big numbers? Youtube Graham's number, and then Tree(3).

Really enjoyed the video I found.
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Where does SCG(13) come from?

The name "SGC" stands for "Sub-Cubic Graph". That name might have something to do with the fact that each vertex of a cube has edges connecting it to 3 other vertices.

A graph is a set of dots, at least some of which might be connected by lines. A planar graph is a graph on a flat surface.

Say you're asked to draw a sequence of planar graphs.

These graphs that you're asked to draw are relatively unrestricted, as regards their connectivity. You can draw a graph with no lines connecting its dots. You can draw one with lines connecting all of its dots. You can even have a looped line with both ends connected to the same dot. And you can have several lines connecting the same pair of dots.

In other words, as regards line connections between dots, you can pretty much do what you want.

The only limitation in that regard is that no dot can have more than three line-ends connected to it.
Of course a looped line connected to a dot counts as two line-ends connected to that dot.

Now, you start out allowed to draw one dot. Then, for your 2nd graph, you're allowed up to 2 dots. And for your 3rd graph, you're allowed up to 3 dots...and so on.

But each next graph that you draw must be a completely new graph, in the sense that it couldn't have been made from one of your previous ones by adding dots &/or lines, or by expanding a dot into 2 dots connected by a line, and sharing, between them, the line-end connections that the original dot had.

Those are the only rules.

The question is, how long a sequence of graphs can you draw, by those rules?

Not very many.

But, if you increase the dots-limit for every graph in the sequence by the same number N, then you can draw more graphs before you run out of completely new graphs to draw.

It's proven that, for any N, there's still only a finite number of graphs that you can draw before you run out of completely new graphs to draw..

But, though, with N = 0, you can only draw perhaps 5 graphs in the sequence (It might have been 5, I'm not sure.), and though the number of possible graphs in the sequence remains finite, even as you increase N, that finite number increases tremendously as N increases.

SGC(N) is the number of graphs that you can draw in that sequence before you run out of completely new graphs to draw, if you allow every graph in the sequence to have up to N extra dots.

SGC(0) = 5 (That's probably what they said.)

SGC(13) is a huge number that's tremendously more than TREE(3), which, in turn, is tremendously more than Graham's number, g(64).

Each of those 3 numbers is so great that, dividing it by (World Population)!! gives a result not noticeably different from what you get by dividing it by 1.

...and so great that the power of (World Population)!! that it is, isn't noticeably different from the power of 10 that it is.

Anything that you could do with (World Population)!! to get SCG(13), you could also get a number not noticeably different from SCG(13) by doing that with 10.

Michael Ossipoff
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I was just checking. A Planck Length may be, but is not definitely, the smallest possible length. If it is, then a cubic Planck Length is the smallest possible volume that can be packed completely in a 3 dimensional space. I guess a sphere with a diameter of the Planck Length would be the smallest possible volume. Then, that would mean that the volume of the universe expressed in cubic Planck Lengths is the largest meaningful number. Yes? No?

But we can still talk about numbers larger than that. The fact that something might be meaningless has never stopped us from discussing it before. A study performed by the University of Delaware Institute for Finding Out Things determined that 53.29% of all subjects discussed on TPF are meaningless. Another 21.79% are silly and/or stupid. [1]

Footnote:
[1] This statement is intended to be ironic, amusing, or irritating.
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I was just checking. A Planck Length may be, but is not definitely, the smallest possible length.

Yes, they say that it's likely the smallest distance that's physically meaningful to speak of.

It's about a hundredth of a millionth of a trillionth of the diameter of a proton.

If it is, then a cubic Planck Length is the smallest possible volume that can be packed completely in a 3 dimensional space. I guess a sphere with a diameter of the Planck Length would be the smallest possible volume. Then, that would mean that the volume of the universe expressed in cubic Planck Lengths is the largest meaningful number. Yes? No?

Yes, it would be the largest straight physical or spatial object-count that could be made. But the size of the universe isn't known, and it isn't even known whether the universe is finite or infinite.

So I spoke of the number of Planck volumes in the observable universe.

But we can still talk about numbers larger than that. The fact that something might be meaningless has never stopped us from discussing it before.

Yes, no one seems to want to get to the point. There seems to be a tacit understanding that metaphysics is a speculative, relativist sort of topic, in which no progress can be made, no definite statements can be made, and discussion can and must be interminable.

But that notion probably comes from academic philosophy, where it profitably serves as an academic philosopher's perpetual gravy-train and meal-ticket..

But, by bringing up metaphysics, I'm getting off the topic of this big-numbers thread.

As for meaningless and pointless numbers, yes the googology hobbyists make a hobby of competition naming the largest numbers, even though they don't enumerate anything.

Obviously, as we all know, for any number, there's a larger one. A number that doesn't enumerate anything isn't meaningful.

But SCG(13) enumerates something. It enumerates a lower bound on the number of successive graphs that can be drawn, in accordance with the rules that I described, when up to 13 extra points are permitted in each successive graph.

...and it's humungously, incomprehensibly, incomparably, larger than (World Population)!!.

(Note the period at the end of that sentence--The "!!" are factorial signs, not punctuation-marks. It's a disadvantage of the factorial notation that it can easily be mistaken as the emphasis-expressing punctuation-mark.)
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As for meaningless and pointless numbers, yes the googology hobbyists make a hobby of competition naming the largest numbers, even though they don't enumerate anything.

I tend to be a pretty pragmatic person who likes dealing with concrete ideas, but that doesn't mean talking about things like this isn't interesting and fun. Also - mathematical things that look meaningless but fun have a way of turning into things that are useful and serious later on.
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Yes, the googology hobby includes efforts to propose more compact and elegant notations for super-large numbers, and, if someday a theorem mentions an even larger number, maybe one of their notations could be useful for describing it.

Also, if the universe turns out to be infinite, then maybe physics or astronomy will someday be able to say things that involve the super-huge numbers. Or maybe the size of the universe, even if it's finite, might require one of those super-numbers, in a super-number-notation, to express it.

But the googologists have so many notations, some quite elaborate, and so many named numbers, that I don't recommend wading into it. Sometimes the names of their websites contain the word "Pointless"

What I quoted about the size of SCG(13) (whether it's true or not) is an extension of g(N) and TREE(N), in which they're recursively iterated. Maybe that sort of recursion could be extended to higher levels of recurrent iteration in some elegant way, in which the number of recurrence-levels itself is equal to the number resulting from the previous level of recursive iteration.

Really, the sky's the limit for how far that level-recursion could go.

Anyway, I haven't found anything, outside of the googology-hobbyists' discussion, about how big SCG(13) really is, in terms of Graham's number.

Michael Ossipoff
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I've enjoyed this discussion. One thing I think it does is put the limits of human conceptual capacity in context. Which I guess means it's not meaningless.
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Also, if the universe turns out to be infinite, then maybe physics or astronomy will someday be able to say things that involve the super-huge numbers.

As I'm fond of pointing out, if the universe instantiates actual infinity, then set theory becomes an experimental science. Physics postdocs would apply for grants to count the number of points in a line segment, to investigate the continuum hypothesis. Large cardinal axioms would have deterministic truth values subject to theoretical derivation and experimental confirmation.

The idea that set theory could ever be an experimental science is so absurd as to provide a strong argument against the existence of an actual infinity in the world. Likewise to the idea of an infinite metaverse. Same argument.

Or, equally interesting, someone would need to prove that the universe instantiates infinity, but that set theory doesn't apply for some reason. That set theoretical infinity is the wrong theory of infinity to describe the physically infinite.

Either way, anyone who thinks the universe instantiates infinity needs to deal with these considerations.
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The idea that set theory could ever be an experimental science is so absurd as to provide a strong argument against the existence of an actual infinity in the world. Likewise to the idea of an infinite metaverse. Same argument.

So, it can't possibly be true because it would be absurd. That's a terrible argument that has been spectacularly unsuccessful so far. Light transmission without an aether was absurd. The Earth rotating around the sun was absurd. Donald Trump becoming President of the US was absurd. As King Leonardo, and I guess Senator Joe McCarthy, said - "That's the most unheard of thing I ever heard of."
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For a long time it didn't seem to make sense, when we're told about infinite density in a black-hole. And I've had some doubts about whether our Big-Bang Universe (BBU) could be infinite. (...or could even be part of an infinite physically-inter-related multiverse?).

Though there are infinitely-many possibility-worlds and life-experience possibility-stories, maybe things have to be finite in a universe (by which word I'd also refer to a physically inter-related multiverse).

Tegmark says that the evidence is, more and more, suggesting that the universe is infinite. Is he wrong about those considerations that you spoke of? Is it that he doesn't know about them? ....hasn't heard about them?

I've read that it's being said that evidently the universe is either infinite, or very large. If so, then maybe it's just very large. Maybe large enough to require the g(N) notation to describe its size, or one of the even bigger iteratively-recursive extensions of it?

But, if most physicists accept infinite density in a black hole, then, if that's acceptable to them, then would they have any reason to not accept an infinite size for the universe?

Michael Ossipoff
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So, it can't possibly be true because it would be absurd. That's a terrible argument

Oh I totally agree. Set-theoretical physics is absurd till we discover it's not. I know that. When professor so-and-so from Helsinki counts the points in a line next week and yes, "Yup. It's the same as the number of reals, and here's the physical experiment that shows that," then the idea goes from absurd to true, as physical ideas often go.

But I do say that the current absurdity of set-theoretic physics is a weak meta-argument against physical actual infinity. It's a valid argument till we discover it's not. If someone tells me they believe in physical infinity, they need to answer the question of whether by infinity they mean set-theoretic infinity. And the infinity believers never have a good answer for that. So I have at least a meta-argument that I'd love to hear a substantive response to someday. I've heard Tegmark considers something along these lines but I'm not familiar enough with the specifics.

There's a pretty good link here. https://mathoverflow.net/questions/201216/applications-of-set-theory-in-physics

My point is that that the infinite multiverse folks have to account for set theory or explain why they don't have to. This is rarely if ever addressed in the literature of the infinitists.
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I don't know about the set-theory consideration that leads you to doubt that there could be infinity in the world.

But most physicists must not either, because they're nearly unanimous about there being black-holes in which there's matter with infinite density.

As I was saying, I'm not interested in cosmic matters, and I don't claim to be qualified to say whether the universe is likely to be infinite. As I mentioned, Tegmark says that the evidence is tending toward support for an infinite universe, but of course physicists are divided about that.

Just speaking for myself, without claiming any qualification to judge the matter, the universe being infinite is, to me, the more plausible and believable possibility. ...that everything in our physical world isn't spatially limited.

But, again, I don't claim any qualification for judging that matter.

Michael Ossipoff
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But most physicists must not either, because they're nearly unanimous about there being black-holes in which there's matter with infinite density.

So I've heard. I just watched a Youtube video last night in which the speaker made that exact same point, that black holes have infinite density.

By the way these are the PBS Space Time videos and I highly recommend them.

Now there are three cases as I see them.

1: When speakers say that a singularity has infinite energy, they are speaking loosely and meaning that the equations break down and we don't really know what happens; or

2: They truly believe that a state of actually infinite energy can exist in our world, and someone should tell them that it's just the equations breaking down at a mathematical singularity and not an actual infinity of energy; or

3: They believe there's an actually infinite energy state, and they're right, and I'm simply wrong and not up to speed on these latest developments.

Now I really believe the truth is #1 and \$2 and most definitely not #3. There are singularities in the equations where there's a division by zero. We don't even need crazy quantum theory to illustrate the idea. Just take good old classical vanilla Newtonian gravity, m1*m2/r-squared. Since we have r-squared in the denominator, if the radius is zero the gravitational energy is infinite. Is this literally true? No, it's just that either there aren't actually any point masses in the world (which there aren't) or that if there are, the gravitational equation is simply not applicable there.

That's what I think this is about. That when a physicist says that a black hole singularity is a point-mass with infinite energy, they're speaking figuratively. Their literal meaning is: "There's a zero in the denominator and the equation blows up."

If someone has a genuine reference to the contrary, I'd be grateful for the link. But just someone in a video or paper saying that there are point masses with infinite energy isn't enough. I would need to be convinced they really mean it literally and have physical proof that there is any such thing in the world as an actual point mass with an infinite energy potential. I don't think any physicist actually believes that but like I say, if I'm wrong someone give me a solid link please.
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For a long time, I didn't believe about the infinite density in a black-hole. Then, eventually, I'd heard it so much, and it seemed so unanimous, that I decided that it must be true. But more recently, it occurs to me that there's really something ridiculous about the notion of places of infinite matter-density scattered here and there around us. Infinite density in our physical world is nonsensical.

I realize that the astrophysicists know their subject a lot better than I do, but I don't care who says it. If physics says that there are places with infinitely dense matter, then it seems to me that physics must need some more work.

Anyway, isn't it widely agreed that general relativity still needs more work? So, if the prediction of infinite mass-density in a black-hole has general relativity as part of how that prediction was arrived at, then doesn't that suggest that the prediction isn't so reliable?

But intuitively I expect that the universe is infinite.

The universe is the whole of all that there is in our physical world. How could that whole universe be finite like us? Sure, the things in the universe, like us, our planet, etc., are finite. But wouldn't the universe be a whole grand order-of-magnitude bigger than we are? If we're finite, must it not be infinite?

I emphasize that that's just intuition, not logic or physics.

Michael Ossipoff
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Because birth, the beginning of a life, is so astonishing and miraculous, it's difficult to believe that we were born in a pocket of space that has a state-able size like we do.

Michael Ossipoff
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But more recently, it occurs to me that there's really something ridiculous about the notion of places of infinite matter-density scattered here and there around us. Infinite density in our physical world is nonsensical.

Are you starting to come around to my point of view?

But intuitively I expect that the universe is infinite.

Or not? I can't square those two statements.

I'm going to look into this question. What the physicists really think about the singularities where the equations break down.

Wasn't this the big deal with renormalization? They had these equations with infinities in them and Feynman and a couple of other guys (Schwinger and Tomonaga) got the Nobel prize for figuring out to finesse their way around the infinities? I confess that's all I know about it, wish I knew more.

One more thought I wanted to toss out is that there's an intermediate idea where something could be unbounded. For any large energy level you can name, there's a small region around the singularity where the energy exceeds that level. You can make the energy as large (but still finite) as you want, by taking smaller neighborhoods of the singularity. But it's never actually infinity. The energy level is always finite.

An analogy is the function f(x) = 1/x for positive real numbers x. Can you make 1/x greater than a million? Yes. Greater than a billion? Yes. You can make 1/x as large as you like, simply by letting x be close enough to zero. But 1/x is always some finite number, even though it's a large one. It is never actually infinity.

I suspect that perhaps the physicists really mean something along those lines. They say infinite but if they had paid better attention in math class they'd say unbounded.

Just a guess. I'm going to look into this.
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I suspect that perhaps the physicists really mean something along those lines. They say infinite but if they had paid better attention in math class they'd say unbounded.

Yes, provided they understand the use of "unbounded" in a given situation to mean
" a closed range of quantities cannot be specified here to satisfy our purposes".
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So I've heard. I just watched a Youtube video last night in which the speaker made that exact same point, that black holes have infinite density.

There are lot of idiots making videos on YouTube.
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Or not? I can't square those two statements.[...that I intuitively reject infinite density, but intuitively expect that the universe is infinite].

It just doesn't seem like the universe, the whole of all that is, in our physical world, would be a piece of space of a name-able size.

But, as I said, that's just intuition.

I'm going to look into this question. What the physicists really think about the singularities where the equations break down.

Your suggestion that the physics just isn't valid in the region in question seems to make more sense than saying that the density there is infinite.

Michael Ossipoff
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But intuitively I expect that the universe is infinite.

The universe is the whole of all that there is in our physical world. How could that whole universe be finite like us? Sure, the things in the universe, like us, our planet, etc., are finite. But wouldn't the universe be a whole grand order-of-magnitude bigger than we are? If we're finite, must it not be infinite?

Intuitively I expect that the universe is finite. I have no more justification than you do. It just seems right. I have always found the formulation of the universe as the surface of a multi-dimensional spherish object plausible. It is finite but it has no end. Of course, what my intuition expects doesn't mean anything.
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There are lot of idiots making videos on YouTube.tom

Yes but this guy had a British accent. And a beard.

Your suggestion that the physics just isn't valid in the region in question seems to make more sense than saying that the density there is infinite.

I really think so but if you look at the multiverse thread on this forum or in many other online conversations and presentations, a lot of people think physical infinities are real. I think the physics popularizers are spreading a lot of confusion. Some people in the multiverse thread are very seriously convinced that there are literally and actually an uncountable infinity of multiverses. I still don't believe that can be true. I think a lot of people are using infinity incorrectly in physical arguments. But I can't get to the bottom of it because even the highly credible PBS physics videos are spreading the same confusion.
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Well, a definite name-able size for everything in our physical world leads to this question: Say it's eventually determined that the universe is a 4D sphere with a diameter of about 5.87 trillion trillion lightiyears. But why that particular large size instead of some other? Why about 5.87 instead of about 5.88?

Maybe one reason why the universe is very large or infinite is because the initiation of life is so vanishingly rare, that a universe that leads to us living things is much more likely to be a super-large or infinite one, instead of a smaller one. But, for any particular large size, why that particular large size?

An infinite size is simpler and un-arbitrary.

Michael Ossipoff
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An infinite size is simpler and un-arbitrary.

As I said, I can provide no evidence that the universe is finite.

Maybe one reason why the universe is very large or infinite is because the initiation of life is so vanishingly rare, that a universe that leads to us living things is much more likely to be a super-large or infinite one, instead of a smaller one. But, for any particular large size, why that particular large size?

This is the same as the strong anthropic principle, isn't it? I am not a fan. Why do you assume life is rare. There is no direct evidence yet. My bet is on life being abundant. That's based on my understanding that we are starting to understand how life might develop out of non-living conditions. As I say - "might."
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"An infinite size is simpler and un-arbitrary." — Michael Ossipoff

As I said, I can provide no evidence that the universe is finite.

I'm just speaking from intuition too.

I'd said:

Maybe one reason why the universe is very large or infinite is because the initiation of life is so vanishingly rare, that a universe that leads to us living things is much more likely to be a super-large or infinite one, instead of a smaller one. But, for any particular large size, why that particular large size? — Michael Ossipoff

This is the same as the strong anthropic principle, isn't it?

Yes, it fits with the metaphysics that I propose.

I am not a fan. Why do you assume life is rare.

Some biologists have said that life is vanishingly unlikely, and, so, most likely vanishingly rare.

There is no direct evidence yet. My bet is on life being abundant.

Then as Enrico Fermi asked, "Where are they?"

Though this galaxy has had life-capable stars for long enough that, if life were abundant, someone could have thoroughly explored and cataloged every star and planet in the galaxy, we've never heard from anyone.

hat's based on my understanding that we are starting to understand how life might develop out of non-living conditions. As I say - "might."

Yes, but they don't know how that happened. Of course it did happen. But it isn't biologically established (though some biologists have an opiniion on that) how rare it can be expected to be. But the Fermi paradox suggests that life is quite rare. The nearest space-faring civilization is probably so far away that, for practical purposes, they aren't there.

By the way, another reason why the anthropic principle might favor a very large, or infinite, universe is that there might be some reason why life is more lilkely (or possible at all) if space is at least nearly flat, Euclidean.

Michael Ossipoff
• 12.1k
Some biologists have said that life is vanishingly unlikely, and, so, most likely vanishingly rare.

Some biologists disagree.

Then as Enrico Fermis asked, "Where are they?"

Though this galaxy has had life-capable stars for long enough that, if life were abundant, someone could have thoroughly explored and cataloged every star and planet in the galaxy, we've never heard from anyone.

That's not much of a paradox. Here are some possible reasons:
• Advanced civilizations tend to destroy themselves. This seems really plausible to me.
• Other species have better things to do with their time.
• If the speed of light really is the limit, it's probably not worth the trouble to go out into the galaxy.
• When you get advanced enough, you'd rather just drink wine and have sex.
• Other civilizations have different motivations than we do.
• The prime directive.
• Why should we assume that a species can live forever. There may be lots of civilizations but they didn't overlap in time and space.
• Our planet is not hospitable to the other kinds of life that are out there.
• 42.
• How the hell should I know?

Yes, but they don't know how that happened. Of course it did happen. But it isn't biologically established (though some biologists have an opiniion on that) how rare it can be expected to be.

I gave an answer for that.

My bet is on life being abundant. That's based on my understanding that we are starting to understand how life might develop out of non-living conditions.

You didn't buy it. I'm ok with that.
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