Is Infinity a number?
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Re: Is Infinity a number?
He's dead now, isn't he? Not saying there's any connection but...

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Re: Is Infinity a number?
Blimey Mick you started something here.

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Re: Is Infinity a number?
Infinite of course!

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Re: Is Infinity a number?
So there you are, from now on when asked "Dad, what does 'infinite' mean? " you can reply "It's the potential length of an FCF thread"

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Re: Is Infinity a number?
Both yes and no, 'cos there's an infinite number of times one of the mods could step in and put a halt itmickthemaverick wrote: ↑07 Aug 2022, 11:00So there you are, from now on when asked "Dad, what does 'infinite' mean? " you can reply "It's the potential length of an FCF thread"
Schrodinger's Infinite Thread

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Re: Is Infinity a number?
Serendipity smiled upon me this week when the New Scientist published an article on extremely big (and small) numbers. They start off with vacuum energy. This number is 10^120, i.e.1 preceded by a decimal point and then 120 zeroes. Going the other way the number of ordinary particles in the universe is reckoned to be 10 billion billion billion billion billion billion or 10^80. Note I said observable universe. Only about 5% of the universe is made of normal matter. The rest is made up of dark energy and dark matter, neither of which we know what they are, just that they must exist by the effects the have on normal matter.
That number pales into insignificance when you think about the question "Does your doppelgänger exist?" Here we are talking about 10 to the power of 10 to the power of 68. 10^10^68 is 1 followed by 100 million trillion trillion trillion trillion trillion zeroes. The author of the article has called this number the doppelgängion, because it relates to the chances of there being another person like you, a doppelgänger, somewhere else in our universe. That's this universe, not another universe the existence of which is implied by the many worlds theory. I'll quote from the article about how large the universe might be.
"The observable universe extends to about 47 billion light years, but it doesn’t stop there. Measurements of radiation left over from the big bang – the cosmic microwave background – tell us that it is at least 250 times larger than what we can see. A further clue to the true size of the cosmos could lie in that leftover radiation, which reveals that our region of the universe underwent a burst of accelerated expansion very early on, helping it grow big in a very short space of time. These bursts of inflation could have happened anywhere in the universe and at any moment, turning small pockets of space into something more gargantuan.
"This allows us to imagine extremely distant worlds – too distant to ever visit, but that are part of the same universe as ours. With the entire universe constantly inflating in one bit of space or another, the idea of a gigantic universe becomes a little less fanciful. If the universe is large enough, your exact copy will be out there, reading an article about fantastic numbers."
Finally, he talks about infinity and it's best if I quote the entire piece on this.
"Infinity: What happens inside black holes?
"The biggest number of all. The number that goes on forever. In maths, there are multiple infinities: there is the infinity that counts the whole numbers and the squares, but also higher infinities that count larger sets, like the set of real numbers between 0 and 1. In physics, too, infinities take us to the limits of our knowledge.
"If we venture into the deepest innards of a black hole, say, or rewind to the moment the universe was born, we are confronted with what we call a “singularity”. This is a region where the gravitational field becomes infinitely strong. In Albert Einstein’s general theory of relativity, gravity is understood to be the warping of spacetime, with planets following curved paths in the distorted spacetime around the sun because it is the most efficient way to traverse the geometry that exists there. At a singularity, that warping in spacetime blows up to infinity, and Einstein’s law can no longer describe what is going on.
"To grasp these singularities, we need a theory capable of describing the strongest and most violent gravitational fields and all the matter that interacts with them. In other words, we need a theory that explains all aspects of the universe.
"In my opinion, the most compelling candidate for this is string theory. In it, all the particles of nature are understood to be made up of tiny vibrating onedimensional entities known as strings. Unlike some of its rivals, we can perform reliable calculations in string theory, and make the infinities disappear. The transition from particles to strings means we no longer need to worry about particles interacting with one another over infinitesimally small distances.
"Those tiny distances were responsible for the infinities that broke our equations, so now they can be vanquished. Quite how this plays out for the singularities at the core of a black hole, or at the moment of creation, we don’t yet know. But once we figure out how to do the maths for them, we should be able to understand the creation of our universe."
Kind of puts everything into perspective don't you think?
That number pales into insignificance when you think about the question "Does your doppelgänger exist?" Here we are talking about 10 to the power of 10 to the power of 68. 10^10^68 is 1 followed by 100 million trillion trillion trillion trillion trillion zeroes. The author of the article has called this number the doppelgängion, because it relates to the chances of there being another person like you, a doppelgänger, somewhere else in our universe. That's this universe, not another universe the existence of which is implied by the many worlds theory. I'll quote from the article about how large the universe might be.
"The observable universe extends to about 47 billion light years, but it doesn’t stop there. Measurements of radiation left over from the big bang – the cosmic microwave background – tell us that it is at least 250 times larger than what we can see. A further clue to the true size of the cosmos could lie in that leftover radiation, which reveals that our region of the universe underwent a burst of accelerated expansion very early on, helping it grow big in a very short space of time. These bursts of inflation could have happened anywhere in the universe and at any moment, turning small pockets of space into something more gargantuan.
"This allows us to imagine extremely distant worlds – too distant to ever visit, but that are part of the same universe as ours. With the entire universe constantly inflating in one bit of space or another, the idea of a gigantic universe becomes a little less fanciful. If the universe is large enough, your exact copy will be out there, reading an article about fantastic numbers."
Finally, he talks about infinity and it's best if I quote the entire piece on this.
"Infinity: What happens inside black holes?
"The biggest number of all. The number that goes on forever. In maths, there are multiple infinities: there is the infinity that counts the whole numbers and the squares, but also higher infinities that count larger sets, like the set of real numbers between 0 and 1. In physics, too, infinities take us to the limits of our knowledge.
"If we venture into the deepest innards of a black hole, say, or rewind to the moment the universe was born, we are confronted with what we call a “singularity”. This is a region where the gravitational field becomes infinitely strong. In Albert Einstein’s general theory of relativity, gravity is understood to be the warping of spacetime, with planets following curved paths in the distorted spacetime around the sun because it is the most efficient way to traverse the geometry that exists there. At a singularity, that warping in spacetime blows up to infinity, and Einstein’s law can no longer describe what is going on.
"To grasp these singularities, we need a theory capable of describing the strongest and most violent gravitational fields and all the matter that interacts with them. In other words, we need a theory that explains all aspects of the universe.
"In my opinion, the most compelling candidate for this is string theory. In it, all the particles of nature are understood to be made up of tiny vibrating onedimensional entities known as strings. Unlike some of its rivals, we can perform reliable calculations in string theory, and make the infinities disappear. The transition from particles to strings means we no longer need to worry about particles interacting with one another over infinitesimally small distances.
"Those tiny distances were responsible for the infinities that broke our equations, so now they can be vanquished. Quite how this plays out for the singularities at the core of a black hole, or at the moment of creation, we don’t yet know. But once we figure out how to do the maths for them, we should be able to understand the creation of our universe."
Kind of puts everything into perspective don't you think?

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Re: Is Infinity a number?
I know what dark matter is I've walked home in it a few times in the days of industry and the Smog.

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Re: Is Infinity a number?
It's a bugger when you walk smack into while inebriated.
An infinity of infinities it seems.
An infinity of infinities it seems.

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Re: Is Infinity a number?
You may have heard of a number called googol; it may have already been mentioned. Where does it fit in above?
A googol is 10 to the power of 100, 10^100. That's a one followed by 100 zeroes. So it's larger than the number of ordinary particles in the universe but smaller than the doppelgängion.
There's another number you might not have heard of and that's the googolplex. If a googol is 10 to the power of 100 then a googolplex is 10 to the power of a googol. That's 1 followed by, well, a lot of zeroes. One mathematician described it as "one, followed by writing zeroes until you get tired" but frankly even that is an underestimate. This number is greater than the observable mass of the universe and therefore could never be written down as there's not enough matter to write upon!
A googol is 10 to the power of 100, 10^100. That's a one followed by 100 zeroes. So it's larger than the number of ordinary particles in the universe but smaller than the doppelgängion.
There's another number you might not have heard of and that's the googolplex. If a googol is 10 to the power of 100 then a googolplex is 10 to the power of a googol. That's 1 followed by, well, a lot of zeroes. One mathematician described it as "one, followed by writing zeroes until you get tired" but frankly even that is an underestimate. This number is greater than the observable mass of the universe and therefore could never be written down as there's not enough matter to write upon!

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Re: Is Infinity a number?
Well that's my kids bedtime story sorted, thanks

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Re: Is Infinity a number?
And if you were to start counting a googolplex at the beginning of the Universe you would run out of time before you ran out of numbers! It made an appearance on QI. You can buy a volume (it has an ISBN number);
http://www.googolplexwrittenout.com/
http://www.googolplexwrittenout.com/

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Re: Is Infinity a number?
I can't wait for the next chapter!! I wonder what's gunna happen? I wonder how many of them have actually been bought....

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Re: Is Infinity a number?
Wow, look at the price!!!

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Re: Is Infinity a number?
Yes I mentioned the Googolplex. Had forgotten the definition, but that came flooding back with reading your post.PaulR wrote: ↑10 Aug 2022, 19:55You may have heard of a number called googol; it may have already been mentioned. Where does it fit in above?
A googol is 10 to the power of 100, 10^100. That's a one followed by 100 zeroes. So it's larger than the number of ordinary particles in the universe but smaller than the doppelgängion.
There's another number you might not have heard of and that's the googolplex. If a googol is 10 to the power of 100 then a googolplex is 10 to the power of a googol. That's 1 followed by, well, a lot of zeroes. One mathematician described it as "one, followed by writing zeroes until you get tired" but frankly even that is an underestimate. This number is greater than the observable mass of the universe and therefore could never be written down as there's not enough matter to write upon!
As a side note I think it's amazing how the Googolplex is basically so massive as to be incomprehensible and yet we can write it as:
((10)^10)^100
I mean if we count the brackets, and I may have been a bit trigger happy adding them in, there's 13 characters there that defines a number bigger than the number of atoms in the observable universe. A ridiculously massively huge number, all sorted in such a short form.
Am I remembering correctly there's also a googolplexplex too, for when the "small change"esk nature of a googolplex just isn't convenient?
Matt