million, billion, trillion... then what?
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Bridgett_largo
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well then why were earlier posts putting a sort of "cap" on the number of atoms in the universe at a googolplex? we dont even know about how many atoms are in our planet let alone the universe of which we dont even know a millionth about? ... and yes that much money would be nice XD
Fraggle Rocker
Staff member
Because:
Assuming that our model of the universe is correct and that it has been expanding at the rate we've measured for the time we've inferred...
1. We know what the maximum volume of the universe can be.
2. We know what the smallest possible volume is that an atom can be squeezed into.
3. Therefore, we know what the maximum number of atoms is that can fit into the universe, if they were squeezed as tightly as possible, given the observed conditions of the universe which do not have them packed like sardines.
4. That number is less than a googolplex.
5. Even if we hypothesized that we could pack them as tightly as sardines, we could write a much larger number that would do the job.
And yes, we do have a pretty good idea how many atoms there are in our planet. Certainly the order of magnitude.
When I say "we" I'm not speaking personally because I'm not a physicist. I don't keep that data on file because situations like this rarely come up where I wish I had it; and I don't have the skills to derive it myself. But the scientific community has it. I'm sure someone will pop up on this thread with those numbers, although it might be a year from now because this thread has a very strange habit of going dark for months at a time and then erupting into a flurry of activity.
The point that needs to be brought home here is this: We have a notational system that allows us to very easily and compactly express numbers that are SO LARGE that they have absolutely no practical application.
When you start using multiple levels of exponentiation, it's easy to get into inconceivably large numbers before you know it. If what you read was wrong and the universe really could hold one googolplex atoms, then we can just write a number so much larger that the concept of "orders of magnitude" isn't of any use in understanding it. How about googolplex^(googolplex^googolplex)?
The calculations I outlined above in the first three steps are trivial. I actually could track down the source data and do the arithmetic, without having to be a physicist. It's that easy. We will end up with a number that is expressed with multiple levels of exponentiation. It will be either greater than or less than a googolplex. If it's greater, we can write an adequately larger number with just a few keystrokes.
Our ability to express large numbers is expanding faster than the universe.
Assuming that our model of the universe is correct and that it has been expanding at the rate we've measured for the time we've inferred...
1. We know what the maximum volume of the universe can be.
2. We know what the smallest possible volume is that an atom can be squeezed into.
3. Therefore, we know what the maximum number of atoms is that can fit into the universe, if they were squeezed as tightly as possible, given the observed conditions of the universe which do not have them packed like sardines.
4. That number is less than a googolplex.
5. Even if we hypothesized that we could pack them as tightly as sardines, we could write a much larger number that would do the job.
And yes, we do have a pretty good idea how many atoms there are in our planet. Certainly the order of magnitude.
When I say "we" I'm not speaking personally because I'm not a physicist. I don't keep that data on file because situations like this rarely come up where I wish I had it; and I don't have the skills to derive it myself. But the scientific community has it. I'm sure someone will pop up on this thread with those numbers, although it might be a year from now because this thread has a very strange habit of going dark for months at a time and then erupting into a flurry of activity.
The point that needs to be brought home here is this: We have a notational system that allows us to very easily and compactly express numbers that are SO LARGE that they have absolutely no practical application.
When you start using multiple levels of exponentiation, it's easy to get into inconceivably large numbers before you know it. If what you read was wrong and the universe really could hold one googolplex atoms, then we can just write a number so much larger that the concept of "orders of magnitude" isn't of any use in understanding it. How about googolplex^(googolplex^googolplex)?
The calculations I outlined above in the first three steps are trivial. I actually could track down the source data and do the arithmetic, without having to be a physicist. It's that easy. We will end up with a number that is expressed with multiple levels of exponentiation. It will be either greater than or less than a googolplex. If it's greater, we can write an adequately larger number with just a few keystrokes.
Our ability to express large numbers is expanding faster than the universe.
ANOTHER BUMP!Bridgett_largo said:
Perhaps. They should try and remember their password this time.
Bridgett_largo
Registered Member
no no its not who ever your thinking of...I actually came across this thred looking for what came after a million, quite helpful really...and thank you I didn't know that we even had a small idea of how big (or small) our universe was, I'm just a highschool student, so alot of this is new to me. Thank you for your help though
Fraggle Rocker
Staff member
I also discovered SciForums with a search engine (probably DogPile) three years ago. I just typed in a rather arcane word that only pops up in discussions of linguistics, and a SciForums thread was one of the hits on the first screen.
I discovered sciforums via Ask Jeeves 3 years ago, looking for something about space. If I remember correctly I found a thread on space warships.
Someone post the answer to Frag's statement about how many atoms are in the universe. I am neither a scientist nor mathematician it’s that I have read all 5 pages and am very interested in this discussion continuing.
And no I’m not the original poster I found this forum by typing (“what comes after trillion”) on the google site. It was the 3rd one down on the page. But, this forum is a very fun read and I think Frag should be writing books on the subject you are very understandable to the people that really don’t have any idea what mathematics are about but are interested.
edit: I did work up a medal for ya but I'm not really all that webucated so I don't know how to post it.
And no I’m not the original poster I found this forum by typing (“what comes after trillion”) on the google site. It was the 3rd one down on the page. But, this forum is a very fun read and I think Frag should be writing books on the subject you are very understandable to the people that really don’t have any idea what mathematics are about but are interested.
edit: I did work up a medal for ya but I'm not really all that webucated so I don't know how to post it.
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Valich:
There is indeed a hierarchy of infinities, and it likely plays in physics in ways not yet contemplated.
To evidence two such infinities, consider the counting-numbers (0, 1, 2, 3, 4 ... infinity). They may be paired one-to-one with some of the first few real-numbers (0, 1/1, 1/2, 1/3/, 1/4), before we even get beyond the number 1. Thus the infinity of the real-numbers is a greater infinity than the infinity of the counting-numbers.
Ben Hong, a mathematician, took first honors at the then-annual Cal Poly mathematics contest in 1967 for high school students (at age 17), giving a discourse on such infinities. I believe Scientific American also had an article about that in the 1960s.
Walter L. Wagner (Dr.)
There is indeed a hierarchy of infinities, and it likely plays in physics in ways not yet contemplated.
To evidence two such infinities, consider the counting-numbers (0, 1, 2, 3, 4 ... infinity). They may be paired one-to-one with some of the first few real-numbers (0, 1/1, 1/2, 1/3/, 1/4), before we even get beyond the number 1. Thus the infinity of the real-numbers is a greater infinity than the infinity of the counting-numbers.
Ben Hong, a mathematician, took first honors at the then-annual Cal Poly mathematics contest in 1967 for high school students (at age 17), giving a discourse on such infinities. I believe Scientific American also had an article about that in the 1960s.
Walter L. Wagner (Dr.)
Georg Cantor was the first to prove that if you had an infinite set, you could make an even "bigger" infinite set by taking all the subsets of your original infinite set. I think the proof is a rather amusing one (see: Cantor's theorem.). It was a while before Cantor himself was taken seriously by other mathematicians, and I think he even spent time in a mental institution as a result.
Fraggle Rocker
Staff member
That's when they started naming the infinite sets. I recall the taxonomy but not how it worked. Aleph-null was the first one. I'm not going to mess around with a character set I probably don't even have. It's aleph sub zero. Aleph is the first letter of the Hebrew alphabet, chosen, I suppose, because the Greek alphabet has been exploited to death and he envisioned a lot of new infinities needing names.przyk said:
I wonder whether any of this has been re-thought since the advent of fractals. It seems that perhaps they make it easier to map infinities onto each other.
Fraggle Rocker
Staff member
I've had the experience of writing part of a book--not even the whole thing--just once. It is nothing like the fun of writing for you folks. It ends up being ninety percent everything else and only ten percent what you really wanted to do. Sort of like playing paying gigs instead of in a garage band. Still, I would probably do it if the financial lure were sufficient, but I don't know how to make that connection.Phade said:
That's okay, I appreciate your kind remarks just fine.
valich said:
There are ways to "number" numbers. If you can create a function that maps the natural numbers N ( N = {1, 2, 3, 4, ...}) to an infinite set that is onto, then the set is called infinitly countable. all integers are countable, the subset of integers of even numbers is countable. All the rational numbers are countable (1, 1/2, 43/2232, -23, ...). However when you try to count irrational numbers, you cannot. Real numbers include both rational and irrational numbers... we know that the rationals are countable but not the rational... so we can see there is another "kind" of infinity. Pretty much this new infinity is bigger than the previous infinity. LOL.
By the way, BUMP!
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