Discussion
10^100 is termed a googol but 10^(10^100) is a googolplex.
That being said, I watched a vid recently on youtube where its said that "if the universe were a googolplex metres in 'width' then there would be more than one of 'you'".
Basically a way to show how large the googolplex as a number actually is.
To say that there would be more than one of 'you' is the implication that every space in the universe has reached its limit on the different possibilities on what can exist in it, in terms of different combinations of particles that can exist within a defined space (be it a 1mm^3 for example).
With all possibilities reached the universe would be left to repeat itself over and over using possibilities that have already been 'done' so to speak.
Its a bit of a mind f##k to say the least.
Its a mathematical concept for sure, and I'm not sure how it ties in with concept of infinity, but the definition of repeating persons with a large enough universe would have to be 'tightened' some what for me to be able to grasp it.
That being said, I watched a vid recently on youtube where its said that "if the universe were a googolplex metres in 'width' then there would be more than one of 'you'".
Basically a way to show how large the googolplex as a number actually is.
To say that there would be more than one of 'you' is the implication that every space in the universe has reached its limit on the different possibilities on what can exist in it, in terms of different combinations of particles that can exist within a defined space (be it a 1mm^3 for example).
With all possibilities reached the universe would be left to repeat itself over and over using possibilities that have already been 'done' so to speak.
Its a bit of a mind f##k to say the least.
Its a mathematical concept for sure, and I'm not sure how it ties in with concept of infinity, but the definition of repeating persons with a large enough universe would have to be 'tightened' some what for me to be able to grasp it.
Fascinating subject. I watched a similar program a while back that said a googleplex is such a big number, that it is larger than all the atoms in the known universe.
However, even bigger is the largest theoretical number possible - Graham's number. http://en.wikipedia.org/wiki/Graham's_number Can't quite get my head around that to be honest.
The other area I enjoyed was regarding our concept of infinity. Not all infinities are equal. For example, if you count straight numbers it technically goes on to infinity. But if you only counted even numbers, which can also go on for infinity, it has to be half as big as the first infinity. Hhhhhmmmm
However, even bigger is the largest theoretical number possible - Graham's number. http://en.wikipedia.org/wiki/Graham's_number Can't quite get my head around that to be honest.
The other area I enjoyed was regarding our concept of infinity. Not all infinities are equal. For example, if you count straight numbers it technically goes on to infinity. But if you only counted even numbers, which can also go on for infinity, it has to be half as big as the first infinity. Hhhhhmmmm
warp9 said:
However, even bigger is the largest theoretical number possible - Graham's number. http://en.wikipedia.org/wiki/Graham's_number Can't quite get my head around that to be honest.
I can't help but feel that I could trump Graham's number by assuming his work into my own number, but with 65 layers...Laplace said:
He's talking about the observable universe I assume.
Our entire universe is thought to extend for infinity and thus by defintion we would experience repetition within our entire universe.
Although the likelihood of actually experiencing repetition would still be vanishingly small. There may be a duplicate me out there in an infinite universe, but the likelihood of me interacting with that duplicate is still essentially 0.Our entire universe is thought to extend for infinity and thus by defintion we would experience repetition within our entire universe.
About a year ago, our 5 year old asked me what the largest number in the world was. I had recollections of a Googolplex from an old Guiness Book of Records so I told him as much as I could recall about it. I then did a discrete Google, during which I found out about Graham's number. I can understand a Googolplex (even though I can't comprehend a million!) but Graham's number was completely lost on me; I don't even get the nomenclature!
Anyway, the following day I told him about Graham's number and thought nothing more about it. A few weeks later he comes home from school and when I asked what he had done that day he said that the teacher had asked everybody what their favorite number was. "Graham's Number," he had confidently replied. I would have loved to have seen the expression on the teacher's face if she knew what he was talking about!
Mike...
Anyway, the following day I told him about Graham's number and thought nothing more about it. A few weeks later he comes home from school and when I asked what he had done that day he said that the teacher had asked everybody what their favorite number was. "Graham's Number," he had confidently replied. I would have loved to have seen the expression on the teacher's face if she knew what he was talking about!
Mike...
No need to worry about replica's. There may well be enough dark matter in the universe to warp spacetime completely around on itself, therefore it is hypothesised that if the transmission of light was instant, then you could look through a very powerful telescope and see the back of your head.
warp9 said:
However, even bigger is the largest theoretical number possible - Graham's number. http://en.wikipedia.org/wiki/Graham's_number Can't quite get my head around that to be honest.
I can just about get how that is generated by following up the link to Knuth's notation, but only in a pretty abstract way.mike_knott said:
I can understand a Googolplex (even though I can't comprehend a million!)
A million is easy enough-A metre is 100 cm
A square metre is 10,000 square cm
A cubic metre is 1,000,000 cubic cm
So if you set a metre rule far enough away that you can see all of it, but close enough to see the cm markings, then with a bit of imagination you can 'see' a million. With good eyesight and imagination if you drop to mm then a billion can be yours.
I wish I never found https://www.youtube.com/user/numberphile
Lots of explanations of mega numbers and other maths oddities.
Lots of explanations of mega numbers and other maths oddities.
Thought some of you might like this article on Graham's number:
http://waitbutwhy.com/2014/11/1000000-grahams-numb...
http://waitbutwhy.com/2014/11/1000000-grahams-numb...
alock said:
Thought some of you might like this article on Graham's number:
http://waitbutwhy.com/2014/11/1000000-grahams-numb...
Oh crap. Thanks!http://waitbutwhy.com/2014/11/1000000-grahams-numb...
alock said:
Thought some of you might like this article on Graham's number:
http://waitbutwhy.com/2014/11/1000000-grahams-numb...
My brain! It broked!http://waitbutwhy.com/2014/11/1000000-grahams-numb...
Anyway, Halmyre's Number: Graham's Number + 1
Fame at last.
mike_knott said:
A few weeks later he comes home from school and when I asked what he had done that day he said that the teacher had asked everybody what their favorite number was. "Graham's Number," he had confidently replied. I would have loved to have seen the expression on the teacher's face if she knew what he was talking about!
I had similar with my 4 year old son recently.He had also been asked his favourite number, and I saw it when I went in to his open day - I thought "he's drawn his 8 sideways..."
Nope - his favourite number* is infinity.
* yes, technically not a number, I know. We had a talk about it later...
technodup said:
I wish I never found https://www.youtube.com/user/numberphile
Lots of explanations of mega numbers and other maths oddities.
Was browsing this before bed and then spent an hour and a half watching videos!Lots of explanations of mega numbers and other maths oddities.
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