A Number so Big that your Brain would Collapse into a Black Hole!

[Twoflower]

We can understand values like infinity, just think about that.

Infinity is not a value, it's a concept. and we are certainly far from understanding it.

On Topic: Obviously some people have memorized it.

Obviously you are wrong.

[Itakas]

Oh how fun, again one of those topics where someone takes some theory or equazion and then trows out some more theories or relative values, describing the given theory in attempt to look smart.

Well here it goes, you can fit that number in nothing more then a dot made by a normal pen. If i theorise that the numbers i write are infinate small then i could fit an infinate amount of numbers in an infinate small area.

So sure the number has a big amount of digits, but attempting to describe the size of a number by comparing it to something as relative as space, is just silly, because it works both ways and no matter how big you make the number look you can go the other way around and make it very small (talking about the amount space it takes, the number of digits that need to be written will ofc always stay the same.)

[Dendrek]

Oh how fun, again one of those topics where someone takes some theory or equazion and then trows out some more theories or relative values, describing the given theory in attempt to look smart.

Well here it goes, you can fit that number in nothing more then a dot made by a normal pen. If i theorise that the numbers i write are infinate small then i could fit an infinate amount of numbers in an infinate small area.

So sure the number has a big amount of digits, but attempting to describe the size of a number by comparing it to something as relative as space, is just silly, because it works both ways and no matter how big you make the number look you can go the other way around and make it very small (talking about the amount space it takes, the number of digits that need to be written will ofc always stay the same.)

Oh how fun. Someone getting butthurt over a thread about big numbers because big things make him insecure. (This is the point where I make a face with keyboard characters that lets you know I'm just messing with you.)

P.S. This is a thread about perspective -- not a "Look at how smart I think I am."

P.P.S. Your example couldn't even be done because each number would be smaller than the size of a sub-atomic particle. If you decide to say 'well I did say they are infinitely small numbers' I'll simply reply: 'You said you could write them.' Oh, ho! Look at how smart I think I am.

[Itakas]

Yes i was a bit too harsh when i generalised the thread, but a few ppl and their explenation of number with the amount of volume/space it takes got me off.

I could also say that in theory humanity has not yet discovered the smallest particle and who knows if we ever will. Since in theory a particle size can be so small it almost reaches inifinity. :P
Gonna stop with infinity now, too much of it already.

Just so i dont derail the thread too much: Yes the number in quite big and i doubt anyone will be able to memorize or write it, maybe in future some AI will, who knows, but i doubt a human will ever be able to do it.

[Immitis]

i bet its 7

[GKLeatherCraft]

I don't mean to be rude but if you're going to post threads that are supposed to be about intelligent things then use the right word.

On Topic: Obviously some people have memorized it.

Oh the Irony, so delicious, If you're going to try and be a smart ass at least make sense, you know maths and Literacy are two different things? right? Didn't think so, SO if you're talking about maths, then it doesn't matter if you use one of the incorrect spellings of a word, he wasn't talking about spelling, Oh and being a Grammar Nazi isn't as cool as you may think

[Deleted]

whatever the answer is - ill add one to it

Quasar's Number

[Ashnazg]

We can understand values like infinity, just think about that.

Actually we can't understand numbers like infinity. Human mind is unable to grasp the concept of infinity.

[Deleted]

Yes i was a bit too harsh when i generalised the thread, but a few ppl and their explenation of number with the amount of volume/space it takes got me off.

I could also say that in theory humanity has not yet discovered the smallest particle and who knows if we ever will. Since in theory a particle size can be so small it almost reaches inifinity. :P
Gonna stop with infinity now, too much of it already.

Just so i dont derail the thread too much: Yes the number in quite big and i doubt anyone will be able to memorize or write it, maybe in future some AI will, who knows, but i doubt a human will ever be able to do it.

The Planck units of volume inside the visible universe may sound esoteric, but it is a sensible limit. Wait, far beyond any sensible limit, but the proverbial "astronomical number" compared down to a theoretical lower bound in quantum mechanics (everything we can measure up to LHC is large compared to it), it would be the largest number in physics.

But it is a number you can write with exponential notation. 2.1*10^5341 or whatever, doesn't matter in this context. To these kinds of large numbers you can create with mathematics, and the Graham numbers being the largest with "real" applications, a physical number is uncomparably small.

Attempting to create an AI capable of expressing its digits by an hyper-advanced civilisation would invariably create a black hole, until the creators realize that it would be extremely stupid. I'd say that is a better paraphrase of the OP, since I've never heard of reports of brains growing in mass from too much thinking

What was fascinating to me is how simple that construction is and how with few steps you get these perplexing results, like a number that literally has not enough space in the visible universe to be computed. But you can know its last digits.

For anyone curious: http://www.mrob.com/pub/math/largenum.html
Robert Munafo's page on Large Numbers. Part of a really wonderful site from the early years of the Web.

[IIamaKing]

The answer is 42.

- - - Updated - - -

Actually we can't understand numbers like infinity. Human mind is unable to grasp the concept of infinity.

It goes on forever, not hard to grasp. I have never understood why people say its impossible to grasp.

[gamingmuscle]

I have never seen that arrow notation before. When civil engineers deal with things bigger than the universe (lol), maybe we will have use for it then.


"It is a damn poor mind indeed which can't think of at least two ways to spell any word."


Hopefully once we figure out a means of three dimensional memory storage and have computers use it to process and store information in an infinitely higher base than base 2 (if not a near infinite base), we will be able to do so.

*tells new supercomputer to calculate Graham’s number*
*supercomputer says Graham’s number is 42*

If Graham's number is as large as they say...there is not enough matter in the universe to calculate it.

[Dendrek]

It goes on forever, not hard to grasp. I have never understood why people say its impossible to grasp.

The problem is that in order to grasp it, we have to simplify it using an abstract metaphor that isn't even accurate. And then, having that metaphor, we simply say "we've go it" and give up on trying to understand it further.

For example, is it actually true to say "it goes on forever"? You might imagine counting, "1, 2, 3, ... 100, 1000, 10000, ... really big numbers, ... infinity". You might inaccurately say "it's at the end of all the numbers" or you might semi-accurately say "you can keep on going but you'll never reach it" but in either case, you're thinking of infinity as some kind of limit that you work towards. You're thinking of growth, or counting. And yet if I say something is infinitely large, there is no growth or counting involved in how large that something is. That something is beyond (practical and theoretical) measure. The issue is that counting is a pursuit of value -- you count if the value is unknown and you wish to find it, or if it's known but you wish to confirm it. If I say something is 1000 meters long, you would simply accept that fact. You wouldn't need an arbitrary way to comprehend that value either. You wouldn't need to say "1000 is bigger than 100, and bigger than 150, and bigger than 500, and bigger than 900, and bigger than 999, but smaller than 1001." But when you try to imagine infinity, you're doing precisely that: you're comparing it to all known and theoretical values to assess it's "value."

Another example, how many digits are in pi? An infinite number of digits, right? Does that mean that the digits go on forever? If you imagine that actual process of writing out those digits on a piece of paper, or typing them out on a computer, than we can imagine the amount of time and space required to write out all the digits of pi as "going on forever." We know that pi exists, no amount of time is required to understand that fact. We even have a simple notation for representing pi so that it takes almost no time at all to see, recognize, and understand it's value: π. It's when we try to write it in decimal notation that we imagine a process involved in writing out the number. But the value of pi is what it is regardless of our ability to write it out or perceive all of its digits. So imagining that process is our brain's way of attempting to accept that we could never see or perceive all of those digits, and because we imagine a process to perceive this value, we also imagine that there is a required amount of time and space needed as well: so then the value of pi, in our minds, has a component of time (forever) and a component of space (every particle in the universe and then some) -- two components that the actual value has neither of, but which we arbitrarily assign it to create a metaphor that we can comprehend.

[shise]

You seem to be missing the fact that it's never been written in base 10 notation, nor can it ever be.

Let's say that this ---------- is 1 hundred digits long. (The actual length of 100 digits would be much longer than that without writing in really small numbers. For example
123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 1234567890
is 100 digits written in the smallest letters this forum can show. But for our hypothetical, we'll assume we can write it ---------- this small.

Then 1000 digits would be
--------------------------------------------------------------------------------------------------------------

10,000 digits would be
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

100,000 digits would look like spam at this point, so we'll reduce the scale even further. Imagine the above (10,000) was this small: ----------. Again, I'm saying ---------- is actually
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
and that ^ is actually
123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 1234567890
written 100 times.

So if ---------- is 10,000 digits, then the digits we're seeing are so small we'd need a microscope to actually see them.
100,000 then would look like:
--------------------------------------------------------------------------------------------------------------
And 1 million would look like:
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Now take 1000 of the above to create 1 billion digits. One thousand of that billion digits to visualize 1 trillion digits, and so on. You've certainly reached a point where you can't even imagine seeing the number I'm describing. Now imagine a number where every one of those individual dashes (-) is actually a trillion digits. Now imagine a number were every dash is actually a trillion-trillion digits. You haven't even come close to the size of Graham's number.

Of course it's possible to write the number.
Everything that's capable of being written is possible to achieve.

[Lucavian]

And yet... g64 is still countered by 2 strokes of the keyboard: / 0

[Biernot]

The first level is 4.434[...] with an exponent of +38. Let's say, and this is not correct at all, but let's say that the answer was 3 trillion. That's just the first level.

Level 2 - There'd be 3 trillion number 3's that you'd need to cube by (again, assuming we're using the number 3). That's essentially doing 3*3*3*3[...] until you've multiplied it 3 trillion times.

Level 3 - Cubing 3 the number of times that was given in level 2. If level 2's answer was 800 quadrillion (it's not), then you'd cube 3, 800 quadrillion times. Essentially, you go on and on until you get to level 64. At that point, well, it's simply not possible to even comprehend just how large the number is.

I guess my comparison would be that if you took all the data ever transmitted across the internet since it's creation, we'd still not even have transmitted the equivalent of 1% of Graham's number in bytes. It's so monumentally big that it's difficult to even compare it to that. The number of digits in length of Graham's number exceeds the maximum value a modern computer can deal with (18446744073709551615) squared by itself (i.e. 18446744073709551615^18446744073709551615). To simplify that to terms you can relate to, if the maximum value a computer could handle was 10, then Grahams number would be more than 10^10 (=10000000000) digits in length.

This comparison comes not even close to vastness of Graham's number, but for someone "not-so-mathematical" it's a step in the right direction.

I believe infinity is more theory/concept than anything. Multiplying anything by infinity is technically not a number, as infinity has no value.

Correct. Infinity is not a number. One of the best and easiest examples to grasp for laymen is this:

y = 1/x
You start with x = 1 and thus get y = 1
Now you make x smaller: x = 0.5 gets you to y = 2 and so forth.
If you do that further and further, you see that the closer x gets to 0, the bigger y gets.
x -> 0+, y -> +inf (for x approaching 0 from a positive direction, y approaches positive infinity)

Now do the same from the negative direction:
x = -1 ---> y = -1
x = -0.5 ---> y = -2
...
x -> 0-, y -> -inf (for x approaching 0 from a negative direction, y approaches negative infinity)

If infinity was a number we would have to be able to calculate y = 1/x with x = inf. But as you can see the result of that calculation would be -inf as well as +inf at the same time, which is not possible.

[Elbleino]

have none of you ever heard of a googolplex? look it up. it'll blow your mind.

[Myrlae]

have none of you ever heard of a googolplex? look it up. it'll blow your mind.

the difference is that graham's number is actually usefull. anyone can create a number that is too big too imagine, but that number isn'T usefull.
f.e. 10^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100 ^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^1 00^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100 ^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^1 00^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100^100 ^100^100^100^100^100^100^100 have fun imagining that. i call it the useless number

[Deleted]

Maybe Graham's number is a prime number, that would blow some minds.

[Orby]

My head collapses into a black hole with maths generally :P

[Deleted]

Maybe Graham's number is a prime number, that would blow some minds.

If you broke Graham's number down you would end up with 3. Isn't that very, very obvious?