Graham's Number compared to anything?

[Researcher X]

I'm not knowledgeable in maths, but this interested me. It's the largest number that was ever used in a serious scientific proof.

"Indeed, it is not possible, given the limitations of our universe, to denote Graham's number, or any reasonable approximation of it, in a conventional system of numeration."

So, does this mean that it is so large that it can't even be compared to other numbers? I can't find any comparison to anything on it's wiki page. We don't even know how large it is? I'm confused about how it can even be defined at all.

A Googolplex may be unwritable, but can at least be said to be 10 to the power of a Googol. It still has meaning.

I get the impression that this is as indefinable as infinity though. Is that correct?

"Even the mere number of towers in this formula for g1 is far greater than the number of Planck volumes into which one can imagine subdividing the observable universe."

How was it even used to prove anything in that case?

 

[Hurkyl]

I get the impression that this is as indefinable as infinity though. Is that correct?

Harder, really. ("Infinity" is generally rather easy to define. Far easier than even, say, $\pi$)

Wikipedia does mention a notation in which it is easy to define. (and later gives an explicit definition)

We don't even know how large it is?

The idea they are trying to convey is that the magnitude of the number is well beyond what (most) people can intuit. However, that really isn't saying much, because numbers as small as a million, or even a thousand, are generally beyond peoples' intuition.

 

[NSK8700]

Many physical constants,such as Mass of elements on the periodic table or at the atomic level are not at all intuitive or rather perceptible(at least for me)-expect perhaps using them for some form of quantification? Perhaps the application scientific logic to derive/ estimate such values remain obscure to the non-specialist as are certain values by people outside the specific domain of experience.However,a thousand and Million is easily intuitive as it provides perceivable opportunities in the real world,I don't understand what Hurkyl implies by mentioning that such numbers are beyond intuition..

 

[Researcher X]

The idea they are trying to convey is that the magnitude of the number is well beyond what (most) people can intuit. However, that really isn't saying much, because numbers as small as a million, or even a thousand, are generally beyond peoples' intuition.

Yes, but one million is one thousand times one thousand and so on.

Even numbers like a Centillion, which may represent in individual pieces something far beyond the mind, are easily understandable when compared to smaller numbers like a Decillion, which in turn can be compared to smaller numbers, and we are able to see exactly how much larger that number is.

Even a Googolplex is comparable to a Googol.


But what is "Graham's Number" comparable to?

 

[ice109]

is graham's number a sequence or using the notation in the wiki article f(64) where all the previous layers are just used to calculate f(64)

 

[DaveC426913]

I don't understand what Hurkyl implies by mentioning that such numbers are beyond intuition..

Ask the average Joe to think of one thousand dice 1cm on a side. Ask him to guess how large a cube would be required to hold all those dice. I'll bet he'll guess something larger than 4".

 

[ice109]

Ask the average Joe to think of one thousand dice 1cm on a side. Ask him to guess how large a cube would be required to hold all those dice. I'll bet he'll guess something larger than 4".

lol that doesn't explain anything except how dumb the average joe is.

 

[DaveC426913]

lol that doesn't explain anything except how dumb the average joe is.

It has nothing to do with dumb. It has to do with intuiting, which has to do with previous experience and comfort level.

Would you be happy to be labeled dumb every time you didn't have an intuitive grasp of something other people do? Say, coming to a smooth stop while driving, or how much flour to add to a recipe?

 

[ice109]

It has nothing to do with dumb. It has to do with intuiting, which has to do with previous experience and comfort level.

Would you be happy to be labeled dumb every time you didn't have an intuitive grasp of something other people do? Say, coming to a smooth stop while driving, or how much flour to add to a recipe?

your anecdote is poor - it's not unlike asking someone what weights more a lb of gold or feathers. and i think we would all call the person that says gold dumb, at least pejoratively.

 

[DaveC426913]

your anecdote is poor

Why? You did not qualify.

My example (it is not merely an analogy) goes directly to numeracy in intuitive situations. Hard to make a better example than that.

Your example is weak because it is merely an analogy - in fact, one step away from a straw man. And the analogy is not relevant, since we are talking specifically about numeracy. The number intuition in your example is 1.

That being said:

Not everyone has a day-to-day dealing with numbers such as thousands and millions in such a way that they have an intuitive grasp in all situations. Even you don't.

Yes, it is easy to find situation where they will, such as "is a thousand dollars a lot" but you are implying that, if a given average joe doesn't intuively know how much a thousand is in any randomly-picked situation, they are dumb.

You are generalizing and being harshly judgmental.

 

[Mensanator]

Your example is weak because it is merely an analogy - in fact, one step away from a straw man. And the analogy is not relevant, since we are talking specifically about numeracy. The number intuition in your example is 1.

Would he still be dumb if he said the pound of feathers was heavier?

 

[CRGreathouse]

Would he still be dumb if he said the pound of feathers was heavier?

What, avoirdupois vs. troy?

 

[Mensanator]

What, avoirdupois vs. troy?

Well, you don't measure gold in avoidupois nor do you measure feathers in troy. So, is a pond of gold heavier than a pound of feathers or isn't it?

 

[CRGreathouse]

Well, you don't measure gold in avoidupois nor do you measure feathers in troy. So, is a pond of gold heavier than a pound of feathers or isn't it?

Well, a troy pound of gold may be lighter than an avoirdupois pound of feathers, but for any reasonable definition a pond of gold would be far heavier than a pound of feathers. :rofl:

 

[DaveC426913]

Well, a troy pound of gold may be lighter than an avoirdupois pound of feathers, but for any reasonable definition a pond of gold would be far heavier than a pound of feathers. :rofl:

Unless it were a very small pond.

 

[CRGreathouse]

Unless it were a very small pond.

I think a pond < 20 mL fails my definition of "reasonable". :uhh:

 

[DaveC426913]

I think a pond < 20 mL fails my definition of "reasonable". :uhh:

My Betta thinks it's a http://www.thetraveladdicts.com/BlogPhotos/2000-09-18-Full-Moon-Party/Mvc-647e.jpg" *.

*not actually mine