The Field Of Large Numbers

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The Field Of Large Numbers

#1  Postby aufbahrung » May 26, 2019 1:18 pm

Where do they begin?
They're always out there. Never forget.
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Re: The Field Of Large Numbers

#2  Postby Cito di Pense » May 26, 2019 1:26 pm

aufbahrung wrote:Where do they begin?


Flattering yourself again? This isn't a riff on mathematics. This is a riff on 'large' or on 'begin'. Stick with philosophy, where your shortcomings in precision will be less of a handicap for you.

If you're interested, there are books to read:

https://bookstore.ams.org/nml-6

But do consider this: the size of something depends in important ways on what it's being compared with. For a real treat, consult "relativism is self-refuting".
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Translation by Elbert Hubbard: Do not take life too seriously. You're not going to get out of it alive.
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Re: The Field Of Large Numbers

#3  Postby Thommo » May 26, 2019 1:41 pm

It's a poorly put question (since field is a word with a technical meaning in mathematics, which you clearly aren't using), but essentially a large number is an informal term for either a contextually large quantity (e.g. as the words appear in "the law of large numbers") or a number that is significantly bigger than those experienced in ordinary life (e.g. geological timescales or cosmic distances like those between galaxies).

It's not an area of mathematics, the question is purely a semantic one.

perhaps unsurprisingly there are loads of examples on wikipedia:
https://en.wikipedia.org/wiki/Large_numbers
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Re: The Field Of Large Numbers

#4  Postby aufbahrung » May 26, 2019 1:46 pm

I thought it might begin in a CPU?
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Re: The Field Of Large Numbers

#5  Postby Cito di Pense » May 26, 2019 1:47 pm

Thommo wrote:It's a poorly put question (since field is a word with a technical meaning in mathematics, which you clearly aren't using), but essentially a large number is an informal term for either a contextually large quantity (e.g. as the words appear in "the law of large numbers") or a number that is significantly bigger than those experienced in ordinary life (e.g. geological timescales or cosmic distances like those between galaxies).

It's not an area of mathematics, the question is purely a semantic one.

perhaps unsurprisingly there are loads of examples on wikipedia:
https://en.wikipedia.org/wiki/Large_numbers


Yeah. Who could have guessed that there would be obvious places to make one's own start on such a question?

aufbahrung wrote:I thought it might begin in a CPU?


Not according to your OP, you didn't. And it doesn't begin with a CPU anyway, since people figured out how to do arbitrary-precision computation in software. You asked a lazy question.
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Re: The Field Of Large Numbers

#6  Postby aufbahrung » May 26, 2019 2:02 pm

There's counting numbers. Field of large numbers begin when the counting numbers become uncountable. This happens in the CPU since you can't count the numbers there albeit they are happening. I'm not precise. I've no idea of modern chip design. And yesterday I learnt the graphics card does counting these days. It is not that I lack precision. Or even there's woolly thinking. It's something more like I've a 80s mindset in a 20s world. Is that a good thing?
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Re: The Field Of Large Numbers

#7  Postby felltoearth » May 26, 2019 2:06 pm

I’ll see your CPU and raise you an abacus.
ETA CPUs have always been about speed of calculating, not size. That’s why we have exponents.
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Re: The Field Of Large Numbers

#8  Postby Thommo » May 26, 2019 2:14 pm

aufbahrung wrote:There's counting numbers. Field of large numbers begin when the counting numbers become uncountable.


Uncountable is also a term with a specific mathematical definition that you aren't using (relating to different sizes of infinity, also known as "cardinalities"). Consequently, in terms of mathematics this sentence is, I'm sorry to say, gibberish.

I can only surmise that what you're trying to say is that you think of large numbers as those which are beyond some arbitrary (you don't specify) level of computational complexity. If you want to think that, you can, I guess, since the term "large number" is no more technical or specific than the term "large man" or the term "large hill". I'm not sure there's anything to discuss in that, but maybe I'm misunderstanding something here.
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Re: The Field Of Large Numbers

#9  Postby newolder » May 26, 2019 2:29 pm

aufbahrung wrote:There's counting numbers. Field of large numbers begin when the counting numbers become uncountable. This happens in the CPU since you can't count the numbers there albeit they are happening...

What is the name of the last countable number? (Hint: There is no such name.)

Which CPU does not "count the numbers there albeit they are happening"? Do you mean code that generates, say, the number 10^10^999 but there is insufficient resources, clock frequency and time to enumerate the list? :ask:

TREE(3) is infinitely closer to 1 than any "large number" along the "counting to infinity" line. So what?

On another hand,
Σp halts 2-|p| is uncomputable (Chaitin) but the number it calculates is less than 1.

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Re: The Field Of Large Numbers

#10  Postby aufbahrung » May 26, 2019 2:56 pm

Would a no deal Brexit lead to the field of small numbers, or through world trade be a return to the field of larger numbers for the UK? Musing...here.
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Re: The Field Of Large Numbers

#11  Postby laklak » May 26, 2019 3:08 pm

Football fields have some large numbers on them. Big enough you can see them from the nose bleed section.
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Re: The Field Of Large Numbers

#12  Postby Blackadder » May 26, 2019 4:20 pm

And this, children, is why you should always say no to drugs.
That credulity should be gross in proportion to the ignorance of the mind that it enslaves, is in strict consistency with the principle of human nature. - Percy Bysshe Shelley
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Re: The Field Of Large Numbers

#13  Postby aufbahrung » May 26, 2019 4:29 pm

Blackadder wrote:And this, children, is why you should always say no to drugs.


....or own a chemistry set even. :think:
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Re: The Field Of Large Numbers

#14  Postby laklak » May 26, 2019 4:57 pm

the dude J.jpg
the dude J.jpg (24.88 KiB) Viewed 268 times
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Re: The Field Of Large Numbers

#15  Postby Thommo » May 26, 2019 5:04 pm

I was going to compose a few comments about finitism and computational feasibility, but meh. Doesn't seem worth it now.
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Re: The Field Of Large Numbers

#16  Postby newolder » May 26, 2019 5:30 pm

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Large enough?
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Re: The Field Of Large Numbers

#17  Postby laklak » May 26, 2019 5:56 pm

Well, I didn't need my reading glasses, so they'll do.
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Re: The Field Of Large Numbers

#18  Postby LucidFlight » May 26, 2019 6:05 pm

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OFFICIAL MEMBER: QUANTUM CONSTRUCTOR CONSCIOUSNESS QUALIA KOALA COLLECTIVE.
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Re: The Field Of Large Numbers

#19  Postby Spearthrower » May 26, 2019 9:45 pm

My son thinks that 'hundred' is an unfeasibly large number which one uses to basically say 'a quantity beyond comprehension'. Is that what you're going for aufbahrung? Perhaps that number just gets larger with age then hits the final roof at zillions?
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Re: The Field Of Large Numbers

#20  Postby surreptitious57 » May 27, 2019 1:47 pm

A MIND IS LIKE A PARACHUTE : IT DOES NOT WORK UNLESS IT IS OPEN
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