|
|
Joined: Jul 2005
Posts: 1,773
Pooh-Bah
|
OP
Pooh-Bah
Joined: Jul 2005
Posts: 1,773 |
While we've discussed this before, in an attempt to explain to a group of Christians a connection between the terms "omnipotent" and "forever" I am trying to express how many serial universes She might already have created
I seek the most economical way to write an unimaginably large number. For example, how would one write the sum of one centillion (ten to the 303'd) factorial, factorialed that many times over again, etc
Thanks to anyone with a bent for mathematical curiosities
dalehileman
|
|
|
|
|
Joined: Jan 2002
Posts: 1,526
veteran
|
|
veteran
Joined: Jan 2002
Posts: 1,526 |
I'm not sure I understand the problem correctly.
((10^303)!) ^ ((10^303)!)
If you write it by hand or with MathType(c), for example, you can get away without the carets and the parens.
|
|
|
|
|
Joined: Oct 2000
Posts: 5,400
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Oct 2000
Posts: 5,400 |
yes we have discussed this before; as a general rule we are polite here, and as in most polite society, we don't discuss religion or politics.
but then you are old and senile (or perhaps old and stupid, or old and rude) and you keep forgetting that. but somehow you are not so old or senile that you forget to bring up topics 'brought up here before' -again and again.
hmm. maybe you're just a troll.
|
|
|
|
|
Joined: Oct 2005
Posts: 557
addict
|
|
addict
Joined: Oct 2005
Posts: 557 |
Most of my dieties prefer to create parallel universes rather than serial ones... takes at least Aleph-null fewer eternities.
|
|
|
|
|
Joined: Jan 2002
Posts: 1,526
veteran
|
|
veteran
Joined: Jan 2002
Posts: 1,526 |
"the sum of one centillion (ten to the 303'd) factorial, factorialed that many times over again, etc"
My last answer is wrong. That 'sum' thing is throwing me off. Regardless my last answer is wrong.
|
|
|
|
|
Joined: Jul 2005
Posts: 1,773
Pooh-Bah
|
|
OP
Pooh-Bah
Joined: Jul 2005
Posts: 1,773 |
Helen: Thank you for sharing that with your friends, however many that might be
dalehileman
|
|
|
|
|
Joined: Jul 2000
Posts: 3,467
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Jul 2000
Posts: 3,467 |
Quote:
Most of my dieties prefer to create parallel universes rather than serial ones... takes at least Aleph-null fewer eternities.
Were they calorie counting?
TEd
|
|
|
|
|
Joined: Jun 2002
Posts: 7,210
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Jun 2002
Posts: 7,210 |
hopefully low-sugar serial.
formerly known as etaoin...
|
|
|
|
|
Joined: Jul 2005
Posts: 1,773
Pooh-Bah
|
|
OP
Pooh-Bah
Joined: Jul 2005
Posts: 1,773 |
Fal yes thank you, that was the sort of expr I was looking for. Now can anyone suggest a much bigger number but using even fewer characters
dalehileman
|
|
|
|
|
Joined: Apr 2000
Posts: 10,542
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Apr 2000
Posts: 10,542 |
wouldn't it be a lot simpler to just use "googleplex"?
|
|
|
|
|
Joined: Dec 2006
Posts: 956
old hand
|
|
old hand
Joined: Dec 2006
Posts: 956 |
Quote:
wouldn't it be a lot simpler to just use "googleplex"?
Is that where all the Googlites hang out.
Last edited by olly; 02/07/07 10:39 PM.
|
|
|
|
|
Joined: Jul 2000
Posts: 3,467
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Jul 2000
Posts: 3,467 |
TEd
|
|
|
|
|
Joined: Dec 2000
Posts: 13,803
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Dec 2000
Posts: 13,803 |
I was going to say Skewes' Number but that turns out to be a lot smaller than originally thought so how about Graham's number?
|
|
|
|
|
Joined: Apr 2000
Posts: 10,542
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Apr 2000
Posts: 10,542 |
Quote:
Isn't it googolplex?
The Googleplex is the Google company headquarters, located at 1600 Amphitheatre Parkway in Mountain View, Santa Clara County, California, near San Jose.
The name Googleplex is a play on words, being a combination of the words Google and complex, and a reference to googolplex, the name given to the large number 10^{10^{100}}. - Wikipedia
-joe (or perhaps it was just a mistake) friday
|
|
|
|
|
Joined: Mar 2000
Posts: 6,511
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Mar 2000
Posts: 6,511 |
Quote:
I seek the most economical way to write an unimaginably large number. For example, how would one write the sum of one centillion (ten to the 303'd) factorial, factorialed that many times over again, etc
Thanks to anyone with a bent for mathematical curiosities
Your OP would have been just as intelligible, and less provocative, without the first paragraph, the example I've cited above. You do this stuff on purpose, don't you, Dale? No wonder you've been kindly invited not to post at some of the other forums you used to pester.
And here I posted a new (to me) neologism URL (WordSpy) to try to give you something to do, but... it seems you have more fun cultivating animosity than discussing words and language [I-give-up]
|
|
|
|
|
Joined: Jan 2002
Posts: 1,526
veteran
|
|
veteran
Joined: Jan 2002
Posts: 1,526 |
All very new stuff to me. Thanks, Faldage.
The wiki explanation is a little unclear.
I'm not sure, but I think Dale's number is bigger than Grahams number,
assuming Grahams Number is specifically G(64).
However, we make a number bigger than Dale's number, I think; namely, G(G(10^303!)!)!, for example. It's kinda hard to tell at this point.
Last edited by TheFallibleFiend; 02/08/07 01:57 PM.
|
|
|
|
|
Joined: Jun 2002
Posts: 7,210
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Jun 2002
Posts: 7,210 |
might be some cool stuff here: numberscool. there's also here: PlanetMath
Last edited by etaoin; 02/08/07 03:29 PM.
formerly known as etaoin...
|
|
|
|
|
Joined: Jul 2005
Posts: 1,773
Pooh-Bah
|
|
OP
Pooh-Bah
Joined: Jul 2005
Posts: 1,773 |
Fal, thank you, that's a good one. To save me the trouble of looking it up, however, does G stand for Googol or Googolplex, and if the former, what's the symbol for the latter
eta: THank you for those links, I have ensconced them anongst my Faves
Anna: Animosity may be in the eye of the beholder, while I can't see anything provocative about the first paragraph. However, I apologize if it somehow offended you
dalehileman
|
|
|
|
|
Joined: Jan 2002
Posts: 1,526
veteran
|
|
veteran
Joined: Jan 2002
Posts: 1,526 |
The 'G' stands for numbers in Graham's sequence that is explained on the page that Faldage gave us the link to.
G(1) = 1
G(2) = 2^2
G(3) = 3^3^3
G(4) = 4^4^4^4
G(5) = 5^5^5^5^5
Pretty big numbers. I like this stuff, but I'm having trouble figuring out what's bigger than what. Normally when I'm faced with big numbers at work, I see how the log works or the log log ... but this stuff is very huge.
My first job out of college, another program had to compute average network capacity as a percentage of total capacity. The final results should be between 0 and 1, but the intermediate results were overflowing the processor - and other alternatives were too time consuming: so I showed him how to use logarithms to make the huge numbers smaller. Worked like a champ. But while those numbers were vastly bigger than any most people are likely to use, they are much closer to zero than to the numbers that you and Faldage are referring to.
|
|
|
|
|
Joined: Dec 2006
Posts: 956
old hand
|
|
old hand
Joined: Dec 2006
Posts: 956 |
Quote:
a reference to googolplex, the name given to the large number 10^{10^{100}}.
A googolplex is 10^googol and a googolplexplex is 10^googolplex. Could we call it a Duplex? Or a twoplex? Perhaps a complex or a perplex!
|
|
|
|
|
Joined: Jul 2005
Posts: 1,773
Pooh-Bah
|
|
OP
Pooh-Bah
Joined: Jul 2005
Posts: 1,773 |
Guys, thank you. It always pleases not to have to look it up. Hwever, I wonder whether there's a symbol for the googolplex, plexplex, etc
dalehileman
|
|
|
|
|
Joined: May 2002
Posts: 1,529
veteran
|
|
veteran
Joined: May 2002
Posts: 1,529 |
Zounds! Forsooth- the latter day Middle Agers here ponder how many Angels can dance on the head of a pin -- the answer is nowt -- meanwhile the Huns are at the door.  May God save the Queen from the Comet and may these idolaters and idlers ponder away in Purgatory for a gobble-de-gook-duplex number of years plus one day. Then, and only then, should they be allowed to enter the gates of Hell. Or Heaven, if perchance they can prove good behavior or worthwhile thought. 
Last edited by themilum; 02/08/07 11:57 PM.
|
|
|
|
|
Joined: Jun 2006
Posts: 5,295
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Jun 2006
Posts: 5,295 |
"Numberless are the World's Wonders", make up the music to this yourself. Give it a just a little swinging chance. 
|
|
|
|
|
Joined: Oct 2005
Posts: 557
addict
|
|
addict
Joined: Oct 2005
Posts: 557 |
I already mentioned in this thread the transfinite number aleph-null which if I could use a Hebrew font for aleph and a subscript 0 for null would be only 2 characters. See: http://en.wikipedia.org/wiki/Aleph_null
|
|
|
|
|
Joined: Jul 2005
Posts: 1,773
Pooh-Bah
|
|
OP
Pooh-Bah
Joined: Jul 2005
Posts: 1,773 |
Myr, thank you for that link, but I'm not much as a mathematician, and anyway infinities don't count, sorry, should have mentioned that. Meantime I'm still looking for the largest finite number than can be expressed in the smallest number of characters
And yes I realize that would entail a few loose ends, but thanks again
dalehileman
|
|
|
|
|
Joined: Oct 2006
Posts: 293
enthusiast
|
|
enthusiast
Joined: Oct 2006
Posts: 293 |
Quote:
Meantime I'm still looking for the largest finite number than can be expressed in the smallest number of characters
How about "lots" or "scads"?
|
|
|
|
|
Joined: Jun 2002
Posts: 7,210
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Jun 2002
Posts: 7,210 |
formerly known as etaoin...
|
|
|
|
|
Joined: Apr 2000
Posts: 10,542
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Apr 2000
Posts: 10,542 |
but, see, dale's looking for a type-3 expression, and ideally it will be a neologism!!
|
|
|
|
|
Joined: Jun 2002
Posts: 7,210
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Jun 2002
Posts: 7,210 |
Quote:
but, see, dale's looking for a type-3 expression
I didn't think anyone understood what that meant...
formerly known as etaoin...
|
|
|
|
|
Joined: Jan 2001
Posts: 1,819
Pooh-Bah
|
|
Pooh-Bah
Joined: Jan 2001
Posts: 1,819 |
I think you'll have to specify the number of characters you want to limit it to Dale. One can write a much larger number with five characters than with two.
If we limit ourselves to two characters (including arabic numerals and operands like +, -, x, ÷, and !, but exempting ^ for exponentiation since it can be accomplished with superscript), then I think the largest number you can write is 9^9, which is equal to 387420489.
If you allow three characters, I think the largest is (9^9)!, which is equal to 387420489! For the non-math folks out there, that's 1 x 2 x 3 x 4 .... x 387420489.
|
|
|
|
|
Joined: Jul 2005
Posts: 1,773
Pooh-Bah
|
|
OP
Pooh-Bah
Joined: Jul 2005
Posts: 1,773 |
Alex: I have this instinctive feeling that there should be a way to express an unimaginatively large finite number in a minimal space. It's been suggested that G(G(10^303!)!)!, is a pretty good one. However, G(G(10^999!)!)!, is obviously bigger and so I suppose one might start by attempting to express this number in even fewer characters. However, if an unimaginatively larger number could be expressed in just a few more characters that would be all right too
It's like defining Type-2 and -3 words. Hard to express though a few liberal thinkers--eta and zm for instance--seem to catch on. As the Zen master might say, allow your intuition freedom to roam without being excessively judgmental
dalehileman
|
|
|
|
|
Joined: Jun 2002
Posts: 7,210
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Jun 2002
Posts: 7,210 |
formerly known as etaoin...
|
|
|
|
|
Joined: Jan 2001
Posts: 1,819
Pooh-Bah
|
|
Pooh-Bah
Joined: Jan 2001
Posts: 1,819 |
Quote:
As the Zen master might say, allow your intuition freedom to roam without being excessively judgmental
Anyway, for your purpose of expressing a vast but finite number to a non-scientific audience I would actually not use the factorial ! or any other operands and stick to simply writing the number using strictly numerals. For any given number of numerals used, a power tower or tetration as it is called will be the highest number.
9^9 is greater than 99
9^(9^9) is greater than 999 and is in fact an incredibly large number. If you were to actually evaluate that number, it would have 369,693,100 digits! Read more about it here. Excerpt follows:
9^9^9
Date: 09/10/97 at 18:53:43
From: Sean H
Subject: 9 ^ 9 ^ 9
Dr. Math,
In my Algebra II class, my teacher asked us what the largest number we
can write is, only with a limit of 3 digits. I answered 9 ^ 9 ^ 9
(nine to the ninth to the ninth) and was correct.
Getting home, and on my computer however, I set out to find the answer
to that question. 9 ^ 9 was easy: 387420489. But now, how in the
world to do 9 ^ 387420489?
I tried writing a C++ program to do it, only the largest data type you
can use, an unsigned long, only supports up to 10 digits. That wasn't
getting me anywhere. On the Internet, I saw one person say that the
answer would have 300,000,000 digits! Is this true?
So my question: Is it really that large an answer? And is there a way
I could find the answer? If it really is that big, how long would it
take to answer on a large mainframe? (I'm talking Cray here). Would it
be hours, days, months, or years?
Thanks a lot,
Sean
--------------------------------------------------------------------------------
Date: 09/25/97 at 15:47:28
From: Doctor Ken
Subject: Re: 9 ^ 9 ^ 9
Hi!
To find out how many digits some number has, the best way is to take
the log base 10 of that number and round down to the nearest integer,
and add 1.
For instance, 42 has 2 digits, and the log base 10 of 42 is about
1.62325: round that down and you get 1, add 1 and you get 2. 34578 has
5 digits, and its log base 10 is 4.5388: round it down and you get 4,
add 1 to get 5. 1000 has 4 digits and its log base 10 is 3. Round down
to get 3, add 1 to get 4.
So we want to find the log base 10 of your number, 9^387420489. Let's
do it:
Log (9^387420489) = 387420489 * Log(9) (Pull out the power)
= 387420489 * 0.954243 (do the log)
= 3.6969309963 x 10^8 (by calculator)
= 369693099.63
So your number has 369,693,100 digits. That's a big number!
|
|
|
|
|
Joined: Jul 2005
Posts: 1,773
Pooh-Bah
|
|
OP
Pooh-Bah
Joined: Jul 2005
Posts: 1,773 |
What's the macro for the upside down v--thanks guys
dalehileman
|
|
|
|
|
Joined: Jul 2005
Posts: 1,773
Pooh-Bah
|
|
OP
Pooh-Bah
Joined: Jul 2005
Posts: 1,773 |
Fal: Thank you exceedingly for your participation, but I am confused about Graham's Number. I have heard it expressed as G(63) or as just plain G, but I don't understand how it can still be Guiness' winner if G(65) is bigger and could just as easily be used in a new problem http://thesaurus.maths.org/mmkb/entry.html?action=entryById&id=2525Not good at math
dalehileman
|
|
|
|
|
Joined: Apr 2000
Posts: 10,542
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Apr 2000
Posts: 10,542 |
Quote:
What's the macro for the upside down v--thanks guys
d'oh.
SHIFT-6: ^
|
|
|
|
|
Joined: Aug 2005
Posts: 3,290
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Aug 2005
Posts: 3,290 |
What's the macro for the upside down v?
What's a macro macro macro, dada? The word, macro, as are all other words, is synonymous with drive. Dada!
Ceci n'est pas un seing.
|
|
|
|
|
Joined: Jan 2002
Posts: 1,526
veteran
|
|
veteran
Joined: Jan 2002
Posts: 1,526 |
Dale, no matter what specific number one is given, she could easily construct a bigger number by adding 1, or a much bigger number by taking the factorial or the graham's function of that number. The interesting thing about Graham's number is that it's the biggest number that was actually used non-parenthetically. http://www-users.cs.york.ac.uk/susan/cyc/g/graham.htm
|
|
|
|
|
Joined: Jul 2005
Posts: 1,773
Pooh-Bah
|
|
OP
Pooh-Bah
Joined: Jul 2005
Posts: 1,773 |
Fal, thank you for that link, and you have to forgive my abysmal mathematical ignorance, but I don't understand it. Is Graham's number G or G(63); and if the latter, how is 63 the upper limit? And does it somehow depend upon the number 3? And why would Guiness cite it if it isn't, inasmuch as upon acceptance all the math whizzes in the world would immediately set about devising a problem using a bigger number
tsu: Thank you for ^. That in using a keyboard some 72 years I had never found occasion for it, is testimony to my mathematical vincibility. For my benefit (and others of my ilk) you might explain its use and limitations; that is, where parens are called for, when not, etc
zm: Not yet anyhow
Myr: Trouble with parallel universes is that each one would have to be serial also. at risk of offending some present, this seems unmanageable even if She is omnipotent
dalehileman
|
|
|
|
|
Joined: Apr 2000
Posts: 10,542
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Apr 2000
Posts: 10,542 |
Thank you for ^. That in using a keyboard some 72 years I had never found occasion for it, is testimony to my mathematical vincibility. For my benefit (and others of my ilk) you might explain its use and limitations; that is, where parens are called for, when not, etc
not me, bro. I don' be no steenken mathematician for about 6^2 years now.
|
|
|
|
|
Joined: Jul 2005
Posts: 1,773
Pooh-Bah
|
|
OP
Pooh-Bah
Joined: Jul 2005
Posts: 1,773 |
d'uh, please endure the confusion of an ancient curmudgeon evidently stepping to the brink of senility, I just glanced at my typewriter. Given the inability of his minions to adequately deal with the superscript, to make room for the ^ I see that Bill has moved the underline from above the 6 to just-to-the-right of the zero
dalehileman
|
|
|
|
|
Joined: Jan 2002
Posts: 1,526
veteran
|
|
veteran
Joined: Jan 2002
Posts: 1,526 |
Dale, it's not the upper limit of all numbers, it's the upper limit on the answer to a specific mathematical question. I think G's number is G(63), but G's notation can be used on any integer. Surely G(99) > G(63), but G(63) is useful because it says that the answer to a specific question cannot be greater than that.
This kind of this is very useful in general in computer science and operations research, for example, although I've never had occasion to use any numbers quite this big. I just have a very vague awareness that there are people looking at much bigger problem spaces.
|
|
|
|
|
Joined: Jul 2005
Posts: 1,773
Pooh-Bah
|
|
OP
Pooh-Bah
Joined: Jul 2005
Posts: 1,773 |
dalehileman
|
|
|
|
|
Joined: Dec 2000
Posts: 13,803
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Dec 2000
Posts: 13,803 |
Quote:
... G(63) is useful because it says that the answer to a specific question cannot be greater than that.
So what's the question for which G(42) is the answer?
|
|
|
|
|
Joined: Oct 2006
Posts: 293
enthusiast
|
|
enthusiast
Joined: Oct 2006
Posts: 293 |
Quote:
Quote:
... G(63) is useful because it says that the answer to a specific question cannot be greater than that.
So what's the question for which G(42) is the answer?
(G)Life, (G)the Universe, and (G)Everything.
"Gee", he said with exasperation.
|
|
|
|
|
Joined: Oct 2006
Posts: 293
enthusiast
|
|
enthusiast
Joined: Oct 2006
Posts: 293 |
Is this what is known as "The G spot?"
"I am certain there is too much certainty in the world" -Michael Crichton
|
|
|
|
|
Joined: Aug 2005
Posts: 3,290
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Aug 2005
Posts: 3,290 |
number of angels that can dance on the head of a pin = G(googolplex) ^ G(aleph sub null)
Ceci n'est pas un seing.
|
|
|
|
|
Joined: Oct 2000
Posts: 5,400
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Oct 2000
Posts: 5,400 |
What about the angels that don't dance?
how do we count them?
|
|
|
|
|
Joined: Jul 2005
Posts: 1,773
Pooh-Bah
|
|
OP
Pooh-Bah
Joined: Jul 2005
Posts: 1,773 |
Careful there Helen, you're skirting a religious issue
dalehileman
|
|
|
|
|
Joined: Dec 2000
Posts: 13,803
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Dec 2000
Posts: 13,803 |
Quote:
What about the angels that don't dance?
how do we count them?
If I can't dance, I don't want to be part of your revolution.
|
|
|
|
|
Joined: Oct 2006
Posts: 293
enthusiast
|
|
enthusiast
Joined: Oct 2006
Posts: 293 |
Quote:
Careful there Helen, you're skirting a religious issue
Do all angels wear skirts?
|
|
|
|
|
Joined: Jul 2005
Posts: 1,773
Pooh-Bah
|
|
OP
Pooh-Bah
Joined: Jul 2005
Posts: 1,773 |
Around here, they'd better, lest lest they be accused, along with my fellow de-'s, of having assumed the posture of symbolic capitulation recently sanctioned by the otherwise conservative State of Massachusetts, a depiction of which is however considered unacceptable in even such a bastion of liberalism as WordSmith
dalehileman
|
|
|
|
|
Joined: Aug 2005
Posts: 3,290
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Aug 2005
Posts: 3,290 |
the posture of symbolic capitulation
quid autem uides festucam in oculo fratris tui et trabem in oculo tuo non uides.
Ceci n'est pas un seing.
|
|
|
|
|
Joined: Jul 2005
Posts: 1,773
Pooh-Bah
|
|
OP
Pooh-Bah
Joined: Jul 2005
Posts: 1,773 |
Quote:
quid autem uides festucam in oculo fratris tui et trabem in oculo tuo non uides
During the late-summer tobacco-chewing festival, in a fit of temper your four-eyed collegiate chums throw off their spectacles, grinding them into the ground without the slightest compunction
dalehileman
|
|
|
|
|
Joined: Jul 2005
Posts: 1,773
Pooh-Bah
|
|
OP
Pooh-Bah
Joined: Jul 2005
Posts: 1,773 |
...to say nothing of Vermont and Connecticut
dalehileman
|
|
|
|
|
Joined: Jun 2002
Posts: 7,210
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Jun 2002
Posts: 7,210 |
formerly known as etaoin...
|
|
|
|
|
Joined: Jul 2005
Posts: 1,773
Pooh-Bah
|
|
OP
Pooh-Bah
Joined: Jul 2005
Posts: 1,773 |
I don't know, but I'll bet it was very tempered, reasonable and scholarly
dalehileman
|
|
|
|
Forums16
Topics13,913
Posts229,326
Members9,182
| |
Most Online3,341
Dec 9th, 2011
|
|
|
0 members (),
739
guests, and
1
robot. |
|
Key:
Admin,
Global Mod,
Mod
|
|
|
|
