Talk:Googolplex

From Wikipedia, the free encyclopedia
Jump to: navigation, search
WikiProject Mathematics (Rated C-class, Low-importance)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
C Class
Low Importance
 Field: Basics
One of the 500 most frequently viewed mathematics articles.

maybe the number isn't THAT big...[edit]

wouldn't the number just be 10^100,000 since 10^100^10^100=10^100^1000=10^100(1000)=10^100,000?

I suggest Wikipedia be the first to write out the entire number[edit]

"...if you had an unlimited supply of ink and paper, you would need around 10^20 times the current age of universe to fully write down a googolplex.." I personally doubt this is true. I could fully write down this number within a year. "A googolplex is the number 10^googol, which means it's a 1 followed by a googol of zeros (i.e. 10100 zeros)." So it would take me 10 to the twentieth power to write 10,100 zeros? I could do that in a month... Please explain, how many zeros (NUMERIC, i.e. 1, fifty, one million) Zeros are after the one??? 96.231.102.185 (talk) —Preceding undated comment was added at 16:30, 8 November 2008 (UTC).

IDIOOOOOT!!!! The number below is 10 raised to the power of googol, therefore it is a googolplex, but it is not the actual number written down. ie a million can be written like this 1,000,000 or like this 500,000*2 or like this 1*10^6. Thus to write a googolplex you need that much time and thtat much space. —Preceding unsigned comment added by Sukhoi.pakfa (talkcontribs) 06:13, 16 April 2009 (UTC) The answer is at https://sites.google.com/site/webpagesorg/Home/smallbookofbignumbers.txt?attredirects=0&d=1 — Preceding unsigned comment added by 24.187.35.225 (talk) 12:05, 9 July 2011 (UTC)


Think of the fame and glory... and to prove its length once and for all.

-G

I am going to attempt to write one googleplex or what maybe a fourteenth of that fourteen times! or atlest 14% of that or 0.014th% whichever comes first. I amattempting to do so and I've got like 16.5 MB of my computer space taken up by that and i am not yet done. Wish me luck. =:) 0.0200014% of a googleplex is probably hard to write and might take up 173³x that of my computer space but I'll try! Chikinpotato11 19:07, 4 February 2007 (UTC) @:)

I am gonna start writing down a googleplex right here right now:

on second thoughts CBA--Chikinpotato11 19:19, 4 February 2007 (UTC)

Millions of people can write it :). See:10^{\scriptscriptstyle10\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000\,000}. Zheliel (talk) 07:53, 29 October 2008 (UTC)
a googleplex is 10^10^100, so lets say you could write 10^3 zeros every second, in terms of typing, assuming a word is ~5 characters, thats 10^3*60/5 or 12,000wpm, i don't think anyone that can type that fast, so therefore it would take 10^10^100/10^3 seconds to do it, division is equal to subtraction of exponents, so thats 10^(google-3) seconds which works out to be 10^9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 seconds to write out at 1200wpm, the universe is (by my math) 10^18 seconds old, that would mean that it would take you 10^(google-3-18) times the age of the universe to write it out at that speed...have fun :) Edman007 (talk) 06:03, 1 December 2008 (UTC)

its all good giving me it to the power of whatever but what the hell is it in full . give me one calculator that fits in a pocket that can do this sum. —Preceding unsigned comment added by 86.140.229.66 (talk) 17:47, 19 January 2009 (UTC)

I'm going to write out the whole number now. 10. There... I use base googolplex, of course. -- Borb (talk) 19:21, 31 March 2009 (UTC) It's impossible, I tell you. Word '03 and possibly '07 told my I could have any more pages at 10^1,326,301,924 69.76.155.202 (talk) 06:13, 5 June 2009 (UTC)

A googolplex has more zeroes than you (who believes it's possible to write it) think. 75.36.213.172 (talk) 00:25, 26 September 2009 (UTC)

There is a difference between typing and writing... But we can always invent new numbers that can't be typed even using superscript. Such as "10^(10^(10^(10^10...)))" where the "..." suggests the pattern continues for 100 light-years. —Preceding unsigned comment added by 66.183.59.211 (talk) 03:38, 12 October 2010 (UTC)

It is impossible, really impossible, because to write any number down you need at least 1 atom (say, to indicate each zero) of 'ink' and the number of atoms in the entire Universe is only about 10^80. So, it is impossible to write or type the number googolplex as suggested in the article: "... which can also be written as the number 1 followed by a googol zeros". Also think about the amount of paper you would need; that would require about 10^23 Universes of ours in paper only. And think about the storage of that paper, the buildings, the size of planets needed, etc. Yes, really, really impossible. The only way it could be possible (hihi), is in the far far future, when the Universe has expanded so much and the matter in it has expanded so much that a number with a googol number of zeros and one one (!) can be spread enough across 10^80 planets as big as our Earth (for each atom in our current Universe, we need a whole planet to store this number) that contain each 10^20 digits of this number, taking up most storage available on those planets, far enough apart, taking care not to create a black hole (see elsewhere in these comments). This is just a rough estimate. Enjoy! Bcurfs (talk) 19:55, 29 March 2011 (UTC)

It still wouldn't be possible in billions of years because new matter isn't added with expansion, you'd still have roughly the same number of particles. Pongley (talk) 12:33, 5 April 2014 (UTC)

Question[edit]

Can we have it written out with 10^100 zeros like there is on Googol? --Menchi 04:31, 7 Oct 2003 (UTC)

Maybe, but we would have to be careful not to have all the digits of a googolplex written too close to each other, or they would probably collapse into a rather big black hole. Κσυπ Cyp 11:38, 7 Oct 2003 (UTC)

Well, I'm very bored, so let's see if we could write out all those zeros (let's forget about that "1" for now):
One line of a word document in size 1 font can hold 864 characters. 1 page can hold about 563 lines. That's 468432 characters per page. Let's say you put it on several documents, 500 pages a piece. That's 243216000 characters per document. Let's say the average system can hold 5000 of these (Im totally guessing here). That's 1.21608^12 zeros per computer (our goal is 10^100, remember). Next, let's be optimistic and say the world has 3 billion computers. That comes to 3.64824^21 zeros. Not even close. Even if I vastly underestimated the storage compacity of the world's computers, it's still not even close. 96.225.64.203 (talk) 02:36, 25 November 2007 (UTC)

Well I believe that I could write it out on my computer...

Faith is very powerful indeed. It will be possible if you are still around at the time the conditions are right. See my previous comment above. Bet the 'I' in your statement must be taken rather metaphysical if you want to believe this to be true now... Bcurfs (talk) 19:57, 29 March 2011 (UTC)

My number is... ...nonedogeneg[edit]

my make up number is nonedogeneg it is

1 with 1 trillion 0's after it —Preceding unsigned comment added by 90.210.165.126 (talk) 17:13, 3 July 2009 (UTC)

But a googolplex is still 10^10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 times bigger. 66.183.59.211 (talk) 03:28, 12 October 2010 (UTC)


My number is: inphigoogolplexplexplex[edit]

10(^10^100^100^100^∞)

seems legit... — Preceding unsigned comment added by Dakoolst (talkcontribs) 20:39, 26 May 2013 (UTC)

(Inappropriate expression deleted)[edit]

i just wrote 1 googolplex 11000on 1 single piece of paper! —Preceding unsigned comment added by 90.210.165.126 (talk) 17:40, 3 July 2009 (UTC)

This is an encyclopedia talk. Be serious.
By the way 11000 = 1. DarkLightA (talk) 21:05, 2 October 2010 (UTC)
since when did being serious enter Wikipedia's rules? Can't find it anywhere. Could creating this talk section offend anyone? No. ...I hope... 66.183.59.211 (talk) 03:21, 12 October 2010 (UTC)

Ackerman numbers[edit]

The ackerman numbers here are wrong as they are stacked to the right instead of the left. I don't have the editing skills to amend 193.164.104.187 (talk) 22:03, 27 October 2009 (UTC)

Can I ask what the difference is between stacking to the right and to the left? Just curious. DarkLightA (talk) 21:06, 2 October 2010 (UTC)

Is it really true that one can't fit the number of zeros in a googolplex into the known universe?[edit]

I heard this articulated by Carl Sagan in the wonderful series Cosmos and reiterated with a slightly different number of total elementary particles in this article. What I wonder about is how the vast emptiness of space fits in here. Don't the elementary particles occupy a tiny fraction of the actual "volume" of space? Maybe the answer is that if that fraction isn't less than 1 / 10**11, it still does not provide the capacity for a googolplex of elementary-particle-sized zeroes. Could someone please enlighten me regarding this?75.18.172.78 (talk) 22:59, 27 February 2011 (UTC)Robert B. Stein

Read the various arguments under Size to get a clearer picture on the answer to this question. With only 10^183 or so Planck spaces in the observed universe, that is far smaller than the 10^(10^100) of a googolplex. Where would you put all the zeros? Nutster (talk) 14:17, 28 February 2011 (UTC)
Edit - Grammar fix Nutster (talk) 02:40, 8 March 2011 (UTC)
To write googolplex you need to write a "1" followed by 10^100 zeros. So you really need 10^100 "boxes" to write the number itself. And as you said, there are ~10^183 Planck spaces in the universe, assuming we can somehow "write" a zero in each of them, we would be able to write Googolplex. However the question remains what to write with if we don't have enough atoms in the universe for making the ink? - Subh83 (talk | contribs) 22:17, 7 April 2011 (UTC)

There are enough Planck volumes in the universe to fit the number of zeroes in a googolplex. But there aren't a googolplex number of Planck volumes.[edit]

Subh83 is correct. When considering the Planck volume, the universe has more than enough "boxes" to store the number of zeroes in a googolplex.. It is easier to understand when working up from a smaller scale.

Hundred has has 2 zeros. It is denoted by 10^{2}. You need 2 spaces to write the number of zeroes in Hundred. Its full form is 100.

Googol has 100 zeroes. It is denoted by 10^{100}. You need 100 spaces to write the number of zeroes in googol. Its full form is 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

Googolplex has 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 zeroes. It is denoted by 10^{10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}. You need 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 spaces (or 10^{100} spaces or 1 googol spaces) to write the number of zeroes in googolplex. Therefore its full form cannot be written here.

However if we take one Planck volume to represent a zero, we need 1 googol of Planck volumes to represent all the zeroes of a googolplex. The universe has 10^{184} volumes, which is equal to 10^{100} * 10^{84}, or in other words, the universe has 10^{84} times more space than is needed to write 1 googol of zeroes.

But if the universe wanted to have a googolplex of Planck spaces, it would need to be 10^{9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999816} times greater. Then it would have 10^{googol} spaces or 1 googolplex spaces. 182.189.110.170 (talk) 13:54, 7 March 2014 (UTC)

How Do Acutally Do It[edit]

We all know the googolplex, the imposibility of writing it. But, if your computer can actually handle all those zero's without crashing, then it is possible. It is pretty much doing this: 10 x 10. 100 (the 10 x 10 result) x 10. 1000 (the 100 x 10 result) x 10. etc, until you get to 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (the result of 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 x 10) x 10. My cpu crashes when i get up to 10 x 1000000 on font size 1. You are going to need a cpu thatcan handle like googolbytes or something that high. Spesh531, My talk, and External links 18:29, 13 March 2011 (UTC)

No. Your computer can't do it, my computer can't do it, Bill Gates' computer can't do it. All the computers in the world combined wouldn't have anything that comes even close to being able to print the Googolplex in its "complete" form. Even if every single atom in every single computer in the world could represent a number (which they can't), you'd run out of memory. Even if the material of the entire universe was losslessly converted into a machine with no other purpose than to print the Googolplex in its "complete" form, it couldn't be done, even if the machine could use itself as printing material. The known Universe doesn't have enough material for printing the number or for printing Googol instances of anything. 212.68.15.66 (talk) 07:51, 18 March 2011 (UTC)
May be with quantum computers in some distant future in which a large number of digits can be represented by the state of one (or a few) elementary particles in one go. But then what's the need/point of doing that when we can always write it in short as 10^{10^{100}}? Alternatively, using a base-googolplex number system it can simply be represented by 10. If you use a base-googol system, you can write it as 1 followed by a hundred zeros. What's the point? Mathematically, googolplex is as far from infinity as the number 1 is. - Subh83 (talk | contribs) 22:32, 7 April 2011 (UTC)


Notation 10^10^100 or 10^(10^100)[edit]

Currently, the article used the notation 10^{10^{100}} which I think is confusing because this notation does not make it clear if it stands for 10^(10^100) or for (10^10)^100.
If nobody objects, I plan to change the notation to 10^{(10^{100})} which avoids the ambiguity.--PowGog (talk) 22:07, 30 October 2011 (UTC)

Very good point about ambiguity: exponentiation is not an associative operation. Note that the article has five more of these ambiguous expressions. They do not contribute to clarity and bring our project into disrepute. For my taste, the expression 10^{googol} is sufficient. Escalating exponentiation may look fancy, but it only causes confusion.Rgdboer (talk) 23:29, 30 October 2011 (UTC)
Since nobody seems to object, I added the brackets to the formulas.--PowGog (talk) 04:45, 1 November 2011 (UTC)
Thank you for cleaning up all of the ambiguous expressions.Rgdboer (talk) 19:58, 1 November 2011 (UTC)

Size vs. Scale[edit]

Should the Size and Scale sections be merged? Many of the arguments in each section are complimentary and really are talking about the same idea: just how amazingly huge a googolplex is and the impossibility of expressing it physically. Nutster (talk) 04:02, 16 November 2011 (UTC)

1963 or 1938?[edit]

"In 1963, Edward Kasner's nine-year-old nephew, Milton Sirotta, coined the term googol..." On the wiki page about googol Kasner's nephew is said to have coined the term googol in 1938. At least one of these must be wrong. Couprie (talk) 10:21, 20 October 2012 (UTC)

Given that both Googol and Googolplex were introduced to the lexicon in 1940's "Mathematics and the Imagination", I don't see how 1963 can be the right date, unless there's evidence that Googolplex was only introduced in a later edition.98.111.203.61 (talk) 18:52, 2 November 2012 (UTC)

writing googolplex on paper/ printing it on book pages[edit]

@ Googolplex#Size--- that whole spiel is helpful in communicating the vastness of the number, but it sounds all stated in pre-digital age terms and somewhat irrelevant in today's world.

can anyone say how easy it might be to "write" all the zeros needed to write a 10googol in a digital file or series of digital files? this seems like a relevant question. I mean, how many more years into the future will people be inclined to think about printing the zeros on book pages & filling up the yet-observed universe with those pages?

can someone with the required math/ scientist chops help us figure out how much digital space would be needed? thanks. skakEL 01:04, 5 November 2012 (UTC)

Storing a googolplex in twos complement would require approximately googol ln(10)/ln(2) = 3.322 × 10^100 bits or 4.152×10^87 TB (terabytes), which is estimated to be more that 10^82 times all the content on the entire Internet right about now. Maybe if the Earth was a supercomputer, as described in Hitchhiker's Guide to the Galaxy, but but otherwise, no, or at least not yet. Nutster (talk) 13:53, 5 November 2012 (UTC)
Interestingly, if the entire observable universe were packed with 2012's technology disk drives, it would roughly be enough to store the digital representation of googolplex on the combined storage device. However, since the universe is so sparely packed, if all the existing matter were used to create such devices, we'd still be a few dozen orders of magnitude short of such representation. I don't know if any of this is worth mentioning in an article. After all, digital representation is no more than a convention. If we are allowed to use binary floating point representation, the number can easily be written out in a few minutes on a single sheet of paper. Owen× 13:42, 5 November 2012 (UTC)
I guess it would depend on how much rounding you allow. To represent it fully would require more than 3 googol of bits. Nutster (talk) 13:57, 5 November 2012 (UTC)

Dust particles analogy[edit]

I'd like to see some calculations for that. I would do it myself, but I'm not entirely sure how. Microphonicstalk 21:19, 1 July 2013 (UTC)

We can calculate it like this: We assume that each particle has a size of 1.5 {\rm\ {\mu}m}, this means (if we assume that it is a cube) its volume is V_{\rm{particle}} = (1.5 {\rm\ {\mu}m})^3 = 3.38 \times 10^{-18}{\rm\ m}^{3}. If the observable universe, which has a volume of V_{\rm{universe}} = 4 \times 10^{80}{\rm\ m}^{3} (according to http://www.wolframalpha.com/input/?i=volume+of+the+observable+universe ), is filled with such particles, the total number n of such particles is n=\frac{V_{\rm{universe}}}{V_{\rm{particle}}}=\frac{4 \times 10^{80}{\rm\ m}^{3}}{3.38 \times 10^{-18}{\rm\ m}^{3}}=1.18\times 10^{98}. The number of different ways in which the particles can be ordered is equal to the the factorial n! of the total number of particles. It can be calculated using Stirling's approximation as: n! \simeq \sqrt{2\pi n} \left ( \frac{n}{e} \right )^n = 10^{\left ( \log_{10}\left ( \sqrt{2\pi n} \left ( \frac{n}{e} \right )^n \right ) \right )} = 10^{\left ( \frac{1}{2}\times\log_{10}\left ( {2\pi n} \right ) + n\times\log_{10}\left ( \frac{n}{e} \right ) \right )} \simeq 10^{\left ( n\times\log_{10}\left ( \frac{n}{e} \right ) \right )} = 10^{\left ( 1.18\times 10^{98}\times\log_{10}\left ( \frac{1.18\times 10^{98}}{2.718...} \right ) \right )} = 10^{\left ( 1.18\times 10^{98}\times97.6 \right )} = 10^{\left ( 1.15\times10^{100} \right )} \simeq 10^{\left ( 10^{100} \right )} = 1{\rm\ googolplex} So it is approximately a Googolplex.--Googolplex2013 (talk) 08:25, 14 December 2013 (UTC)

Incorrect Misconceptions[edit]

This article contains errors on the numerical value of googolplex.

Googolplex is just 1 followed by one thousand zeroes. You can use a calculator to prove it but note that not all calculators have the ability to compute it. Using the built-in calculator in Windows 7, if you type 10 to the power of 10, you get 1 followed by 10 zeroes; then if you raise it to the power of 100, you get 1e.1000 which means 1 times 10 to the power of 1000, which is equivalent of one followed by one thousand zeroes.

You can prove it using inductive reasoning. 10^10 is equal to one followed by ten zeroes. If you square that result, then it would be the equivalent of 10^10^2. 10^10^2 is equal to one followed by twenty zeroes. Each time you increase the exponent by a whole number, you would expect another 10 zeroes which is true. So you would predict that 10^10^10 is equal to 1 followed by 100 zeroes and 10^10^9 is 1 followed by 90 zeroes. Therefore, you can conclude that 10^10^100 is indeed, 1 followed by 1000 zeroes.

With that said, it would be incorrect to say that if a person wrote googolplex by using zeroes (i.e. 1,000,000,000,000...) until they reach 1000 zeroes, would take up more time than their lifetime. Instead, it would only take about 8 minutes and 20 seconds assuming the person writes on average, 2 zeroes per second. (1001/2)/60 On the other hand, it would be reasonable to state that writing the set of whole numbers leading to googolplex (i.e. 0,1,2,3,4,5,6,7,8,9,10,11...) would take up more space than the observable universe since doing so would get exponentially longer to increase the number of digits. For example, writing the whole numbers leading up to 9 starting with zero would take 10 tries, going from 10 to 99 would take 89, from 100 to 999 would take 899 and so forth.

I wanted to note that this only applies to 10^10^100. If googolplex means 10^(10^100), then it would be a completely different number. This is because what is inside the parenthesis needs to get evaluated first. In this case it would be 10^(1 followed by 100 zeroes). By using a little bit of mathematical induction you can conclude that it has a googol amount of zeroes. For instance, 10^7 has 7 zeroes, 10^10000 has 10000 zeroes, and therefore 10^(10^100) has 10^100 (googol amount of zeroes). But it seems like the article doesn't put the parenthesis.

2601:0:780:29F:148A:34EE:8ADE:1C0A (talk) 04:23, 25 October 2013 (UTC)

In general misconceptions are incorrect, so you do not have to repeat yourself. The value of (10^10)^100 is indeed quite different form 10^(10^100), the latter being the definition of a googolplex, a 1 followed by a googol of zeros. The parenthesis tend not to be used because exponents are generally considered to associate right-to-left, not left-to-right. So, a^b^c and a^(b^c) are evaluated the same way, but (a^b)^c is done differently. When you have a power of a power, you can multiply the exponents, so (10^10)^100 = 10^(10*100) = 10^1000, as you say, but this is not a googolplex. Nutster (talk) 10:47, 25 October 2013 (UTC)

Original Research[edit]

@Nutster: I removed this section:

A Planck space has a volume of a Planck length cubed, which is the smallest measurable volume, at approximately 4.22×10105 m3 = 4.22×1099 cm3.[1] Therefore 2.4 cm3 contain about a googol Planck spaces. Only about 4×1080 cubic metres exist in the observable universe,[2] giving about 9.5×10184 Planck spaces in the entire observable universe; therefore, the number googolplex is about 10^{(googol-185)} /* rounding */ times larger than even the number of the smallest measurable spaces in the observable universe. If one Planck space is used to represent each digit of a googol, a mere 2.4 cm3 of volume gives us enough Planck spaces for that task - but there are not enough Planck spaces in the observable universe to represent a googolplex.

This is original research because the only source cited is a Wolfram Alpha page on Planck length. This qualifies as synthesis under WP:SYNTH (the editor was using sources to piece together an argument rather than simply drawing from a source). I removed this paragraph because it was the site of many disputed edits and does not have any other references. I don't see any value to this paragraph. Unless a WP:RS is found which would support the claims made in that paragraph, then it should not be included in the encyclopedia. Wikipedia is not an indiscriminate collection of information. – FenixFeather (talk)(Contribs) 05:42, 20 May 2014 (UTC)

  • By this argument, pretty much everything in the Size section should be trimmed, except for the first paragraph that directly references Dr. Sagan. Each of the other paragraphs are logical extensions from a single fact of measurement, such as this one is, by the reference to the Planck length. So where to stop trimming? All of this section (along with Scale, following it) is to give a scope of just how vast and big these numbers are. I am not saying we should keep this if it does not belong, but let's make sure that 1) everything that should be removed is and 2) the purpose of the size section is still preserved in the article. Nutster (talk) 13:31, 20 May 2014 (UTC)
  • @Nutster: If other parts of the section need to be removed, then so be it. That is not an argument for why this text should be kept. If there are no third party reliable sources that support the claims the article is making, then unfortunately it has to go. "Logical extension" is not good enough. Just because information is useful does not mean it belongs on the encyclopedia. It may belong better in alternative outlets, where such trivia is welcome. As for now, if there has already been so much confusion and dispute over this uncited segment of information, it is clear that it provides nothing useful. But it is deletable based on original research and synthesis alone, even if the information is valuable. – FenixFeather (talk)(Contribs) 15:10, 21 May 2014 (UTC)

Googolminex[edit]

The word googolminex sounds like original research and should probably be removed from the article. The only given citation for this word seems to be a broken link to some private website. If you search the web for the word googolminex, nearly all hits seem to be web pages which directly or indirectly copied their content from Wikipedia.--Googolplex2013 (talk) 18:00, 20 July 2014 (UTC)

@Googolplex2013: You're right, it doesn't seem like there is much mention of Googolminex in the literature. Only one hit on Google Scholar with only a listing of the term in the index. Doesn't seem notable to include in the article. – FenixFeather (talk)(Contribs) 04:12, 21 July 2014 (UTC)
    • ^ "Planck volume". Wolfram Alpha. 
    • ^ Cite error: The named reference wolframvolume was invoked but never defined (see the help page).