Talk:Googol

Picture

I feel the picture should be changed or removed as it seems to imply an an infinite sequence, like in the "0.999..." article. It should simply be replaced with "10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000", which is more informative, and less "OOO! DAT IZ A FUNKEE GRAFIK!!!11!".

Known Universe

Many folks dont understand that universe and known universe its different. They mean by "known universe" the part that can be seen by the Hubble telescope only. And the number of particles for this section only can be estimated very precisely. On the other hand, the whole universe is infinity, endless, meaning that there is no number that could represent the total number of atoms, or planets or galaxies in the universe. This is the real meaning of infinity and eternity. There are very big number like googolplex or (googolplex to the power of googolplex googolplex times). But even these unthinkable big numbers dont come any closer to infinity than number one is.

Most people actually believe space is curved in the fourth spacial dimension, like a hypersphere. Looping, but not infinite.

Junulo 21:15, 8 November 2007 (UTC)[reply]

Al osorio 07:27, 14 October 2007 (UTC)[reply]

Googol not accurate

The beginning of the article is not accurate, it says 10⁹⁹, == 1 with 100 zeros, this is not accurate, its eather 10*10⁹⁹ or 99 zeros , coz 10² =100, two zeros!!

The article is accurate and I believe you answered your own question. 10² is 100 which is one followed by two zeros. 10³ is 1000 which is one followed by three zeros. 10¹⁰⁰ is one followed by one-hundred zeros.

According to some scientists, a googol is probably greater than the number of atoms in the universe. Since this is also the number of zeroes in a googolplex, it would not be possible to write down or store this number (googolplex) in decimal notation, even if all the matter in the universe were converted into paper and ink or disk drives.

hang on, we do write this in decimal above don't we? Do we mean that a gp is greater than the no of atoms?212.42.97.53 11:49, 7 Oct 2003 (UTC)

A googol can be written in decimal, however a googolplex can not because it contains a googol number of zeros- meaning it has more zeros than all the atoms in the universe. Er.. but you probably knew that. I dunno. Evil saltine 11:57, 7 Oct 2003 (UTC)

Based on the assumption that there was a big bang, and that there was only one big bang, and that far away things have a different colour, and some kind of weird space observations, some think that there are less than a googol atoms in the universe. And even though the alien lord Fnord Meow Squeak told me otherwise, through the voices in my head, some stubborn people still think the universe is that small. Κσυπ Cyp 12:00, 7 Oct 2003 (UTC) (Posted via edit conflict.)

Well, 10^100=10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 so I guess I could write it down googol :) However to the point of this article, attempting to calculate the googolplex using Mathematica causes overflow error. Oh well.. mattabat

| --81.134.180.92 15:15, 4 Sep 2004 (UTC)

Adding the googolgon picture

I just put in the message about drawing a googolgon into this article now that googolgon is on its final day of Vfd and will probably have a consensus of re-directing here. Can anyone put in the picture?? 66.245.126.39 13:54, 19 Sep 2004 (UTC)

I finally put it in. Any comments about improving the googol article?? 66.245.19.157 16:45, 19 Sep 2004 (UTC)

Reverted Basekid25

It isn't necessary to note it is a 1 followed by 100 zeroes since that is at the very beginning of the article. Also it doesn't fit the category which is how to write a googol. The definition is already provided. --RoyBoy 22:50, 23 Dec 2004 (UTC)

Anonymous opinion about Googol

The googol is of no particular significance in mathematics, nor does it have any practical uses, other than to give you a sense of how powerful Google has become.

The first half of that might have merit, but since I heard of the term googol long before Google started (probably before I was aware of the Internet), the end is pure fantasy. - Cafemusique 11:46, 24 Jun 2005 (UTC)

Ditto -- but I still understand where this person is coming from. --Lenoxus

Particles in the Universe

"A googol is greater than the number of particles in the known universe, which has been variously estimated from 10^72 up to 10^87."

How do we know how many particles are in the universe? Is there a reputable source? It seems a bit preemptive to say that we know how many particles there are in the universe when we don't even know where most of the mass is!

A: Well, "googol" for sources:-) Parameters are:

Size of universe: some 10¹⁰ Lightyears => 10⁷⁹ m³
Density:
- either around a few particle per m³
- or using cosmological "critical density" 4.7 x 10^-27kg m³

The given range will easily accommodate for a lot of uncertainty. But notice that many numbers are nowadays around 1 googol. --Mipsy 08:28, 25 July 2005 (UTC)[reply]

Counting or Measuring?

Does a googol refer to a number of objects, "ordinals" so to speak, or to other concepts of size, using "real numbers"? In the latter case it is very simple to generate giant numbers by using tiny units...

Also I find the mentioning of pocket calculators confusing, as they have a limited precision of 10 digits max... They just use tricks with a logarithmic representation..

I have owned two calculators that retained more than 10 significant digits. The TI-57, 58 and 59 used 13 digits, and I believe the HP-15 did as well. Also the HP-45. Although I have not used a scientific calculator in many years, the reasons for those extra digits have not gone away. What is the market like now?Marzolian 04:32, 11 January 2007 (UTC)[reply]

Perhaps you could add a reference to Archimedes who invented large numbers 2200 years ago...The_Sand_Reckoner --Mipsy 08:28, 25 July 2005 (UTC)[reply]

What do you mean by "invented large numbers"? --Lenoxus 14:07, 2 June 2006 (UTC)[reply]

I don't think googol refers to either number of objects or concepts of size. I haven't read the book Mathematics and the Imagination, but as I recall one of my professors relating the story, the author's nephew was impressed by the sight of a very large number with many, many zeros, and blurted out the word "googol" to describe it. It's more of an emotional concept, rather than a precise mathematical concept. --Quicksilver^{T @} 07:02, 19 November 2005 (UTC)[reply]

Hmmm, I think someone's confusing the name for the object here. Yes, "gogol" is a nonsensical word, but it also happens to refer to a number which does exist in mathematics. Still, it is a great story, and I'm glad someone's sharing it somewhere. --Lenoxus 14:07, 2 June 2006 (UTC)[reply]

Googolhedron

I have removed the following section from the article:

A googolhedron is a three-dimensional shape bounded by 10¹⁰⁰ similar polygons. Because of this great many number of polygons, this shape would look very much like a sphere. Having this many sides or facets would make it smoother than any man made object. There can, however, never actually be a googolhedron because there are not a googol particles in the known (observed) universe.

This is nonsense. What should it mean? A regular googolhedron cannot exist (see Platonic solids), so that cannot be it. What is meant by similar poygons? In math, it means polygons of the same shape, but not necessarily of the same size. Did the author really mean that, or did (s)he mean congruent polygons (having the same size, too)? Either way, here's a googolhedron very unlike a sphere: Take half-a-googol isoceles triangles, each with a height about 0.1 googol times the base, and join them to form the sides of a pyramid with a regular half-a-googol-gon as its base (indistinguishable from a cone). Join two such pyramids base-to-base to form a googolhedron that is no way near a sphere.--Niels Ø 10:13, 30 September 2005 (UTC)[reply]

I removed the comment again; how smooth the googolhedron would be depends on how the faces are put together. User:Ben Standeven as 70.242.135.236 19:29, 20 December 2005 (UTC)[reply]

Mistake?

The article says:

The Internet search engine Google was named after this number. The original founders were going for 'Googol', but ended up with 'Google' due to a spelling mistake. Lawrence E. Page: "Lucas Pereira: 'You idiots, you spelled "Googol" wrong!' But this was good, because google.com was available and googol.com was not. Now most people spell 'Googol' 'Google', so it worked out OK in the end."

http://www.google.com/support/bin/answer.py?answer=487&topic=367 says:

The name "Google" is a play on the word "googol," which was coined by Milton Sirotta, nephew of American mathematician Edward Kasner. A googol refers to the number represented by a 1 followed by 100 zeros. A googol is a very large number. There isn't a googol of anything in the universe -- not stars, not dust particles, not atoms. Google's use of the term reflects our mission to organize the world's immense (and seemingly infinite) amount of information and make it universally accessible and useful.

More information about Google can be found at http://www.google.com/corporate/history.html

So was it originally a play on words or a spelling mistake? --Petros471 19:40, 20 December 2005 (UTC)[reply]

The date mistake

The article says that Milton Sirotta has coined the term in 1938. But the article on Milton Sirotta himself says that he was born in 1911 and thus invented the term in 1920. One of these can't be right!

I remember reading two other maths books which both state that Milton was 9 years old when he invented the term, so it is likely that the 1938 date is incorrect. However, keep in mind that there is a possibility that the Milton Sirotta article is incorrect and that he might have been born in 1929. -- Daverocks 12:58, 6 January 2006 (UTC)[reply]

Well, using google :) suggests that the invention date is 1938, so probably Milton Sirotta article is incorrect, and he was born in 1929.

Trivia mistake

The article claims (under trivia) that "If you drew a regular polygon with a googol sides that was 10²⁷ times the size of the known universe, it would still appear circular, even on the scale of a Planck length." I'm pretty sure this is wrong. The Planck length is about 10^-34m. A regular polyhedron with a googol sides would be formed from a googol isoceles triangles placed side by side (with a common top vertex), each one having a base angle of (10¹⁰⁰-2)π/(2*10¹⁰⁰). This gives a radius of around 10^-19m, while the radius of a proton is 10^-15m. Did I make a mistake, or should this be deleted? -- athaler 18:13, 28 March 2006 (UTC)[reply]

This annoys me enough that I've removed it. If someone can give me some explanation for why it's correct, then I will have no objections about restoring it. -- athaler 18:25, 28 March 2006 (UTC)[reply]

I haven't checked your math but I agree about removing that item. It seems a rather contrived example anyway. I think in the near future I'm going to add a reference to the trivia section concerning Avogadro's number (a huge number that's smaller than a googol) and possibly the third number of Ackerman's seqeuence (on the high end). Unless anybody objects. Kaimiddleton 22:15, 28 March 2006 (UTC)[reply]

Googol and google

This was added by someone to the top of the article in bold "Using this word "googol" Lary Page and Sergey named their company: Google! - Amber R. Marfatia". Was this vandalism or a legitimate edit? I don't think we need to mention that at the very top of the article. 24.127.224.173 16:12, 25 May 2006 (UTC)[reply]

Hard to tell. In either case it's an edit that does not fit. Googol is the number 10¹⁰⁰. This usage has been known for about 70 years. The connection to "google" is given later in the page. Kaimiddleton 22:50, 25 May 2006 (UTC)[reply]

Possible inconsistency

"Back when it was named in 1938, the googol was undeniably large. However, with the invention of fast computers and fast algorithms, computation with numbers the size of a googol has become routine. For example, even the difficult problem of prime factorization is now fairly accessible for 100-digit numbers."

If a computer can compute googol sized numbers, wouldn't it be possible to write a googolplex out then? Meaning a 1 followed by a googol zeros. According to the googolplex article, it's not possible. Someone clarify. Malamockq 18:48, 30 May 2006 (UTC)[reply]

I can work with numbers like 131 and 240 by writing only three digits. A computer needs only eight bits to represent these numbers. We can add them and subtract them, multiply and divide them, factor them, and so forth, with only a very few digits (or bits). But just because I can work with the number 240 doesn't mean I can write out a 1 with 240 zeros at the end. Maybe I don't have enough ink for that, or my page is too small, or I don't have enough time.

In much the same way, computers can easily add, subtract, multiply, and divide 100-digit numbers, because such numbers only require 335 bits or so to represent. Even I could add two 100-digit numbers together—it would take me two or three minutes, but it's not that hard. Give me a while longer and a lot of paper and I could probably multiply two 100-digit numbers together, though I would probably make some mistakes. But there's no way I can write a googol zeros. Even a computer cannot write a googol zeros. There aren't enough atoms in the universe to write on, and there haven't been anywhere close to enough nanoseconds since the Universe began. —Bkell (talk) 19:13, 30 May 2006 (UTC)[reply]

Of course, in theory (that is, ignoring the physical universe we live in), it would be possible for even a very slow computer to write a googolplex, as long as it could count to a googol (which would require about 335 bits of memory). I don't know what it would write on, and it would take just short of forever, but there are no theoretical reasons that writing a googolplex is impossible. But in reality we live in a finite universe, we don't have forever to wait, and we have only a finite amount of usable energy. These are the reasons it's impossible to write out a googolplex. —Bkell (talk) 19:19, 30 May 2006 (UTC)[reply]

Googol/Googolplex merge

Who chose this?? I think it might result in a large article. Check the size of how big an article will be. Georgia guy 19:46, 10 June 2006 (UTC)[reply]

I think this is a terrible idea. I see the articles as having two different characters:

googol is a somewhat basic idea mathematically. It is a huge number that can be rather easily explained. The mathematics, physics, chemistry and pedagogy that can be discussed in relation to it are not particularly deep. And of course there is the relation to the search engine.
googolplex is a second order concept. Some people can understand the idea of a googol without quite grasping a googolplex. In fact, it's quite difficult to think of real-world quantities of this magnitude. So the discussion and related topics are of a much deeper nature. Here there is no obvious association to Google, Inc.; although their corporate campus is termed the 'googolplex', this is not that widely known.

Let us not get caught up in merger-mania just because merging articles is possible. To merge googolplex into the googol article would dilute it's effect. I say let it stand as it is now as the separate and unique subject that it represents. Kaimiddleton 17:21, 19 June 2006 (UTC)[reply]

Googol bigger than the known particles in the universe?

What particles are we talking about here? Quarks? Mathmatically speaking, isn't there no such thing as the absolute elementary unit? What I mean is, a fraction can be infintely small, which is reflected in matter in the universe. Atoms, protons, not even quarks can be said to be the smallest, because they are all made up of something smaller. Malamockq 14:56, 9 August 2006 (UTC)[reply]

I think we're talking about protons and neutrons. The idea of "how many particles are there in the universe" goes back before the quark-gluon model, so traditionally folks are talking about the sub-atomic particles that were well known in the 1950s. That's my understanding. From there it's not too hard to do a few simple calculations that illustrate the orders of magnitude that are being discussed. Kaimiddleton 17:54, 9 August 2006 (UTC)[reply]

Yes, but my point is, while a googol might be larger than the amount of protons and neutrons in the universe, you can't say that a googol is larger than the amount of elementary particles in the universe because theoretically there are no elementary particles, as something would always be smaller. Malamockq 13:44, 11 August 2006 (UTC)[reply]

It depends on what theory you're using. I believe that current physical theories of the universe state that quarks (and leptons?) are fundamental particles and cannot be divided, so you cannot have "half an electron", for example. Also, even if the "particles" referred to are protons and neutrons, counting quarks will only increase this by a factor of three, certainly not enough to bring the count up to a googol. —Bkell (talk) 15:53, 11 August 2006 (UTC)[reply]

I don't believe theories state that quarks can't be divided or aren't made up of smaller particles, they are simply the smallest particles discovered thus far due to our current understanding of such things. Malamockq 15:02, 15 August 2006 (UTC)[reply]

The Standard Model says that quarks, leptons, and gauge bosons are elementary particles. If these particles are found to be made up of yet smaller particles, then we will have to come up with a new theory to replace the Standard Model. Therefore, this widely held theory does state that quarks cannot be divided.

In any case, the argument that things should be infinitely divisible because mathematics works that way ignores the fact that mathematics is not a perfect model of the universe. Read about the Planck length and the Planck time, for example; length is not infinitely divisible, at least not in a physically meaningful way, and neither is time. If two events are separated by less than one Planck time, they can be considered to happen simultaneously. Electric charge is another property that is not infinitely divisible; you can't have an electric charge less than the elementary charge (or a third of the elementary charge, if you count the fractional charges of quarks). —Bkell (talk) 20:40, 15 August 2006 (UTC)[reply]

Googol "ill-named"

I removed this from the article:

Many people feel that googol is ill-named, because numbers are named every three decimal places. Googol, however, is named at 10,000,... making some people think that googol should be one followed by 99 zeros to make its nameng correct.

I have a degree in math but I've never heard this criticism, either from teachers, peers or students. If this feeling that googol is ill-named is widespread and documentable, then I think it would bear mention in the article, otherwise, my opinion is that it's not notable. However, to enhance clarity in the article, I think this phrase or something similar would be appropriate if someone wants to add it in a strategic location: "...so googol has 101 digits." Kaimiddleton 19:27, 1 September 2006 (UTC)[reply]

The Shrinking Googol

This section reads:

Back when it was named in 1938, the googol was undeniably large. However, with the invention of fast computers and fast algorithms, computation with numbers the size of a googol has become routine. For example, even the difficult problem of prime factorization is now fairly accessible for 100-digit numbers. Computations of a googol steps are still completely out of reach.

I emphasized the last sentence: how would it be even theoretically possible to do a googol steps? Are we talking quantum computation? Is even that plausible? And, importantly, do we have a citation for this kind of claim? Kaimiddleton 01:16, 1 November 2006 (UTC)[reply]

Importance of Kasner's religion?

The text currently reads: "... of Jewish American mathematician Edward Kasner" Is it relevant to mention his religion at all? Is there something different about Jewish mathematics? Marzolian 04:37, 11 January 2007 (UTC) I see that his religion has been deleted. I think it's a good idea.Marzolian 05:24, 2 February 2007 (UTC)[reply]

Contradiction between "Googol" and "Googolplex" articles

The Googol article says that the term "googol" was coined in the 1920s, while the Googolplex article says it was coined in 1938! What am I supposed to do now!? vilem 20:31, 28 January 2007 (UTC)[reply]

Lokking at Edward Kasner#Googol, the confusion seems to be between Milton Sirotta's coining of the term in about 1920 and Kasner's use of it in a book published in 1940. I'll correct Googolplex accordingly. --Mel Etitis (Μελ Ετητης) 10:09, 29 January 2007 (UTC)[reply]

Awesome. Wikipedia saves itself again...--Lenoxus 16:18, 29 January 2007 (UTC)[reply]

Date of coining

There seems to be a little confusion over exactly when the term was coined. This link (found in the "External links" section) states the date to be 1938, which is what I changed it to when I thought I was reverting vandalism. Are there any definite sources on it, or is the exact year a matter of speculation? Robotman ¹⁹⁷⁴ 11:57, 10 March 2007 (UTC)[reply]

Oh, for crying out loud. I just saw the comments directly above this. I'll fix it. Robotman ¹⁹⁷⁴ 11:58, 10 March 2007 (UTC)[reply]

Not to worry — easily done. (I got there before you with the fixing.) --Mel Etitis (Talk) 12:49, 10 March 2007 (UTC)[reply]