2.1.7 - Largest Numbers Theoretically Possible
2.1.7
The Largest Numbers theoretically possible
in Modern Cosmology
Go Back Home
Return to Section 2 - 1
PREV>> 2.1.6 - Even Larger Numbers In Science and Astronomy
We are now going to take the ideas set up in the previous article to the extreme. If one combines various facts and theories from well known science, one can produce very large numbers ! Much larger than most people realize. We've already seen that these numbers can easily exceed a googol, but just how far can we go ? What is the largest number that could theoretically represent a physical quantity ? We still have a long way to go ...
ONE NOVEMDECILLION VIGINTILLION VIGINTILLION
10^186
Unsexagintillion = 10^186
As stated before, the if the universe continues to expand, the volume could become even larger !
Currently we live around 15 billion years after the big bang. The volume of the universe 150 billion years after the big bang would be 47 novemdecillion vigintillion vigintillion cubic planck lengths !
ONE VIGINTILLION VIGINTILLION VIGINTILLION
10^189
Duosexagintillion = 10^189
The volume of the universe 1.5 trillion years after the big bang would be 47 vigintillion vigintillion vigintillion cubic planck lengths.
ONE THOUSAND VIGINTILLION VIGINTILLION VIGINTILLION
10^192
Tresexagintillion = 10^192
The volume of the universe 15 trillion years after the big bang would be 47 thousand vigintillion vigintillion vigintillion cubic planck lengths.
ONE MILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^195
quattuorsexagintillion = 10^195
The volume of the universe 150 trillion years after the big bang would be 47 million vigintillion vigintillion vigintillion cubic planck lengths.
ONE BILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^198
quinsexagintillion = 10^198
The volume of the universe 1.5 quadrillion years after the big bang would be 47 billion vigintillion vigintillion vigintillion cubic planck lengths.
ONE TRILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^201
sexsexagintillion = 10^201
The volume of the universe 15 quadrillion years after the big bang would be 47 trillion vigintillion vigintillion vigintillion cubic planck lengths.
ONE QUADRILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^204
septensexagintillion = 10^204
The volume of the universe 150 quadrillion years after the big bang would be 47 quadrillion vigintillion vigintillion vigintillion cubic planck lengths.
ONE QUINTILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^207
octosexagintillion = 10^207
The volume of the universe 1.5 quintillion years after the big bang would be 47 quintillion vigintillion vigintillion vigintillion cubic planck lengths.
ONE SEXTILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^210
novemsexagintillion = 10^210
The volume of the universe 15 quintillion years after the big bang would be 47 sextillion vigintillion vigintillion vigintillion cubic planck lengths.
ONE SEPTILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^213
septuagintillion = 10^213 ( from the latin word "septuaginta" meanging 70 )
The volume of the universe 150 quintillion years after the big bang would be 47 septillion vigintillion vigintillion vigintillion cubic planck lengths.
ONE OCTILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^216
unseptuagintillion = 10^216
The volume of the universe 1.5 sextillion years after the big bang would be 47 octillion vigintillion vigintillion vigintillion cubic planck lengths.
ONE NONILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^219
duoseptuagintillion = 10^219
The volume of the universe 15 sextillion years after the big bang would be 47 nonillion vigintillion vigintillion vigintillion cubic planck lengths.
ONE DECILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^222
treseptuagintillion = 10^222
The volume of the universe 150 sextillion years after the big bang would be 47 decillion vigintillion vigintillion vigintillion cubic planck lengths.
ONE UNDECILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^225
quattuorseptuagintillion = 10^225
The volume of the universe 1.5 septillion years after the big bang would be 47 undecillion vigintillion vigintillion vigintillion cubic planck lengths.
ONE DUODECILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^228
quinseptuagintillion = 10^228
The volume of the universe 15 septillion years after the big bang would be 47 duodecillion vigintillion vigintillion vigintillion cubic planck lengths.
ONE TREDECILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^231
sexseptuagintillion = 10^231
The volume of the universe 150 septillion years after the big bang would be 47 tredecillion vigintillion vigintillion vigintillion cubic planck lengths.
ONE QUATTUORDECILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^234
septenseptuagintillion = 10^234
The volume of the universe 1.5 octillion years after the big bang would be 47 quattuordecillion vigintillion vigintillion vigintillion cubic planck lengths.
ONE QUINDECILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^237
octoseptuagintillion = 10^237
The volume of the universe 15 octillion years after the big bang would be 47 quindecillion vigintillion vigintillion vigintillion cubic planck lengths.
ONE SEXDECILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^240
novemseptuagintillion = 10^240
The volume of the universe 150 octillion years after the big bang would be 47 sexdecillion vigintillion vigintillion vigintillion cubic planck lengths.
ONE SEPTENDECILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^243
octogintillion = 10^243 ( from the latin word "octoginta" meaning 80 )
The volume of the universe 1.5 nonillion years after the big bang would be 47 septendecillion vigintillion vigintillion vigintillion cubic planck lengths.
ONE OCTODECILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^246
unoctogintillion = 10^246
The volume of the universe 15 nonillion years after the big bang would be 47 octodecillion vigintillion vigintillion vigintillion cubic planck lengths.
ONE NOVEMDECILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^249
duooctogintillion = 10^249
There is a theory about the stability of sub-atomic particles which provides a theoretical half-life for the proton. Most sub-atomic particles can only exist for very tiny fractions of a second before decaying into other lower energy sub-atomic particles. Neutrons and protons are the 2 lowest energy baryons that exist. Because of this , high energy particles will often decay into a group of these ( along with electrons and neutrinos ). Neutrons and protons are relatively quite stable. Neutrons will not decay as long as they are within an atomic nucleus. However a free-neutron is said to have a half life of about 5 minutes. This is a virtual eternity by particle standards ! What this means is that for every 5 minutes the neutron is free there is a 50:50 chance it will decay into a proton and electron.
Protons have never been seen to decay. Does that mean that protons alone are eternal ? Well there is a theory that states that the half-life of the proton may be about 10^32 years ! This is an increadibly long period of time. The universe is only 15 billion years old, that is , it is about 10^10 years old. But protons can exist billions of billions of times longer than this !
If this theory is true, then it puts definite limits on how long the universe can "live". How so ? Eventually everything would decay to fundamental particles, such as protons and electrons. After 10^32 years however, there is a 50:50 chance that each on of these particles will decay. The theory says that the proton will literally decay into nothing ! Actually it says it will decay into pure energy. This means that after 10^32 years, half of the universes matter will cease to exist. After every succeeding 10^32 years, the remaining matter in the universe will again be halved. Just how long can this go on ? let's find out ...
The volume of the universe 10^32 years after the big bang would be 14.1 novemdecillion vigintillion vigintillion vigintillion cubic planck lengths. The mass of the universe would be about half of what it is now.
ONE VIGINTILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^252
treoctogintillion = 10^252
The volume of the universe 10^33 years after the big bang would be 14.1 vigintillion vigintillion vigintillion vigintillion cubic planck lengths. The mass of the universe would be less than 0.1% of what it is today.
ONE THOUSAND VIGINTILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^255
quattuoroctogintillion = 10^255
If we continue this theoretical trend indefinitely, then eventually the universe will gradually evaporate into nothingness. As the remaining mass is repeatly halved every 10^32 years, the remain mass will eventually contain only a handful of sub-atomic particles. Eventually only a single particle would be left, and sooner or later this particle would finally vanish marking the death of the physical universe. Assuming that there is roughly 10^78 sub-atomic particles is the universe, this process would take about 260 half-lives for the universe to completely fade out of existence. This means the death of the universe is scheduled sometime around 2.6x10^34 years after the big bang. It may seem depressing to think of the universe finally coming to an end, but keep in mind this is a ridiculously long period of time. In comparison the universe is still in it's embryotic state.
The volume of the universe 2.6x10^34 years after the big bang would be 249,369 vigintillion vigintillion vigintillion vigintillion cubic planck lengths.
To put this into perspective, this means that the total volume of the universe at the "end of time" would be roughly 10^72 times greater than it is today ! In otherwords the universe today is nothing but a pinpoint compare to what it will grow to by the time it reaches it's end.
Alright, now we must definitely be at the end, right ?! Well ... if we are willing to be open minded, there is still one more trick that can allow for even greater quantities. We haven't considered "time" yet.
Recall that I said at small enough scales, do to quantum effects, that the space-time fabric becomes severely distorted to the point where measurement on smaller scales is impossible. We can call this the "Planck scale". But this effect doesn't just effect space, it also effects time. This means that not only is there a smallest measurable distance, but there is also a smallest measurable duration of time. This duration, called a "Planck time" is roughly 10^-43 seconds. It is said that cosmosologists are unable to explain what happened before 10^-43 seconds after the big bang because the laws of physics break down.
So we have measured space using the smallest measurable unit of distance. But now consider, that space-time fabric itself could be measured using a smallest possible unit of "space-time".
What would this be ? A cubic planck length times a planck time ( Pl^3 x Pt ). We will call this the quartic planck unit. Note that this unit is 4-dimensional, just like the fabric of space-time.
Now we want to know what the entire "hyper volume" ( amount of 4-dimensional space) of the space-time continuum is in quartic planck units. Factoring in an expanding universe, this number ends up being a ways off. The following powers of 1000 are listed here for reference purposes...
ONE MILLION VIGINTILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^258
quinoctogintillion = 10^258
ONE BILLION VIGINTILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^261
sexoctogintillion = 10^261
ONE TRILLION VIGINTILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^264
septenoctogintillion = 10^264
ONE QUADRILLION VIGINTILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^267
octooctogintillion = 10^267
ONE QUINTILLION VIGINTILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^270
novemoctogintillion = 10^270
ONE SEXTILLION VIGINTILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^273
nonagintillion = 10^273 ( from the latin word "nonaginta" meaning 90 )
ONE SEPTILLION VIGINTILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^276
unnonagintillion = 10^276
ONE OCTILLION VIGINTILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^279
duononagintillion = 10^279
ONE NONILLION VIGINTILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^282
trenonagintillion = 10^282
ONE DECILLION VIGINTILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^285
quattuornonagintillion = 10^285
ONE UNDECILLION VIGINTILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^288
quinnonagintillion = 10^288
ONE DUODECILLION VIGINTILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^291
sexnonagintillion = 10^291
ONE TREDECILLION VIGINTILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^294
septennonagintillion = 10^294
ONE QUATTUORDECILLION
VIGINTILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^297
octononagintillion = 10^297
ONE QUINDECILLION
VIGINTILLION VIGINTILLION VIGINTILLION VIGINTILLION
10^300
novemnonagintillion = 10^300
ONE CENTILLION
10^303
centillion = 10^303
One Centillion is the largest officially recognized illion, and can even be found in dictionaries with the precise definition of being equal to 10^303. Like the "Googol", this number is regarded as too large to represent anything "real". Yet we still have alittle more to go before we hit the limits of physics ...
ONE THOUSAND CENTILLION
10^306
uncentillion = 10^306
ONE MILLION CENTILLION
10^309
duocentillion = 10^309
ONE BILLION CENTILLION
10^312
trecentillion = 10^312
ONE TRILLION CENTILLION
10^315
quattuorcentillion = 10^315
ONE QUADRILLION CENTILLION
10^318
quincentillion = 10^318
ONE QUINTILLION CENTILLION
10^321
sexcentillion = 10^321
ONE SEXTILLION CENTILLION
10^324
septencentillion = 10^324
ONE SEPTILLION CENTILLION
10^327
octocentillion = 10^327
ONE OCTILLION CENTILLION
10^330
novemcentillion = 10^330
ONE NONILLION CENTILLION
10^333
decicentillion = 10^333
ONE DECILLION CENTILLION
10^336
undecicentillion = 10^336
ONE UNDECILLION CENTILLION
10^339
duodecicentillion = 10^339
We've finally reached the limits of numbers that represent measurable quantities ...
The hyper-volume of the entire space-time continuum, from the birth to the death of the known universe, is 507.47 undecillion centillion quartic planck units ( 5.0747x10^341 Pl^3 Pt ).
Using the "unofficial nomenclature" we can say that this is 507.47 duodecicentillion quartic planck units.
We have now measured the entirety of known existence with the smallest possible units of measurement. Not only is this number much much greater than a googol, it is also greater than a Centillion. This means that these numbers, which were previously considered fantasticly unrealistic, are potentially just as real as the more familiar numbers. We have demonstrated that by restricting ourselves to theoretical physics, we can still generate huge numbers with tangable meanings. Back in 2004 I was already aware that the volume of the universe was about 10^183 cubic planck lengths. But it was only recently that I thought to measure the space-time fabric. Originally I wasn't even going to factor in the expansion of the universe, but factoring this in increases the figure by many magnitudes. Even I didn't think it would manage to pass up a centillion !!
But now we really have reached the limits of tangible numbers. Numbers that represent countable physical objects, or measurable quantities.
------------------------------------------------------------------------------------
CONCLUSION
So what are we to learn from this ?
Firstly, we should take numbers like a googol and centillion more seriously, and not just assume that they are purely whimsical and meaningless. We should also come to the conclusion that the universe is WAY bigger than most people realize !
But there is another important point I wanted to make. Did you notice that the headings were purely made of combinations of official illions ? For example , One quindecillion vigintillion vigintillion vigintillion vigintillion would be 10^300. This is a very long name for such a number. Based on adapting latin however, we can simply give this number a unique illion name, novemnonagintillion. Basically that means it's the "99th illion". This name is readily available and more sensible than quindecillion vigintillion vigintillion vigintillion vigintillion. And one can not argue that such numbers don't occur in science.
The point is, there really is no valid reason not to include a proper set of illions to fill the gap between vigintillion and centillion. Not when such a set is already well established and sensibly constructed.
The problem is that scientists, the ones who really make use of numbers this large on a regular basis, use scientific notation to handle such numbers. And the common people ( who like to use names for numbers ) rarely need numbers larger than a trillion to get along in life. None the less, these numbers do exist, and there seems little reason to deny them their own names.
After all, what are the alternatives. Are we really happy with calling these numbers things like "10 to the 273 ". Furthermore, scientific notation is about magnitudes, it was not intended to facilitate counting, or providing names for numbers. What are we to call " 14 treoctogintillion 2 trillion". Scientific notation will simply round this off as 1.4x10^253 or we would need to invent some way to combine scientific numbers, perhaps with " 14x10^252 + 2x10^12" which would read "14 times 10 to the 252 plus 2 times 10 to the 12", which actually takes longer and is arguably more confusing.
But it's not easy to figure out what power of 10 , treoctogintillion is ?
True. But then why do we need to think of it as a power of 10. The name simply means that there are 83 groups of 3 zeroes after the first 3 zeroes.
In other words treoctogintillion = 1,000,000,000,000,000, ... ... ... ... ,000,000,000,000,000
where there are 83 groups of 3 zeroes, plus the last 3 zeroes.
This works just as well to convey the magnitude of these numbers than any other method ( after all, these numbers are so huge and remote, no illustration really serves to make the magnitude sink in ).
Of coarse one does have to translate the latin "treoctoginta" into "83" mentally, but that's just a matter of alittle practice.
But scientists have no use for such labels, and they are inconvienent for calculation ...
I'm not saying that scientific notation isn't very useful, or that scientists shouldn't use it. Of coarse scientific notation is an art of calculation, and is designed solely for that purpose. So naturally it is much better to work with than the illions names. But who says that I'm talking about scientists using such labels. I'm talking about ordinary people who like numbers to have names.
Why this abritrary cut off point at a vigintillion ? After all, a vigintillion is rarely used, and one could argue that it is no more useful than treoctogintillion. Why did anyone even bother to provide names past a trillion ? If scientific notation is so useful, why do we need such well established names like sextillion, septillion , octillion ,nonillion, decillion ,undecillion ,duodecillion , etc.
And perhaps most absurd, why name a "centillion". What possible use could such a number have had when it was first coined ? Why the tremendous gap between it and a vigintillion ?
But it is a waste of time and energy naming such numbers ?
Perhaps, but does it really take that much time an energy to name them ? Not really. Simply adapt the latin numbers, ( this is no more difficult that learning to count to a hundred in latin ) and you have an established way to name every power of a thousand from 1 to 101. If we can be bothered to learn numbers like ,...
one , two , three , four , five , six , seven , eight , nine , ten ,...
why is it so much more work to learn the latin prefixes such as ...
un , duo , tre , quattuor , quinqua , sex , septen , octo , novem , decim , ...
After all Chuquet, the guy who originally coined the terms billion , trillion , etc. went as far as nonillion without any inkling that these number names would be useful. In fact, they were regarded as trivia for a long time and ignored. Even a "billion" took a long time to be accepted, because people back then didn't use numbers like that too often.
Such names were never created solely for practical reasons. People come up with them because they spring to the mind easily, and perhaps because secretly we suspect that even if we have no use for them now, they may come in handy later. And finally because they are just fun to make up. After all, the centillion was probably coined simply because it could be formed by combining the latin word "centim" for 100 , with -illion, and coined purely for kicks. But now I've shown that numbers as big as this can occur in cosmology, which means they are more than some mathematical pass time.
And what is the alternative ? What if we do want to have some kind of name for these numbers, but restrict ourselves only to the official illions. Then we are forced to use repetitions.
Even many science books, written for the general public, rarely use words like a quintillion. Instead the authors fall back on familiar terms like " a billion billion " ( similiar to the way people didn't like using million but prefered "thousand thousand" when the term was first coined ).
Just recently I saw a "quadrillion" in print. It was in a book called " 10 questions science can't answer (yet)" published in 2007. I was surprised to see a name above trillion being used, but then given the expected readers (ie. myself for example ) it's not surprising he expected his audience to be familiar with the name. Yet even this author seemed to systematically avoid any name above "quadrillion", even when such larger names could have been easily employed.
So even the "official illions" are promptly ignored. But using repeated names is not very practical either. For example, if a science writer wants to convey to ordinary people the size of something like 10^78 he would have to use something like " a million trillion trillion trillion trillion trillion trillion ". This is not uncommon to see in print, but as a "naming convention" it's not very reasonable.
Why this silly resistence towards larger illions ? Are they really all that confusing ?
But most people are never going to remember what a septenseptuagintillion is ?
That is a valid point. Most people have limited interest in math and science, and aren't going to be bothered to remember such a naming convention that has only limited applicability. But then, when do ordinary people speak about decillions and vigintillions in public ? Do you think the people who first coined these terms were worried about their use being wide spread ? Of coarse not. They were invented to be used by those who would find them interesting ( perhaps they considered these of some use to scientists ). Take the SI units for example, most people know about a kilo and milli, but only a few people are interested to know about yotta and yocto. They weren't created for general use, but instead for scientists to use "at their convience", meaning when and if they choose to.
The higher illions don't have to be for everyone. They should be there for the interested, and regarded as specialized knowledge, or at least as trivia. Also, there use does not have to be wide spread in order for them to be legitimate. Again, such terms should be there for "convience". It doesn't mean these terms are to be forced on anyone, but simply that they will be available to anyone interested in making use of them.
So maybe there isn't a strong objection, but can you make a case for their neccessity ?
That actually is the best counter-arguement I can think of. Yes, maybe there aren't very good reasons not to extend the illions, but then is there any good reason to do so ? It is true that their "usefulness" lies on a very thin band between "science" and "enthusiast". People would probably get along just fine without all these extra -illions, and of coarse they have.
But I can't help but feel that the system should be extended and sanctioned for the sake of completeness. Why invent a partial system , especially when a full system is so easy to construct from the latin , and when it's been shown that these numbers do seem to represent real quantities ?
Also, there are people who find these kinds of names appealing. Many people's fascination to large numbers seems to border somewhere between a "hobby" and an "obsession". So however narrow the spectrum, there is a 'want' if not a genuine 'need' for such number names. If the hobbyists want to treat a unvigintillion like it's a real name, then why deny them that right just because some governing body thinks it's "not established".
Actually this same issue arrises in any esoteric subject matter. For example, in the study of higher dimensions, there are many "hobbyists" who like to give names to distinct higher-dimensional objects. The term "polychoron" is used to refer to the 4-dimensional analog of "polyhedron". Yet this term is not recognized in professional math circles. Yet one finds this name used regularly by a small but noticable group of individuals who are neither professional mathematicians nor mere diletantes either. There are other names too, such a "glome" used to refer to a 4-dimensional sphere. As is often the case, there is a severe lack of alternatives from the professionals. The "glome" can simply be called a "4-sphere", and the polychorons are simply "4-space figures". Note very interesting names. Since there is a lack of good names for these things, why is it that the people who study these things seriously aren't openly adopting these terms? The reason is that to them such names are trivial. As long as they know what they are talking about, and other professionals do as well, the actual name is unimportant. Also there is a different emphasis. The professionals are interested in the deeper mathematics underlying the objects, where as the hobbyists are interested in the objects themselves.
But does the interests of one group out weigh the other ? Each group has its own subject matter and develops it's own specialized terminology to deal with it. Perhaps some subjects seem more important than others, but then as humans we hardly care solely about important matters. We often find ourselves immersed in trivial ones as well.
Perhaps the subject of large numbers is nothing more than a hobby. That means it's adherents are no more unusual than people who collect bottle caps, stamps, marbles, are other trivial trinkets. The difference here however is that the objects are purely conceptual.
This theme will be revisited again much later when we learn more about large numbers. I will also be revisiting the precarious existence of the larger illions and unofficial illions in a later chapter which will devote much more attention to their origins and development.
------------------------------------------------------------------------------------
NOW WHAT ?
So were done with tangable numbers, right ? That depends on what you consider "tangable". Let's say for argument sake that "tangable" refers to physically measurable quantities. In this case we have reached a limit of "tangability". But that doesn't mean that even larger numbers don't still have practical applications in science. What am I talking about ?
Even larger numbers can arrise in the studies of statistics, probability , and combintorics. If we are willing to consider "the number of ways a set of objects can be arranged", or "the number of ways an event can play out" as something real, then yes, much much larger numbers can still be of scientific use, and possess a kind of "reality" to them.
In the next article, we begin anew and explore large numbers that occur in probability and combintorics. As we will see, these numbers quickly pass up the largest numbers we have yet considered !
Read on to learn more ...
Go Back Home
Return to Section 2 - 1
NEXT>> 2.1.8 - Larger Numbers in probability, Statistics, and Combinatorics