The Pointless Gigantic Timeline of Large Numbers
THE POINTLESS GIGANTIC TIMELINE OF LARGE NUMBERS
by Cookie Fonster
Introduction
Given that my site has a massive list of numbers, I feel it would be good to also have a list of dates in which events related to large numbers, i.e. a history of large numbers. I think this is important because no field, no matter how obscure it is, is complete without some known history. So I present to you, the Pointless Gigantic Timeline of Large Numbers, aiming, similarly to my list of numbers, to comprehensively cover the history of googology out there, beginning with the origins of numbers.
So let’s get started with the origins of life, which is important because without life there are no beings to perceive and work with numbers.
This timeline is updated frequently, so be sure to take a look for new events now and then.
The Innate Era
3,800,000,000 BC ~ 33,000 BC
Events: 6
3,800,000,000 BC
Life begins on Earth
This is the time life on Earth started. This is important because if there is no life on Earth, then there is no knowledge or even intimacy of numbers, and therefore no googology. Therefore I decided to start my timeline here.
Of course, it’s needless to say that life didn’t spring out with a knowledge, awareness, or even implanted sense of numbers. It’s a few billion years of evolution that allowed that.
542,000,000 BC
First animals
After some 3.3 billion years, finally animals evolve. Animals are known for being far more advanced than any other organisms, and the ones that can really know and feel numbers. Of course, the first animals were very primitive, almost certainly not having a sense of numbers beyond the innate one, two, three, and maybe four.
225,000,000 BC
First mammals
About 300 million years after the first animals, mammals, the most advanced type of animals, first evolved. This is important because mammals are the ones that are really sentient and can think for themselves, and therefore the ones that can create ways that they are able to recognize numbers beyond the building blocks of one, two, three, four, and maybe five or six.
55,800,000 BC
First primates
Not too long after the dinosaurs were wiped out 65 million years ago, the first primates evolved. Primates, as we know, are the mammals most like us humans, and the most advanced mammals. Many primates have demonstrated very human-like intelligence, and those are the types of organisms that will really work with numbers.
Whoa now. This seems more like a biology timeline than a googology timeline! Why is that?
Because the very origins of googology must necessarily lie within life itself and the onset of recognizing numbers. Don’t worry, soon we’ll really get to the history of numbers as numbers.
5,000,000 BC
Start of humanoid organisms
5 million years ago is usually given as the start of humanoid organisms. Though this designation is arbitrary, this makes sense because this is the point where the organisms are becoming really human-like. Needless to say, with that event life became one step closer to googology.
200,000 BC
First anatomically modern humans
This is the time where humans really became anatomically modern, with the first beings now known as Homo sapiens. Those humans are the ones that are destined to start using large numbers, and things really blast off from here with the start of denoting large numbers.
By large numbers, here I mean numbers larger than what humans can recognize at once - the lower limit of such numbers varies from place to place, but in my idea the smallest such number is probably seven. Seven as the smallest such number isn’t too important, but the usage of such numbers is very important.
The Numeral Era
33,000 BC ~ 290 BC
Events: 9
33,000 BC
First known record of mathematics: The Lebombo Bone
At this time, humanity was still quite primitive. Humans were just starting to spread from outside Africa, and they were all still hunter-gatherers with no knowledge of agriculture. However, one thing they certainly did have was a dawn of some mathematics.
That mathematics was found on the Lebombo Bone, a bone discovered on the Lebombo Mountains between South Africa and Swaziland. Sources vary on what how old it is, and the dates vary from 30,000 to 43,000 years ago.
What is that bone? It is the fibula of a baboon, a broken bone with twenty-nine notches in it. We have no way of knowing what the bone was used for, but it was almost certainly used to record something, perhaps members of a tribe or animals killed. Maybe it was used as a calendar of some sort, because the 29 notches may signify the ~28 days in a lunar month. However, that calendar idea is debatable because the bone had part of it broken off.
In any case, the Lebombo Bone is a very interesting artifact because it signifies very early mathematics. What’s especially interesting is that people used it to document numbers of things definitely beyond numbers like one, two, and three that they could innately recognize. And better yet, the bone was tens of thousands of years earlier than recorded history!
18,000 BC
The Ishango Bones
The Ishango Bones are a group of bones that were also found in Africa, estimated to be around 20,000 years old. That makes them somewhat younger than the Lebombo Bone.
The Ishango Bones, like the Lebombo Bone, have many notches, and have clearer usage of not just tallying something, but actually performing calculations! Historians have extensively analyzed those bones’ marks, and found logical relation between the marks and calculations of addition.
The Ishango Bones therefore represent advancement in mathematics, from merely tallying to actually calculating. In some sense the Ishango Bones are a lot more mathematical than the Lebombo Bone. Therefore this represents a major step in googology to calculating numbers.
11,000 BC
Beginnings of agriculture
This is around the time of the first farming in our world. This is important to googology because agriculture relied on mathematics a lot, more so than hunting. Therefore, mathematics at this point was gaining some more use in our world.
3400 BC
The Sumerian civilization
Now let’s go to the Sumerians, among the very oldest civilizations, and the first with a numeral system. Their system used 60 as a base, with a systematic system of symbols for numbers 1 through 59. After that, place value was used, and numbers became somewhat ambiguous in usage. For example, since there was no symbol for 0, there was no way to write the number 60.
Nevertheless, this is sanother important step, because these numerals can name FAR FAR LARGER numbers than just tally marks on bones. I can’t help but think that some Sumerian scribe began to imagine larger and larger numbers with place values. For example, with just 57 “59” symbols, we can reach over 59^57, which is about 8*10^100, which is already more than a googol!
The Sumerians also had the first system of weights and measures. This is also a useful application of mathematics, and it connects with the usage of base 60.
So all in all, the Sumerian numerals were revolutionary to googology, and paved the way for some great numeral sytstems.
3100 BC
Egyptian numerals
Ancient Egypt likely had the first purely 10-based numeral system. In that system, there were symbols for one, ten, 100, 1000, etc, up to a man raising his hands up in astonishment for a million. To show how this system works, let’s say | is the symbol for 1 and n is the symbol for 10.
Then:
1 is |
2 is ||
3 is |||
...
9 is |||||||||
10 is n
11 is n|
12 is n||
...
20 is nn
etc.
That system is notable for two reasons. First, it’s the first system that is really based on ten, and ten is by far the most common base in our world.
But the second reason is more interesting. The man raising his hands in astonishment, used to denote a million, was often used to denote any large number. Interestingly, that’s very analogous to how we often use “million” to mean any large number today. Therefore, Egypt can be seen as the first place where large numbers were used for hyperbole!
However, that system is a little different from our numeral system, because this really isn’t a place value system like our modern system and the Sumerian system. However, it’s still another step up for noting numbers.
2700 BC
The abacus
Mesopotamians invented the abacus somewhere around 2700 BC. The abacus is notable because it is a machine to perform quick calculations. It is the ancestor of the calculator, an essential tool in advancing mathematics. The calculator further evolved to computer mechanisms, as we will see with things like calculating large primes, or the terminating digits of Graham’s number. Those are notably pretty relevant to googology.
2589-2566 BC
The Great Pyramid of Giza
This is the time during which the Great Pyramid of Giza was built. The pyramid has a perimeter of 1760 cubits and a height of 280 cubits, and dividing 280 into 1760 gives us 6.2857, which approximates twice pi. Therefore, some Egyptologists concluded that the Egyptians had knowledge of that super-important constant. Assuming the ratio's proximity to 2π is not a coincidence, this might be the earliest use of pi by humanity, though there are records with more solid evidence of intentional use of pi that lie later in our history.
1750 BC
Babylonian numerals
Around 1750 BC Babylonians devised a base-60 numeral system, borrowed from the Sumerian system about two thousand years earlier. Babylonians are also usually credited for coming up with the idea that a minute is 60 seconds and an hour is 60 minutes
300 BC
Roman numerals
Almost everyone knows what Roman numerals are. Some time around 300 BC they first evolved in Ancient Rome. The system, as you probably know, is similar to the Egyptian numerals but more systematic. It has the symbols I (1), V (5), X (10), L (50), C (100), D (500), and M (1000). Of course, those symbols didn’t go like that right off the bat, but rather evolved from a system that wasn’t quite as nice.
The cool thing about Roman numerals is that in some contexts they’re still used today. For example, the pages in introductions of many books are numbered with Roman numerals while the rest of the pages are numbered with our usual numerals. Also, titles of books, movies, games, etc, often make use of the small Roman numerals (e.g. III instead of 3).
The Naming Era
290 BC ~ 1484
Events: 11
250 BC
The Sand Reckoner
Around 250 BC (give or take 40 years), Archimedes published a book, The Sand-Reckoner. In his book, he devises a large number system to extend upon the Greek system, and uses it to estimate the number of grains of sand that would fill up the universe. The largest number he named was 108*10^16, or 1 followed by a whopping eighty quadrillion zeros!
In some sense, this is the first googology, naming large numbers for the sake of largeness, so large that they’re well above practical use in the real world - at the time there was almost no use for numbers larger than a million. It’s also the first event Googology Wiki lists on its timeline on googology.
Therefore, I feel The Sand Reckoner is a turning point in googology, and thus the start of a new era. I think the “naming era” is a suitable name for that time period, because that was the point when people really bothered to name big numbers.
250 BC
Olmec usage of zero
While Archimedes was busy extended Greek numerals to eighty-quadrillion-digit numbers, on the other side of the planet, people were, for the first time, making use of zero. Those people were the Olmec, a Native American civilization in what is now Mexico. As we know, zero is a very important digit that was overlooked until a few thousand years ago. Interestingly, they used zero before Europeans or even Indians/Arabs did.
190 BC
Conics
In 190 BC Apollonius of Perga, another ancient Greek mathematician, wrote Conics, a book about conic sections in mathematics. His book is notable in googology for using giving a specific notation for exponents. That notation used Roman numerals in exponents. For example, x*x*x would be noted xIII, which eventually evolved to just x3.
50 BC
Hindu-Arabic numerals
50 BC is around the time the most common numerals today began developing. They’re known often as Arabic numerals because Arabs spread that usage to Europe, but they actually first developed in ancient India. Those numerals are similar to ours because they use base 10 (like Egyptian numerals) AND they used place value (like the Sumerians and Babylonians).
100-800 AD
Avatamsaka Sutra
Avatamsaka Sutra is a piece of Buddhist literature that was written over several centuries. In the 30th chapter, the Buddha teaches the king about large numbers. It has numbers even bigger than Archimedes’, reaching up to numbers with 10^35 digits!
The Buddha, in that chapter, starts with taking ten billion, and squaring it repeatedly until he gets a number equal to 102^104, a 2*10^32 digit number, saying that it is “incalculable”. Then he takes it to the fourth power a few more times, giving each a name reminiscent of “undescribable” or “unspeakable”. The largest number he defines is 1010*2^121, a 5*10^36 digit number!
That number is the largest number to appear in Buddhist literature, but it isn’t quite as large as a googolplex, which was defined about a millenium and a half later. The passage even has an article on Googology Wiki.
300 AD
Earliest Indian usage of zero
300 AD is around the earliset time the Indians used zero as a digit. This is important because it exemplifies that zero took a long time to be recognized as a number list 1, 2, 3, etc were, and that is also reflected in the fact that “zero” came not from Indo-European roots, but Arabic. Zero also represents an advancement in numerals, one that would soon arrive to Europe.
550 AD
Recognition of zero in India
Around 550 AD India began to generally recognize zero as a digit.
1000
Indian numerals to Europe
Around the year 1000, Pope Sylvester II introduced the abacus to Europe, with Indian numerals nearly like the ones we use today. Soon after the Indian numerals we use today really started to replace Roman numerals as a digits.
1030
Nawasi’s math treatise
Persian mathematician Ahmad al-Nawasi, in 1030, wrote a treatise on both decimal and base-60 mathematics, showing how to calculate numbers with methods almost like how we do it today.
1100
Hindu-Arabic numerals
Around 1100, Arab mathematicians modified the Indian numerals to form the numeral system we know of today. Soon after, Arabs spread those numerals came to Europe and became the dominant system throughout Europe.
1370
First use of the word “million”
Main article: Numbers in the English Language
The name “million” came into the English language from an Italian word “millone” meaning great thouand. Its earliest known use was 1370. At first “million” was regarded an unusual slang word, but after a few centuries it became a well-recognized word, and paved the way for the origin of the illions. This starts to bring us to the next part of our googology timeline: the illion era.
The -illion Era
1484 ~ 1900
Events: 5
1484
Chuquet’s illions
Main article: Numbers in the English Language
The -illion era began, undoubtedly, with Nicholas Chuquet’s illions. He decided to extrapolate from a million to get the names “byillion, tryillion, quadrillion, quyllion, sixyllion, septyllion, ottyllion, nonyllion” for higher powers of a million. Those names are the ancestors of the illions (up to nonillion) that we use today.
What’s interesting is that Chuquet was doing googology A LOT like we know it today. He was extrapolating names like many googologists (especially Andre Joyce) do, and he used a systematic idea with the Latin prefixes, which is once again a classic point of googology!
Another thing he did was propose separating numbers in groups of 6 with apostrophes. For example, 356 million 434 thousand 326 would be written 356’434326.
However, his -illions and system took a while to catch on, as we will see.
1549
Peletier’s illions
Main article: Numbers in the English Language
Another French mathematician, Jacques Peletier du Mans, decided to extend upon Chuquet’s numbers, and rename some of the numbers. The system went up to nonilliard, 10^57, and his names were exactly like the long scale used today in most of Europe. For information on the short scale read my page on history of the illions.
Peletier had a particularly good idea: writing numbers with commas separating groups of 3 digits, i.e. in groups of thousands.
For example, 4294967295 would hereafter usually be written 4,294,967,295. That’s a great innovation because the commas make numbers easier to read, preparing for a time where millions and billions will come into everyday use. Eventually the -illions would become widely recognized.
1600 (ca.)
Mersenne primes
In the early 1600s yet another French mathematician, Marin Mersenne, studied prime numbers that are one less than a power of 2. Those primes came to be known as Mersenne primes. The first few are 3, 7, 31, 127, 8191, 131,071 ... For more on them see my number list's entry for 127.
Mersenne primes are notable to googology because the largest known prime, since the 1800s, has almost exclusively been a Mersenne prime. Better yet, the current record has a staggering seventeen million digits!
1857
Further extended illions
Main article: Numbers in the English Language
Some people further extended Peletier’s illions to get names up to vigintillion and also centillion - those became dictionary numbers as well.
I used 1857 for this even because 1857, according to the online Merriam-Websiter dictionary, is the first usage of “vigintillion”, the name for 10^63 in the short scale and 10^120 in the long scale. Vigintillion is actually one of my own favorite illions.
1860
Henkle’s illions
Main article: Numbers in the English Language
The next next step in the illions in the illions coined by someone called “Professor Henkle” and published in an Ohio journal. His illions had a simple system to name one million illions with its own advantages and drawbacks. His largest -illion is the famous “milli-millillion”, equal to 1 followed by three-million-and-three zeros, which is known for its amusing pronunciation.
The Sub-Googol Era
1900 ~ 1938
Events: 6
1904
The Hardy Hierarchy
Main article: [upcoming]
The Hardy hierarchy is a cousin of the fast-growing hierarchy defined by G.H. Hardy in 1904. It was created before both the fast-growing hierarchy and the slow-growing hierarchy - it is notable for having interesting connections with the fast-growing hierarchy - for example, Hw^2(x) in the Hardy hierarchy is exactly equal to f2(x) in the fast-growing hierarchy.
1908
Veblen’s phi function
Oswald Veblen, in 1908, defined a function that can take any number of arguments to generate infinite ordinals. The function is very notable in googology because of its use in the fast-growing hierarchy.
The phi function is denoted φ(a,b,c ... ... z) with any number of arguments, and it is limited at the small Veblen ordinal (SVO for short), an important point in ordinals and the fast-growing hierarchy. It is applied to the fast-growing hierarchy because it uses infinite ordinals, e.g. fφ(a,b,c ... ... z)(x). This makes it an important function in googology.
Also, it’s the very first googological array notation, predating even Bowers’ arrays by over 90 years.
1928
The (original) Ackermann function
Main article: The Ackermann function
In 1928, a German mathematician, Wilhelm Ackermann, developed a 3-argument recursive function in a mathematics journal. The function was intended as an example of a function that is computable but not primitive recursive, and it grows surprisingly fast - it was the fastest-growing googological function at the time.
That function is the ancestor of what is now known as the Ackermann function, and it’s a bit more complicated than the function we now know as such.
1933
Skewes’ number
Up next is Skewes’ number, a number used by Stanley Skewes as an upper bound on the first point when the prime counting function crosses the logarithmic integral function (assuming the Riemann hypothesis is true). The number is equal to ee^e^79, or a number with roughly a 10^34 digit number of digits (~1010^10^34 in exponent form). So it’s pretty big alright.
Skewes actually broke the record for large number used in a mathematical proof with his number, although it was itself dethroned with another bigger number of his (see 1955).
1935
Peter’s Ackermann function
Main article: The Ackermann function
In 1935, Rosza Peter published a paper on recursive functions that used a simplified version of the 3-argument Ackermann function. It was defined much more simply than Wilhelm Ackermann’s, being a 2-argument function instead of a 3-argument function, but it still has some complexities that were changed further by Robinson (see 1948).
1936
Turing machines
In 1936 Alan Turing first studied the concept of Turing machines, hypothetical machines that can generate long taps. They led to the creation of a very powerful function 26 years later (see the busy beaver function at 1962).
The Googol Era
1938 ~ 1976
Events: 14
1938
The origin of “googol” and “googolplex”
Main article: Googol and Googolplex
This is a classic event in googology, the origin of the googol. It originated from a mathematician named Edward Kasner asking his 9-year-old nephew Milton Sirotta what a name for 1 followed by 100 zeros should be. Sirotta suggested the name “googol”. Eventually the name “googol” got much cultural significance - see next entry.
Sirotta then suggested “googolplex” to be 1 followed by writing zeros until you get tired, but then Kasner redefined it as 1 followed by a googol zeros. Both numbers became very culturally significant.
1940
Mathematics and the Imagination, Kasner’s publication of “googol”
In 1940 Kasner published “Mathematics and the Imagination”, a math book which also introduced googol and googolplex to the world. Therefore 1940 can be seen as the year googol really became a cultural thing.
1947
ENIAC
ENIAC, Electronic Numeral Integrator and Computer, is celebrated as the world’s first computer. It was a giant computer that took up many rooms of a buildings and was quite capably programmable to perform mathematics. ENIAC is important to googology because it represents the very beginning of the computer era, and computers, as we know, are super-important to googology, and to everything these days.
1947
Goodstein and the hyper-operators
Main article: Up-Arrows and the Hyper-Operators
In 1947, Reuben Goodstein, the same guy who discovered the fast-growing Goodstein sequences, decided to give names for the operators beyond addition, multiplication, and exponentiation - repeated exponentiation is tetration, repeated tetration is pentation, and repeated pentation is hexation. See my up-arrow article for examples of those powerful hyper-operators.
It is of note that those operators were named about 30 years before up-arrow notation, a generalized notation for these operators, was created. an was sometimes used for tetration (i.e. a power tower of a n’s), but there was no standard notation for pentation and higher before Knuth’s arrows came to be.
1948
Robinson’s Ackermann function
Main article: The Ackermann function
In 1948, Raphael M. Robinson published a paper based upon Rosza Peter’s function, and devised a function based on the Ackermann function and simplified from Peter’s. That function is what is now known as the Ackermann function, though I like to call it the Ackermann-Robinson function.
1950
Mathematical Snapshots
Main article: Steinhaus-Moser Notation
Hugo Steinhaus has published several editions of a book called Mathematical Snapshots, a book about all kinds of subjects on recreational mathematics. It has a passage which briefly discusses some very large numbers, introducing his polygon notation, and the gigantic numbers, mega and megiston.
The earliest edition of the book that I can find to have the large number notation is 1950, though the numbers may have existed as early as 1938, the first edition of the book.
1951
Primes on electronic computers
In 1951 the number 180*(2127-1)2-1, a 79-digit number, was proven to be prime. It , breaking the record for largest known prime soon after a 44-digit number was proven to be prime with a mechanical calculator - that 44-digit number broke the record for the first time in 76 years.
The 79-digit number is notable because it was the first number proven to be prime with a computer. All record-breaking primes thereafter were proven using a computer.
1955
Second Skewes’ Number
After the very large Skewes’ number, Skewes used an even bigger number in a mathematical proof. It was the same proof Skewes’ number came from, but assuming the Riemann hypothesis does not hold true. The value is about 1010^10^963, so it has over a googolplex digits!
1962
The busy beaver function
In 1962, Tibor Rado defined a whole new kind of googological function at Ohio State University. The function (noted Σ(n) or BB(n) ) was defined as the maximum number of marks an x-state Turing machine can make before halting. The function grows very quickly:
BB(1) = 1
BB(2) = 4
BB(3) = 6
BB(4) = 13
BB(5) ≥ 4098
BB(6) ≥ 3.515*1018,267
BB(7) > 1010^10^10^18,705,353
and BB(22) is the smallest value of the busy beaver function known to be greater than Graham’s number.
The function is the original uncomputable function, a function that you cannot program a computer to calculate, even if it has infinite time and memory. Many uncomputable functions grow faster than any function, no matter how powerful, that you can devise with iteration. That means that even if you extend a powerful function like Bowers’ or Bird’s arrays as high as you could, it will still eventually be beaten by uncomputable functions.
Because it is the original uncomputable function, the busy beaver function is very important to googology.
1963
Peanuts comic mentions “googol”
In 1963, the famous comic strip Peanuts mentioned googol in a comic (image link). This is notable because it exemplifies how famous googol has become. And that was about a generation before Google (as opposed to googol) existed!
1965
The Busy Beaver S function
Along with the busy beaver function, not long afterwards an S function was defined. S(x) is the number of steps a n-state Turing machine can take before halting. The function grows a bit faster than the busy beaver function, but it’s harder to work with and not as well known. It's also referred to as the frantic frog function.
1971
The original Graham’s number
In 1971 Ronald Graham first worked on the problem in Ramsey theory that led to Little Graham, a number used as an upper bound in the proof that is smaller than the far more famous number that is now known as Graham’s number. See 1977 for more on the number that is now known as Graham’s number and how it came to be.
1973
My Hero, Zero
On January 20, 1973, the legendary series of short 3-minute educational videos known as School House Rock aired their very first episode on television. It is called My Hero, Zero and it is part of the Multiplication Rock series, the first series in School House Rock. The song talks about the importance of the number 0 along with the powers of ten.
Why is that song notable to googology? Look at part of the lyrics:
Place a zero after one, and you’ve got yourself a ten -
See how important that is!
When you run out of, you can start all over again -
See how convenient that is!
That’s why with only ten digits, including zero,
You could count as high as you could ever go,
Forever, towards infinity ...
No one ever gets there, but you can try ...
with ten billion zeros.
The line “with ten billion zeros” clearly implies writing ten billion zeros after some digits in order to create a very large number - for more on this read my number list’s subpage on the number equal to one followed by ten billion zeros.
1974
Short scale in Britain
Britain once used both the short and long scales for naming large numbers - that is, it was ambiguous whether a billion meant 109 or 1012. However, largely due to influence from the USA which always used the short scale, in 1974 the prime minister of Britain declared that from now on the short scale will always be used for official communications, meaning that a billion now officially meant 1,000,000,000 and not 1,000,000,000,000. This designation can therefore be seen as completing the transition of Britain from a long-scale country to a short-scale country.
The Knuth-Graham Era
1976 ~ 1996
Events: 7
1976
Knuth’s up arrows
Main article: Knuth’s up-arrows and the hyper-operators
Mathematician Donald Knuth defined his famous up-arrows in 1976 in a mathematical journal, a notation that is notable because it extends intuitively upon the familiar operations of addition, multiplication, and exponents. Also, it shows up in the definition of Graham’s number. For more about the fascinating notation read my page on Knuth’s arrows (link above).
1977
Graham’s number
1977 was the year Graham’s number was published in a math journal by Martin Gardner. As the story usually goes:
Ronald Graham in 1971 was working on a problem in Ramsey theory, and proved an upper-bound to the answer to be an extremely large number. In 1977 he caught the attention of Martin Gardner, who published that amazing number in a mathematics journal. The number found its way to Guinness World Records the largest number used in a mathematical proof, and it remains the largest number used in a mathematical proof to this day.
However, a lot of this is myth. A more accurate story would be:
Ronald Graham in 1971 was working on a problem in Ramsey theory, and proved an upper-bound to the answer to be an extremely large number. He even caught the attention of Martin Gardner. Since Gardner found the number Graham found hard to explain, he devised a larger and easier-to-explain number. That number found its way to Guinness World Records the largest number used in a mathematical proof, but it has later been dethroned by far far larger numbers like TREE(3), though that was after that title was removed from Guinness World Records. Therefore many people still think Graham’s number is the largest number used in serious mathematics, or the largest “useful” number.
Graham’s number still receives a lot of hype to this day since so many people still misguidedly think Graham’s number is the largest “useful” number. Seriously, just look at Google’s results.
Nonetheless Graham’s number is a hugely significant number to googology, because it is a force that still lures many people into the wonderful world of very large numbers. Therefore the hype about Graham’s number isn’t entirely a bad thing.
1980
Graham’s number in Guinness World Records
In 1980 Graham’s number made it to Guinness World Records as the largest number used in a mathematical proof. However, the title was removed from Guinness World Records a few years later, which is a shame in my opinion, because otherwise people would hear of better numbers that appeared in serious mathematics like TREE(3).
1982
The Kirby-Paris hydra
In 1982, the Kirby-Paris hydra was devised. It is a simple single-player game that leads to an extremely fast-growing function, with a growth rate of epsilon-zero in the fast-growing hierarchy. Some faster-growing functions have soon been devised with a similar idea, like the more powerful Buchholz hydra.
1987
The fast-growing hierarchy
Main article: [upcoming]
The fast-growing hierarchy (FGH for short), considered the one true benchmark in googology, was first devised by mathematicians around 1987. It is based upon infinite ordinals, which is why Veblen’s phi function (see 1908) and other ordinal notations are important to googology. For further discussion of the FGH, look at entries on my number list that discuss some milestone points (such as epsilon-zero or the SVO) and numbers definable in the FGH, and my article on the fast-growing hierarchy (coming soon).
1991
Sbiis Saibian’s childhood googology
Sbiis Saibian, who today is one of the central people in googology with his large number site and Extensible-E system, has been interested in large numbers since second grade, when he was eight years old. Since pages like his fictionpress.com profile suggest that he was born 1983, his childhood large numbers therefore were probably made around 1991.
Sbiis Saibian first found out about the -illions in a dictionary after his dad told him about a million, with “centillion” meaning 1 followed by 303 zeros quickly becoming his favorite illion.
But then, his imagination really sparked when he and his best friend were waiting to be picked up by his best friend’s father. When her father arrived, Sbiis told him about large numbers he had read about. Then his friend's father told young Sbiis (Sbiis Saibian is a pseudonym) about a number scientists had come up with called a googolgong, equal to 1 followed by 100,000 zeros. Sbiis was amazed by that number, and thought that if scientists had come up with a very large number, he would come up with something bigger!
The funny thing is his friend’s father was actually incorrectly explaining the googolplex, but somehow botched up the name AND definition. First off, it’s googolplex and not googolgong, and secondly, it’s 1 followed by a googol zeros and not 1 followed by 100,000 zeros. Furthermore, scientists didn’t even come up with the number, a single mathematician did! Nonetheless that really got Saibian’s gears rolling.
But then, he learned of infinity, and learned it as something that is so big that it cannot be reached. However, he refused to accept that it can’t be reached, and set on a quest to reach the infinite! From there on he began inventing some large number notations, which evolved into his current Extensible-E system.
He even wrote a book on some of his dad’s copy paper called “One to Infinity” about very large numbers, starting from 1 and in the end reaching (or trying to reach) the infinite. Unfortunately he has lost the paper now, but it has become the basis of his current large number site.
1995
Conway’s Book of Numbers
Main articles: Extensions to the -illions and Conway’s chain arrows
In 1995 the famed mathematicians John H. Conway and Richard K. Guy published a book called The Book of Numbers, a book about recreational mathematics of all kinds. Two major things in googology came from that book.
The first is Conway and Guy’s illions, a Latin-based illion system that is quite popularly used, and often simplified a little bit. Those are discussedon my page on extensions to the -illions.
The second is Conway’s chained arrow notation, a large number notation that extends upon Knuth’s arrows to create pretty big numbers bigger than Graham’s number, but it is itself dwarfed by Bowers’ cleverly devised linear arrays, which he invented in 2002.
The Early Online Era
1996 ~ 2008
Events: 15
1996
Robert Munafo’s large number site
In 1996 Robert Munafo published his website on large numbers. This is important because his site is probably the very first major online resource on large numbers, before Wikipedia even existed! Therefore Robert Munafo can be seen as a pioneer in modern googology, along with Jonathan Bowers.
His site’s publication can actually be seen as the start of a whole new era in googology, with the majority of the information googology moving to the Internet.
1997
GIMPS
GIMPS (stands for Great Internet Mersenne Prime Search) is an online project which anyone can participate in, devoted to find large Mersenne primes. It was founded 1997. Every record-setting prime since 1997 has been discovered in GIMPS, and the current record has 17 million digits.
Sep 4, 1998
Google founded
In 1998 the technology superpower company Google was founded. This is notable to googology because Google helped transition googology from found mostly only in math journals to mostly in easy-to-access websites. But also, it’s notable because Google named itself after the famous large number “googol” because its goal was to locate anything and everything on the seemingly endless Internet.
1999
First million-or-more digit prime discovered
Two years after GIMPS was founded, the number 26,972,593-1, a Mersenne prime, was proven to be prime. The number has a bit more than two million digits, and it was the first prime number with a million or more digits to be discovered. Such prime numbers are known as megaprimes.
Jan 15, 2001
Wikipedia founded
Wikipedia was founded in early 2001. This is important to large numbers because Wikipedia is probably the best-known web source for pretty much everything, and yes, large numbers count as part of “pretty much everything”. However, it would still be nearly eight years till there was a wiki all about large numbers.
Dec 2001
Bignum Bakeoff
Early into the Early Online Era of googology, something interesting was done. A man named David Moews, who had a website with some mathematical and programming information, decided to hold a programming contest that went like so:
Write a program in C with no more than 512 characters to produce as big of a number as you can, assuming the computer had infinite time and memory.
Entries were submitted through email, and people were allowed to submit as many entries as they wanted. One guy named Pete submitted nine entries.
In the end, twenty programs were submitted. Of these, six of them either didn’t terminate or only ended up outputting one, but the other fourteen produced very large numbers. Most of them used recursive functions similar in design to the Ackermann function, but two of them are different and more interesting.
marxen.c (by Heiner Marxen), the second place program, cleverly used a variant of the fast-growing function known as Goodstein sequences to reach past the level of epsilon-zero in the fast-growing hierarchy, larger than any of the recursive functions used in the other twelve (not counting loader.c).
loader.c (by Ralph Loader), the first place program, was far more esoteric. By diagonalizing over the calculus of constructions, a whole new kind of computable number was created. Its output, now known as Loader’s number, is the largest named computable number. The program uses rather unusual methods to make the writing used in it concise, and people like LittlePeng9 of Googology Wiki who attempted to analyze the program quickly ran into problems - it’s just that cleverly devised of a program.
For more on each of the entries submitted to Bignum Bakeoff look here.
2002
Jonathan Bowers’ original work
Main articles:
Introduction to the Work of Jonathan Bowers
Bowers' Linear Array Notation Part 1
[more upcoming]
In 2002, an American amateur mathematician and polytopist (studier of dimensions beyond our familiar 3-dimensional world) by the name of Jonathan Bowers did something notable in googology. He invented a powerful array notation to denote very large numbers, more powerful than Knuth’s arrows, Steinhaus-Moser polygons, the Ackermann function, or even Conway’s chain arrows! He also devised an extension to that notation called Extended Array Notation, which allowed him to denote arrays of higher dimensions - for example {10,10(2)2} solves to a 10x10 grid array of tens.
Bowers named lots of numbers with his array notation, with colorful names ranging from giggol to tetratri to trossol to colossol and beyond. Then he discussed ways to go further with his notation. He said that these methods aren’t perfected yet, but allow us to name larger numbers like dulatri, tridecatrix, golapulus, big boowa, and guapamongaplex, which was at the time his largest.
However, after extended array notation it was not exactly certain how to work with his numbers - these refinements would come some time later.
Bowers is often considered the father of modern googology. Why is that?
He did not create the first array notation, Veblen did. He did not name the first googolisms, Chuquet was one of the first. He did not create the first large number site, Robert Munafo did. So what did he do?
He was the one who really got the modern ideas of googology rolling - inventing a notation and continually extending on it, and inventing a wide array of names for numbers as you go. Now THAT’S something Bowers was the first to do. Other googologists later followed Bowers’ ways, like Sbiis Saibian with his thousands of names for numbers in his Extensible-E system.
2002
Harvey Friedman and TREE(3)
In 2002, mathematician Harvey Friedman (who I have met in person before) did work regarding Kruskai’s tree theorem in graph theory, and discovered the TREE(3), which is the maximum length of a sequence of 3-labeled trees can be such that no tree is homeomorphically embeddable into a previous tree, is, in short, really fucking huge.
How huge is TREE(3)? Even by googologists' standards it's quite large. It leaves a googolplex in the dust, and it leaves Graham’s number in the dust, and yes, it even leaves many mighty Bowerian googolisms like a gongulus in the dust. It’s so big that it’s very difficult to make a large number notation that reaches as far as this number! It passes up epsilon-zero, gamma-0, the Ackermann ordinal, and the SVO in the fast-growing hierarchy, creating a number that’s at least comparable to the level of ψ(ΩΩ^w*w) in the fast-growing hierarchy. Among Bowers’ numbers it’s believed to fall between a humongulus and a golapulus.
The best thing about TREE(3) is that it was used in a mathematical proof, just like Graham’s number, but unlike Graham’s number TREE(3) isn’t just an upper bound, but indeed a huge answer to a fairly simple problem! Even though it’s far harder to explain than Graham’s number, TREE(3) deserves far more recognition than the adorable little Graham’s number in my opinion - for more on this ginormous number read its entry in part 6 of my number list. (although there are EVEN LARGER numbers to find their way to "serious mathematics" like SCG(13) which was also discovered by Friedman)
Feb 24, 2003
Wikipedia’s page on large numbers
Two years after Wikipedia was created, Wikipedia’s article on large numbers was created, seven years after Munafo’s site. At that time googology was somewhat more well-known, but still kind of obscure. Nonetheless this is a notable event in googology (see founding of Wikipedia on Jan 15, 2001).
2004
Sbiis Saibian’s return to googology
We’ve earlier discussed Sbiis Saibian’s childhood interest in large numbers. After his childhood book, he had several times considered writing a new version of the book, but he didn’t return to the subject at all until 2004. That was when he learned about Knuth’s up-arrows, Conway’s chain arrows, and Bowers’ arrays. Eventually he began working on the new version of his book in June 2008, and soon after he published it to the Internet.
2006
Bird’s arrays
Main articles: [upcoming]
In 2006, an English mathematician named Chris Bird first devised his own array notation, related to Bowers’ but designed a little differently, with less theory or array structures and more logical abstraction - in other words, while Bowers’ arrays are concrete, Bird’s are quite abstract, and don’t have the ambiguities Bowers’ have.
However, Bird’s arrays lack the appeal Bowers’ have, because Bird doesn’t name numbers with his notation. Nonetheless, Bird’s arrays are important in googology because of their usefulness as a benchmark, and how they helped make Bowers’ arrays work better.
Every so often Bird has updated his arrays to add on to the notation and make it more powerful, most recently in 2014.
2007
Bowers’ improved arrays
Main articles: [upcoming]
In 2007, Jonathan Bowers updated his array notation, giving a lot more notation for things past dimensional arrays. He gave a notation for the tetrational arrays based upon Bird’s arrays, and further devised ideas of structures for arrays that are a lot more systematic. He even made a notation for legion arrays, the next part of array notation past defining structures.
With his tetrational arrays, even though he provided no definition, his examples of tetrational arrays make their mechanics quite clear, and there is now consensus among the googology community on how tetrational arrays work. This also helped shed some light on the mysteries of pentational or higher arrays.
Unfortunately (for me at least) the majority of people on Googology Wiki seem to just accept that it’s uncertain and do nothing about it. I myself am currently working on a proposal for defining Bowers’ arrays past tetrational arrays. Pentational arrays up to linear-array-arrays are actually pretty easy under my idea, but after order-type of the ordinal known as the SVO the arrays QUICKLY become very difficult.
As for legion arrays, the mechanics are interesting, but quite haphazard as they build upon an operator (array-of) whose mechanics are uncertain in and of themselves, and often is not clear enough just from examples Bowers gives. Nonetheless they allow for colorful names like wompogulus, bukuwaha, goshomity, and the current largest googolism of Bowers’: meameamealokkapoowa oompa.
Jan 26, 2007
Big Number Duel
January 26, 2007, was an especially important day in googology. Why is that? Because that was the date of the Big Number Duel.
What was the Big Number Duel? It was a competition between two math professors at MIT (Massachusetts Institute of Technology). In the competition, player 1 and player 2 must take turns naming a number bigger than the previous number, until one player can’t come up with a significantly bigger number.
In addition, in MIT’s website’s own words, “there is to be a 'gentleman's agreement', to the effect that each new entry must name a number big enough so as to not be reachable in practice using only methods introduced earlier in the game[, and t]his means that it would be considered unsporting to win by adding one to your opponent's last entry.”
In the Big Number Duel, Adam Elga was player 1 and Augustin Rayo was player 2. First, Elga wrote 1 on the board, and then Rayo responded with writing a string of ones in the board. Then , Elga turned half the ones into factorials, and after that Elga and Rayo began to devise their own functions. They threw more and more powerful large number functions at each other, until Elga devised a function that was, in fact, uncomputable.
After that, the functions continued to grow more complicated, until Rayo wrote on the board:
“The smallest number bigger than any finite number named by an expression in the language of first-order set theory with a googol symbols or less.”
Elga, at this point, couldn’t think of a significantly bigger number, and Rayo was declared the winner.
The number came to be known as Rayo’s number, and it for a time was the largest number anyone has named (not counting any elementary extensions (e.g. Rayo's number with a googolplex symbols). It is very hard to come up with a significantly more powerful function, though there are several attempts shown later on this timeline.
Also, Rayo’s number can be generalized by a function, Rayo(x), defined as the smallest number bigger than any finite number named by an expression in the language of first-order set theory with x symbols or less - therefore Rayo’s number is Rayo(10100).
Apr 9, 2008
Ballium’s Number
On April 9, 2008, a parody YouTube video by a channel called Meerkats Anonymous was uploaded. In that video, a fictional physicist named Samuel Ballium claimed that he had discovered the largest of all numbers, saying that it is impossible for numbers to be large after that point.
The number is defined as:
_
794,843,294,078,147,843,293.73⋅eπeπ (line above indicates repeating digit)
and it came to be known as Ballium’s number.
The number isn’t so big after all: it only has about 138 billion digits, making it much smaller than a googolplex. Therefore, it would be really disappointing to the googology community if this was indeed the largest number. Also, the number is just too small: it is still a number small enough to have physical meaning in our universe - see this page for more on that.
June 10, 2008
Construction of Sbiis Saibian’s site
In June 2008 Sbiis Saibian finally decided to work on the “new version” of his childhood book, One to Infinity. It was under private beta for four months before it was publicly released to the world.
The Community Era
2008 ~ present
Events: 18
Dec. 5, 2008
Creation of Googology Wiki
An eleven-year-old boy named Nathan Ho who at the time went by the name “Followed by 100 zeroes” on the Internet (now Vel!) had recently discovered large numbers at that time, and he was upset that there was no site on the Internet that really collects large number information. So he decided to go to Wikia, and start a wiki all about googology. He quickly put in lots and lots of major googology on the wiki, and slowly it grew into a large number community.
The creation of the wiki is what I dub as the start of the community era, the start of a real community of people interested in large numbers.
Dec. 8, 2008
Sbiis Saibian starts his large number site
Coincidentally, Sbiis Saibian launched his large number website three days after the wiki was created. Sbiis Saibian’s site is also one of the best sources on large numbers out there, known for its exceptionally detailed coverage of numbers big and small. It is still far from complete though, and he plans for it to grow as the coverage of large numbers on the web does.
It is of note that Sbiis Saibian found out about the wiki at most four months after he started his site.
Jan 11, 2009
A googol is a tiny dot
Not long after starting Googology Wiki, Nathan Ho set up a blog titled “A googol is a tiny dot” to have some googology. It was mostly for fun, but had some interesting googology like an idea of hypermathematics where, for example, 2+3 = 23, and applying it to googology functions. He now utterly regrets ever making the blog - I think that may be largely because the blog is ridiculously apologetic, though I think he’d prefer calling it flat out terrible.
Mar 18, 2009
Last post on A googol is a tiny dot
The last post on “A googol is a tiny dot” was made March 18, 2009. After that it was seemingly abandoned. I think we can safely see it’ll never see an update again since the creator regrets it so intensely.
April 27, 2009
Followed by 100 zeroes’s disappearance
On April 27, 2009, Followed by 100 zeroes forgot about his wiki, and disappeared from Googology Wiki. After that, the wiki was left without any moderation or anything, and few improvements were made to the wiki for the next year-and-ten-months.
Aug 11, 2009
Sbiis Saibian’s site hiatus
On August 11, 2009, Sbiis Saibian released his last update to his site for more than a year, and had to quit working on his site because of real life stuff. For the next year or so, googology seemed to fall silent as both Googology Wiki and Sbiis’s site were abandoned.
Oct 10, 2010
Sbiis Saibian’s site’s return
On October 10, 2010, Sbiis Saibian returned to work on his site with some brand new stuff, marking a revival of the googology community.
Feb 22, 2011
Nathan Ho’s return as FB100Z
After nearly two years, Nathan Ho finally made a serious return to Googology Wiki under the new shortened name FB100Z, shortly after a new user by the name of Cloudy176 (who is still active on the wiki today) appeared. He deleted some articles that cite no sources and went back to working on the wiki.
May 25, 2011
First admin of Googology Wiki
On May 25, 2011, a user on the wiki by the name of Ace45954 was given admin rights by a Wikia staff member. This is important to googology because it marked that Googology Wiki was starting to become a serious thing, and evolving into a proper community.
Nov 19, 2011
Hyper-E Notation
Main article: Poly-Cell and Hyper-E Notation
On November 19, 2011, Sbiis Saibian publicly released his Hyper-E and Extended Hyper-E notation, a modernized version of his childhood googology (see 1991). The notation had many fresh googolisms such as grangol and graatagolthra, and the largest at the time was the grand grand godgahlahgong.
Feb 2, 2012
Very Small Very Large Numbers
On February 2, 2012, Sbiis Saibian wrote a post on his blog titled "Very Small Very Large numbers", the goal of which was to answer the question of "what is the smallest large number". He answered the question by saying that 1 is the boundary between large numbers and small numbers - numbers greater than 1 are large and numbers between 0 and 1 (including 0 but not 1) are small - 1 is neither large nor small. This designation is convenient because the large numbers are mirrored across the small numbers with the reciprocal function, and as far the negative numbers, we can have "large negative numbers" and "small negative numbers", which are the negatives of large and small numbers respectively.
Because of this post, about a year later Googology Wiki decided to remove its lower limit of 100 for numbers that can have articles, and the users created articles for numbers 0 to 99.
Apr 1, 2012
April Fools Day Googology
On April Fools Day 2012 Sbiis Saibian wrote an article on the amazing acrobatic feats of Graham’s number.
Aug. 21, 2012
Improvements to Extensible-E I
Main article: Poly-Cell and Hyper-E Notation
In August 2012, Sbiis Saibian decided to improve his Hyper-E and Extended Hyper-E numbers, renaming some of the numbers like goolda to gugold, goohoolgol to throogol, and new numbers like gaspgol and ginorgol.
Jan. 6, 2013
The xi function
Adam P. Goucher invented an uncomputable function called the xi function in January 2013. Unlike the busy beaver function, it doesn’t explode immediately, yet paradoxically, it produces much larger values overall. Goucher claimed that his function grew faster than Rayo’s function (the function used to generalize Rayo’s number), and that claim was not contested for two months: therefore for two months the xi function was believed to be the fastest-growing function in googology.
Jan 12, 2013
Sbiis Saibian’s first contribution to Googology Wiki
On January 12, 2013, Sbiis Saibian made his very first contribution to Googology Wiki. Soon after he became a fairly active contributor to the wiki and began communicating with its fellow users.
Jan 22, 2013
Cascading-E Notation
Main articles: [upcoming]
Sbiis Saibian released his Cascading-E notation in early 2013. It is a logical extension to Extended Hyper-E notation that reaches order-type epsilon-zero in the fast-growing hierarchy, with many brand new number names such as gotrigahlah, godgathor, graltothol, and the mind-blowing tethrathoth.
Mar 12, 2013
Xi does not beat Rayo
On March 12, 2013, Deedlit11 of Googology Wiki debunked Goucher’s claim that the xi function beats Rayo’s function, causing the googology community to realize that Goucher misunderstood Rayo’s function, and that Rayo’s function was indeed the fastest-growing.
April 2013
Hyperfactorial array notation
Main articles: [upcoming]
In April 2013 Lawrence Hollom introduced the googology community to his hyperfactorial array notation, which extended the factorial into the realms of googology. He caused quite some debate in the community when he claimed his notation reached past anything Bowers has named, but nonetheless it’s a pretty powerful notation. I don't really understand how the notation works, though it reportedly reaches past functions like Buchholz hydras which reach the level of the incomprehensible Takeuti-Feferman-Buchholz ordinal in the fast-growing hierarchy.
Aug 10, 2013
Cookie Clicker
On August 10, 2013, the browser game Cookie Clicker was released to the world by a French game developer who usually identifies as Orteil. It quickly developed a hype following, though it eventually died down.
Why is Cookie Clicker relevant to googology? First off, it is a rare example of a game to use number names larger than “million” - it uses names as big as decillion! Also, it’s part of how I myself discovered googology; the -illion names it uses caused me to start looking them up online and stumble upon Googology Wiki.
Oct 19, 2013
Fish number 7
On October 19, 2013, Kyodaisuu of Googology Wiki did something interesting. He defined Fish number 7, the largest number in his family of seven googolisms he dubs the Fish numbers - the previous ones were defined 2002-2007. Fish number 7 is a particularly interesting one, one that extends upon Rayo's number in an attempt to break the record set by Rayo's number. He extends upon first-order set theory (FOST for short), the language used to define Rayo's number, by adding some new elements.
It's a notable step up from Rayo's number, and a step in the right direction as described by Nathan Ho, but people of the wiki who know more about the set theory and stuff behind Rayo's number than I do found out that Kyodaisuu's extensions, although they're a step in the right direction, don't put a very big improvement on the already internally complex language of FOST. Therefore we need to do more ... a WHOLE LOT more to REALLY transcend Rayo's number. And that's where LittlePeng9's work comes in about a year later.
Dec 6, 2013
Nathan Ho's Ordinal BEAF
On December 6, 2014, Nathan Ho began his attempt at formalizing BEAF. He decided to base it upon ordinals, hoping to allow this to be as clean and unambiguous as possible. It was continuously expanded until he found a flaw in the notation (see Aug 3, 2014).
Jan 30, 2014
Extended Cascading-E
Main articles: [upcoming]
On January 30, 2014 Sbiis Saibian updated his Extensible-E system by greatly extending Cascading-E all the way up to order-type φ(ω,0,0) in the fast-growing hierarchy. This time he created thousands of new numbers, such as tethriterator, tethracubor, tethrarxitri, pentacthulennon, hexacthulhum, grand godsgodgulus, and many many many many more.
Feb 12, 2014
My first contribution to Googology Wiki
In February 2014, I have read quite a lot of Googology Wiki, and I eventually decided to contribute to it - I used my Wikia account (WikiRigbyDude) that I had made in 2011 to edit Regular Show Wiki to make my first mark on the wiki, by creating an article on one of Sbiis Saibian’s new googolisms, a gigantic number called pentacthulhum.
Eventually afterwards, I became a regular contributor to the wiki.
Feb 25, 2014
Sam’s Number
On February 25, 2014, some guy who identifies as SammySpore created an article on the wiki about a “number” he calls Sam’s Number:
“Sam's number is so gigantically huge it cannot be described. It boggles the mind. Actually, it would boggle a megafugafzgargoogolplex minds.
If you want a small glimpse of how big it is, here. Sam's Number is enormously larger than Rayo's Number. It can fill a greagol multiverses. Actually it can fill so much more than that, it is undescribable.”
For obvious reasons, Sam’s Number isn’t a number. The article was deleted because the wiki doesn’t allow unsourced original content, but Sam’s Number grew to be an in-joke among the googology community about lazy and undefined googology.
Mar 24, 2014
Rayo’s number on Wikipedia
On March 24, 2014, seven years after Rayo’s number was defined, it finally was given an article on Wikipedia.
Mar 26-31, 2014
"Word of God" on BEAF
In late March 2014, Jonathan Bowers himself (under the name Polyhedron Dude) posted on a forum thread about large numbers, giving important clues at how he himself really intends his array notation to work. Here, he talks about how we can apply Sbiis Saibian's ordinal up-arrow notation theory as presented in Extended Cascading-E, making his array notation more powerful than commonly thought - for example, with his own idea pentational arrays hit not zeta-zero, but the larger gamma-zero.
Sbiis Saibian soon discovered that thread, and he eventually told the googology community about it. Some time later, the shared publicly on Googology Wiki (by Cloudy176 discovering the link to that page on my site's homepage), and Cloudy176 decided to dub it "Word of God", for obvious reasons. Although many people in the googology community argue that Bowers' claims don't mean that much or lead to a well-defined notation, Sbiis Saibian based his Extended Cascading-E notation upon Bowers' description of his ideas of BEAF.
May 28, 2014
My large number site created
May 28, 2014 (coincidentally 2000 days after the wiki was created) is the day I created the site you are viewing right now. It started off as mainly just some random articles about googology others haven’t bothered to cover, but it soon grew into a more serious coverage of large numbers, which is why this timeline exists.
Now I aim for this site to be a general resource on large numbers, similarly to Sbiis’s site, the googology wiki, Bowers’ site, Wikipedia’s pages, Robert Munafo’s site, Chris Bird’s work, and the other sites on googology out there.
Jul 19, 2014
Googology Wiki IRC
On July 19, 2014, Nathan Ho decided to set up an IRC chat for the googology community, which is now used as a chat room in addition to the wiki itself.
Aug 3, 2014
End of Nathan Ho's BEAF
On August 3, 2014, Nathan Ho ran into a crucial snag in his BEAF formalization: he found that many of the ordinals used have ambiguous fundamental sequences. This snag caused him to abandon his attempt at formalizing BEAF. Although I see no reason why he couldn't just specify what specific kind of fundamental sequences he uses or something like that, nonetheless this is an important turning point in the community's views on BEAF. People started to abandon trying to define or make guesses on how powerful BEAF is, and a large portion of members decidedly have their opinion on BEAF that it's meaningless and not worth studying past tetrational arrays.
Aug 2014
Start of improvements to Extensible-E II
Main articles: [upcoming]
In August 2014, Sbiis Saibian started his improvements to his Extensible-E system. He renamed numbers like tristo-throogol to throotrigol and godextathol to godhathor, and then some brand new numbers like guppybyte, googoltoll, grangolbong, gargantuul, and googondol. Then he greatly expanded his Extended Cascading-E (xE^) numbers to name over 15,000 googolisms - I'm not kidding, he has a HUGE list of all these xE^ numbers (see Feb 20, 2015).
Sep. 14, 2014
Rebranding x2 Combo
This is an event on the wiki dubbed so by Cloudy176 on his wiki timeline. It’s named so because two users changed their username on Wikia at about the same time: FB100Z renamed himself to Vel!, and I changed my name from WikiRigbyDude to Cookiefonster.
Oct 2-3, 2014
Revamping this website
On October 2-3, 2014, I found that I was dissatisfied with my site’s layout, and I decided to revamp the layout entirely, with plans for A LOT more new pages, while keeping all my old pages. The plan of new pages is still not even close to complete though.
Oct. 7, 2014
Return of Sam’s Number
On October 7, 2014, Nathan Ho, the founder of Googology Wiki, decided to bring Sam’s Number back to Googology Wiki because of its significance as an in-joke and how NOT to make a very large number.
Oct 30, 2014
BIG FOOT
On October 30, 2014, LittlePeng9 of Googology Wiki finished his first order oodle theory (FOOT for short), a generalization and extension of first-order set theory. The system, unlike Kyodaisuu's, is a simple but effective extension upon FOST, and one that even has a number to go with it. The name is BIG FOOT (name suggested by Sbiis Saibian), and it's defined as:
FOOT10(10100)
where FOOT(x) is the largest natural number that can be defined in FOOT with at most x symbols (the exponent next to FOOT indicates function recursion). Nathan Ho even decided to publish it as an article on his own website (which, unlike mine and Sbiis's, does not have any one single subject). The article is LittlePeng9's blog post with some additions, along with an introduction which discusses Rayo's number and how people have previously tried to extend it, and how they are not very good extensions. Here is what LittlePeng9 had to say about the number:
"So, uhhh, I guess I just made the biggest number in the existence."
March 3, 2015
Improvements to Extensible-E II complete
This is the day where Sbiis Saibian finally completed his improvements to his Extensible-E numbers. His expansion of his Extensible-E numbers were so huge that he had to split his xE^ numbers from 2 parts to a total of five parts, with a grand total of 15,610 Extensible-E googolisms! Suffice to say that Sbiis Saibian's work in naming googolisms vastly exceeds any other googologist.
May 2015
Jonathan Bowers' "Spaces" article lost
Jonathan Bowers updated his large numbers pages in 2016 with some new googolisms, new pages, released and planned, to explain his large numbers (more on that a few entries down). But the most promising new article of his, a page which may finally firmly solve the mystery of pentational arrays and beyond, was lost in a hard drive crash in May 2015, as Bowers says on his large number hub page. The page reportedly went all the way up to expandal arrays when the hard drive crashed, and Bowers says that he will need to retype that article.
January 1, 2016
Sbiis Saibian's hiatus
On the first day of 2016, Sbiis Saibian decided to put his large number site on hiatus to finish or make substantial progress on another project of his which he had been working for several years but never finished. Although he doesn't say what that project is, when I emailed him about it he told me that it is part of a video game he's been working on for years which he mentioned on the wiki's IRC chat a few times and which I had previously presumed to be the project he paused his site to work on. He promises to end the hiatus either when he finishes his project or at the end of 2016, whichever comes first.
February 2, 2016
Bowers' large number pages update
In early 2016, Jonathan Bowers released an update to his large number pages for the first time in over five years. He devised a variety of new googolisms to fill in the spaces between his existing numbers, devised new names for his various levels of array structures, and even came up with a googolism called "Oblivion" to try and trounce Rayo's number and BIG FOOT. At the moment it's not clear how well-defined the function Bowers uses for that number is. It's very similar to the recurring attempts by Googology Wiki users to create "largest number definable in x symbols" functions, so some people found it rather disappointing.
Bowers says that he lost a very promising article about the spaces for his higher-level arrays which have long been unclear to a hard drive crash some months back, and that he'll need to retype it. Hopefully it will be released soon. If I were Bowers, I would have posted bits of the page, one at a time, and let readers give input on it. Even though BEAF's reputation has been tarnished over the years, it's still a shame that he lost the file for that page.
Later events?
Will there be later events in the timeline? As googology continually grows, so will this timeline. I intend it to be a semi-comprehensive catalog of events in googology, any and all I find to be important. Therefore, yes, I will add any and all googology events that I find to be notable as they come, or as I find out about them.