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Home / [ENG VER] These are the Definitions of Googology, the Study of Large Numbers (Also History and Googologist Lists)

[ENG VER] These are the Definitions of Googology, the Study of Large Numbers (Also History and Googologist Lists)

Assalammu‘alaikum Wr. Wb.

Hello guys! Do you like studying Mathematics? Are you interested in learning about Numbers or Big Numbers? Usually we only know to the Exponential only to recognize Large numbers. Introduction, namely Googology. Indeed, studying Googology is fun because it transcends the instinctive limits of the Human Brain and also transcends the Limits of Astronomy and Physics.



Article Sources : Wikipedia.org and Googology.wikia.org

DEFINITIONS  AND ETYMOLOGY

Googology is a field that studies big numbers like Googol, Faxul, and others. A person who studies large numbers is called a Googologist, while a mathematical object that deals with Googology is called a Googolism. Googology is known by the comic names given to Googology, such as "Meameamealokkapoowa oompa", "a-ooga", and "Wompogulus".

Although the word Googology is relatively new, the study of this field has been recorded as old as the 3rd Century BC. Namely in a book called Sand Reckoner, written by Achimedes. Notably, he developed a number system for numbers ranging from 0 to .

The Antithesis to Googology is Ultrafinitism, which states that large numbers simply do not exist.

HISTORY

Although the term Googology is modern, the subject has been around for as long as humans have been fascinated by a Large Number of people.

The earliest known work by a "googologist" is probably the Sand Reckoner written by Archimedes, a Greek polymath, sometime in the 3rd Century B.C. In it he develops a system of numbers extending to 108 × 1016. There are other examples in Ancient History that illustrate mankind's fascination, and even adeptness, with large numbers. Some religious texts contain some very large numbers. Although the Bible contains no definite numbers greater than 108, it uses figurative language in many places to relate very large numbers such as "the stars in the sky" or "the sands of the sea".

With the advent of Modern Mathematics, and the impending invention of the computer, mathematicians of the 19th and 20th Centuries had access to numbers larger than ever before. This fascination was relayed to the laymen through popular books on mathematics. "Googol", "Googolplex", and "Mega" were all introduced in books of popular mathematics, written by mathematicians who wanted to explain to the laymen what mathematicians meant when they invoked Infinity.

Eventually, the fascination of large numbers spread to a class of amateurs who took it upon themselves to extend the ideas hinted at in these popular books on mathematics. These became the early Googologists. This took on something of a form of a hobby that still continues today, with amateurs writing papers claiming to have "invented the largest number ever". That being said, not everything produced is brilliant, nor is it all Crank Mathematics. There is a variety of skill levels, and some of Googology actually comes from professional mathematicians, not amateurs. In particular, there seem to be 3 (Three) Classes :
  1. Googologisms that arise in Professional Mathematics as side-effects of more serious math problems, such as Graham's number and Skewes' number.
  2. Googologisms devised recreationally by Professional Mathematicians, such as Chained Arrow Notation and Steinhaus-Moser Notation.
  3. Googologisms created solely by amateurs, such as array notation and Hyper-E notation.
During most of the 20th century, early googologists worked in isolation. Since the advent of the internet however, there has been a greater confluence of ideas, and several websites have sprung up to gather the loose bits of information that form the body of knowledge, methodology, and conventions known as Googology. Perhaps the most important of these sites are Googology Wiki, Robert Munafo's site, and One to Infinity (Sbiis Saibian).

Furthermore, from 2002 through 2013, a loosely knit community of Large Number Enthusiasts, dubbing themselves Googologists, has emerged, building websites, sharing information, and developing a culture with a unique approach to one particular challenge: "What is the largest number you can come up with?" Googologists generally avoid many of the common responses such as "infinity", "anything you can come up with plus 1", "the largest number that can be named in ten words", "the largest number imaginable", "a Zillion", "a hundred billion trillion million googolplex", or other Indefinite, Infinite, ill-defined, or Inelegant responses. Rather Googologists are interested in defining definite numbers using efficient and far reaching structural schemes, and don't attempt to forestall the unending quest for larger numbers, but rather encourage it. So perhaps a more accurate description of the challenge is "What is the largest number you can come up with using the simplest tools?"

As far as mathematical fields go, googology is an oddball. It precariously teeters on the edge of what we call "Science", becoming more of an art form as opposed to a mathematical study.

Although googology remains, and shall probably always be, an Obscure, Esoteric, and Impractical Study, it at least now has a Name, a History, and a Community.

Origin of the Word "Googology"

The word "Googology" is taken from 2 (Two) Words, and the one who came up with the idea for this name was Andre Joyce.
  • The First was "googol." This name was given by a 9-Years-old boy, Milton Sirotta, who was a cousin of the mathematician, Edward Kanser, in 1921, for a number equal to 10100.
  • The last one is "logy" which is taken from the word "logos" which means "study".


LIST OF GOOGOLOGIST

Here are some people who are experts in the field of Googology.

1. Chris Bird

Chris Bird is the British Mathematician who invented the Bird's Array Notation, and helped develop and correct errors in the Bowers Exploding Array Function (BEAF) Notation. His extension to Array Notations, outlined in his 75-Page Papers, Array Notations for Super-Huge Numbers, led to the development of the modern Bursting Array Function. He also proved that Array Notation with 5 Entries or more grew much faster than Chained Arrow Notation.

2. Jonathan Bowers

Jonathan Bowers is an American amateur mathematician, and invented the BEAF (Bowers Exploding Array Function) Notation. He is the father of modern Googology. He introduced Array Notation to the public in 2002, a simple function that defines a provably larger number than the Knuth Arrow, Steinhaus Polygon, or Chained Arrows. Years later, with help from Chris Bird and John Spencer, Bowers developed a generalization called BEAF, which competed with many of the larger Functions in the Fast Growing Hierarchy.

3. John H. Conway

John Horton Conway was a British mathematician active in Finite Group Theory, Node Theory, Number Theory, Combinatorial Game Theory, and Coding Theory. He also contributed to many Branches of Recreational Mathematics, most notably the invention of the mobile automaton called the Game of Life. Belaulah also discovered the Chained Arrow Notation.

Born and raised in Liverpool, Conway spent the first half of his career at Cambridge University before moving to the United States, where he held the John von Neumann Professorship at Princeton University for the rest of his career. As of April 2020, at the Age of 82, he has died of Complications from COVID-19.

4. Hyp cos

Hyp cos invented Strong Array Notation, arguably the fastest growing Computing Function in Googology.

5. Harvey Friedman

Harvey Friedman is a Mathematical Logician who taught at Ohio State University until his retirement in Summer 2012. He has also investigated various combinatorial functions, including n(k), TREE(k), dan SCG(k) in Googology.

6. Nathan Ho

Nathan Ho is the man who invented the Googology Wikia Site and created the number of BIG FOOT.

7. Larwence Hollom

Lawrence Hollom is a Googologist (Googologist) who invented the Hyperfactorial Array Notation. He wrote about it on his large number of websites, and claimed that his dimensional array also reached the Large Veblen Ordinal (LVO).

8. Andre Joyce

AndrĂŠ Joyce coined the word "Googology" and established one of the first large number naming systems.

9. Donald Knuth

Donald Ervin Knuth Knuth is an American Computer Scientist, Mathematician, and Professor Emeritus at Stanford University. He was the recipient of the 1974 ACM Turing Award, which is informally considered the Nobel Prize in Computer Science. Knuth has been called the "Father of Algorithmic Analysis". In Googology, he has also discovered Knuth's Up Arrow Notation.

10. LittlePeng9

LittlePeng9 defined what was supposed to be the largest named number at the time, BIG FOOT. Later it was found to be ill-defined.

11. Hugo Steinhaus dan Leo Moser

Hugo Steinhaus was a Jewish-Polish mathematician and educator. Steinhaus earned his PhD under David Hilbert at the University of GĂśttingen in 1911 and later became a professor at Jan Kazimierz University in LwĂłw (now Lviv, Ukraine), where he helped found what became known as the LwĂłw School of Mathematics. He is credited with the "inventor" mathematician Stefan Banach, with whom he made important contributions to functional analysis through the Banach-Steinhaus theorem. After World War II Steinhaus played an important part in the establishment of the mathematics department at Wrocław University and in the revival of Polish mathematics from the destruction of the war.

While Leo Moser was an Austrian-Canadian mathematician, known for his Polygon Notation, which is called the Steinhaus-Moser Notation and the Moser number. His work was one of the first notations to reach , even though the Ackermann Function is older.

The Two Scientists (Googologists) have discovered the Steinhaus-Moser Notation
in Googology.

12. Tibor Rado

Tibor Rado was a Hungarian Mathematician who moved to the United States after World War I. He also designed the Busy Beaver Function, the original Uncomputable Function.

13. Agustin Rayo

AgustĂ­n Rayo discovered the famous function famous function named after him (Rayo's Number), one of the fastest-growing functions known.

14. Sbiis Saibian

Sbiis Saibian is an American recreational mathematician and "megalo-arithmologist" best known in the Googology Community for maintaining the Web Book entitled A Guide to the Finite (Formerly A Finite Journey). In the book, he introduced and explained various googological notations and created his own, called Extensible-E System. This site was first publicly launched on December 9, 2008 (Dzulhijjah 11, 1429 H), Four Days after the Googology Wiki was first created.

15. P進大好きbot

P進大好きbot (Or Read as P-Suzumu daisuki botto) discovered the largest named number today, the Large Number Garden Number. Indeed, from the his name in Japanese because this Googologist comes from Japan.

16. Aarex Tiaokhiao

Aarex Tiaokhiao is a young American Googologist. The name is believed to be a pseudonym. He developed several extensions of the known notation and published them on his own site. He invented various extensions to other notations.


To see this Article in Indonesian, can be see in here.

Oh hey, Stay Tuned for the next Article on Inzaghi's Blog, which is about "Ordinal Formulas in Googology".

Thank You 😄😘👌👍 :)

Wassalammu‘alaikum wr. wb.

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