“There exists among the most primitive tribes of Australia and Africa a system of numeration which has neither 5, 10, nor 20 for base. It is a binary system, i. e., of base two. These savages have not yet reached finger counting. They have independent numbers for one and two, and composite numbers up to six. Beyond six everything is denoted by “heap.””

—  Tobias Dantzig

Number: The Language of Science (1930)

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "There exists among the most primitive tribes of Australia and Africa a system of numeration which has neither 5, 10, no…" by Tobias Dantzig?
Tobias Dantzig photo
Tobias Dantzig 25
American mathematician 1884–1956

Related quotes

“Without the parallel development of systems of monetary - and credit-based exchange there could have been no development of economies beyond the most primitive organizational forms and the most geographically restricted sales.”

Peter Dicken (1938) British geographer

Source: Global Shift (2003) (Fourth Edition), Chapter 13, The Financial Services Industries, p. 437

Gerhard Richter photo

“The first 'Colour charts' were unsystematic. They were based directly on commercial colour samples. They were still related to Pop Art. In the canvases that followed, the colours were chosen arbitrarily and drawn by chance. Then, 180 tones were mixed according to a given system and drawn by chance to make four variations of 180 tones. But after that the number 180 seemed too arbitrary to me, so I developed a system based on a number of rigorously defined tones and proportions... Based on mixtures of the three primary colours, along with black and white, I come up with a certain number of possible colours and, by multiplying these by two or four, I obtain a definite number of colour fields that I multiply yet again by two, etc. But the complete realization of this project demands a great deal of time and work.”

Gerhard Richter (1932) German visual artist, born 1932

Quote on Richter's 'Colour Charts', in an interview with Irmeline Lebeer, 1973; as cited on collected quotes on the website of Gerhard Richter: on 'Colour-charts' https://www.gerhard-richter.com/en/quotes/subjects-2/colour-charts-8
1970's

Peter Greenaway photo

“Counting is the most simple and primitive of narratives -- 1 2 3 4 5 6 7 8 9 10 -- a tale with a beginning, a middle and an end and a sense of progression -- arriving at a finish of two digits -- a goal attained, a dénouement reached.”

Peter Greenaway (1942) British film director

Fear of Drowning By Numbers

Giuseppe Peano photo

“All systems which satisfy the five primitive propositions are in one-to-one correspondence with the natural numbers.”

Giuseppe Peano (1858–1932) Italian mathematician

On what became knows as the Peano axioms, in "I fondamenti dell’aritmetica nel Formulario del 1898", in Opere Scelte Vol. III (1959), edited by Ugo Cassina, as quoted in "The Mathematical Philosophy of Giuseppe Peano" by Hubert C. Kennedy, in Philosophy of Science Vol. 30, No. 3 (July 1963)
Context: These primitive propositions … suffice to deduce all the properties of the numbers that we shall meet in the sequel. There is, however, an infinity of systems which satisfy the five primitive propositions. … All systems which satisfy the five primitive propositions are in one-to-one correspondence with the natural numbers. The natural numbers are what one obtains by abstraction from all these systems; in other words, the natural numbers are the system which has all the properties and only those properties listed in the five primitive propositions

Ray Bradbury photo

“Only if the third necessary thing could be given us. Number one, as I said: quality of information. Number two: leisure to digest it. And number three: the right to carry out actions based on what we learn from the interaction of the first two.”

Ray Bradbury book Fahrenheit 451

Source: Fahrenheit 451

Kevin James photo

“This annoyed me: I was on the phone with somebody today tryin to get a phone number from that person and write it down, but they didn't have phone number rhythm and that pissed me off. You know what I'm talkin about? Phone number rhythm. Especially if there's like an area code involved, like 'two one two - bum bum buh - bum buh bum buh!' That is the rhythm I think we're all familiar with. This guy had no clue! I was like "Okay, Hank. Gimme the number." He's like "Alright. It's two one two nine - fifteen eight eleven six [mumbling incoherently] fou.. tw.. five.. eight.. seven.. two." "Did you throw in your zip code? Cause I got a lot of extra numbers over here. I have extra. I can almost start a new number! What do ya got?! Start again from the top!" They really screw you up on the last four numbers. That's where they get ya. "Five five five - six.. teen forty one" "Dude, I already wrote the six! I made the dash too close, I can't shimmy the one in there now! Forget you!"”

Kevin James (1965) American actor and comedian

Sweat The Small Stuff (2001)

Abdullah Öcalan photo

“Without an analysis of women's status in the hierarchical system and the conditions under which she was enslaved, neither the state nor the class-based system that it rests upon can be understood.”

Abdullah Öcalan (1949) Founder of the PKK

Source: The Political Thought of Abdullah Ocalan (2017), Liberating Life: Women's Revolution, p. 69

Richard Dedekind photo

“Addition is the combination of any arbitrary repetitions of the above-mentioned simplest act into a single act; from it in a similar way arises multiplication. While the performance of these two operations is always possible, that of the inverse operations, subtraction and division, proves to be limited. Whatever the immediate occasion may have been, whatever comparisons or analogies with experience, or intuition, may have led thereto; it is certainly true that just this limitation in performing the indirect operations has in each case been the real motive for a new creative act; thus negative and fractional numbers have been created by the human mind; and in the system of all rational numbers there has been gained an instrument of infinitely greater perfection. This system, which I shall denote by R, possesses first of all a completeness and self-containedness which I have designated… as characteristic of a body of numbers [Zahlkőrper] and which consists in this, that the four fundamental operations are always performable with any two individuals in R, i. e., the result is always an individual of R, the single case of division by the number zero being excepted.”

Richard Dedekind (1831–1916) German mathematician

p, 125
Stetigkeit und irrationale Zahlen (1872)

Prasanta Chandra Mahalanobis photo

“In the absence of social awareness and appreciation of the scientific objectivity among sufficiently large number of civil servants or political leaders, the need of validity has not yet been accepted in the official tatistical system in India. Ofcial statistics in India is treated as an integral part of the dministrative system which is regulated by the principle of authority. Approval of statistical estimates at a high level of authority is accepted as a bstitnte for validity in many ases there is continuing opposition to independent cross-hccks for the validity of the data. Officials have the feeling that two independent estimates, which might differ would be confusing and, in fact unthinkable; therefore independent cross-checks in statistics should be eliminated.”

Prasanta Chandra Mahalanobis (1893–1972) Indian scientist

Quote, Professor P.C. Mahalanobis and the Development of Population Statistics in lndia

“The term system has a number of meanings. There are systems of numbers and of equations, systems of value and of thought, systems of law, solar systems, organic systems, management systems, command and control systems, electronic systems, even the Union Pacific Railroad system. The meanings of "system" are often confused. The most general, however, is: A system is a set of interacting units with relationships among them. The word "set" implies that the units have some common properties. These common properties are essential if the units are to interact or have relationships. The state of each unit is constrained by, conditioned by, or dependent on the state of other units. The units are coupled. Moreover, there is at least one measure of the sum of its units which is larger than the sum of that measure of its units.”

James Grier Miller (1916–2002) biologist

Source: Living systems, 1978, p. 16; As cited in: Sven Rasegård (2002) Man and Science: A Web of Systems and Social Conventions. p. 29

Related topics