African Windscreens are made from two directions of overlapping straw woven together. Long rows take less straw and less time, but are less protective against the wind. Since wind speed increases the higher you are off the ground, the lengths of weaves decrease logarithmically as the height increases.  This is an excellent example of logarithmic engineering as distinct from any integer system of calculation. from a windscreen maker near Bamako, Mali.  Courtesy Ron Eglash. He includes a tutorial to learn windscreen weaving patterns.

African Windscreens are made from two directions of overlapping straw woven together. Long rows take less straw and less time, but are less protective against the wind. Since wind speed increases the higher you are off the ground, the lengths of weaves decrease logarithmically as the height increases.  This is an excellent example of logarithmic engineering as distinct from any integer system of calculation.

from a windscreen maker near Bamako, Mali.  Courtesy Ron Eglash.

He includes a tutorial to learn windscreen weaving patterns.

Why don’t the English words for “eleven” and “twelve” take the form #-teen like the rest of their neighbors? When Glen Lean was studying counting systems in Indonesia, he formalized a system to categorize the language of numbers, and was able to depict migration patterns during the settling of the islands. Cyclic Patterns: this language (above chart) has unique words for 1-4, as well as 20. So it is said to have a cycle of 4, and a super-ordinate cycle of 20 Operative Patterns: symbols like + and ×, which are spoken when speaking the name of the number.  An analog in English would be to say the number 9 is to say “4 times 2 plus 1” Number Morphs are the numerals which have distinct words (1, 2, 3, 4, 20).  This sequence of number morphs is called the Frame Pattern. developed by Z. Salzmann and Glen Lean afterthought- often in Indian-European base-10 systems’ number morphs are separated from each other exponentially, all number morphs after 10 occur at 10ⁿ.  It’s sufficient to just describe it by its Number Base.

Why don’t the English words for “eleven” and “twelve” take the form #-teen like the rest of their neighbors?

When Glen Lean was studying counting systems in Indonesia, he formalized a system to categorize the language of numbers, and was able to depict migration patterns during the settling of the islands.

Cyclic Patterns: this language (above chart) has unique words for 1-4, as well as 20. So it is said to have a cycle of 4, and a super-ordinate cycle of 20

Operative Patterns: symbols like + and ×, which are spoken when speaking the name of the number.  An analog in English would be to say the number 9 is to say “4 times 2 plus 1”

Number Morphs are the numerals which have distinct words (1, 2, 3, 4, 20).  This sequence of number morphs is called the Frame Pattern.

developed by Z. Salzmann and Glen Lean

afterthought- often in Indian-European base-10 systems’ number morphs are separated from each other exponentially, all number morphs after 10 occur at 10ⁿ.  It’s sufficient to just describe it by its Number Base.

(Source: uog.ac.pg)

Oksapmin’s 27-body part counting system (NW Papua New Guinea)

(Source: culturecognition.com)

Etymology of Algorithm Muhammad ibn Musa al-Khwarizmi (ca.780 - ca.850 AD) contributed heavily to Arab mathematics and astronomy, substantiated algebra as a method of calculation, and introduced Indian numerals to the west. The second of his two landmark works on mathematics was lost in its original Arabic form, but Latin translations (~12th century) still survive. The image depicts how the document begins with Dixit algorizmi, Latin for “so says Al-Khwarizmi”. Algorism and algorithm began to refer to the technique of performing arithmetic using the Hindi-Arabic numeral system.

Etymology of Algorithm

Muhammad ibn Musa al-Khwarizmi (ca.780 - ca.850 AD) contributed heavily to Arab mathematics and astronomy, substantiated algebra as a method of calculation, and introduced Indian numerals to the west. The second of his two landmark works on mathematics was lost in its original Arabic form, but Latin translations (~12th century) still survive. The image depicts how the document begins with Dixit algorizmi, Latin for “so says Al-Khwarizmi”. Algorism and algorithm began to refer to the technique of performing arithmetic using the Hindi-Arabic numeral system.

(Source: maa.org)

Etymology of Algebra By the 5th century AD, algebraic techniques from Indian astronomy that were used to handle calculations with variables garnered a name, Bijaganitam- “the other math” (bija- another or second, ganitam- mathematics). Bija also has etymological ties to “seed”, the implication being algebra was recognized as the original method of computation. The 13th century saw the Islamic Renaissance and India was a frequent target of invasion. The Arabs assimilated this Indian form of calculation, and named it Al-Jabr- “the reunion of broken parts” (Al- the, Jabr- reunion), from which we get “algebra”. Image credit: Agathe Keller, Making diagrams speak, in Bhaskara I’s commentary on the Aryabhatıya

Etymology of Algebra

By the 5th century AD, algebraic techniques from Indian astronomy that were used to handle calculations with variables garnered a name, Bijaganitam- “the other math” (bija- another or second, ganitam- mathematics). Bija also has etymological ties to “seed”, the implication being algebra was recognized as the original method of computation.

The 13th century saw the Islamic Renaissance and India was a frequent target of invasion. The Arabs assimilated this Indian form of calculation, and named it Al-Jabr- “the reunion of broken parts” (Al- the, Jabr- reunion), from which we get “algebra”.

Image credit: Agathe Keller, Making diagrams speak, in Bhaskara I’s commentary on the Aryabhatıya

(Source: web.archive.org)

“The success of Indian mathematics [in the Gupta period] was mainly due to the fact that Indians had a clear conception of the abstract number as distinct from the numerical quantity of objects or spatial extension.”
A.L. Basham, The Wonder That was India

History of zero as a placeholder

like in the number 103

Babylonian tablets show Babylonian math from as far back as 1700 B.C.E., but it wasn’t until about 400 B.C.E that a placeholder showed up, looking like two marks “.  103 would have appeared like 1”3 (granted, their number system appeared entirely different from ours).  In Babylon before 400 B.C.E., 103 was expressed as 13, and its difference from the actual 13 was intended to be derived through context.  (we still do this: “three-fifty bus fare” and “three-fifty airplane fare”)

Meanwhile, the subject was of no concern to the Greeks because their math was geometry based and consisted of pictures.

In India, a similar system of a dot as a placeholder slowly transformed into a small circle up top º eventually becoming 0.  Western culture assimilated their system and here we are.

(Source: www-groups.dcs.st-andrews.ac.uk)