Chisanbop was one I remember there was a book being sold on TV to teach kids an easier method of arithmetic.raecoffey wrote: Tue Feb 07, 2023 6:50 pmCan you name some others?Tdarcos wrote: Tue Feb 07, 2023 11:40 am There are other math systems that use intrinsic properties of numbers to make calculations easier than the standard single multiply and shift mode for multiplying two numbers. One I happen to like is the Trachtenberg System. There are others.
Because it [Trachtenberg System] was the first one I ever discovered after finding the 1960 book by Ann Cutler. Wikipedia gives a partial description of the system.
Now, realize that mathematics were mostly developed by Arab scholars during the dark ages. Consider this: how is multiplication done? From right-to-left, the way Arabic is written. Trachtenberg developed his system while in a Nazi Concentration Camp as a way to keep his sanity; the system relies on using as little paper as possible because it was very hard for Trachtenberg to obtain. Some calculations are done right-to-left, others left-to-right depending on which is easier.
One example is how to multiply by 2; you would normally do it right-to-left, so 316802 x 2 is computed as 2x2=4, 0, 2x8=(carry 1)6, 2x6+1=(carry 1)3, 1x2+1=3,2x3=6, or 633604. But using Trachtenberg's system it's done left-to-right using 1 rule:double each digit (with carry) so you can compute double almost as fast as you can write it 483267 x 2 is 8 16 (so add 1 to first digit making it 96) 6 then 4, 12, so make that 52, 14, making it 534 for result of 966534.
Now, let's do 6% sales tax. The rule for multiply by 6 is:
* From right, add half of the neighbor (digit to right) to each digit. If the current digit is odd, add 5.
$710.43 - 3 has no neighbor, add 5 =8
4 + 1 (1/2 of 3) =5
0 +2 (1/2 of 4) =2
1+5+0 =6
7+5+0(1/2 of 1)=12, write 2, carry 1
0 (digit to left of 7)+3+1(carry)=4
426258 or $42.63
E.g. in this system, the intrinsic for multiplying by 6 is you add each digit plus 1/2 of digit to right plus 5 if this digit is odd. There are specific rules to make each number calculation. A separate set of rules for large numbers, for division, and others.raecoffey wrote: Tue Feb 07, 2023 6:50 pm What is your definition of intrinsic here dealing with math?
I am a computer programmer. Algorithms - the method of describing how to solve a problem - will be done with the mathematical notations of the language used to write the code used to perform the function. But the general method of how it is done is generally described in English.raecoffey wrote: Tue Feb 07, 2023 6:50 pm And can you please give me an example of one of these " intrinsic propetries" in motion, mathematically? I don't understand how anyone can try to talk about science, especially mathematics using only words.
