![]() Issue 28 – Cunning Computational ContraptionsĬlick below to find out more… Click to read the latest issue of CS4FN magazine Lego Computer ScienceĬlick to read our Lego-themed series featuring pixel puzzles, compression algorithms, number representation, gray code, binary and computation.Predicting the future: marbles, binary and the I Ching.Investigating the I Ching pattern helped Leibniz to work out the mathematics of binary arithmetic and on to thinking about machines to do calculations using it. It is just a different way of writing down numbers. In binary, however, 1011 represents instead one eight plus no fours plus one two plus a one (8 0 2 1) so eleven. 1011 in decimal represents one thousand plus no hundreds plus one ten plus a one (one thousand and eleven). So in decimal, 123 represents one hundred plus two tens plus three ones (one hundred and twenty three). To work out the value that the number represents you multiply each digit by its column value and add the results. Whereas in decimal each column of a number like 123 represents a power of 10 (ones, tens, hundreds, …) in binary each column represents a power of 2 (ones, twos, fours, eights, …). The order, as Leibniz realised, is a counting system, equivalent to our decimals but where you only have two digits (0 and 1) rather than our ten digits (0…9). Think of a break in the lines as a 0 (yin) and no break as a 1 (yang). How do the hexagrams correspond to binary? It is not in the lines themselves but the pattern of line breaks down the middle that matters. Shao Y\0x014Dng had apparently picked the sequence deliberately because of the binary pattern, so understood it as a counting sequence, if not necessarily how to do maths with it. Thought to be written by a Chinese scholar, Shao Y\0x014Dng, it is this version that Leibniz was given and that aroused his interest because the order of the hexagrams follows the pattern we know of as binary (see Predicting the future). However, in a later version, from around 1000 AD the order in which they appear is different. In the earliest versions of I Ching, the order of the hexagrams suggests that they were not thought of as numbers as such. The chosen hexagrams then told the person something about their future. This was done in some unknown but random way, using stalks of the Yarrow plant, standing in for dice. To use I Ching, a series of hexagrams were chosen. In I Ching, they each represent possible predictions about the future (a bit like horoscopes). The 64 hexagrams are all the possible symbols that can be made from six rows of lines in this way. HI, my name is Steve Ma Ching I am of Chinese/Samoan descent.Born in New Zealand and lived in Western Samoa for a Few years,educated over there at Chanel College(Moamoa) and then St Josephs College(Lotopa).Im 47 years old and have been tattooing for 32 years. Each row is either a solid horizontal line or two shorter lines with a gap in the middle. It uses 64 hexagrams: symbols consisting of six rows of lines (see right). The earliest copies date from around 3000 years ago. I Ching is one of the oldest Chinese texts. I Ching the ancient Chinese divination text, several thousand years old, is based on a binary pattern…
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