Science: The Limitations of an Electronic Calculator
Capricorn Construction #2: quick construction of pi in perfect proportions of Nature.
From the Capricorn Construction we know we can construct the ratio of 11/22.454, which is of course equal to the ratio of the larger numbers 11,000/22,454 = 0.489890442...,
and ratio 0.489890442... times line sqrt(6) equals 1.199981614...,
and line 1.199981614... times ratio Phi^2 [2.618033988...] = line (Pi * 1),
because the value 1.199981614... equals Pi * (0.618033988...)^2
(This Pi is constructible using only the compass and straightedge.)
The resulting value for Pi will not be exactly equal to the value on your electronic calculator because the means to produce Pi on the calculator are either beyond total control or are industrial secrets, or both. Here is the problem in a nutshell: An electronic calculator, however large or small, however carefully constructed, must confront and choose solutions to four separate calculation problems:
1) How to add and subtract, multiply and divide;
2) How to establish a value for Pi, and for specific trigonometric functions;
3) How to produce squares and values raised to higher powers;
4) By what means will a multiplication of two numbers be exactly equal to the multiplication of one number times the sum of two other numbers, that is, how will the calculator make 5*7 exactly equal to 5 * (4+3). This may be easy when the numbers involved are integers, but not so easy when the numbers are Pi * Z where we know, or believe, that [tan(54) + sqrt(21)] = Z, exactly.
The functioning parts of the calculator that accomplish the calculations are physical materials, human artifacts, just like boards and nails are human artifacts. They can contain chemical impurities. They do not necessarily achieve the perfection of Nature. For number 1) How to add and subtract, multiply and divide, we know that the chemical composition of the electronic parts - microchips - and microscopic circuits are chosen and designed to effectively render a binary number system, and the ability to compute by employing the “binary” qualities of the semi-conductor parts and other electronic components. This is fine, and reasonably reliable. But do we know with certainty how the device computes or “builds” a value for pi, and for the trigonometric ratios? And do we know what scheme is used to make A * B = exactly A * (D+E) where (D+E)=B?
We cannot assess the alleged “perfection” of the calculator unless and until we know exactly what methods are used to address these issues, AND the percentage of purity of the chemical elements and compounds in the electronic components. This argument in itself should persuade even the most religious scientist that the calculator “does not achieve the perfection of Nature” or its infinitely true proportions. I claim that the equation is correct, and the equation stands waiting for a scientist who believes a total and rigorous de-construction of the calculator is worth the possible outcome: the conclusion that the electronic calculator has limitations that can be clearly defined, and the equation either is true or may be true, exactly. The equation is important enough to be carefully ruled out rather than arrogantly dismissed.
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