FAKE MATH EXPOSED!Blonzonics News Network - Sept. 2, 2017.Numerous textbooks on advanced math display the famous identity: e^{πi} = -1 Fake Math. The correct way to evaluate mathematical expressions, tirelessly iterated by top-notch Facebook postings, is PEMDAS: Parentheses, Exponentiation, Multiplication/Division, and then Addition/Subtraction. So to compute e^{πi} , PEMDAS dictates that the exponentiation e be done ^{π}first, followed by multiplication by i. This yields a value of about 23.14i, plus state tax where applicable. That numerous textbooks, and professionals such as Euler and Cotes, would make such a careless error is shocking evidence of how mismanaged the math business was for centuries. But with Facebook we are now witnessing a renaissance of top-flight mathematics, much as National Enquirer brought Top Scientists to the the fore. But does this affect the Facebook multitude, proud to not do any algebra each day? Alas it does, because the error permeates numerous computer programs for engineering, including those used to design the cars and airplanes in which the unalgebraics and their loved ones travel. These programs often use the Discrete Fourier Transform, which involves the expression e^{-2πijk/n}, suspiciously close to a Σ rumored to be of foreign origin. Careless programmers have computed the exponentiation last. But if they had remembered PEMDAS, they would know to do the exponentiation e^{2} first before multiplying by those other letters and dividing by n. Worse, the correct order of operations decimates the frequently used, if sadly mistaken, Fast Fourier Transform (FFT). Several Top Algorithmists are working on fast implementations of the corrected transform.Reactions from other notational quarters were mixed. A spokeshacker for the Church of S-Expressions stated that "We teach PAB - Parentheses Are Beautiful" and declared that "Infix was invented by Satan to confuse humanity". Veterans from the HP Calculator side of the 70's Minimal Keystroke Wars, savagely fought with sums of products and products of sums until the dropping of the Spreadsheet Bomb, expressed puzzlement over what parentheses are, or why anyone would need them. The C++ Guild intoned that PEMDAS was just a first step on the path to Full Precedence Knowledge, expressed by: PSrSiSdFcFcSMaPiPdUpUmLnBnCcIAoSoDmPmMDRASLsRsLtLeGtGeEqNeBaBxBoLaLoTcToAC which is surprisingly easy to memorize if you know the right tune. Contrary to initial reports, the exponentiation-first problem does not impact JPEG, which relies on a Discrete Cosine Transform. Hence photographic postings on Facebook are as reliable as they always have been. |