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#1
12-10-2011, 4:37 PM
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Reverse Polish?
There exists a logical structural methodology in symbolic logic and applied mathematics that is sometimes easy, sometimes difficult to quite get or understand at first, until simplified by use and practice.
The applications of and for these concepts in the real world of human communications can shine a whole new light on impedance mismatches within and around learning, and understanding. "Reverse Polish notation (RPN) is a mathematical notation wherein every operator follows all of its operands, in contrast to Polish notation, which puts the operator in the prefix position. It is also known as Postfix notation and is parenthesis-free as long as operator arities are fixed. The description "Polish" refers to the nationality of logician Jan Łukasiewicz, who invented (prefix) Polish notation in the 1920s. The Reverse Polish scheme was proposed in 1954 by Burks, Warren, and Wright and was independently reinvented by F. L. Bauer and E. W. Dijkstra in the early 1960s to reduce computer memory access and utilize the stack to evaluate expressions. The algorithms and notation for this scheme were extended by Australian philosopher and computer scientist Charles Hamblin in the mid-1950s. During the 1970s and 1980s, RPN had some currency even among the general public, as it was widely used in handheld calculators of the time – for example, the HP-10C series and Sinclair Scientific calculators. ..." - Wikipedia The example given above in Wikipedia clarifies: Reverse Polish (postfix) notation: 3 4 + Prefix notation: + 3 4 Infix notation: 3 + 4 The answer is all cases above is equal (mathematical) and identical (symbolic logic). Practical applications abound: Sudoko puzzles ... electronic circuits ... criminal investigation ... music writing ... International diplomacy ... data base heaps ...  Follow along and hit the + sign, enter, for the number column total at the tutorial end ...  Sound track not worthy, but concept video shows some of the power behind this throne. ....... This is not a brain teaser, this is an immensely powerful tool for learning ...
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"Mr. President, if your #1 priority is fixing the problem, let's abolish the #IRS and ensure it NEVER happens again!" - Texas Senator Ted Cruz - 6/2/2013 First: Every single IRS employee from top to bottom should immediately be put on unpaid administrative leave until the gangs of sharks, liars, thieves and pranksters are discovered and prosecuted to the fullest extent of Federal and State laws ... RICO statutes applied, UnConstitutionality discovered and treasonable offenses established. Last edited by FastEddy : 12-10-2011 at 5:01 PM. 
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#2
12-11-2011, 1:48 AM
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RP used to drive me nuts, on them early calculators.
Eventually, after business school and my trusty HP12C, I have been seduced into the RP frame of mind. I would rather use that device than fumble with mouse clicks using Microsoft Calc or whatever they call it. You may be old enough, as am I, to remember the good old adding machine with that hand crank mechanism. I once saw a demo on television (no YouTube in those days, let alone internet) wherein an abacus expert beat an adding machine expert in summing a column of figures. I wonder how the abacus user would fare against the modern RP calc user? ..
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.. There comes a time when the wealthy privileged class becomes SO rich, SO powerful, that they see themselves as gods, and the rest of us as slaves. At that time there will be some who will serve those gods as priests and house slaves, thinking that they have a route to immortality for themselves, blaming the slaves for their inability to become gods too. How wrong they will find themselves ... but by then it will be too late.
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#3
12-12-2011, 10:10 AM
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Quote:
 The Slide Rule (remember those?) can likewise be "ambidextrous": Either-or multiplies/divides by Reverse Polish and Prefix type, in effect ...  By looking at several ways to manipulate numbers (and logic symbols) you see that it is the thinking processes and the manipulation of the "calculator" that opens the brain cells to alternate ways of thinking about numbers ... mental speed and acuity improves ... Final scene in "A Few Dollars More" in which Blonde' performs interpolation and summation of a "heap" of numbers: No Name Clint: "... 22 ... 22? ... [shoots] ... 27 ..." Lee van Cleef: "Any troubles boy?" No Name Clint: "No Old Man ... 'thought I was havin' trouble with my adding ... It's all right now. ... [spit]" ... middle of this video ...
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"Mr. President, if your #1 priority is fixing the problem, let's abolish the #IRS and ensure it NEVER happens again!" - Texas Senator Ted Cruz - 6/2/2013 First: Every single IRS employee from top to bottom should immediately be put on unpaid administrative leave until the gangs of sharks, liars, thieves and pranksters are discovered and prosecuted to the fullest extent of Federal and State laws ... RICO statutes applied, UnConstitutionality discovered and treasonable offenses established. Last edited by FastEddy : 12-12-2011 at 10:39 AM.
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#4
12-12-2011, 2:38 PM
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I drive my kids nuts when I think out loud calculating a number, be it dividing or multiplying. My high school algebra teacher failed me on one test, and when I went to talk to him after class he said flat out "I dont see how you ever got the right answer based on your work" I had to show him how I was using exponents to shortcut the calculation process. After he understood what I was doing, he changed my fail to a nice letter higher up the alphabet. One of my memories out of the history of mathematics is of those who went back and re-examined each of Euclid's premises, and found two that were not "inherently obvious" and out of those came two new (at the time) branches of mathematics. Sorry, cant remember which branches - something about curved space or curved surface areas or something. Any case, I enjoyed the take from A Few Dollars more ..
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.. There comes a time when the wealthy privileged class becomes SO rich, SO powerful, that they see themselves as gods, and the rest of us as slaves. At that time there will be some who will serve those gods as priests and house slaves, thinking that they have a route to immortality for themselves, blaming the slaves for their inability to become gods too. How wrong they will find themselves ... but by then it will be too late.
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#5
12-13-2011, 12:16 PM
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 ].Same, same happened to me in first semester college calculus. I left a "plus C" off of an integration and a dy/dx off of a derivative on the final exam ... Leaving that "plus C" off is nothing new in modern calculus, (Einstein did it: E does not equal M*c^2, but it does equal M*c^2 + C) but my college calculus teacher wasn't having any of it = A big fat "F" fur sure. By the By: Einstein's energy equivalence, E = M*c^2 + C, can also be written in Reverse Polish Notation as M*c^2 C + is total E (total energy) ... In astro-Physics, that C is almost always accepted as the "background noise" of the Universe and was first detected with radio telescopes as "the thermal left over" from "the original creation", a subtle hint of the Big Bang = thermal static of about 2 to 3 degrees Kelvin. Total-e
__________________
"Mr. President, if your #1 priority is fixing the problem, let's abolish the #IRS and ensure it NEVER happens again!" - Texas Senator Ted Cruz - 6/2/2013 First: Every single IRS employee from top to bottom should immediately be put on unpaid administrative leave until the gangs of sharks, liars, thieves and pranksters are discovered and prosecuted to the fullest extent of Federal and State laws ... RICO statutes applied, UnConstitutionality discovered and treasonable offenses established.
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#6
12-13-2011, 4:16 PM
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Quote:
__________________
.. There comes a time when the wealthy privileged class becomes SO rich, SO powerful, that they see themselves as gods, and the rest of us as slaves. At that time there will be some who will serve those gods as priests and house slaves, thinking that they have a route to immortality for themselves, blaming the slaves for their inability to become gods too. How wrong they will find themselves ... but by then it will be too late.
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