At the beginning of the 1960's, I was concerned, for my students, by the tempting exhortation of Timothy Leary (and other sharp extremists) to "Drop Out! And Turn On!" But I remembered the flat extremeness of the 50's for "Giving in". Then there began to develop, in the "WeatherMen" and other groups, the terrible noise of terrorism. So, connecting all this to my own natural wamping, I exhorted my students with, "DON'T DROP OUT! DON'T GIVE IN! DON'T BOOM! SIDE-STEP!" For I intuited that creative thinkers and actors, throughout history, used diversionary tactics to avoid confrontation and to "direct traffic" into a more "peaceable and useful" direction.
Later, the Canadian mathematician, Z. A. Melzak, wrote a book, Bypassing, A Simple Approach to Complexity, about the principle of conjugacy in group theory -- which Melzak now applicatied in various daily, technical and scholastic ways.
The bypass strategy bypasses a difficult or "impossible" problem or situation by accomplishing the same intent through solution of another problem. Melzak shows how BYPASSING can be used in math, science, technology, and in daily life problems.
I'll illustate how BYPASS is used to transform the difficult problem of finding the harmonic mean of data into the easy problem of finding an arithmetic mean, and transforming the answer.
harmonic mean of data --------------------> invert| ^inverted numbers| |arithmetic mean x -> 1/x| |is harmonic | |mean V-------------------^ calculate arithmetic mean
BYPASS PATTERN TABLE TYPE DIFFICULT
OR IMPOSSIBLE TASKTRANSFORMATION OF TASK PERFORMANCE OF NEW TASK INVERSE
TRANSFOR-
MATION"Stone Soup" Folk Tale Tramp bypasses peasant woman for handout Gets boiling pot of water with stone for stone soup Gets vegetable and meat bits, salt pinch, "to make stone soup tasty" Removes stone, sups soup Folk Tale Farmer complains to his priest about scolding wife, noisy children, small hut Priest says, first, to take a goat into the hut, then chickens, then farmer's mother-in-law Farmer does so but reaches "breaking point" Then priest says get rid of all of them, and happy farmer says he'd never realized how roomy his hut was Prehistoric Water for suppliant Water in jug Transport jug Hold for drinking Tribal Laws Violate taboos Mythic drama or story Perform or tell Catharsis Theology Christian view of man's "fall" and the "post-fall" conditions Original sin and "fall from grace" Temporal existence in world Redemption through Christ Communi-
cationThoughts to minds Articulated thought Speak or write language Hear or read and receive thoughts Business Goods or Services Exchange Sell goods or services Store money Buy goods or services Arithmetic Repeated counting Recursive definition Addition State count Arithmetic Repeated adding Recursive definition Multiplication State sum Arithmetic Repeated multplication Recursive definition Exponentiation State product Construction Reach height Set up ladder Climb and work Descend, move ladder Consumption Food for future Collect foodstuffs Store Distribute later Criminology Cope with criminals Sentence to prison Incarcerate Release Decoration Dye part of egg Wax masking Dip in dye Remove wax Electric Engineering Power transmission Electric generator Transmission line Electric motor "The Great Escape"
movieEscape prison camp Tunnel down Escape underground Tunnel up to surface
and escapeMeans (averages) Harmonic mean h Reciprocate data Arithmetic mean of reciprocals Invert as harmonic mean h Means (averages) Geometric mean g Logarithms of data Arithmetic mean of logs Anti-log as g Orthopedics Heal broken limb Splint break Splinted healing Remove splint Telephony Voice across space Transduced to electricity Current along line Transduced to sound Transpor-
tationMove scattered belongings Pack belongings Move package Unpack, scatter Counting Count sets Russell's cardinal definition Cardinate Obtain set count Geometry Circle to square Circle to ellipse homologize Square to rectangle Geometry Geometric construction Coordinatize Construct Remove coordinates Gödel's undecidability proof Test proposition p Gödel number of p Diagonalize Undecidable form Group theory Partition group G Subgroup g of
G(norml subgroup) H:Hg (inv) gHg=H Information Conserve information Magnetic mapping Store Degauss information Kenning Sea-stallion:ship Ship:sea Homologize (::) Stallion:land Metabolism Small body "pipes" Solid to liquid Liquid transport Liquid to solid Military Tank crossing ditch Pontoon over ditch Cross pontoon Remove pontoon Mining Transport problems Ore to slurry Transport slurry Drain slurry Respiratory or circulatory Transport problems Gas to liquid Liquid transport Liquid to solid Satire Lampoon the powerful Aesopian format:
Humans replaced by animalsLampoon animals Understood
as satirizing
powerful humansScot Clans Represent a Scot Clan name Name to clan "The Mac-
Donald" as
representativeSolid state physics Paramagnetic cooling Impose magnetic field Thermal insulation Remove magnetic field Tarski modeling Truth-value of proposition Language to metalanguage Truth predication Evaluate proposition Transpor-
tationNew destination Place A: map A Map A to B Map B:Place B Elimination algorithm Eliminate equation from
equations-setDualize equations Subtract like-terms Reduce equation set Logical law of
excluded middle
(tertium non datur)Direct proof of theorem Treat statement to be proven as false Show this
assumption leads to
a contradiction(by "double negative is
positive") claim indirect
proof of statementMathematical problem Solving a difficult functional equation for an unknown function f Take an integral transform
of function fSolve the easy
functional equation satisfied
by transform of fTake in inverse
of the integral transform,
returning to the functional
domainElectronic Production Producing IBM PC clone without violating patent rights Analyze properties of ROM chip, only component unique to IBM PC Translate properties into specifications "Reverse engineering": engineers (who don't know ROM properties) satisfy spe-
cifications with new chip, making clone legalDouble Blind Testing Possible bias from doctors evaluating their own work Doctors administer drug or method to some of sample, "placebo" to others List of sample passed to doctors who know nothing of treatment distribution Independent doctors examine all of sample, reporting possible improvements or declines, providing for evaluation of drug or method
Taking a tip from BYPASSES, I now revised my slogan: "Don't Drop Out! Don't Give In! Don't Go Boom! BYPASS!!!"If you return "evil" by "evil", you INCREASE "the evil in the world". If you return "evil" by an exemplary "kindness", you may DECREASE "the evil in the world", while BYPASSING your own "contamination".
response to evil-doing --------------------> transform| ^enjoy evil deed| |your good into good| |conscience deed | | V-------------------^ pass on good deed to offenderIf you can't do this, try BYPASSING the offender's territory. If you can't do that, say you've heard that schools and workplaces and neighborhoods can now imbed dot-size cameras all around to maintain security.