DIFFICULT OR IMPOSSIBLE PROBLEM
-------------------------------->
transform-| ^transforming
ing to a| |to answer
solveable| |original
problem| |problem
V-------------------------------^
solving the problem
Humanizing Hominid
--------------------->
Hominid| Z. A. Melzak ^Hominid
develops| says "Hominid |becomes
external| may have become |Human
Bypasses| human by interior-|thru
(such as| izing bypassing" |Bypassing
some of | |
those | |
below) | |
V-------------------->
Interiorizes Bypassing
_____________________________________________________________________________
How to GLIDE along
--------------------->
From | ^Restore
upright| |stable
stable| BIPEDAL |position
position| WALKING |on outstretched
fall | |leg
forward| |
V-------------------->
extend (say) left leg
(digitized gliding)
_____________________________________________________________________________
Marrow "fork" at site
--------------------->
Take| ^Store
likely| TOOL MAKING |"fork"
bone or| |in bone
stone| |remains
"home"| |for future use
V-------------------->
shape marrow "fork"
_______________________________________________________________________________
Water for bed-ridden
--------------------->
Take| ^Empty into
shell or| |mouth of
pot to| |suppliant
stream| |
V-------------------->
Carry to suppliant
______________________________________________________________________________-
Food or goods at another site (Transport and Storage
---------------------> for two large classes
Pack| ^Empty of Bypasses)
into| |out for
"bag"| |use
V-------------------->
Transport to site
_____________________________________________________________________________
Sharing thoughts another
--------------------->
Transform| LANGUAGE AS ^Heard words
thoughts | BYPASS |transformed
into words| |into thoughts
| |in hearer
V-------------------->
Speak words
_____________________________________________________________________________
Measure inaccessible object
--------------------->
Measure| ^
shadow (b)| |Proportion:
cast by| |a:b::x:c or
shadow-stick| |a/b = x/c
of known| |hence,
length (a):| |x = ac/b
tangent of| |
shadow-triangle| |(Erastothenes estimated
/|a | | the diameter of the
/_| | | Earth by a similar
b V--------------------> Bypass)
Measure shadow cast at
same time by object
(say, pyramid) /|
another tangent / |x
/__|
c
_______________________________________________________________________________
(Arab riding camel in de-
Solve problem with insu- sert sees 3 Arab brothers
ficient structure quarreling, amid 17
---------------------> camels. Seems their father
Puts| ^Re- willed elder 1/2 camels;
his| |claims 2nd, 1/3 camels; youngest
camel| |his 1/9 camels. Division pro-
with| |camel vokes quarrel. Stranger
other| |& de- adjoins his camel to
camels| |parts theirs. Assigns elder 1/2
| | (18) = 9 camels; 2nd, 1/3
| | (18) = 6 camels; youngest,
V--------------------> 1/9(18) = 2 camels. 9 + 6
Apportions camels + 2 = 17. Stranger re-
claims his camel, departs.
_____________________________________________________________________________
Reach/work at high places
--------------------->
Put| ^Climb down
ladder| |ladder &
in place| |remove it
| |
V-------------------->
Accomplish Task
______________________________________________________________________________
Flee across guarded space
--------------------->
Dig| ^Emerge (As in 1963 film, The
tunnel| |from Great Escape)
out of| |tunnel
sight of| |beyond
guards| |guardsight
V-------------------->
Flee underground out sight
________________________________________________________________________________
Walk on broken leg
--------------------->
Splint| ^When leg
broken| |heals,
leg| |remove
| |splint
V-------------------->
Walk on splint-supported leg
________________________________________________________________________________
Eat meat/fish/vegetables procured raw
--------------------->
Put in| ^Eat
cooker| |food
| |
V-------------------->
Soften "food" for mastication
________________________________________________________________________________
Dye Easter egg, leaving undyed portion
--------------------->
Rub| ^Remove (Similar for batik
"undyed"| |wax dyeing)
with wax| |
| |
| |
V-------------------->
Immerse egg in dye
________________________________________________________________________________
PENETRACTION OF ATOM BY WAVE
-------------------------------->
transform-| ^transforming
ing to | |to wave
particle | |state
state| |
V-------------------------------^
penetrate the atom
BYPASS PATTERN TABLE
TYPE DIFFICULT
OR IM-
POSSIBLE TRANSFOR-
MATION PERFOR-
MANCE 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-
cation Thoughts 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 * (mid) 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 * (mid) "The Great Escape"
movie Escape prison camp Tunnel down Escape underground Tunnel up to surface
and escape *
Means (averages) Harmonic mean h Reciprocate data Arithmetic mean of reciprocals Invert as harmonic mean h * (mid) Means (averages) Geometric mean g Logarithms of data Arithmetic mean of logs Anti-log as g * (mid) Orthopedics Heal broken limb Splint break Splinted healing Remove splint * Telephony Voice across space Transduced to electricity Current along line Transduced to sound * Transpor-
tation Move 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 animals Lampoon animals Understood
as satirizing
powerful humans * Scot Clans Represent a Scot Clan name Name to clan "The Mac-
Donald" as
representative * Solid 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-
tation New destination Place A: map A Map A to B Map B:Place B * Elimination algorithm Eliminate equation from
equations-set Dualize 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 statement
Mathematical problem Solving a difficult functional equation for an unknown function f Take an integral transform
of function f Solve the easy
functional equation satisfied
by transform of f Take in inverse
of the integral transform,
returning to the functional
domain
Electronic 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 legal
Double 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