Notes from the Court Jester:
Math can describe the universe as it is - our most powerful mental
ability; no question about it
You have to be "right" at every step of the way when you use math -
inconsistency points to a lack of logical connection between steps and
is tantamount to error
Why people spend so much time trying to be 'right' and checking each
other's calculations, trying to catch each other out somehow
It's a very absorbing game to play and does lead to genuine insights.
Real science can be done in this way and mostly is
However
The universe is evolving and changing at all scales from moment to
moment, just as the cells in our bodies are in the constant act of
renewing themselves continually
One observer moment is probably never going to be the same as another
etc.
Can mathematics describe an EVOLVING universe as accurately as it can
describe a static one? Newton's laws and Einstein's relativity and all
the subtle variants on these help to do so. Bruno's comp hyp seems to
address an 'eternal' if not somewhat static reality that might even be
taken as 'transcendental'.
Who is dealing with the CHANGING nature of the universe?
I believe that human consciousness is probably a kind of time machine
which, when fully cranked up, can visualise or simulate alternative
futures
We need to be able to do this as well as we can to avoid 'drift' or
'vortex' by the most obviously gravitating future tugging our present
into its flow
'The past can be studied but the future can only be created' (Edward
de Bono) - well, we might say on this list 'selected' - I won't dare
to try and relate this to the "Free Willy" debate!!!
Rather than describe "What IS"
Isn't it time to talk about "What COULD BE"??? We have very little
mental apparatus set up and well-rehearsed to do this
This is also where Math and Logic (IMHO) fail to meet our (rather dire
by now) needs
Lateral Thinking ("possibility thinking") and Critical Thinking
("vertical thinking")
Critical thinking is primarily concerned with judging the truth value
of statements and seeking errors. Lateral thinking is more concerned
with the movement value of statements and ideas. A person would use
lateral thinking when they want to move from one known idea to
creating new ideas. It can also be put as, critical thinking is like a
post-mortem while lateral thinking is like diagnosis
Example 1 of Lateral Thinking (Full Perceptual Scan)
It took two hours for two men to dig a hole five feet deep. How deep
would it have been if ten men had dug the hole for two hours?
A standard high-school arithmetic question; but who can be certain of
the ultimate value of the right answer if the universe is changing
between the time the problem was posed and the answer was arrived at?
The "right" answer appears to be 25 feet deep. This answer assumes
that the thinker has followed a simple mathematical relationship
suggested by the description given. Vertical thinking quickly arrives
at this academically correct, though potentially simplistic or crude
result. Anyone proclaiming that "25 feet is the only correct answer"
would not want to be in a job as an engineer or works foreman.
Lateral Thinking (which can involve intentional humour or other
provocative statements) involves a thorough perceptual scan of the
situation BEFORE any attempt at an answer is made. Using this
technique, we can generate the following highly pertinent observations
that make the "correct answer" seem almost useless by comparison:
• Time remaining the same, the answer (25 ft.) assumes a linear
proportionality between the Number of men and the Work quantity, which
is not necessarily true. There
can be quantitative/qualitative factors affecting the
relation and thus the answer. The following points for instance may
alter the relation:
• A hole may need to be of a certain size or shape so digging might
stop early at a required depth.
• The deeper a hole is, the more effort is required to dig it, since
waste soil needs to be lifted higher to the ground level. There is a
limit to how deep a hole can be dug by
manpower without use of ladders or hoists for soil removal,
and 25 feet is beyond this limit.
• Similarly, the men need to be able to get out of the hole later -
which depending on how steep the sides are. Normally, getting out of a
25 foot deep hole requires
ladders, rope or other equipment.
• Ten men would need more room to work side-by-side, and so may need
to dig the hole wider rather than deeper. Each man digging needs space
to use a shovel.
• Deeper soil layers may be harder to dig out, or we may hit bedrock
or the water table.
• Digging in soil, clay, or sand each present their own special
considerations.
• Ten men are more likely to disagree on a digging method than two men.
• Holes required to be dug beyond a certain depth may require
structural reinforcement to prevent collapse of the hole.
• The shape of the hole may not be a prism: if it is a cone-shaped
hole, which is wider at the top than the bottom, then even if the
volume of the hole is five times that of
the first hole, it may not be five times as deep.
• Digging in a forest becomes much easier once we have cut through
the first several feet of roots.
• It is possible that with more people working on a project, each
person may become less efficient due to increased opportunity for
distraction, the assumption he can
slack off, more people to talk to, etc.
• More men could work in shifts to dig faster for longer.
• There might be fewer shovels than available men.
• The two hours dug by ten men may be under different weather
conditions than the two hours dug by two men.
• Rain could flood the hole to prevent digging.
• Temperature conditions may freeze the men before they finish.
• A wild bear may approach the hole and maul the men while they are
up to their shoulders in said hole.
• Would we rather have 5 holes each 5 feet deep?
• The two men may be an engineering crew with digging machinery.
• Maybe one of the 10 men will die, less likely if only 2 men are
working.
• One man in each group might be a manager who will not actually dig.
• The extra eight men might not be strong enough to dig, or much
stronger than the first two.
• There must be a reason for digging and ten men are more likely to
hinder each other's progress, due to personal profit and
expectations : competition, disagreement on
the place where it would be better to dig, disagreement on who
should use a shovel to dig and who should use a bucket to carry the
soil out of the hole, ...
• A greater number may induce a greater diversity and the babel tower
syndrome may occur: incompatibility within the workers and failure to
understand each other
effectively.
• With ten men you are five times more likely to break a shovel.
• Assuming that they will dig the hole five times faster, they first
take a 96 minute break; however, at the end of their 24 minute shovel
dance, they have only a three foot
deep hole because the mathematical variables were far too
complex for mere hole diggers to consider.
• The men could begin digging horizontally after reaching their depth
of five feet, leaving the 10 men with a wider, 5 foot deep hole.
• "Digging holes" may actually mean something extremely vulgar.
The most useful ideas listed above are outside the simple mathematics
implied by the question.
Example 2 of Lateral Thinking (Provocation to induce idea movement)
Consider the statement "Cars should have square wheels."
When considered with critical thinking, this would be evaluated as a
poor suggestion and dismissed as impractical. The lateral thinking
treatment of the same statement would be to speculate where it leads.
Humour is taken intentionally with lateral thinking. A person would
imagine "as if" this were the case, and describe the effects or
qualities. Someone might observe: square wheels would produce very
predictable bumps. If bumps can be predicted, then suspension can be
designed to compensate. This leads to the idea of active suspension. A
sensor connected to suspension could examine the road surface ahead on
cars with round wheels too. A car could have a sensor for determining
when it was going to hit a bump that feeds back to suspension that
would know to compensate. The initial "provocative" statement has been
left behind, but it has also been used to indirectly generate the new
and potentially more useful idea.
Example 3 of Lateral Thinking (Changing the way a situation is viewed)
A man and his son are in a car crash. The man is killed and the son is
taken to hospital gravely injured. When he gets there, the surgeon
says "I can't operate on this boy - he is my son!" (Surgeons are
forbidden to operate on their own offspring) How is this possible?
This is an example of a quick assumption blocking the mind's ability
to explore alternatives. In this case the assumption is that the
quintessential doctor is a male; this leads to the conclusion that
either the surgeon or the "father" in the car crash was not the boy's
real father.
If you change your perception to allow for a female surgeon, then the
answer is suddenly obvious, the surgeon is the boy's mother. Using
lateral thinking, we can see the problem from a different view rather
than operating on the immediate and more obvious assumptions.
Other examples of lateral thinking: One assumes the surgeon is telling
the truth. Maybe he was simply wrong (the son might have looked
exactly like his own son) or maybe he was lying, because for some
reason he didn't want to operate on him (he could have felt bad or
drunk alcohol before).
The son could have two fathers - one of them could have been his
adoptive father. Or if the boy was one of two separated twins, with
the other growing up with the surgeon for whatever reason, then the
surgeon would have recognized the boy as his own son.
regards,
Kim Jones
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