“There is no problem the mind of man
can set that the mind of man cannot solve.”
― Samuel Johnson
― Samuel Johnson
If you recall this quote, it may be from the 1946 Sherlock
Holmes movie, “Dressed to Kill” starring Basil Rathbone. It does make you think, but it also gives you
hope. It gives hope we can solve anything we come across. It gives hope we can ultimately answer every
question – though some may take more time than others.
Unfortunately, Dr. Johnson was wrong.
The problem here is
that from the work of mathematicians, particularly Kurt Gödel (1906-1978), we
see there are true propositions that cannot be proved, and can never be proved,
true. Many have already been discovered. It seems almost paradoxical that we can prove
them unprovable, but cannot not prove them. The implication is that problem can be set and
then found can never be proved. Such problems are beyond unknown unknowns, they
are undecidable. In other language, we
can with a slight linguistic stretch prove there will be Black Swan events, but
we cannot prove what they will be.
In today’s Coronavirus
event, we find a middle ground for this.
We can agree that a disease will present that will rock the world, but
we can never predict the disease itself, the time it occurs, or where it will
arise.
In terms of computing we can say a problem is decidable
if we can construct a Turing machine which will halt in finite amount of time
for every input and give answer as ‘yes’ or ‘no’. A problem is undecidable
if this is not so. And there are many such problems.
It is simple to say that Samuel Johnson was
wrong. Lots of important people have been
wrong but remain luminaries in our world. But in a deeper meaning, it indicates
we may have one day two entirely different fully compatible explanations of the
universe but will never be able to determine which, if either, is correct. Being more theosophical, we may never be able
to decide whether or not there is a God, maintaining the ages-old feeling it is
a matter of faith.
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