Tuesday, May 18, 2021

Certainty

 

Impossible

Impossible, for a plain yellow pumpkin to become a golden carriage,
Impossible, for a plain country bumpkin and a prince to join in marriage,
and four white mice will never be four white horses.
Such fol-de-rol and fiddle-dee-dee of course is
Impossible.

Do scientists ever say that something is impossible?

People crave certainty.  They want to know that an answer is 100% right, or 0% right, with nothing in between.  This appears to be true in many cases in science.  What a scientist is actually saying is not certainty, but the probability of an event occurring within known physical laws.  When scientists say that there is a 0% chance that something will fall up, they are saying that it there is 0% probability of something falling up in the domain constrained by Newton’s Law of Gravity.  They are not saying that it impossible, just that in this domain there is a zero percent probability of something falling “up”. 

The problem occurs when the constraints of the domain are not well understood, it may appear to people that scientists are not certain.  The fact is that scientist are never certain.  They only state a probability of an event.  When the probability is rounded, it may appear that there is certainty, but that does not mean that there is certainty.

A coin flip is said to be fair if it is 50% heads and 50% tails.  This is because the probability of heads or tails are being rounded.  In fact, for an American nickel flipped on a flat surface, there is a 1 in 6,000 chance that the coin will end up on its edge.  The true odds are thus 49.9992% chance of heads, a 49.9992% chance of tails and a 0.0016% chance of it ending on its side.  It is common to round this to 50%/50%/0%.  Scientists are not saying that it impossible for a coin to land on its side.  They are saying that the probability is so small that it is typically ignored.  While scientists may appear to be certain, they are rounding probabilities and constrained to a known domain.  If the rounding is not ignored, and the constraints of the domain are not known, then they will not appear to be certain.  But they were never certain in the first place, it is just that non-scientists are ignoring the rounding and the knowledge of the constraints.

That is also why there is confusion about what constitutes a scientific theory.  A theory might explain 99.9999% of all cases, but since it can never explain 100% of cases it is called a theory.   A theory has been tested, explains almost all cases, but calling it a theory only acknowledges that there might be some small chance that it might not explain everything, is impossible.  After all the only certainty is death and taxes, not science.

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