Bicycles and Probability Theory Share a Secret
What can a physical object and a mathematical theory share. They are from distinct realms. Probability theory is not essential to make a bike.
Their shared secret is neither one was invented until centuries after the fundamentals on which each were based were known.
Back in Roman times, there were wheels and gears; but no one thought to put them together into a bicycle under the early 1800s. Yes, the Appian Way may have busted a bike rider’s buttocks, but we’ll never know because no one thought to make a bike until the 1800s.
Since ancient Egypt, betting games using dice have been a popular pastime, but no one could understand how to apply numbers to the possibilities. Something either happened or it did not. There was no intermediate position.
Until Blaise Pascal and Pierre de Fermat in the 17th century. They showed useful mathematical results arose from considering the likelihood of throwing die before it was done.
Today, probability is used where knowledge is uncertain or incomplete.
Delayed Invention Logical Implication
Not The creativity necessary to make a bike and to assess the chances in life waited a long time for a particular person to come and put the elements together in a useful collection that we now take for granted.
For more than a millennium, we were limited to horses, mules, and a few other animals to help us travel. And, on the other side, we lacked an essential tool to plan for aggregates of individual events of statistical regularity.
Another lesson the secret revealed is that logic does not reveal all consequences embedded in its premises.
Citation: Bing (DALL-E) drew the image of the strange bicycle.
Logic and Illogic