My first exam at university was Logic and I still remember the joke told by proffesor. Now this very joke one can find everywhere on internet. As well as in a Marc Hadon’s book “The Curious Incident of the Dog in the Night-Time“ chapter 181.
There are three men on a train. One of them is an computer scientist and one of them is a engineer and one of them is a mathematician. And they have just crossed the border into Scotland (I don’t know why they are going to Scotland) and they see a brown (or black) cow standing in a field from the window of the train (and the cow is standing parallel to the train).
And the economist says, “Look, all the cows in Scotland are brown.”
And the logician says, “No. We can say there are cows in Scotland of which one, at least, is brown.”
And the mathematician says, “No. We can say there is at least one cow in Scotland, of which at least one side appears to be brown.”
There are different options for passengers but in my mind these three works best since a computer scientist just wants to get within an order, an engineer wants a realistic approximation within the permissible error, and a mathematician wants it precisely right. Story makes it clear to us the level of accuracy we are striving.
Story speaks of the nature of generalization and needs for precision. On the edge of a cliff one millimeter makes a difference between life and death, while in the light of the evolution one millennium is just a blink in the eye of time.
“At least one” is a mathematical term meaning one or more. It is commonly used in situations where existence can be established but it is not known how to determine the total number of solutions.
Is this the only possible conclusion one can come to here? Try to flip it around: is there a way to criticize the mathematician and praise the computer scientist?
The moral of the story is that we should be careful making generalizations. Examples of wrong generalization you can find everywhere. People make conclusions based on a single case.
Prepared by Danilo Borovnica.