“If John is married to Mary, then Mary is married to John,” Duh, who doesn’t know that? “The computer won’t know this unless you add that statement into its algorithm,” the tutor continued.
Math class in the computing department of a local university in the 1980s. That’s where I was first presented with vocabulary: premises, logic, algorithm and conclusions. I was happy to have words to pin down ideas were already floating namelessly in my head. Having words to articulate my thoughts made me feel clever and empowered.
In order for a computer program to perform a desired task to produce an logical conclusion, the programmer has first to build a base of relevant premises which are defined by him. He then builds the logic which is, broadly speaking, a set of if-then-else statements that eventually leads to a conclusion.
When the completed program receives an input, the input is tested against its premises. If the input is acceptable, it is pushed through the logic statements to produce a logical conclusion. An error message will flash if the input is unacceptable.
Going back to John and Mary, here’s a scratchy example.
X = John
Y = Mary
Mary is tall.
John is tall.
1. X must be human and male.
2. Y must be human and female.
3. If X and Y are married, then they can produce Offspring.
If X & Y are married, and X is tall, and Y is tall,
then there is a 90% chance that Offspring will be tall.
There is a 90% chance that John and Mary will have a tall child.
Had the programmer failed to define X and Y as humans with genders in the premise, then it is perfectly logical for John and Mary to be 2 tall trees that have a 90% chance of producing a tall offspring as a result of their union.
Thus the phrase: If you start with wrong premises, you can end up with a perfectly logical conclusion that is perfectly wrong.
The functional usefulness of math is mostly covered in Primary School. Beyond that, math is about disciplining the mind to reason, and providing the tools for the exercise to take place.
If a student’s conclusion is wrong, check the student’s logic.
If the logic is sound, then examine the student’s premises for flaws.
When the problem is found somewhere therein, the good student will celebrate, while the indifferent student rolls his eyes and says “who cares”.
Society and civilisations are built on existing premises. Its easier to expose a student’s lack of reasoning skill and wrong premises on a math paper than on a public platform where he is shouting to everyone, insisting that 2 tall tree can produce another tall tree. Make sense?
Of course, also never disregard the possibility of the question being wrong.