I am trained as a mathematician. Mathematicians are some of the most anal people in the world. Everything have to be precise to a fault: an omitted word, a changed sign, or a misplaced symbol could turn a long mathematical proof null and void.
I am trained to proofread many times. If people try to scare me while filling in government forms, by saying “you must fill this form carefully, make sure the are no mistakes, otherwise they will reject your application,” I laugh at their face, and I tell them to chill, dog, because you’re talking to Mister Details here.
Consider these statements:
- Statement 1: “Everyone is this class is a math major OR a physics major.”
- Statement 2: “You will either get at least a C- OR fail the class.”
Statement 1 makes sense in mathematics and also in plain English. Statement 2 makes perfect sense in English, but not in mathematics.
In mathematics, OR a logical disjunction, not simply a part of speech. If we say, “A or B”, then what we mean is “A, or B, or both”. That is the mathematical meaning of OR.
Statement 1 makes sense because each person in the class could be a math major, a physics major, or both. However, in Statement 2, you can either get at least a C-, or fail the class. It is not possible to get both: getting at least a C- and failing at the same time (presumably that is what the teacher means). A mathematician would say Statement 2 like this:
- Statement 2a: “You will either get at least a C- OR fail the class, but not both.”
Some mathematicians bring this speech pattern to everyday life. Once I asked a math professor where I could find him if I wanted to discuss homeworks. The professor replied, “I will usually be in my office, or in the common room, but not both.” Duh. What are you, Teleporter Man?
As if that is not enough:
- Statement 3: “A rainbow has seven colors.”
- Statement 4: “A rainbow has five colors.”
A regular guy on the street would say that Statement 3 is correct, while Statement 4 is incorrect. A trained logician would say that both Statement 3 and Statement 4 are correct. And he would be right, because a rainbow has five colors: violet, indigo, blue, green and yellow. The statement doesn’t specify that “five” covers “all” colors on the rainbow, so the statement “A rainbow has five colors” is correct.
To create the distinction, the statements must be made precise:
- Statement 3a: “A rainbow has exactly seven colors.”
- Statement 4a: “A rainbow has exactly five colors.”
Aha. Now the logician would agree that Statement 3a is true, while Statement 4a is false.
That’s not all. Consider these statements:
- Statement 5: “X is open.”
- Statement 6: “X is closed.”
In English, if one of the statements is true, then the other must be false (for example, let X be “the window”, or “that jar”, or “my fist”.)
However, a mathematical object (specificially, a set in a topological space) could be either (i) closed and not open, (ii) open and not closed, (iii) both open and closed, or (iv) not closed and not open. Try to wrap your mind around that one.
Being trained as a mathematician, I like to talk, think and write in a precise manner (that’s why I’m a big fan of Strunk & White). I cannot stand ambiguity and vagueness, whether in speech, thought or writing. Sloppy speeches and sloppy ideas lead to sloppy actions. It is grating to see people using words imprecisely, especially corporate bullshit. God helps those people who write and speak with much pretentiousness, using big words devoid of precise meaning.
Pomposity is the enemy of precision.