Q: Whats worse than getting a flat tire?

A: Getting ** two** flat tires.

Q: Whats worse than finding a worm in your apple?

A: Finding ** half** a worm in your apple

We promote math knowledge and understanding with situations, anecdotes, jokes, photos, videos and anything else that will make you smile, laugh, think and enjoy things mathematical.

Q: Whats worse than getting a flat tire?

A: Getting ** two** flat tires.

Q: Whats worse than finding a worm in your apple?

A: Finding ** half** a worm in your apple

A student returned home from a date at 3 AM. Her parents were very upset, “You’re late! You said you’d be home by 11:45!”

“Actually,” the girl replied, “I’m right on time. I said I’d be home by 1/4 of 12.”

[Origin: unknown; several variations of this joke appear on various web; a version of this joke, submitted by Zhang Wenyi, was published in *Reader’s Digest*, July 2009, “Laugh!:)”, p. 27]

Is it always true that if you have a good thing, then having more of it is better and, conversely, if you got something bad having more of it is worse? Case in point, consider the following situation (usually told as a joke):

“What is worse than finding a worm in the apple you are eating?”

“I don’t know… Two worms.”

“No. Half a worm!”

It is common among friends and relatives of professionals to expect a favorable treatment, that is, a discount or a freebie, when they need the service or product of their professional friend. And it is almost just as common practice for the professional to oblige with such an expectation. For example, if you have a friend who is a plumber, I dare presume that, when your toilet is plugged and you urgently need a plumber, you might call your plumber friend, ask his assistance and expect him to give you a discount or perhaps even a freebie. You may then reciprocate buying him a dinner or a bottle of wine but the value of this thank-you gift is much lower than the value of the service.

Or, say, your friend is an author who just published a new book. You probably expect her to give you a free copy of the book, perhaps even an autographed one with a personal dedication.

*My question is this:*

In mutual relationship, why it is the pro who has to favor you? Why dont you favor the pro?

Consider the example of your author friend. Why should she give you a free copy of her book? Why shouldnt you buy her book and pay double its price?

OK, I know, the bookseller cant take a payment larger than what they sell it for but you get the idea. Beside, we can figure out a workaround this formal limitation. For if you truly like your friend and want to (a) encourage her writing and/or (b) encourage her publisher to publish more of her books and/or publish more books of this kind, then you can send the extra payment with an explanation to either the publisher or your friend the author. Or at least, buy the hardbound book at a full-price retailer, not a paperback at discounter, and then, when the paperback comes out, buy it too.

Where is the math here?

Think of positive and negative numbers and especially think of the duality between the positives and negatives. In this case, why the positive should be a discount for you and the financial negative to your friend and not the other way around?

This is a clear example how positive and negative numbers are often set by the relevant context. For example, if I owe you money, then, as far as I am concerned, my debt to you has a negative value while, from your perspective the debt has a positive value. Similarly, for pilots going up is a positive experience and ascending is indicated by positive numbers and descending by negative numbers. On the other hand, for a scuba diver going into the ocean depth is a most positive experience, so for her descending is measured by positive numbers, which also indicate the increase in pressure, while ascending is measured by negative numbers.

When I talk to students, teachers and others about negative and positive numbers, I like to say:

*There is nothing negative about the negative numbers.*