### Embarrassing Moments

Had this conversation with my girlfriend:

My girlfriend: If each menu item were assigned a different prime number, you could communicate your entire order in one number, which would be the multiple of all the items you want to order.

Me: That system wouldn't work, because there could be more than one order that would result in the same number.

My girlfriend: No there couldn't. You just factor the number and you know exactly what was ordered.

Me: But what if the number could be factored in different ways? Like, how can the waiter tell if you wanted two "4's" or one "8"?

My girlfriend: That's why you use prime numbers, none of the numbers is a factor of another.

Me: But what if one of the prime numbers

My girlfriend: If a number has factors other than itself and one, it's not a prime number.

By that point she was embarrassing herself so much that I had to stop the conversation. Apparently she's never heard of the "no true Scotsman" fallacy. In this case, she might as well have said: "No true prime number has factors other than itself and one." Yes, dear. [Nodding dutifully.] Whatever you say. I sometimes wonder whether two people, like us, who are so different in terms of intelligence, can really be happy together.

My girlfriend: If each menu item were assigned a different prime number, you could communicate your entire order in one number, which would be the multiple of all the items you want to order.

Me: That system wouldn't work, because there could be more than one order that would result in the same number.

My girlfriend: No there couldn't. You just factor the number and you know exactly what was ordered.

Me: But what if the number could be factored in different ways? Like, how can the waiter tell if you wanted two "4's" or one "8"?

My girlfriend: That's why you use prime numbers, none of the numbers is a factor of another.

*Neither*of your numbers is prime.Me: But what if one of the prime numbers

*is*a factor of another prime number? What will the restaurant do then?My girlfriend: If a number has factors other than itself and one, it's not a prime number.

By that point she was embarrassing herself so much that I had to stop the conversation. Apparently she's never heard of the "no true Scotsman" fallacy. In this case, she might as well have said: "No true prime number has factors other than itself and one." Yes, dear. [Nodding dutifully.] Whatever you say. I sometimes wonder whether two people, like us, who are so different in terms of intelligence, can really be happy together.