Tanya Khovanova's Math Blog

I recently updated my collection of my favorite xkcd webcomics.

Today I would like to discuss the comic entitled “Regrets”. When I saw this comic, the first thing I did was go to Google to check the numbers. All my numbers were taken on September 9, 2008 at around 3:00 p.m.

Here are the Google hit counts:

• “I should have kissed her” — 10,600
• “I shouldn’t have kissed her” — 3,220

The numbers are slightly different than those in the cartoon, but the idea is the same; we regret we didn’t kiss. Does it mean that if you want to kiss someone you should go ahead, or otherwise you would contribute to this pile of regrets? The answer is coming later, but first, let’s see what happens if we change gender:

• “I should have kissed him” — 3,170
• “I shouldn’t have kissed him” — 1,240

The same story overall, but for some reason, there are fewer reports by people who either tried or didn’t try to kiss HIM. Is kissing him less interesting or important? Most probably we still expect men to take the initiative in kissing her.

Then I checked the genderless case:

• “I should have kissed you” — 15,700
• “I shouldn’t have kissed you” — 1,800

Wow. Looks like we really should start kissing each other. Right? But wait. Let’s check the point of view of a kissee, rather than a kisser:

• “You should have kissed me” — 494
• “You shouldn’t have kissed me” — 1,020

We see a completely different picture. It is easy to explain why the numbers are smaller: passive people would be less likely to discuss their feelings. But, even so, they claim that they preferred not to be kissed. Maybe it is OK that people mostly regret that they didn’t kiss. After all, if they had tried to kiss, they might not have been greeted with enthusiasm. This leaves you with a choice between your own regrets that you should have kissed and his/her regrets after you did.

I did regret that I hadn’t kissed you, but I so much prefer that I regret not kissing you than you regret being kissed by me. This small research made me feel better. I will not continue regretting any more.

Ken Fan is running a math club for girls in Cambridge, MA, called “Girls’ Angle”. When I heard about it, my first reaction was surprise. When I was a girl, I would never have been interested in a girls-only math club.

Am I prejudiced? When I was growing up in Russia, there were not very many girls who were really good at mathematics. I would have expected that a girls’ math club would be less challenging than just a math club.

What if someone organized a boys-only math club? I would have been furious. I would have felt it was discriminatory. Should I then feel an equivalent fury about the girls’ club? But I do not feel furious, and I wonder why. Is it because deep down I think no boy would bother being interested in joining a girls’ math club? Is it because I still think a girls’ club would be weaker than a general club? I do not know.

At the same time I agree with Ken, for there are a variety of reasons why girls might prefer a girls-only club. For example, shy girls might feel more comfortable with girls or some girls might feel better able to concentrate without the distractions of boys. In some cases, the parents might have made the decision.

Obviously, since the club has students, there is a demand for it. If there is a demand, there should be a supply. I will support anything that works and helps improve American math education. I even volunteered to give a guest lecture at Girls’ Angle.

Was my lecture at the girls’ club different from my other lectures? Yes, in a way. I asked the girls to help me to finish a sequence. I started writing 1, 1, 2, 3, 5, 8, on the board and no one was shouting the next number. In great surprise I turned back to face the class and saw a forest of raised hands. They patiently waited for my permission to speak. Yes, it felt different.

I decided to check the pricing. It appears that the girls club is twice as cheap as other math clubs, like The Math Circle or S.M.Art School. I can’t help but wonder if the girls are signing up at the Girls’ Angle not because they want to study in the girls-only group, but because it is cheaper.

I am glad that Ken Fan is good at finding sponsors and that there are so many people sympathizing with his cause. However, this situation does seem unfair to boys. Should I be furious that boys are not allowed in this very affordable math club? I do not feel furious, but I decided not to give any more lectures at Girls’ Angle for free. At least not until I give a free lecture to a mixed-gender math club. I want to be fair.

This puzzle is a generalization of a problem from the 1977 USSR math Olympiad:

At the beginning of the game you are given a polynomial, which has 1 as its leading coefficient and 1 as its constant term. Two people play. On your turn you assign a real value to one of the unknown coefficients. The person that goes last wins if the polynomial has no real roots at the end. Who wins?

It is clear that if the last person’s goal is for the polynomial to have a root, then the game is trivial: in this case, he can always make 1 a root with the last move. Also, an odd degree polynomial always has a real root. Therefore, to make the game interesting we should assume that the degree of the polynomial is even.

Though I can’t imaging myself ever being interested in playing this game, figuring out the strategy is a lot of fun.

Here is a math puzzle for kids from a nice collection of ThinkFun Visual Brainstorms:

Wendy has cats. All but two of them are Siamese, all but two of them are Persian, and all but two of them are Maine Coon. How many cats does Wendy have altogether?

This puzzle has two answers: the expected answer and an unexpected answer. Can you find both?

Chris Burke gave me his permission to add his webcomics to my collection of Funny Math Pictures.

This comic doesn’t qualify as a math picture, but it is geeky enough for me to like it.

Here is an arithmetic problem for you:

You have $700 dollars in your checking account. You are sloppy and forget how much you have. You write three checks for $600, $200 and $200. For every bounced check you are fined $25 by your bank. How much in fines will you have to pay for your sloppiness?

Solution: the fine depends on the transaction order. If they process your $600 check first, you will have two bounced checks. If they process a $200 check first, then only your $600 check will bounce.

The question is, what will your bank do if all three checks need to be processed at the same time? There are three options:

• Your bank doesn’t have a good mathematician on the staff and is not aware of this situation, and it processes the checks in random order. In this case you will have either two bounced checks (with a probability of 1/3) or one bounced check (with a probability of 2/3).
• Your bank is evil, and purposefully processes your $600 check first. In this case you are guaranteed to have two bounced checks.
• Your bank cares about its soul and purposefully processes the $600 check last. In this case you are guaranteed to get only one bounced check.

Assuming the worst — your bank is evil — what is the answer to the problem? Do you think you will be fined $50? If so, you are wrong. The company to whom you wrote the check will fine you too. Supposing that the company has the same $25 fine as the bank, can we say that you will be fined $100? Nope, this is not correct either. You are forgetting that companies will reprocess your bounced checks two days later and the checks will bounce again. You will be fined twice for each check by two different entities. Thus, you can face $200 in fines.

My next question is: what do you think is a fair fine in my arithmetic problem above?

Banks and companies have never heard of double jeopardy and do not think that it is unconstitutional to fine you twice for the same mistake. No doubt, the second reprocessing of your checks is done “for your convenience”. “For your convenience” they assume that the bouncing was due to a computer glitch, so they should reprocess your check immediately after it has bounced. “For your convenience” no-one will disturb you to notify you that your checks are bouncing. I also believe that if your fine depends on the random order of processing of checks, the banks should be graceful and shouldn’t pick the more profitable order for themselves. I do think that charging you more than $50 in my example is against the law and is not fair.

The law should protect us against entities that rob us “for our convenience.”

I added some new jokes to my collection of math, computer and geek humor:

* * *

— What do you do to protect yourselves from viruses?
— We use disposable computers …

* * *

Microsoft offers a new service. They sell ad spots in their error messages.

* * *

Sysadmin:
— I do not care if everyone insists that using the name of my own cat as a password is a bad idea! RrgTt_fx32!b, kitty-kitty-kitty …

* * *

Due to technical difficulties the release of Windows 2000 is delayed until February 1901.

* * *

A doctor looking at patient’s X-rays:
— Hmm, multiple hip fractures, tibia and fibula fractures. Oh well, Photoshop can fix all that.

* * *

After learning how much money Bill Gates has, Satan offered him his own soul.

* * *

Question: What did one math book say to the other?
Answer: Don’t bother me. I have my own problems.

* * *

Student: Teacher, would you punish me for something I didn’t do?
Teacher: No, why?
Student: I didn’t do my homework.

* * *

— My teacher said we would have a test today, rain or shine.
— Then why are you so happy?
— Because it’s snowing.

* * *

Question: How many sides does a box have?
Answer: Two — the inside and the outside.

* * *

Question: What did the calculator say to everyone?
Answer: You can count on me.

Just updated my collection of Funny Math Pictures.

Here is a puzzle that my ex-brother-in-law, Dodik, gave to me today:

Prove that every group with more than two elements has a non-trivial automorphism.

I usually love puzzles that are solved with a counter-intuitive brilliant idea. This puzzle is different — I didn’t solve it in one elegant swoop. But I still love the puzzle: it feels so natural, and it’s solution feels so natural, that I even decided to call this puzzle “organic.” Or, maybe, I am just in an organic mood today waiting for my organic bananas to be delivered from Boston Organics.

Here is a funny puzzle from Kvant (1996, vol 4), the best Russian journal of recreational math.

When Alice goes through the looking-glass, she might meet many multi-headed, multi-armed, multi-legged beings. A being with H heads, A arms and L legs is considered:

• smart, if H > A+L,
• strong, if A > H+L,
• fast, if L > H+A.

Can there exist a well-rounded personality behind the looking-glass: someone who is smart, strong and fast at the same time?