Tanya Khovanova's Math Blog

by Gregory Marton

I recently had the following chat with a particular calculator:

• e^(e^(e^(e^e))) = 10^(10^(10^6.219196780089781))
• e^(e^(e^(e^(e^e)))) = 10^(10^(10^(10^6.219196780089781)))
• e^(e^(e^(e^(e^(e^(e^(e^(e^e))))))) = 10^(10^(10^(10^(10^(10^(10^(10^6.219196780089781)))))))

It seems odd to me that putting a few more e’s down the bottom should result in it thinking there were the same number of extra 10s at the bottom. In fact, I’ve never seen a calculator answer in this form at all. I’m especially intrigued that the final power of ten seems to be the same in all three cases, so it can’t even just be estimating. Do you have any thoughts on what screwy counting could be behind these particular answers?

May the Mass times the Acceleration be with you!

John Conway taught me how to tell time at night. But first I need to explain the notions of the “time in the sky” and the “time in the year.”

The clock in the sky. Look at Polaris and treat it as the center of a clock. The up direction corresponds to 12:00. Now we need to find a hand. If you find Polaris the way I do, first you locate the Big Dipper. Then you draw a line through the two stars that are furthest away from the Big Dipper’s handle. The line passes through Polaris and is your “hour” hand. Now you can read the time in the sky.

The hand of the clock in the sky makes a full rotation in approximately 24 hours. So if you stare at the sky for a long time, you can calculate the time you spent staring. Keep in mind that the hand in the sky clock is twice as slow as the hour hand, and it turns counter-clockwise. So to figure out how long you’re looking into the sky, take the sky-time when you start staring, subtract the sky-time when you stop staring and multiply the result by 2.

To calculate the absolute time, we need to adjust for the day in the year.

The clock in the year. A year has twelve months and a clock has twelve hours. How convenient. You can treat each month as one hour. In addition as a month has about 30 days and an hour has exactly 60 minutes, we should count a day as two minutes. Thus, January 25 is 1:50.

Fact: on March 7^th at midnight the clock in the sky shows 12:00. March 7^th corresponds to 3:15. So to calculate the solar time you need to add up the time in the sky and the time in the year and multiply it by 2. Then subtracting the result from 6:30, which is twice 3:15, you get the solar time.

You are almost ready. You might need to adjust for daylight savings time or for peculiarities of your time zone.

This time formula is not very precise. But if you are looking into the sky and you do not have your watch or cell phone with you, you probably do not need to know the time precisely.

In my life as a female mathematician I have quite often encountered a mathematician’s wife who, despite not knowing me, already hated me. It was clear that it had nothing to do with me personally, so being clueless and naive, I assumed that most men were cheaters and that their wives were extremely insecure and jealous.

Then one day one of the wives decided to be frank about her feelings. It wasn’t about cheating, she told me. It was that she felt distant from her husband. He lived in a world of mathematics from which she was excluded. I on the other hand shared this world with him.

It was very sad. It meant that I incurred their jealousy, not because of my sins, but because I am a female mathematician.

Let me tell you another story that helped me realize how all-encompassing this world of mathematics can be for some people. Once I had a very close friend who we will call Jack. I do not want to name him as he is a famous mathematician. Jack told me that the strongest emotions he feels are related to mathematics. He can only feel close to someone if he can share a mathematical discussion with them.

Now I understand the wives better. Husbands like Jack invest so much more in their math world and their colleagues than they do in their home life, that it is not surprising the wives are jealous. Because women mathematicians are scarce, when I appear in their husbands’ world, it adds another layer of worry.

Another thing that Jack told me is that he gets such a euphoric feeling when he discovers a new math idea that it is better than any orgasm. Of course, this statement made me question the quality of Jack’s orgasms, but in any case, for some mathematicians math is an aphrodisiac.

If math is an aphrodisiac, then tattooing a formula on the lover’s body may well enhance the orgasm. I just remembered the movie by Ed Frenkel. But I digress.

If math is an aphrodisiac, then I understand jealous wives even better. Without sex I can give their husbands pleasure they can’t.

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I am taking my dog to tweet. He’ll check other dog’s posts at every pole and will leave his comments.

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Not many people know that 1000 chameleons is a chabillion.

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The Internet paradox: it connects people who are far apart, and disconnects those who are close.

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We bought a cell phone for our TV set. We attached it to the remote control, so that we can call our TV when the remote is lost.

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Mary’s mom failed arithmetic. Actually, that is why Mary was born.

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Your call is very important to us. Please, hold. And in the meantime, to protect your health, our customer care team encourages you to drink a glass of water at least every two hours.

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Who is your favorite computer game character?
The stick from Tetris.

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Our new boss invited everyone to bring their keyboards to his office. He kept the employees who had worn letters and laid off the ones with worn arrows.

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My son will be a hacker. He started his career before he was born: he found a flaw in the condom.