Sunday, April 30, 2017

Google Autodraw

Imagine playing pictionary with a computer.

Google Autodraw let's you do just that. You doodle/sketch on a board, and the computer continuously tries to guess what you are drawing. In a short amount of time, my guess is that it is going to get pretty good!

Here's an example:

Friday, April 28, 2017

History of the Logarithm of Negative Numbers

Not too long ago, I did a blog post on how matlab and python have different responses to logarithms of negative numbers.

It turns out that the history of the logarithm of negative numbers is truly fascinating, and had Leibnitz, Bernoulli, Euler, and the other greats embroiled. Take a look at this article (pdf) by Deepak Bal.

Here is the abstract:
In 1712, Gottfried Leibniz and John Bernoulli I engaged in a friendly correspondence concerning the logarithms of negative numbers. The publication of this correspondence in 1745 sparked an interest in the mathematical community on the topic. In this paper I will discuss the evolution of the logarithmic concept in the time leading up to their discussion. I will then give a synopsis of the correspondence followed by a description of a paper by Leonhard Euler in which he addresses the issue.

Sunday, April 23, 2017

End of The World

As I sat bewildered and amused, I knew it was a story that I had to be save for her wedding reception.  Next to me, my older daughter was sobbing inconsolably, "why does it all have to end this way?"

Rewind ten minutes. It was not a conversation that was supposed to go like this.

You see, my dad is absolutely fascinated by the night sky. I thought I'd play the role of a good son and father, by testing whether talking about space would ignite my daughter's interest in the subject. Perhaps, next time they met, they could obsess over a shared interest.

Me: Do you know the name of our galaxy, M.?
M.: Of course, the Milky Way!
Me: Good! They teach you good stuff in school. Now, harder question; do you know which galaxy is right next to ours?
M.: No, which is it, Baba?
Me: Andromeda. And I bet you haven't heard this. Billions of years later, Andromeda and the Milky Way are going to smash into each other. It is going to be spectacular!

M.: (troubled) Can't we do anything to stop it?

I cracked open a laptop, and fired up a browser.

Me: Look this is Tallahassee. This is Florida. This is the Earth. This is the solar system (zooming out each time). This is the Milky Way, and this is Andromeda. We are too tiny to do anything meaningful.
M.: (definitely worried) What does that mean? Does it mean we all die?
Me: (scoffing) Oh, don't worry about that. This is going to happen after BILLIONS of years. We will all be dead long before that. In fact, perhaps the Earth will be gone before that.
M.: What do you mean, Baba?
Me: You know how the sun is a star, right?  Like all stars, it shines by burning gas. It has tons of gas, kinda like Baba's tummy. But once it runs out of most of that gas, it might expand to about 3 times its size, and gobble up Mercury, Venus, and probably Earth.

I noticed tears streaming down her cheeks. I had to console her. And I had do it fast.

Me: But don't worry. Dont' worry! This is not going to happen for  BILLIONS of years more. We will all be gone by then.
M.: (now sobbing inconsolably) why does it all have to end this way?

After a few minutes, she regained her composure. I was debating whether it would be tone-deaf to talk about the real things to be scared of, like global warming, or pandemics, or..., when she interrupted me with a plea.

"Baba, can we please not talk about space, anymore?"

Tuesday, April 11, 2017

Strogatz and Art of Mathematics

For some reason, these Steve Strogatz' columns from 2015 on the "Art of Mathematics" have resurfaced.

Here are two blog posts, which explains the origins, inspiration, and mechanics.

The associated website is chock full of useful resources and ideas designed to help liberal arts students appreciate the art and joy of mathematics.