## More Infinite Number Weirdness

Some time back, I had a bad habit. I would open a cupboard to get something, then forget to close it. My wife was somewhat miffed by this – understandably, because our kitchen had an infestation of moths at the time. So, she found herself having to tell me, again and again – close the cupboard doors!

## Deconstructing April Fool’s Day

Okay, I admit it – my previous blog post was published on April 1. The foundations of mathematics are not really under attack, not now. But they were once!

Here’s a famous puzzle: imagine a village barber, who cuts the hair of everyone who doesn’t cut their own hair. Sounds simple enough, but who cuts the barber’s hair?

## Foundations Of Mathematics Under Attack!

Trinity College researcher finds fatal flaw in mathematics’ logical foundations.

## Arithmetic Of The Infinite

Infinite numbers are weird. They gnash their teeth against our intuition. They don’t behave how, deep down, we think numbers ought to behave.

That should not be surprising, since our intuition was formed around tiny little numbers like 3.1, 4000 or seven billion and two.

## What Is Counting?

My son asked me a riddle this afternoon – “What goes up but never down?”

I said “An elevator!”

He seemed surprised by my answer, so I said “Voyager I!”

Then he complained that the riddle was so generic, there were millions of possible answers. I asked him if there was some traditional answer I was supposed to give, and he said that he didn’t know of one.

Do you?

## Circles wherever you look.

You see a silhouette of a three-dimensional shape. The silhouette is a circle. Then, you turn to get another view. The new silhouette is still a circle, so you turn again. And again. Every time you look at the shape, you see a circular outline.

Is it a sphere?

## How To Find Big Prime Numbers

The best way to find big prime numbers is to use a thing called “modular arithmetic” and another thing called “fermat’s theorem” – not the famous “Fermat’s Last Theorem” – Fermat’s theorem is much less famous and much more useful than Fermat’s Last Theorem.

## Solar Powered Saffron

My solar panels have generated 1500 kWh of energy since they were installed 6 months ago.

Now, Einstein tells us that energy has mass. How heavy is 1500 kWh? We can use E = mc2 to find out.

Here, E is 1500 kWh, the speed of light c is 186000 miles/second. Unfortunately, we can’t just divide 1500 by the square of 186000. Sure, that would give the mass, but not in any unit I’m familiar with – when you tell me how much something weighs, I want to hear it in pounds, or kilograms, or ounces… even centiweight would do, if I have Google handy.