By some guy on the internet:

Dear Internet,

I am not sure whose idea it was to make me choose impossible to remember passwords making it inevitable that I will forget them - but it was a silly idea.

But not nearly as silly as letting me recover my password using my mother’s maiden name and my place of birth both of which pieces of information are readily available online. Even if they weren’t, I gave the same super-secret pieces of information to every single web site on the internet. Oh! And my first pet and my favourite movie.

Let me give you a hint: THOSE AREN”T SECRET

Luckily for me, when you ask me your silly questions, I type random crap into the answers.

Ha! You can’t fool me!

Love,

R. Clown

I don’t know why but Pat Robertson is suddenly on my TV and he and his co-host are taking it in turn to say things like:

I am sensing that one of our viewers has a torn meniscus but God says it’s gonna be fine.

and

The viewer with a mass in your stomach that you think might be cancerous…you just need to pray some more and God will make it right.

I don’t know what that’s about but I just got through reading a huge thread in which two communities of atheists are arguing whether Richard Dawkins is intellectually lazy because he attacks a strawman version of religion, the hypothetical adherents of which believe in a personal God who intervenes in our lives. Apparently no one believes in that kind of God any more and Dawkins should address more sophisticated conceptions of the divine.

The accommodationist atheists also say it’s rude to point out that people like Pat Robertson might not be telling the truth.

[The argument happens way down in the comments of a post claiming that the New Atheists are right-wing, foreign policy hawks. I read it so you don't need to. ]

Regular readers know that I am a big fan of Better Explained in which Kalid makes mathematical ideas accessible.

Today’s installment:

Integration is just multiplication when one of the operands is changing.

Most people grok integration as area under a curve but, as Kalid explains, area is just one convenient way of visualizing multiplication…but we don’t need to visualize multiplication as multiplication is already pretty straightforward - in the simplest case, it’s just repeated addition.

Many ideas in maths start out simple like that and then gradually generalize to a more complex idea. In Kalid’s words:

Our understanding of multiplication changed over time:

• With integers (3 × 4), multiplication is repeated addition
• With real numbers (3.12 x sqrt(2)), multiplication is scaling
• With negative numbers (-2.3 * 4.3), multiplication is flipping and scaling
• With complex numbers (3 * 3i), multiplication is rotating and scaling

We’re evolving towards a general notion of “applying” one number to another, and the properties we apply (repeated counting, scaling, flipping or rotating) can vary. Integration is another step along this path.

In other words,

Integration is just a better multiplication

or, conversely,

Multiplication is a special case of integration when the values are static.