Month: September 2014

Prevent errors or fix errors

Posted on by John

The other day I was driving by our veterinarian’s office and saw that the marquee said something like “Prevention is less expensive than treatment.” That’s sometimes true, but certainly not always.

This evening I ran across a couple lines from Ed Catmull that are more accurate than the vet’s quote.

Do not fall for the illusion that by preventing errors, you won’t have errors to fix. The truth is, the cost of preventing errors is often far greater than the cost of fixing them.

From Creativity, Inc.

Sum of geometric means

Posted on by John

Let xn be a sequence of non-negative numbers. Then the sum of their running geometric means is bounded by e times their sum. In symbols

\sum_{n=1}^\infty \left(x_1 x_2 \cdots x_n\right)^{1/n} \leq e \sum_{n=1}^\infty x_n

The inequality is strict unless all the x‘s are zero, and the constant e on the right side is optimal. Torsten Carleman proved this theorem in 1923.

Inverted sense of risk

Posted on by John

Watching the news gives you an inverted sense of risk.

We fear bad things that we’ve seen on the news because they make a powerful emotional impression. But the things rare enough to be newsworthy are precisely the things we should not fear. Conversely, the risks we should be concerned about are the ones that happen too frequently to make the news.

Steep learning curves you wish you’d climbed sooner

Posted on by John

I asked on Twitter today “What steep learning curves do you wish you’d climbed sooner?” Here’s a summary of the replies:

  • R
  • Version control
  • Linear algebra
  • Advanced math
  • Bayesian statistics
  • Category theory
  • Foreign languages
  • How to not waste time
  • Women

IgorCarron‘s response didn’t fit into the list above. He said “I wish I had known that sensing all the way to machine learning is about approximating the identity” and gave a link to this post.