Misunderstanding dynamical systems

I once argued with a woman online — can you imagine? Me, arguing online! — Who claimed that global warming couldn’t possibly be due to human activity, because of the small amount of CO2 our activities release compared to the total in the atmosphere. 

So I slipped her 500 µg of LSD, and said “Let’s see what small amounts of a chemical can really do!”

Ha ha! It was online, so I could not do that.

But imagine if she had never encountered ice but only water between 100°F and 32.5°F. I’m sure if I tried to explain to her that the next drop of 1° would make a huge difference, she would scoff, and say “No, the water is just going to get a little more dense and a little more sluggish.”

Dynamical systems experience phase transitions, where a small move past some point throws the system into a whole new form of behavior. 


  1. Don't you mean between 212 °F and 32.5 °F?

    1. No. I meant what I said. I could have said 212, but it would make zero difference to the example.

    2. So you finally figured out the comment problem on your blog.

    3. Nah, I didn't figure out anything! It just worked!

  2. Also, the search function on your blog is now broken.


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