The point is that it’s not always so easy to know when our thoughts are irrational, and it can happen even to brilliant people. It requires some effort and vigilance to avoid that trap.

It certainly would be a smaller hit on performance than switching to the iGoogle page (which is fast anyway, but relatively more bandwidth intensive).

Thanks for the suggestion.

I suppose that would work, though I’ve always stuck with the “regular” Google homepage because I prefer it to iGoogle. I think even iGoogle would benefit from that simple notifier — it would take much less space.

The Pythagoreans were a science “cult” that followed the teachings of Pythagoras who described everything as rational quantities. They were a group that believed that science was meant only for the chosen few and that commoners should have nothing to do with it.

When one of their students (could be Hippasus but no one is sure) discovered that the square root of two was not rational they decided that no one was to know of this since their world view would be incomplete. It remains as a question whether the one who made the discovery was killed or not.

To say “However, Pythagoras was unwilling to accept that he was wrong”, i think undermines the genius that was Pythagoras because the truth of the proof that the student found was SO obvious no one would dare to deny its validity. The proof is so elementary that even school children can understand it.
Wikipedia proof

The inability to accept change and challenges to theorems is a barrier not only to the introduction and propagation of new ideas, it even keeps individuals from growing and learning themselves. It’s a symptom of comfort: if an idea or a state is comfortable and then is challenged, it shakes things up and makes then not so comfortable.

But there are two other stories about Hippasus. The first says that Hippasus was expelled from the Pythagorean school because he published doctrines of Pythagoras, while the second says that he was drowned at sea for revealing the construction of the dodecahedron in the sphere and claiming it as his own. But since the Pythagoreans’ supposed pledge to secrecy was most likely false, the authenticity of these stories is questioned

Different story here.

Awesome post. I just wonder how Pythagoras was able to sentence Hippasus to death? Was Hippasus his slave? Or was Pythagoras able to sentence his students to death? Would love to know more…

rule #1: im #1

Don’t worry about the above comments - the truth is, MOST native speakers don’t know how to do that particular proper punctuation. Your English is fine

Also, I’m impressed with how quickly Godwin’s Law played out….

By the way, I am also thankful for the quote you put at the end of your article. I’ve been looking for something along that lines to counter an email signature quote of a colleague. I didn’t want to be brutal about it, and this has the subtlety I needed.

Interesting. Thanks!

http://www.bartleby.com/141/strunk.html#1

Some people have no appreciation for the classics…

Sorry if I wasn’t clear. I meant that we don’t expect someone who hasn’t studied physics to be any good at PHYSICS, so why do we expect someone who has never studied probabilistic thinking to be any good at that.

I’ll check out the works you suggested, thanks. I’m very interested in cognitive biases and heuristics. I actually have “Judgement under Uncertainty” (the Kahnemann/Tversky/Slovic book) on my desk, but I haven’t read it yet. I also have “Rational Choice in an Uncertain World” by Dawes.

It would be interesting to trace out what learned, embodied metaphors are the basis for what types of probability we *are* good at and them examine how we either 1) might map our badly intuited cases to existing metaphors (essentially forms a systematic teaching method for important but hard to intuit probabilities) or 2) construct alterations to childhood environments that could generate the metaphors that would aid our badly intuited probabilities.

I’ll only involve the name of “Nassim Taleb” and “Black Swan” this once but he gives the simple example of how we might have bad rare probability estimation because we may use our intuitions based on embodied metaphors of area (R = p * C, after all) which breakdown when the area is formed by a long, skinny rectangle because we are bad at estimating physical dimensions that vastly exceed our physical body scope of distance. We can estimate “yards”, “feet” and “cubits” well because these are based on our body lengths but longer distances are not.

The key probability probably of most interest is a power-law probability. This can be “reduced” to a straight line with a logarithm but we don’t have a natural intuition for logarithms - there is no embodied metaphor that captures it. In fact, there is no simply embodied metaphor for multiplication or division either (Lakeoff co-wrote a book on mathematics and embodied metaphors - don’t have my copy handy). Part of the problem is the simple visualization of “powers of ten” but then it also needs a linkage to “cause-and-effect” and “time arrow” metaphors in some way. Again our intuitions of time are very badly constrained to scales as narrow as length. Realistically that’s between about 1 second on the low end and maybe a few minutes for most people to at most an hour on the population tail - everything else outside this range is “tool-aided” and abstracted learned understanding.