Rationality Quotes September 2012

Jayson_Virissimo

Here's the new thread for posting quotes, with the usual rules:

Please post all quotes separately, so that they can be voted up/down separately. (If they are strongly related, reply to your own comments. If strongly ordered, then go ahead and post them together.)
Do not quote yourself
Do not quote comments/posts on LW/OB
No more than 5 quotes per person per monthly thread, please.

Here's the new thread for posting quotes, with the usual rules:

Please post all quotes separately, so that they can be voted up/down separately. (If they are strongly related, reply to your own comments. If strongly ordered, then go ahead and post them together.)
Do not quote yourself
Do not quote comments/posts on LW/OB
No more than 5 quotes per person per monthly thread, please.

There are lots of total orderings on the complex numbers. For example:

a + bi [>] c + di iff a >= c or (a = c and b >= d).

In fact, if you believe the axiom of choice there are "nice total orders" for any set at all.

Importantly, however, the complex numbers have no total ordering that respects addition and multiplication. In other words, there's no large set of "positive complex numbers" closed under both operations.

This is also the reason why the math in this XKCD strip doesn't actually work.

0Spinning_Sandwich14y

The well-ordering principle doesn't really have any effect on canonical orderings, like that induced by the traditional less-than relation on the real numbers. This doesn't affect the truth of your claim, but I do think that DanArmak's point was quite separate from the language he chose. He might instead have worded it as having no real solution, so that any solution must be not-real.

0DanArmak14y

Gah. You're quite right. I should refrain from making rash mathematical statements. Thank you.