army1987 comments on Rationality Quotes March 2012

Comment author: Eliezer_Yudkowsky 03 March 2012 08:10:32AM 18 points [-]

With the great historical exception of quantum mechanics.

Comment author: CasioTheSane 08 March 2012 03:52:45AM * 7 points [-]

I suspect this is because we're still missing major parts of quantum mechanics.

Richard Feynman's famous quote is accurate. Before I studied physics in college I was pretty sure that I still had a lot to learn about quantum mechanics. After studying it for several years, I now have a high level of confidence that I know almost nothing about quantum mechanics.

Comment author: Eliezer_Yudkowsky 08 March 2012 05:36:28AM 2 points [-]

Try reading this.

Comment author: Thomas 03 March 2012 08:48:22AM 4 points [-]

In fact, most people don't understand the Relativity. Most still rejects Evolution. It wasn't easy to understand the Copernican system in the Galileo's time.

It is easy to understand for a handful, and it seems obvious only to a few, when a new major breakthrough is made. Galileo was wrong. It may be easier, but not "easy to understand once a truth is revealed".

Comment author: [deleted] 03 March 2012 10:27:24AM * 1 point [-]

It wasn't easy to understand the Copernican system in the Galileo's time.

I suppose people didn't understand it because they didn't want to, not because they couldn't manage to. (Same with evolution -- what the OP was about. I might agree about relativity, though I guess for some people at least the absolute denial macro does play some part.)

Galileo was wrong.

More like stuff that was true back them is no longer true now.

Comment author: Thomas 03 March 2012 10:55:37AM 2 points [-]

I suppose people didn't understand it because they didn't want to

I suppose not. Why? People either have an inborn concept of the absolute up-down direction, either they develop it early in life. Updating to the round (let alone moving and rotating Earth) is not that easy and trivial for a naive mind of a child or for a Medieval man.

A new truth is usually heavy to understand for everybody. Had not been so, the science would progress faster.

Comment author: [deleted] 03 March 2012 11:25:15AM * 2 points [-]

I don't see how that contradicts my claim that it's not that people couldn't understand the meaning of the statement “the Earth revolves around the Sun”, but rather they disagreed with it because it was at odds with what they thought of the world. iħ∂|Ψ⟩/∂t = Ĥ|Ψ⟩, now that's a statement most people won't even understand enough to tell whether they think it's true or false.

Comment author: [deleted] 03 March 2012 10:33:44AM * 2 points [-]

Historical? I know you count many worlds as “understanding”, but I wouldn't until this puzzle is figured out. (Or maybe it's that I like Feynman's (in)famous quote so much I want to keep on using it, even if this means using a narrower meaning for understand.)

Comment author: shminux 06 March 2012 12:57:19AM 1 point [-]

I certainly hope that EY means that the problem of the origins of the Born rule is still open, not that the MWI has somehow solved it.

Comment author: [deleted] 11 March 2012 01:25:50AM 2 points [-]

IIRC he said something to the effect that it is no longer true that nobody understands QM since we have the MWI; my point is that I wouldn't count MWI as ‘understanding’ if the very rule connecting it to (probabilities of) experimental results is still not understood.

Comment author: Will_Newsome comment score below threshold [+] (10 children)

Comment author: Luke_A_Somers 05 March 2012 05:41:39PM 6 points [-]

It's hard to engage with someone whose readiness to opine so vastly exceeds their readiness to meaningfully opine.

Comment author: Will_Newsome 05 March 2012 05:50:29PM 0 points [-]

Eh?

Comment author: [deleted] 05 March 2012 09:10:18PM 3 points [-]

QM is a solid theory that reliably predicts every known experiment dependent on it.

And it seems you need to brush up on your arithmetic theory. There is a progression in the usual number fields, Naturals (w/ or w/o 0), Integers, Rationals, Reals, Complex, Quarternions, Octonions, Sedenions, etc.

Naturals have a starting point, countability, no negatives, no inverse elements and no algebraic closure.
Integers sacrifice a starting points to gain negative elements.
Rationals sacrifice finiteness of subsets to gain inverse elements.
Reals sacrifice uniqueness of representation to gain uncountability.
Complex numbers sacrifice absolute order to gain algebraic closure.

Then it gets a bit hazy in memory, but I know Quarternions sacrifice commutativity of multiplication and Octonions aren't associative but I can't remember what neat tricks you gain there. The Sedenions have zero divisors but I can't remember what they loose.

Now the point is that complex numbers are the most interesting because they have algebraic closure; you cannot construct an equation with multiplication and addition or almost any other operation in which the solution isn't a Complex number. Not so with the Reals (sqrt -1). Thus Complex numbers are completely logical to be physics rather than Reals.

Comment author: komponisto 19 April 2012 06:19:11PM 3 points [-]

Reals sacrifice uniqueness of representation to gain uncountability.

Not what I would have said. Instead, I think it would be better to say that the reals sacrifice countability in order to gain completeness.

("Uniqueness of representation" isn't a big deal at all. In fact, it doesn't even hold for the natural numbers, which is why there is such a thing as "arithmetic".)

Comment author: [deleted] 19 April 2012 08:36:42PM * -1 points [-]

Well, the simplest way to represent a real number is with infinite decimal expansion. Every rational number with a finite digit expansion has two infinite digit expansions. Every Natural has one corresponding string of digits in any positional number system with natural base.

I think at the time of writing I considered 'completeness' to be ill defined, since the real numbers don't have algebraic closure under the exponential operator with negative base and fractional exponent, while with ordinary arithmetic it is impossible to shoot outside of the Complex numbers.

(EDIT: I cant arithmetic field theory today) The best I can come up with is uniqueness of representation, since it implies infinite representations and thus loss of countability. (insofar as I remember my ZFC Sets correctly, a set of all infinite strings with a finite alphabet is uncountable and isomorphic at least to the interval [0,1] of the reals)

EDITED to fix elementary error.

Comment author: wnoise 19 April 2012 10:05:47PM 4 points [-]

Every rational number has two infinite decimal expansions.

No. Every terminating number has two infinite decimal expansions, one ending with all zeros, the other with all nines.

1/3, for instance is only representable as 0.333... , while 1/8th is representable as 0.124999... and 0.125.

Comment author: [deleted] 19 April 2012 10:19:39PM 0 points [-]

Oh right, thanks for catching that.

Comment author: komponisto 20 April 2012 09:13:14AM 1 point [-]

Technically limits work with Rational Numbers too, so that isn't an unique property either

No, they don't; that's precisely the point. There are Cauchy sequences of rational numbers which don't converge to any rational number. For an example, simply take the sequence whose nth term is the decimal expansion of pi (or your favorite irrational number) carried out to n digits.

Comment author: [deleted] 20 April 2012 09:19:52AM 1 point [-]

Noted and corrected.

Comment author: Zack_M_Davis 07 March 2012 06:13:24PM * 5 points [-]

what the hell are complex numbers doing in the Dirac equation?

As I've pointed out to you before, if you have a problem with physical applications of complex numbers, you should be equally offended by physical applications of matrices, because matrices of the form [[a,-b],[b,a]] are isomorphic to complex numbers. In fact, your problem isn't just with quantum mechanics; if you can't stand complex numbers, you should also have a problem with (for just one example) simple harmonic motion.

In detail: we model a mass attached to a spring with the equation F=-kx: the force F on the mass is proportional to a constant -k times the displacement from the equilibrium position x. But because force is mass times acceleration, and acceleration is the second time derivative of position, this is actually the differential equation x''(t) + (k/m)x(t) = 0, which has the solution x(t) = ae^(i*sqrt(k/m)t) + be^(-i*sqrt(k/m)t) where a and b are arbitrary constants.

It's true that people tend to write this as ccos(sqrt(k/m)t)+dsin(sqrt(k/m)t), but the fact that we use a notation that makes the complex numbers less visible, doesn't change the underlying math. Trig functions are sums of complex exponentials.

Complex numbers are perfectly well-behaved, non-mysterious mathematical entities (consider also MagnetoHydroDynamics's point about algebraic closure); why shouldn't they appear in the Dirac equation?

Comment author: Giles 04 March 2012 03:05:55PM 4 points [-]

I would say instead that many truths are easy to understand once you understand them. But still hard to explain to other people.

Comment author: Thomas 01 March 2012 12:04:50PM 0 points [-]

Generally, yes. But in this particular casa we can trust, that the later Darwin's bulldog really felt that way and that this was a justified statement. He obviously understood the matter well.

All those English animal breeders had a good insight. It was more or less a wild generalization for them. Non so wild for Huxley.

Comment author: ciphergoth 01 March 2012 03:56:06PM 0 points [-]

So that I can google for it - what's the original text? Thanks!

Comment author: [deleted] 01 March 2012 04:36:56PM * 6 points [-]

The version I've read is "Tutte le verità sono facili da capire quando sono rivelate, il difficile è scoprirle!" But that sounds like suspiciously modern Italian to me, so I wouldn't be surprised to find out that it's itself a paraphrase.

ETA: Apparently it was quoted in Criminal Minds, season 6, episode 11, and I suspect the Italian dubbing backtranslated the English version of the show rather than looking for the original wording by Galileo. (Which would make my version above a third-level translation.)

ETA2: In the original version of Criminal Minds, it's "All truths are easy to understand once they are discovered; the point is to discover them" according to Wikiquote. (How the hell did point become difficile? And why the two instances of discover were translated with different verbs? That's why I always watch shows and films in the original language!)

ETA3: And Wikiquote attributes that as “As quoted in Angels in the workplace : stories and inspirations for creating a new world of work (1999) by Melissa Giovagnoli”.

Comment author: ciphergoth 10 March 2012 08:08:07PM 0 points [-]

Edited Wikiquote - thanks!

army1987 comments on Rationality Quotes March 2012 - Less Wrong

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