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drc500free comments on Welcome to Less Wrong! (2010-2011) - Less Wrong

42 Post author: orthonormal 12 August 2010 01:08AM

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Comment author: drc500free 17 December 2010 08:24:59PM 7 points [-]

Hello, My name is Dave Coleman. I was raised Atheist Jewish, and have identified as a rationalist my whole life. Browsing through the sequences, I realized I had failed to recognize some deeply ingrained biases.

I value making myself and others happy. Which others, and how happy, is something I've always struggled with. I used to have a framework with Jewish ethics, but I'm realizing that those are only clear in comparison to Christian ethics. Much of what I learned and considered was about how to make the Torah and Talmud relevant to modern, atheistic life.

I'm realizing the strong bias we had against saying "maybe it's not relevant, since it was written by immature goatherders 3500 years ago who had no knowledge of science or empathy for those outside their tribe." Admitting that wouldn't sound wise, so we twist and turn with answers, cluttering what could be a solid system of ethics.

For a while I've considered myself a reconstructionist Jew, with the underlying ethos of "do all Jewish traditions by default, but don't do anything that has a good reason not to be done." I've realized that not polluting my mind with incorrect and biased thought patterns is a good reason to avoid many things.

Another recent change has been an understanding of Judaism in terms of evolutionary fallacies. There is a strong sense in Judaism of being a Chosen People, and of a universal intention that Jews survive as Jews. Assimilation may be the biggest struggle for Jews, bigger even than persecution.

I realized that this is the same fallacy that sees intent in a species's characteristics. I had been labeling aspects of Judaism that lead to survival as being virtuous themselves - all of the dietary rituals to keep separate from goyim, the fear and guilt of assimilation. Even the love of learning and the drive to succeed has undertones of "thrive, for that is how you will survive the next pogrom." Preservation of the culture is virtuous, therefore anything that keeps the culture alive is virtuous.

I remember my first Differential Equations class, when we learned that the function that is its own derivative is f(x)=e^x, and the function that is its own second derivative is f(x)=sin(x). There was this eerie confusion as I first thought that those functions were just a possible solution, and then realized that they described the only solutions. I found it very disturbing that I couldn't describe whether the sine looked as it does by virtue of being its own second derivative, or whether it was its own second derivative by virtue of looking as it does. I still feel slightly uneasy that I can't assign a causal relationship in one direction or the other.

That's how I view Judaism now. The characteristics of all species and memes are a solution to the equation of survival. There is no intent or deeper meaning than that, and I think I've finally let that go.

Oh, and I got here from Reddit, where someone posted a link to the Paperclip Maximizer.

Comment author: Eugine_Nier 17 December 2010 09:22:01PM 3 points [-]

I found it very disturbing that I couldn't describe whether the sine looked as it does by virtue of being its own second derivative, or whether it was its own second derivative by virtue of looking as it does. I still feel slightly uneasy that I can't assign a causal relationship in one direction or the other.

Causality doesn't have much meaning when applied to mathematics.

Comment author: Eliezer_Yudkowsky 17 December 2010 09:10:23PM *  3 points [-]

e^-x is its own second derivative. sin(x) is its own fourth derivative (note relation to e^ix).

And welcome to LW! (he said)

Comment author: JGWeissman 17 December 2010 08:34:25PM 1 point [-]

There was this eerie confusion as I first thought that those functions were just a possible solution, and then realized that they described the only solutions.

Of course, you mean they are the only solutions that satisfy certain initial conditions.

Comment author: drc500free 17 December 2010 08:50:12PM 1 point [-]

Well, that they are the family of solutions, allowing for various transformations.

*-Disclaimer, I haven't looked at a differential equation in 6 years.

Comment author: Perplexed 17 December 2010 09:27:00PM 1 point [-]

Following up to EY's comment:

e^x is its own second derivative too. There are two functions that are their own second derivative, and four which are their own fourth derivative.

Cool! So what are the other two (out of three) functions that are their own third derivative? What does their graph look like? And does all this have anything to do with Laplace transforms? Does a sufficiently smooth function have a 1.5th derivative?

Yes, welcome to LW.

Comment author: Eugine_Nier 17 December 2010 09:31:57PM 2 points [-]

There are two functions that are their own second derivative, and four which are their own fourth derivative.

More precisely there is a 2-dimensional parameter space of functions that are their own second derivative, i.e., any function of the form Ae^x+Be^-x for any constants A and B.

Comment author: drc500free 17 December 2010 10:29:02PM 1 point [-]

Is there a generic form of that for any nth derivative?

Comment author: Eugine_Nier 17 December 2010 10:34:08PM 2 points [-]
Comment author: JGWeissman 17 December 2010 10:36:01PM *  1 point [-]

Sum over integers k from 1 to n of A(k)*e^(e^(2*i*pi/k)*x) is its own nth derivative, for all A.

Comment author: ata 17 December 2010 09:32:36PM 1 point [-]

Does a sufficiently smooth function have a 1.5th derivative?

I think so.