PhilGoetz comments on The Math of When to Self-Improve - Less Wrong

6 Post author: John_Maxwell_IV 15 May 2010 08:35PM

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Comment author: PhilGoetz 19 May 2010 04:34:25AM *  2 points [-]

Great observation! But...

You should try to figure out why the equation makes sense for yourself.

I dislike "It is left as an exercise for the reader". I don't know why there's a factor of g-1 in the equation. It's likely I will never have the time to check this post again; so you may have lost your one chance to convince me that it's correct.

I sometimes avoid revealing an answer in a post, but only when it's either a teaser for a future post, or when I want the reader to guess first because I want their guess to be used as evidence.

Comment author: gwern 12 August 2010 10:00:04AM *  1 point [-]

I think it comes from the units in the definition of g:

(For example, if working on improving their tools currently offers the software developer the opportunity to improve their wealth creation skills at a rate of a 50% increase in their ability per year, their growth factor would be 1.5.) We'll call that g for growth.

At that point, you've accounted for current present value of your current skills, but now you want to add in the value of future growth. The '1' in '1.5' is what you have now, and is always what you have now by definition; the '.5' is additional growth. To remove what you already have, you do '-1'. Hence you multiply by 'g-1'

Comment author: PhilGoetz 18 August 2010 03:54:00PM 1 point [-]

Oh, right. I was forgetting he defined g that way. Thanks!

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