Help me start an lj/blog meme

In a comment on carelessflight's page, I posted this and thought it would make for an interesting meme if it caught on.

The basic idea is this: many people in the U.S. believe that they pay too much in taxes, and so are very ammenable to calls to cut federal income taxes. The fact is, federal income taxes are a small part of the story for people making less than $100K/year, and even for people making more than that, the federal taxes are less significant than might be suspected. The interplay between federal income tax rates and state and local taxes makes cutting federal income taxes an even more dubious proposition for many people.

So, to spread this meme, take out your last paycheck of 2003 (with the annual totals on it) and then post all the deductions from it, taken as a percentage of the gross pay line.

Here are my numbers:

Federal Income tax    10.5%
Social Security tax    5.9%
Medicare tax           1.4%
NJ State income tax    1.9%
NJ SUI/SDI tax         0.25%

Now the non-tax expenses, for completeness:

Disability insurance   0.12%
Medical insurance      4.7%
401K                  13.4%

I should also note that we routinely get a federal income tax refund of about 1.5% of the gross pay line. Since we start to get extra income tax (but not social security tax) reductions this year(*), I'm sure my numbers for 2004 will show even less federal income tax.

An interesting outcome of this exercise is the conclusion that a 40% across-the-board federal income tax hike that also eliminated my medical insurance costs would be a net gain for me, and we're in the top 25%.

I wonder what Bill Gates' numbers look like?

(*) Katherine Grace Martin, born 2004-01-03.

Don't wake the baby

A math problem vaguely inspired by life:

Say you have to walk from point A to point B. Now, the catch is that you have to take each step so as to not wake the baby sleeping at point A. If you wake her, you have to go back to point A and spend the time during which you could take n steps comforting her until she goes back to sleep. The probability of the baby waking during any step is equal to the portion of the distance covered during that step - in other words, if you try to go from A to B in one step, she'll certainly awaken (longer steps are louder, you see). If you try to take it in two equal-sized steps, you have a 1/4 chance of making it across.

Now, you're trying to get to point B as quickly as possible. (Assume that each step takes the same amount of time). What's your optimal strategy? What is the expected number of steps taken?

First take this problem with n = 0; that is, the only penalty for waking the baby is that you have to start over from point A.

What if we change things so that the probability of her waking is equal to k times the portion of the distance covered? (So that for k=2, she is certain to wake if we try to cover half the distance in a single step)