Studying Math
tara_li
I really really need to get past my hang-ups in calculus, so I can start to understand Special and General Relativity better.  I keep getting hung up on this one "thought experiment" that is supposed to illustrate the equivalence of "Inertial Mass" and "Gravitational Mass".  Because, except at the very limit...  it doesn't show that at all.

Ok, the thought experiment is the classic one of the person in an enclosed room.  Using a pendulum, timing the swings, said person is in theory unable to distinguish whether the room is resting on a planet, or if the room is aboard a spaceship undergoing the equivalent acceleration.

However, unless the gravitational source is very distant, all it takes is two, non-swinging pendulums to make the determination.  On a ship under thrust, the two pendulums will be parallel.  On a planet, the two pendulums will will each point towards the center of mass, meaning that they will make - admitted, in most circumstances extremely tiny - angles with each other.

So, since this thought experiment is supposed to illustrate the equivalence of inertial and gravitational mass - I'm left with the conclusion that in fact, except at the limit where the gravitational field is indistinguishable from flat, the two masses are *NOT* the same.

And that makes my head hurt.  Because I'm pretty certain I'm not smarter than Einstein, Feynman, Guth, et al., who have been all over this territory.  But, damn, that's some scary math, too.
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Tax Rates & Happiness
tara_li
The following article is presented as "research":  http://www.sciencedaily.com/releases/2011/09/110906152459.htm

My problem is - it sounds like rather poor research.

"A more progressive tax system makes people happier" is the title.

It's almost one of those "DUH!" moments.

Now, I do understand the need to verify that what you think is true, actually is true, and that's the source of a number of these otherwise "DUH" research reports.  However, what they present in this summary is fairly useless.  Taxes aren't about making people happy.  I'm sure most people would say they don't much at all.  Taxes are, at least in theory, about spreading the burden of running a government fairly.

And that's where I have the problem.  Sure, take from the rich, give to the poor - it's considered the great virtue of Robin Hood - except Robin Hood wasn't really so much taking from the rich, as taking from the tax collectors monies collected in excess of the needful amount.

So, 10,000 people get free money, while 10 or 100 get their pockets stripped bare.  It doesn't matter how they got the money - tax collectors generally couldn't care less (see the IRS and drug dealers).  So 10,000 people get happier and 100 get sadder - the naive assessment is that society over-all gets happier.  And maybe it does.  But does it do so *fairly*?

Perhaps we should extend this principle.  Let's apply it to *ALL* transactions in society.  Walk into WalMart to get a gallon of milk.  If you make less than $20,000 a year, you pay $1/gallon.  If you make less than $60,000 a year, you pay $2.50/gallon.  If you are in the upper income brackets, though, you get to pay $12-$15 a gallon.  That's fair, right?  Rich person wants something, they should have to pay more for it!  Certainly, we seem to feel that if a rich person wants a fair government, they should have to pay for it.  Perhaps - just perhaps - that's why so many seem to do so.

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