Posted in Mathematics, number theory on July 22, 2011| 9 Comments »
So I’ve been working on one of my papers where we need to compute some numbers. They end up being determined by a cubic equation.
However, one often finds surprising identities when Mathematica spits out a bunch of numbers expressed in algebraic form. Here is one of them:
PS: I use italics in the word surprising above only because if one does not know the origin of these identities they might seem surprising.
Seeing as the battle over raising the debt limit seems to have hit yet another impasse, it is time for me to speculate what could happen should the US default on its obligations, or follow the silly “cap, cut and balance” approach, with no tax increase on the horizon.
These speculations are just that. The markets are getting jittery and already gold is worth a lot more than it should.
Just let me digress.
Scenario 1: the Aug 2nd deadline is missed.
My gut feeling is that the market will punish the US very heavily for being so irresponsible. Money will flee the US, and the cost to further borrow for the government would go up. A lot.
If the US does not pay whoever it owns money to, either people will go hungry (from cuts of their retirement checks, etc) and the capacity of the populace to buy stuff would go down. The other option is not to pay some of the bondholders in which case the US debt would be considered junk and the crisis in confidence will not be something the US can recover from in any reasonable term.
Either way, the prospects for the US economy to grow would be shot for the short term and probably also the intermediate term. The interbank loan rate should go up and interest rates for mortgages etc will also go up, thereby slowing the economy further. The dollar should devalue, but its likely that a race to devalue currencies would ensue: after all, the US market keeps many of the other world economies going. This is a situation where inflation would be king.
Scenario 2: Cap, Cut and balance.
In this case, the US does not default (slightly less bad), but given that I live in California where a similar set of laws exists, I can not tell you how lousy this option is. This is, the US would not be able to borrow to stimulate the economy, it would have to fire a huge number of individuals in government and the recession will continue: no one will be able to afford stuff. Moreover, funding for innovation would be cut down. The prospects for the US economy to grow would go down and shrink: for the US to grow one needs a clear signal that the US government is willing to stimulate the economy. Shrinking the participation of the government in the economy is not going to do it. Again, I would expect that the stock market would also punish the US because the economy will shrink. I mean, who’s going to be buying stuff in the store when the number of layoff is increasing?
Currently in California we require a 2/3 majority to raise taxes: under a mandated balanced budget formula and given that there is a political party that treats the ‘no raise taxes’ as a religious mantra, the only way to keep things running is to cut, and keep cutting, even when there is nothing left to cut. This leaves the future generations paying for the mistakes of today by dismantling their chances of education, or even their availability of health care. We’re already seeing this. The only way for the University of California system to cope is to increase tuition. This is a tax on poor people: in some sense it forces them out of the ability to be educated and condemns them to be poor forever. I don’t wish this on the rest of the US.
Overall, I think it is in the best interest of the US to not tie itself into a straitjacket and to be able to respond to crisis by borrowing to stimulate the economy. Worse case scenario just print money and take a bit of a hit on inflation.
Posted in Music on July 14, 2011| 5 Comments »
Today as I was typing my long paper, my mood was to hear something slightly different, so I started looking for stuff that I had not heard in a while in my itunes library. Turns out that there are some songs that have not seen airplay on my desktop since 2005 (I might have heard them since, but not from this platform). I was surprised by that. It seems to indicate that I’m listening more to the playlists I made than to the random song selection available in the program, especially since the genius feature was introduced. Just for statistics sake my current library seems to have about 3500 songs, but this was smaller then (probably by a factor of 1.5 to 2).
Posted in Academia, Personal, Physics on July 13, 2011| 3 Comments »
Right now I’m in the middle of writing a long paper. This is a rather intense and time consuming effort that I don’t find particularly gratifying. On a good day, I can write a lot. But when I get annoyed at how something is organized I usually copy/paste and end up reorganizing things and that is usually not bad (it’s easier than retyping). However…
![\frac{1}{42} \sqrt[3]{\frac{1}{2} \left(90720 \sqrt{7446}-2859138\right)}-\frac{7893}{7\ 2^{2/3} \sqrt[3]{2859138+90720 \sqrt{7446}}}=0](https://s0.wp.com/latex.php?latex=%5Cfrac%7B1%7D%7B42%7D+%5Csqrt%5B3%5D%7B%5Cfrac%7B1%7D%7B2%7D+%5Cleft%2890720+%5Csqrt%7B7446%7D-2859138%5Cright%29%7D-%5Cfrac%7B7893%7D%7B7%5C+2%5E%7B2%2F3%7D+%5Csqrt%5B3%5D%7B2859138%2B90720+%5Csqrt%7B7446%7D%7D%7D%3D0&bg=ffffff&fg=333333&s=0&c=20201002)
Shores of the Dirac Sea 