Wednesday, February 7, 2018

Perpendicularity and Dot Product

It's a well-known fact that when two vectors are "perpendicular" (in the Euclidean geometric sense) then their dot products are $0$, i.e. for two vectors $A$ and $B$, $A \cdot B = 0$ iff $A$ and $B$ are perpendicular.

I think one can construct a slightly complicated argument for this fact, starting with the standard basis vectors $e_j \cdot e_k = 0$ for $k \neq j$ and arguing this relation survives a change of basis. You would then have to argue that two perpendicular vectors can then be transformed to a pair of standard basis vectors by the operations of transformation and scaling. Horribly inelegant though - ugh. ("There is no place for in the world for ugly mathematics." - G. H. Hardy

Nonetheless, lately, I have been reading Sergei Lang's "Calculus of Several Variables" - highly recommended. In that book, he gives this much more elegant argument.

The argument should be pretty easy to follow for anyone familiar with the dot product. I think You need to see that two triangles are similar in Figure 18. 

Saturday, November 26, 2016

Finimize Resources On Finance

I found this gem of a website called finimize that tries to teach basic financial knowledge to people who may not already be well informed on finance.

Here's their explanation of Quantitative Easing:
Quantitative Easing (“QE”) is when a central bank directly buys its government bonds. The idea is that it’s enacted when a central bank’s target interest rate has already been cut close to zero. By directly buying government bonds, it decreases the yield those bonds pay (because when the price of a bond increases, its yield declines – see below). Many types of loans are based, directly or indirectly, on the yield of government bonds and so by depressing those yields, the central bank makes it cheaper for companies and people to borrow money than a low target interest rate would do on its own – and it’s hoped that the borrowed money will used to do things that boost the economy (like buying machinery or hiring workers).
 Now compare that with Wikipedia's explanation, which kind of starts to make sense after you've read the Finimize explanation.

Friday, November 25, 2016

Damning Statistics on Democracy

Jason Breannan, in his book Against Democracy, provides the following selection on how ignorant the electorate in the US are:
I could write an entire book just documenting how little voters know. But since many others have already done that, I’ll only offer a few examples: 
•During election years, most citizens cannot identify any congressional candidates in their district. 
•Citizens generally don’t know which party controls Congress. 
•Immediately before the 2004 presidential election, almost 70 percent of US citizens were unaware that Congress had added a prescription drug benefit to Medicare, though this was a giant increase to the federal budget and the largest new entitlement program since President Lyndon Johnson began the War on Poverty. 
•In the 2010 midterm presidential election, only 34 percent of voters knew that the Troubled Asset Relief Program was enacted under George W. Bush rather than Barack Obama. Only 39 percent knew that defense was the largest category of discretionary spending in the federal budget. 
•Americans vastly overestimate how much money is spent on foreign aid, and so many of them mistakenly believe we can significantly reduce the budget deficit by cutting foreign aid. 
•In 1964, only a minority of citizens knew that the Soviet Union was not a member of the North Atlantic Treaty Organization. (Yes, that’s right: NATO, the alliance created to oppose the Soviet Union.) Keep in mind this is just a short time after the Cuban Missile Crisis, in which the United States almost went to (nuclear) war with the USSR. 
•Seventy-three percent of Americans do not understand what the Cold War was about. 
•Most Americans do not know even roughly how much is spent on social security or how much of the federal budget it takes up. 
•Forty percent of Americans do not know whom the United States fought in World War II. 
•During the 2000 US presidential election, while slightly more than half of all Americans knew Al Gore was more liberal than Bush, they did not seem to understand what the word liberal means. Fifty-seven percent of them knew Gore favored a higher level of spending than Bush did, but significantly less than half knew that Gore was more supportive of abortion rights, more supportive of welfare state programs, favored a higher degree of aid to blacks, or was more supportive of environmental regulation. Only 37 percent knew that federal spending on the poor had increased or that crime had decreased in the 1990s.18 On these questions, Americans did worse than a coin flip. Similar results hold for other election years. 
(Check the book for references.) If we assume that there are independent standards for evaluating elected and appointed officials (i.e. standards besides from the fact they were elected), the fact that large numbers of the electorate are so ignorant should give us reason to suspect that the electorate are incapable of voting into office public officials who can govern well.

That several Trump-like presidents in the past has not been elected should be considered a serendipity.

And by and large, I think the statistics about the US electorate are the norm.

Sunday, November 20, 2016

Baker on Healthcare Cost Drivers In The US

I had previously posted about the drivers of healthcare costs in the US. The following from Dean Baker's book "Rigged" is illuminating:
A big part of the difference in costs is that our doctors are paid twice as much as doctors in other wealthy countries. Average pay for doctors in the United States is over $250,000 a year, and in some highly paid areas of specialization the average is over $500,000. Paying our doctors the same as Germany, Canada, and other wealthy countries pay theirs would reduce our health care bill by close to $100 billion a year. 
Doctors are able to maintain such high salaries in large part because of measures that protect them from competition. We have limits on the number of people who go to medical school and on the number of foreign medical school graduates who can enter U.S. residency programs, the completion of which is a requirement for practicing medicine in the United States.[84] State laws also limit the extent to which nurse practitioners and other health care professionals can perform tasks, such as prescribing medicine, that might limit the demand for doctors.
Baker also expands with the following example:
The average pre-tax earnings for orthopedic surgeons in the United States was $442,500, compared to an average of $215,500 in the reference countries.

Saturday, November 19, 2016

Family Conglomerates and Failed States

Damodaran's latest piece makes me ponder the following: Is there a correlation between the number/prominence of wealthy family conglomerates in a nation and the failure of that nation state? Here's an informative snippet (do read the whole thing though):
In many countries, including populous ones like India, influence is wielded and decisions are made by a surprisingly small group of people who know each other not just through their business networks but also through their social and family connections. These “people of influence” include bankers, rule makers and regulators that determine which businesses get capital, what rules get written (and who gets the exceptions) and the regulations that govern them. Family group companies have historically used these connections as a competitive advantage against upstart competition (both from within and without the country), especially in an environment where you have to pass through a legal, bureaucratic and political thicket to start and run a business.
I would say exactly the same connection-based cronyism applies in Turkey, Russia, Ukraine and Greece.

In fact, such cronyism is so pervasive that if you meet a person from the 3rd world who happens to be from a wealthy family, it may be reasonable to suspect that the person's family benefitted from corruption.

Note that family companies were also prominent in developing Japan and Korea. See this Wikipedia entry and here. It would be good to compare those Japanese and Korean companies with those in India.   

Friday, November 18, 2016

Patent and Profit As Promoting "Wasteful" Scientific Efforts

While espousing why he thinks patents are bad overall, Dean Baker makes the following point in Rigged  [Emphasis mine]:
For example, Merck and AbbVie, along with several smaller drug manufacturers, are rushing to market alternatives to Sovaldi as a treatment for hepatitis C. In the context in which Gilead Sciences, the maker of Sovaldi, has a monopoly on effective treatments for hepatitis C, this sort of competition is highly desirable because it will lead to lower prices. However, if Sovaldi were being sold in a free market at $500 to $1,000 for a course of treatment, there would be little incentive to invest research dollars finding treatments for a condition for which an effective drug already exists. If drugs were sold without protection, research dollars would usually be better devoted to developing a drug for a condition where no effective treatment exists than developing duplicative drugs for a condition that can be well-treated by an existing drug.
He is right that competition in biotech for markets of established drugs is essentially wasteful. You could make a similar argument for any kind of industrial research lab as well.

Any time someone is doing research in secret, there may be other researchers who are duplicating those secret efforts.

Science advances best when it is cooperative. The profit motive introduces wasteful competition.

This is why the mathematicians' polymath project was such a success in some of their collaborations. It was open and directly accessible - no peer review, etc.

Baker's idea is also reminiscent of how the chess engine development took off once developers started open-sourcing and sharing their code.

But I have to object when Baker quotes $500 to $1000 as the "free market" price of Sovaldi. He's clearly not accounting for the development costs.

Baker favors a model where government contracts researchers directly and then subsequently claims any rights on their inventions. He says that such a model is already being used by the defense industry. Will you get as many biotech inventions once the research is essentially socialized? I would like to think so but I have my doubts.

Also consider the following. Because of Apple's dominance in the smartphone market, Samsung decides to enter the smartphone market by . Based on this, should we conclude "oh well, the smart phone is really a solved problem; Samsung's dollars would really be better spent elsewhere"? Should we have a consistent reaction to competition in drugs and smart phones?

I think not. I think that drugs are different from smartphone's in that they can effectively cure a disease as to make any further research superfluous. Smart phones can be improved in a lot of different ways. These improvements would be spurred by competition; whereas in drug development, it's hard to develop on your competitors' ideas due to patent protections.

Nonetheless, Baker's point about drugs makes one wonder... What if you could get everyone to cooperate as opposed to compete?

Thursday, November 17, 2016

The Financial Industry: The Administrative Cost of Running an Economy?

I have been reading more of Dean Baker's book "Rigged". Here he makes an apt analogy that eloquently argues the dangers of an overblown financial sector.
In this regard the financial sector is like the trucking industry. Trucking, like finance, is essential to the economy. We need it for moving raw material to factories and finished products to stores. But an efficient trucking industry is a small trucking industry: we want to have as few resources as possible devoted to getting goods from point A to point B. This means that we don’t want to see a huge expansion in employment in the trucking industry or an explosion in the number of trucks and warehouses just to move the same quantity of goods. 
The same story applies to the financial industry. We should want to see as few resources as possible committed to it, or the minimum needed to enable it to support the productive economy. Instead, we have seen a massive expansion of the financial sector, from 4.5 percent of GDP in 1970 to 7. 4 percent in 2015. 20 The more narrow securities and commodities trading sector increased from 0.49 percent of GDP in 1970 to 2.03 percent in 2015,21 corresponding to $290 billion a year in additional spending in the 2016 economy.
Of course, if the transportation needs of the good produced got more complex (Amazon and internet retail?), we should expect the trucks and warehouses to expand both in size and in real dollar terms.

So perhaps the corresponding question for the financial sector should be: have the financing needs of the economy changed to require a bigger financial sector?

The answer is likely to be no but my point is that it's not just sufficient to point to a growth in the financial sector as immediately proving an increase in waste.