deRham said:
This refers to a fascinating topic, at least to me. I've always wondered what benefit funding the innovation of new math has to that CEO/general.
Ask the NSA. They probably know more about factoring large numbers than anyone else in the world. For that matter, I've seen some very interesting work in applied math in financial firms. If your algorithms are faster than the people across the street, then you can sell financial products that they can't.
I mean, is the math developed private and only at the disposal of that funding source?
It depends. In my situation, it's understood than any new mathematical technique is going to be known by everyone eventually (usually in a matter of months), however, the game is to be able to exploit the edge that you have. Also, you can't chain people to the office, so usually the firm across the street finds out about a new technique when they give the person that invents it enough money to switch firms.
For stuff that the NSA develops, you can't do that, and people that do that sort of work are under a lot of legal restrictions. For the stuff that the NSF produces then there aren't.
There are also odd situations in which someone wants everyone to know about something without anyone knowing who discovered it.
For example, some major banks have close relationships with academics so that the academic will with the bank's blessing publish mathematical work that was developed by the bank. There are some legal reasons for this. If a bank publishes a mathematical paper that is obviously likely to be used to price some financial product, then the regulators can get annoyed, whereas if the bank hands the research over the an academic, who builds on it and then publishes it without the banks name, this doesn't trip over securities regulations.
For that matter, there is a ton of development on open source software that is done anonymously by major financial firms.
Productive meaning they end up doing whatever is both useful for themselves and the rest of the people running the world.
Define "useful"
Being forced out of academia does not imply the individual is going to end up doing a high stress job that prevents world revolution. That would perhaps be true of working in banks were a career that is "second choice to academia."
Even low stress jobs prevent world revolution. All that matters is that you are in the office and not in the street. However, one curious thing is that most menial jobs are in fact quite high stress. Working as a waiter, a cashier, or a telemarketer is extremely high stress.
Now, teaching is noble. Having great teachers is important. However, it doesn't seem to benefit generals and CEOs much directly.
Yes it does. In order to keep yourself in power, you have to tell a story to explain to people why they must kill and die for something. When people are no longer willing to kill and die for a cause, then countries collapse. In the 1940's, people in Russia were willing to kill and to die for the hammer and sickle, but in the 1990's, people stopped and everything collapsed.
One of the major functions of schools is political indoctrination. In the US for example, one message that gets taught starting from elementary schools is that freedom and democracy are important. So you need lots of people that come up with these stories, and lots of people to teach these stories. One other thing is that starting from elementary school, you are to stand in line, raise your hand before being speaking, and turn in your assignments on time. It's all so that you end up as a cog in the machine.
Almost... The tricky part is that you don't want people to be "complete robots" because if they are, then the system is going to fall apart. So what you want is for people to work against the system within the system.
Basically: why fund someone to be trained in string theory when you want better toasters?
Same reason it turned out to be a good idea to fund people to research heavy metal ores in the 1920's. You never know what is going to turn up, and if something does turn up, you want it first.
It turns out that string theory is useful in valuing mortgage backed securities.
Wouldn't it be better never to give them the chance to learn string theory (from the point of view of toasters and bombs)?
Most people in fact don't get the chance to learn string theory. The number of people that do is controlled by funding levels, and the political system adjusts those levels to get the number of people that they want. Which isn't high. Maybe a dozen a year.
This leads back to the earlier question of whether some "profound new useful math" actually benefits the CEO's direct needs.
If it didn't, they wouldn't be paying me as much as they do.
A lot of my thinking involves taking Marxist ideas and then figuring out how to make use of them. I'm very heavily influenced by Marx, Trotsky, and Chomsky, but the big difference is that since I grown up when the Soviet red dream was dying and the biggest political event in my life was when it finally died, I don't have very much support for using Marxist ideology to advance world revolution or overthrow the status quo.
So what I've done is to take Marxism and try to figure out to use it for my advantage. What does it take to get me money, and that involves understanding why people behave in the way that they do.
