An interesting question on Slashdot: What is the future for Financial Mathematics?

[petertribo]

Re: An interesting question on Slashdot: What is the future for Financial Mathematics?

Totally true. Mathematics is the queen and servant to the sciences. It is not a science. It is self-contained.

Take that one up with your local University. At any University, the Department Of Mathematics is a subset of the Faculty Of Science. Look it up.

[TRake]

Re: An interesting question on Slashdot: What is the future for Financial Mathematics?

Main Entry:

mathˇeˇmatˇics

Pronunciation:

\ˌmath-ˈma-tiks, ˌma-thə-\

Function:

noun plural but usually singular in construction

Date:

1573

1 : the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations 2 : a branch of, operation in, or use of mathematics mathematics of physical chemistry>

[Spartacus]

Re: An interesting question on Slashdot: What is the future for Financial Mathematics?

You do make a case

AND
our conception of science has changed a bit since that date. Guys like Popper came a lot later than that.

I had this conversation at the graduate students' pub with a bunch of guys from the math department at my school one time - one was doing a PhD in topology, and I can't remember the topics for rest.

None considered themselves scientists or even scientists-in-training.

"are you a scientist? "

"no"

"do you do science?"

"no"

Also, if browse some google searches
"math is not science" - very few hits, but some are by mathematicians
"math is science" - lots of hits, but just browsing, none are by mathematicians
"math is a science" - lots of hits, but just browsing, none are by mathematicians

Main Entry:

mathˇeˇmatˇics

Pronunciation:

\ˌmath-ˈma-tiks, ˌma-thə-\

Function:

noun plural but usually singular in construction

Date:

1573

1 : the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations 2 : a branch of, operation in, or use of mathematics mathematics of physical chemistry>

[Sharky]

Re: An interesting question on Slashdot: What is the future for Financial Mathematics?

Good points but I'm not sure it was just worshipping of models. I posted in the Video section a great interview with Janet Takavoli. When she was asked about those funny financial models she said:

"There weren't any outliers... there were just a lot of outright liars."

Financial models assume their inputs are accurate. In the real world, we know they won't be. Therefore, a real mathematician would tell you that the models won't work: garbage-in, garbage-out. But the models were used anyway.

Look at option pricing as an example. The model assumes lognormal distribution of future prices -- easily proved to not be true. It assumes that future prices will be distributed based on today's "volatility" (one of the model's inputs) -- also not true. And it assumes that volatility can be derived from current option prices ("implied" volatility) -- very, very not true. Yet the model is followed religiously.

What is that, if not model worship?

The response of the financial community to option model pricing problems has been predictable: they developed new models that address some of the high-level deficiencies (Cox-Rubenstein, for example). But the new models are still as fundamentally flawed as the old ones.

[oddlots]

Re: An interesting question on Slashdot: What is the future for Financial Mathematics?

Ran across this in a piece from Steve Keen entitled "Neoclassical Economics: mad, bad, and dangerous to know" which deals with the problems of what's wrong with neo-liberal economics and what should replace it....

"[Regarding reforming Economics curriculum] ... the physicist Joe McCauley responded that, though some of the objections were valid, the problems in economics proper were far worse. He therefore suggested that:

the economists revise their curriculum and require that the following topics be taught: calculus through the advanced level, ordinary differential equations (including advanced), partial differential equations (including Green functions), classical mechanics through modern nonlinear dynamics, statistical physics, stochastic processes (including solving Smoluchowski–Fokker–Planck equations), computer programming (C, Pascal, etc.) and, for complexity, cell biology. Time for such classes can be obtained in part by eliminating micro- and macro-economics classes from the curriculum. The students will then face a much harder curriculum, and those who survive will come out ahead. So might society as a whole. (McCauley 2006, p. 608; emphasis added)"

Punching above my weight here but thought it was an interestingly specific wish list that someone might find enlightening.

[Chris Coles]

Re: An interesting question on Slashdot: What is the future for Financial Mathematics?

Ran across this in a piece from Steve Keen entitled "Neoclassical Economics: mad, bad, and dangerous to know" which deals with the problems of what's wrong with neo-liberal economics and what should replace it....

"[Regarding reforming Economics curriculum] ... the physicist Joe McCauley responded that, though some of the objections were valid, the problems in economics proper were far worse. He therefore suggested that:

the economists revise their curriculum and require that the following topics be taught: calculus through the advanced level, ordinary differential equations (including advanced), partial differential equations (including Green functions), classical mechanics through modern nonlinear dynamics, statistical physics, stochastic processes (including solving Smoluchowski–Fokker–Planck equations), computer programming (C, Pascal, etc.) and, for complexity, cell biology. Time for such classes can be obtained in part by eliminating micro- and macro-economics classes from the curriculum. The students will then face a much harder curriculum, and those who survive will come out ahead. So might society as a whole. (McCauley 2006, p. 608; emphasis added)"

Punching above my weight here but thought it was an interestingly specific wish list that someone might find enlightening.

You punch well.

McCauley should have added another heading to the curriculum, Philosophy. One of the great mistakes made over the last century was the use of mathematics to drive the underlying debate about the veracity of the results obtained. Without a full philosophical debate there is no way forward to any understanding of the merits of the "junk" put into the equations.

[*T*]

Re: An interesting question on Slashdot: What is the future for Financial Mathematics?

Take that one up with your local University. At any University, the Department Of Mathematics is a subset of the Faculty Of Science. Look it up.

As I say, the queen and servant to the sciences. They are close but not the same.

At my undergraduate university, Mathematics students got a BA, not a BSc.

There is no interaction with experiment in mathematics, therefore it is not a science in the strict sense.

[petertribo]

Re: An interesting question on Slashdot: What is the future for Financial Mathematics?

As I say, the queen and servant to the sciences. They are close but not the same.

At my undergraduate university, Mathematics students got a BA, not a BSc.

There is no interaction with experiment in mathematics, therefore it is not a science in the strict sense.

I hope you will be contacting the many Universities all over the World and informing them that you have got it right and they have got it wrong. Once again: Department of Mathematics within the Faculty of Science. Good luck jousting with those University Windmills.

[petertribo]

Re: An interesting question on Slashdot: What is the future for Financial Mathematics?

For those who may be interested in not only how corrupted Mathematics has cost us TRILLIONS but how corrupted Science itself may do us much greater harm, here is a story on Sociopaths In Science:

Writing in the Seattle Times, William Calvin, a Neurobiologist at the University of Washington, wrote: "There is a class of people with ‘delusional disorders’ who can remain employed and pretty functional for decades. Even if they are only one percent of the population, that’s 20,000 mostly untreated delusional people in the Puget Sound area. Even if only one percent of these has the intelligence or education to intentionally create sustained or widespread harm, it’s still a pool of 200 high-performing sociopathic or delusional techies just in the Puget sound area alone."

The malevolent actions of such individuals and small groups using the GNR technologies pose a large and even mortal danger to our civilization.

This threat will manifest itself, for example, as genetic engineering techniques provide the ability, perhaps in about 20 years, to use software to create new, highly contagious and deadly "designer pathogens." Nanotechnologists have similarly recognized that out of control nanobots could destroy the biosphere; a first quantitative study of this possibility of "Global Ecophagy" by Robert Freitas was recently published in response to the article I wrote on this subject in Wired in April. His study is quite troubling, showing the clear dangers we face from unrestricted nanotechnology and the extreme difficulty and enormous scale required of any "defense."

Such pestilences are beyond our direct experience. The Black Death killed a third of the population of 14th century Europe and smallpox devastated the native population in the Americas in the 16th century, but these are distant historical events. Even the influenza pandemic of 1918 is largely out of living memory. Antibiotics and improved sanitation have given us grace from such disasters, at least for a time. But to believe such things cannot recur is untrue and our failing memory of them is quite dangerous.

Since technologies are creating these new dangers some have hoped for the answers to be technological too, some sort of defense. But a strong defense against genetically engineered pathogens would seem to require a nearly perfectly augmented immune system, which seems quite unlikely in the timeframe of interest; this may even prove to be impossible without large-scale reengineering of the germline of our species. A "doomsday nanoshield" appears to be so outlandishly dangerous that I can’t imagine we would attempt to deploy it. As with nuclear technology, the destructive offensive uses here have a seemingly deeply sustainable advantage over defensive efforts.

http://www.pugwash.org/reports/pim/pim18.htm

Lots more problems than just Sociopaths whose damage we have seen extensively on Wall Street.

[Sharky]

Re: An interesting question on Slashdot: What is the future for Financial Mathematics?

I hope you will be contacting the many Universities all over the World and informing them that you have got it right and they have got it wrong. Once again: Department of Mathematics within the Faculty of Science. Good luck jousting with those University Windmills.

Those sound like the same wonks who think that economics is a science. They no doubt believe it, and even teach it that way. That doesn't make it true.

"Science" and the "scientific method" define an approach involving a cycle of hypothesis, experiment and explanation. Math involves no such approach.

FWIW, my degree was a BA in Math, not a BSc.

[Sharky]

Re: An interesting question on Slashdot: What is the future for Financial Mathematics?

McCauley should have added another heading to the curriculum, Philosophy.

Excellent point. Many of the mistakes in present-day financial modeling, including the bulk of modern economics, immediately appear under the light of an appropriate philosophy.

[*T*]

Re: An interesting question on Slashdot: What is the future for Financial Mathematics?

I hope you will be contacting the many Universities all over the World and informing them that you have got it right and they have got it wrong. Once again: Department of Mathematics within the Faculty of Science. Good luck jousting with those University Windmills.

It makes sense administratively putting it in with the mathematical and physical sciences. This does not make it a science. Science is something that is informed by experiment, to highlight one difference.

[allenjs]

Re: An interesting question on Slashdot: What is the future for Financial Mathematics?

"Science" and the "scientific method" define an approach involving a cycle of hypothesis, experiment and explanation. Math involves no such approach.

FWIW, my degree was a BA in Math, not a BSc.

Yes, in classic times, arithmetic and geometry were grouped under the arts. During the middle ages, they were grouped into the "quadrivium" (as opposed to "trivium"), but still under what was then called "liberal arts". The modern university system developed from this middle ages taxonomy.

My copy of Sister Miriam Joseph's book breaks it out like this:

LIBERAL ARTS
-------------
Trivium: the three arts of language pertaining to mind
* Logic: art of thinking
* Grammar: art of inventing and combining symbols
* Rhetoric: art of communication (ha!)

Quadrivium: the four arts of quantity related to matter
* Arithmetic: theory of number
* Music: application of the theory of number

* Geometry: theory of space
* Astronomy: application of the theory of space

Of course, people doing science would need to be skilled at Logic, Arithmetic, and Geometry. (And in fact, these weren't intended to be specializations -- university students were expected to learn all/most of these subjects to get a liberal arts education).

As another commenter pointed out, a proper grasp of philosophy would also be essential for people doing science.

[Chris Coles]

Re: An interesting question on Slashdot: What is the future for Financial Mathematics?

Yes, in classic times, arithmetic and geometry were grouped under the arts. During the middle ages, they were grouped into the "quadrivium" (as opposed to "trivium"), but still under what was then called "liberal arts". The modern university system developed from this middle ages taxonomy.

My copy of Sister Miriam Joseph's book breaks it out like this:

LIBERAL ARTS
-------------
Trivium: the three arts of language pertaining to mind
* Logic: art of thinking
* Grammar: art of inventing and combining symbols
* Rhetoric: art of communication (ha!)

Quadrivium: the four arts of quantity related to matter
* Arithmetic: theory of number
* Music: application of the theory of number

* Geometry: theory of space
* Astronomy: application of the theory of space

Of course, people doing science would need to be skilled at Logic, Arithmetic, and Geometry. (And in fact, these weren't intended to be specializations -- university students were expected to learn all/most of these subjects to get a liberal arts education).

As another commenter pointed out, a proper grasp of philosophy would also be essential for people doing science.

In fact, I immediately had misgivings for not including the word logic when talking about philosophy. Philosophical thought is all about the application of logical argument to everything downstream of the answer to that most useful of questions - why?

Science has run into many difficulties simply because, when faced with the need for a logical philosophical explanation as a primer for further investigation, its practitioners instead stumbled into using mathematics alone to provide the explanation. Mathematics alone, without logical philosophical explanation, can become an unseen blind alley.

[petertribo]

Re: An interesting question on Slashdot: What is the future for Financial Mathematics?

Coming down from the Ivy Tower of Theory, there is the Practicality. Heard on the radio station this morning was a Joe Blow Accountant declaiming on the Science behind portfolio management. No challenge, of course, from the Bingo Caller. This is exactly what Nassim Taleb talks about:the corrupted Science behind Portfolio Management.

So, there is a vast difference between theoretical ideas of the various Human Disciplines and how they are actually put into use. In this Age Of Fraud, Science is just another commodity to be manipulated and corrupted,like the air, water, politics. (See FIRE, PHARMA, AGRIMOB, for starters). Maybe we will get Ratings Agencies for Science.

There are not many so-called Scientists complaining about or even talking about this. Hard to believe it is because of ignorance of the issue.