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The Numbers Game - From Cosmology to the Credit Crunch
by The Soupdragon

May 8, 2009
 
While many people are aware of the increasing role of mathematical modeling in society in general, and science in particular, very few have dared to question this situation. The idea that mathematical models somehow reveal universal truths, in both business and science, has been successfully promoted, despite strong historical evidence to the contrary.

Let us examine some of the pitfalls of a purely mathematical approach, in both historical and contemporary contexts.

A Road Less Travelled

Did science take a wrong turn?
 
Fork in the road
[Click to enlarge]
 
Science is synonymous with the philosophical discipline known as empiricism, based on measurement and observation or at least it was. Because of the difficulty in measuring a lot of the stuff out there, a degree of mathematical speculation began to creep into astronomy. This was fine for a while, until it began to spread like cancer, and took over. Today, astronomy and cosmology are fields dominated by mathematicians, not empirical scientists.

Although the mainstream seems happy with this situation, for the most part, there is growing unrest in many quarters about the uncritical acceptance of such a distorted approach to science. Those who are ignorant of history are condemned to repeat it, as the saying goes. There are, in fact, many warnings from history about placing too heavy a reliance on mathematics.

Ptolemaic epicycles are perhaps the most famous example of the dangers of the mathematical approach. They were a series of orbits within orbits designed to explain the motions of the planets, and with a few tweaks they would still work today. However, despite being mathematically correct - and indeed elegant - they failed to reflect the underlying reality.
 
Ptolemaic epicycles
[Click to enlarge]
 
In another famous example, Scientific American ran an article ridiculing the alleged flights of the Wright Brothers ... some years after they had been flying successfully! This pseudo-skepticism was based on the inertia of prior belief - that heavier than air flight was not possible. Needless to say, they had the math to prove that it was impossible, too.

Some people still react angrily to any criticism of the role of mathematics in science, which is strange when you consider what might seem to be an obvious, common sense notion: that mathematics should be the 'servant' of science, not the 'queen'. Evidence should always trump theoretical expectations, however highly the theory might be regarded. Let's not put the cart before the horse, in other words.
 
Got the math wrong
[Click to enlarge]
 
Philosophical issues lie at the heart of this problem. While the term 'proof' may be acceptable in a mathematical context, as in a 'mathematical proof', it is not appropriate, strictly speaking, in a scientific context. The term 'scientific proof' is a misnomer, in so far as scientific theories can never be conclusively verified, only conclusively falsified. The term 'proof' implies 'a result that is final and beyond doubt', whereas scientific theories, by definition, should always be vulnerable to being replaced by new or improved theories. Again, new math might be required. Mathematical proofs, therefore, do not equate to scientific truths.

Furthermore, mathematical descriptions are often confused with empirical explanations. For example, it is easy to overlook the fact that we do not understand the mechanism behind gravity. Newton admitted as much, and stated that he framed no hypothesis in this regard. He had merely described it in mathematical terms, but not what it was. In the hope of bringing gravity back down to earth, so to speak, the search still goes on for a physical mechanism. Gravity waves and/or graviton particles are the favored speculations of the mainstream, although the particle responsible for mass, the Higgs-Boson (or so-called God particle) still remains elusive. (Gravity is often described as a property of mass.)

Famously, billions of dollars have recently been thrown at the LHC (Large Hadron Collider) in Switzerland, in the vain hope of pinning down this mystical beast. So far without any luck.
Einstein was quite simply contemptuous of experiment, preferring to put his faith in pure thought.
- Paul Davies.
Einstein further muddied the waters when he replaced a mathematical description of gravity with an abstract mathematical description, by factoring in time as a physical dimension - the fourth dimension. Few, however, now dare to question this scientific scripture, but can empty space really be curved?
To the extent that the laws of mathematics refer to reality, they are not true; and to the extent that they are true, they do not refer to reality.
- Albert Einstein.
Even if you think Einstein had his tongue firmly planted in his cheek when he said this, one has to admit that many a true word is spoken in jest.

The black hole is another famous example of a mathematical abstraction. Although based purely on theoretical assumptions, their existence is now regarded as fact in mainstream science. Because gravity is a near infinitely weak force, division by zero (a schoolboy error, no less!) results in the famous 'point' with zero volume and infinite mass!
A 'point', however, is an abstraction, not a physical object. In other words, a point is a purely mathematical object. No one has ever observed a point, and no one ever will, because nature does not make points.
- Stephen J. Crothers.
Wal Thornhill discusses Crothers' work in his article, The Black Hole at The Heart of Astronomy.

Many eminent scientists throughout history have also warned against placing too heavy a reliance on mathematics. Experimentation, they warned, should be king:
We have to learn again that science without contact with experiments is an enterprise which is likely to go completely astray into imaginary conjecture.
- Hannes Alfvén, the father of Plasma Physics, Nobel prize winner 1970.
Ignoring such wisdom, it is all too often assumed that a theory must be correct if the math appears to be correct, and on this basis it has become acceptable to factor in numerous exotic hypotheticals in order to balance the equations. Dark matter and dark energy now allegedly make up at least 90% of the universe, despite all attempts to pin them down. Small wonder some refer to them as the blank checks required to postpone the falsification of bankrupt theories.

I'm sure at some point in the future we will look back on the current obsession with mathematical abstraction and laugh out loud, just as we do now at the flat earth society of years gone by.

Before Hannes Alfvén, another famous pioneer of Plasma cosmology, Kristian Birkeland, also favored experimentation over math, despite having trained as a mathematician. He was famous for proposing that the auroras were powered by electrical particles emitted by the Sun. They laughed at him, but he went on to demonstrate this with his famous terella (little Earth) experiments and, always a practical man, he even led expeditions to auroral regions. His adversary at the time, Sydney Chapman, had favored a purely mathematical approach, and refused to believe that the auroras could be powered from outside the earth. Chapman was wrong, but some still cite his work.

Phil Plait, the self-proclaimed Bad Astronomer and critic of the Electric Universe, is also an advocate of the mathematical approach to science. For example, on this YouTube video at 03:33, Plait says: “It has to be that way for the math to work out.” This is an incredible statement when you think about it. Since when has Mother Nature been obliged to adhere to man-made mathematical laws? Plait is talking about black holes, but he fails to mention that the only safe prediction that can be made about them relates to the alarming rate at which research consumes tax-payers' money.
 
Down the gurgler
[Click to enlarge]
 
Nikola Tesla, for one, had little time for such arrogance:
Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.
Space, once thought to be a tenuous vacuum, of course, has been found to be alive with plasma and electromagnetism, much as Tesla had alluded. Moreover, the math behind the Kinetic Theory of Ordinary Gases is simply not relevant for plasmas, sometimes referred to as ionized gases.
The approach which Hannes Alfvén suggested must ignore the elegant and simplistic ordinary gases theory as the electromagnetic forces within a plasma dominate.
- Wal Thornhill.
Alfvén went further: “Such theories are developed with the most sophisticated mathematical methods and it is only the plasma itself which does not 'understand' how beautiful the theories are and absolutely refuses to obey them!

Are mathematicians afraid that electromagnetism would mess up all their elegant equations because it is so difficult to model mathematically? It's a shame when you consider that taking into account plasma and its electrodynamic behaviors would obviate the necessity for the current heavy reliance on exotic hypotheticals.
It is an embarrassment that the dominant forms of matter in the universe remain hypothetical.
- Jim Peebles, Princeton University.
Of course, no sane person would deny the importance of mathematics. I agree with Lord Kelvin when he said “I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind.

However, for the sake of clarity, I say again: Math should be the servant of science, not the queen. It really comes down to a question of priorities. But don't take my word for it.
Science is mathematical not because we understand so much about the physical world, but because we understand so little.
- Bertrand Russell.
Another problem with the mathematical approach relates to the inability of mathematicians to agree on technical definitions. There are, in fact, numerous ambiguous definitions for 'lines' and 'points', and both of these concepts are critical to the math behind so much modern cosmology, particularly black holes. Bill Gaede does an excellent job exposing this fatal flaw in "What's the point."

The Credit Crunch

The current worldwide economic crisis is often referred to as the credit crunch, and it cannot be denied that increasingly esoteric financial dealings contributed to this situation. Currency was once backed by real assets, principally gold. Likewise, science was once based on empiricism - measurement and evidence.

Money can now be printed at the whim of powerful international financiers, much as ad hoc hypotheticals are contrived to balance scientific equations at the whim of influential scientists.

The following quotes from Rolling Stone magazine, in an article by Matt Taibbi, neatly sum-up the situation that led to recent financial meltdown:
The mess Cassano created had its roots in an investment boom fueled in part by a relatively new type of financial instrument called a collateralized-debt obligation. A CDO is like a box full of diced-up assets. They can be anything: mortgages, corporate loans, aircraft loans, credit-card loans, even other CDOs. So as X mortgage holder pays his bill, and Y corporate debtor pays his bill, and Z credit-card debtor pays his bill, money flows into the box.

[..]

The problem was, none of this was based on reality. “The banks knew they were selling crap,” says a London-based trader from one of the bailed-out companies. To get AAA ratings, the CDOs relied not on their actual underlying assets but on crazy mathematical formulas that the banks cooked up to make the investments look safer than they really were. “They had some back room somewhere where a bunch of Indian guys who'd been doing nothing but math for God knows how many years would come up with some kind of model saying that this or that combination of debtors would only default once every 10,000 years,” says one young trader who sold CDOs for a major investment bank. “It was nuts.”
While it is widely acknowledged that the financial markets are in crisis, few people are aware that cosmology has hit similar dire straits. It is not easy to hide facts from business people and the public, especially when they are hit in the pocket, but the high priests of science still hide ensconced in their ivory towers, safe in the knowledge that most people are unaware of their costly devotion to redundant ideology.
 
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For further investigations of these themes The Soupdragon recommends: Plasma Cosmology.net
 
 
 
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