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Why Math Counts August 29, 2006

Posted by thebeam in The Byways.

Over at Good Math Bad Math, they are discussing one of the beneficial side-effects of strong math skills. A Harvard research group is publishing a paper that presents strong experimental evidence that supports the premise that Cold Dark Matter (CDM) exists in our universe. The existence of CDM is an important part of the cosmological description of the behavior of the universe, without it all of the theoretical constructs come up short when compared to the observable universe.

For those of you who might not know what Dark Matter is, this excerpt from Wikipedia sums it up fairly well “…dark matter refers to matter that does not emit or reflect enough electromagnetic radiation (such as light, x-rays and so on) to be detected directly, but whose presence may be inferred from its gravitational effects on visible matter.”

Estimates are that CDM constitutes about 22% of the mass of the universe. A massive 4% is normal everyday matter, and the rest (72%) is really weird stuff, Dark Energy. Dark Matter and Dark Energy are both experimentally deduced from mathematical models that take into account estimates of the mass of the ‘known universe’ and the deviations between the predicted and observed models.

From A Stunning Demonstration of Why Good Science Needs Good Math

They used a combination of optical and X-ray telescope to produce maps of the gravitational fields of the clusters. This was done by computing the gravitational lensing effect distorting the images of other, more distant galaxies visible behind the collided clusters. By carefully computing the distortion caused by gravitational lensing, they were able to determine the distribution of mass in the collided clusters. And what they found was the bulk of the mass was not in the light matter. It was in the places that the center of gravities of the clusters would have been without the shock-wave effects of the collision. So the bulk of the mass of these two clusters do not appear on our telescope images; but it behaves exactly as the math predicts it would if it were dark matter.

The prediction and the result are both based on very careful computations based on the mathematical predictions of gravity and relativity. They were able to predict precisely what they would expect from the interaction using a mathematical model of the how the gas clouds would interact to be swept away; and how the dark matter would interact gravitationally to predict where the dark matter masses should be. Then they were able, via a separate computation to determine how much mass was in what location based on gravitational lensing. And finally, they were able to compare the two separately computed results to see if the reality matched the prediction.

Now that is both good math and good science! And the science could not have been done without the math.

While my math didn’t cover much about cosmology, I do use it on a regular basis. Everything from figuring out how many ounces of flour to add to a recipe that is three times what is in the book, to trying to determine what the failure rate is for a given industrial process, graphed as a function of time-in-que.

Give your children a chance, make sure that they get the opportunity to immerse themselves in math. While I don’t believe that everyone has the capacity to do work at this level, I do believe that they can be shown why those who use good math in the process of understanding a problem, often have a better chance of arriving at a correct solution.

Life and Hearts is in session. Are you ready to “Hunt the bitch?”



1. Prashant Singh - September 1, 2006

Hey Greg,

I do agree completely with you that maths is essential for development of human mind not only in higher science but in day to day life.

What else I have felt is that understanding Mathematics gives you an objectivity, which helps you resolve most of the issues.

The children do need to understand mathematics and apply it aptfully. It is because of understanding mathematics that the countries like India and china are growing at a much faster rate.

2. thebeam - September 1, 2006

I agree on the Indians and Chinese, at least from what I see here. When I look at US Colleges, I see a disproportionate number of people from both those cultures, in the math and technical fields graduating, as opposed to those of European descent.

We’re losing our technical edge, and too many of our young are too busy watching Hollywood nonsense to care.

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