Where is the Derivation, Dude?

p1120407All over the internet and even in underpasses, as photographed above, we are seeing more of science’s and mathematics’ iconic formulas advertised as never before.  On the surface they seem comforting to aficionados, but are they really making the public more likely to delve into the fields?

Anyone can use a hammer, so to a society, the knowledge and skill needed in making one is more important than the skill involved in using it. Similarly anyone— even computers– can plug numbers into mathematical or scientific formulas, so how to derive them is key. Yet schools struggle just to get students to acquire the simple mechanics and end-products of math and science. Increasingly most high schools, perhaps due to preconceived notions, do not emphasize or even cover derivations, acting as if the formulas were brought down on two stone tablets by Moses.

As a result, you can argue that the crux of math and science are not really taught to those who don’t continue to specialise in math and science. This is part of the reason why in the United States, evolution is not understood and why there is a large fraction of climate change deniers in the population. Many other countries’ educational systems are not that far behind in misguiding their youth.

In the same vein,  due to oversimplified models of matter we carry around a bricks-and-mortar-simplification in our heads every day. When some say, “we are nothing but an assembly of molecules”, they don’t realise how much they are shortchanging our understanding of chemistry, physics and biology.

Even if we don’t buy arguments along the ideas of those of Philip Goff, who suspects there are aspects of matter itself that play a key role determining the nature of consciousness, there is simply the fact that atoms and molecules are not solid lego blocks. On the contrary they are something quite special, and the sophisticated models we have arrived at , are just that, models. We have no conclusive, final understanding of what they are.

More precisely, the atom’s constituents: protons, neutrons and electrons are not like anything we experience at the macroscopic level. Sometimes they behave like particles, but in other experiments they also show wave-like properties. (Light also has a dual nature, but it’s distinct from particles because light has no mass.) When atoms bond into molecules, the energy levels of electrons change significantly. And the relationship between molecules and their energetic environment is a very dynamic one, leading to an assortment of effects, ranging from colour, synthesis and decomposition.

Several storms of Jupiter caught by NASA’s Juno

And things get far more complicated when molecules are part of a living entity. It’s even far more complex than having to account for the weather of both Earth and Jupiter. If the reference seems outlandish, here’s what I mean. On Earth, storms are caused by the uneven solar heating of our surface and the ensuing pressure differences. On Jupiter, storms result from the uneven heating from within the Jovian planet. In living systems, molecules not only respond to external energy and to molecules from outside of cells, they respond  to the energy provided from ingested molecules and to the information provided by genetic material. The latter is not static itself–its molecules are also subject to the environment.

And it continues. At every level that molecules enter, new realities emerge. There are beautiful mutual relationships that occur between organisms: trees and orchids whose roots need ectomycorrhizal fungi to absorb adequate ions; lichen who associate with algae in order to get energy-rich molecules; microbiota in our gut that increase our ability to harvest otherwise inaccessible nutrients; parents who cling to their children from birth to adulthood to nourish them with molecules, habits, morals, skills and knowledge.

Isn’t it then an intellectual crime to proclaim “we are nothing but an assembly of molecules” ? The concepts of math and science are too intricate for parents to handle by themselves. But schools, books and the internet have to do a better job. Simple advertising, mere use of formulas or articulation of technical vocabulary alone will leave children’s minds unnourished.

N.B. And in case you were curious about the origin of eπi + 1 =0, here it is:

Start with the MacLaurin series for e, and use xi as its power. After simplifying the powers of i, select-terms turn out to be the MacLaurin series for cos x, and ,after factoring out i, the series for sin x. Then if we let x = π radians and evaluate the trigonometric terms, we end up with our equation.


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