Beware of Overgeneralized Science and Math

It is foolish to rely on the certainty of exact science because this certainty doesn’t translate to the flexibility of biological evolution, cognition, and creativity.

This sentence, written in Chapter 1 of Trial, Error, and Success, is not saying that the laws of science are useless. We know how professionals use these laws for specific tasks. The aim of Chapter 1 is to show the intellectual gap between the exact science and the real world. In a nutshell, the laws of exact science are mathematically perfect, which is never the case with experimental data. The following real-world example shows how this idealized science can lead to wrong decisions: ??

An elegant physics once misled a business strategy

In the days of the first personal computers, the semiconductor industry was using ultra-violet light to “print” millions of tiny features on each microchip. However, functionality of these microchips and computers was primitive in comparison to today’s smart phones. Many more and much smaller features were needed to enable more powerful microchips but, according to all experts at the time, the reduction of feature sizes by the use of light was approaching the ultimate physical limit.

The physical limit was the wavelength of light (physics tells us that light is a wave and, just as in the case of water waves, the distance between two adjacent crests or troughs is the wavelength). Believing the wave interpretation and modeling of light behavior, the experts reached the following firm conclusion: Light cannot create a narrower line than its wavelength, period.

To move beyond this physical limit, many companies and governments invested a lot of money into development of microchip “printing” by X-rays. One of these investors was Hoya—a large Japanese company with expertise in advanced optics technologies. Hoya’s managers saw an opportunity for almost certain success. With wavelengths at least twenty times shorter than ultra-violet light, X-rays were the next available option in the radiation spectrum. Machines that generate X-rays were available, but commercial masks needed for the “printing” were missing. With adequate investment, Hoya’s engineers developed a new material and technology, and the company was ready to offer X-ray masks as their new product.?

Surprisingly, the need for this product did not evolve. The semiconductor industry continued to use ultra-violet light. They broke the apparent physical limit by creating much smaller features on microchips than the wavelength of ultra-violet light!

This was not simply bad luck for Hoya’s managers. The experts misled them by overgeneralizing the wave model. Their firm conclusion ignored the fact that light consists of tiny photons as individual and randomly jiggling particles. The observed wave patterns of light in various experiments are idealizations analogous to observed purchase patterns after many customers buy a certain product. This idealization ignores the unpredictability of individual purchase events, analogously to the ignored random jiggling of individual photons by the wave model of light.

The analogy with a purchase pattern tells us that, in spite of the existing degree of randomness and unpredictability, individual purchase decisions can be influenced by sales conditions, marketing, and so on. In the example with individual particles of ultra-violet light, engineers changed the conditions by altering the path that each light particle travels through the mask and from the mask to the microchip. This constrained the random paths of individual light particles, shrinking the apparent wavelength of the aggregate wave pattern.?

The takeaway here is that the wave equations provide an elegant model for an averaged behavior of many particles, but physics overgeneralizes this elegance by ignoring the randomness and the size of individual particles.

The bottom line is that, even if you can stay away from physics and high-tech issues in your everyday life, you need to learn how to distinguish between useful generalizations and harmful overgeneralizations.

Be aware of the ignorance that creates the general laws of science.

I have friends around the world who use a law of chemistry to grow moissanite—a silicon-carbide based jewel, considered a diamond alternative, but with higher indexes for brilliance, “fire,” and luster than diamond. To grow this crystal, they supply silicon and carbon atoms by mixing certain gasses at certain pressures in a heated furnace. Setting this growth condition is all they can do. It is not possible to get the gas molecules to follow Newton’s laws of motion and to deliver silicon and carbon atoms directly to their positions in the crystal. The molecules fluctuate randomly and the first structures they make on the surface of the growing crystal are crap. Ernest Hemingway’s remark, captured in the memoir published by his deck hand Arnold Samuelson, that “the first draft of anything is shit” is a metaphor for this chemical process. The atomic structures that do not fit in the crystal order are short lived, just as the messy word structures disappear when the sentences are revised. It takes many short-lived attempts before the random shuffling of silicon and carbon atoms locks them into the stable structure of the growing crystal. Therefore, the following conclusion is the same, whether we think of crystals or sentences: The beauty of gems is not made by elegant processes but by the messy trial-and-error method. This metaphor can be generalized to state that nature is not governed by perfect laws of physics; it evolves by trial-and-error processes—and this is not an overgeneralization.

You wouldn’t know this from your formal education and by reading textbooks. The formal laws of physics and chemistry assume all carbon atoms as identical, but that’s not true. Atoms are not static objects with identical shapes, because—analogously to the light particles—the electrons, protons, and neutrons of each atom exhibit random jiggling. Scientists ignore these random behavior when they present the theory that all carbon atoms obey the same general laws of physics and chemistry.

Trusting the textbooks, you’d be right to expect that the laws of physics could pack carbon atoms into identical diamond crystals. And, as expected, diamonds cut in the same shape and labeled with the same price in a jewelry shop do look identical, but only because we don’t see the positions of individual atoms in the crystal grains. In reality, every diamond grain has its own distribution of inevitable defects in the atomic order. These random crystal defects are differences that make every single diamond grain unique, just as the random fluctuations are differences that make every carbon atom unique.

Science has to ignore irrelevant differences to create general concepts, and we are not saying that these generalizations are not useful. Of course they are. It’s helpful to classify many diamond jewels as an identical product. That way, we can distinguish diamond from moissanite, which the shops offer as a bit shinier and yet a lot cheaper alternative to real diamond.

Accepting the classification of these jewels as diamond and moissanite, we are happily ignorant of the bonding defects between their atoms. However, it’s not helpful to ignore the bonding defects between the atoms in our genes. Some of these defects result in gene mutations, possibly with dramatic consequences. On the negative side, mutations can cause disorders and lead to diseases, such as cancers. On the positive side are small genetic differences, which would not exist without gene mutations. Can you imagine a world where all humans are clones of Adam and Eve? The genetic difference between us—the humans—and chimpanzees is less than two percent, but we cherish it. The genetic difference between you, us, and Adolf Hitler is less than half a percent, but it makes a big difference.

The laws of physics and chemistry ignore atomic fluctuations but, analogously to crystal defects, the gene mutations also originate from these fluctuations. The lack of this insight is the gap between the rigid laws in exact sciences and the flexibility of biological evolution, cognition, and creativity.

This insight about fundamental randomness and uncertainty is useful, as hinted by the titles of the remaining sections in Chapter 1:

·?????? Use math for calculations, but stay away from its infectious perfection.

·?????? Accept that chance can trigger unpredictable cause-and-effect chains.

·?????? Do not forget that chance has two faces: bad luck and good luck.

·?????? Ignore the authority of experts if they put reason ahead of facts.

·?????? Do not believe that the law of large numbers removes uncertainty.

·?????? Be aware that comparisons of percentages can hide both large differences and large similarities.

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