Equations that reveal the mind of God

Modern science can be said to have had its beginning in the work of Galileo Galilei (1564-1642)

Modern science can be said to have had its beginning in the work of Galileo Galilei (1564-1642). Since then, science has achieved a broad understanding of the natural world at all levels, writes Dr William Reville

Much has been discovered across many disciplines, from the ultimate building blocks of matter, the quarks, to the geography of the universe; from the origin of the universe in the Big Bang about 15 billion years ago to the eventual heat death of the universe in the distant future; from the origin of life on Earth about 3.6 billion years ago as a single simple form through its evolution by natural selection to the myriad life forms that now populate the planet.

The whole picture hangs together as one coherent story universally accepted by the scientific community. Truly, this has been the most successful intellectual project ever pursued by humans.

The reason that the whole scientific picture hangs together so well is that it is all underpinned by a relatively small number of physical laws. Physics is the oldest and most fundamental of the sciences. Its function is to study the basic nature of matter and energy and the fundamental forces that determine what happens in our world.

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Because it would be impossibly complicated to study everything in the world at the most fundamental level, other branches of science arose: chemistry, to study how atoms combine with each other to form various compounds and to study the properties of these compounds; geology, to study the structure and behaviour of the planet; biology, to study the structure and behaviour of living things, and so on. These other sciences applied the approach already established in physics to their study of the world.

Basically, physicists study a phenomenon by building a model of it, based on how they think it works, using mathematical equations to describe the behaviour of the model. They then test the model by observing how it behaves under various conditions known to exist in the real world. If the behaviour of the model mimics the behaviour of the real phenomenon, as revealed by experiment, then the model is taken to be a good one that is able to tell us something true about the nature of the phenomenon.

For example, in a physical model of gas in a container, the gas would be composed of many individual gas molecules moving randomly about within the space of the container, colliding with each other and with the container walls. The pressure exerted by the gas on the container wall is determined by the number of collisions of molecules per unit area of wall per unit time.

The movement of the molecules is described by mathematical equations. These predict that as the temperature increases, the molecules move faster and hit the walls more often, thereby increasing pressure. The equations can be used to predict how gas pressure increases with temperature.

Now, in an experiment with a real container of gas, pressure can be measured as temperature increases. If the model results closely mimic the experimental results, then the model is good. If not, the model must be discarded.

When studying a complex phenomenon, physics tends to break it into its component parts, studying each part individually and then putting all the bits together again to explain the whole. This is the reductionist approach and it has been used widely and very successfully in all science.

However, we may now have reached a stage, particularly in biology, where the reductionist approach alone will not solve super-complex questions such as how the human brain works. In this and many other cases, the whole is clearly greater than the sum of the parts, and success in understanding the whole will only be achieved by studying the whole.

The fact that the world is comprehensible to the human mind has struck many great scientists as being of major significance. Einstein said in 1936: "The eternal mystery of the world is its comprehensibility." Why is this comprehensibility so striking?

You will recall that I said that the models drawn up by physicists behave in accordance with mathematical equations. It has been found time and time again that the correct mathematical equations are those that are the most beautiful.

Mathematical beauty, like physical beauty, is difficult to describe, but is instantly recognisable to a mathematician. And so physicists consciously seek out beautiful equations when building their models.

The world is rational and transparent and seems everywhere to bear the fingerprint of Mind. Einstein, along with other great scientists, believed that in deciphering the book of nature he was revealing the mind of God. Of course, human beings are also part of the natural world. Perhaps the explanation for the harmony between the reason of our minds and the reason found in the structure of the outside world is that they both have a common origin in the reason of the creator.

So, there I will leave it. I hope you didn't find my speculations in the last several paragraphs too irritating, but I found I was seriously boring myself with all that stuff about physical models and containers of gas.