Mathematics and Natural Laws

In the image:

Flowering of haematite in a piece of Brazilian quartz

“In mathematics you don’t understand things. You just get used to them. —John von Neumann”

 Matter, Mind, and Discovery


“Some of the conditions of mental development” is the subject of a lecture given by Paul Kingdon Clifford. He was an English mathematician and introduced what is now termed geometric algebra. What I’ve read in his pages is something with which I fully agree:

“There is no scientific discoverer, no poet, no painter, no musician, who will not tell you that he found ready made his discovery or poem or picture – that it came to him from outside, and that he did not consciously create it from within”.

There is something in this expression reminding me of Picasso. He was famous for his saying: “I don’t search, I find”.

Clifford is often remembered for his talking of mind-stuff. He defined “mind-stuff” as follows (1878, “On the Nature of Things-in-Themselves”, Mind, Vol. 3, No. 9, pp. 57–67):

“Briefly put, the conception is that mind is the one ultimate reality; not mind as we know it in the complex forms of conscious feeling and thought, but the simpler elements out of which thought and feeling are built up. The hypothetical ultimate element of mind, or atom of mind-stuff, precisely corresponds to the hypothetical atom of matter, being the ultimate fact of which the material atom is the phenomenon. Matter and the sensible universe are the relations between particular organisms, that is, mind organized into consciousness, and the rest of the world”.

“That element of which, as we have seen, even the simplest feeling is a complex, I shall call Mind-stuff. A moving molecule of inorganic matter does not possess mind or consciousness, but it possesses a small piece of mind-stuff. When molecules are so combined together as to form the film on the underside of a jelly-fish, the elements of mind-stuff which go along with them are so combined as to form the faint beginnings of Sentience. When the molecules are so combined as to form the brain and nervous system of a vertebrate, the corresponding elements of mind-stuff are so combined as to form some kind of consciousness; that is to say, changes in the complex which take place at the same time get so linked together that the repetition of one implies the repetition of the other. When matter takes the complex form of a living human brain, the corresponding mind-stuff takes the form of a human consciousness, having intelligence and volition”.

What was meant there? It is the intelligent organization of matter in the universe and the ability of the human mind to enter in connection with and understand it. The matter is intelligent even in the sense intended by Ray Kurzweil when asking: How smart is a rock?

 Evidence of Design inside a Rock

“How Smart Is a Rock? To appreciate the feasibility of computing with no energy and no heat, consider the computation that takes place in an ordinary rock. Although it may appear that nothing much is going on inside a rock, the approximately 1025 (ten trillion trillion) atoms in a kilogram of matter are actually extremely active. Despite the apparent solidity of the object, the atoms are all in motion, sharing electrons back and forth, changing particle spins, and generating rapidly moving electromagnetic fields. All of this activity represents computation, even if not very meaningfully organized. We’ve already shown that atoms can store information at a density of greater than one bit per atom, such as in computing systems built from nuclear magnetic-resonance devices. Thus, the state of the rock at any one moment represents at least 1027 bits of memory.”

Moreover, in the same  chapter, to highlight the great potential inherent in matter, Kurzweil added: “One cubic inch of nanotube circuitry, once fully developed, would be up to one hundred million times more powerful than the human brain.”

― Ray KurzweilThe Singularity is Near: When Humans Transcend Biology

Happily, we all live in an intelligent universe and all of us, of course, enjoy intelligence. Every single element in our organism is intelligence. Our mind is created in order to be able to comprehend the universe around us, to interpret it and elaborate it into our own ideas. So the universe is made on the basis of laws that are the same we can find operating in our mind. Our brain is as a supercomputer that can perform an infinite number of marvelous operations but, as a computer, it needs a project that obviously comes from outside. You can read and write because there are special parts of your brain that are deputed for that task. It’s the same reason for which you can enjoy maths or physics, music or poetry.

Maths and beauty and physical laws

One of the outstanding characters in twentieth-century physics said, “God chose to make the world according to very beautiful mathematics.” As the author of an article appearing in the May 1963 edition of Scientific American, Dirac wrote:

“It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better”.

Similarly, Bertrand Russell expressed his sense of mathematical beauty in these words:

“Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry”.

Evidence of Design in Natural Laws

In many articles posted on this blog, I have often emphasized the beautiful arithmetics underlying the measures of the flat earth. Numbers are on the basis of wonderful patterns clustering in plots constantly multiplying the digits 111 and 666. To any intelligent mind, the mathematical model of the cosmos is one of the most indisputable evidence of design.

Mathematics has always had a special role in the human understanding of the universe. But the reasons why this happens apparently remain mysterious.

One remarkable feature of the natural world where we live is that all of its phenomena can be expressed by relatively simple laws. If all natural events have always been regulated by strictly binding principles, we should presume that their laws were preexistent. Could you imagine anything different? How could the whole universe have ever respected laws that did not even have been formulated?

How could the whole world of nature have always precisely obeyed rules that did not yet exist? Natural phenomena such as the periodic movement of the celestial bodies, the movement of the sun over the earth, the regular alternation of the seasons allow the measuring of the time. Anyway, they are not the measuring minds. We are the only intelligent entities able to understand measure. Just superior beings, in fact, are capable of mathematical insight.

A natural law is simply a conceptual idea and ideas can only exist in someone’s thinking mind. Is there a mind in nature? Does nature possess its own intelligence? Is nature aware of the laws which govern it?  Of course, your answer would always be negative. Since there is no mind in nature, nature itself has no intelligence of the laws which govern it.

The power to make things happen in obedience to universal natural laws cannot reside in any entity ignorant of them. Would it be more reasonable to suppose that this power resides in the laws themselves? Of course not. Ideas have no intrinsic power. They affect events only as they express the will of a thinking person. Only a thinking person has the power to make things happen. Since natural events were lawful before man ever conceived of natural laws, the thinking person responsible for the orderly operation of the universe must be a higher Being, a Being we know as God.


Nature as an Impersonal Machine

The scientist Robert Boyle (1627–91) attacked the contemporary prevailing notions of the natural world which depicted ‘Nature’ as a wise, benevolent and purposeful being. Boyle, one of the leading mechanical philosophers of his day, believed that the world was best understood as a vast, impersonal machine, fashioned by an infinite, personal God.

He was arguing that it was inappropriate to speak of Nature as if it had a mind of its own: instead, the only true efficient causes of things were the properties and powers given to matter by God. About Him, calling to mind the letter to the Romans, he wrote:

“From a knowledge of His work, we shall know Him.”

Boyle attracted people with his enthusiasm for science.  That enthusiasm came directly out of his Christian faith.  To Boyle, love of God came first, and everything else second.  Science was a means to a higher end: loving God with all one’s heart, soul, strength, and mind. He studied the Scriptures in the original languages and accepted the Genesis accounts as literal, historical truth.  His faith was well reasoned and not traditional.

He applied II Tim. 3:16 (“All Scripture is given by inspiration of God”) to the entire Bible, including Genesis.  Furthermore, he believed in verbal inspiration, meaning that God’s revelation was contained in the very words, not just the meaning, of the text.

He said he had no problem in speaking of the laws God had given to physical bodies and he used to name them as laws of nature. But he couldn’t imagine as a body deprived of its own intelligence could control and determine its own motions and conform them to the natural laws.

Deep thinkers often wonder why mathematics, a pure human construction of the mind, possesses the ability to explain our reality. It proves to have the ability of describing and often predicting the different phenomena of the outer world. It’s on this subject that John von Neumann notes that maths can help us to get used, but not always to understand reality. Bye bye, my reader.


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