Yet while it has been a fundamental tool in researching the inorganic physical world mathematics has been unable to access or discuss life as such mathematically. We can mathematically describe most of the commonplace aspects of life (blood pressure, blood sugar, cholesterol, etc.), but not life itself. What makes something alive, rather than dead or not alive is still beyond our comprehension. We know that life has evolved (evolution is an absolute fact), and we know that neo-Darwinism has been the mainstream working theory of evolutionary scientists, producing ever increasing (but still incomplete) fitting explanatory results. [2] (Even so, a small but growing number of scientists, foremost amongst them the late Lynn Margolis, have been questioning the neo-Darwinist model.) We know mathematically and empirically what happens as life becomes more complex. We know about genes, chromosomes, reproduction, population, but life qua life is still the greatest mystery within the greatest mystery of existence per se. 

Mathematics is the abstraction of reality; it is not reality as such. As author Howard Bloom notes: "…abstractions may be indispensible but they don't accurately reflect reality".[3] Theoretical cosmology and theoretical physics, being essentially mathematical constructs, are besot with abstractions – indeed, they are one big abstraction; they help us relate to reality, comprehend it, manipulate it, but they are not identical with reality.  They are descriptions of reality (and sometimes it seems of non-reality). Theoretical mathematics can also deal with non-reality (re: Escher Bach) as efficiently as it can with the phenomena of reality, but not necessarily with reality as such. 

This is the salient point that both Eric J. Lerner [4] and Mordechai Nessyahu  [5] make. Bloom makes the same point in The God Problem. [6] Reality can be described mathematically but that description is not reality as such.  Mathematics is the language, the grammar of reality and since math can rationally describe a non-reality just as well as reality, non-reality is often mistaken for reality; something that is difficult in the everyday language of human intercourse. 

For example "The Earth is flat" is a perfectly grammatical sentence; it reflects the logic of grammar, it is internally consistent. But just because we can say it grammatically does not mean that the earth is flat. As Kenneth Boulding put it "Mere internal consistency is not enough, for there may be views of the world which are internally consistent, but which are, nevertheless, not true, in the sense that the real world does not conform to them". [7] This confusion between reality as such and mathematics as the language of reality has become a real stumbling block to the advance of human knowledge as we close in on the border between physics and metaphysics; the border between the empirically accessible finite and the inaccessible infinite. 

Mathematics is especially obstructionist if we assume evolution to be the grand narrative of ultimate reality (not only the descriptive metaphor for the development of organic reality), as Ervin Laszlo so eloquently argues [8].  Evolution is characterized by qualitative change, by the dialectic of the internal unfolding and development of reality. Mathematics can only deal with quantitative change and movement, with the externals of ultimate reality as we perceive them, with the phenomenal world not with the noumenal world, with the appearances of the world not with the essence of the world. This is the essential message of Kant's Critique of Pure Reason. Kant uses reason or rational (from ratio) in its precise technical sense, referring to the laws of non-contradiction inherent to mathematical ways of thinking. There is a limit to knowledge not available to empirical investigation but only capable of mathematical description (pure reason). With this critique he sets the stage for Hegel's dialectical way of thinking; a mindset better suited to evolutionary development than Aristotelian stasis. Nessyahu was within the Kantian tradition when he defined the limits of possible experience by creating a practical metaphysics that defined the border between the finite and the infinite. He was clearly within the Hegelian tradition when he identified the essential dialectic inherent in the evolutionary synthesis. 

Reality is much richer than the mathematical language we use to describe it. Indeed mathematical language tends to desiccate the luxuriant richness of reality. A good prosaic example of this is economic theory (which is as mathematical as quantum physics) as it relates to the reality of the business world and human economic activity. Business is not just bookkeeping or a reflection of economic theory; it is passion, belief, imagination, falling in love with your own creativity; it is often a sense of mission reflecting a sincere desire to change the world for the better.  

Starting a business is an act of creation no less than an artist painting a mural or a musician writing a symphony. This is because human creativity is indivisible: whether used to make a better mousetrap, plant a different crop, paint a picture or start a new business it stems from the same source: the human desire, unique amongst species, to make sense of itself and its environment and leave its mark on the future. Human creativity is its own justification and needs no other sanction; it is what makes human beings human and thus godlike – God creates and we create. God creates cosmos from chaos and we create cosmos (paintings, music, statues, products, manufacturing systems and services) from chaos. In point of fact God did not create us in his image, we created him in our image – God is an induction, not a deduction.

Economic theory is useful and even essential for the formulation of economic policy but it is utterly insufficient for understanding what is happening in society and the economy. Empirical proof of this is that economists rarely if ever succeed in the real economy of products and services. At most they can serve a useful function in the financial sector. I cannot think of one economist who ever started and ran a new business, let alone created a whole new sector of economic and business activity. Economists are limited by the 'rationality' of their mathematical way of thinking. Since one cannot mathematize imagination or creativity or passion (the hallmarks of the entrepreneur), or comparative social energy and cultural values, they are stuck in their analytical thinking and prevented from entering the world of synthetic thinking intrinsic to the artist, inventor and entrepreneur. And yet it is the inventors and entrepreneurs who create economies, not economists; just as it is artists that create art and not art critics.

Another instructive historical example of the limitations of mathematics would be the mathematical models Robert McNamara and the Pentagon used to prosecute the war in Vietnam and the catastrophic failure this resulted in. These models had nothing to do with the human passion on the ground. McNamara could never mathematize the Vietcong and North Vietnamese refusal to lose and the cultural differences that explained their 'willingness' to suffer loses inconceivable to the American mind.

This is one reason why the hyper-rationality of intellectuals is suspect in the eyes of the ordinary human being – too much abstraction, not enough passion and gut feeling. Non-intellectuals care little for learned sociological, psychological and anthropological explanations regarding the source of their patriotism and various venerations, or why they love their children more than others, or biological explanations of why they fall in love. They deeply resent the tone of superior understanding implicit in these explanations and are deeply suspicious of the analytical coldness of the explainers – they sense there is something non-human about it. 

This explains the non-rational need for literature and poetry and love. Rationality is never more productive than when it sails on the ocean of the non-rational imagination. The daydreaming of Newton and Descartes and others has been the necessary fertilizer for scientific flowering. The unsophisticated imagination of Edison and Ford and others has been the necessary fertilizer for economic flowering. Bronowski in the television production of The Ascent of Man cited the three 'Bs' as the source of creativity: the bedroom, the bathroom and the bus. Einstein was hard put to explain the source of his own revolutionary ideas; his explanation was reminiscent of one of Red Skleton's characters (Klem Kiddlehopper) who said: "I was just standin on the corner doin nothin and it hit me"

Reason is not the source of creativity; reason is used to explain non-rational intuitions in a rational way. It is not the cause of ideas; it is the instrument necessary to turn ideas into effective tools. It is a necessary tool but certainly not one sufficient to explain the human condition within ultimate reality. This is why mathematics should be viewed as the most useful tool in humanity's intellectual toolbox but not as the ultimate arbitrator of what is right and wrong. It should continue to be our democratic intellectual servant but never our tyrannical intellectual master. 

Notes

[1] Novum Organum xcvi

[2] Stem cell research is now revealing that epigenetics changes DNA and that these changes can be passed on to next generations.  The inheritability of acquired characteristics has been resurrected and neo-Lamarckianism is now a complementary to neo-Darwinism. 

[3] Bloom, Howard. The God Problem; Prometheus Press, Amherst New York, 2012 Pg 28

[4] Lerner, Eric J. The Big Bang Never Happened; Vintage, 1992

[5] Nessyahu, Mordechai. Science of the Cosmos and Scientific Society (in Hebrew) Katavim, Tel Aviv, 1953  

[6] Bloom pg 38

[7]Boulding, Kenneth E. "Towards an Evolutionary Theology" in Science and Creationism Pg 146

[8] Laszlo, Eervin. Evolution: The Grand Synthesis. New Science Library, Boston, 1987