The God and The Devil!

 
Alexander Pope said:

"Nature and Nature's law lay hid in night;
God said, let Newton be! and all was light."

 
Then came Einstein with his theory of relativity, and some
wit added the lines:

"But not for long. Let Einstein be! the Devil said,
And lo, 'twas dark: the light had fled."

 From Book Einstein, Kuznetsov.

Historical progress of all sciences..

...the historical progress of all sciences leads only through a multitude of contradictory moves to the real point of departure. Science, unlike other architects, builds not only castles in the air, but may construct separate habitable storeys of the building before laying the foundation stone.

-Marx (A Contribution to the Critique of Political Economy)

Axioms of mathematics and incompleteness..

Painting by Escher.[1]

The so-called axioms of mathematics are the few thought determinations which mathematics needs for its point of departure. Mathematics is the science of magnitudes; its point of departure is the concept of magnitude. It defines this lamely and then adds the other elementary determinations of magnitude, not contained in the definition, from outside as axioms, so that they appear as unproved, and naturally also as mathematically unprovable. The analysis of magnitude would yield all these axiom determinations as necessary determinations of magnitude. Spencer is right in as much as what thus appears to us to be the self-evidence of these axioms is inherited. They are provable dialectically, in so far as they are not pure tautologies.

Engels

Dialectics of nature

(A reflection on mathematics by engels which later was explored (independent of Engels) by Godel in his Incompleteness theorem.)

[1] Hofstadter calls this Escher work a “pictorial parable for Godel's Incompleteness Theorem.

Identity and difference

 

The dialectical relation is already seen in the differential calculus, where dx is infinitely small, but yet is effective and does everything.

                                  - Engels

Negation of Negation

 With most insects, this process follows the same lines as in the case of the grain of barley. Butterflies, for example, spring from the egg by a negation of the egg, pass through certain transformations until they reach sexual maturity, pair and are in turn negated, dying as soon as the pairing process has been completed and the female has laid its numerous eggs. We are not concerned at the moment with the fact that the process does not take such a simple form with other plants and animals, that before they die they produce seeds, eggs or offspring not once but many times; our purpose here is only to show that the negation of the negation really does take place in both kingdoms of the organic world.
    Furthermore, the whole of geology is a series of negated negations, a series in which old rock formations are successively shattered and new ones deposited. First the original earth crust formed by the cooling of the liquid mass was broken up by oceanic, meteorological and atmospherico-chemical action, and these fragmented masses were stratified on the ocean bed. Local elevations of the ocean bed above the surface of the sea subjected portions of these first strata once more to the action of rain, the changing temperature of the seasons and the oxygen and carbon dioxide of the atmosphere. These same influences acted on the molten masses of rock which issued from the interior of the earth, broke through the strata and subsequently cooled off. In this way, in the course of millions of centuries, ever new strata were formed and in turn were for the most part destroyed, ever anew serving as material for the formation of new strata. But the result of this process has been a very positive one: the production of a soil out of a mixture of the most varied chemical elements and in a state of mechanical pulverization, which makes possible the most abundant and diversified vegetation.
    It is the same in mathematics. Let us take any algebraic quantity we like: for example, a. If it is negated, we get -a (minus a). If we negate that negation by multiplying -a by -a, we get + a ², i.e., the original positive quantity, but at a higher degree, raised to its second power. It makes no difference in this case that we can obtain the same a ² by multiplying the positive a by itself, thus likewise getting a ². For the negated negation is so securely entrenched in a ² that the latter always has two square roots, namely a and -a. The fact that it is impossible to get rid of the negated negation, the negative root of the square, acquires very obvious significance as soon as we come to quadratic equations.
Engels

Dialectics..

(The general nature of dialectics to be developed as the science of interconnections, in contrast to metaphysics.)

It is, therefore, from the history of nature and human society that the laws of dialectics are abstracted. For they are nothing but the most general laws of these two aspects of historical development, as well as of thought itself. And indeed they can be reduced in the main to three:

The law of the transformation of quantity into quality and vice versa;

The law of the interpenetration of opposites;

The law of the negation of the negation.

All three are developed by Hegel in his idealist fashion as mere laws of thought: the first, in the first part of his Logic, in the Doctrine of Being; the second fills the whole of the second and by far the most important part of his Logic, the Doctrine of Essence; finally the third figures as the fundamental law for the construction of the whole system. The mistake lies in the fact that these laws are foisted on nature and history as laws of thought, and not deduced from them. This is the source of the whole forced and often outrageous treatment; the universe, willy-nilly, is made out to be arranged in accordance with a system of thought which itself is only the product of a definite stage of evolution of human thought. If we turn the thing round, then everything becomes simple, and the dialectical laws that look so extremely mysterious in idealist philosophy at once become simple and clear as noonday.

Engels 

(Dialectics of Nautre)

On negation of negation..

So, what is the negation of the negation? An extremely general — and for this reason extremely far-reaching and important — law of development of nature, history, and thought; a law which, as we have seen, holds good in the animal and plant kingdoms, in geology, in mathematics, in history and in philosophy — a law which even Herr Dühring, in spite of all his stubborn resistance, has unwittingly and in his own way to follow. It is obvious that I do not say anything concerning the particular process of development of, for example, a grain of barley from germination to the death of the fruit-bearing plant, if I say it is a negation of the negation. For, as the integral calculus is also a negation of the negation, if I said anything of the sort I should only be making the nonsensical statement that the life-process of a barley plant was integral calculus or for that matter that it was socialism. That, however, is precisely what the metaphysicians are constantly imputing to dialectics. When I say that all these processes are a negation of the negation, I bring them all together under this one law of motion, and for this very reason I leave out of account the specific peculiarities of each individual process. In fact dialectics is nothing more than the science of the general laws of motion and development of nature, human society and thought.

 Engels 

(Anti Duhring)

Polar opposites in natural science..

Dialectics has proved from the results of our experience of nature so far that all polar opposites in general are determined by the mutual action of the two opposite poles on one another, that the separation and opposition of these poles exists only within their unity and inter-connection, and, conversely, that their inter-connection exists only in their separation and their unity only in their opposition. This once established, there can be no question of a final cancelling out of repulsion and attraction, or of a final partition between the one form of motion in one half of matter and the other form in the other half, consequently there can be no question of mutual penetration or of absolute separation of the two poles. It would be equivalent to demanding in the first case that the north and south poles of a magnet should mutually cancel themselves out or, in the second case, that dividing a magnet in the middle between the two poles should produce on one side a north half without a south pole, and on the other side a south half without a north pole.

Frederick Engels

(Dialectics of Nature) 

Dirac on religion

I cannot understand why we idle discussing religion. If we are honest—and scientists have to be—we must admit that religion is a jumble of false assertions, with no basis in reality. The very idea of God is a product of the human imagination. It is quite understandable why primitive people, who were so much more exposed to the overpowering forces of nature than we are today, should have personified these forces in fear and trembling. But nowadays, when we understand so many natural processes, we have no need for such solutions. I can't for the life of me see how the postulate of an Almighty God helps us in any way. What I do see is that this assumption leads to such unproductive questions as why God allows so much misery and injustice, the exploitation of the poor by the rich and all the other horrors he might have prevented. If religion is still being taught, it is by no means because its ideas still convince us, but simply because some of us want to keep the lower classes quiet. Quiet people are much easier to govern than clamorous and dissatisfied ones. They are also much easier to exploit. Religion is a kind of opium that allows a nation to lull itself into wishful dreams and so forget the injustices that are being perpetrated against the people. Hence the close alliance between those two great political forces, the State and the Church. Both need the illusion that a kindly God rewards—in heaven if not on earth—all those who have not risen up against injustice, who have done their duty quietly and uncomplainingly. That is precisely why the honest assertion that God is a mere product of the human imagination is branded as the worst of all mortal sins.                                                                                                                                 -Paul Dirac

Causes..

Of course the speed of light is the same under socialism and capitalism, and the apple that was said to have fallen on the Master of Mint in 1664 would have struck his labour party successor three hundred years later with equal force. But whether the cause of tuberculosis is said to be bacillus or the capitalist exploitation of workers, whether the death rate from cancer is best reduced by studying oncogenes or by seizing control of factories- these questions can be decided objectively only within the framework of certain sociopolitical assumptions. 

Levins 

Lewontin 

Religion: A Fantastic Reality

Now all religion is nothing but the fantastic reflection in men's minds of those external forces which dominate their daily life, a reflection in which terrestrial forces assume the form of supernatural ones. In the beginnings of history it was the forces of nature which were first so reflected, and which in the course of further development underwent the most manifold and motley personifications among the various peoples. Comparative mythology has traced back this first process, at least in the case of the Indo-European peoples, to its origin in the Indian Vedas, and in its progress it has been demonstrated in detail among the Indians, Persians, Greeks, Romans, Germans and, so far as material is available, also among the Celts, Lithuanians and Slavs. But side by side with the forces of nature, it is not long before social forces begin to be active, forces which confront man as equally alien and at first equally inexplicable, dominating him with the same apparent natural necessity as the very forces of nature. The fantastic figures, which at first only reflected the mysterious forces of nature, at this point acquire social attributes, become representatives of the forces of history. At a still further stage of development, all the natural and social attributes of the numerous gods are transferred to one almighty god, who in turn is himself only the reflection of the abstract man. Such was the origin of monotheism, which was historically the last product of the vulgarized philosophy of the later Greeks and which found its incarnation in Jehovah, the exclusively national god of the Jews. Religion can continue to exist in this convenient, handy and universally adaptable form as the immediate, that is, the sentimental, form of men's relation to the alien, natural and social powers which dominate them, so long as men remain under the domination of these powers. However, we have repeatedly seen that in present-day bourgeois society men are dominated by the economic conditions they themselves have created and by the means of production they themselves have produced, as though by an alien power. The actual basis of the religious reflex action therefore continues to exist, and with it the religious reflection itself. Although bourgeois political economy has opened up a certain insight into the causal connection of this alien domination, this in no way changes the matter. Bourgeois economics can neither prevent crises as such, nor protect the individual capitalist from losses, bad debts and bankruptcy, nor secure the individual worker against unemployment and poverty. It is still true that man proposes and God (that is, the alien domination of the capitalist mode of production) disposes. Mere knowledge, even if it went further and deeper than that of bourgeois economic science, does not suffice to bring social forces under the domination of society. What is above all necessary for this is a social act. When this act has been accomplished, when society, by seizing all the means of production and using them on a planned basis, has freed itself and all its members from the bondage they are now kept in by these means of production which they themselves have produced but which confront them as an overpowering alien force; when man no longer merely proposes, but also disposes -- it is only then that the last alien force which is still reflected in religion will vanish and that the religious reflection itself will also vanish with it, for the simple reason that there will be nothing left to reflect.

Fredrich Engels