Exit from Eden: Milutin Milanković and his cycles

Milutin Milanković is a very interesting figure of mathematician.
His theory of cycles of glaciers is the scientific explanation of the historical fact of an Exit from Eden.
That exit triggered the advanced civilizations of the Nile and Mesopotamian valleys, and most likely lived in the memory of subsequent generations of men and women, building the myth of expulsion from Paradise.
The biblical narration was just the most influential of all the mythical reconstructions of that climatic shift; totally unable to make any sense of what Milutin explained from the vantage point of 20th century science.
Both Asimov (“New Guide to Science”) and Lee Silver (“Challenging Nature”) talk about him.

Investigate this paper: EMAM

Manchester vs Athens


Mathematics is the combination of two traditions, the deductive greek science whose Idealtypus was geometry, and the manipulative algebraic techniques that Middle Age inherited from Arab science.

Freeman Dyson, in the Gifford lecture “Infinite in all Directions”(1985) talks about a somewhat related juncture: Manchester vs Athens .

Briefly, Athens – i.e. the tradition of high philosophical ideas and deep ideas necessarily embedded in the practice of Western science – is just one possible strategy, one locus, to approach mathematics.

Another one was historically embodied by Manchester, the cradle of Industrial Revolution, where a more engineering or applied style was given full citizenship.
As Frederick Engels said, “If society has a technical need, that helps science forward more than ten universities”.  And that was indeed the case with Manchester.

This distinction operates across all mathematics. A big ideas and deep philosophical questions approach can be accompanied by a manipulative, algorithmic approach. That links to the very English taste for algorithms, see G. Boole characteristic polynomial of second order ODE, Cayley-Hamilton ideas about Characteristic polynomial of a matrix and indeed A. Turing, who gave full rank to the idea of algorithm (Turing worked in Manchester his last years).

Need to expand, talking about examples from within Mathematics. Is this same ideas as Gilbert Strang, of MIT mathematics fame, when he says that going forward Algebra is going to be more important than analysis?

That has ramifications in the problem of the gap Continuum vs Discrete. More later.

See Arnold Thackray “Natural Knowledge in Cultural Context” (American Historical Review, 1974(79:3))

Kant’s Einbildungskraft, Popper and Lem

Another take on the same topic. Popper falsificationism amounts basically to a view of the scientific process where science in its march places increasingly more stringent bounds on the possible explanations that are supported by a verification process. It is in a way pruning more and more the tree of possible outcomes, the tree of the scientific explanations supported by facts.

Immanuel Kant came along (earlier). He said that human mind has the capability of creating images of things that are not necessarily existent (yet). The question is then the following: does our reason have the capability to “cast into images” outcomes that are not coming from the existent reality and so does it have the ability to bypass the mimesis and proceed way ahead of the already-seen?

If that is the case (back to Stanislaw Lem) then we can probably argue that the blind watchmaker that created (for example) a horribly inefficient structure as the human spine (see N. Wiener,The Human Use of Human Being), can be improved upon by our conscious effort to perfect that ex-post-only design.

Of course it is our rationality (as a species) that needs to be invoked, not any supernatural design. Would that mean we could overcome the mimesis? Exit the cave maybe?

Need to read Lee M. Silver ‘Challenging Nature’, he may have an idea how to step out of this question. As an aside, such a Gedanken thread may even account for the sympathy Lamarckism enjoyed in USSR and for the success that F. Engels books and articles on science had in the former Soviet bloc. See Sebastiano Timpanaro (preface to the Italian translation to d’Holbach ‘Good Sense’).

Renaissance: Perspective and birth of mathematical Infinity


The birth of modern world in the Middle Age out of perspective in painting (Greeks did not have perspective) was due to innovations in Middle Age theology. The actuality of the infinite was born from Middle Age theology.
See Paolo Zellini, Breve Storia dell’Infinito, pgg.101-103;148-149

The best place where to learn all of this would be Panowski, Perspective als Symbolische Form (see this in Italian)