NEVER A GOD'S EYE VIEW
For Jacob Bronowski’s (1978: 69-70) the relationship between scientific endeavor and the truth hinges the notion that our conjectures always do violence to a “totally connected” universe:
Since… every fact has some influence on every other fact, then it follows that any cut you make at all is a convenient simplification. But in essence it is a distortion… it is natural that your decoding cannot be right. And it is not surprising that while you keep on getting approximate good answers (the answers get better and better as you progress because you exclude less and less), it is in principle out of the question that we should ever have an ultimate explanation. That would involve setting up experiments in which the whole of the universe was perceived from a God’s eye view.
OPENING AND CLOSING A FORMAL SYSTEM
Bronowski (1978: 108) offers a view of science which acknowledges the necessity—albeit temporarily—for subjectivity in the process, without compromising the overarching goal of objectivity and formalism: For Bronowski science is
an attempt to represent the known world as a closed system with a perfect formalism. Scientific discovery is a constant maverick process of breaking out of the ends of the system and opening it up again and then hastily closing it after you have done your particular piece of work.
In a passage that resembles Kuhn’s revolutionary science and paradigm shifting, Bronowski stresses that all fundamental scientific discoveries go beyond pure analytical thinking and requires reopening (and subsequent closing) of the system:
The symbolism of the language is found to be richer than had been supposed. New connections are discovered. The symbolism has to be broadened. Symbolism, language, scientific formulae here are all synonymous. What opens it? That function of the brain which in fact is not the function of a digital computer.
DIONYSIUS THE AREOPAGITE
Bronowski (1978: 70) concludes his "from metaphor to algorithm" thesis with an astonishing quotation from Dionysius the Areopagite:
God's love is universal; it infuses the whole of nature, and it therefore infuses every piece of matter. And, therefore, not only does God's love draw every piece of matter to him, but every piece of matter must be drawn to every other piece.
Bronowski is sympathetic to the claim that this metaphor may have influenced Newton’s big-picture thinking on the gravitational attraction between two bodies. If this were the case, the law of inverse squares would have been influenced by the Areopagite via Nicholas of Cusa and Kepler respectively.
Bronowski, Jacob. (1958) The Creative Process. Scientific American, September 1958.
Bronowski, Jacob (1978) The Origins of Knowledge and Imagination. Yale University Press, Princeton.
THE PATH FROM METAPHOR TO ALGORITHM
Bronowski (1978) holds that “Nature is not a gigantic formalizable system.” In order to formalize something that is inherently not formalizible:
[W]e have to make some assumptions which cut out some parts. We then lose the total connectivity. And what we get is a superb metaphor, but it is not a system which can embrace the whole of nature.
We are really saying there is no system of axioms which can embrace the whole of nature, or for that matter the whole of mathematics.
Bronowski (1978: 70) is careful to differentiate between pure mathematics, “as an abstract system,” and mathematics as “a formal language for extracting something from the universe.” He (1978: 45) characterizes the latter as “the path from metaphor to algorithm”:
When Newton saw the moon as a ball that had been thrown round the earth, he was initiating a gigantic metaphor. And when it finished up, it… it was an algorithm (a formula with which you can calculate).
Newton ’s inverse square law of gravitation states (in formal prose) that:
[T]he gravitational attraction between two massive bodies is proportional to the product of their masses divided by the square of the distance between some point m of each mass.
Put more succinctly in mathematical symbols:
Bronowski (1978: 45-46 ) makes a bold comparison between a couplet from The Auguries of Innocence by William Blake and Newton’s inverse squares formula for gravitational attraction:
A Robin Red breast in a Cage
Puts all Heaven in a Rage.
He stresses that neither are syllogisms. They are general statements that succeed in saying something about the real world. The verse may lack Newtonian formal structure but we comprehend it “with an immediacy which we derive from language and experience.” Bronowski finds this extraordinary:
[L]et no one tell you that this quotation is only a particular statement. It derives its general appeal to us all from its high specificity, and that is the miracle of this kind of remark; but it is a statement which says something about the human situation and not just about a robin or a cage.
Polish born, British Mathematician and Polymath (1908-1974)
For Bronowski (1958) acts of creative imagination reveal connections between things previously assumed unalike:
A man becomes creative, whether he is an artist or a scientist, when he finds a new unity in the variety of nature. He does so by finding a likeness between things which were not thought alike before…
Blake, William (1795) Newton. Color print with pen & ink and watercolour. Tate Gallery.
Joseph Wright of Derby (1768) An Experiment on a Bird in an Air Pump. Oil on canvas. National Gallery, London.
In his scholarly writings Dionysius the Areopagite claimed to have been an original disciple of Paul. In fact, Dionysius was an invented character. The writings attributed to him were planted by an anonymous theologian from the 5th century (known as Pseudo-Dionysius).