Coherence Quotes (13 quotes)
…reality is a system, completely ordered and fully intelligible, with which thought in its advance is more and more identifying itself. We may look at the growth of knowledge … as an attempt by our mind to return to union with things as they are in their ordered wholeness…. and if we take this view, our notion of truth is marked out for us. Truth is the approximation of thought to reality … Its measure is the distance thought has travelled … toward that intelligible system … The degree of truth of a particular proposition is to be judged in the first instance by its coherence with experience as a whole, ultimately by its coherence with that further whole, all comprehensive and fully articulated, in which thought can come to rest.
Great thinkers build their edifices with subtle consistency. We do our intellectual forebears an enormous disservice when we dismember their visions and scan their systems in order to extract a few disembodied ‘gems’–thoughts or claims still accepted as true. These disarticulated pieces then become the entire legacy of our ancestors, and we lose the beauty and coherence of older systems that might enlighten us by their unfamiliarity–and their consequent challenge in our fallible (and complacent) modern world.
I have mentioned mathematics as a way to settle in the mind a habit of reasoning closely and in train; not that I think it necessary that all men should be deep mathematicians, but that, having got the way of reasoning which that study necessarily brings the mind to, they might be able to transfer it to other parts of knowledge, as they shall have occasion. For in all sorts of reasoning, every single argument should be managed as a mathematical demonstration; the connection and dependence of ideas should be followed till the mind is brought to the source on which it bottoms, and observes the coherence all along; …
If I go out into nature, into the unknown, to the fringes of knowledge, everything seems mixed up and contradictory, illogical, and incoherent. This is what research does; it smooths out contradictions and makes things simple, logical, and coherent.
Nature is disordered, powerful and chaotic, and through fear of the chaos we impose system on it. We abhor complexity, and seek to simplify things whenever we can by whatever means we have at hand. We need to have an overall explanation of what the universe is and how it functions. In order to achieve this overall view we develop explanatory theories which will give structure to natural phenomena: we classify nature into a coherent system which appears to do what we say it does.
One evening at a Joint Summer Research Congerence in the early 1990’s Nicholai Reshetikhin and I [David Yetter] button-holed Flato, and explained at length Shum’s coherence theorem and the role of categories in “quantum knot invariants”. Flato was persistently dismissive of categories as a “mere language”. I retired for the evening, leaving Reshetikhin and Flato to the discussion. At the next morning’s session, Flato tapped me on the shoulder, and, giving a thumbs-up sign, whispered, “Hey! Viva les categories! These new ones, the braided monoidal ones.”
Physical science comes nearest to that complete system of exact knowledge which all sciences have before them as an ideal. Some fall far short of it. The physicist who inveighs against the lack of coherence and the indefiniteness of theological theories, will probably speak not much less harshly of the theories of biology and psychology. They also fail to come up to his standard of methodology. On the other side of him stands an even superior being—the pure mathematician—who has no high opinion of the methods of deduction used in physics, and does not hide his disapproval of the laxity of what is accepted as proof in physical science. And yet somehow knowledge grows in all these branches. Wherever a way opens we are impelled to seek by the only methods that can be devised for that particular opening, not over-rating the security of our finding, but conscious that in this activity of mind we are obeying the light that is in our nature.
Pure earth does not petrify, because the predominance of dryness over [i.e. in] the earth endows it not with coherence but rather with crumbliness. In general, stone is formed in two ways only (a) through the hardening of clay, and (b) by the congelation [of waters].
Reality is what kicks back when you kick it. This is just what physicists do with their particle accelerators. We kick reality and feel it kick back. From the intensity and duration of thousands of those kicks over many years, we have formed a coherent theory of matter and forces, called the standard model, that currently agrees with all observations.
Scientific work, especially mathematical work which is purely conceptual, may indeed possess the appearance of beauty, because of the inner coherence which it shares with fine art, or may resemble a piece of architecture.
The goal is nothing other than the coherence and completeness of the system not only in respect of all details, but also in respect of all physicists of all places, all times, all peoples, and all cultures.
The mutton in the study gathered over it a thick blanket of Penicillium. On the 13th [December 1875] it had assumed a light brown colour as if by a faint admixture of clay; but the infusion became transparent. The ‘clay’ here was the slime of dead or dormant Bacteria, the cause of their quiescence being the blanket of Penicillium. I found no active life in this tube, while all the others swarmed with Bacteria. In every case where the mould was thick and coherent the Bacteria died, or became dormant, and fell to the bottom of the sediment … The Bacteria which manufacture a green pigment appear to be uniformly victorious in their fight with the Penicillium.
There is one great difficulty with a good hypothesis. When it is completed and rounded, the corners smooth and the content cohesive and coherent, it is likely to become a thing in itself, a work of art. It is then like a finished sonnet or a painting completed. One hates to disturb it. Even if subsequent information should shoot a hole in it, one hates to tear it down because it once was beautiful and whole. One of our leading scientists, having reasoned a reef in the Pacific, was unable for a long time to reconcile the lack of a reef, indicated by soundings, with the reef his mind told him was there.