Dear Roger,
I read your essay with great interest. It once again confirms the fact that Mathematics and Physics - two fundamental sign systems but ontologically is not justified. However, like all Knowledge. Fundamental science is experiencing a "crisis of representation and interpretation", "crisis of understanding", methodological and philosophical crisis of foundations. About it well said Carlo Rovelli in article SCIENCE IS NOT ABOUT CERTAINTY: A PHILOSOPHY OF PHYSICS :
«This is a standard idea of how science works, which implies that science is about empirical content, the true interesting relevant content of science is its empirical content. Since theories change, the empirical content is the solid part of what science is. Now, there's something disturbing, for me as a theoretical scientist, in all this. I feel that something is missing. Something of the story is missing. I've been asking to myself what is this thing missing? I'm not sure I have the answer, but I want to present some ideas on something else which science is.
This is particularly relevant today in science, and particularly in physics, because if I'm allowed to be polemical, in my field, in fundamental theoretical physics, it is 30 years that we fail. There hasn't been a major success in theoretical physics in the last few decades, after the standard model, somehow. Of course there are ideas. These ideas might turn out to be right. Loop quantum gravity might turn out to be right, or not. String theory might turn out to be right, or not. But we don't know, and for the moment, nature has not said yes in any sense.
I suspect that this might be in part because of the wrong ideas we have about science, and because methodologically we are doing something wrong, at least in theoretical physics, and perhaps also in other sciences. »
As a result of the crisis - the concept of "multiverse" and misunderstanding of "time". Problem of the foundation of mathematics over a hundred years. But this problem is "swept under the carpet", it is not even included in "The Millennium Problems" Clay Mathematics Institute. How can mathematics be able to "close the physics" (mathematician Ludwig Faddeev an interview «The equation of the evil spirit»)?
At the time Henri Bergson wrote a good book "Matter and Memory". But unfortunately, he not found a deep connection between these two fundamental categories. Physics was on the way phenomenological unification, but now need deep ontological unification of matter to "grab" the structure of SPACE and then "grab" «TIME» as multivalent phenomenon Ontological (structural, cosmic) Memory. In the physical picture of the world no deepest meanings of the "LifeWorld " (E.Husserl). Physicists and lyricists must have the unified picture of the world rich in meanings of the "LifeWorld".
You give a good key concept of "structure". Fundamental science needs "general framework structure" (David Gross, an interview "What is in the space-time"). We have a good idea of N.Bourbaki - "mother structures". Going to the "absolute generative structure " ("general framework structure") should start from "Architecture Mathematics" Bourbaki and Cartesian «Cogito ergo sum». As is well said in his article A.Zenkin in his article SCIENTIFIC COUNTER-REVOLUTION IN MATHEMATICS ::
«The truth should be drawn with the help of the cognitive computer visualization technology and should be presented to" an unlimited circle "of spectators in the form of color-musical cognitive images of its immanent essence.» But in order to "draw" the truth, it is necessary to understand more deeply the Cartesian "Cogito ergo sum".
"Science formulas" is not an assistant, need "Science forms" and " The General Theory of structures."
I hope that the category of "Memory" will be the central category of the scientific picture of the world and then to manage the future of Humanity will be easier. The New Era and a New Generation demanded action. We need a new "Big Common Cause" to save Peace, Nature and Humanity. Time has come and we start the path.
I agree: «The future is the past». High score. I look at your blog and remember the wonderful words Henry David Thoreau:
"It is by a mathematical point only that we are wise,
as the sailor or the fugitive slave keeps the polestar in his eye;
but that is sufficient guidance for all our life.
We may not arrive at our port within a calculable period,
but we would preserve the true course."
I invite you to comment on and appreciate my ideas.
High regard,
Vladimir