"Correlations without correlata" is a phrase by David Mermin that captures some of the sense that some people get out of Quantum mechanics. (https://arxiv.org/pdf/quant-ph/9801057.pdf%3E and then goes on to http://www.nature.com/news/physics-qbism-puts-the-scientist-back-into-science-1.14912) This expression resonates in me when thinking about the modes of existence that the book Inquiry into the Modes of Existence presents. I would try to think of some definite entities, delineated, described, projected in some space of features, flowing along these different lines that [REP] or [REL] or [FIC] present. But then it was like a flow that leaves you with an after-effect. Something passed but one cannot really say what it was. Or perhaps one mode needs to cooperate with another (or others) so that some account of what went on to be felt (felt by whom? By a community of conversants I guess, a group of people communicating with one another: so the passage of the beings of each mode has similarity with the passage of signs among discussants -these too disappear when one tries to focus straight on them)
This analogy between our effort to come into terms with what everyday life presents to us and what we see ingrained in the way non-humans interact, is not something new. The book of Nature may be writen in mathematics but what are mathematics and what is their relation with our broader experience of life? Mathematics do not have to be the handmaiden of bifurcation. Even is basic Physics, in Newton's laws, when going beyond formalism, one can find all kinds of resonances: the third law talking to us about the need of others in order to move ourselves, the second law telling us about the need for gradual movement, the distance between will and action. Some time people find in them structure supporting them to express quite intimate experiences like the following:
For Mr. Grimes Who Tried To Teach
Me Physics After My Father Died (John Hodegen)
He spoke of ellipses,
of things coming round again.
He spoke of resistance,
of the forces that act upon us.
He spoke of gravity,
of the earth that draws us to itself.
He said the mass of the earth,
the changes of state.
He said that a body at rest
would remain at rest.
He said that a boy
standing at the end of a moving train
could toss the red ball of his life
up into the heavy air
and catch it again.
Is this a random coincidence?
Inquiry into the modes of Existence, makes me think of structure. Chapter upon chapter of the book, one has the sense of the effort so that the same structure gets incarnated in different aspects of modern experience. Still the book speaks about more than that, it tries to accompany the real life of the moderns, to use some kind of maieutics so that moderns are lead to a new understanding of what they care about, what orients their lives. But it also has a common structural element which is evident also in the pivot table at the end of the book.
This relation between structure and openness (the modes of existence are open, they may be more or different) brings in my mind the practical, working element that I see in Lawvere (as presented in Andrei Rodin's book) and in presentations like this one:
(When he speaks about halping mathematicians and scientists, one does not have to see this under the light of the bifurcation that Whitehead spoke about)
I really wonder what would mathematicians make of this common structural element that exist in the AIME approach. Still I understand that both Mathematics and life (the life whose lingusitics AIME tries to tease out) go beyond structure.
It seems to me that people who think on their foundations, reveal a structural side that goes very deep in delineating "comming to a mutual understanding", or "agreeing". There is so much beautiful work (but I am like a blind person, just sensing shades of it due to my lack of mathematical training) about the basis of our thinking like Homotopy Type Theory (HoTT)(https://pdfs.semanticscholar.org/ed39/68860c64f00a0229e9f1c247327acce46f89.pdf) and the approach of Univalent Foundations (as in this article that makes an effort to bring it closer to the understanding of simpler people http://philsci-archive.pitt.edu/12824/1/A.Meaning.Explanation.for.HoTT.pdf). When I read about the geometrical interpretation of HoTT in Tsementzis work , I wonder on the one hand about the connections between this geometrical account and the geometrical account of the moderns' experience in the Inquiry book. On the other hand I wander about the understanding that the AIME approach brings to the self understanding of the mathematician (who is not just a mathematician but something much more complex) and of the interplay between his/her mathematical experience and their broader experience.
But then Mathematics is a performative art. Mathematics itself, or more general life, is a dance. It goes on in real time, dealing with past, present and future. The hybris, according to my opinon, is wanting to project this dance into structure: to make it spit out its reality. This is to me is the essence of bifurcation, and it is too much. (Perhaps another way to say it would be that it is an effort to erase history from being an irreducible source of wisdom). And it seems to me that both AIME and approaches in the foundations of mathematics that move away from formalism, are moving away from this hybris. (But, moving away from it is not just an issue of ideas: the practical consequence is very difficult for all of us. It is one thing to see it in a movie https://www.youtube.com/watch?v=Z8eKxVCFoUk. It is another thing to leave the realization hit you in real life https://www.youtube.com/watch?v=dbfvTzIWoIQ, unprotected by the Utopean cocoon that Tim Howls talks about https://logisticsofreligionblog.wordpress.com/2017/03/13/latour-and-the-non-space-and-non-time-of-modernity-part-1-of-3/#comments)
Maybe one day we will see a summer school devoted on the communication between AIME and HoTT/UF
This analogy between our effort to come into terms with what everyday life presents to us and what we see ingrained in the way non-humans interact, is not something new. The book of Nature may be writen in mathematics but what are mathematics and what is their relation with our broader experience of life? Mathematics do not have to be the handmaiden of bifurcation. Even is basic Physics, in Newton's laws, when going beyond formalism, one can find all kinds of resonances: the third law talking to us about the need of others in order to move ourselves, the second law telling us about the need for gradual movement, the distance between will and action. Some time people find in them structure supporting them to express quite intimate experiences like the following:
For Mr. Grimes Who Tried To Teach
Me Physics After My Father Died (John Hodegen)
He spoke of ellipses,
of things coming round again.
He spoke of resistance,
of the forces that act upon us.
He spoke of gravity,
of the earth that draws us to itself.
He said the mass of the earth,
the changes of state.
He said that a body at rest
would remain at rest.
He said that a boy
standing at the end of a moving train
could toss the red ball of his life
up into the heavy air
and catch it again.
Inquiry into the modes of Existence, makes me think of structure. Chapter upon chapter of the book, one has the sense of the effort so that the same structure gets incarnated in different aspects of modern experience. Still the book speaks about more than that, it tries to accompany the real life of the moderns, to use some kind of maieutics so that moderns are lead to a new understanding of what they care about, what orients their lives. But it also has a common structural element which is evident also in the pivot table at the end of the book.
This relation between structure and openness (the modes of existence are open, they may be more or different) brings in my mind the practical, working element that I see in Lawvere (as presented in Andrei Rodin's book) and in presentations like this one:
(When he speaks about halping mathematicians and scientists, one does not have to see this under the light of the bifurcation that Whitehead spoke about)
I really wonder what would mathematicians make of this common structural element that exist in the AIME approach. Still I understand that both Mathematics and life (the life whose lingusitics AIME tries to tease out) go beyond structure.
It seems to me that people who think on their foundations, reveal a structural side that goes very deep in delineating "comming to a mutual understanding", or "agreeing". There is so much beautiful work (but I am like a blind person, just sensing shades of it due to my lack of mathematical training) about the basis of our thinking like Homotopy Type Theory (HoTT)(https://pdfs.semanticscholar.org/ed39/68860c64f00a0229e9f1c247327acce46f89.pdf) and the approach of Univalent Foundations (as in this article that makes an effort to bring it closer to the understanding of simpler people http://philsci-archive.pitt.edu/12824/1/A.Meaning.Explanation.for.HoTT.pdf). When I read about the geometrical interpretation of HoTT in Tsementzis work , I wonder on the one hand about the connections between this geometrical account and the geometrical account of the moderns' experience in the Inquiry book. On the other hand I wander about the understanding that the AIME approach brings to the self understanding of the mathematician (who is not just a mathematician but something much more complex) and of the interplay between his/her mathematical experience and their broader experience.
But then Mathematics is a performative art. Mathematics itself, or more general life, is a dance. It goes on in real time, dealing with past, present and future. The hybris, according to my opinon, is wanting to project this dance into structure: to make it spit out its reality. This is to me is the essence of bifurcation, and it is too much. (Perhaps another way to say it would be that it is an effort to erase history from being an irreducible source of wisdom). And it seems to me that both AIME and approaches in the foundations of mathematics that move away from formalism, are moving away from this hybris. (But, moving away from it is not just an issue of ideas: the practical consequence is very difficult for all of us. It is one thing to see it in a movie https://www.youtube.com/watch?v=Z8eKxVCFoUk. It is another thing to leave the realization hit you in real life https://www.youtube.com/watch?v=dbfvTzIWoIQ, unprotected by the Utopean cocoon that Tim Howls talks about https://logisticsofreligionblog.wordpress.com/2017/03/13/latour-and-the-non-space-and-non-time-of-modernity-part-1-of-3/#comments)
Maybe one day we will see a summer school devoted on the communication between AIME and HoTT/UF
Δεν υπάρχουν σχόλια:
Δημοσίευση σχολίου