Addiction to Time as a Super-Structure

[AshvinP]

I see what you are saying, but for me that "language" already exists. When we see "time machines" in movies, or other ways of exploring past-present-future intermingling through artistic expression, I believe what is being expressed is the actual nature of Reality as we experience it every moment; every moment we are sleeping, dreaming, or awake. Of course, we have forgotten this Reality most starkly in the modern era. We have idolized concepts of space and time in the most unhealthy way. So, put another way, we only need a shift in perspective to remember how our future-Self is always attracting and being-attracted by our present-Self. All else, including language of mathematics, are tools to help us remember. And re-membering is, in its essence, the integration we have been discussing.

With that said, I think you're pointing to a real problem here -- we have a tendency to reify metaphorical or poetic language and miss the truth it's trying to express, missing the moon for the finger pointing at it and all that.

What I mean is concrete and reified formal language. Which is also "context-free" in the sense that it does not refer to expressions of natural language with alphabetic or other concrete signs. So yes, we can call building elements of a formal mathemetical language tools. An intuitionist language of mathematics is an "integration" of natural and formal language, but instead of term "integration", which in contemporary mathematical language is reserved for other purpose, better term in this context is coherence and coherence theory of truth.

From my empirical perspective, new and creative intuitions from the idealist ontology come mostly as vague and nebulous pre-linguistic "feels-ideas". There's long and hard process of nebulous intuitions solidiying into concrete written language, a relation of natural and formal language. I'm with Wittgenstein and don't consider the concept or practice of metalanguage helpful or valid, because that leads to abstract and incoherent and in case of metalanguage of axiomatic set theory, non-computational and non-demonstrable formalism, but make-believe of Empreror's new clothes.

Concrete formal computational languages, such that are running under the hood or our written natural language, are very concrete in the sense that they can compute and do things which become sentient interactions, like this discussion here.

For formalism, there's nothing outside an abstract and arbitrary language game. And as said, for intuitionist philosophy, the idealist ontology cannot be exhausted by by any mathematical language. But empirically, there is a movement of nebulous ideas seeking concrete self-expressions. Biological DNA is such a concrete language. Certain bacterial DNA can do knot-theory better than any human mathematician, for whom they remain mathematical mystery.

In summary, for formalism, mathematical language is abstract. For intuitionism, a coherent formal mathematical language in the trinity of intuitive ontology, natural language and formal language needs to be concrete, constructible and sensually demonstrable, to be coherent and "integral" part of a process.

I really can't imagine anything more concrete, and more distant from "vague and nebulous" idealism, than Steiner's "spiritual science". Not only in terms of its high resolution on all things idealist and spiritual, but also it's instantiation in fields of education, art, engineering, medicine, etc. around the world. From a Google search, I located this article and wonder how it relates to the mathematical intuitionist approach you are pursuing?

Waldorf Education does not teach math in isolation of other subjects. It is part of a holistic learning approach, which connects the child’s inner self (that Waldorf’s founder Rudolph Steiner refers to as “will”) and body through muscle-memory exercises. Waldorf Math is really a kinesthetic or whole body learning experience for the Class 1 child. Math is also closely related and taught with music, furthering the important connecting between a child’s body, and their understanding of numbers. As an adult I know that the most lasting memories for me are always those with more than one sense being used. I still remember vividly walking by a jam factory near my house when I was a child on the way to school, and counting the metal fence rungs while breathing in the aromas.

By moving to math in the early grades, even before reading and writing, the child develops a proficiency much like a musician memorizing their scales. It is a slow and unhurried approach that does not push the child to count or read too early, which has been found to taint a child’s passion to learn. Once a child is moving to math, he or she may begin to use beans or glass beads to better understand the relationships that additions and subtractions make with the whole. Imaginative math fairy tales are told, where the children get to participate by solving the same word problems the main characters do. This allows for a real “living” math to develop within the children. When children begin writing, they begin with roman numerals and integrate this lesson within their form drawing block. Roman numerals have much easier forms and more straight lines than our common curvy numerals.

Waldorf starts off the introduction to math by asking a seemingly simple question, “What is the largest number in the universe?”. My son (aged 5) came home from school and asked me the same question. I answered “Well, erhmmm, it’s infinity.”. He said “No, one is the biggest because I am one.”. Other responses discussed in class are “One is the biggest because without it there isn’t any 2, or 3, or even a million.” “One is the biggest because everything there is is in one Universe.” “One is the biggest because it can be any number it wants.” All sorts of philosophical and mathematical truths become evident through just this “one” discussion. This gets them thinking in a whole new way about numbers, and how they relate to us and the world. Eventually the children arrive at “I am one!”, they see how their bodies are shaped like the number one, they relate themselves to the vastness of the Universe, and realize at that point that they are co-creators.

[Soul_of_Shu]

"Waldorf starts off the introduction to math by asking a seemingly simple question, “What is the largest number in the universe?”. My son (aged 5) came home from school and asked me the same question. I answered “Well, erhmmm, it’s infinity.”. He said “No, one is the biggest because I am one.”. Other responses discussed in class are “One is the biggest because without it there isn’t any 2, or 3, or even a million.” “One is the biggest because everything there is is in one Universe.” “One is the biggest because it can be any number it wants.” All sorts of philosophical and mathematical truths become evident through just this “one” discussion. This gets them thinking in a whole new way about numbers, and how they relate to us and the world. Eventually the children arrive at “I am one!”, they see how their bodies are shaped like the number one, they relate themselves to the vastness of the Universe, and realize at that point that they are co-creators."

Or ... one plus one equals greater oneness, and so on, and so on, ad infinitum.

[SanteriSatama]

I really can't imagine anything more concrete, and more distant from "vague and nebulous" idealism, than Steiner's "spiritual science". Not only in terms of its high resolution on all things idealist and spiritual, but also it's instantiation in fields of education, art, engineering, medicine, etc. around the world. From a Google search, I located this article and wonder how it relates to the mathematical intuitionist approach you are pursuing?

By "vague and nebulous" I don't mean anything else but the phenomenal experience of intuiting new math ideas. The situation is very comparable with psychadelic experiences of the "Snake" of infinitely complex geometries etc. ineffable.

Ineffable does not mean here absolute but a relative state, more like deep humility with a sense of challenge, as very often there is deep motivation to try to express the ineffable by means of poetry, music, painting, philosophical writing, etc. art. Including the art and poetry of new mathematical languages.

[SanteriSatama]

"Waldorf starts off the introduction to math by asking a seemingly simple question, “What is the largest number in the universe?”. My son (aged 5) came home from school and asked me the same question. I answered “Well, erhmmm, it’s infinity.”. He said “No, one is the biggest because I am one.”. Other responses discussed in class are “One is the biggest because without it there isn’t any 2, or 3, or even a million.” “One is the biggest because everything there is is in one Universe.” “One is the biggest because it can be any number it wants.” All sorts of philosophical and mathematical truths become evident through just this “one” discussion. This gets them thinking in a whole new way about numbers, and how they relate to us and the world. Eventually the children arrive at “I am one!”, they see how their bodies are shaped like the number one, they relate themselves to the vastness of the Universe, and realize at that point that they are co-creators."

Or ... one plus one equals greater oneness, and so on, and so on, ad infinitum.

"One is the biggest" is genuine mathematical thinking, but not the last word of process philosophical intuitionism.

Note that the semantics of "biggest one" is the holistic perspective of division/partition, not the atomistic-reductionistic perspective of addition. It's becoming gradually more clear to me, that there's deep and very beautiful supersymmetry between addition and division-partition.

For example, if we start from CPT symmetry of quantum physics, where T stands for (revercimal/palindromic) time, postulating holism (a whole is more than sum of parts) and reductionism (a whole is a sum of parts) as an either-or question, that becomes very futile and naive metaphysics. Of course holomovement of dynamic holography involves both directitions, top-to-bottom, bottom-up as well as p2p relations. Integration is not in exclusive contradiction with disintegration-partition. There's only creative contradiction.

Wildbergers novel construction of integers with a trinity of mark, antimark and identity element of no-thing remains in the additive perspective, but as such this idea has been very inspiring also towards the division-partition of "biggest one". Instead of the classical metaphor 'one', my starting area has been process philosophical idea-form of open interval 'both increases and decreases', <>. Partitioning-dividing <> with concatenating mediants, ie. more internal resolution and form, without becoming as isolated and separated as prime numbers, but discrete interpretation of coprimes of rational numbers in their reduced form, further inter-related by their Stern-Brocot type structures. Sorry for the dense language, I can try to open it up if you dare to ask.

What I was trying to come to is that I had just a major inspiration, when trying to think what could funtion as the algebraic identity element of division-partition in the sense I'm speaking (from continuum to parts and discrete relations). It suddenly hit me: what about Golden Ratio, phi???!!! Which is the basic idea-form of division by itself, with classical algebraic presentations e.g. in the form of continuous fraction of one.

For reference:

[DandelionSoul]

To be honest... while I feel like I can follow the work of Kastrup (or others with similar perspectives like Freya Mathews or Philip Goff or Miri Albahari) pretty well, the discussion on intuitionism and formalism and the nature of language itself falls beyond the scope of my education so far, and I sorta feel like I'd need to expand my reading list somewhat to grasp what you're trying to say. Is there a place I can start with that? I hope that doesn't come across as dismissive, just that I've read that comment a few times in a row, slowly, and still can't get my head around what you're saying, and I assume the shortcoming here is on my end.

[DandelionSoul]

Oh I see you shared videos, too. Thanks for that! I'll try to watch those after work.

[AshvinP]

To be honest... while I feel like I can follow the work of Kastrup (or others with similar perspectives like Freya Mathews or Philip Goff or Miri Albahari) pretty well, the discussion on intuitionism and formalism and the nature of language itself falls beyond the scope of my education so far, and I sorta feel like I'd need to expand my reading list somewhat to grasp what you're trying to say. Is there a place I can start with that? I hope that doesn't come across as dismissive, just that I've read that comment a few times in a row, slowly, and still can't get my head around what you're saying, and I assume the shortcoming here is on my end.

Don't worry, I am as mathematically inept as you are or more. SS posts provide a great learning challenege!

[AshvinP]

I really can't imagine anything more concrete, and more distant from "vague and nebulous" idealism, than Steiner's "spiritual science". Not only in terms of its high resolution on all things idealist and spiritual, but also it's instantiation in fields of education, art, engineering, medicine, etc. around the world. From a Google search, I located this article and wonder how it relates to the mathematical intuitionist approach you are pursuing?

By "vague and nebulous" I don't mean anything else but the phenomenal experience of intuiting new math ideas. The situation is very comparable with psychadelic experiences of the "Snake" of infinitely complex geometries etc. ineffable.

Ineffable does not mean here absolute but a relative state, more like deep humility with a sense of challenge, as very often there is deep motivation to try to express the ineffable by means of poetry, music, painting, philosophical writing, etc. art. Including the art and poetry of new mathematical languages.

Ok well maybe I took your post in the opposite way as intended then. One of by biggest concerns lately has been how we who have gone beyond common reductionist philosophy of dualism often get stuck at low resolution. Of course the mystic will say "there is nothing low resolution about directly experiencing the ineffable One!", but by LR I mean lack of detail. I believe that detail is necessary to fully internalize what we mean when speaking of Unity, Oneness, Consciousness, Etc. So I agree art, math, etc. is great tool for challenging ourselves to bridge that gap and we can never assume our journey has ended.

[SanteriSatama]

To be honest... while I feel like I can follow the work of Kastrup (or others with similar perspectives like Freya Mathews or Philip Goff or Miri Albahari) pretty well, the discussion on intuitionism and formalism and the nature of language itself falls beyond the scope of my education so far, and I sorta feel like I'd need to expand my reading list somewhat to grasp what you're trying to say. Is there a place I can start with that? I hope that doesn't come across as dismissive, just that I've read that comment a few times in a row, slowly, and still can't get my head around what you're saying, and I assume the shortcoming here is on my end.

That's a good question and you're not the first to ask that. But sorry, no, there's no simple and quick introduction to what I'm speaking about, except perhaps most generally these about the foundational crisis of mathematics:

https://en.wikipedia.org/wiki/Brouwer%E ... ontroversy
https://personal.us.es/josef/pcmCrisis.pdf

More genarally, Wittgenstein's comment's on philosophy of mathematics were a turning point in my dance with mathematics.

Norman Wildberger's videoss, especially the foundations series, has been major influence and inspiration, on which my own approach has been building on from a complementary perspective. Which AFAIK is quite novel, and very much WIP and ongoing discussion. A main reason why I - a non-professional - try to talk math with other non-professionals - is to keep on learning how to speak math in more comprehensible and accessible way. But when we don't approach math simply as rule-following, following some set of rules by some supposed authority somewhere, but as creative and participatory process, the first task is to try to liberate from the expectations of rule-following. Foundational thinking is a free game, "rule following" from a foundational approach is not about "rules" as such, but about the ethics and esthetics of mathematical rigour, logical honesty and not least, communicability.

In a "rebel base" of more or less dissident math enthousiasts we've had also some discussions about relation of philosophy and foundations of mathematics and the general public. People are generally naive about math, not because they are stupid, but because they are not motivated to attend to mathematics beyond simple practicalities and/or indoctrination into the formalist-materialist academic dogma. To dig deeper in the foundational issues, generally you need loads of cold rage for the motivation, and loads of idle time to be practically able to do that.

Why so little motivation? The jargons of set theory mathematics, as well as financial capitalism etc etc are really difficult and confusing to get through, and that's by design. They are obnoxious and uninviting for the same function that medieval Monk Latin served.

I consider my own approach fanatically simple, and if we could genuinely start from a clean slate tabula rasa, perhaps it could appear so. But of course that's not the situation, there's the existing and established jargons to communicate with, as well as expectations created by the standard conditioning to tackle. And of course genuinely deep philosohical etc. questions to try to make sense of in a coherent and communicable way.

[SanteriSatama]

This is very good introduction to the difference between counting and measuring, and Greek way of thinking of measures as continua without counting units:



My approach is about innovating a new kind of bridge between the divide described in the presentation above.