Bernado's Mathematical Universe

[AshvinP]

I am talking of idealist monism - all is ideating activity (which also shows it is all dynamic process in essence, not static substance). That activity can be considered a Tri-Unity of Willing-Feeling-Thinking activities, but, in essence, we are actually speaking of the activity of living beings, who are not other than us in essence. What we call "meaning" in conventional language of modern age, like the meaning we experience when perceiving a color or a tree or a bird, is the shadowy reflection of that activity. It is the qualia of our experience. That phenomenal meaning, however, is not pointing us to something other than meaning in the noumenal realm - it is pointing us to much deeper and enriched meaning of those essential activities. Something more akin to the meaning we experience when we are with a loved one, but even that is a shadowy reflection of the noumenal (spiritual) meaning it is pointing to.

Why couldn't everything you say is going on be the very nature of a substance? Ie. Positing a fundamental substance doesn't necessitate static entities. Process could still be what a substance is doing, while also leaving space for a deeper understanding of the mechanisms of process

I don’t understand what you mean by "fundamental substance"? Let's think of our own experience of living activity - is there a fundamental substance that sums up who we are and what we do? Certainly we cannot resort to any material descriptions for that. So then we say we are evolving psychic processes and meta-processes centered around an Ego-Self. But is that really a satisfactory characterization of who we are and what we do (which, in my view, are basically two ways of pointing to the same Reality)? When using conventional language in these forums, the best way I find to characterize our essence is to say that we are the meaning of all those principles and archetypal processes. What we experience as "meaning" when we contemplate those processes is who we are and what we do, albeit only as shadowy reflections of the true meaning when contemplating with normal cognition. I would rather not call that essential meaning a "substance" for a variety of reasons, but what matters is not the label, only our understanding of what it is pointing to. The meaning of the meaning. Monism is essential label IMO bc only it captures the essential continuity of meaning. There is no activity we engage in, no experience we partake in, that is essentially disconnected from other activities and experiences. That disconnect crops up a lot in Western philosophy including idealism, so it's important to be clear on that.

A concrete example will help here. Take this quote from Hegel:

The bud disappears when the blossom breaks through, and we might say that the former is refuted by the latter; in the same way when the fruit comes, the blossom may be explained to be a false form of the plant’s existence, for the fruit appears as its true nature in place of the blossom. The ceaseless activity of their own inherent nature makes these stages moments of an organic unity, where they not merely do not contradict one another, but where one is as necessary as the other; and constitutes thereby the life of the whole.

- Georg Wilhelm Friedrich Hegel, Phenomenology of Spirit (1807)

To sum up the essential meaning at very low resolution, living essence is "that which ceaselessly metamorphoses to bring forth all potential Perfection and Wholeness - Goodness, Beauty, and Truth - from fragmented appearances". In my view, all is alive and therefore has living essence. To dig deeper into our own role in the living essence, which is also that of the "Spirit", consider this quote from Steiner:

It is quite arbitrary to regard the sum of what we experience of a thing through bare perception as a totality, as the whole thing, while that which reveals itself through thoughtful contemplation is regarded as a mere accretion which has nothing to do with the thing itself. If I am given a rosebud today, the picture that offers itself to my perception is complete only for the moment. If I put the bud into water, I shall tomorrow get a very different picture of my object. If I watch the rosebud without interruption, I shall see today's state change continuously into tomorrow's through an infinite number of intermediate stages.

The picture which presents itself to me at any one moment is only a chance cross-section of an object which is in a continual process of development.

- Rudolf Steiner, The Philosophy of Freedom (1894)

The meaning here is, "the human spiritual activity of Thinking weaves back together the fragmented experiences of form-progressions into an organic unity which satisfies our need for harmonious knowledge". The other key thing to understand is that, as long as we continue searching for essential meaning within the realm of abstract conceptual thinking, we will remain unsatisfied. That conceptual space simply cannot enrich the meaning of the above to its true qualitative essence. We do not need to actually go beyond the abstract concepts to recognize the truth of that assertion - and recognition of its truth is very helpful when considering all of these various philosophical frameworks people propose. You will find that materialists, dualists, idealist philosophers of Will, certain mystical frameworks, etc. have that one thing in common - they simply fail to notice or actively deny this distinction between abstract thinking and higher cognition. That is because a) they are thinking abstractly and have never considered such a higher cognitive perspective could exist and/or b) they sense semi-consciously that all of their objections to idealist philosophy of Thinking (which is always intimately tied to Western spirituality) will evaporate once that distinction is admitted.

[Squidgers]

Why couldn't everything you say is going on be the very nature of a substance? Ie. Positing a fundamental substance doesn't necessitate static entities. Process could still be what a substance is doing, while also leaving space for a deeper understanding of the mechanisms of process

I don’t understand what you mean by "fundamental substance"? Let's think of our own experience of living activity - is there a fundamental substance that sums up who we are and what we do? Certainly we cannot resort to any material descriptions for that. So then we say we are evolving psychic processes and meta-processes centered around an Ego-Self. But is that really a satisfactory characterization of who we are and what we do (which, in my view, are basically two ways of pointing to the same Reality)? When using conventional language in these forums, the best way I find to characterize our essence is to say that we are the meaning of all those principles and archetypal processes. What we experience as "meaning" when we contemplate those processes is who we are and what we do, albeit only as shadowy reflections of the true meaning when contemplating with normal cognition. I would rather not call that essential meaning a "substance" for a variety of reasons, but what matters is not the label, only our understanding of what it is pointing to. The meaning of the meaning. Monism is essential label IMO bc only it captures the essential continuity of meaning. There is no activity we engage in, no experience we partake in, that is essentially disconnected from other activities and experiences. That disconnect crops up a lot in Western philosophy including idealism, so it's important to be clear on that.

I am on the same page with you here. Although I would say the only difference between a dual-aspect monism and a monism is that the former tries to explicitly acknowledge and understand the appearance of an "outside world", even if fundamentally it is an "illusion" and happening within or as a part of a single substance/thing/existence.

What I am not getting from your description of the fundamental "stuff" (which is essentially coming back to the OP of this forum post) is how a "material universe" emerges and evolves out of what you have described as "meaning", and from this how to model the interface between "meaning" and what we call the "material world"

[Squidgers]

The meaning here is, "the human spiritual activity of Thinking weaves back together the fragmented experiences of form-progressions into an organic unity which satisfies our need for harmonious knowledge". The other key thing to understand is that, as long as we continue searching for essential meaning within the realm of abstract conceptual thinking, we will remain unsatisfied. That conceptual space simply cannot enrich the meaning of the above to its true qualitative essence. We do not need to actually go beyond the abstract concepts to recognize the truth of that assertion - and recognition of its truth is very helpful when considering all of these various philosophical frameworks people propose. You will find that materialists, dualists, idealist philosophers of Will, certain mystical frameworks, etc. have that one thing in common - they simply fail to notice or actively deny this distinction between abstract thinking and higher cognition. That is because a) they are thinking abstractly and have never considered such a higher cognitive perspective could exist and/or b) they sense semi-consciously that all of their objections to idealist philosophy of Thinking (which is always intimately tied to Western spirituality) will evaporate once that distinction is admitted.

I am interested to hear more about the distinctions you want to make here.

One way of modelling this I have seen is via Jung and his thinking vs intuition.

I agree that a purely abstract model is missing a big piece of the puzzle. But I also think an accurate map is a kind of psychoactive for our intuitions to navigate with.

[AshvinP]

Why couldn't everything you say is going on be the very nature of a substance? Ie. Positing a fundamental substance doesn't necessitate static entities. Process could still be what a substance is doing, while also leaving space for a deeper understanding of the mechanisms of process

I don’t understand what you mean by "fundamental substance"? Let's think of our own experience of living activity - is there a fundamental substance that sums up who we are and what we do? Certainly we cannot resort to any material descriptions for that. So then we say we are evolving psychic processes and meta-processes centered around an Ego-Self. But is that really a satisfactory characterization of who we are and what we do (which, in my view, are basically two ways of pointing to the same Reality)? When using conventional language in these forums, the best way I find to characterize our essence is to say that we are the meaning of all those principles and archetypal processes. What we experience as "meaning" when we contemplate those processes is who we are and what we do, albeit only as shadowy reflections of the true meaning when contemplating with normal cognition. I would rather not call that essential meaning a "substance" for a variety of reasons, but what matters is not the label, only our understanding of what it is pointing to. The meaning of the meaning. Monism is essential label IMO bc only it captures the essential continuity of meaning. There is no activity we engage in, no experience we partake in, that is essentially disconnected from other activities and experiences. That disconnect crops up a lot in Western philosophy including idealism, so it's important to be clear on that.

I am on the same page with you here. Although I would say the only difference between a dual-aspect monism and a monism is that the former tries to explicitly acknowledge and understand the appearance of an "outside world", even if fundamentally it is an "illusion" and happening within or as a part of a single substance/thing/existence.

What I am not getting from your description of the fundamental "stuff" (which is essentially coming back to the OP of this forum post) is how a "material universe" emerges and evolves out of what you have described as "meaning", and from this how to model the interface between "meaning" and what we call the "material world"

That is the biggest difference between the mystical idealism of Schopenhauer and Western idealism in the spirit of Steiner - the former has no interest in the physical world and its natural forms, because it considers all of that hopelessly disconnected from the noumenal realm. Steiner, on the other hand, always encourages the utmost curiosity and investigation of the physical world so that its spiritual origins may be revealed in great detail. That difference stems from their respective treatments of Thinking activity - Steiner does not put any arbitrary limits on that activity's ability to penetrate into the spiritual through the physical. We shouldn't get too caught up on the label "Thinking", though, as past experience on this forum suggests that is a major stumbling block for people. For some reason (I have my speculations why), calling it "Thinking" makes people automatically associate with abstract intellect and some sort of egoism. But the point is that each individual has the capacity to empirically and systematically investigate the noumenal relations through 'higher cognition', or whatever we want to call it, as long as we understand its essential function.

Under that view, there is only one essential realm - the spiritual. The physical is the outer expression of the spiritual, certainly not an "illusion", what Emerson refers to as "the terminus or the circumference of the invisible world". There are no structural reasons why we cannot work from that circumference of the spiritual back towards its center, only ones that are self-imposed. As to the question of how this circumference with forms came about, at the most general level, we can say its the manifestation of unified Spirit differentiating itself into many perspectives and the relations between those perspectives 'interfering' and bringing forth what we call the physical world. The meaning of the physical world is contiguous with that of the spiritual - they are not two separate kinds of meanings - but I will say there is a danger if we assume exoteric scientific investigation of the appearances is sufficient to uncover essential meaning. That must be accompanied by inner psychic investigation so that the outer and inner truths can be reunited in our Thinking - what Jung refers to as the "union of opposites".

I am interested to hear more about the distinctions you want to make here.

One way of modelling this I have seen is via Jung and his thinking vs intuition.

I agree that a purely abstract model is missing a big piece of the puzzle. But I also think an accurate map is a kind of psychoactive for our intuitions to navigate with.

Exactly. I write about this some in essay on Metamorphoses of the Spirit - Transfiguring our Thinking.

Nevertheless, what we learn here in abstract concepts prepares our soil for the seeds to be planted within us later, so that our plants may grow and flower in full health. In that sense, it is an invaluable exercise. It is like venturing into unknown territory with a map prepared for us - the map is a small, two-dimensional rendering with little icons and shapes which look nothing like the three-dimensional territory being mapped. Yet, who among us would prefer to leave the map behind when entering? If we carry the map with us, then we will find it a lot easier to navigate the territory and understand what exactly we are encountering along the way.

Jung's approach is a very fascinating topic in and of itself. We now know that he had visionary experiences of the spiritual realm early on and that actually informed many of the questions he decided to ask in his scientific inquiries. Yet his "#1 personality" was still heavily invested in maintaining academic credibility and therefore his writings are mostly speaking from abstract intellect, although his much later writings certainly delve into imaginative thought when discussing astrology, alchemy, etc. Ultimately, its difficult to recommend any such models when first exploring this topic, since I now know Steiner discusses it without abstract models and in such amazing detail throughout his books and lectures. Most of those are available here. That being said, my essays generally explore these intuitions with reference to many different thinkers, mostly to show how great minds who had never met or even come across each other's work could be led by the same intuitions to remarkably similar conclusions about the structure of Reality. And, in my experience so far, all of those thinkers find great essential value in Christian spirituality. An example of that is in Incarnating the Christ installment.

I would further argue that Hegel's thought marked the pinnacle of Western idealist philosophy up until the end of the 19th century. Right around the end of the 19th century and beginning of the 20th, however, a plethora of thinkers appeared on the scene and engaged the metamorphic phenomenon in amazing detail. I cannot include them all in this essay, so below are a few who still stand out the most for me in my personal quest for knowledge and have provided me with the clearest and most comprehensive evidence and reasoning I have come across on this topic.

Before we embark on this metamorphic tour, I want to draw attention to two common threads you will see in the references. First is the thread of phenomenology - each person below started their analysis with the experiences and appearances which presented themselves in the world, rather than abstract intellectual concepts about the world which then serve as a basis for rational deductions. Whether dealing with patients, church-goers or academics, they always remained grounded to experience in their philosophical thought. Second is the thread of Christ. Not only did all of the below thinkers consider themselves as philosophizing from within the Christian perspective, they explicitly incorporated the phenomenon of the 'Christ events' into their philosophy and science.

(note: I failed to consider Coleridge as within "Western idealist philosophy" when writing that, as he was writing in the early 19th century, but I do quote him in the essay, and I would put him right up at the pinnacle as well)

I was thinking about writing an essay about the relationship of physical to spiritual experience-knowledge, as it really deserves a lot deeper treatment. But I am happy to discuss that with you here and see where we can get, if you want.

[Squidgers]

That is the biggest difference between the mystical idealism of Schopenhauer and Western idealism in the spirit of Steiner - the former has no interest in the physical world and its natural forms, because it considers all of that hopelessly disconnected from the noumenal realm. Steiner, on the other hand, always encourages the utmost curiosity and investigation of the physical world so that its spiritual origins may be revealed in great detail. That difference stems from their respective treatments of Thinking activity - Steiner does not put any arbitrary limits on that activity's ability to penetrate into the spiritual through the physical. We shouldn't get too caught up on the label "Thinking", though, as past experience on this forum suggests that is a major stumbling block for people. For some reason (I have my speculations why), calling it "Thinking" makes people automatically associate with abstract intellect and some sort of egoism. But the point is that each individual has the capacity to empirically and systematically investigate the noumenal relations through 'higher cognition', or whatever we want to call it, as long as we understand its essential function.


Under that view, there is only one essential realm - the spiritual. The physical is the outer expression of the spiritual, certainly not an "illusion", what Emerson refers to as "the terminus or the circumference of the invisible world". There are no structural reasons why we cannot work from that circumference of the spiritual back towards its center, only ones that are self-imposed. As to the question of how this circumference with forms came about, at the most general level, we can say its the manifestation of unified Spirit differentiating itself into many perspectives and the relations between those perspectives 'interfering' and bringing forth what we call the physical world. The meaning of the physical world is contiguous with that of the spiritual - they are not two separate kinds of meanings - but I will say there is a danger if we assume exoteric scientific investigation of the appearances is sufficient to uncover essential meaning. That must be accompanied by inner psychic investigation so that the outer and inner truths can be reunited in our Thinking - what Jung refers to as the "union of opposites".

While I agree with what you have said in principle, I find the language obscuring and vague. This is why I lean towards more mathematical and scientific metaphors and descriptions, and expect more rigor and logic in explanations (which no doubt you provide in your essays)

I get that some people can just accept the notion of an underlying spirit which differentiates itself (which is the same as BKs description for the mechanism of cosmic consciousness disassociating) - but I think the same thing can be said in more specific and nuanced ways.

Why not marry spiritual, experiential and scientific knowledge in the metaphysics?

[AshvinP]

That is the biggest difference between the mystical idealism of Schopenhauer and Western idealism in the spirit of Steiner - the former has no interest in the physical world and its natural forms, because it considers all of that hopelessly disconnected from the noumenal realm. Steiner, on the other hand, always encourages the utmost curiosity and investigation of the physical world so that its spiritual origins may be revealed in great detail. That difference stems from their respective treatments of Thinking activity - Steiner does not put any arbitrary limits on that activity's ability to penetrate into the spiritual through the physical. We shouldn't get too caught up on the label "Thinking", though, as past experience on this forum suggests that is a major stumbling block for people. For some reason (I have my speculations why), calling it "Thinking" makes people automatically associate with abstract intellect and some sort of egoism. But the point is that each individual has the capacity to empirically and systematically investigate the noumenal relations through 'higher cognition', or whatever we want to call it, as long as we understand its essential function.


Under that view, there is only one essential realm - the spiritual. The physical is the outer expression of the spiritual, certainly not an "illusion", what Emerson refers to as "the terminus or the circumference of the invisible world". There are no structural reasons why we cannot work from that circumference of the spiritual back towards its center, only ones that are self-imposed. As to the question of how this circumference with forms came about, at the most general level, we can say its the manifestation of unified Spirit differentiating itself into many perspectives and the relations between those perspectives 'interfering' and bringing forth what we call the physical world. The meaning of the physical world is contiguous with that of the spiritual - they are not two separate kinds of meanings - but I will say there is a danger if we assume exoteric scientific investigation of the appearances is sufficient to uncover essential meaning. That must be accompanied by inner psychic investigation so that the outer and inner truths can be reunited in our Thinking - what Jung refers to as the "union of opposites".

While I agree with what you have said in principle, I find the language obscuring and vague. This is why I lean towards more mathematical and scientific metaphors and descriptions, and expect more rigor and logic in explanations (which no doubt you provide in your essays)

I get that some people can just accept the notion of an underlying spirit which differentiates itself (which is the same as BKs description for the mechanism of cosmic consciousness disassociating) - but I think the same thing can be said in more specific and nuanced ways.

Why not marry spiritual, experiential and scientific knowledge in the metaphysics?

That is why I mention the bolded phrase - don't get too caught up on the labels. It's all about the underlying meaning of the labels. I hope you can see the relationship there - the philosophy I am endorsing says modern people get too caught up on the outer appearances of natural forms, like a tree, a rock, a river, the moon, etc., when they should be trying to discern the inner meaning of those forms. The same holds true for language and words - modern people get too caught up on the outer appearances of those as well. We need to penetrate into the meaning of the words as symbols, i.e. what they are pointing us towards. The best words are really the ones which convey the shared meaning with just enough detail to see how things start to fit together, but also general enough to encompass the principles at work. As with everything, it is all about balance.

That being said, I have no idea how strictly mathematical descriptions of these things could be considered less "obscure and vague" than "spirit" or what Emerson said about the physical world being the "terminus or circumference" of the invisible world. I think that is another inversion of the modern age that people do not consider carefully enough. It only holds true if we forget that what is important is the underlying meaning. Anyone who has roots in the Western world will automatically have a sense of the underlying meaning for "spirit", and people in general will automatically visualize the imagery of a sphere from "circumference", etc. That goes much closer to the meaning than, for ex., the strictly mathematical terms that Langan strings together when trying to describe the underlying Reality.

Finally, as you say, I am just briefly summarizing some key points here and go into more detail in the essays. Steiner's entire endeavor is about marrying spirituality and science, hence it is called "spiritual science". If you start reading some of his books and lectures, I guarantee you will initially have the opposite complaint - it will seem like he is making spirituality way too scientifically detailed. After awhile, though, and with effort, you will see how it all holds together with Reason and how the terms he uses are really the best ones to convey the underlying meaning. I am also posting below an excerpt from recent essay on poetry with quote from Emerson, which should help clarify this physical-spiritual relationship further.

Spiritual Aesthetics: The Rebirth of Poetry (Part II)

The transcendentalist American poet, Ralph Waldo Emerson, also discussed this 'mystery' of language and words with high resolution and clarity. He explained, "Nature is the vehicle of thought, and in a simple, double, and threefold degree."

1. Words are signs of natural facts.

2. Particular natural facts are symbols of particular spiritual facts.

3. Nature is the symbol of spirit.

1. Words are signs of natural facts. The use of natural history is to give us aid in supernatural history. The use of the outer creation is to give us language for the beings and changes of the inward creation. Every word which is used to express a moral or intellectual fact, if traced to its root, is found to be borrowed from some material appearance. Right originally means straight; wrong means twisted. Spirit primarily means wind; transgression, the crossing of a line; supercilious, the raising of the eye-brow. We say the heart to express emotion, the head to denote thought; and thought and emotion are, in their turn, words borrowed from sensible things, and now appropriated to spiritual nature. Most of the process by which this transformation is made, is hidden from us in the remote time when language was framed; but the same tendency may be daily observed in children. Children and [archaic men] use only nouns or names of things, which they continually convert into verbs, and apply to analogous mental acts.

2. But this origin of all words that convey a spiritual import—so conspicuous a fact in the history of language—is our least debt to nature. It is not words only that are emblematic; it is things which are emblematic. Every natural fact is a symbol of some spiritual fact. Every appearance in nature corresponds to some state of the mind, and that state of the mind can only be described by presenting that natural appearance as its picture. An enraged man is a lion, a cunning man is a fox, a firm man is a rock, a learned man is a torch. A lamb is innocence; a snake is subtle spite; flowers express to us the delicate affections. Light and darkness are our familiar expression for knowledge and ignorance; and heat for love. Visible distance behind and before us, is respectively our image of memory and hope.
...
Throw a stone into the stream, and the circles that propagate themselves are the beautiful type of all influence... And the blue sky in which the private earth is buried, the sky with its eternal calm, and full of everlasting orbs, is the type of Reason. That which, intellectually considered, we call Reason, considered in relation to nature, we call Spirit. Spirit is the Creator. Spirit hath life in itself. And man in all ages and countries, embodies it in his language, as the FATHER. It is easily seen that there is nothing lucky or capricious in these analogies, but that they are constant, and pervade nature.

3. What is true of proverbs, is true of all fables, parables, and allegories. This relation between the mind and matter is not fancied by some poet, but stands in the will of God, and so is free to be known by all men. It appears to men, or it does not appear. When in fortunate hours we ponder this miracle, the wise man doubts, if, at all other times, he is not blind and deaf; “Can these things be, And overcome us like a summer’s cloud, Without our special wonder?” for the universe becomes transparent, and the light of higher laws than its own, shines through it. It is the standing problem which has exercised the wonder and the study of every fine genius since the world began; from the era of the Egyptians and the Brahmins, to that of Pythagoras, of Plato, of Bacon, of Leibnitz, of Swedenborg. There sits the Sphinx at the road-side, and from age to age, as each prophet comes by, he tries his fortune at reading her riddle.

There seems to be a necessity in spirit to manifest itself in material forms; and day and night, river and storm, beast and bird, acid and alkali, preexist in necessary Ideas in the mind of God, and are what they are by virtue of preceding affections, in the world of spirit. A Fact is the end or last issue of spirit. The visible creation is the terminus or the circumference of the invisible world. A new interest surprises us, whilst, under the view now suggested, we contemplate the fearful extent and multitude of objects; since “every object rightly seen, unlocks a new faculty of the soul.” That which was unconscious truth, becomes, when interpreted and defined in an object, a part of the domain of knowledge—a new weapon in the magazine of power.

- Ralph Waldo Emerson, Nature (1836 - emphasis in original)

[SanteriSatama]

I get that some people can just accept the notion of an underlying spirit which differentiates itself (which is the same as BKs description for the mechanism of cosmic consciousness disassociating) - but I think the same thing can be said in more specific and nuanced ways.

Why not marry spiritual, experiential and scientific knowledge in the metaphysics?

I like the word "marry", with connotations of "biblical sense of knowing", cosmic love making, deep participation etc. I just learned that word-concept 'cosmos' goes back to Pythagoras, the deep experience of Beauty which is both sensual and rational, the "divine proportions" at the root of theology of mathematics.

Coherence theory of truth and mathematics as general study of relations can help to remarry mathematics with Cosmic participation. For Pythagoras and Neo-Platonists the Cosmic participation was expressed as mythological sense of numerology (see especially Iamblichus: The Theology of Arithmetic) as well as Sacred Geometry. Euclid's Elementa is teleological proof narrative to establish the Cosmic truth and beauty of the five Platonic Solids.

How to (re)marry mathematics, which has been so far mainly static system building, with continuous motion which is prerequisite with our ideal of ethical ans spiritual progress? Greek geometry in the form of drawing instructions with straight edge and compass was continuous motion, but current standard math built around analysis with real numbers has lost touch with cosmic participation, as point reductionism makes motion impossible and numerological sense of number evaporates in the gap of Dedekind cut. The post-modern math of formalism has become deeply nihilistic and alienated, which manifests in our lives mainly as the sadistic tyranny of administrative use of quantitative measuring that denies our humanity and empathy.

Most manifestly and self-evidently continuous motion as well as many our progressive questions of practical ethics occur in the massively parallel computation, which has reached the level of complexity that is not accessible to any single human mind. We don't have any decent foundational theory of pure mathematics available for sense making of the mathematical reality of our everyday lives, to be able to participate meaningfully and refind cosmic meaning and beauty of mathematics coherent with progressive spiritual and practical ethics.

This challenge of cosmic participation is the motivation of my foundational hobby.

[Eugene I]

How to (re)marry mathematics, which has been so far mainly static system building, with continuous motion which is prerequisite with our ideal of ethical ans spiritual progress? Greek geometry in the form of drawing instructions with straight edge and compass was continuous motion, but current standard math built around analysis with real numbers has lost touch with cosmic participation, as point reductionism makes motion impossible and numerological sense of number evaporates in the gap of Dedekind cut. The post-modern math of formalism has become deeply nihilistic and alienated, which manifests in our lives mainly as the sadistic tyranny of administrative use of quantitative measuring that denies our humanity and empathy.

Most manifestly and self-evidently continuous motion as well as many our progressive questions of practical ethics occur in the massively parallel computation, which has reached the level of complexity that is not accessible to any single human mind. We don't have any decent foundational theory of pure mathematics available for sense making of the mathematical reality of our everyday lives, to be able to participate meaningfully and refind cosmic meaning and beauty of mathematics coherent with progressive spiritual and practical ethics.

This challenge of cosmic participation is the motivation of my foundational hobby.

This manifesto sounds very beautiful. But the challenge that I see is how to drop the nonsensical real number theory, set theory and axiomatic formalism foundation and replace them with the computational foundation without losing the power of the analytical math and calculus. So far the analytical math and calculus have been solely rooted in the real number theory, which in turn has been rooted in the set theory that includes Kantor's cardinal numbers theory. Analytical math and calculus have tremendous explanatory and prediction power and are used widely everywhere is science and engineering. There is no way scientists/engineers will stop using them no matter what philosophical or ethical reasons you can throw against them. So the challenge for you and for the computational mathematicians is to develop the new foundation but still retain/re-formulate the analytical math and calculus. In other words, you need to replace the foundation but keep the building (and that is not an easy thing to do if you ask any home builder ).

[SanteriSatama]

This manifesto sounds very beautiful. But the challenge that I see is how to drop the nonsensical real number theory, set theory and axiomatic formalism foundation and replace them with the computational foundation without losing the power of the analytical math and calculus. So far the analytical math and calculus have been solely rooted in the real number theory, which in turn has been rooted in the set theory that includes Kantor's cardinal numbers theory. Analytical math and calculus have tremendous explanatory and prediction power and are used widely everywhere is science and engineering. There is no way scientists/engineers will stop using them no matter what philosophical or ethical reasons you can throw against them. So the challenge for you and for the computational mathematicians is to develop the new foundation but still retain/re-formulate the analytical math and calculus. In other words, you need to replace the foundation but keep the building (and that is not an easy thing to do if you ask any home builder ).

I don't belittle the challenge. Good challenges make life worth living.

This just came in, also according to these guys Fourier analysis is indeed a very central issue, as you pointed out. Algebraic calculus predates analysis and Wildberger has made some significiant new progress in that area, but field extensions get algebraically very complex, not at all easy job.


There's loads of math we'd like to retain in coherent foundation. It's not at all clear that Euclid's proof of five platonic solids is reproducible in the Cantor-Hilbert-Fermelo paradigm and analysis. Euclid's proof gives dynamic instructions on how to draw with straight edge and compass, and drawing is a contintuous motion. Actual drawing as well as actual computation becomes impossible if line etc. consists of infinite set(s) of points, if actual computation occurs in Minkowski space-time.

The challenge goes both ways, and we'd like to have a foundation that can include and make good sense of both platonic solids and Fourier etc. etc.

That's why I start from dynamic tetralemma and 'both more and less'. Open interval <> interpreted as a symbolic relation with Bergson-duration.

IIRC the idea of dynamic tetralemma came up when discussing static tetralemma with Scott, and the foundational combinations 'both more and less' <> and 'neither more nor less' >< of Relop formal language obviously deny the universality of both LNC and LEM.

Only quite recently I realized that <> and >< are highly analogical to Schönfinkel's S and K combinators.

[Eugene I]

Well, my approach is simple and pragmatic: I agree with the foundational inconsistency of the real numbers and cardinal numbers theories, but when I use analytical math and calculus, I take them simply as practical recipes, as "thinking algorithms". It's like in mechanical engineering: everyone knows that Newton laws are inconsistent and inaccurate on the micro and mega scales, but no one takes them literally as having any relevance to actual physical reality. Engineers simply used them as simplified modeling recipes/algorithms/math tools for solving engineering problems.