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Welcome to Math 4 Wisdom

an Investigatory Community for Absolute Truth

What is your relationship with truth?

Kirby Urner: I see truth as a defensive strategy to keep one's effectiveness in the world intact.

Where do find yourself in the landscape of truth?

John Harland: There's a tremendous asymmetry between truth and untruth, or truth and bullshit. Bullshit is a lot easier to arrive at then truth. Truth is a difficult path and it's fraught.

Do you wish for absolute truth?

Kirby: I often think that the quest for absolute truth is oftimes the height of folly.

Welcome! I am Andrius Kulikauskas, the host of Math 4 Wisdom, an investigatory community for absolute truth. This flows out of my lifelong quest to know everything and apply that knowledge usefully.

John: Your questions are way broader scope than mine!

Kirby: What's the relationship between truth and wisdom? Maybe they're not related at all.

Wisdom is knowledge of everything, and as such, is the content of absolute truth. Mathematics is the study of structure, and as such, is the form of absolute truth. Math 4 Wisdom relates the language of wisdom and the language of mathematics. What do wisdom and math reveal about absolute truth?

With this video, Welcome to Math 4 Wisdom, I am overviewing where we are seven months since my first video, Introduction to Math 4 Wisdom. Since then, I have uploaded 19 videos. We have about eight active participants. I invite you to join the Math 4 Wisdom discussion group, which is the hub of our activity. You will find a link at the description of this video and also at Math4Wisdom.com You can also find me tooting at the Mathstodon server and participating at Discord servers such as for Carl Jaimungal's Theories of Everything podcast and for the Summer of Math Exposition.

In 1993, I received my PhD in mathematics from the University of California at San Diego. I studied math with the hope that it would be useful for expressing a new science for the knowledge of everything. Over the years I have documented an abstract language of cognitive frameworks which makes sense to me but others do not comprehend. The way I am thinking is very unusual. What could I do to be understood?

Recently, I have recognized that these cognitive frameworks appear in advanced mathematical thinking, some of which I need to master. Such concepts include the Yoneda Lemma and adjunctions in category theory, Bott periodicity in algebraic topology, Möbius transformations in complex geometry and the four classical families in Lie theory. I believe that the essence of these concepts could be understood by, for example, a teacher of high school math, such as Kirby Urner, or a motivated person with a high school education, such as Bill Pahl.

Bill Pahl: I'm an amateur at math. Slowly I've been getting more of a grasp of the subjects being discussed.

I have mapped out the learning paths that I wish to explore in the coming year. My goal is not to learn math for its own sake but to show how advanced math runs up against the limits of imagination which are described by cognitive frameworks such as divisions of everything. I am trying to communicate, clarify, validate and apply such frameworks.

What I have learned from our interactions is that I myself seek absolute truth but personally we all have very different relationships with truth.

Jinan KB: Children are in truth, you know? Which means that existence itself is truth.

Andrius: In your life, how does truth work? What is your view practically, how you deal with the issue of truth in your life?

Bill Pahl: I would say there is a lot of relativity to it. Observer bias, whatever. Obviously, you're an absolute truth guy, and I don't have a very structured or defined category for that term. I would generally defer to things being relative to one another. So, if you've got ten opinions, they all have some value at some level. Maybe I'll be convinced of absolute truth by you and arrive at it. It has something to do with time and place for me. So, today is one thing. Someone's perspective from a previous era, from a different culture, it all has value.

I will talk about that as I introduce our current participants, starting with myself. Along the way I will discuss the videos I have uploaded and the ones I intend to create with your participation, your help and support.

For me, the most important videos are in the playlist called Wondrous Wisdom, where wondrous rhymes with my name Andrius. Wondrous wisdom is the name that I give to the language of cognitive frameworks which I also call simply the language of wisdom. Here is my story.

As a six-year-old child, I resolved to know everything and apply that knowledge usefully. But this is very dangerous. So I engaged God, "Give me the freedom to think whatever I need to think, maybe you exist and maybe you don't, maybe you are good and maybe you aren't, but regardless of what I learn, I will always believe in you." Then I proceeded to learn everything I could. In high school, I came to realize that in the quantum world, reality fades away, so that must not yield the knowledge of everything. It must be there where we are most able to find it, but nobody wants to look, which is the study of wisdom.

Michael Schreiber: It's really noticeable that you have a positive attitude about it. It is one of the things that will help people to go over the shaky bridges. Shaky not necessarily because of their construction because if you go over a bridge made out of glass, you look down, you feel that little bit anxious.

Andrius: The bridges may be shaky, as you said, but the real issue is the altitude. I am walking on bridges that are very high. I am doing things that could anger God. So if people don't believe in God even, the whole thing is just very...

In 1982, I entered the University of Chicago. We were encouraged to ask the big questions in life, but we were discouraged from thinking that we could ever answer them definitively. All knowledge was relative. Back then, in academia, many subjects were taboo, such as consciousness, causation, the reason "why" in biology, the emotions of animals, prayer, wisdom and the reality of God. To this day arguably the greatest taboo is the concept of absolute truth. I had to develop this concept on my own by documenting the limits of my imagination.

The video Preliminaries: Building Blocks: Frameworks of Perspectives explains the fundamentals, starting with the concept of everything, and then proceeding to divisions of everything into two or three or four or more perspectives.

Michael: We are in a difficult spot because we use a linear medium like video or text and part of the structures are not linear. Technology of communication is an extra complication and so I very much like diagrams and two-dimensional representations. So maybe a good thing is that you do a bit of theater about it.

Andrius: You like that?

Michael: Yeah because it gives a chance for people who have no real way to relate to what you want to say on a content level, especially if they are new to that, so when they observe your emotion that it might create some resonance which works even if there is only a very fragile level of knowing the terminology and methods that you are introducing.

For example, we are familiar with the argument between free will and fate. Rather than get sucked into this argument, we can simply observe that these two perspectives complement each other. We need two perspectives for matters of existence, as when we ask a question, whether or not this chair exists, but then refer to a definite answer, if it exists, then it exists, and if not, then not. In trying to explain this framework, I have found it helpful to suppose there are two puppets, one which argues for free will and the other which argues for fate, so that together they make up the theater of the mind. Thinking abstractly, we can say that one puppet claims that opposites coexist, black and white, whereas another puppet claims that things are all the same, they are just shades of grey. The point of Math 4 Wisdom is to recognize that this framework occurs in mathematical thinking. A surface may be orientable, as in the case of a sphere, which has an inside and an outside, so that opposites coexist. Or a surface may be unorientable, as in the case of a Moebius strip or a Klein bottle, where we can't distinguish inside and outside as it is all the same. This mathematical example helps define, clarify, validate and apply the framework.

The division of everything into three perspectives is the learning cycle of taking a stand, following through and reflecting. This is the scientific method - we state a hypothesis, conduct an experiment and observe the results. Wherever such a three-cycle appears in mathematics, I suspect that it is modeling the learning process. I think of the Jacobi identity and I contemplate how a Lie algebra is the structure of learning for a Lie group. In homological algebra, I imagine the Mayer-Vietoris sequence as describing how the learning cycle proceeds dimension by dimension.

The division of everything into four perspectives distinguishes four levels of knowledge: whether, what, how, why.

Kirby: I think one of the greatest errors people make in communication is they quickly assume that we are all speaking the same language. Whereas my model is more that we all speak our own private language. We think we are communicating but everyone says God or true or whatever in their own world. And so a first step, when you are communicating, is to do some translation.

I could appeal to philosophers such as Plato, Aristotle, Kant, Hume, as practically every philosopher speaks of these levels in their own private language. However, my goal is not to create my own private language but rather to foster a language of wisdom within a scientific community. That is why I will be creating videos about the Yoneda lemma to show how it functions as a knowledge switch for these four levels. And more generally, I will show how these divisions of everything appear in exact sequences, where the perspectives correspond to maps. In particular, a short exact sequence has four maps and I argue that they express these four perspectives, whether, what, how, why.

How can I show that such cognitive frameworks are real? I need to do this within a community, and that is coming together through the Math 4 Wisdom discussion group, which you are welcome to join. Kirby Urner is the first person to engage me there. He majored in philosophy at Princeton, with a focus on Wittgenstein, and grew to champion Buckminster Fuller as a visionary who straddled the humanities and sciences. Kirby teaches high school students to program in Python, and broadens their thinking by contrasting Earthling math, based on cubes and independent dimensions, with Martian math, based on tetrahedrons and interdependent dimensions. You can see his influence on my video, 120°+120°=90° in Dynkin Diagrams. Teamwork in Creating Learning Paths. This is the first in a series, What is Geometry? I am showing how we can understand the classical Lie families in terms of very concrete facts.

Kirby gave a presentation at the 52 Living Ideas community, and our interaction there brought Jon Brett into the Math 4 Wisdom discussion. He and his wife Yoshimi are the developers of a cognitive framework, Emergently, which facilitates understanding and decision-making, and is based on the tetrahedron. Emergently expresses metaphorically how water unifies, fire energizes, earth solidifies and air transforms. The fact that Jon and I have worked so personally with cognitive frameworks helped us understand each other in ways that I had not suceeded with Kirby. Discussion between the three of us made apparent what I should have realized long ago, which is that we all have different relationships with the truth. For Jon, truth is metaphor. His position is understandable because it allows him to apply Emergently as a useful metaphor without having to defend it as literally true. For Kirby, truth is a defensive strategy that keeps him from being attacked as a fabricator, which liberates him to be both truthful and creative. For me, truth is subsumed in absolute truth, and so my strategy is to center myself in absolute truth, and thus align at the source with God's vantage point. Our various relationships with truth suggest that we identify with different locations on the landscape of truth, distinguished by the layers of reality, inside ourselves and out in the world, whatever we take to be real, and so we take up distinct strategies accordingly. Each of us has valuable experience by which we can try to appreciate the entire landscape of truth.

Two years ago, I had the opportunity to study quantum physics with John Harland, and we talk every week or two. We became friends in graduate school. He is a functional analyst with a passion for physics, and you will encounter him in many videos. For John, truth is a hard journey, where we often are wrong, yet by correcting our misconceptions, we can advance. In studying Schroedinger's equation, I became interested in the combinatorics of the orthogonal polynomials, for my PhD was in algebraic combinatorics. Physicists seem to think that these polynomials are simply tools they use, whereas I imagine that they encode what nature has to say. Indeed, the combinatorics of orthogonal Sheffer polynomials is very suggestive, particularly their fivefold classification, which I think accords with five zones in the scattering of particles, but especially, with the division of everything into five perspectives for decision-making in space and time, whereby every effect has had its cause; but not every cause has had its effects; and so there is a critical point for deciding. In the playlist for the Fivesome you will find presentations, some technical and some informal. You will find me tutored by John and also by experimental psychologist Shu-Hong Zhu.

Theoretical physicist Thomas Gajdosik also joins us sometimes. He teaches quantum field theory and general relativity at Vilnius University. Every month he sets aside an evening where for four hours I share with him the progress that I am making in my research on theology, philosophy, mathematics, physics and personal growth, and we also pray together. His deepest value in life is awareness that he is loved by God, where this love is the gift and key to all of reality. Thomas appreciates my theological explorations, as in the video series Wondrous Wisdom, where I imagine a top-down overview from God's perspectives, as in my videos Defining God and Human and God does not have to be good.

I was happy to introduce John and Thomas, so that John could present his original research in quantum physics, which was meaningful for both of them.

I am likewise learning from our participants that our different levels of mathematical knowledge, and our various situations in life, can help us think fresh as to the meaning of math, wisdom and truth.

But what is the practical use of wondrous wisdom? The general idea is that God does not have to be good, which means that we have to face hardships if we are to grow and learn and live forever, here and now. Our hardships show that we can choose to be good, let go of ourselves and care about others, and also we can choose to think outside of the system we find ourselves in, from God's vantage point. Specifically, this is detailed by four frameworks by which we address our body's needs, our mind's doubts, our heart's expectations and our will's values. For example, we can make explicit the life of our heart, not just our basic emotional responses but a language of thousands of moods, as investigated in the video A Geometry of Moods: Evoked by Wujue Poems of the Tang Dynasty. Six Mobius transformations - inversion, shear, rotation, dilation, squeeze, translation - reshape the boundary between self and world, as if we were circles on a sphere. If you could know anything, what would you like to know?

The intelligence of our mind is made explicit when we address our doubts with counterquestions. An example is given by the video How do you know that you are not a robot? where we can reply to this doubt with the counterquestion, Would it make any difference? I have documented a framework of eight counterquestions and have applied that as a peacemaker to systematize the ways of loving our enemy by looking at everything from their point of view: be straightforward, act step-by-step, be vulnerable, let them win, let them teach us, stick to our principles, have something to share. I created a video Bring peace to Russia and Ukraine to suggest this approach along with twelve practical activities. Subsequently, Namejs Rossman and I wrote the text for the video Call for Essays: Vision for Our Future which was read by eleven people from four continents. I'm recording and publishing video essays to contribute to global dialogue so that individual Russians and Ukrainians would likewise speak out, interact and seek solutions. Additionally, Silvijus Pokštas and I organize workshops for independent thinkers at the prison in Alytus, Lithuania, not far from my village home, and we are including prisoners in this dialogue. What is your vision for our future?

How can we work together to recognize, clarify, develop and apply this language of wisdom? We can collect, sort and systematize the ways of figuring things out in all manner of disciplines, starting with mathematics. My most popular video Surface Structure vs. Deep Structure is the first in a series, Math Epistemology, where I will present 24 ways of figuring out how to solve mathematical challenges. I have sketched out similar systems for physics, biology, neuroscience, chess and the business innovation games known as Gamestorming. I welcome support from Patreon supporters so that we could work out the epistemology of their favorite discipline. Similarly, I have mapped out my own ways of figuring things out. I have sketched them out for Jesus and for the Gaon of Vilna. Whose thinking would you like us to flesh out with an epistemological portrait?

I want Math 4 Wisdom to be a supportive environment for my own investigations and yours as well. In the series Wondrous Wisdom I am leading up to presentation of my current research to understand the wisdom in our life experiences. Each of us has a unique treasure of experience and a unique vantage point. Please ask yourself, what is your deepest value, which includes all of your other values? What is a question that you don't know the answer to but wish to answer? What is your relationship with truth? Your answers will help us appreciate each other and work together on the basis of truth and even absolute truth.

If you like this video, if you subscribe to this channel, then you make Math 4 Wisdom more visible to others. Thank you also to all who support Math 4 Wisdom financially through Patreon.

Welcome to Math 4 Wisdom, an investigatory community for absolute truth.

The Participants

Interviews with

• Thomas Gajdosik
• John Harland
• Bill Pahl
• Jon Brett
• Kirby Urner
• Raimundas Vaitkevičius
• Silvijus Pokštas
• Michael Schreiber