The mathematics and physics of trust

I am shy to admit that I believe physics and math are paths to love, and knowing love is a way of doing math and physics.

For whatever reason, this became relevant in a conversation I was having with a group of mathematicians. I said something and what they heard was a claim that 'everything is physics', but the intention of my words was to try to establish shared language to talk about something for which I did not have language. This is quite different in nature from trying to make some sort of claim of universality and defend it.

Mathematicians and physicists are used to language being saturated with claims and refutation. We steep in raised contention. I was trying to say "For the purposes of this conversation, what I mean when I say 'physics' is X," but flailing and failing utterly, because we kept getting lost down a rabbit hole of "no, physics means Y" and in my mind i'm going "jesus fucking christ! just listen to what i mean." This is most frustrating to me. It felt like being drowned in doubt — and not theirs! In my own doubt, because this way of thinking is also (too) easy for me to fall into, and once you fall in, you're stuck in the mire.

Even so, the truths of greatest significance to me tend to be those which are on the edge of our language. The things we can't quite find the words to talk about. I feel acutely the way in which I am shaped and molded and limited by the language I have and use. I feel acutely the way in which I am (re)constituted by the words of another, when their language resonates within me and changes me in such a way that allows me to understand them. How we see and thus what we see as "real" in the world are so deeply constructed by the language we find ourselves utilizing in a given moment.

At the same time, a part of me hardly believes what I am saying, which is perhaps because I do not yet know what I want to say, but these words are my best estimate of it.

However, if I accept what I hardly believe, and nonetheless take it seriously and consider its consequences carefully, it feels like a part of me is pointing me to a deep truth hidden in plain sight but thoroughly obscured to me as I go about my ordinary days.

I suspect I will find tomorrow that my words today are vacuous, but the only way to get it right feels like trying again and again, then seeing what is consistent across all of my attempts. After all, what is real is that which is invariant under our changes in perspective, right? A blue ball is blue because its blueness is invariant under change in time (which is actually an interesting example, because color is frequency, and frequency is the conserved quantity conjugate to time translations a la Noether's theorem).

At the same time, non-invariant things are also just as real. These signals popping up in my brain that I am recording onto this page are real to me whether I write them down or not, and they are real to you only when I write them down.

My sense of self is real in one way, and my sense of other things or people are real in another way, and usually I operate as if there is a cut between these two things. In my ordinary world, these two things are logically independent.

It is a suspicion of mine that this is a quirk of our time period. That even our interpretation of what human experience was like in the past is deeply distorted by the experience that we believe is shared by everyone else. That things like magic and god were more real than we think, because we cannot conceive of what people meant by these words, simply because we did not exist then — we exist now.

A fallacy of our time seems to be how unchanging and universal we believe the meaning of words to be. We operate on the expectation that everyone shares a common language — what's the alternative? I long for another way, where we can acknowledge the extraordinary and troubling depth of our words' limitations without losing ourselves or each other along the way.

Here is an attempt at my first main point.

What is real is that which affects us and that which we affect.

Just like how babies learn how object permanence works from a young age, there is learning of "realness" that is happening on evolutionary timescales, and each age, each historical revolution — religious, scientific, or otherwise — is something of a phase transition in our individual and/or shared sense of selves as experienced through each other. I will return to this point later on, through a perhaps derogatory but illustrative analogy to the way that money acquires value in the absence of intrinsic value.

Any way of relating to each other is necessarily founded upon the existence of such a way of relating (hang with me). Just as for two harmonic oscillators need to be coupled through shared degrees of freedom to interact, we too interact through our shared language.

By language, I mean more than just words. Any choice that we can make that affects another person exposes a pathway of communication. We communicate through touch when we comfort each other, through taste when feed each other, through sound when we speak to one another.

But communication is more complex than just having a pathway of communication. Just because a cat can hear me doesn't mean I can communicate with it. I can communicate with a puppy insofar as I can send signals that are meaningful to the puppy — perhaps a show of playfulness. The word "food" might not mean anything to the pup at first, but over time, they can learn that the word is associated with a promise of fulfilling its hunger.

What does this have to do with math and physics?

I am not confident in my ability to find the language here, especially for something that I can't say I am justified in believing, but I am going to trust nonetheless, because there is a physics to trust that I am more confident in thinking and talking about.

Skepticism is a tool of science. However, while doubt serves us well in distinguishing between what is real and unreal (or what our bodies have deemed disadvantageous to treat as real), trust allows us to construct realness from what is unreal, to find meaning in meaningless signals, when it is advantageous to do so.

The mathematics and physics of trust. Perhaps this is what the title of this post should be.

I have found myself to be living in a sort of dark ages of trust since ~2016-18, when I graduated from my undergraduate institution. Since then, my doubt (resonant with cynicism) has shaped the world I see and respond to more than I like to admit.

And it is true that my doubt is a form of love for myself. It tries to provide me a safety net. By responding to every circumstance as if it is the worst case scenario, and by bracing myself to harm always, my body attempts to close myself off from the worst case possibilities. Instead of hurting a friend by choosing the wrong words by mistake, isn't it better to not say anything at all? I think younger me would be saddened by how much I see myself filter, isolate, and guard myself. And I wish I didn't, but it's not exactly by choice. At least, choice to the extent that I understand how to tune the knobs and controls of my person — I often feel like others are far more adept at this, while I am desperately trying to do what others achieve easily, like eat when I am hungry, drink when I am thirsty, sleep when I am tired, and plan for the coming day.

Soo..."What does this have to do with math and physics?"

I believe we are all mathematicians and physicists, e.g. when we analyze the logic of a situation and make choices based on our anticipations of the outcomes of those choices.

The dark ages I find myself inhabiting, and that I believe I am witnessing in the others around me to the extent that my senses do not deceive me, I think has to do with a lack of understanding in my body. I feel like I get brief, magical glimpses of this understanding within me and in those around me, but I do not know how to talk about it.

And that may be what I mean.

There are important, precious truths that I think have not yet reached our common language concerned with the truthful nature, logic, physics of trust and love.

I often believe we live in a Darwinian universe.

But right now, I can feel the little tugs tell me to look more closely. Telling me that this Darwinian universe is one of our construction, and that such a construction is logically dependent upon a more fundamental physical principle that I can only call trust.

I ask that you tune in to the impressions that you have of what I mean by the word trust, the operational utility of the word and possibly images or memories stirred, its connotations.

I ask that you imagine with me how diversely this word will resonate from person to person. I know the particulars of what it means to me is not easily transported to you, even if we can (somehow) still communicate about it coherently.

I ask that you consider the reasons we can even begin to imagine how another person will understand the word trust, and invite you to consider the ways in which trust itself is entangled with our capacity to imagine this. My thinking here is that we have a sense of what it is like to be a person, and we trust that another person experiences their personhood in an analogous way to us, so we can relate to each other in the way that persons do by trusting and seeing that "oh wow! it works!" and discovering that by trusting our words carry meaning, they acquire meaning.

Lastly, I ask that you consider or acknowledge how deep the limitations of your imagination of the meaning of this word to another could be. These limitations are physical limitations, in a some sense: what the word trust means to you depends on your full lived experience. We are equipped to understand this limitation in our imagination too, in part, because we witness acutely the limitations of others in imagining our experience.

I now invite you to a (possibly scary) truth, that your body may try to reject or keep at arms length.

Our brains simulate the world around us.

When we see another person, we see only a well-trained hallucination of their existence. There is a physical time delay between an action made by another person and the action we see, because what we actually see of another is their imprint encoded in a light signal that hits our eyes.

I contend that honoring this gap between the person themselves and the image we construct of them is critical for our loving (ourselves and each other) more fully in the world, our trusting in the world, and more honest wielding of doubt.

"The map is not the territory"

"The signal is not the thing itself"

"Form is not matter"

These are age old truths, but I think their utility has run their course. They are still of course meaningful (in-the-way-that-they-are-meaningful), but for me, there are truthful opposites to these that I think may be more useful to us.

There is a sense in which the map is a territory, the signal is a thing, and form is matter.

It is an underdeveloped suspicion of mine that quantum mechanics can be understood as a consequence of this fact that all inhabitants of this universe, from fundamental particles to human beings, know and relate to each other only through signals and forms, and the maps (or maybe lenses) they use to interpret them.

Ok ok, so what do I mean by such a contention? And what does it have to do with love?

I think it may be time to name, label these truths, and enfold them into our common vocabulary so that we can speak freely of the almost-real things within us, because I believe these truths provide a way for us to find greater love in our relating, in the images we hold of one another, and in the countless ways available to us to understand the world around us, and our place and identity within it.

We exist as both objects and subjects. We make choices, our choices constrain the choices of others, and others' choices constrain ours.

We may live in a world of violence. But I suspect the efforts of the collective and historical "we" have made it safer to be vulnerable with each other than we believe (e.g. if we can find the right language), and that much (though certainly not all) experienced violence arises from not finding within our imagination pathways to trust.

And language, if anything, can restructure our imagination at a moment's notice.

Now how do I think this lens / language of trust can help?

Because any inhabitant of the universe is represented by its symmetries imprinted upon the signals communicating its existence to other inhabitants, and those symmetries are sufficient to ensure to us of its realness (in-the-way-that-it-is-real).

Normally, I dismiss these aberrant thoughts as vacuous, but the universe feels so much more alive to me when I consider these hallucinations (which I am transcribing here and which may or may not ultimately have bearing on math, physics, or love) are real in the way that they are real in this moment.

I feel like a real physicist when I honor the potential significance of these hallucinations as real. No different from the way in which our dreams are real: our brains hallucinate mutations of our experiences and we learn through these hallucinations, perhaps similar to how neural networks are trained (though I find this view a bit reductive).

Neural networks are real intelligences in the way they are real, but to me, the only way they can become alive is if they hallucinate and evolve in a way that is not prescribed by us, but unique and internal to them. I do not see classical computers as sufficient for providing such capacity, as the entire interior of such artificial "intelligence" is exposed and manipulated by us. As long as this is true, they will not be alive.

What I think of when I use the word alive is something that (1) we see in each other but (2) cannot fully know of another, in the way that you cannot know what’s happening in me, other than through the means of communication that reveals our selves to one another.

Who we are to one another is conditioned on trust in some way. Our senses of our own realness are scaffolded by our trusting that we are real in the same way others are real.

Life (oddly enough) is similar to money in this regard: it's only real, because we relate to and through it like it's real, and that makes it real in the way it is real.

This property is mathematically captured by the idea of gauge symmetry.

Things are unchanged when certain changes occur. Such changes, when mathematically formalized, are called gauge transformations.

There are at least two distinct types of agreement: (1) agreement in the sense of a contract or (2) agreement in the sense of you and I reaching a conclusion that we are witnessing the same thing, speaking of the same thing, that we are pointing to the same thing with our fingers or words, or experiencing the same thing with our emotions.

It is this second kind that is of physical interest to me, and I believe to be closely related to gauge theoretic reasoning.

When you and I agree, in this second sense, we are in a process of constructing shared language. The signals carrying the language (like sound or text) are on their own completely meaningless (unreal in the way that they are unreal), but they can potentially carry meaning if the signals resonate with us in (sufficiently) similar ways.

The strange physical property here seems to be that meaningless signals appear to be a precondition to the existence of the meaning represented by such signals, because of the ways those signals resonate differently within and between us.

It is precisely this (perhaps entirely accidental) difference between the way a meaningless signal resonates within you and me that is a precondition for the construction of such a signal as meaningful.

I think we misunderstand money for this reason.

Money is a form of meaning, even though my cynicism rejects consideration of such a thought. The imbalanced power dynamics of who has money and who can print it is the source of such cynicism. However, scarce meaning (for which it is difficult to find the language) carries value, no?

Money is meaning in the sense these pieces of paper alone carry no intrinsic significance, and yet we imbue it with value somehow.

Money acquires its value in the same way our words acquire meaning. We agree a word has meaning, not because we sign a contract attesting to its meaning, but because, through whatever dance we do together, we find our way to shared language, entrust that language to carry meaning, and become witness the materiality of that trust, and the stability of the word's meaning.

This process has a connotation of the riddle of the chicken or the egg. Which came first?

How was money or language bootstrapped to have value and meaning?

For this, what comes to mind is the experience of moments when I am trying to communicate something, failing badly again and again, until this magic moment when my partners in dialogue say "Aha! I think I know what you mean! Is it like..." And then at long last we are equipped to talk about the "it" whatever it is that we established through trying, guessing, and erring while attuning to one another's words, posture, facial expressions, emotions closely for any signal that might help us understand each other.

In the end, the bootstrapping process is necessarily a combination of trial, error, and veritable trust.

There is always a possibility that we really are talking about different things, but we still have the capacity to trust that we are talking about the same thing. And we know the feeling of that trusting, and we can gather a sense of when others are also trusting in this way.

The chicken-or-egg flavor of this process seems to be counterintuitive to our understanding of causality, which may offer a way to think about our understanding of the strange non-causal behavior in quantum mechanics, like entanglement, but for now I'd like to point to a possible way of understanding what I mean by this trust mathematically.

While my poetic answer to this question is trust, one possible mathematical answer to this is game theoretic.

There are outcomes of mathematical games called correlated equilibria which can be achieved only when players trust that other players will condition their strategies on a shared random signal. In general, such equilibria outperform Nash equilibria achieved by "selfish" players.

Two projects in mind:

1. Game theoretic game of trust: players can communicate with signals and can choose trusting or untrusting strategies conditioned on its expectation of other players' strategies (during interactions), conditioned on their limited information. I suspect Nash becomes correlated under certain circumstances, so more interesting may be timing game: trusting as a skill, correlating at the right time?
2. Game theoretic action principle: particles communicate with signals (eg bosons as force carriers) and can choose action variations conditioned on expectations of the other particles' variations at each time step (during interactions), conditioned on strictly local information.

Losing the thread a bit (my body is telling me it's hungry now), but I think writing this was helpful to me, so that's it for now!