Spectrum of duality


This post is so overdue! I’ve been saying clever things about “the spectrum of duality” without actually explaining further. Well, let’s fix it.

In a comment exchange on a post on “the illusion of trees” a while ago, I mentioned to Livelysceptic that duality was a terrible misunderstanding and that I would show it. I then went away and looked at duality as two branches on a tree and then I got lost in a forest of deep thoughts. But not before determining that dualistic opposites are two entirely different things and at the same time, they are the same. Let me elaborate.

You know those forks in life, when we are left with two stark choices. Do we do the right thing and follow our heart, or do we use our head and do what is logical. Mind vs heart. A duality. One or the other but not both.


When you look back at your life, these choices stand out like milestones. Good or bad, we know exactly what we did and what we didn’t and now, for better or for worse, we are here. Can’t change the past, we have followed this path.

We could have followed another path and ended up somewhere else.

A different path.

Choice is not about T-junctions in the road, it is about paths from somewhere to somewhere else. Many times that choice is an illusion, i.e. we think can choose but we can’t. Brain scanning research has shown that our brain knows our choice a full 6 (six!) seconds before we are conscious of our decision. So, while we are still deciding, a decision is already made!

‘Ciocolate or Vanillia’, Mario is beaming, scoop in hand, ready to fill you cone.

‘Chocolate’, says your brain.

‘Oh, I love both! This is so hard’, you say to Mario.

‘Chocolate’, your brain repeats.

‘I must choose. Eh, vanilla. No! Stop! Chocolate.’

‘Chocolate’. Your brain is impatiently drumming its fingers on your skull.

‘OK, final word: Vanilla.’, you say with determination.

Mario smiles and digs his spoon into the creamy white waves of ice cream.

‘Sorry… Can I have chocolate!’

‘Whatever’, say Mario and your brain in unison.

Many choices are not made by us. What we call “making” a choice is in fact “becoming aware” of the choice that is made for us by a biological calculator. It is dictated by habit and circumstances and not by a free will that could make random decisions. If they were random, we wouldn’t be making them and if they are not random, then they must follow some sort of logic and we simply execute that.

But we don’t choose.

What looks like choices are in reality two different paths in life. The bends are where we thought we had choices but any other path that diverts from there, is a different life altogether. Not yours.

So duality of choice is an illusion concerning two completely separate paths.

On the other hand.

When we consider the world around us, we can see black and white. Social and antisocial behaviour. God and no-God. Life and death. To be or not to be.

These are not choices. They are opposite states, positions and viewpoints that make up our world, i.e. who we are. These are proper dualities.

Or are they?

All of these dualities depend on our point of view, our perspective. Someone who believes in God sees impossible denial of existence in a person who believes in no-God. That feeling is reciprocal. The atheist believes that the God believer is denying fact and reason deliberately and stupidly.

God and no-God duality: denial of a deity or denial of good sense?

The state of death, viewed by the living is a very dark place that ought to feared. It represents absence of existence, annihilation even. Yet, if we were to take some distance and look at life as sandwiched between pre-birth darkness and post-death darkness. From that perspective, the darkness is the contrast that makes life possible. On the long scale of time, our passage in the light is. “Is”, as in, it happens and will never unhappen.

Life and death duality: existence that is annihilated or existence that is eternal?

Let’s stop there.

These dualities are seemingly irreconcilable opposites. Surely we cannot be, and not be at the same time? The answer to that Shakespearean conundrum lies in the way humans perceive the world. It lies in root of that which connects us: language. (which by the by, was Shakespeare’s expertise!)

Language is a powerful attribute of our species but it has a fundamental flaw: it serialises our perception of the world. Language cannot say “love” “you” “me” all at the same time and so it chops it into separate words. “I love you”. By doing so it has separated you from me and made loving a separate act. But it isn’t like that. When I love you, it is a full sensorial totally integrated state of bliss.

Whatever thing we look at, our language forces us to turn a multidimensional experience, observation or state into a straight line. If that line is well crafted, our brain will attempt to reconstruct what was conveyed in the first place. Many times we fail badly at serializing a complex matter and the escalation of such flawed communication have caused more than a few wars of all degrees.

Dualities are entirely rooted in our inability to think and speak in many dimensions. We can describe one side of the dualism and we can describe the other but somehow we fail to convey the holistic dependency and unity of the two.

One approach is to stand in the middle. To say things like, ‘well, death is very much part of our existence. We die a little every day’ Or, ‘I believe in God but not all of the miracles and powers attributed to him’. And the other guy might say: ‘Look, God is an outdated concept but I do believe that there are special people that do amazing things’.

Why would we do that?

Because most of the time we are not at one extreme of a duality or another. Because when we view the duality from the middle, we begin to see that the extremes connect and overlap.

We begin to see that a duality is in fact a spectrum of ideas, states and positions that are all connected. It will allow us to allow for the other impossible opposite. It allows us to take a many dimensional view point.

This is perhaps an odd position to take, to suggest that there is a place between black and white, existence and nonexistence, between being and not being. On the other hand, it is perfectly obvious.

In the world outside us, there is no distinction between things. The distinction comes from our perception, from our serialized language and ‘trains of thought’. There is no distinction between the head and the tail of a fish. Nature doesn’t know where one ends and the other starts. A fish is whole. That is what yin-yang is trying to tell us: The head faces the tail but it is one and the same.

Duality is the human need to serialize complexity. In reality dualism represents a spectrum of choices.

For the scientifically inclined, in a recent comment to bloggingisaresponsibility I mentioned non-equative mathematics. Now don’t scratch your head: it doesn’t exist. It was something I dreamed up to deal with a fundamental limitation in mathematics: the equal sign “=”. An equal sign divides an equation into before and after. One formulation becomes another. The equal sign (and its siblings >, < etc) are pretty much in every piece of mathematics you will ever see. I tried to drop the equal sign (“non-equative maths”) to go beyond the duality but the whole thing reduces to mathematical dust.

The equal sign turns every equation into a duality. And since I have argued that duality is a feature of human language – which includes mathematics, it puts a limitation on mathematics for pursuing the description of the real world in a non-dualistic manner. Or does it?

If dualism represents a spectrum of choices, as I indicate, than that spectrum is somehow hidden behind the equal sign “=”. For a mathematician, that is an extraordinary observation. I don’t know about the others, but I have always taken the equal sign for granted. Something that separated me from a solution I couldn’t find. To think of it as a symbol that represents the spectrum between dualistic positions triggers a lot of thoughts.

What does the equal sign in 2 x 4 = 8 represent? It is connecting a multiplication with a number. Two different dualistic states. What spectrum are we not seeing with the serialized limitation of our language? In this case that spectrum is the fundamentals of multiplication and number theory. Huge! And all that behind an equal sign. I am willing to stick my neck out and declare the equal sign the most powerful symbol in science.

I will leave you with the same thought that I left bloggingisaresponsibility with. One of the most fundamental tenets in eastern philosophy is: Tat Tvam Asi.

You are that. That are you. You are it.

You are.

You is.

You =

Postscript on non-equative maths

On non-equative maths, when I cooked this up some 10 years ago, I defined it as a system where the whole family of relational symbols such as =, <,> as well as their opposites ≠, >=, =< and their discrete set cousins (member of etc) are absent. So there is only ever one side of “an equation” , which is not an equation anymore.

When you follow that through you end up asking what the meaning of such mathematical objects is when they are not related or referenced to anything. Like, what is walking if there isn’t a floor? It’s dangling legs in space. What do any of the operators *,/,+,-, sin, exp, integral, Laplace transform etc mean when the one sided object can’t resolve to anything or relate to anything?

My conclusion was that by removing the = sign and its siblings, mathematics becomes quite meaningless. So when I made this up, at a first glance it appeared useless. But…

But if the removal of the = sign (and siblings) make mathematics meaningless than by implication those same signs actually give mathematics ALL of its meaning. So in a bizarre way, non-equative maths proves that equative maths is meaningful through an reductio ad absurdum argument.

We don’t have to stop here. If we look at non-equative and equative maths as a duality then by my own spectrum argument there has to be something in between. Although I can’t demonstrate it clearly, I have a hunch that what lies in between is “creation from nothing”. I have been looking for a formulation that creates something from nothing and this is what brought me to non-equative maths in the first place. I have more work to do on this and my research in fractals relates to that as well. One day I hope to be able to formulate a convincing argument and formulation for creation-from-nothing.

Or perhaps I will prove that it can’t be done and I shall rest frustrated for the rest of my life.


22 thoughts on “Spectrum of duality

  1. Reading this article prompts me to say that I’d be really sad if you went off into the realm of mathematics and forgot about philosophy! Sure, that’s not a duality either, but your observations are priceless. They really are.
    Looking for the hidden spectrum in duality is a task that will keep me busy for days, I suspect. 🙂
    And I fully agree withy your description of the limits of language. It’s possible that language and conceptualisation are the main culprits when it comes to our anthropocentric view, that we could see the ‘whole fish’ as soon as we forget about the head and the tail. But society is often impatient for us to choose either chocolate or vanilla and we’re lucky if Mario is as philosophical about it as you described him. 🙂

    1. Thanks Livelysceptic – don’t worry, I’m a pedestrian philosopher and an even poorer mathematician! Both intrigue me though. Alas,I didn’t invent any of this and even though wiser people than me have known about the problem of language for centuries if not millennia, it hasn’t stopped us from hardly taken notice of that. Still, if we can understand at an individual level, we are already greatly advanced.

  2. Great post!

    I love your observations on how language serializes our perception of the world. I never thought of it that way, but it puts a lot of things (usually involving the problems revolving around language) into a new light.

  3. This is the best post I’ve read in a very, very long time. Jung discussed “syzygy”, the union of irreconcilable opposites, Bergson worried about discreteness, Gurdjieff said, “There is only one thing, and “I” am it”.

    Man o’ man, you’ve stirred my pot. I feel like starting a post on prose style now, believe it or not.

  4. I honestly regret I did not afford more time to reading your articles… since they are the most interesting read I have found on WP. 🙂 Thank you for thought provoking pieces…

      1. No, it is YOU that has made me blush… there I go with my Lost in translation blog trying “to convey meanings” and as you, yourself said words are meaningless .. which is exactly the reason why I resorted to photography and music instead :D. Being a linguist (translator) and finding language futile and unreliable can be very frustrating 😉 Thank you GF …. (God, that sounds like girlfriend :lol:)

      2. I’ll be your GF 😉 and you did the right thing to pick photography and music to express yourself. Language is an appalling medium and why on earth we’ve made it our primary means of expression beats me.

      3. 😦 maybe at some higher stages of human evolution we will find a better medium …. Thank you GF 😆 I appreciate it 🙂

  5. Hi Henk. Just wanted to toss in a few of my thoughts
    stemming from your postscript on non-equative maths.

    Take the equation F = ma (force = mass x acceleration). If we imagine a stone that’s not moving, we could say that 0 = m x 0 = 0. It doesn’t matter what the mass of the stone is in this case; so we can simply say 0 = 0. The stone is still there but it’s not part of the equation anymore. At this point we have a stone with no mathematical properties (the one-sided object that can’t resolve or relate to anything?), and an equation that says ‘no force is equal to no acceleration’.

    Now by removing the = sign, as you have said, the mathematics becomes meaningless. What happens now if we pick up the stone and fling it? In a world where mathematics is meaningless, it’s a phenomenon; not in the disciplinary sense of phenomenology, but in the sense that something is being observed to happen. The motionless stone could have been called a phenomenon too, but only in the sense that nothing was seen to be happening.

    Does this equate to a situation in which “creation from nothing” becomes possible? It seems to be, since we now have an accelerating mass with any number of useful functions, and no need to think of it as anything other than a mathematically non-equative phenomenon that gives useful results – like when you successfully skip a stone on the water for the first time and your eyes light up.

    1. Yes, in this thought experiment, I think that is right. When you make the stone onesided it loses its place in universe. In a way, it ceases to exist as a stone that obeys the laws conferred to it. When you then throw it, it reappears as if out of nothing and is created.

      The point being that these one sided equations form a ‘space’ of potentiality that becomes something when you confer it a place in reality.

      Should we view the act of turning a one sided equation into an equatin as a creationary process? I.e. the equal sign is an creative operator and not a relational symbol?

      1. Should we view the act of turning a one sided equation into an equation as a creationary process? Absolutely! We should! Except to say:

        a) that the phenomenon on the one side (of which no mathematical equation is truly held to exist yet), rather than becoming something, becomes something ‘else’. Something displaying self-similarity by extension? Not sure. Is force the same thing as an accelerating mass, or is the = sign an operator for plying something else out from the phenomenon – like an act of creation? I’ll pin my suspicions on the latter.

        b) just because I said we should doesn’t mean we should.

      2. The idea of an = sign dividing two sides still disturbs me. It is a dualist is view of something whole and continuous. Even though it appears to be a creative action, I wonder if without it, i.e. a one sided object, we would see an unlimited evolution of that object, not limited by human observation that chops it into discrete snapshots.

        The = sign would then be a camera of human consciousness, turning a real phenomenon into something we can comprehend.

  6. I would see the word ‘nonduality’ as describing this sublation of all dualities.

    It seems directly relevant that Aristotle begins his laws of thought with ‘A = A’. Perhaps you are right, and this is an act of creation.

    Also Russell, with his observation that our sentences always begin ‘There is an x such that…’ (Ie. X = ).

    Does the subject-predicate form of our language force an equal sign on us? I think so. Thus Bradley remarks that in metaphysics the subject-predicate form is necessary but indefensible.

    1. Good thoughts. I don’t think you can get away from defining something, somewhere, sometime. Can ever know anything without such primal creative definitions? Probably not. But we can experience it.

      A new born infant (in a safe environment) shows that knowledge isn’t necessary to joyfully experience “it”. What’s more, we lose that joy as we constrain our reality through definitions, starting with “Mama=Mama” (she exists) followed by our first duality Papa vs Mama.

      It is perhaps not surprising that all great religions sought to understand and teach the non-language experience of “it” through meditation, dance, music etc. Sadly, we tend to seek meaning in the ancient writings rather than the “thing” they are pointing at.

      I’m perfectly guilty of this myself 🙂

  7. “Can ever know anything without such primal creative definitions?”

    Logically speaking, it ought to be possible to know what we are without any intervening concepts. Although ‘knowing’ would imply a division of knower and know, so ‘Being’ might be a better word, or ‘knowledge by identity’.

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