The Soul in Mathematics

I feel a new energy running through my veins… speaking of what Iknow gives me back a level of confidence I haven’t felt for a long long time. I realize it was difficult to believe others would respect me, for I was having a hard time respecting myself.. knowing I was somewhere avoiding speaking my truth, allowing my fear to run me. So right after writing my second blog, I knew waht the thrid one needed to be. On dispelling the myth that science stand opposite to spirituality.

Before we can continue our exploration of what physics looks like within the paradigm of the Sacred Feminine, thereby offering new metaphors that can help us all to find more sustainable solutions, we need touncover some ‘truths’ that have been shoved down on us. For haven’t we always been told that mathematics speaks only of what is measurable and tangible? Haven’t hard facts and physics become almost synonymous? Hasn’t even reality been kidnapped by hard core scientists, waving a flag  of objectivity and materialism? To be very honest with you, science, even mathematics and physics, have incorporated the nontangible  and imaginary long ago. To be precise, it started in the year 1545 by  Geralamo Cardano and continued to be developed until Hamilton completed the foundation with his work on quaternions in 1843. But as we have seen in so many other disciplines, even when the facts are right there under your nose, if the ruling paradigm doesn’t allow you to see it, you don’t see it. So physicists have truthfully thought that science excluded anything nontangible. As the paraadigm is shifting, it becomes possible to see something else. And here I am, standing at that pinnacle in time.

So what is soul, and where do we find it in mathematics? Soul is that something that stays long after the person has gone. It is that something that lingers after the meeting is over, after the person has left the room. It is what stays, yet it is fleeting.  It is that unnamable something that photographers try to catch on their plate. So far, almost everyone agrees. You could say it is that part of someone’s presence that is untangible and cannot be pinned down to clothing, physical appearance, background or any other outer thing- but that definitely is a part of the presence. if you would meet the same person in very different circumstances, different clothes and function and style, if you would recognize them it would be because of the quivering of their soul in the manifest.

Now in the past era of patriarchy, rationalism and modernism, of course the soul too became subject to being pinned down, made abstract, needing to be defined. This led, of course, to big confusions. For instance, in Hebrew, the words for soul and breath are almost the same; neshama and neshima.  You could understand that as: it is how a person breathes, that almost unnoticable action, that somehow creates that part of someone’s presence that we cannot pin down to anything factual. It is said, that when the last breath leaves the body, it takes the soul with it. Originally, this was seen as a metaphor- and what a beautiful one! However, it became to be interpretated literally, as if the soul was the letter in the envelope that could be taken out. This has led to a whole lot of confusion, and on one side it led to the soul not being a concept people used much, rather we hear talking now about the aura or the energy field which have a function much like the soul used to have. But whatever the name we call it by, we need something that helps us relate to the unseen part of our presence. Also, eventually it gave space for science and spirituality to become pitched against each other. So, for our life’s sake and also for the sake of this enquiry, let’s go back to that older and more open sense of soul: that untangible something that somehow cannot be missed when you want to describe someone’s presence.

Now let’s go to a little history of numbers. Did they always have souls? As a layman, when you hear ‘number’ your first association is probably 1, 2, 3 4, …., right? Well, in ancient times that was indeed how numbers started out. It was assumed that when we wanted to count, we needed only to address what was whole and could be placed before us, like one apple, two apples, three apples etc. In a way, you could say this is the same approach to matter as fluffy fluffy spirituality holds to life: we look only at what is beautiful, whole and harmonious, and we assume that is all there is to life, the rest is just a mistake and a confusion of the mind. It’s not real, this view says.

Well, as in life, there came a time when mathematicians realized this was not enough to address reality. What if you’re in debt, and your debt rises? How do you express that? Zero and the negative numbers got added. It’s like someone growing up and facing the world and admitting that negativity exists in it’s own right. Like admitting darkness exists in it’s own right, with it’s powers of numinosity and fertility, and it is not only the absence of light. Introducing negative numbers means we see them as something existing in it’s own right. As something real. Mathematicians say, they move from the collection of natural numbers N to the collection of Z.

Though we have always been told that mathemtics is absolute and independent of nature, again, this is one of the greatest lies there is.  Simply looking at history contradicts it. Mathematics came forth out of wanting to deal with life. Interestingly enough, the same is said about the mind: many people think mind is something independent of reality, while there has recently been some very exciting research showing that actually language, the way we think, and therefor our mind (as how we think creates paths for the neutrons) models reality over and over. I’ll look up the reference for you, it’s some very elegant and powerful interdiscplinary research. So mind and mathematics both developed in harmony with nature and reality as we humans experience it through our senses. And just like spirituality.

Now with a mathematics that uses only the numbers you can find in Z, you don’t come very far. For what if there’s one piece of land and three sisters who inherit it? Two apple pies and five hungry brothers? Three orchards to be harvested and 11 workmen, of whom one is a child?

Again, a new type of numbers was created to deal with all of this. and nowadays mathematicians call all those numbers the fractals and the collection of all these fractals is Q. By the way, already around 1000 BCE these fractal numbers were used in Egypt.

Still, life wouldn’t fit in such a small jacket. The famous pi ( 3.14159265359…..) is an example. For it turns out, that if you take a stick, hold one end and draw a circle in the sand by turning it around, and if then you want to know the surface area, there is not one of all those numbers in Q that can describe that. Another example: if you have a square piece of land and you know the lengths of the sides, and you want to make a path from one corner to the corner diagonal across, how much stones do you need? Again, there is no number in Q that can describe that for you. So, what to do? Some smart and brave ancestors let go of their illusion that life is neat and everything always fits, and introduced a new type of numbers.  Here is pi, e, square root of 2, and all those other queer ones. Mathematics is actually very tolerant, it doesn’t say: ‘you don’t fit my expectation, I’ll just deny you’, no it says: ‘oh gosh, there’s even more to life than I thought, well let’s deal with it and get to understand it’. The collection of all of these regular and queer ones together is called the Real Numbers,  it is denoted by R, and the name lets you feel how the mathematicians were somehow hoping that now they had their hands on reality and could deal with anything. Around 600 BCE in the Vedic Sulbra Sudras the first indication that people realized this extension was needed can be found, and Pythagoras is better known for his work on this one century later, around 500BCE, focusing on the square root of 2.

So you see, the history of mathematics is the history of humankind getting to sort out all that is happening around them. But so far, there’s been no soul, and only tangible things have been studied. They tried, they really tried, if they could leave all those confusing intangible things out. If they couldn’t make sense of the world by focusing on the tangible. They might have succeeded, if they were willing not to evolve. But as they dove deeper into the factual world, they discovered what Taoists could have told them all along: they found the opposite rearing its head. It wasn’t so that not until Quantum Mechanics did mathematics discover this. It was already discovered centuries earlier, when the complex numbers with their imaginary parts were introduced.

It turned out, to deal with the full complexity of life, even as a mathematician, you needed at least a rudimentary way to include the unseen, the intangible, that what is sensed but not felt, the imaginary. Numbers from now on- we’re talking Golden Age, 16th to 19 the century- were not seen as complete unless they had a soul. In the typical way of mathematics, they invented the most simple way you could do this, and it actually brought them- us- quite far. So, they said, it’s like the real part of a number, a presence, is on the horizontal axis, and the farther out is is the bigger number, and the imaginay part, as they called it, is on the vertical axis, and the farther out the bigger the imaginary presence. Think of imaginary presence as the soul.  It’s like saying some people have big ego, small soul, other small ego, big soul, and some have little ego and little soul and some have big ego, big soul. Ok, it’s oversimplified, but the soul is in there!

What where these ancestors studying that they now needed something they hadn’t needed before? It was like they started asking questions the other way around. They were not only asking: if I have this and that, what does that imply. Like the question of the orchard and the reapers, or the stick and the circle. They started asking questions like: If the outcome is this, then what could I have started with? An example:  if I have Stonehenge and how it maps the rising of Sun and Moon, what would be the actual movement of Sun and Moon? Another example: the ‘old’ question would be: if my boat goes 5 knots, than what is the friction and the wave resistance? The ‘new’ question takes into account that when I go out on the water, I don’t know beforehand what my speed will be. So it would be; if the wind is 6 knots, and this is how my friction depends on speed and that is how my wave resistance depends on speed, than what speed will I go? The first question  relates to a fixed world where everyone goes around at fixed speeds, like on our highways. You just hit your gas pedal a bit harder if you want to go faster. The second one relates to a world with uncertainty, where what will actually happen will depend on many seen and hidden factors ( for, in practice, one sailor will go at a different speed then the next, even if they’re in the same boats!). The old enquiry was about: ‘this is how it is, calculate that aspect for me’, or: ‘this is how I want it, what do I need for that?’ The new enquiry is about: ‘what will happen?’

You can relate this to the famous story of Job. God and the Devil were looking down at Job. God said: ‘Job is my favourite, he is so pure whatever happens’. The Devil said: ‘he is only pleasing you because you are so generous to him. Let go of your protection for him and see what happens.’ The Devil was bringing in here the enquiry the other way around: ‘what would happen if we change the circumstances? How would Job show up?’ Well, in the case of Job, he showed up pretty awesome. No matter what hardship the Devil created for him, and no matter how absent God was, Job was honest, loyal, pure and happy. Wouldn’t you need soul to explain that? Well, mathematicians needed imaginary numbers.

It turns out complex numbers have a lot to do with the fact that everything moves in cycles. If we have only phases of good fortunes, we don’t need much soul. But to deal with good fortune and misfortune, and the one changing into the other, we need soul.

Hamilton was the one who gave the imaginary numbers their form as we know them now, in 1843. This was also the time that quantum physics was about to hit the scene. Quantum mechanics couldn’t exist without Hamilton, without imaginary numbers. So it was not true that when the wave particle duality started showing up that Taoist principles started entering physics. It is not true that nature started behaving weird once we started looking at tiny particles. Quantum behaviour also happens in the case of boat speeds, as everyone who has sailed dingies knows (‘regular’ sailing versus ‘planing’, and the sudden transition between the two).

What is true, is that mathematics expanded herself to include phenomena and ways of enquiry that are the territory of spirituality and Taoism especially: the alternating of yin and yang, light and dark, the truth that the only cetrainty we have is that everything is ever changing- and the question: who are we within that reality? So, we’re leaving the static worldview of the Greeks, and we’re entering the dynamic worldview of Taoism and the Sacred Feminine.

What is also true, is that the men one century ago who were playing with these new mathematical toys, didn’t fully understand the philospohical consequence of what they were doing. They did not see they were shifting from one paradigm to the other, from a static world to an ever changing world. They were dealing with the first signs of the new paradigm, but they were not understanding that yet, didn’t have that perspective yet- as is common in these times of transition. It is only with hindsight that we recognize those early signs.

So when these scientists then half a century later discovered that earth was ever changing and unpredictable, they did not realize this was because this was the new earth they had allowed to enter their mathematical world when they included complex numbers. They were shocked. They were horrified. And as people do at such moments, they started blaming the other. Earth was showing up really weird when studying these small particles. So, they concluded, it must have something to do with those tiny particles. It must be their fault.

With that, they created a big deal of confusion that we’re still in the middle of. Most of us think that quantum behaviour is something that has to do with small particles. No, it has to do with pushing a system to its edges, with pulling oneself up by the bootstrap, with enquiring the other way around. It has to do with soul. Quantum Physics is not a proof of soul. It is a consequence of mathematicians having included soul in their mathematics to better describe the world. Quantum physics is a consequence of soul.

What would have happened if these early quantum scientists had added the humble Taoist approach to their enquiries? If they had accessed the capacity trained in the Sacred Feminine traditions to be with the unknown? As it was, they did not include their own soul, and when adversary came, in the sense of reality no longer fitting into their wave particle models, they did not show soul. They just went pressing on and telling everyone nature is a fool, makes no sense, is unpredictable like a woman.

Now is the time the Sacred Feminine is rising again. We are no longer abusing women and earth for being unpredictable and not fitting into the systems men thought out. We are enquiring into ourselves, into life. Now is a wonderful moment to go back to that time in history when the complex numbers were fully introduced. Let’s understand deeper what happened there, including everything we know now, and from that viewpoint check whether the conclusions these white men with their high hats and chainwatches made, would still hold today.

Klara Adalena, priestess and Dr. in theoretical physics