There is something pretty cool about numbers; it is that everyone knows what they are. I don’t need to explain what numbers are to you; you’ve undoubtedly used them before. Numbers are surprisingly useful and that’s what is important: their utility. But, what are numbers? Are numbers Real? Those are questions a mathematician doesn’t need to ask and really, neither do you; unless you are a philosopher. Those questions are metaphysical questions, more precisely ontological ones. This however won’t be a journey into mathematical metaphysics but rather a synthesis. I shall tell you the story of Gods; Gods that you already knew but maybe have never thought about it in these words.
If I ask you, are numbers real? There are three possible answers to that: Yes, No, Sorta-ish! Yes numbers are real, how else are we able to use them, better yet- I can write them down and show them to you before your very eyes. Lol, I was just playing with you. No numbers are real, they are imaginary. We think them up and agree on what they look like. I can write something down that’s a number and you would have no clue what it was unless I told you. Finally we can say that numbers are kinda real, they are the combination of something real and something imagined. We imagine them up and then use them to do things – certainly what we do is real. You can have arguments for and against any of these three possible answers, which begs another question. Is any of this questioning relevant? Welcome to the world of Meta (meta-world); where nothing makes sense and there are more questions than there are answers. It is a hard world to consciously navigate through and that is why your brain does things for you without your awareness. We were born with a number of pre-established reflexes. These reflex responses aren’t something you are aware of but they constitute your very survival to its core. This is where I begin to lay the foundations for the synthesis. These reflexes get us started on the journey of survival. As we interact with the world around us we integrate our pre-established reflexes into some social context. So, whereas one might have only been concerned about eating apples, they may later wonder where apples come from to begin with. As we grow our brains develop and integrate itself with more complex patterns we encounter. From eating apples to wondering where they come from. Why would anyone even wonder where apples come from to begin with? Well for one, they weren’t hungry for sure; otherwise they’d be eating apples instead. Apples however, had to be present in that persons range of interactions none the less. The response I have for why would someone even wonder that, is the same response to the question: Is any of this questioning relevant?
There is a lecture series by Jordan B. Peterson on YouTube: Maps of Meaning. His fifth lecture for 2017 class, titled Story and Meta Story (Part 1) is more or less what I’ll be drawing on to explain the peculiarities of what drives someone to ask questions like: What are numbers? Are numbers Real? At this point I’ll relay to you a story about a cat with no brain. As Patterson describes it in the lecture, you would remove the entire brain of the cat except for the hypothalamus. Such a cat if surgery was done properly can still, “eat, drink, regulate body temperature and engage in defensive aggression.” Said cat would also be hyper curious or as Patterson puts it, “a cat with no brain is curious about everything”. In that statement lies a nugget. Curiosity is deeply embedded in not just human evolution but animals even older than us. What we do as we grown up and encounter the world is learn to ignore things; by that I mean we learn things and because we’ve learnt about them, we don’t have to be curious about them. You were taught how to use numbers and I’m sure you use them well. As far as you are concerned, the functional application of numbers or your use of numbers represents the reality of numbers. So numbers are real once you don’t think too much about them and just use them. Asking questions, is like striping away the cortex from your brain; it forces you to unlearn things and this makes you again curious. Since you haven’t actually stripped away your cortex, questions are tools your said cortex came up with to achieve similar enough an effect so you can experience wonder. You not just want to eat apples; you want to know where apples come from. You not just use numbers; you want to know, what are numbers? Questioning is relevant because it serves as a reminder about something we’ve learnt but can no longer see. Since the world changes, it is prudent for our very survival that we often take another look, and questioning things helps us do that.
On the other hand, everything can’t be relevant at the same time, it would be too overwhelming. Imagine if you could hear all the sounds around you; see all the colours, smell all the scents; feel all pressure fluctuations on your skin; taste the very air you breathe, and that isn’t even close to everything. Immanuel Kant called the world of pure sensation and no filters of perception, the Noumenal World. This would be the world if we could see everything as it is; if our minds were unhinged so to speak from the doors of perception. Perception only lets some light through but to really kick that door down would be a real eye opener. Now, whether or not you might think kicking down doors of perception and seeing everything as it truly is, would be something you really want to do is an issue on its own. An issue I’m going to jump right into. This is the issue of Values. We do not just live in an ecosystem; we also live in a value system. So along side this world of pure sensation (the Noumenal World) we have an inner subjective world, the world of personal values. It is your value system that determines what is relevant. What you see is mediated by your social environment. Just as how you are born into an ecosystem, you are born into a value system. It is this value system that determines how you answer the questions: Are numbers real? It is your value system that determines if you want to see everything as it truly is or not.
A summary of what I’ve outlined so far is that, your exposure and learning for the most part serve as limits to your curiosity. Curiosity itself being an animal instinct. While on the the internal side of your person, the limiting thing to what appears to you as significant is Values.
Here begins another trip. This one involves a story about eyes. How do you decide what to look at? The answer to that question is simple. You are told. Your eyes dart around in your head and looks at everything in its line of sight, so I don’t mean told in that sense. If you are a female baby, you would look mostly at faces; a male baby would look mostly at inanimate objects. Most of all though, a baby can only look at what is before them and what is before them is put there by people that are usually older. Your little baby eyes might dart around rapidly, but once your head is aligned you only see what is ahead. You see in the direction you are walking towards. But a baby can’t walk first, they are carried. You might be carried facing up, your eyes fixed towards the heavens; you may be carried facing down, eyes towards the earth; you may be carried facing forward to where your mother or father is walking; you may be carried facing backwards. You can look to the heavens or look to the earth for answers; you may look to the future or to the past for directions. Which you choose are the ones you are told are best by those who have lived longer and birthed you. Just as how your eyes and head are moved by the history or your biological evolution, so are your values shaped by your cultural history. We are embedded in a value system based on prior negotiations of our ancestors. Those that survive pass on not only their genes but also their values. For Kant, the nominal world was the Real world, everything else was appearances. He valued seeing it all more than seeing only a little. Having more eyes or more faces would mean you can see even more and value more. Those who have many faces and more eyes than to norm implicitly tell you what they value- They want to see more, know more. The third eye sees all. Three was the symbol of plurality for the ancient Egyptians. God had three aspects for the later Christians, the face of the father, the face of the son and the face of the ghost. The Pythagoreans valued the holy four, and from the four the Hebrews had the Tetragrammaton (Ten); systems of values. Note here that when I begin to talk about many faces and many eyes I’m being symbolic and not literal. This symbolic shift is an extension of the literal into a more abstract representation of reality. Where as two eyes represents the real world, the third eye is an abstraction to seeing more. Where as the family was a real thing constituted by mother, father and child the symbolic abstract extension of that is a Triple God. The thing that I’m then introducing here is symbolic abstracts and its relationship with numbers.
For ancient cultures, numbers were the realest of things because they were useful. The Rhind (Mathematical) papyrus which dates back to between 1650 BC – 1550 BC and in turn was a copy of the teachings passed down from the Twelfth Dynasty of Ancient Egypt is said to have these words written in it, “Rules for enquiring into nature and for knowing all that exists, every mystery, every secret.” What are numbers? For the ancients, the answer was simple, numbers were Gods. Numbers were eternal and unchanging, yet they manifest in many forms: two apples, two arms, two eyes, two legs. With so many abundant forms, man was still able to inexplicably perceive Two (2) out of the many. Numbers to us (modern man) are merely abstractions; patterns we notice within a myriad of things and capture them in symbols. It is this symbolic world I refer to earlier as Meta. You enter the meta-world by stripping away what you’ve learned by asking questions, so you may see everything as it is. Ask enough questions and all will be revealed to you – well sorta. What is revealed must also work in this world. So numbers work, so are numbers Gods or are numbers abstractions? I can answer that question, easy: those are the same thing – gods are abstractions. Where as man no longer symbolically represent mysteries in terms of Gods as the ancients did but we now represent these mysteries of nature in terms of Numbers. The utility the Ancients represented found in the abstractions called Gods we now represent in the abstractions called Numbers.
The meta-world is a world of the ineffable; it is the weird world of the human mind that is older than language and even numbers. The meta-world is where one becomes all and all becomes one. The meta-world is beyond the senses and where you find more questions leading you deeper. It seems boundless, it is maddening, and it is dark. The meta-world is where one goes to fish for new understandings, to figure out new ways to use numbers, to figure out things generally.
Metaphysics is the dragon of the intellect; it is both dangerous and bountiful. It is the dragon with the gold and you must enter its leer and bring back treasure for the benefit of humanity. If you are not careful you may be trapped in the meta-world; lost. Earlier I asked how do we decide what to look at? The response to that was, you are shown things to look at. Well, in the meta-world where you see all, the more appropriate question is how do you decide not to see everything? How, do you close that third eye? The meta-world has no values placed before you; all value must be taken upon yourself freely or created. If the treasures you have garnered from the meta-world helps you survive, you may place them before the youths of the world. But first you must get out of the meta-world. One such means of getting out is being able to articulate oneself. Words become the gateway between worlds; language become tools of escape. Through articulation one can move from the abstract to the practical; the metaphysical to the physical. Mathematics is one language that can help us bridge this gap. Numbers are units of information we throw out to each other. Math is not just numbers but a system of using numbers to communicate precise ideas; more precise ideas than words can. Not only can we reduce abstractions into words in a qualitative manner, we can also reduce abstractions into mathematics in a quantitative manner. So then we can say that numbers act as a means through which we can communicate about ideas that have no direct analogy in human experience.
Another way of leaving the meta-world is through values of convention, you hold tightly to the values that you were instilled with and you will be carried back on a well travelled path once you hold onto those values. You see, our cultural systems are designed to keep us safe from the overwhelming effects of the noumenal world; they tell us what to look at so you don’t get overwhelmed with seeing everything. They simplify the world. Mathematics and languages in general simplify the world. So when we ask questions like, are numbers real? Those that answer Yes, value the world of abstraction as the Real; those that answer No, value the physical world as the Real; those that answer Kinda, see both worlds as having their own merits-you value the many than the one. The meta-world is dubious and you may slip into it unknowingly. Questioning reality is undoubtedly one sure way of slipping into the meta-world. As Peterson would put it, the meta-world of abstraction is not separate from the world of the body, our abstraction are played out in our actions. The functions of numbers are their embodiment – things are real insofar as they are functional. Questioning the value in social conventions is surely another way of kicking down the doors of perceptions; making everything relevant, curious and wondrous. When one asks of themselves enlightening questions, enlightening things happen. But be warned, to go deep into the world of abstraction is to risk being burnt by the dragon. Some may themselves become dragons. Regardless, in the fires of life we burn so others may survive.