Disclaimer:

1. This topic is a little meta, and as such, you’ll have to provide some grace to some of the circular reasoning. As a consilation however, if you can make it through the article, hopefully I can have helped you understand why circular statements happen in the first place. Think, “with only a ball, how does one explain what a ball is?” and you’ll understand a bit of why I must be crazy for even attempting to ask these questions…
2. I am not a mathematician, philosopher, nor logician and none of the claims made in this article have been reviewed by such. So…
3. Have fun, and explore with me and…
4. Dont be afraid to be critical, but…
5. If you dont have the time or patients to read this all, scroll down to the TLDR; and just get it over with already.😅

Ok. So, the title was a bit hyperbolic, but the thought which I plan to detail is quite profound — I hope, in fact, that by the end of this article, you share the same giddy “I see what you did there” smirk I had when the thought came to my mind.

So, what the hell am I talking about? Well, I’m glad you asked. But full disclaimer, I have to take you on a bit of a journey first. (Sorry)

So, what the hell am I talking about?

How We Got Here

It all started with a crazy conversation with a collegue at work (shout out to Jake) about the axioms of mathematics — moreover, the assumptions made when dealing with more advanced forms of maths such as calculus.

We explored the possibility that perhaps at the limits of an infinite function, things don’t behave as expected based on the observations which led us there. I’d brought up the fact that even in reality, the assumption that the quantum world bahaved like our physical one, for a long while kept us from seeing it in the first place. So then, perhaps it stands to reason that when you take a function into infinity, something quite strange and unexpected should happen.

Xavier, to the other side of me, laughed at Jake’s candor to entertain my silly thought experiments. He, for (lets be honest) good reason, pointed the both of us to an article detailing the axioms of mathematics and the basis upon which they were formed, and simply remarked “Jamel. Why do you waste time with all this theoretical ________ (I’ll let you fill in the blank)? Why don’t you use your talents to do real math?” (…really. It sounds worse then it really was) We all laughed, said a few more words; then put on our headphones, went back to work, and said nothing more of it.

Why do you waste your time…

But then the next day (or couple days, idk, I’m not good with time), Jake came to work and brought up that conversation we had yesterday (the other day?). In any case, he said that it reminded him of this book he’d read (been reading? 😅I’m terrible at this). The book was essentially a pragmatic deconstruction of the axioms and tools of mathematics. I presumptiously asked “You’re letting me borrow this?” to which he replied “Uh. Yeah. Sure.”.

I’m still not sure whether he intended to give me the book, but I’m sure glad he did. I dont know about you, but I have these moments in life when I’m given a resource which enlightens me in the very best way — and all the things that I’ve been thinking about and toying with in my head are suddenly given names that I can comprehend, and my excitement is, perhaps embarassingly, uncontained. Thank god there was no one around. Because I certainly was not running around my apartment and jumping on my couch like tom cruise circa katie holmes. I can guarentee you, I’m not that crazy.

So, to wrap this all up, all of this: the book, the conversations, the Jake and Xavier; all of it, gave me so much to think about. My weekend was consumed with thought. And during this session with myself and my journal(s), I started theorizing how it is that one could construct maths from the ground up, not assuming anything sourced from the current axioms of mathematics.

What does that look like?

I have no clue why I always choose the hard questions…(ok. maybe a little crazy) But truly, after being given this book — aside, its called Concepts of Modern Mathematics by Ian Stewart — I finally felt like I had the tools to attack such questions. So, thanks Jake, I owe you bro!

Ok. So now I’m rambling…

The Good Stuff

“ … how [ could one ] construct maths from the ground up, not assuming anything about the current axioms of mathematics ”

So the hardest thing about trying to answer this question was, “What tool does one use to establish an axiom?” Then, “If a tool is established, on what grounds is the tool itself reliable and valid?”

Hmmmmm…..

Ponder, ponder…

Think, think, think… 🤨

This was a tough one for me too. Primarily because, anything which one could use, also requires that it too be proven in much the same way as the thing which one is attempting to establish.

A good way to think about this is to imagine you have been given the task of measuring paper. What do you use? You might say something akin to “Well, I’d use a ruler.” Which, at first, seems self evident. However, in order for a ruler to be reliable for measuring paper, there is a basis upon which we can establish that the ruler is valid and reliable to do the job. In the ruler’s case, there are standards boards which we trust to provide us with said basis, and it is given from them a set of promises:

That…

1. Each unit of this tool will be consistant and equal given all intents and purposes of the tool (namely, measuring things which can be marked by one of the tool’s measurements)
2. Each measurement will be marked in a repeated and predictable pattern.
3. 2 marks of the same length (l) represents 2 marks which are of a distance (d) apart from one another equal to a magnitude (m) of the space between 2 adjacent marks of the same length (l).
4. …

I would go on, but you should get the point. There must be a contract, by which, all participants, both in the creation and utilization of the tool, must agree.

But how does one come to an agreement?

Well, this was the largest thought chasm for me to traverse — so get ready, it’s gonna be a bumpy ride.

So to assume that one can just start spouting words and concepts and simply establish that it is true, is a fools errand. To do that, is to assume that words themselves are self evident — and I take quite alot of pride in letting you know that they are not. Words, by design, are not self evident in fact. Their very nature is requires participants that have an ability to declare and interpret them.

We only even use words to express an experience not currently present. In order for this mapping to occur, it requires assumptions be made on behalf of the participants. For instance, both participants must assume that they both know and have heard the word in question; that when transferred from one party to the other, the word holds the same meaning when interpreted; that both parties have the ability to see/hear the word to a standard that they can agree is substantial for interpretation.

Words do not provide the necessary atomicity to reliably be the foundation for anything ; not without introducing at least some level of ambiguity (which we can’t have).

The reason for this is because in order that we construct our axioms, we must first establish a truth that upon observation is always true.

It is not always true that the participants both know the word. It is also not always true that the word will always hold the same meaning between participants. And it most certainly isnt always true that both participants possess the necessary ocular or auditory acuity to adequately see or hear the word declared.

… get ready, it’s gonna be a bumpy ride.

(Sorry this is soooooo long. But I promise we’re gonna get there. 😅)

So, we’ve established that we cannot use words. Ok, but what can we use?

Well, I gotta warn you, this is where it gets a bit meta. Because it all boils down to the thing which the words are ultimately describing — and that, of course, is the actual, real objects in our world.

But, before you get ahead of yourself, this is just the start. Because, even the objects move and change. Thus, even they cannot reliably be used to justify an axiom— not by themselves anyway. And this, because of all the same reasons stated above.

It was through this process that I discovered (or at least encountered mentally) t̵h̵e̵ ̵f̵i̵r̵s̵t̵ ̵c̵o̵u̵p̵l̵e̵ ̵a̵x̵i̵o̵m̵s̵ ̵a̵b̵o̵u̵t̵ ̵a̵x̵i̵o̵m̵s̵ the first axioms of origination (we’re still working on the name). That being:

1. There exist one or many axioms of everything, upon which all other axioms can derive.
2. The elemental basis upon which these atomic axioms are formed, must be constant and unchanging.
3. There exists constants which are unchanging.
4. Given the axiom’s atomicity, a constant therefore must be atomic.
5. To be atomic, is to be self evident.
6. A constant, then, is self evident.

Ok. Good. Now we’ve gotten that out of the way. The rest should be easy then 😉. So this is where I spent the most of my time, consumed in thought… deep in the rabbit hole now.

Because, when you think about it, there is nothing in this universe that I can imagine that does not change; which makes absolutely everything in the universe absolutely unreliable for our purpose 😒(Except certain forces, but more on that later). It started making me wonder what the hell kind of question I even asked… Is there anything that comes to mind for you?

…

……..

Yeah. At first me neither. Until — of course — I did! lol (← — shameless). And ironically (coincidentally?) it was one of those things that was clearly written on the proverbial wall, I just wasnt choosing to look at it. Most people probably wouldn’t but, it’s hilariously obvious.

The easiest hint I can give you, is to think about, what, in all of this article, is constant? In me writing this; you reading it; the axioms; the words; the theories… What, in absolutely all of this, is constant and self evident?

I’ll let you ponder a little bit more on that before I spill the beans.

…

…….

…………

……………….

Ok. So before I say it, I’ll start by quoting the guy who immediately came to mind upon making this (self-proclaimed) discovery. And thus, no man ever said it better, for:

“I think, therefore I am.”

What a statement, right? It was after this process that I wondered if Descarte thought about the same things as me; If he’d, perhaps, gone down the same line of deductive reasoning as I? Wouldn’t that be something?

Anyway, If you havent realized it by now, the constant to which I am referring is self. One’s being. That which one would call “I”.

Sound crazy? Well, think about it. The only thing one can reliably validate is himself. In fact, without this self validation, we cannot establish existence at all. Which, if you havent noticed yet, is all one is ever really trying to do when it comes to numbers, logic, and philosiphy. One is establishing existence, and measuring one form of existence against another.

And, I know… its like “Duh, of course I exist.”. But if you remember correctly, that’s exactly the sentiment you should have. The tool we’ve been looking for all along required a very particular property of being self-evident — self being the optimal word here.

This is very imporant, because if one were to, say, make it such that absolutely anything else in the universe was the object of self evidence — the color green perhaps — that would imply that he himself was a member whose definition is reliant upon that “self-evident constant”. This, on its surface, presents no issue. Until you consider the one declared green’s self evidence.

What do I mean?

Well, if an agent theorizes that he himself is a relative member of observation, then the agent himself cannot be the source of said truth. Perhaps what he says may be true, but we must consult with the thing he declared to be self-evident to know whether its true or not. Thus, the agent is a member, and nothing more.

Put simpler, if someone were to profess to me “People are stupid”, this would require simultaneously that the agent delivering the message is not a “person” himself. Because, if he is a person, then he too is “stupid”. Which would make his analysis of intelligence invalid.

These types of paradoxes arrise from the fact, that you have not established self as absolute. Establishing this is key, it allows us to see the agent as a constant which is separate from logic and evaluation. Moreover, it allows an agent, who is acting as a member of a set, to make statements about his parent set whilst detaching himself from the property given that set. The statement “People are stupid” only makes sense if the agent is self-evident.

Thus, we can establish a few more axioms:

1. Arriving at a paradox in deduction is an indicator that the thing being described either:
   1. Does not have enough information to form a valid conclusion
   2. Is self evident.
2. Descibing oneself is paradoxical. Self cannot be defined without also referencing self in its own definition.
3. Without self, there is nothing to deduce.
4. Self is Self Evident. I am I.

And that last bit is whats most important. The fact that self references itself, and can express that it is. This brings us to the long awaited TLDR;

TLDR; “I AM I.”

So, I know, I know… much ado about nothing, right?

Well, actually, yeah! What did you think? I mean, seriously… sixty-six and a sixth percent of the title literally was a 0. 😅 What did you think this was about?

All Jokes aside, the statement “I am I” is far more interesting then you may be giving it credit for. By establishing this statement as true, we have determined:

1. “I”, or that there exists a symbol which acts as a mapping between actual self and abstracted self.
   But more importantly the fact that…
2. “I am”, or that “I” has the ability to “be”. And, that “I” by itself is meaningless without this ability of it to exist.
   And,
3. “I am I”, or that “I”, in its existance, is itself.

So what does this all have to do with the title anyway?

Nothing!

No seriously. It has to do with “nothing” and what it represents (you like what I did there, huh). The idea of nothingness, arises from some thing being observed yet it is immeasurable. Like the space between two points at the same location; or the brightness of outer space. We attribute the number 0, to concepts which are observed yet immeasurable — or in otherwords, things which are self-evident.

Thus, if I were to attribute a numeric value to represent self, the most natural value to represent it would be the number 0.

With a mapping for 0, let us now scruitinize the nature of equality. Equality, at its root is simply an agreement — one which follows that a unit or set of units are the same given their countable measure are also the same. Thus, to say that something “equals” is to say that something “is”.

And so, the statement “I am I” is functionally equivilent to “0=0”.

The implications of this is truly amazing and bizarre. To agree with this, implies that all things are described by its relationship to self. That all things in existence can be infinitely derived from self. And most strangely, that perhaps all constants, such as gravity or pi or plancks constant, all of them are simply instances of the self that have been abstracted away from your direct view. (More on all of this in my next article).

Actually, I want to explore that last one a little bit now before I forget. Read at your descrection.
So, think about it, defining constant forces relative to self is truly the only thing which makes sense in the grand scheme of things. It also simplifies what they truly mean into something more tangible. For instance,rather than interpreting the speed of light as some ridiculous number which has no meaning aside from what we derive from it relative to other numbers. It can be better defined by the thing it affects for the observer. Namely:
Light is the limit by which an oneself can observe and measure all things.

This fits into the model that time dilates the closer you get to the speed of light because time is a biproduct of the fact that we sense light, and our ability to sense time is determined by the size and frequency of our mental frames of this light. There apparently exists a limit, at which point both a stationary observer and the light speed observer both cannot determine the light speed observer’s existance. This is the moment when time stops for the light speed observer.

Using that model, we can extend the idea for gravity perhaps. It could then be defined as:
Gravity is the limit by which an oneself can exert force.
etc. etc. But we can talk more on this in another article.

But to bring this all to a close. Zero is interesting. It is important. And it means far more than nothing. We came to these conclusions by throwing out preconceptions and acting atomically to form our own conclusions based on our observation. Maybe now I can take Xavier’s suggestion and do some real math. 😂

If I’ve done my job well, then you will either walk away from this article completely enlightened, or you will have experienced first hand how fake news is made. 🤷🏽‍♂️ You decide… afterall, thats what this was all about in the first place. Anyway, I hope you enjoyed, and until my next thought.