Universal Languages Introduction

By Tomislav Tomšić

Science’s goal is to explain everything using as few assumptions as possible, so that anyone can print it on one’s t-shirt, as popular understanding goes.
From the point of view of Mathematics, that goal is already achieved... And we need only one concept.
So… Why don’t we use it?
Easier said than done. We use numerous ways to represent said concept, furthermore, we constantly devise new ways of representing it; and all of them have their use.
Is that a problem?
Let’s try it this way, we can not solve a problem that we are not able to conceptualize. Immediately it follows that better our conceptualization is, better are our chances of solving any problem.
Am I implying that all we have to do, ever, is to find appropriate representation of fundamental Mathematical concept, mentioned above, and we are done?
Or should we try the opposite? To try to find the best possible one for all cases?
Whatever is your opinion, we do not use it, though there are immediate benefits.
This book attempts to show few.

• Language: English
• Publisher: Lulu.com
• Release date: Jun 9, 2017
• ISBN: 9781387028573

Book preview

Chapter 1.

Why can't we know everything?

At a glance that question is easy to disregard. After all, it is a badly formed one, because it implies that we can’t, indeed, know all. Hence, let’s dare to correct that and ask, can we know all?

Now what?

How can we even attempt to answer it? What knowing something actually means? Don’t let yourself be swayed by its seeming simplicity, it is a deep question, and thus, one vast in its consequences. Having thought about it, I see no wiser course of action but to limit ourselves, hopefully, only temporary, to knowledge that we can rely on, i.e. facts.

Immediately we can see where that realization leads us. Reliable, or practical knowledge to us is synonymous to scientific knowledge. I’ll take that at face value, if you are confused by that, I invite you to find out more about scientific methods. Going deeper into that subject is outside the main scope of this introductory text.

Again, what now? Do we have anything useful to continue on?

Presumably, if one wants to know all scientific knowledge, one has to start from one science, learning all there it is to it, and then move to another, than another…

It doesn’t seems feasible, doesn’t it?

Our best minds tend to specialize, which is to say, to know more and more about ever decreasing scope of reliable knowledge, and now we are suggesting precisely the opposite. 

But what else could be done? Indeed, that doesn’t seems feasible course of action because, at the end of it all, we live so shortly. Imagine, if one decides to concentrate fully on Chemistry or Physics for instance, then one would, presumably, also need to keep up with the all the new knowledge generated daily, while also learning new science. How many sciences are there anyway? Again, it doesn’t seem feasible, doesn’t it? Who has enough time, not to mention sheer mental power? 

Furthermore, what about technology and mathematics? They are reliable knowledge too. When will their turn come?

Conceivably, can’t we understand those as different perspectives on the same subject? Shouldn’t practical and theoretical knowledge go hand in hand? 

Judging by the efforts in our ever evolving educational systems, answer is yes.

Apparently, obstacles to our current approach appear increasingly insurmountable, therefore, it is time to try a new one. What are we trying to do? What would be ideal goal of such effort?

To learn everything factual that we collected over the millennia, and then find a way to pass all of that knowledge in more efficient way? While staying in touch with all new developments?

Again we are staring it the same obstacles, our new approach is not new enough...

Or we could stop laying to ourselves.

Demonstrably, there is nothing wrong with how we gain new factual knowledge, though I am sure it can be further improved and perfected; which leaves us with unavoidable conclusion. 

There is something wrong with how we represent it.

Which leads us to what, exactly?

Don’t get me wrong, it does seem as a sensible conclusion, self-understandable even, but how can we use it? How can we build upon it?

In my knowledge, there are only two general paths we can take on, in order to solve any problem, after making sure that we are, indeed, dealing with the problem not its consequence. 

First approach is to acquire facts and follow where they lead us.

We already tried that. And I do not see how it leads us to an answer, probably I am just not smart enough. 

Second approach is to imagine an ideal, perfect solution and the n backtrack from it, to determine what needs to be done in order to achieve it.

I hope it is obvious how those two are not mutually exclusive, quite the opposite, they should mutually enrich each other.

Therefore, what should be our ideal solution? What should we ask specifically? Perhaps… is there a concept, an idea if you prefer, that can be whatever we need it to be, but also a practical one, that has its rules we can then rely on, and use?

Seems too much to ask?

Well, it isn’t. There is such a thing. Unsurprisingly it is a root of Mathematics itself.

Remember that old aphorism that Science’s goal is to explain everything, but with so few concepts that one can later put them all on one’s t-shirt?

Well, Mathematics has done that already, and there is a need for only one root concept from Mathematical point of view. 

We just never bothered to apply it on the subject at hand.

Chapter 2.

Set. 

That is the concept I was referring to. Immediately we see how our previous line of reasoning can be made more straightforward. For instance:

Can we know All?

Whatever All and knowing are, we can circumvent those deep problems with the observation that our accumulated factual knowledge constantly increases, therefore, it is increasingly inaccessible, or not accessible as we would wish, hence our problem must be how we represent said accumulated knowledge.

And who is responsible for representation of our rational knowledge?

Mathematics.

Which is another problem, isn’t it? If there is an epitome of inaccessible knowledge, we need to look no further than Mathematics, I think most of us would readily agree.

Indeed, it is easy to quip something along those ancient Archimedes’ words that there is no King’s path to Mathematics, but does that mean we shouldn’t ever try? Not even today?

Except that we did. Repeatedly so. And yet, here we are, despite the effort of so many Sciences and other rational disciplines that constantly re-think and re-question their basic concepts and the ways they represent them, we are still in the same place with Mathematical notation.

Is it tradition, or should I say traditions, main reason why we