There are certain concepts that are enormously and startlingly important, but no one seems to pay attention.
One of those things is language. And by language I don't mean french or dutch, although human natural languages can be included but what I mean when I say language is any arrangement of other primitive concepts that would enable you to communicate another concept and draw conclusions.
For example, numbers, different civilizations adopted different ways to express numbers.
But only one of these "languages" prove to be powerful enough to meet the needs of humanity.
Sure you can express numbers by Roman Numerals, or by Indian Numerals, Let's consider Roman Numerals, since, we have been told Romans had such a great "empire".
Try to multiply two Roman numerals, say MCMIIX and MMCXV, , the rules of a the game is you can not use any thing but Roman numerals to carry out the calculation.
It's very difficult to carry out this task.
Now let's do the same thing using Indian Numerals, (Notice, there is no such a thing as Arabic Numerals, Indians came up with it, and Iranians communicated it and expanded on it)
The rules are straight forward, and there are even ways to do speed calculations.
Another example, find the root of a quadratic equation, two languages, Algorithmic, and Algebraic. Needless to say, Algebraic formula is much more powerful, its power is revealed when you consider how you can simplify it, how you can use it to find sum and product of the roots.
While the Algebraic language is more powerful in expressing simple functional dependencies, there are other areas that it reveals its limitations. Suppose you want to explain the intricacies of chaotic systems, cellular automata, game of life or things of that nature. The Algebraic language falls short and the Algorithmic language shows its strength and flexibility.
Is there another language there ready to be discovered ? We look at the nature around us, and we see things, and we understand its beauty and universality but we can't find, express or use the universal principle behind them. Machine vision provides examples, so does the field of human natural languages.
There might be a new language needed to describe non-locality, the entire mathematics is based on the principle of locality. That what happens here and now, only depends on what is happening at that point or in some point in the past and some far place.
Do we need a new language to describe things that happen simultaneously and quite possibly affect each other at the same time ?
Some of our most difficult problems of science and technology could be simply hard to solve, because we are using an incorrect language to describe or to approach them. Just like we are trying to multiply two numbers that are described with Roman Numerals, rather than properly by Indian-Iranian numerals.
Mathematics is described by symbols, and by relations between those symbols. Is this the right language for every thing ? Is it possible to describe Mathematics by a totally different language ?
Could that language accelerate understanding and reasoning, concluding and producing new concepts, faster, easier and deeper ?
How about organization of ideas ? Is there a new language that allows you to describe the "totality of this situation" without attempting to look at parts to combine and get the "whole" ?