Suppose you wish to write a simple document -- a memorandum, an essay, a set of instructions for your family or staff, etc. But you cannot write it solely in English.
To say the ordinary things you wish to say, suppose that you must resort to French for one or more of the sentences. And, for one or more other sentences, you must resort to German, Italian, Spanish, Hungarian, Russian, Chinese, Japanese. Tough toenails, huh?
Fortunately, you can avoid all this by resorting to your familiar English.
Well, that, currently, is the burden of any student or mathematician or physicist or engineer who wishes to use the language of quantum theory -- a giant algorithm for solving the kind of problems that have produced the laser, transistor, microchip. remote control, and other goodies that make our life easier and richer.
To "speak QUANTUM", you must speak in numerical algebra, trigonometry, linear algebra, differential equations, vectors, tensors, differential forms, group theory, Lie algebra -- to say the least. That's horned toenails!
There's an event described in The Bible (Genesis 1-9) that sounds like this latter case. In Babylon, on the plains of Shinar, descendants of Noah (whose Ark survived "The Flood") began to build a great tower, "to reach Heaven". But Jehovah, angered, confounded these builders of The Tower of Babel. Each builder began to understand and speak a different language than another. They could not communicate and work together, so the building stopped. Then these people were scattered over the earth, seeming to explain the plurality of language over the earth.
Thinking of this story, people often have spoken of the "babelization" of language.
That is what has happened in the "quantum" case: babilization of mathematical language.
Yet, all this is as unnecessary as trying to write a simple document in all those languages described above -- English, French, German, etc. Just as you can use a single language, English, for your purpose, so THERE IS A SINGLE MATHEMATICAL LANGUAGE THAT WILL DO ALL OF THIS!!! -- AND MORE!!!!! It's usually referred to as Clifford Algebra, although I prefer to refer to it as The Arithmetic of Clifford Numbers, since it is simply a natural extension of the arithmetic of natural or counting numbers.
It took me 35 years to learn its essentials, after I first heard about it while an undergraduate physics major (with equivalence of math major) at Columbia University. At first, I found it difficult to understand. Then, one evening, in a flash, I saw how to derive, on a level of high school algebra, the multiproduct (Clifford product) that is unique to it and gives it the power that no other math has -- subsuming at least 25 different fields of math!
But, as I note elsewhere, I have not been able to get an editor to read through my simple derivation, let alone publish it, so is not a problem involving the MESSENGER (moi), but the MESSAGE-- since many have tried to break through this censorship.