Geek in Practice

The past weeks I have posted some thoughts about math (here and here). At first, I didn’t know how to conclude the series. So I had chats with people around me to farm for ideas until I talked to my friend Abdulrahman Musazay (Physics major buddy all along) he reminded me of a theory we discussed with Dr. Fatah Khiari. That theory will be the focus of this post.

Undoubtedly, all sciences are interconnected, all of them. No wonder, after all, science is nothing but the deduction of human brain over the years. Let’s imagine all sciences as a tree. At almost the top of the tree, there is General Relativity and Quantum Field Theory from which we get Special Relativity and Quantum Mechanics. Those last two, we know, are the ascendants of Electromagnetism, Classical Mechanics, Atomic Physics…etc. In short, all Physics are one level lower than Special Relativity and Quantum Mechanics. Social sciences, engineering, medicine and all the other sciences all come down the line. So what’s on the very top?

First, let me explain how the tree is formed. As we go higher, we have more mathematical equations and less words to explain how these equations are related (concepts) and vice versa. By this, we can say that at the bottom come sciences that are only conceptual with the minimum amount of mathematical equations like Psychology per se. Let’s take Quantum Mechanics, for example, is always represented by few equations and three postulates that are written in plain English. As we go down the tree more concepts are introduced (Quarks, Neutrons, atoms, molecules, cells, organisms, organs, cultures … etc) which are just a matter of convenience to explain the equations above (so we don’t have to recourse the theories above).

On top of the tree, there is one thing. Something purely mathematical with zero concepts or postulates, something that every physicist dream of deriving but know that it’s underivable. Something from which everything else can be derived.

To put it in a way more familiar to the world, on top of the tree there is the theory of everything. This theory, has to be pure mathematical equations from which we can derive General relativity and Quantum Field Theory. As far as physicists are concerned, it is well known that there is something missing due the lack of consistency of the established theories we have so far. So what if this theory still have concepts within? Obviously, we will try to find a mathematical explanation to those concepts which, in turn, will lead us to a more fundamental theory. By deriving the properties of this universe, the properties of its inhabitants and their perception of the universe, one can derive the whole theoretical tree from these equations. One with infinite mathematical intelligence can only do that alone.

I used a very valuable source here.

Earlier this week, I posted a question that has been running through my mind for a while. I really appreciated the feedback, it was interesting and thoughtful. Thanks! In this post, I will try to quote the world’s most recognizable Physicist, Einstein, as he had many a say about the subject.

Einstein once said “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality”. Let’s take a moment and analyze. From the face of it, Einstein didn’t believe that math is what actually governs the world. But I think he meant something else. That is, math is too perfect to be applied into this imperfect world. Imperfections are always there to be added, that’s why we have perturbation theories, chaos theories, specified models, statistics … etc. In reality, most theories used in applied/basic sciences have things to neglect (reasonably and unreasonably). Heat in Electric Engineering is a good example. Also, we are trained to think in linear terms whereas the world has many highly nonlinear elements (in a strictly mathematical sense) and as any Engineering student can testify nonlinearity complicates problems exponentially. I think Einstein means that the world would be too easy to figure out if it was as straight forward as the Math involved.

“How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?”. I’m not surprised that even the world’s greatest minds are baffled by the mystery! He follows up with another question “Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things?” (here). Now that’s thought provoking! So what does all that mean? Would that mean that a child can comprehend the realities of this world? After all, children are the least experienced albeit being the fastest learners and most creative thinkers. Math is purely logical and is just a toolset, use the right tool in the right place and you’re set! (Thanks @TRBG for the analogy). Math has the ability to prove the most simple ideas to the most complex ones. From the fact that a straight line is the shortest way between two points to the fact that Euler-Lagrange formula is an optimizing equation. However, Einstein answered his own questions with the quote in the previous paragraph.

I would like to analyze a little bit more in Einstein’s thoughts but, alas, one post is not enough. Obviously, Einstein, being deeply into the world of Physics and Math, knew many things we cannot yet comprehend. He realized the deep connection between the language and poetry of science yet still bewildered by its most simplistic notions. Nevertheless, he conveyed the message ever so eloquently.

Yet still, again, he has one last thing to say “The most incomprehensible thing about the universe is that it is comprehensible”. Albert Einstein, you’re not making it any easier!!

Follow up post here

Any Twitter follower may have noticed that I have been tweeting about the strangeness by which our world works. How does the Mathematics that we logically deduct forces other fields to comply as an application. I understand that fact for fields that rely on statistics and/or simple math. But I’m really mystified how does old mathematical abstracts forces the most complicated Physics concepts to follow. For example, the concepts of curl, Boolean Algebra … etc.

Or is it the other way around? Do we model our Math to fit what we see? Four-vectors is a good example for that case.

As I’m writing this post, I’m having diverging thoughts on where to go next. Should I indulge myself investigating the nature of the fact? or should just go on with examples? In anyway, the subject is highly philosophical and is as old as the invention (or discovery) of math.

For all I know, as I have immersed myself into the world of physics, I was always taught a way where Math works perfectly. From the simplest ideas to the most complex ones, math has been always there. Can math go wrong? No, only us using it in a way that doesn’t replicate the subject at hand. There have been many examples where the math went wrong because of that (Blackbody radiation problem, for one). After all, when we used the right maths, it, not only solved the problem but also, propelled our advancement into a certain field (in case of Blackbody radiation problem, it lead us to Quantum Mechanics).

So what does that mean? Is Math a universal truth? or do we only portrait it this way?

I’ll try to investigate the subject more. I have already ordered Mario Livio’s book “Is God a Mathematician?” and I’m waiting for it to come. For all those who are interested I suggest they’d read the book (Courtesy: @MaanMH)

What do you think? Please contribute, I would love to hear(read) your thoughts! you can read part two here and part three here

PS. I’m hoping this is not just another false start to blogging!