Part 5 - Theory of Everything

For several decades, physicists have worked to reconcile the theory of the small (quantum mechanics) with the theory of the large (general relativity). This is their effort to arrive at a Theory of Everything (ToE). They themselves can best explain the intricacy and complexity of this effort, but such a unified theory would offer an incremental leap in our grasp of the broader universe and perhaps even our mastery of space and time.  

Quantum Mechanics

General Relativity

I propose that for us to have a ToE, one that can truly explain absolutely anything, we need to draw on the amazing contributions of physics but also go well beyond this particular science.

What it will take

First, to arrive at a ToE, we have to account for all theories that we have ever come up with.

 Not just in modern day times, but going back in time to the earliest, most fundamental forms of thought and insight. We have to account for everything that humankind has formulated and grasped in its history.

Second, we also have to account for things we have yet to know, that is, the unknown, and the theories we have yet to formulate to help us grasp these unknown things.

 Our world, our universe, and well beyond, consist of so many things we haven't yet discovered. Things we may have no inkling about whatsoever, yet. Things that we cannot even dare to imagine, because it’s the unknown-unknown.

Let's pause a moment, and think about this:  A ToE, by definition, must span all fields of knowledge.

(image credit)

In Part 4, I introduced my Tripartite Model.  Here, I propose that all fields of knowledge fall under the broad categories of science, art, and religion.

• Diverse disciplines such as (but not just) medicine, mathematics, and geology have a play in this (Science).
• Diverse arts such as (but not just) film, poetry, and theatre have a play in this (Art).
• Diverse sectors of theology such as (but not just) Christianity, Judaism, Islam and Hinduism have a play in this (Religion).

So in my conceptual framework, the Tripartite Model is a step toward, and is a part of, the ToE.  

Now if you think this is a phenomenal, maybe impossible undertaking to collate all known theories, think how much more complicated and daunting it is to account for things these storied, sacred fields have yet to discover, grasp and formulate.

I propose that while this is indeed vastly complicated, it is very possible to truly come up with a ToE.

My equation for a Theory of Everything

This is my working equation.

This is a work in progress, which will take many years of undertaking. But I hope to finish it, before the end of my lifetime. Otherwise, my daughter will inherit thousands of pages of notes, and I will task her with something that may bore her silly!

So this ToE accounts for both known (i.e., already formulated) and unknown (i.e., yet-to-be-formulated) theories.

Unpacking the equation 

In terms of quantity, Tk is an awesome but finite figure.

For one, Google is well underway to making vast amounts of information accessible online: from their Books Project, to their Art Project. So technology and engineering have already been laying the platform for Te.

Mathematically, a geometric progression (as opposed to an arithmetic progression) and the Fibonacci Sequence give us clues, I believe, for how to scale up our efforts and extend reach, in order to account for and synthesize (if only in part) vast quantities of theories. 

I also think that a Mozart Opera gives us clues for how to do this.  Which I'm working on. 

Tu, on the other hand, is an infinite figure.

Accounting for all things we have yet to know and for all theories we have yet to formulate to grasp all these things pits us, I argue, face-to-face with the infinite, the uncertain, and the unpredictable, too.

This is so enormous and so complicated of an undertaking that most likely some of us go about our lives and our work thinking that what we know is greater than what we don’t know, that is, as if this were true:  Tk  > Tu.

Or alternatively we may believe that we can arrive at a ToE, based simply on what we know, that is, as if this were true:  Te = Tk.

In actuality, Tk  < Tu and Te = Tk + Tu are true.  What we know is so infinitesimally small compared to what we don’t know, and our ToE must account for both.

Once again I hope to finish this work before the end of my lifetime. (BTW: I'm 53 now.  My parents are well into their 80s, so I have reason to believe that I have up to 30 years left.)

The basic linear equation

Here's a simple breakthrough in my thinking, after working with my daughter on her math homework.

A line is a one-dimensional, perfectly straight graph, which runs to infinity in opposite directions. There is no way we can possibly list all the points that lie on that line. However, we can, and do, have a simple equation that categorically accounts for the infinity of points:

Where x and y represent coordinates on the x- and y-axes, m is the slope of the line, and b is the y-intercept.

This is an essence of an algorithm. It can account for the infinite.

I made a more significant breakthrough in my work on Tu, which tap into a multidimensional space. It's more complicated, and I'm too early stage, so I need to keep working at it.

Abiding Queries, Working Insights

From films like "Star Trek," to "Predator" and "A.I." the figures we imagine to be aliens or beings of the future seem, at first blush, radically different from who we are and what we are. Yet, from my point of view, these very figures still have the basic human form. What we imagine of the unknown or the foreign, for instance, are still tethered to what we already know or what we are quite familiar with.

A.I.

In a way, this makes perfect sense. We have to have a familiar framework, platform, or language with which to weigh the unknown.  Yet, our fundamental challenge is how to grasp and depict that unknown, with the possibility that the unknown requires an entirely new, yet inconceivable, yet unimaginable set of frameworks, methodology and language.

Let’s go back now to my equation.

I’ll portray them graphically in a conventional, quite familiar way, first, then attempt to portray it in a way that I hope speaks to the unconventional and the unfamiliar that is the unknown. 

Tk has a shape, because it’s finite. But what shape Tu has, in truth, we don’t know. The theories we don’t know, and have yet to formulate, may not have any shape, or rather have a shape that is the product of a more complicated, multidimensional universe.

We can agree that Tu is unimaginably phenomenal in size, comparatively speaking. But remember that Tu is actually an algorithm, and in this respect it offers a way to account for that unimaginably phenomenal size, like that linear equation I showed earlier.   In the following graphic, then, I portray Tu as being more or less diffused into the whole of the graphic via its high degree of transparency.

What of Te, then?  It’s obviously larger than Tk. It’s not as large as Tu, but it must account for Tu. So I propose that it’s mid-size between the two, and its transparency is also a degree between that of Tk and Tu.

Finally, I use + and = because these are simple, conventional symbols, which we are familiar with and which speak to a working relationship among all three elements here.  Again, however, I’m not particularly sure, yet.

Taoism and T'ai Chi

In Taoist philosophy and T'ai Chi practice, for example, it is said that Wu Chi (or Great Void) is the mother of all things. It gives rise to the 10,000 things that are life and matter.  In this regard, the relationship between Tk and Tu may be some kind of multiplication, instead of addition, or an entirely different operation.

In turn, that equals sign may be another symbol altogether, which better accounts for the complex relationship between Tk and Tu and their relationship to Te.

Perhaps our colleagues in Mathematics, and certainly in other disciplines, can advise on this.

© 2013 by Ron Villejo, PhD