Theory of Algorithms - Video Narration

Here is my video narration of the five articles introducing Theory of Algorithms (click on video title to read the corresponding article):

Lecture 1 - A Beautiful Matter

Lecture 2 - Every Problem has a Solution

Lecture 3 - From Split-Brain, to Meta-Brain

Lecture 4 - The Tripartite Model

Lecture 5 - Theory of Everything

© 2013 by Ron Villejo, PhD

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.

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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

Part 4 - The Tripartite Model

I was chatting with a friend, and she asked “Do you believe in God?”

“Yes,” I said.

“Does God exist?”

“I believe so.”

She continued, “How do you prove that God exists?”

Well, as they say in the US, that’s the $6 million question. But not only is it a difficult question, it’s also a delicate, sensitive one for scores of people.

I said, “That’s a tough one. Honestly I don’t know, yet. I’m still thinking about it, and working on it.”

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Quandary of science vis-a-vis religion

Science has been hard-pressed to prove the existence of God. I imagine that in some sectors of science, physicists don’t believe it’s a worthwhile endeavor or, if they do, they focus on the physical universe, instead. Here, they have worked centuries to understand exactly how nature works and how it all began.

The announcement from CERN, in July 2012, about the discovery of the Higgs boson is phenomenal, largely because it may well explain not just how matter began (e.g., stars, planets, and life itself), but also more importantly how the universe was created. In fact, some have dubbed the Higgs boson as the “God particle.”

It was well-known physicist Stephen Hawking, who remarked in 2010 that "it is not necessary to invoke God," because physicists could now explain how the wild-and-wooly cosmos began. That is, the physical universe, through physics.

Before I tell you my reaction to the esteemed professor’s remark, let me say that the Wall Street Journal published a well-argued debate between two thinkers, Karen Armstrong and Richard Dawkins, essentially pitting science against religion.

We all seem to love a debate, and as is the nature of such, we are expected to take clear position and defend that position. Fine. Constructive debate is good. Such discussion allows for a sharper, more enriching knowledge about a subject.

But my question is, Are science and religion necessarily antithetical? In other words, are they innately at odds with one another and maybe even mutually exclusive? 

God expects us to reason

I lived in Dubai for many years, and was coaching a Muslim colleague on her leadership development. In part, our conversation focused on Islam and the expectations of God. Muslims are not just expected to have faith in Allah’s will, she explained. They’re also expected to think, to reason, to analyze and apply logic.

Put differently, both science and religion are critical in the day-to-day lives of many people.

My reaction to Prof. Hawking’s remark about God not being necessary? I took umbrage at it. I thought it was a foolish remark. Millions of people, from all sorts of religion, most certainly believe that God exists and, yes, God is necessary.

Different religions have varying views of God, but many do believe that God created the universe. That humankind began with Adam and Eve, which many Christians believe.

Is this to say that the evolutionary process that Charles Darwin expounded on is suspect or, worse, sacrilegious? Some people would say so.

We can forgive Prof. Hawking, I think, for falling into the common trap of either-or. That is, the common tendency to take a side on something and dismiss other sides. Indeed his work on the physical nature and origins of the universe has been a brilliant, illuminating effort.

But even with a modestly open mind, we may consider the possibility that God indeed created the universe.

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Northwestern University, where I studied for my PhD, subscribed to the scientist-practitioner model for clinical psychologists. As part of years of training in diagnosis and therapy, we were duly schooled in the scientific method. So I have a fundamental understanding for how science works and fully appreciate its power to help us understand everything from ourselves to the wider milieu that Hawking and Einstein focused on.

But as any scientist is expected to cover in a publication, limitations are part-and-parcel of writing about their findings. For example, Where were the shortcomings in their methodology?  Up to what point do their findings speak, beyond which more research is required? What questions warrant further studies?

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Reconciling science and religion

The Tripartite Model aims to reconcile science and religion. It recognizes the importance and power of both in our day-to-day lives and our professional endeavors. It also reminds us to put these in their proper perspectives, that is, how far they can reach and beyond what point they are limited.

Here’s what I told my friend, with whom I was chatting, more specifically.

Proving the existence of God is outside the purview of science. So how do we prove this?  We have to use religious, not scientific, frames of reference, methodology and language. I believe that faith is one key method for proving the existence of God.

So let me relate a personal story.

I worked for a manager, who was the number two leader in our big department. My younger colleagues looked at her with a combination of disdain and fear. I saw her as a troubled lady, who sometimes acted in an immature, unprofessional manner.

In one very tense episode with her direct boss, the head of the department, she angrily and repeatedly shouted at him. Her voice reverberated past the closed door, and some colleagues were so disturbed that they walked out of the office.

Personally I prayed that she go away, perhaps get fired.

Literally a week and a half later, a good friend of mine in the department called me, and said off the bat, “Ron, there is a God.” In an instant, I knew exactly what she meant, and I exclaimed, “Oh, my God!” That number two manager just resigned, she said. My face felt flush, and I was astounded by the notion of God indeed answering my prayer.

I mentioned nothing about my prayers to my good friend, as it was a private matter, really. But the fact that the very first thing out of her mouth was “Ron, there is a God” floored me. It was as though she had read my mind, and heard my prayers, without knowing it!

Now, of course, there can be a host of understandable, logical explanations for this. It doesn’t require a whole lot of thinking to reason that this unprofessional manager was in career jeopardy in the organization and that she was not going to last long in her position.

But this is just one of several instances, where God answered my prayers. So, without diminishing alternative explanations, I can tell you that my faith through prayer is one way I know that God exists.

The Tripartite Model 

The Tripartite Model houses a trinity: Besides science and religion, art is very much part of what we have to take into account to understand ourselves and our universe.  Art assumes the third vertex on the triangle I showed earlier.

Some of us make the choice to devote our lives and our career on one ‘camp.’ This is perfectly well-and-good, of course. They do a ‘deep-dive’ into a particular field, and perhaps assume a singular focus on certain issues.

But regardless of how brilliant and tectonic a discovery the Higgs boson is, for example, this, and the very science on which this was ultimately spring boarded, can explain only so much. That it is, after all, just one explanation. There are other explanations about the origin of matter and life from different platforms of knowledge and learning.

The Tripartite Model aspires to be a complete epistemology. ‘Deep-dive’ specialists, notwithstanding, the more holistic understanding of ourselves and our universe requires, I posit, analytic (scientific) | creative (artistic) | spiritual (religious) perspectives, methodology, and terminology.

For now, let me suggest the following queries to help reconcile these three, and tap into the richness of such an epistemic framework.

Art → Science  ▪  Can the creativity of Mozart or Picasso help shed new light into quandaries that physicists face?

Science → Art  ▪  Can poets benefit from a more analytic, technical review of their verse and a more systematic approach to writing poetry?

Religion ↔ Science  ▪  Can we allow faith and reason not just to co-exist, but also to complement one another and shed light on areas that the other cannot?

Religion → Science  ▪  Can we allow scientists to bring their personal beliefs and religious worships, for example, in some way to their endeavor?

Science → Religion  ▪  Can some religious practices be subjected to the rigors of science and to more systematic forms of inquiry?

Art → Religion  ▪  Can we revise our long-held depictions of God, Jesus, saints and angels, in other fresher, more creative ways?

Religion → Art  ▪  Can painters create works that exalt the religious Zeitgeist of an era, the beliefs and practices of their patrons and neighbors (rf. Caravaggio)?

From the imagined, to the unimagined

As you see, there is quite a lot more to think about and work through. This is an introduction, and The Tripartite Model is a work in progress.

© 2013 by Ron Villejo, PhD

Part 3 - From Split-Brain, to Meta-Brain

It’s often fun to consider, Am I Left-Brain or Right-Brain?



So let’s think about this for a moment. In your day-to-day life, at school, home or work, how do you tend to understand things:  analytically and logically, or creatively and intuitively?

The Myers-Briggs Type Indicator (MBTI) is a popular tool in organizations, as some of you may know, and it measures personality.

• One dimension has to do with what you usually focus on when faced with situations:  facts and information (Sensing) or implications and possibilities (iNtuiting).

• Another dimension has to do with what you tend to take into account, when making decisions: more logic and objectivity (Thinking) or more emotion and values (Feeling).

Which qualities describe you most?

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Dispelling simplicity and dichotomy

“Simple and practical” was the mantra of one of my previous managers, and after a while it made me crazy.

“Keep it simple, Stupid!” (KISS) is another exhortation we Americans sometimes hear.

Moreover, we are often schooled to take a stand on an issue. Focus your career on a field of endeavor. Take a side on a debate:  pro or con.

One time my daughter and her classmates participated in a debate at school. She described both sides of the argument, and I asked her “Well, what did you think?” In her thoughtful way, she explained that she could see both sides, and was actually more in the ‘middle’ of the issue.

My wife and I are blessed to have a very bright kid, who has seeds of wisdom already budding in her thinking. She already has the semblance of a Cross-Brain, which rises above the Split-Brain level, so to speak.

Yes, we can simplify the things we face in the world we live in as an either-or. As black-or-white. As Left-Brain vs. Right-Brain.

But in actuality we ourselves and our very surroundings are often more complicated and multi-sided than we would like to believe. Many things in life reside in the so-called gray zone.

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The Cross-Brain

We may be inclined to think more analytically than creatively. Conversely we may be more inclined to think intuitively than logically. Either way, the two hemispheres of our brain actually work in conjunction with each other more than we may know.

Iain McGilchrist, for one, emphasizes that we need both hemispheres for reasoning, imagination, language and emotion. He therefore debunks the common notion of the Left Brain as the seat only of language and logic, and the Right Brain as the seat of only creativity and intuition.

So I ask, What if we can promote greater ‘porousness’ between the two hemispheres? At any given moment, in any given situation, can we not have the best of both brains at our disposal? If so, then, we can cross from one hemisphere to another, consciously or deliberately, and face issues with a better integrated, more fully functioning brain.


So I suggest that we dispense with the either-or notion, and draw on the best of our analytic and intuitive sides, regardless of our preferences, especially when we’re faced with more unusual, complex problems.

Artistic sorts, for example, may read up on neutrinos and the Higgs boson, and grasp why they are important developments in physics. Conversely, scientific sorts may visit a Picasso exhibit or attend a Mozart opera, if they’re stuck in solving a research problem.

Michael Merzenich speaks about our brain’s lifelong plasticity, that is, ability to adapt, learn, change, and evolve, for greater functionality. So it’s well-within our abilities to cross between both sides.

The Meta-Brain

What is The Meta-Brain?  It’s what I call the ability of our brain to examine itself, essentially to function as a mirror for itself.



When I meditate, for example, I reflect on myself meditating, and ‘watch’ calmly as thoughts pass my mind and gradually slow and settle down.

It’s the ability to step back, and take a ‘helicopter’ perspective, so things can be considered more holistically and completely.  Beyond the divisions of the brain hemispheres, beyond the simplicity and dichotomy of more conventional view of things.

This is like lifting ourselves from walking on the forest floor, and looking at its entirety above the treetops.

This is the essence of emotional intelligence, which Daniel Goleman expounded on and popularized. It’s a specific aspect of EI, which is self awareness. Psychological mindedness or mindfulness are other related terms.

The Meta-Brain is also able to reflect deeply on things. To see what lies below the surface, to see things that are not so visible or discernible. To my point in Part 1 - A Beautiful Matter, John Nash is able to peer through things and extract the algorithms.

Why is this important?

There will be people who prefer to stick with either Left-Brain or Right-Brain, whichever may be their preferred style. But to grasp, analyze and solve problems more effectively and fully, whether simple or complex, we have to develop our Cross-Brain and Meta-Brain.

Later on, I will offer ways to strengthen our abilities in these respects, and extend our thinking however far we can.  At the present, though, how well can you navigate this transition?

1. Go from Left-Brain vs. Right-Brain
2. To Cross-Brain, i.e., crossing back-and-forth
3. To Meta-Brain, i.e., rising above, reflecting on itself

© 2013 by Ron Villejo, PhD

Part 2 - Every Problem Has a Solution

Your friends, colleagues and family like you and care about you. When you run into trouble, when you have some issue or need, they're keen to help. They're keen to advise, and solve your problem. They may even expect you to take their advice and solution, and they get annoyed if you don't.

All this, sometimes, without really grasping what your situation is or without knowing what you want to do with it.

How many times have you been in this situation? 

Jumping ahead, without knowing

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One time, I engaged a web developer to work with me on an important internet project. We had really good conversations over several weeks. So when we agreed to work together, it was exciting.  He got cracking on the logo design, first, and eagerly sent me his first "cuts." They were clever, well-created designs.  Of squares and cubes.

The issue? The shapes that fit my style best are circles and spheres and also triangles and pyramids. My conceptual models reflect more of these shapes, not squares and cubes!

The web developer pushed forward to solve a problem (i.e., how to represent my project symbolically), without grasping more specifically what I wanted.  In fact what I wanted for this particular project was an entirely different shape:  ∞ (the symbol for infinity).

We lost valuable time on the project, and it was very aggravating.  It was only one of many difficulties in his project delivery, and it was clear I had to dismiss him.

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Letting the problem speak

Let the problem “speak” for itself.  It's delving enough into a problem to understand what it's all about.

One senior manager asked me, What problem are you trying to solve? I was so excited about a program I was working on, for which I sought approval, that I neglected to clarify for him what I was actually trying to accomplish.  He needed to understand what the problem was, and more importantly he wanted to make sure I myself was clear.

So letting the problem speak means paying attention to, and reflecting on, the problem (i.e., issue, situation, or difficulty).

Second, letting the problem speak also means suspending our preconceptions about it and setting aside, at least at first, our fine arsenal of methods, techniques, and solutions. So not being hasty or premature in coming up with solutions is important for actually solving that problem.

Put differently, it's emptying our "toolkit," then letting the problem guide us on what "tools" to put in there and to use to solve it.

Some of these tools, which we need to fix a problem, we may have already. But some we may have to get, because we've never thought about it before. Some tools we may have to design and create from scratch, because it doesn't exist yet. 

My seminal thesis

In other words, there is always a solution to a problem.  I shared this seminal thesis with a fellow PhD friend, Hector, and his response was perfectly on-target. He said, "Otherwise, it's not a problem."

The solvability of any and all problems we face now, and may ever face, is a premise at the heart of Theory of Algorithms.  I'm working on the proof for this.  I don't have it completed, yet, but gradually I’m getting there. 

Every day, corporate and worldwide problems - small or large - all have solutions.

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An example 

I lived in Dubai, and I had a business meeting in Abu Dhabi, the capital of the United Arab Emirates. It was a two-hour drive from my apartment to the meeting venue.

Unfortunately there was a serious accident en route, and traffic was badly snarled. Even though I left in plenty of time, it became clear that I was not going to make the meeting. I would have had to ride in a helicopter, and in that situation it was an impractical, unlikely solution.  I was aggravated and pissed off.

But what was the problem? The traffic accident prevented me from attending this meeting.

So, what was the problem, really?  Upon reflecting on this further, I reminded myself that I really wanted to participate in the discussion and the plans we were making.  The more I thought about it, the more I realized that the problem was less about the traffic snarl and more about a missed participation.

What did I do? I optimized an aggravating situation as best as I could, upon hearing the problem speak for itself, by contacting the chair, sharing my thoughts with her, and following up later on.

In the end this solution worked out perfectly fine. I missed the meeting with my colleagues in person, but I effectively solved the problem.  Plus, I saved four hours of driving and a few gallons of gasoline! 

The trouble we run into
  

It took Albert Einstein many years to work out the Theory of General Relativity, more years to correct a problem he discovered, and to arrange for its proof.

The problem? He was working out an alternative notion of gravity, that is, as a warping of time and space, different from that of Newton or Galileo. Obviously this is complex stuff, and he and other physicists have engineered comparably complex theories to help us grasp the universe better.

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In contrast, many of the problems we face in our day-to-day lives are probably simple, or at least simpler than physics. It doesn’t mean simple problems ought to be dismissed or ignored, because they can become more serious over time, if left unchecked. 

Rather, the Theory of Algorithms says that simple problems can be solved with simple solutions, but complex ones require solutions of comparable complexity.

© 2013 by Ron Villejo, PhD