Building intuition

Why working from first principles is more than just understanding component parts (but also component relationships)
To build intuition, learn the parts of a system, learn how those parts communicate. Neil Keleher.


Building intuition from understanding

With intuition, the better you understand a system, the easier intuitions about the system can arise.

To acquire understanding, the typical approach from a first principles perspective is to break a system down into its component parts. We then learn the system in terms of its component parts, assembling the model within ourselves, piece by piece.

A friend recently pointed out that this isn't the only approach, that working from first principles doesn't always work. My friend, trained as a pure mathemetician, told me that sometimes you have to actually "do the math" in order to build intuitive understanding. The idea seems to be that this part, doing the math, isn't actually working from first principles.

What I'm going to show (or attempt to) is how it can be.

Defining Intuition and Understanding

I'll define "intuition" as the sudden knowing, without having to think.

I'll define "understanding" as having a model within our brain, or within our consciousness, of the system in question.

A type of intuition based on the understanding a particular system

Note, before going on, I should mention that the type of intuition that is the focus of this article isn't the sort of intuition that comes from a higher power.

The intuition I'm talking about is one that arises from understanding a system, from having deeply studied it.

A video about side bends and the thoracolumbar fascia

How this conversation got started was me mentioning a video that I'd just finished that morning. I'd decided to do a video on side bending since I'd taught a class that included a large side bending component and I thought it would be a good thing for my youtube subscribers. I also have a website and one of the search terms I'd noticed my website getting hits for was the "thoracolumbar fascia" as well as thoracolumbar stretches.

Both the website and the youtube channel in question focus mainly on yoga. Actually I use yoga and other exercises to teach people to better feel and control their body, using what I believe to be an approach from first principles.

Off the cuff, I mentioned in the introduction to my video that one of the reasons for doing sidebends is as a potential stretch for the thoracolumbar fascia.

I had no idea how I would bring a deeper discussion of this into the video but it happened almost organically. Having trouble in one of the poses as I was filming, I then suggested that if viewers encountered a similiar problem one approach could be to activate the transverse abdominis. And then I started talking about how that muscle can affect the thoracolumbar fascia (as well as the SI joints and the hip bones and the hips).

Some models of the thoracolumbar fascia suggest that the aponeurosis of the transverse abdominis divides into two layers. Those two layers create a structure called the paraspinalis rectinalicular sheath, a tube of connective tissue that encases the spinal erectors but also forms a major component of the thoracolumbar fascia.

When you understand a system you can talk about it freely

And so even though I had not planned a video that talked deeply about the thoracolumbar fascia, that's in part what I ended up with. And it happened because I understood the subject matter. I'd studied it deeply. But I hadn't studied the thoracolumbar fascia with respect to side bends. And even though I'd never associated the thoracolumbar fascia with sidebending until that moment, because I'd understood the thoracolumbar fascia from first principles, I was easily able to talk about in in the context of side bends.

My friend pointed out that my understanding (my immersion) in this subject allowed me to do this. And I totally agree with him.

First principles, AKA an axiomatic approach

Working from first principles is about breaking things down functionaly. In math, my friend told me the equivalent is working from axioms. The axioms are the building blocks or components in the pure math world. So another way to indentify or name first principle thinking is to call it an axiomatic approach to learning a system. And the common notion seems to be that first principles thinking is limited to understanding the building blocks of the system. That the first principles approach is to break a system into component parts and that is it.

I would suggest that that is a very limited understanding of first principles. And while it's useful, it doesn't unleash the full power of working from first principles.

From systems design: choosing how to define a system

I studied systems design engineering when I was in university. This was after a five year stint in the British army fixing guns. One of the things we learned in systems design, and note that this was the study of systems in general, not just computer systems or electrical systems, was that we could choose how we define the system.

Apart from learning about systems, we also learned about solving problems. In one particularly memorable lecture, one of my professors told us that it was very important to understand the problem. It may be that a slightly different definition of the system in question can lead to being able to specify the problem differently and in such a way that it is so much easier to solve.

Defining the components of a system (and the relationships)

When we define a system, we draw a boundary between it and its environment. And that boundary is where the system talks or communicates with its immediate environment. Within the system itself we could repeat this process, dividing the system into components. In so doing we could also notice how one component talks or communicates to another (or, as in some cases, doesn't.)

What we then have is two potential ways of looking at a system. We can look at its component parts. Or we can look at the relationships between those component parts.

Learning a new system

After university, one of my jobs was working with a telehealth system. This was at around the turn of the century. Cell phones weren't yet common. I don't think skype had yet been invented, or if it had been it wasn't that widely spread.

The telehealth system I was working on was like a precursor to skype. It was a system designed for remote diagnosing. Medical centers with nursing staff would be posted in out of the way communities and the system would allow a doctor to remotely diagnose patients without actually having to visit them. The terminal in the remote location would be operated by a specially trained nurse.

The system included cameras, video cards, codecs (coder/decoders) and a modem for transmitting data over high bandwidth phone lines.

Learning the components of a system and how they communicated

When I first got the job, transferring in from a different department, I took the time to learn the system inside and out. I learned the components and what they did. And I learned the various signals as they travelled from component to component. So for example, a video signal would be generated by a camera, travel through a switch box to the codec, where it was compressed and passed to the modem. At the other end the signal would go from the modem to the codec to the video card and from there to the monitor.

There were other signals and I learned the pathways of them all. I knew the system well enough that I could talk customers through fault finding procedures over the phone without requiring a manual. As a result, when one of our customers requested a change to the system, where all the other engineers suggested a change that involved buying new equipment, I was able to suggest a solution that involved a simple rewiring of a few components. My suggested solution was cheap, easy to implement and it came as a flash of inspiration, an intuition that was built on my understanding the components of the system and how they were connected, how they related.

We did test my recommendation first, but it worked.

The signal view of a system as a compliment to the architectural view

I learned how to fix guns in the army in more or less the same way. I understood weapons both from a component view but also from understanding how change was transmitted through the rifle as it operated.

This understanding of how parts relate, how they transmit change or information between each other could be thought of as the signal view of a system or the system view (the view of the system as it is working.) Note that the component view may be referred to in some circles as the architectural view.

In my experience, we need both views to develop understanding.

Or perhaps better put, if we only have one view, then our understanding, and possibly our ability to intuit, is limited.

Understanding component parts and how they relate

Studying systems, it's not just about understanding the component parts. It's also about understanding how they relate. In the context of electronics, say for example the telehealth system, it's about understanding the components but also about understanding how the components talk to each other.

And so I'll suggest here that relationships are how parts connect to each other. And they are also how parts communicate with each other. The relationship or "signal" view is another way of breaking a system down so that we can understand it

Doing the math

Continuing the conversation with my friend, I mentioned the time my Dad, my uncle and I build a custom built harley. None of us had a clue what we were doing. We'd often go to the neighborhood customizer and talk about the possibilities.

I once asked about changing the primary drive from the usual 2 inch to the super cool looking 3 inch belt drive. In order to make this "simple" change, we would have to reposition the engine, or the transmission, and also the rear wheel. Basically, one so called simple change would have an effect on the whole system.

So as well as having to understand the parts, in order to build a bike that worked, we also had to understand how the parts related, and how changes in one part could affect how other parts related.

So how does this relate to pure maths were the components are equations or theorems?

Conscious embedded systems

My friend said that one of his professors said that sometimes you get a better understanding from simply doing the equations, figuring them out.

That is the equivalent of the signal view.

In this instance, instead of the system being something external that we are studying, like, say a rifle, a telehealth system or a motorcycle, it is something that we are a part of. We are doing the math. We are building a model of the mathematics in our brain.

In the same way when learning a system we build a model of that system in our brain (or in our consciousness).

The "doing the equation" part is the equivalent of learning how change is transmitted from one part of the system to another. The main difference is that with math, the system is embedded in ourselves, much the way a software program is embedded in a computer.

When we practice doing equations, we improve the signal view of the model that is in our brain and thus improve the likelyhood of intuition.

The intuitions may not always be right and so a big part of this process is checking the work. So for example, when I came up with the fix for the telehealth system, we didn't take my word for it. We checked to see if it would work first. And it did. (But it might not have!)

Developing understanding as it is required

When dealing with problems, we don't always have the necessary understanding right from the get go. The nice thing is, with first principles thinking and the ability to look at components and/or the way we relate, we can acquire understanding relatively easy.

And sometimes, we don't have to learn an entire system in order to fix a problem. We only have to learn the part that has the problem. It's not always the case, but it is good to be aware of the possibility.

Working to build that custom harley, I often had to solve problems. I didn't try to understand how the whole bike worked. Instead, when there was a problem with the break reservoir, I focused on learning about that. When there was a problem with the starter motor, that was what I focused on. Put another way, when you know what needs to be done, you can get on with doing it.

But back to building intuition.

Better models equals better understanding

The idea of understanding is to build models within our consciousness.

The better both views fit together, the better our understanding.

As a "yoga teacher", teaching students to feel and control their body, what can help is to think of the mind and the body as to distinct systems. By teaching students via muscle control to feel and control their body in isolated chunks, they then build a better model of their own body in their consciousness.

For myself, talking about the thoracolumbar fascia, it's not just a structure of bodies in general. It's something I've learned to feel and to an extent control in my own body. (Actually, this structure is more like a system. What I can feel and control, and what I teach others to feel and control, are parts of that system.) And likewise side bending. In this mornings videos, the idea was on feeing the short-side of the side bend, noticing the contraction of muscles on the short side (and deliberately contracting them versus relying on gravity.) Doing this, the result is a side bend that can be felt as well as controlled.

So what I have is a reasonably good model of my body. It is built into my consciousness. It's a model that I can access easily, without having to think and one that provides me with intuition.

Understanding from book learning and direct experience

Note that this understanding of the body isn't built from just book learning. It isn't built solely from the study of anatomy texts. Learning muscles, not so much their names, but their attachment points is important. But then so is directly experiencing those muscles in my own body.

This direct experiencing is the equivalent of doing the math.

The important point, the really important point is that, as with breaking down a system into components, I don't struggle to feel and control my whole body all at once. Instead, I isolate the signals. I'll focus on one particular muscle or set of muscles, or one particular joint. I break down the signal view of my body so that I can learn the signals as isolated components.

And so I experience my body (and teach my students to experience theres) bit-by-bit

Switching a light switch on and off (repeatedly)

Muscles generate sensation when they activate. They activate when they have a force to work against. Connective tissue can be felt when it is tensioned. It is thus transmitting force. All of these are sensations that can be isolated, identified, felt and controlled as easily as flicking a light switch on and off repeatedly to see which light bulb it controls.

Thus I build up the signal view of my body from a first principles approach.

Intuitively writing Chinese

One of the things that I have liked to practice is Chinese calligraphy. In some ways this is similiar to math. Calligraphy isn't just about how you write the characters, having first memorized them, it's also about how to put characters together, for sound and meaning and even structure. But that's way beyond my level. From a learning perspective, from the perspective of understanding, of intuition, calligraphy offers another way to show how breaking things down in the signal view is a first principles approach.

Training intuition in small doses

The general teaching and learning methodology for Chinese characters is to paint a character (or write it) over and over again until it is memorized. It can be quite tedious. An approach I somehow picked up by accident was to take a particular character and break it down into component strokes. I would paint a small set of strokes from memory over and over again until I could do them smoothly. The goal here wasn't prettyness. It was simply memorization of those few strokes. Then I would learn the next few strokes.

At each point the idea was to practice a set of strokes that were small enough that I didn't have to think about them in order to paint them. Basically, I was training my intuition in small doses. Or if you like, I was working from short term memory.

The idea was, once I'd learned a character, I could then paint it freely. And while the first goal might be to make it look pretty or just like the character I was painting, another goal would be to express myself via the character. So instead of thinking about how to write a character I would paint it intuitively. And I would extend this to learning to paint an entire poem.

Now, instead of brush strokes, or sets of brush strokes, I would memorize short sequences of characters, always working within the limits of short term memory, or intuition.

The need for checking intuitive results

I should point out here that an important idea that I learned from my first calligraphy teacher who himself studied with a Japanese calligraphy teacher was that when doing calligraphy you never correct mistakes. You carry on painting. I've done paintings like this and created works of art only to realize afterwards that I've forgotten a few characters. But it didn't matter. The painting was still beautiful. It was art and so it didn't matter. More importantly I was in the zone when I painted, the place the Japanese call No Mind.

With art, presence is much more important than correctness.

That said, working intuitively with math, with engineering, with other endeavours, the mistakes do matter. And that again is why we checked my suggested solution for the telehealth system.

Intuiting math

Before going on, I should mention an interesting experience that occurred while trying to answer simple math questions as quickly as possible.

When we've practiced simple math equations for a while, doing them becomes easy. We know for example that 2+2 = 4. We don't have to think. And we don't have to figure it out. We know it intuitively.

Trying to answer 100 simple math questions as quickly as possible as part of a brain training program, I found that in order to write as quickly as possible I had to look at the next question ahead while my hand wrote the answer to the previous question. I didn't think about the answers.

Checking my answers after completion, I found that I didn't actually get that many answers wrong, thus helping to cement the idea that when we learn basic math, we are actually memorizing results. And so to improve my performance, I would practice not a whole test, but only the questions I got wrong, repeating them in the same way that I would repeat any brush strokes of a particular character that I had trouble remembering or painting smoothly.

Note that I didn't practice the whole test, just the parts that I got wrong. And so this again is first principles thinking.

Understanding intuition

So what is actually happening when we work from intuition?

Yes it's based on understanding, or if you like, having memorized something. But what actually drives intuition?

The thousand radiant heads of Patanjali, each with an IQ of one.

A few years ago I was attending a yoga workshop taught by a fairly famous yoga teacher named Richard Freeman. He reminded me a bit in look and manner of speaking of a bushy eye-browed Agent smith from the Matrix.

His workshop was easily one of the best, and most fun that I've ever attended.

At one point he mentioned the thousant radiant snake heads of patanjali.

Imagine if each snake head had an IQ of one. But, there's a lot of snake heads and so all together that's a pretty big IQ.

What if, when we build up a model, both with a component view and a signal view, each of those models is the equivalent of one of patanjali's snake head. A small, limited intelligence subconscious entity. It could actually be similiar to the idea of a function in computer programming.

Writing functions when programming

An important idea in programming is to create functions to make blocks of code smaller, more manageable, more understandable. This ideally makes a program smaller. But it also makes it easier to debug (and easier to understand).

When you are in the throws of writing a program it can be easy, particularly if not formaly trained, to write a big long block of code. It may work, but when you leave the code for a while, and then come back to it, it can be challenging to figure out how it works, to remember why you did things the way you did.

And so one way to work around it is, once you have code that works, is to refine it. Create functions. Or from the very get go work at creating functional blocks with clearly defined jobs.

Then, coming back to the code, or even working on refining it, instead of trying to figure out how a big block of code works, you understand it relatively easily via the functions that are used. And this could be thought of as working from first principles. The better you divide the code into functions, the easier it is to re-use those functions, both within the same program, but also across other programs.

Functions do a clearly defined task. They are like miniature programs that are part of the bigger program. The bigger program doesn't know what goes on inside these smaller programs. It just calls them when necessary and they do their work when called.

And it's possible for one function to call another function.

What if our brain, our consciousness, works in a similiar way. What if, given enough practice, there's a location within our brain that can recognize 2+2 and automatically outputs either via our mouth or our hand the answer 4.

Or what if having learned to ride a motorcycle, a location within our brain has the necessary smarts to recognize when something is blocking our way forwards and either causes us to operate the brake stop or the steering to go around the obstacle?

Or what if, having learned to understand a telehealth system from two points of view, our brain can then allow us to tour a virtual model of that system, in our own head, or even come up with ways to change the system easily, using the parts that are already a part of the system because it is made up of the rough equivalent of patanjali's 1000 radiant snake heads, each component, each relationship a unit of IQ that with all the other IQ's in that model can provide answers, which to us seem like intuition?

Bigger parts of littler parts, which is more flexible?

Basic principles is about reducing to component parts of relationships based on a particular goal. It can be really really handy if you want to be a problem solver, a designer, or simply get better at dealing with change. And it can be a handy tool if you have to teach or somehow convey information. And it's also really handy if you are a programmer.

In terms of intuition, when we build , understanding up from the smallest useful building blocks, we develop a more flexible model within our brain, one that is easily adaptable to change. This isn't to say that you can't develop understanding in other ways. But one advantage of building understanding, and intuition, from smaller usefully sized building blocks is that it can make the acquisition of understanding a more enjoyable process.

Once you have a way of breaking down a system, you can focus on actually learning the component parts and how they relate. And while doing so you can immerse yourself in the act of learning or doing.

The interesting thing is, this is the mind-state where intuition is more likely to pop up. Intuition doesn't occur when you are mentally efforting or thinking. It comes from a more relaxed mindstate. And you can practice being in that mindstate if you learn to break systems down into components and relationships.

Your breakdown might be wrong, or less than perfect. It doesn't matter because that in itself is part of the process. You get better at breaking things down by practicing breaking things down.

Learning the components and learning the signals.

The first step can be to define the components. The second step can then be to recognize the signals that pass between those components.

And when it comes to systems that are not quite outside of ourselves, math, calligraphy, our own body, that second step can include directly experiencing these signals.

With the signal view the point is to realize that it may be possible to break a signal into component parts. What matters is being able to clearly define and being able to recognize those parts. It's exactly like breaking a non-working system into component parts. But instead you break down a system while it is working into component signals.

One thing that can make this signal break down easier is defining components in such a way that signal break-down can be specified in terms of the components. The signal element is then the change or information that is transmitted from one component to the other.

by: Neil Keleher
Published: 2021 01 07
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