The Map of First Principles

I have often come across that whenever I mention the words 'first' and 'principles' together, it is often followed by, 'What does that mean for me?'. While there are more generally well known mathematical examples for this concept, it is more difficult to describe it when not looked at as a definition.

From Google to ChatGPT, it is almost as if every time I attempt to research a more accessible way to explain the concept, I am left with this horrible definition as the "basic building blocks" upon which the next step can be taken. That definition, to me, is not helpful in the least bit.

So I thought to give it a shot. Perhaps it may become an even greater pool of confusion, or perhaps it may spur someone else to create a better attempt.

Rethinking Analogies

Why is this important right now? In an age of AI, fundamentally rethinking what we do, who we are and what we create appear to be questions which may throw some into existential crises. It is an approach toward innovation, and uniqueness. Through utilising first principles as a tool for coping with the times, businesses and people can begin to make a move toward becoming better equipped to deal with such change. This approach is difficult in and of itself, but it may just be the greatest - yet most rewarding - challenge of our time.

Perhaps we can start a trend. Let me know if you think this is actually more feasible than just a provocation.

#firstprincipleschallenge

Here it goes.

Maps

First Principles is a conceptual attempt toward relooking at the various ways in which a problem can be solved - from a place of a known position moving toward an unknown solution. It is directional in nature - meaning we know approximately where we want to go, but not how to get there.

A metaphor that I believe is the most useful is to discuss anything related to direction is that of a map: the problem of getting from a location to a destination. For ease of reference, the word we will be using here to state one's current position is location and the desired place to arrive as destination.

In a case where one may be looking for the shortest distance to get from a location to a destination - the straight line distance path may help. Another may be looking for the most scenic route - and this may also become evident by plotting a path against the number of points of interest.

A final route may be one that has the most number of rest areas - whatever it is, these are different ways to get from point A to B.

With each of these routes, you are able to logically determine how far you are from or toward a destination, and how to trace your steps to get back to from where you began.

But here is the game changer - a generic map is only in one dimension. It does not always account for changes in elevation.

Assumptions

If you had looked at the problem from the top view, side view and perhaps even as a function of time, you could deduce that more than 1 method could work i.e. another mode of transport may be necessary to get from one point to another. This we consider to be challenging the assumptions.

In this case, there were 2 assumptions: 1) the map's visual representation expressed everything you needed to know and 2) you only required a single mode of transport to get there. So in opposition to these assumptions, you might need to by-pass the mountain by taking a subway through it, moving onto a ferry to get across a channel and riding a bi-cycle once on land to avoid heavy vehicular traffic.

Sound sensible?

If so, such is the case with first principles...

Derivation

One is able to see all the paths taken to solve a problem, map them toward the solution and if one does not work out, we can always follow the steps back and reroute or select an alternate method. One can change the route, the mode of transport and sometimes even plot an entirely new, unchartered path. This sounds quite logical - but deriving a logic is exactly the kind mental exercise we need. And I was fortunate enough to realise this in my early years.

Whilst still in high school, I attended a mathematics class and noticed the derivation of the quadratic equation by 'completing the square method'. Trying not only to manipulate the formula, but create what looked like something else entirely, marked a change in me.

Following this about a semester later whilst attending a calculus class on finding limits, the demonstration of reducing limits toward 0 - neatly expressed on a chalkboard - changed something inside of me: at once I could see that there was a path which followed a logic to generate - or 'derive' a solution. First principles allowed one to derive a solution - perhaps seen as generating such - which is based on the nature of the problem trying to be solved.

These were my earliest conscious encounters with the concept of first principles. Shortly afterward, I began to see it in everything - I began to pick up the logic. And if something lacked it, I immediately caused to question the basis of the information communicated (a note here, not an advisable attitude when time is limited and stakes are high in the immediate future).

For the best insight, I would recommend that you look at limits, derivatives, differentiation and calculus.

Etymology and Derivation

As mentioned, I began to notice the patterns everywhere. Around the same time in high school, I became aware of the word sagacious for the first time (yes, quite late - I know). And it dawned upon me that through splitting the word into 'saga' and 'cious' I could derive a narrative in my head that one who has experienced many sagas must have accumulated much knowledge - hence its meaning.

I began to research this method to understanding words - which I'd been doing for some time already - and noticed that there was a way to construct meaning (semantics) from words by deconstruction: by analyzing it through its etymology.

Finding roots of words occurred naturally to me but now that I found what appeared to be a method to do it, I could now express this epiphany to others who might find it useful.

And so was my new attempt at deriving words as a function of the new lens through which I saw the world.

So what?

Fast forward to a decade later, and I was lecturing a class on number series and patterns, showing them how to derive formulae.

At the same time, I was trying to reconcile how one would introduce discrete mathematics and programming into the architectural curriculum as part of an undergraduate qualification.

And one afternoon it dawned upon me that if I approached discrete mathematics and etymological derivation as procedural steps toward creating meaning - I was ultimately equating them to being a language.

This deep connection between the two - language and mathematics - is quite obvious, but one should understand that in the context of linking these together in an architectural curriculum is not quite so.

By introducing discrete mathematics as a language to be learnt, it allowed us to move onto more computer science concepts to be incorporated into the curriculum. Students would be learning a new 'language' as a means to explore the creation of architecture.

We could now officially see (in terms of architectural curriculum) architecture, discrete mathematics and language as belonging to the same frameworks - following a set of parameters to produce a meaningful product.

This, as many architectural practitioners may know, sounds like Parametricism; but for the first time in architectural education in South Africa did we have a justification for it to underpin an entire undergraduate qualification.

A key factor was the procedural method of following steps along a path toward or away from a solution - akin to following a path backward or forward on a map. And it was my fundamental understanding of these concepts from a first principals perspective that allowed me to see this.

How is this related to AI?

In early 2023, ex-Google Ethicist, Tristan Harris and Aza Raskin published a short documentary explaining the progress in AI and caution we should take as a result of where it could go. Tristan described a significant break for AI - where if AI could pick up everything we do as set of procedures with parameters, i.e. that it could pick up our fields as languages through deep learning, it could translate data across disciplines in intelligible ways.

Raskin mentioned that previously machine learning disciplines could be separated - computer vision, speech recognition, etc. with incremental gains made in each. However, this is no longer the case. They could now all be interconnected.

Essentially, if AI could these integrate various disciplines in machine learning - solving problems, create images, identify objects - as a codified language to be followed in a series of steps, it could allow AI to make gains which previously were out of reach.

Still not following?

All I am referring to above is the 'T' in 'GPT' - that being 'transformers'. ChatGPT is essentially a GPT ('Generative Pre-Trained Transformer) trained to chat - and now using GPTs we can do a host of various other tasks as well.

My small realization which was able to integrate concepts from programming, architecture and discrete mathematics through the lens of each being a language, allowed me to integrate what appeared to be unrelated fields. The same thinking applied to GPTs allowed it to integrate various forms of machine learning progress into one step closer in creating what we refer to as AGI, or artificial general intelligence.

Now I'm lost

Ironic being that the metaphor for this topic is based on maps. Pardon my lack of communication skills - so here's a diagram I drew to help me construct this article for better flow:

Upon seeing this diagram - or map of information - I hope a few things happened in your mind:

1. You saw the big picture and how all the topics fit together
2. If you did not follow any part, you could locate exactly at which part it did not make sense
3. You were able retrace the arguments or paths of logic following routes from beginning to end, and all the way back
4. Looking at the whole possibly made you wonder if there is still a better way or method of presenting the topic of First Principles

This can be easily correlated to our map analogy in the following points:

1. Direction = Big picture thinking
2. Situational Awareness = Location
3. Retrace arguments = paths/routes
4. Better way = Alternate method

If this is what you got, then congratulations - you have achieved the end goal of first principles thinking. You can now see the entire idea, follow a path back to a place of familiarity if you were lost and you can challenge this path in the hope you find a better way to explain it.

And for the success of this article and the future for us as thinking humans, I hope you do.

REFERENCES & FURTHER MATERIAL FOR ENGAGMENT:

1. The AI Dilemma
2. FS Blog - First Principles Thinking
3. Byjus - Quadratic Formula through First Principles Derivation
4. First Principles Thinking; Break it Down, Build it Up | Sagar Makwana | TEDxTKMCE
5. Sagacious Etymology