Mathing the Loops: An Integral Perspectival Mathematics Approach to Transformational Learning Processes

by Bruce Alderman

In my previous essay, Sex, Pronouns, and Prepositions, I made the case for expanding Ken Wilber’s integral perspectival mathematics system with a set of prepositional operators. I wanted to show how an enriched relational vocabulary can really open up new territory for Wilber’s perspectival notation. If you’re one of the very rare people for whom that actually sounds interesting or attractive, keep reading. Otherwise, just back away slowly and hopefully no one will get hurt.

To illustrate how the expanded set of prepositional operators work, I took Otto Scharmer’s 3 Levels of Listening as a use case and offered some simple (or simple enough) notation to map certain relational dynamics involved at each stage.

Here, I’d like to do something similar – this time to stretch the notational system a little more and demonstrate a more sophisticated use of it. Because I will mostly focus on mapping out a particular use case, a different (but similar) one this time, this paper will honestly be more of a slog to read than the last one. If you’re one of those people, like me, whose eyes glaze over when equations fill a page, I encourage you to relate to those sections mostly as aesthetic objects, and to focus on the descriptions that follow.

When Wilber first introduced his “integral mathematics of indigenous perspectives,” back in the early ‘00s, he commented that he would probably need to wait for some 20-something young gun to come along and really work the whole thing out. That person isn’t me. I’m 30 years too old for that shit.

But I do have my little piece to add. And I do feel it opens up something useful, and potentially illuminating. I just don’t know how far it can go.

So, anyway, let’s give this a shot.

In the context of preparing to author a text on information technology, I got to exploring the difference between “information” and “meaning”. Let’s just say that the definition of meaning is slipperier. However, because it’s an IT text, there is a need to pin things down. My best shot at it is - meaning requires context. In pure IT terms, the payload of a packet means different things depending on how it is framed and depending on the context of where and how it lands.

With all this mind, I’m visualizing the cascading learning loop model (single-loop, double-loop, triple-loop …) as a problem solving strategy to increase the transparency of information at one level, by supplying additional context at a higher level. At what Bruce describes as the triple-loop learning level, we basically have what John Verkaeke calls recursive relevance realization, the function of which is specifically to identify a meta-context for meaning-making.

To me, it’s an open question if even the most capable artificial intelligences can produce meta-contextual frameworks for meaning-making on their own. I lean instead towards the view that human intervention will be needed at some point to sort out what matters and what does not. But running small experiments - not attached to dangerous things - would certainly shed light on these matters.

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What i would like to add to the three loops is that fixes are never universal fixes at any level.
Every learning and implementation has a cost that includes the opportunity cost of the options not taken.

For example, Integral Practice has deeply enmeshed itself with the capitalist model. This has advantages but also the cost of choosing not to explore other options. We might say that we are “addicted” to the capitalist solution and when it goes down, Integral Practice will go down with it.

Economic system is just one example of a dozen that come quickly to mind where Integral Theory / Practice has wedded itself to something seen to be a solution without understanding that all solutions are relative. Thus all learning must consider this fundamental when learning to find a solution to a problem.

I guess regarding the math I would suggest the “feedback loop” is highly complicated function. Its also the most important part of the equation IMO because it informs us when to change course but that urge is often (usually) misleading the more myopic our perspective.

Hi, yes, I agree - that’s an essential systems insight, and personally I’d say any approach that didn’t remain cognizant of the ‘contextuality’ of fixes likely isn’t integral. The use of the word ‘universal’ in my essay, in relation to the triple-loop process, is meant more like ‘universalish’ – meaning, seeing broad, cross-context applicability. But that, also, is never generally final in an evolving universe.

Anyone not feeding themselves from a subsistence farm is deeply enmeshed in the capitalist model. One can certainly imagine other global economic systems, but as a practical matter, in the getting from here to there process, some sort of relationship with capitalism will be required. By contrast, family-level or community-level non-monetary cooperation is very common. So why does that break down at larger scale? If it’s better than capitalism, why don’t such non-exchange economies scale up better?

There are degrees in all enmeshments. Everyone has different degrees which they allow themselves to participate.

There are various “sharing” cultures and these are growing as more people realize certain absurdities of capitalism and these communities dont break down on larger scales. This is due to swift exile policies. There are also people who do buy things from Amazon, for example but buy locally when possible. Due to USDA regulations things like raw milk products must be traded outside of the system.

Two large scale groups that come to mind are “buy nothing” groups and “couch surfing”. There are others of course that Im unfamiliar with like urban foragers, whose goal is to never buy food. There are also spiritual traditions where the devotees only eat what is given to them.

I think if we want to find more examples we could

Every system competes with every other system for resources. If the non-exchange systems you favor are to supplant capitalism, they need to out compete it. That they exist and can be found is not under dispute. They all seem like niche models, however, compared to the exchange economy that is massive in comparison. (Non-compensated work of women, primarily, in the home is the still the most substantial counterweight to the exchange economy with respect both to scale and social importance).

What remains unclear is why some sort of futuristic barter system or scavenging system or voluntary sharing system could outcompete capitalism on a global scale for production and distribution of resources everyone needs. It’s also not clear to me why integral theory is to faulted for not imagining some system like that, which would highly speculative, to say the least.

People always think wholesale replacement, which is absurd.
“All or nothing” kind of stuff. This is always surprising to me in people who otherwise are able to see degrees and nuances in ideas.
This form of Capitalism we have settled upon in 2024 is far from even the only version of Capitalism that ever could have been or ever will be.
Nor do ideas critical of the current system need to fully prove an alternative system will work better.

If even 10% of the population just decided to consume only that which brought them long term benefit the entire economic system would spiral into a depression. The stores are filled with foods that literally are bad for your health and shorten your lifespan. Mechanical items are engineered to fail more quickly. Again, I can go on and on and on with examples. The increase in prices no longer reflect an increase in quality, but a decrease in quality. We now pay more for less and worse.

We can look at China as an example of how quickly a thriving capitalist economy can just start to fail. Suddenly people just realize they don’t want to buy stuff except what is necessary and don’t want to work to buy extras. There is no system that “needs to out compete” China’s failing system - it’s just failing on its own spectacularly. That’s the entire problem - the basic necessities and bedrock of societies have been destroyed by large scale consumption based Capitalism - so there is no backup plan now. The only “solutions” to an economic crisis are to double down on the extremes and force the system to be more fragile decade after decade. Grow, Grow Grow even if that Growth destroys underlying structures and increases the risks of failing bigger and harder later.

This is something that I don’t have to convince anyone of. I see it on the road ahead and plan for it. Will there be another global pandemic? Of course there will be, because nothing was fixed. Will mental health continue to decline decade after decade? Of course, because there isn’t even the concept of a solution except “more meds”. Will obesity and all the associated problems continue to increase? of course, because the next “Extreme Super Cheese” potato chip is “progress” and growth.

Capitalism is a zero sum game. I don’t need to convince everyone to stop consuming. I just need to stop consuming myself and only make sensible purchases and I will be financially better off and less reliant on credit. I can go farther and say I don’t need to change the credit system. I just need to know that they will lend me anywhere from 30k-50k every 7-10 years and if I don’t pay them back they will still offer me more money again in 7 years when my credit goes back up. I only have to understand the holes in their system to exploit it. Right now I’m still on the fence if I want to convert consumer credit to building supplies to equity over the next 3 years. We’ll see.

When there is another financial crisis (there will be) with a corresponding stimulus legislation (there will be) that is rushed and full of holes and opens the whole process to massive fraud (of course it will). I will laugh as stupid incompetent people get greedy and they encourage other people to commit fraud and collect a percentage of the prize. Then five years later I’ll decide if I want to take their money to help them reduce their financial problems created by their greed fueled by consumption, which in turn was fueled by poor mental health.
How long this can continue is soon going to be an easy math problem. The fall of real purchasing power is accelerating. How long will people continue to even be able to borrow 2-3 years’ salary to buy an average new car when their credit is already maxed out? Or how long will they be able to afford $2-5k visits to the mechanic to fix their old car? There are dozens of such holes in consumption Capitalism starting to show in every sector of the economy.
I don’t need to develop a new replacement economic system before people start spending less. It’s inevitable that the smarter people are, the earlier they will reduce unnecessary purchases and in the process accelerate the pain for those who are less insightful.