There is a certain kind of insight that I’d like to give a name to because it matters. And ideally I’d love to collect examples of this kind of insight from you and from other experts.
I’ll call them “No Man’s Land insights”.
NML insights for short.
NML insights are born out of expertise and experience. I could have called them “expert insights” or “experience insights” (or arguable just “insights“). But that would have been too general.
There is no platform for me to publish my NML insights. I have evoked some of them in introductions and conclusions of papers. But I think I’ve noticed my papers are more quickly accepted when I don’t do that, and when on the contrary, I invest the extra effort to make my papers look more brutally mathematical. Despite the key enabler role my NML insights play with regards to the brutal math I publish, they seem unwelcome in the usual math venues of my field. I’ve tried once to publish in a philosophy venue. They hated it. Clearly, I know nothing of philosophers’ lingo. And probably the little nuts and bolts of Boolean Automata Networks don’t interest philosophers half as much as they interest me.
So the kind of insights I want to make matter are insights that might be somewhat personal and definitely very specific to the way you approach a certain abstract piece of knowledge or concept in your field. Perhaps they generalise outside of your niche, but the most accurate way you have of expressing them today remains by using very specific concepts — similar to how my NML insights are most accurately expressed in terms of Boolean Automata Networks even though they are very general ideas concerning the circulation of information across networks of interacting objects.
Your NML insights are very useful to you on a daily basis for what you do, or very obvious. But there is no dedicated public venue to express them. Typically, you will share your NML insights with some of your colleagues. Not necessarily all your colleagues. Your NML insights will be just as obvious to some of your colleagues as they are to you. But to some other colleagues, they will be less intuitive, perhaps overshadowed by different NML insights, closest to those colleagues’
I couldn’t recommend enough the beautiful article written by Andy Matuschak and Michael Nielsen : “How can we develop transformative tools for thought?”. In it, the authors give several examples of NML insights, some personal, some fictional, some real. One insight is Michael Nielsen’s, relative to what gets students stuck when learning quantum mechanics. Another NML insight evoked in the article relates to the “many non-obvious ideas” captured in the design of Hindu-Arabic numerals.
There are probably almost as many university level courses of classical mechanics as their are teachers of classical mechanics. Why is that? Why isn’t there exactly 1 course of classical mechanics? Why do we need any more than 1? Why aren’t all physics teachers using exactly the same courses, at least for the well established knowledge they teach? The reason can be summed up in terms of NML insights. NML insights are dense in the teaching profession.
My physicist friend Guillaume Chevereau teaches physics in an engineering school. He feels the need to rewrite the courses he teaches. He can’t recycle existing courses — existing textbooks — without significantly adapting them. Most of what he teaches is established knowledge. Whether the knowledge is new and still evolving or not, isn’t the question here. The reason why existing courses can’t be recycled as they are, is rather a question of modularity and granularity in the textbook documentation of knowledge. Existing courses are narratives. The narratives are not exactly the knowledge itself. Textbooks record narratives which in turn convey knowledge. Knowledge and narratives are meshed together. We haven’t yet got the format that allows the kind of modularity and granularity in the expression of knowledge, that would allow to easily, systematically, distinguish between knowledge and narrative (I’m working on it by the way).
In presenting scientific knowledge, a lot of the choices we make are part of the narrative. The order in which we choose to present different parts of the knowledge is part of the narrative. Factors that determine the order are for instance prerequisite notions, and a teacher’s experience of what is easier for a particular kind of student, what pre-existing intuitions to build on, what pre-existing intuitions to avoid invoking. Definitions and notations are also part of the narrative. Notations, as suggested by Andy Matuschak and Michael Nielsen, have deep ramifications. They are deeply tied to definitions.
To teach the notion of force in classical mechanics, you usually need the notion of projection, and in particular the Euclidian scalar product. Mathematically, there are different ways you can define the scalar product, depending on the context. One definition takes a geometric perspective requiring a prior understanding of the notions of magnitude and angle. The scalar product can alternatively be defined in terms of vector coefficients. Guillaume Chevereau tells me that in this context, he prefers the algebraic definition. The geometrical definition is then presented as a property that follows from the algebraic definition, rather than as a definition per se. There are many reasons for GC to do that. One of them is that the algebraic definition doesn’t require a deep dive into geometry. It is more self contained. It doesn’t invoke a prior understanding of what an angle is. Another reason has to do with minimising the amount of student memory space used. Also this approach makes GC’s course more self-contained in a rigorous manner. It minimises the amount of prerequisite assumptions. This allows to have better control over which questions students are likely to ask in order to have more time to address each question thoroughly. In different contexts, GC doesn’t especially focus on the algbraic definition.
This is an example of how an NML insights apply and shape the narrative. GC knows the scientific content of his course, the official objectives of his course, he knows his students and their relationship to math, etc. All this knowledge translates into the narrative he chooses to transfer knowledge to his students. But none of this is explicitly documented in GC’s courses.
The knowledge expert is not just expert of the knowledge. They are also expert in how knowledge is accessed and expressed. They have intuitions on what works and what doesn’t. They make informed decisions based not only on their familiarity with the knowledge but also their familiarity in manipulating the knowledge in many different contexts, under a variety of different conditions, towards (slightly) differing objectives, and observing it being manipulated by a variety of different people. Knowledge experts are experts at so much more than the knowledge of their field. I’m almost tempted to say knowledge experts are fields in themselves. But that would ruin the way we usually use the word “field” to circumscribe experts who share comparable expertise. Still, there is a lot to be said about knowledge that isn’t written in textbooks and articles but that directly influences the expression of the knowledge that is written in textbooks and articles. Knowledge experts are fine masters of a collection of subtle parameters that other people often don’t even suspect. The knowledge is just one of the parameters, albeit the central parameter. The formalism and notations in which the knowledge is expressed is another. The profound relationships between the different parts of the knowledge is another. Mastery of these parameters allows researchers to formulate the right new questions to derive new answers and it allows teachers to adapt their presentations to their students.
If you are reading this, I’d love it if you could help make NML insights and knowledge expertise matter by sharing your own examples.
I mean to equip myself with a collection of examples in order to do the following: add an optimistic nuance to one specific idea that Andy Matuschak and Michael Nielsen convey in their paper.
Like them I understand how human thinking can be impacted by “tools”, be it software tools, number systems or just language. I am also convinced that even though plenty tools for thought are actually being produced, especially software tools, the ability of these new tools to impact our civilisation’s thought habits is very limited. Optimising tools for thought for civilisational transformation requires a combination of conditions. One of them is simply work. Experimentation and open-ended exploration. Another is expert insight, typically NML insight since regular expert insight already tends to get translated into the usual field-specific venues. Andy Matuschak and Michael Nielsen call attention to the “insight-through-making loop”. In very short, synergising thinkers and makers more systematically could restart our civilisation’s ability to produce transformative thought tools for itself.
The idea I want to nuance is expressed in the following quote:
“The musician and comedian Martin Mull has observed that “writing about music is like dancing about architecture”. In a similar way, there’s an inherent inadequacy in writing about tools for thought. To the extent that such a tool succeeds, it expands your thinking beyond what can be achieved using existing tools, including writing. The more transformative the tool, the larger the gap that is opened. Conversely, the larger the gap, the more difficult the new tool is to evoke in writing.”
The idea is echoed further down in the article:
““What will new tools for thought be like?” is a question we hear often. And yet, almost by definition, we cannot say. As we noted earlier, if we could communicate the experience in an essay, then the tools would be failing at their job; they would not be transforming a person’s thinking, or even their consciousness. […]. One of the most famous papers in the philosophy of consciousness is entitled “What is it like to be a bat?” Each tool for thought poses a similar question, near impossible to answer without immersion in the tool: “What is it like to be a language user? A musician?” and so on.”
We might not have the tools yet but we already have plenty raw material to inspire and produce them: the NML insights of experts. Experts’ thinking already is expanded in a certain direction beyond the present civilisational status quo. In the distant future, transformative tools for thought will impact our thinking in ways that are ineffable for now. But perhaps we don’t need to think of tools so long in advance that we can’t even formulate what they will be like. Perhaps there are tools with huge transformative power in the near future that we can already describe the core of because the core is NML insights. With all the raw material available in the form of NML insights, we have so much to exploit already. The raw material is not exactly ineffable. It is challenging to express, especially outside of the domain in which it emerges. But perhaps the main reason little ado is made about NML insights is because of whose hands it is in: typically, domain specific experts who aren’t interested in building tools because they already are busy doing something else — they are more interested in using their NML insights to do what they are expected to do, to inspire new mathematical proofs and to tailor new physics courses. So NML insights stay caught in the silos that allowed them to be had instead of getting translating into generalisable tools for thought that could be transformative. Still, we have going for ourselves that experts, by definition, are already experiencing some sort of immersion. The ‘mediums’ they are immersed in are not yet realised in software form but they do have form as long as the experts can at least talk about their NML insights.
And I cycle back to one of the main arguments of Andy Matuschak and Michael Nielsen’s paper: a well oiled “insight-through-making loop” could do wonders.
Andy Matuschak and Michael Nielsen, “How can we develop transformative tools for thought?”, https://numinous.productions/ttft, San Francisco (2019).
NB: this post only refers to one of the many ideas discussed in Andy Matuschak and Michael Nielsen’s article. The article has much more to give…