I spent some time in the last few weeks developing a sense of order around what sort of mathematical concepts I wish to learn. These concepts I arrive at are necessarily derived by the problem set in front of me. Or rather, I can’t necessarily know what it is I’m supposed to learn if I don’t know what problem I am hoping to solve. And I can’t necessarily know what problem I have if I don’t have some sort of motivated or at least disciplined interest in the field that generates those problems. Looking back at my notes in the last few weeks I have come up with some sort of general field of interest as it relates to the following:

  • having a story arch of some kind and understanding the purpose of mythology in story telling
  • modeling that story through visual and interactive systems (i.e. game design)
  • deriving a model of interaction that is, in part, based on realistic representations (i.e. physics)
  • writing my thoughts out as a means of furthering my intuitive understanding of the overall direction

This has led me to today’s post on developing intuition. I came across an article about the adjective fallacy. In this article the explanation is fairly simple: it is not necessarily explicit knowledge that is all that is necessary to developing an intuitive understanding but the presence of “tacit knowledge” that can be derived from experience and analogy. Based on this I hope to build my own sort of foundations in game development and computer science by using the complementary approach. With this I lay out the following suppositions:

Let’s start with the supposition that the purpose of existence is to manifest potential, that is move from a state of lower entropy to more entropy and new perhaps more precise information. That is to say, I know in some sense how I would like things to be, or perhaps I am aware of how things are not (in the negative sense) and that brings me either confidence/hope/confusion/positivity/negativity. By being aware of the potential, or in the negative how things are in the negative sense, then it follows that manifesting a potential only comes out of directing action in some disciplined form. You can also say that if the potential is vague or imprecise, then it follows that the only way to improve precision is to attempt to develop an intuition through mental modeling or interaction. Chaotic representation necessitates chaotic (but also sometimes creative) interaction and (flexible yet imprecise) modeling, so to speak, while ordered representation necessitates precise (and sometimes limiting) interaction and (sometimes abstraction but sometimes inflexible) models.

From this supposition, we move into effective game design as a combination of primary functions: story telling, systems building, modeling physics and deriving an actual game through mathematical foundations, and of course the relationship of furthering my own mental model through writing and experimentation. From here, I have a discovery process of goals and the production of material that supports these principal points. Laying all of this out creates a logical framework from which to pursue how to learn and build intuition.

In game design, we also have additional constraints that simply do not exist in reality. Memory, processing, time, and even design constraints limit and necessarily direct implementation. Nevertheless, fundamental concepts like trigonometry, vector space models, fluid dynamics, orbital mechanics, are areas that can be utilitized given the problem set. If we were to create a space faring colony type game, then we might pull from many different fields of scientific research as well as make use of the wide range of mathematics. Education, in these sense of the word, requires both explicit knowledge based on the foundations but it also requires application - something that actually requires that knowledge to be put into use. It follows that prior to knowledge being put to use, intuition of that knowledge as it relates to utility is required.

So what is intuition exactly around a field like say trigometry? Developing an intuition here requires knowing how and why the field developed and to what sort of problem sets did the field manifest itself from? There is a lot more history here that I am hoping to explore more, but the overall sense of this is that:

  • logic is the result of observing that actions have consequence and consequences can sometimes be predictable
  • logic follows from observation about imagined consequences due to various actions
  • actions are interactions with and manipulations of internalized and external information (derived from observation)
  • fundamental axioms and suppositions are derived from observing repeatable resolvable experiments

When the worldview is setup in this way, it follows that someone is bound to utilize that framework in the generation of a new kind of abstraction, thus creating a formal way of understanding measurements, shapes, as well as the relationship of different points along those measurements.

  • Euclid’s elements, as an example, is a logical framework derived from interacting and measuring the world and approximate shapes the seem to regularly show up. While other mathematicians may have stated similar formula, the derivation of these axioms coming out of a logical deduction framework is what made this work foundational. It builds on intuition.

I can appreciate the work of Euclid, and that of Einstein, because the fields are generated precisely out of the realization and application of formalized logic and developing intuition. A great reason many might understand some of Einstein’s work is precisely due to his way of imagining vivid scenarios that most of our minds are well equipped to handle. If most of our brain has been dedicated to visual processing, then it might follow that the way to present knowledge is most effective through visual but more importantly relatable analogies.