Scattered Thoughts Regarding Appropriate Modelling

By: Danny Geisz | July 18, 2020

Project: Orchid

Sup readers. Prepare yourself for a post that will make absolutely no sense. Or it might. I’m not really sure yet. Basically, I’m revisiting Orchid, and I’m attempting to determine how to make it fundamentally useful.

The fundamental shift in my thinking that I just recognized is that in order for a mathematical model to be useful, it must be defined within a particular context. I realized two nights ago that if the entire game of complexity comes down to stable structures with well-defined behaviors, and humans are good at categorizing such structures, then in order to replicate it, you need a machine that is able to meaningfully describe the set of characteristics and structures of a particular stable structure it encounters by means of data. So the goal is basically three steps. One: Develop a universal method for describing the characteristics and behavior of stable structures in terms of computer data structures. This is and has been the entire purpose of Orchid, as mathematical entities are essentially perfected abstractions of perfectly stable structures. Two: Develop a method for extracting a set of characteristics and behaviors about a particular stable structure encountered in a data set into the data structures discussed in step one. Three: Develop an algorithm by which computers can meaningfully interact with these data structures in order to make meaningful and increasingly refined predictions about the structures in question.

I’ve already worked out a good deal of the difficulties of step one during my previous efforts with Orchid, but it’s really step two that’s giving me trouble. I presume step three will be the most difficult, but I’ve logically decided not to even consider that yet as to preserve the amount of unpolluted thinking space that currently exists in my brain. Anyway, step two. How do we possibly do this? My first goal is to essentially translate simple statements into mathematical structures that are meaningful. So take this, “If I stack blocks on top of each other, I end up with a taller structure.” Incredibly simple statement, right? Well, how do I translate that statement into a working mathematical entity? That’s a pretty tough question.

I think my mistake for the past day of thinking about this is that I was attempting to match any object or stable structure with a corresponding mathematical entity. Ideally this mathematical entity would be sufficiently robust to fully describe the object in question, including the object’s behaviors. But that’s really tricky. Take me for example. If I jumped off a cliff, a meaningful question might be, “How long is it going to take this boi to hit the ground?” Good question, reader. I certainly would like to know how many seconds of life I have remaining. However, imagine I insulted a friend of mine, causing them to be angry (purely hypothetical, (hehe)). Based on my previous method of description, I would have come up with a mathematical entity that described Danny Geisz and used that object to model the two previous situations I described. But what sort of object would I be? Like, for real? Should I be modelled as a mapping from my environment to a particular phrase, which would in turn be modelled as a mapping from my friend’s previous emotional state to his/her final emotional state? What about the first situation? Should I simply be approximated as massive object as traditionally used in kinematics? If that were the case, then I would be a simple scalar: mass.

I’d like to think that there’s a bit more to me than my mass, so that’s clearly not the way to go. Maybe a slightly better method for modelling myself would be as a cartesian product of a variety of sets that together describe my characteristics and interaction with reality. Still, though, that seems insufficient and highly disorganized.

What I’m realizing even as I write this is the importance of context. The context of me jumping off a cliff ought to be modelled differently than the context of insulting a friend. Specifically, (and now I’m really going stream of consciousness) a particular question should be posed, and a particular quantity studied. More specifically, the characteristics and behavior of the entity being studied should be described in as great a depth as reasonable by mathematical language, and everything else ought to center around that main model. For the example of me jumping off a cliff, the two important quantities are time and my height off the ground. When my height reaches 0, we measured the time elapsed, and wala! We found an accurate prediction of the time I have left to live. (Congrats, Danny, you’ve done basic kinematics).

The situation of the emotional state is a bit less traditional. I think in this situation, the important quantity is the friend’s emotional state. Then we can regard my insult as a mathematical mapping of the previous emotional state to the final emotional state. Furthermore, we could model me, Danny Geisz, as a mapping from my current emotional state, to the words I said to my friend, which affected his/her emotional state.

In Quantum Mechanics, a particle is described as a wave vector. Why? Because simple mathematical manipulations on a wave vector yield interesting quantities like a particles position or momentum (specifically the probability that a particle will have a specific position or momentum). So basically, the interesting quantities of a particle (within the context of QM) are modelled as a wavevector, and any other entities that interact with the particle are modelled as transformations on the wavevector. Neato.

I suppose my goal, however, is to build a computational system that’s capable of analyzing a set of data and generating mathematical models that describe the data. These mathematical models could then be used to make a more cohesive and robust set of predictions about the world than the models traditionally associated with machine learning. If I’m trying to build a computer that beats a human, I need it to be able to replicate the human experience and do it in a manner superior to humans. Humans are really quite good at classifying objects and using logic to make predictions based on their “modelled” view of particular stable structures. So I want Orchid to do this, but better.

After writing this, I’m realizing that simply regressively generating mathematical models isn’t sufficient for the level of classification I require. I think I need to do some more thinking about the relationship between a structure and a mathematical context, because that’s the space where computers could excel relative to humans. Ok, that’s all for now.