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Tags, AI, and dimensions

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Beyond two dimensions

This makes sense. We're all used to 2D graphs with horizontal and vertical axes. These are the graphs that locate things according to two different factors: 

risk and reward, mile per gallon and acceleration, house price and number of bedrooms, etc. But we well might want to add a third dimension, such as square feet to the house chart. Or a fourth: distance to the nearest school. Or a fifth: the crime rate. It wouldn’t be hard to come up with a 20-dimensional house-buying chart. It’d be an impossible-to-read chart, but a computer might be able to make sense out of it and perhaps find some unexpected relationships.

In truth, there are many, many more factors than that, because house prices, like everything else, are affected by everything else. We live in a multidimensional world.

If you have any doubt about all this, let's go back to language. Let’s say you want your machine learning system to learn how to chat with us by analyzing the patterns of word sequences found on the internet and elsewhere. There are so many interrelationships that there can be millions and billions of dimensions. The actual number gets complex, because dimensionality in a model has to do with the number of parameters, and parameters are the variables the model adjusts during training in order to iterate toward accuracy. But any way you slice it, it’s a heck of a lot of dimensions.

If the idea that we live in a high-dimensional world starts to seep into our understanding of our self and our world, it won’t be in machine learning’s densely technical and mathematical sense. In fact, if it’s going to change how we think that the world and our thinking are structured, it’s going to have to be in the nontechnical sense that you don't need to be an expert to grasp. A world of infinite dimensions is a world in which an infinite number of tags could be applied to each thing, and that's a world that is super-saturated with meaning. That’s the type of metaverse I'd like to live in—and that I think we already do.

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