Author: AndriusKulikauskas Format: TextI am grateful to [[Jocelyn Ireson-Paine]] for his ideas about [[generalisation as an adjunction]]. I have related ideas about understanding linear regression in terms of an adjunction between a category of "ideal" linear models and a category of "empirical" sets of data points. I talk about that here https://www.youtube.com/watch?v=xmqa4RwdlJQ&t=660s and how it relates four levels of knowledge (whether, what, how, why). We suppose Whether there is a linear model but don't have direct access to it. We perceive it through What we see as a set of data points. We model those data points with an ideal linear model that tell us How to work with them even though our model is not the actual underlying model. The reason Why we do this is to be able to talk about the reliability of our model, which is to say, to be able to have expectations about the data points. At Math 4 Wisdom, http://www.math4wisdom.com, I work to study how cognitive frameworks, such as levels of knowledge, appear in advanced mathematics, such as adjunctions. I would be happy to explore generalisation as an adjunction.
I am grateful to Jocelyn Ireson-Paine for his ideas about generalisation as an adjunction. I have related ideas about understanding linear regression in terms of an adjunction between a category of "ideal" linear models and a category of "empirical" sets of data points. I talk about that here https://www.youtube.com/watch?v=xmqa4RwdlJQ&t=660s and how it relates four levels of knowledge (whether, what, how, why). We suppose Whether there is a linear model but don't have direct access to it. We perceive it through What we see as a set of data points. We model those data points with an ideal linear model that tell us How to work with them even though our model is not the actual underlying model. The reason Why we do this is to be able to talk about the reliability of our model, which is to say, to be able to have expectations about the data points. At Math 4 Wisdom, http://www.math4wisdom.com, I work to study how cognitive frameworks, such as levels of knowledge, appear in advanced mathematics, such as adjunctions. I would be happy to explore generalisation as an adjunction.