A taste of what my papers on physics are like.

Kuhn's simplified model of science overstates the extent of “Normal Science” and is part of an overstated dichotomy. Multiple contradictory models of interpretation often exist side by side, providing a fertile valley in between where normal science, as he defines it, is useless. A scientist cannot just blindly use the contradicting standard models here without careful consideration of their foundations. The rift between Relativity and Quantum Mechanics is such a fertile and dangerous area. Scientists here are not comparable to a janitor mopping up, as Kuhn fondly analogizes, but are instead more like kung-fu masters. According to Bruce Lee, a kung-fu master's style is formless. They can switch schools of thought with such fluidity that their style escapes categorization. So too, these scientists are aware of the paradigms in which they work and must be fluid with their use of both.

Lambda calculus for Tensor Analysis

I know I cant shut up about it, but I really like lambda calculus. Even better llama calculus, the anything goes fast and loose version I use for everything. In fact, the only place I dont like using lambda calculus for is theoretical computer science. I think it offers an abstraction thats really needed in clean math and this is extremely apparent now that im taking this tensor analysis course. Take for example, pullbacks, where we're essentially dealing with higher order functions. Or the fact that we can make a map from a vector space V to its dual with a bilinear. In math notation, Wikipedia says this is done by the map:

$ v \rightarrow \textless v , o \textgreater$

This just seems ... wrong to me. I prefer because of its possibility to handle more complex ideas:

$ \lambda v. \lambda x. \textless v, x \textgreater $

More commonplace is to see this definition of the tensor product:

$ \tau \oplus \theta(v,w) = (\tau v) (\theta w) $

where i feel more comfortable writing in my notes:

$\oplus = \lambda \tau, \theta. (\lambda v, w. (\tau w) (\theta w)) $

Truth be told, I would write both, but trust the lambda notation more. The ideas are defined much more concretely. For pullbacks:

$ F* = \lambda p. p \circ f $

Then of course we have an easy way to talk about the function that makes a pullback:

$ \lambda f. \lambda p. p \circ f $

Iono, maybe Im crazy for mixing different notation like this, but it makes things clear to me.

This all ties back with earlier content in this blog -- Good notation concerns me alot. The symbols used for math reflect the content of the framework we are working in and can be seen as agents of them. Not only do concretely defined notations that are intuitive make learning and recording content easier, they may as I have argued free us from unintended psycholinguistic effects.

Soft Science Paranoia

It exists, I swear it does. Mention anything to a person in a soft science that doesn´t explicitly mention the value of their field of study and theres a good chance theyll freak out at you. Even if youre trying to be helpful (hey a computational approach might offer insight into this), be wary of the Liberal Arts student who may feel their domain of control threatened. People who believe in the inferiority of ¨easier majors¨dont even speak their mind to cause a defensive reaction.

Meanwhile, the soft science people prejudge anyone from the more the rigorous fields - God knows Ill get angry people who are upset I think physics is more rigorous than Comparative Literature. Apparently knowing calculus makes me incapable of enjoying poetry, or some stupid crap like that. Theres some sort of strange anti-intellectual thing going on when someone can proudly declare they dont know basic college level math and are proud of it. If I were to say the same about literature Id never hear the end of it.

To the people of Soft Sciences: We have never claimed that your field of study was inferior, so please stop being paranoid and treating us like shit because we are smarter than you.