The Lambda Calculus

So now in addition to the stuff about music I'll be posting about math. And MAYBE physics or something (aka applied math) but we'll see.
So this is a random thing I was reading about in a book I have called "The Lambda Calculus: Its Syntax and Semantics." I'm not sure whether to call it strictly math, actually. It's definitely closely tied to formal logic and computer science as well, and whether or not those are a "part of mathematics" is not really my expertise.
At any rate, the lambda calculus is a pretty interesting concept, developed to investigate the "foundations of mathematics," it basically tries to describe functions (functions as rules, that is) in a very fundamental and abstract way. An interesting thing is that, whereas we normally make a distinction between different mathematical objects like functions and their variables, the lambda calculus makes essentially no distinction -- all objects considered are "lambda terms," which are like functions, and there is a well-defined way in which lambda terms can operate on one another.
The book at any rate is pretty hilarious... I'll discuss a few highlights. In the preface, I was pleasantly surprised by the statement, "in spite of the paradoxes, the possibility of using the lambda calculus as an alternative foundation is still open," which sounds really funny out of context, but I'm pretty sure it actually makes sense in context.
I also liked the fact that there was a section after the preface called "Hints for the Reader," which begins with "This book is essentially self-contained," immediately after which is the sentence "Occasionally some elementary parts of first order logic, topology, set theory, recursion theory and category theory are needed." [contains 100% Juice! Some added ingredients.] They then proceed to list 8 texts in these areas which can be consulted for the necessary information. There's also a map of the book in this section (shown below) which shows the chapters and how they relate to each other.



I also liked the comment beneath the map.
On top of all this, this book is definitely the only math text I've ever seen that contained a moral:



They even PROVE the moral! Wow! I think Philosophers have a lot to learn from this.
All in all, it's an interestingly written book about an even more interesting topic. I encourage you to read about the lambda calculus, it's pretty cool. I'm considering posting about it in the future, focusing more on the actual theory itself.