Death in the Modern World

Death is something much different for me than it was for my parents at my age. It's because the internet makes us manage our friendships differently now.  Its easier to keep in contact with more people, and easier to hear about everything thats happening in their lives. I've heard stories where, in the past, people would learn that their old friends had died - often in things like highschool reunions and chitchat when they ran into people they remembered. I can't even imagine this happening today. These days it seems like with anyone you've known, you learn about their death about as soon as their close loved ones do.

To my parents, it seems as if bad things are always happening to my friends. They're always astounded how many have caught some terrible disease, are in trouble, or have recently died. While they probably attribute it to bad luck, I know it's more the fact my network extends farther than they can imagine. They've never been aware of the social web.

I don't know what this means for death and mourning. Does more exposure to it mean that it will feel like less of a big deal?  Am I less likely to go far out of my way to mourn someone who wasn't a close friend or relative? Or maybe the enormity of it will that much more evident.

Algorithm

I was thinking about an old job interview question the other day:

You have a list of numbers. Each number has a duplicate on the list except for one number. How do you find this number?

This is clearly linear time. A little less obvious is that it can be done in constant space. As far as I know, I was the only one to actually come up with a solution to this one. It's not easy, at least in my appraisal. My solution, however, wasn't exactly the one they were looking for. I'll cover my line of thought, and then cover "the" answer and explain my feelings on them.

The constant space part led me to try adding all the numbers together. Fortunately, the sum of the numbers has an important relation to the exceptional number in the list: if it is even or odd, so is the exceptional number. This is due to the fortunate fact that the sum of two even numbers and two odd numbers is even. I immediately told this to my interviewer and convinced him it was true. He didn't seem to be impressed, so I abstracted my result using group theory and showed that the same process could be essentially used to derive the value of the number bit by bit. (The full thing is a fun bit of math. I'll leave it to the reader until I get around to writing it up.) 

My interviewer wasn't impressed. Here's the official answer:

Bit-wise xor all the numbers together.

It's immediately clear why this works and I might have thought of it had I been more into low level programming. This solution seems so simple compared to the one I promised. So why is it so unappealing to me? It is the illusion of simplicity, nothing more.

There's nothing particularly natural about bitwise Xor. The solution works, but its not clear how you could get to the solution other than to conveniently know a function which does what Xor does. More importantly, the solution doesn't reveal where the power of the solution comes from. Understanding this solution doesn't help with related problems. When I was asked the problem, I approached it abstractly -- which probably hurt my ability to solve it. Thinking more about programming would have helped, but it wouldn't have led to the deeper solution I found. This is why I am more fond of my own solution, and why I believe in abstract mathematical reasoning. Thinking about computers when trying to solve computers tends to lead to concrete thinking, destroying creative thought. Creative thought is rare.

Saul Kripke & Computers.

I think there's a general problem with how Saul Kripke and others like him, treat computation. To him, computers really are second class to human cognition. Take this excerpt from Naming and Necessity:

[Some philosophers] think that if something belongs to the realm of  a priori knowledge, it couldn't possibly be known empirically. This is just a mistake. ... To give a really common example: anyone who has worked with a computing machine knows that the computing machine that the computing machine may give an answer as to whether such and such a number is prime. No one has calculated or proved that the number is prime. We, then, if we believe that the number is prime, believe it on the basis of our knowledge of the laws of physics, the construction of the machine, and so on.

If this already seems completely ridiculous to you, you already have the basic idea of my argument. Computers do not do anything unless they are instructed to by a programmer. Computers are an extension of our own computational power. How do we know the processes on the computer tell us whether a number is prime or not? The knowledge that the algorithm on the computer is correct is a priori. We have merely taken an a priori knowledge and loaded it onto another computational machine than our own brains. It is the same process our brains would use to determine whether a number is prime or not. At the very least, this supposedly simple example is anything but that. 

Why is Kripke so intent on treating the computer differently from our brain? If I taught someone how to do the prime detection algorithm in their head and asked them instead of the computer, would this not be the exact same situation? The human brain is not one piece of computational machinery, but a massively parallel device. The process of outsourcing computation from one part of the brain to another is normal and essential to us. There's no reason why the outsourcing of computation to my laptop should be treated differently. 

This misunderstanding of what computation is deep, and probably the source of my strong and general disagreement with his arguments.

Book Reveiw

I don't know why I picked up Inside Cyber Warfare at the library. Maybe because it had an awesome cover. I'm not really interested in the subject area, yet this book was really interesting. The author covers the nature of modern cyber warfare in as non-technical of a manner as possible, instead focusing on the social and political aspects. The book isn't at all a survey text. I actually found myself a bit bored by how it covered, in detail, the international political dialog surrounding the issue, but if you are willing to skip over parts, it's not bad. If I were into security, I'd probably love this.

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.