Tuesday, November 25, 2008

New Phrases

I've just come up with a new phrase synonymous with sympathetic magic: Malleable Induced Macroscopic Synchrony. Any of you neo-pagans out there feel free to use it if you want a technical-sounding term for your gibberish.

Thursday, October 23, 2008

Pithy Question

Would you rather have medicine which works whether you think it's working or not, or medicine you think is working, whether or not it actually is?
Hint: The two options presented are not the same thing, as some people would like to believe.

Wednesday, September 17, 2008

So Wrong It's Funny

This post is here to serve two purposes. First, I'd like to start recording some of the more comical mistakes I encounter while marking assignments, tests and whatnot. Second, I found something which allows for LaTeX equations to be embedded in a blogger post and I'm testing it out.

Obviously, whenever I post something from an assignment I mark I will not include any names or other identifying information.

The question:
$\mbox{Let }x\mbox{ be a real number. For what values of }x\mbox{ is the identity}\\ \log(x^2)=2\log(x)\\ \mbox{ valid? Explain and justify.}$

$\log(x^2)=2\log(x)\\
\log(x^2)-2\log(x)=0\\
\log(x)(\log(x)-2)=0\\
\mbox{So }\log(x)=0\mbox{ or }\log(x)=2\\
x=1\mbox{ or }x=100$

$\log(x^2)=2\log(x)\\
\log(x)(x)=2\log(x)\\
\log(x)=2\log\\
x=2$

Now, for a little context. The course for which I am marking is intended for first-year university students who want to major in math. The course is designed to teach basic proof techniques, some very elementary number theory, and the basic idea of sets. The professor currently teaching the course is also placing emphasis on communication skills and the ability to express ideas in words as well as equations (something I find astonishingly lacking among most science and engineering undergraduates) and proper, unambiguous use of notation. Clearly she has her work cut out for her, but the reason I bring this up is that these mistakes are only funny (and disheartening) if made by people who should know better; if these same mistakes were made by high school students I would be less likely to find them funny or surprising.

I would also like to add to those of you who feel like you might make similar mistakes: If you are not actually planning to focus on a mathematical area, you have very little reason to know how to properly use logarithms in these kinds of situations. You should not feel bad for not seeing the mistakes above unless you actually should understand the math in question.

On a lighter note, the LaTeX appears to be working quite well.

Tuesday, July 8, 2008

Video Memory

I just had an idea for one of the worst video games ever. First, some philosophical setup.
As a species, we remember things by passing them down the generations first orally, then in pictures, then in writing. Each of us reads the writing of previous generations about events in our past and creates anew our own interpretation of the experiences.
In modern times, we have already developed video into another medium in this same vein, allowing a memory to be retained more accurately as more details are directly imparted. We are in the process of developing computer controls in such a way as to create what I believe will be the next stage in inter-generational memory: the interactive virtual experience.
Essentially, it won't be very long before people will be capable of recording their sensory input to digital form in real-time and others will then be able to experience what they did through playing that back directly into their nervous system. One step beyond that, however, is to allow the person experiencing the memory to take an active role in the experience and have the computer relaying the experience judge likely outcomes for actions the person takes. This idea amounts, basically, to full-realism in a completely free-form video game constructed directly from someone's real experience. I'm guessing 50 to 100 years at most before this technology is feasibly in place.

Scaling that idea back to modern technology, it roughly translates into constructing a video game with a real physics engine, detailed psychological AIs for characters other than the player, and with characters and setting drawn from real experience and constructed as true-to-life as possible.

Now, if you're still reading this, you're probably thinking "Why would I want to play a video game where I actually have to sit through an hour of driving just to get somewhere an hour away? Why would I want to play something so close to real life when I could just live?"
My answer is that some things should be remembered, and it might be worth recreating them as thoroughly as possible in order to do so.

So here's the idea: Auschwitz.

Take a high-powered realistic physics engine, construct a full-scale 3D rendering of the death camp as it existed during the war, populate it with guards and prisoners with AIs based on psychological profiles of people who historically were there.
There is no goal, no quest, no "good ending". The only purpose of this game is to deliver an experience of what it may have been like to be there.
No restrictions on the player - if you want to escape, try and probably get killed in the process. If you want to take on the guards, try and get killed anyway. If you do as you are told, experience the horror of watching almost everyone around you get gassed, shot or worked to death.

As I said, one of the worst video games ever. In fact, I doubt it should even be called a game - I envision it more as an interactive cultural memory.

Why make a game like this? Because some things should be remembered.

Okay, now you can go ahead and tell me how appalled you are at the idea.

Tuesday, February 19, 2008

Reflections on the Brutal Murder of Small Rodents

For quite some time now, there have been a good number of mice living in this house. As with almost everything, I am extremely tolerant of the mild annoyances mice present. I am slightly surprised whenever I see one scurry across the floor and I generally attempt to guide it away from myself and the wires attached to my various electronic devices. I was mildly annoyed upon discovering that they had eaten most of my packets of chicken soup, but I can hardly blame the mice for obeying their instincts and soup is not exactly expensive or difficult to replace.

The only thing these mice have done to particularly annoy me is to chew loudly on something in my room while I try to get to sleep. In these circumstances I usually attempt to scare them out of the room, but for amazingly this rarely seems to work. I have grown accustomed to whispering to them when I hear them, often referring affectionately to an individual mouse as "you stupid little shitling" and musing on how, if the mouse were to encounter my foot, I might sustain a mild injury easily remedied by a bandage and a rabies vaccine, they would have every bone in their tiny body broken and be splattered into a bloody pulp. Of course, this is not something I would ever deliberately do.

Chances are, I would not have actually taken the initiative to get any traps until they chewed up something I consider valuable, and perhaps not even then. Of course, I am not the only one who lives in this house, and one of my housemates indulges in screaming fits whenever she sees one of these mice. She decided, after a failed attempt at poisoning, to get some mouse traps from the landlord and she set them up today. Of five traps the landlord gave us, she set up three and then returned to her parents' house for reading week. Within hours, two of the traps had killed mice, and I haven't been able to find the third. I then set up the remaining two, one of which has also already killed a mouse. Chances are, I will have to ask the landlord for more traps tomorrow.

These are the standard mouse-traps you see everywhere and, ironically, they seem to me to be more humane than the "humane" traps my parents used when I was younger.

The first kid of "humane" mousetrap was a sort of cage designed to trap the mouse inside when it tried to eat the cheese so that it could then be released outside alive and healthy. From what I remember, these traps didn't really work at all. Either the trigger wasn't sensitive enough or the mice never entered the trap to begin with.

The second kind of "humane" mousetrap I only saw my parents use once because of its effect. It was a small tray of strongly adhesive material designed to stick to the mouse's feet when it went after the peanut in the middle of the tray. This adhesive would not kill the mouse, and it was designed to lose its adhesive properties when soaked in luke-warm water. The idea was that you would take the trapped mouse outside, pour some luke-warm water over it and the mouse would scurry away. Unfortunately, that's not what happened. It being winter, my parents took the trapped mouse outside and poured the warm water into the tray. The mouse struggled, but couldn't get free. They continued to bring more warm water attempting to keep the water's temperature from dropping and to allow the tray to de-adhere, but the mouse continued to remain fixed to the tray. Eventually the mouse froze to death, still struggling to get free.

These standard mousetraps are designed to break the mouse's neck when they go after the cheese. Earlier today I saw one activate - it was very fast. The mouse twitched for a few seconds (which was painful to watch), but it died fairly quickly. All in all, I'd say a quick broken neck is more humane than hours of torture followed by freezing to death.

So yes, friends, I am now a mammal-murderer. However, seeing as I don't actually have a moral difficulty with killing small rodents, why have I been going on for so long about this experience? Essentially, I am going over this because I thought I would not participate in this particular endeavour, but I wound up taking part despite my finding it aesthetically displeasing. I suppose I don't know myself quite as well as I thought.

Monday, February 11, 2008

Skepticism and the Obvious

Once we thought it obvious that the universe was infinite. After all, how else could it be? If the universe is finite, then that means we'll eventually hit a wall traveling in some direction, but whatever is past that wall must still be part of the universe, right?
Relativity turned that idea on its head. Now we are fairly certain that the universe is, in fact, finite in diameter but without any boundaries.

Once we thought that time could not have a beginning or an end, after all what would that even mean? From relativity again we learn that in all likelihood time is finite in a similar manner to space.

Once we thought it was trivial that a thing is either here or not, but quantum mechanics tossed that idea in the trash. When not being observed, a thing can be in a superposition of "here" and "not here" - not merely that we don't know, but that neither intuitive possibility captures the fact of the matter.

What is the lesson from all this?

The more obvious a proposition is, the more thorough you must be in proving its validity - never accept "how else could it be?" as an argument.
If presented with a list of possibilities, always question the exhaustiveness of that list.

Sunday, January 27, 2008

A Truly Horrible Super-Power

A week or so ago, I was thinking as I tried to sleep. For some reason, superhero role-playing games came into my head and I started to think of an interesting character to play if I ever get the chance again.
The fairly cliché character who is afraid of their own power came to mind, and as usual I decided to put my own twist on it by taking it to real extremes.
I wanted to play a character who was not new to their power, no longer surprised by it, but who has been so traumatized by their power's effects that they really hate to use it. Of course, for this to make sense, the power would have to be truly horrific to watch or experience.
More difficult than simply an excruciating power, it had to be one which might actually be useful to a party of characters and which could be considered balanced in-game, so this basically eliminated large-scale blanket powers like making everyone in a 5-mile radius suddenly become severely schizophrenic.

The power I came up with was as follows:
The power is used through application of will on a specific person who is relatively nearby and concentration and line-of-sight must be maintained until it is completed.
Upon activation, the target begins having their blood systematically replaced by stomach acid, starting at their venous capillaries near their extremities and moving inward through their veins to their torso and finally their heart.
I imagine that this would be quite disgusting and painful to watch. First they would scream in pain as every nerve ending in their body simultaneously began dissolving. The next thing to happen would be their skin becoming loose and sliding down their flesh (I think skin takes a little longer to dissolve than some internal tissues), as skin separates from muscles internally. Next their limbs would fall limp and their bones would begin to disarticulate as tendons are separated from bone and flesh begins to dissolve. About here we would probably begin seeing pieces of the skin dissolve and they would be unable to maintain a standing position.
Next, I think, their screaming would stop as the stomach acid reaches the inside of their heart and they die, but their body continues to dissolve over the next few minutes until they are basically left as a pile of bones and pieces of partially dissolved flesh in a pool of blood and stomach acid.

Like I said, this would probably be pretty traumatizing to watch and any moral human being who knew they were the cause of this would try to avoid it almost pathologically from then on.

Of course, I haven't done any medical research to see how long any of this would take or even if I've got the basic order of things right, but since I'm not going to be playing in a superhero game anytime soon, I don't really see the need.