Odd Scales

Daniel Thompson has a blog where he shares some musical compositions created with unusual scales. The 12-note version that you see on the piano goes out the window. In one case he uses a 26-note scale. I had some fun playing around with the math to see which of these produced the best fit for certain types of note ratios.

Can I help you? No, I can't help you.

In the seminar class I participate in, we profs decided we wanted to videotape the students so they could critique their own speaking styles. After trying it out with a borrowed video camera, we decided the department should buy a digital cam that records on DVD. I checked WallyWorld and found a Sony in our price range, researched it on Amazon, and decided that was the one.

So this morning I went in and showed the salesperson the one I wanted. She poked around a bit and announced that it wasn't in stock. My next question was, naturally enough, when can you get me one if you order it today? She looked. Nope--we're not stocking that one anymore. Well, then, can I buy the display model I ask. Nope, we don't do that.

This was getting ridiculous. They had a Hitachi and a Samsung DVD video recorder on display beside the untouchable Sony. Do you have either of those? Nope.

This is the world's most efficient supply chain? I'm off to BetterBuy...



So tonight I was working my way through this book on the philosophy of science that I borrowed and want to return soon. There's a bit about Parmenides that gave me pause for thought. According to this interpretation, the universe is full of unchanging stuff, and our perceptions of change are nothing more than rearrangements of it. In other words, combinatorics is what makes the world go 'round.

I have to admit, the idea apeals to me. So imagine for a moment this world:

The 'stuff' of existence is nothing but arrangements. It doesn't make sense to ask arrangements of what because there probably isn't any stuff. Just arrangements. Wait, it gets stranger. There are all kinds of these arrangements. Let's call them frames. There is no space or time, but the frames can be related logically to one another purely by classification. That is, there is an identity relation (that one is the same as that other one), and other more complicated kinds of relations. Let's hypothesize that some of these relations have interesting properties. In particular, some have properties that we could call 'cause and effect'.

For example, let's take a zero-dimensional frame {1}. Suppose that a frame has a causal relationship to an effect frame if the latter is the same or double the first. In this case {1} -> {1} or {1} -> {2}. There are two possible outcomes for the 'cause'. Note that this is not a deterministic cause and effect. Don't get hung up on that.

Let's call a sequence of cause and effect frames like {1} -> {1} -> {2} -> {4} -> {4} a world history.

Have you ever noticed how tightly linked the notion of time is to the notion of cause and effect? Suppose we have it all backwards and the latter is the cause of the former? That is, the causal link between these frames creates a literal timeline.

But wait a minute--where's "now"? In this model, all moments in time are the same. There's no priviledged one that we can say is special. That's really okay. Each one is its own little "now".

If you lived in such a world history, you'd experience life just the way you do now (perhaps with one small caveat, as we'll see). But your view of the universe would be very narrow. You wouldn't notice that the 'you' that exists this instant is no different from the 'you' that exists five minutes in the past or future. Each was fulfilling its part in the causal chain. So all of the 'yous' that have ever existed or will ever exist simultaneously experience time moving forward.

Because of all the branching of world histories, the you that exists right now and the me that exists right now will go our separate ways down different world lines. We'll never notice this because at every instant "our" histories will have the same causes and effects, but the continual branching would assure that most versions of you and most versions of me diverge.

In this version of reality, one wouldn't be too surprised to find ways of looking at the world that were ambiguous--that is we find places where cause and effect begin to break down. This can happen only in such a way that it never really violates the relationship, but it can be ambiguous, as in quantum behavior.

Finally, the way I constructed the one-dimensional world wouldn't work because multiple histories collide. That is, {1} -> {2} -> {2} ends up in the same place as {1} -> {1} -> {2}. Could it be that the dimension of the frame has something to do with the possibility of constructing a causal relationship? There are differences in random walks in one, two, ... dimensions, for example. Perhaps there's something special about three-D frames? Alternatively, is it possible that we can find examples in our own world where different histories arrive at the same frame? So you and I could legitimately disagree about who won the Super Bowl and we'd both be right, from our own perspective.

If all else fails, one could invoke the anthropic principle and claim that without causes there would be no time, and therefore we wouldn't be here to worry about it.


Games Yeast Play

Okay, admit it. At least once when you were a kid, you grabbed the last piece of pizza and put it on your plate while you were still only half-finished with another piece. It seems that some fungi have figured out a more sophisticated way to place food off limits to others. There's a cool article (subscription required) in New Scientist (Dec. 23-Jan 5 2007, page 32) about the yeast used in brew-making. Like lots of critters, yeast feed on sugars:
Most organisms that generate energy from sugars use oxygen to break the molecules down into water and carbon dioxide.
The yeast in question, however, turns the sugar into alcohol. The problem with that is that the organism only gets 1/18th the energy it would get from the latter process as it would from the more common one. Why would evolutionary pressures allow for the adoptions of such an inefficient process? The answer to this riddle was figured out by John Aris of the University of Florida. It's ingenious.

First, alcohol is poisonous to most other microbes. The production of alcohol allows the yeast to fend off competition. Once it runs out of sugar, the yeast turns the ethanol into acetaldehyde. It uses available oxygen to break this down further to reclaim energy, according to the article.
[The yeast] turns sugars into a poison that kills off any rivals, and then feasts on the poison.
The trick for brewers is to make sure there's not enough oxygen around to complete this process. So seal those bottles of home-brew up tight. Now you know why.



The Tooth and Nothing But

I went to the dentist for a cleaning (of my wallet, as it turned out) on Tuesday. Whilst I was waiting, these two other ladies struck up a conversation. Something like this:

Mabel: You here for an appointment?

Gladys: (turns white) Oh no! No! No, I'm here to pick up my husband. (whispers) He's gotta have three teeth pulled. Been in there for two hours already. No, I have to take valium just to drive someone else to the dentist. Just thinking about it, my heart starts pounding.

Mabel: (nods appreciatively, goes back to reading the book of Job)

Gladys: I had tooth what needed to be pulled once. But the dentist convinced me to 'save the tooth'--save it, he said--and have a ROOT CANAL. Oh, Lawsey, I shouldn'ta done. (nods sagely) But I did. He numbed it up, but it didn't do any good. When he hit that nerve, I thought I'd die. I'd rather give BIRTH. I'd rather give birth every day than do that again. And a few days later the tooth cracked itself in half and I had to come back. He pulled it then all right, but I got a dry socket. You know what that is?

Mabel: I hear they're bad.

Gladys: As long as I kept my tongue in the hole it was okay, but oo-ee if I took it out to eat or talk... So he had to fill it up with some kinda stuff until the bone filled in.

I was thinking it might not be such a bad thing if she had another one.

Gladys: (whispers loud enough for the receptionist to hear) Do you know what dentist it was? (dramatic pause) This 'un right here! (points in the presumed direction of dentist) Him! But it's funny--it done me good being terrified of the dentist and all. I had to have another tooth pulled later on. Not by him (pointing again), but I was so terrified that the dentist sent me off to the surgeon to have me put to sleep. And you know what? The end of the tooth was attached to my sinuses, and would have left a big hole if I hadn't been right there in surgery to fix it. So it was a good thing I was so scared, and the dentist done said so afterwards. He laughed about it.

Mabel: I see those poor people over at Angelo's that look like they've been through it.

Gladys: Well, over there you can get a tooth pulled for $35. Here it'll cost you $300. If you have to have five or six of em pulled--people just can't afford that.

Mabel: They come out with their mouths all full of gauze. (shakes her head)

Gladys: Mostly they pull them all out and fit them for dentures right there and then. Lawsy, I'd think that would hurt! Go in with teeth and come out with that thing stuck in your mouth. Have to learn how to talk and eat all over again. My sister had to have her jawbone ground down so her dentures would fit right. I went to Angelo's once for a filling. I MADE SURE I told the girl--I'm here for a filling. I don't want no teeth pulled! She said, you just sit over on that side. We won't pull your teeth.

Mabel: Still, at least they have a place to go.

Gladys: Yes, thank goodness for Angelo's.

Receptionist (to me): The dentist will see you now.



There's some cool stuff at lunchtimers.com. I like the puzzles the best, but here's a refrigerator magnet set: