A better yodeling contest

Today I was out driving in the bright sun, on a shopping errand, when something caught my interest on the radio. My perverse interest.

There was a radio preacher apparently advertising trips to the Holy Land. He wasn't just giving it a passing mention–there was more salesmanship than that. A significant portion of his airtime was being used. He even gave the mic to a middle-eastern-sounding tour guide, who said travelers would be eating fine cuisine, staying in some of the finest hotels in Israel (porters would be provided, of course), and riding in the most luxurious of tour buses.

In total luxury, they would hit all the hot spots: the cramped stable where Christ was born, the wilderness where He went without food, the hill where He died thirsty and bleeding, not to mention the location where Christ told us "blessed be ye poor," and "woe to you who are rich."

I thought it all sounded strangely medieval, maybe something to be pedaled by one of the more corrupt characters in The Canterbury Tales. Or maybe like something from Nathaniel Hawthorne's The Celestial Railroad, in which the hard path to the Celestial City had been improved with a convenient train system.

It's the kind of thing that makes me want to sell all my stuff, including this silly laptop, and give graciously to the poor.

Because maybe then I could say someday, after much poverty and toil, not with a lot of outward arrogance, but softly to myself, "Now, Mark, you–as opposed to them–have lived an exemplary life."

I could maybe quote Robert Frost or something: "Two roads diverged in the wood, and I–I took the one less traveled by, and that has made all the difference." Yeah, all the difference, you opulent tax collectors.

Maybe, on second thought, I could just pray for the radio preacher and all those rich crusaders. Because, I believe in God, you know. At least I'm not like those heathens.

Or maybe I could just ask for mercy.

I am trying something new.

Current Mood: Alarmed

During my time at Calgary so far I have often found myself in a certain kind of trance-like state while considering a mathematical problem. It is especially difficult to engage in witty conversation when I am simultaneously trying to find the right hypotheses to patch things up just after I find a counterexample has driven a hole right through it.

And even if I'm not trying to be otherwise clever, people are often put off when I just sit in place, thinking. In mathematics, thinking is frequently punctuated by groans of frustration.

Those of us who knew Bing well avoided raising mathematical questions when he was driving.

RH Bing was a topologist of some note. His given name is "RH": the initials do not stand for anything. I'll take the liberty of quoting in full this anecdote Calvin pointed out to me.

It was a dark and stormy night when R H Bing volunteered to drive some stranded mathematicians from the fogged-in Madison airport to Chicago. Freezing rain pelted the windscreen and iced the roadway as Bing drove on - concentrating deeply on the mathematical theorem he was explaining. Soon the windshield was fogged from the energetic explanation. The passengers too had beaded brows, but their sweat arose from fear. As the mathematical description got brighter, the visibility got dimmer. Finally, the conferees felt a trace of hope for their survival when Bing reached forward - apparently to wipe off the moisture from the windshield. Their hope turned to horror when, instead, Bing drew a figure with his finger on the foggy pane and continued his proof - embellishing the illustration with arrows and helpful labels as needed for the demonstration.

In this respect cycling is safer since muscle and brain both require carbohydrates to function, and so the legs steal all energy which might otherwise go into reckless mathematics.

Currently listening:
Freely generated
By Strange and Charmed
Release date: 23 February 1998

As most of you know, I am going to be in St. Louis from December 22 through January 6.  Two of my friends from Calgary are also going to be there, for a lesser period of time, and are wondering how one ought to spend a day or two for best effect.  Here are some of my thoughts:

• See the City Museum.
• Stroll through the Missouri Botanical Gardens by January 1 to catch the Chihuly glass exhibit.
• Visit Fitz's and the Loop.
• Meet the creatures at the zoo and Forest Park.

Does anyone have any other suggestions?  Feel free to repeat for emphasis.

Current Mood: Alarmed

• push (Study poset games)
• push (Attempt to prove Stratification Conjecture)
• push (Discover generalized poset product)
• push (Inform advisor)
• push (Type up results)
• pop
• push (Wait for responses from advisor's contacts)
• pop
• pop
• push (Understand contacts' references)
• push (Read Linear Orderings by Rosenstein)
• push (Read Cardinal and ordinal numbers by Sierpinski)
• pop
• pop
• push (Read "A note on discrete Conduché fibrations" by Peter Johnstone)
• push (Read "Méthode de la descente" by Jean Giraud)
• push (Learn French)

(sigh)

Currently listening:
Some Adventure
By Some Adventure
Release date: 15 June 2006

Since I can recall having any opinion on the subject, I have considered myself a mathematical formalist: "Doing math" means formal symbol manipulation, and its relevance lies solely in the utility or beauty of the maths. Formalism can be contrasted with platonism, since a platonist believes that a statement, like the axiom of choice, undecideable in a given system may still have an objective truth value, and it is reasonable to discuss whether such a statement is true or false, even though it cannot be proved either way. A formalist laughs at such assertions, and simply explores all the possibilities available: and in this case an axiomatic system which rejects the axiom of choice may be just as interesting as one which accepts.

I considered myself a formalist until Thursday. On that day, the BBC online published an article entitled 1200-year-old problem 'easy' which celebrated a crank's solution to the problem of dividing by zero. Reading his papers, it was obvious that he was mostly assigning the symbol $Phi$ to mean "undefined", and any operation which is not closed under the reals goes to $Phi$. To a formalist, thiskind of thing is fine, if useless. We can create whatever symbols we want, and assign whatever meanings we want, and then see what happens. Granted, it is frustrating that someone could be regarded as a "genius" by doing this, even if only by a journalist for an online newspaper.

Actually, outrage is an appropriate response to him hoodwinking a local school to teach children this kind of nonsense.

I was disturbed, though, by a thought that gripped me as I read his papers, though: $1/0=infty$? $-1/0=-infty$? Wait, he defines $0^0=Phi$ instead of 1? It's not only useless, it's wrong.

I had to sit back and recollect myself. How could it be wrong? How can any consistent mathematical statment really be wrong? Surely, I'm not having such platonist thoughts, am I?

Then I remembered an experience I had reading through Sierpinski's Cardinal and Ordinal Numbers earlier in the week. Why is he spending so much time on philosophy of the Axiom of Choice when it is obviously true? It can't be "obviously true" to a formalist, since it is well known that its negation is consistent with the relevant axioms in set theory.

And the, the most damning evidence. I had written up a brief note on a particular product on posets, which seemed more useful than the one given in Harzheim's Ordered Sets. One point being that it could be seen as a generalization of both cardinal and ordinal exponentiation, and so by introducing a bit of notation to distinguish finite cardinals (as antichains) and finite ordinals (as chains) we can remove some of the ambiguity of the exponentiation notation. The paper's working title? The correct poset product.

I'd like to use some of my newfound freedom in making pronouncements about concepts I know I can't prove, but I don't know where to start. I will begin by re-affirming that the axiom of choice is obviously true, and $0^0$ is obviously 1. I wish I could weigh in on the continuum hypothesis, but I find I can't. It seems clear that we cannot take it as an axiom, but I simply don't know yet whether it is true or false; although I rather suspect it to be false.

And so I must be off to find some more mathematical statements to believe in the absence of proof. (I know this is ridiculous, but not nearly so ridiculous as the lengths some constructivists will go to.)

Currently listening:
Specular Highlights
By Plint
Release date: 3 January 1992

1. "[Before loading a wheelbarrow] Always point the wheelbarrow to where you're headed."

2. "You don't only gotta do good work, you gotta look good doin' it!"

Current Mood: Alarmed

You may have noticed that I have changed the name of the blog, from "A better ice cube" to "A better MySpace". One reason for that is that there is really far too much ice in my life right now. I just looked outside my window and was surprised to see a blue sky. For as long as I can remember, it has been gray. In three hours it drops just enough snow to hide the tracks laid down by humans and their vehicles as if to deny it can be mastered.

It can, of course, be beaten temporarily. Yesterday I wore, from the feet up: hiking boots, two pairs of socks, "expedition"-grade long underwear and jeans, long-sleeved wicking t-shirt,"medium"-grade thermal shirt, sweater, cycling jacket, thick thermal hoodie, fall jacket, thick, multi-layer gloves, and balaclava. This basically seems to work, but is extermely annoying. I have been avoiding cycling in this weather since I took several nasty falls when it began and temperature fluctuations led to ice being everywhere. The worst is when it has melted and refroze around the snow, creating slippery ridges which deflect the front wheel just at the time when there is no traction. Of course, it has been far too cold to see that kind of ice lately, there is only snow. Yet I still wound up walking my bike this weekend after slipping in traffic while trying to bring home a 14 pound turkey, gallon of milk, several pounds of potatoes, and other groceries needed for the Saturday dinner.

So I have been walking to school lately. Monday morning was the worst - I have to climb this snow-covered hill up by the hospital, and then decide which side of 29th street to take most of the rest of the way. This side has no sidewalks, but feels a bit more direct in some ways; the other is a bit better traveled, but has more ups and downs. By the time I got to the university my face was mottled into all kinds of colors, and my hands were freezing - I cursed the decision to buy gloves instead of expedition mittens. My balaclava was filled with condensed breath and snot, and my boots were slipping at most of the parking lot entrances I have to cross.

Enviroment Canada reported a wind chill of -41 degrees yesterday. It literally (as in "not metaphorically") doesn't matter what scale that's in. On average one Albertan has died due to cold every day of this weather, but a group of Calgarians did all they could to prevent a temporary shelter from opening in their neighborhood, just for the few days it would be needed for some to survive.

Even if you have a home in Calgary, the ice will find some way to invade. Plates of ice and gnarled deposits of rime have attached themselves to the inside surface of several windows in the house, including my kitchen and bedroom. I have had to wear extra layers of clothing and order the blankets just so, to keep as much heat as possible from escaping at night.

I have some kind of aversion to wearing more than a t-shirt at home, so I have been carrying almost permanently a blanket across my shoulders. Our upstairs neighbors just moved out this past week, and now we don't have access to the thermostat, which they would sometimes adjust for us when it became too cold here in the basement.

Longtime Calgarians usually scoff at my stories of comparably mild winter storms in the Midwest, but when it gets this cold out, you begin to hear a strange consensus. That, really, "it's ridiculous that anyone should actually live here." So two people were willing to admit to me, in private and out of earshot of fellow Canadians. "We should really be living in the jungle, just pulling fruit down from trees."

Me, I don't know what to think. For as ridiculous as it is, I'm getting tired of moving every 2-4 years, having to re-establish myself and make new friends. I don't think humans were made for that, either.

Currently listening:
Unicorn Crying Party
By Frumpulous!
Release date: 5 February 2003

I would like to take this opportunity to inform all readers that Kevin is now allowing a greater degree of otherness on his weblog. This is to say that I am other than Kevin, and although future entries from Kevin should be obvious in their authorship, I would like to emphasize that any views expressed by "Mark" are not necessarily the views held by Kevin or those commonly associated with Kevin.

I would also like to thank Kevin for allowing me a place to try my poor powers as a somewhat ephemeral blogger.

Okay, how would you interpret this symbol if it showed up in your weather feed?

I'll give their intended meaning after I receive guesses from three distinct people.