Everything's a Goat

I ran into an amusing site today, Goatism, in which the author maintains that the main principle of the life, the universe, and everything is that everything is a goat. That's right, a goat. You're a goat, I'm a goat. Ba-a-a-a. Bleat, bleat. The whole world's a goat. He has devoted some pages to the consequences of this. But his most interesting parts are when he proves that everything is a goat. His first proof has some obvious non-sequitors in it, so I will present a revision of his proof, and show that indeed, everything is a goat:

Theorem: Everything's a goat.

Lemma: If a set X contains a goat, then all elements of X are goats.

Proof: by induction on X = n. If n = 1, then if X contains a goat, then the only x in X is a goat, and since x is the only element of X, all elements of X are goats.

Suppose that for all Y with Y <= n, that if Y contains a goat, then all y in Y are goats. Let Zbe an n+1-element set with at least one goat g. Pick an h in Z<> g, and pull it out; i.e., consider Z- {h}. This set has n elements and it has g in it, so all elements of Z- {h} are goats.Remove another element k from the set, not g, and replace it with h. That is, consider Z - {k} union {h}. This set also has n elements, and contains g, so all elements in it are goats. This means that h is a goat also, so all elements of Z are goats.

There exists a goat g. I can take you to the zoo and prove that for you, or click here. Let a be anything, and consider {a,g}. This set has at least one goat in it, so it is all goats. Hence a is a goat. So anything is a goat. This completes the proof.

Note that I can also use this proof to prove everything is a leprechaun, since leprechauns do exist. I can use it to prove everyone's an orange, everyone's a genius, and everyone's anything. So where is the flaw in the proof? I say to remove another element k from the set, and that it can't be g. Of course not, since then I could not guarantee that there is a goat in the resulting set. But it also isn't h, since h has been pulled out. So the set out of which I pull my k has two elements less than the overall set, so it has number n - 1. However, when n+ 1 = 2, then n - 1 = 0. So the set out of which I have to pull my k has nothing in it, so I can't pull anything out of it. That destroys the entire proof, since we can't even proceed to n = 2 in the induction.

There are lots of neat little tricks on the site, such as a proof that if there is a goat, then there are not two goats, so the Entire Universe is One Big Goat. It's good for a laugh, but watch the math. There are traps ahead that will get your goat.

Hurricanes and the Coyote

This has been an active hurricane year, and already we have had A, B, and C storms come by our way in Virginia. I want to know about these monsters well in advance, so I go to the Internet to find information on upcoming hurricanes, such as Weather Underground, the Weather Channel, Terrapin, and others. But this is information processed either by news organizations or by NOAA. The Internet provides raw data now, so you can look at it and make up your mind. This data consists of results of weather simulations such as NOGAPS, ETA, GEM (a Canadian model), and GFS. The last one stands for Global Forecasting System and is an amalgam of the former MRF (Medium Range Forecast) and AVN (Aviation) models. As of late, GFS has been somewhat of a clown on the hurricane scene. In fact, it has been a trickster, the Coyote of weather models.

In early July, GFS models suggested that a hurricane would strike the Carolinas in the week of July 18-24, which for me is SUUSI week. The worst thing that could happen at SUUSI is a hurricane. Even though it is inland, a sufficiently powerful one would produce another Isabel. The fun and renewal that we would get at SUUSI would have ended abruptly with the first power outage. But a few runs after the one suggesting such a SUUSI hurricane, the hurricane simply vanished. Poof. Gone. No trace of it any more and we had good weather for SUUSI with only one rainy day.

GFS could not track Alex until he became a fully-grown hurricane. It had some problems with Bonnie and Charley, too, although eventually it got on track. But it is now that it is clowning around. First of all, it said that Tropical Depression 5, then Tropical Storm Earl, would not do much of anything. It would peter out in the Gulf of Mexico. The meteorologists said that it was wrong, that it would intensify instead and become a major storm, and one run of NOGAPS suggested a monster storm striking Louisiana, causing oil prices to hit the roof before the hurricane could blow it off. But guess what? It petered out and became a mere tropical wave. GFS was right, and the meteorologists were wrong!

Then there was Danielle. It looped to the north and east well before it could get close to North America. But one run of GFS suggested it would escape from the Bermuda high and head for the Canadian Maritimes. It is clear now that this won't happen. And now there is Frances. Yesterday evening, GFS was calling for Frances (now an unnamed wave in the eastern Atlantic) to strike the Carolinas and go up to SUUSI land, just like the SUUSI hurricane threatened to do. Then it showed it wimping out near Florida today So now they are all saying this wave won't amount to much. But the latest run (2004 Aug 17 18Z) shows that it's back now, and it is turning away from land in the western Atlantic. So it's off again, on again with this storm, and it says another one may be following it, either Gaston or Hermine.

So keep a watch of the hurricane and weather reports, and also the GFS (which now has loops or movies, which are interesting to watch at high speed), NOGAPS, and other computer models, brought to you courtesy of the Internet.

Hurricane Coincidences

This hurricane season is producing a number of interesting coincidences, including some that are nostalgic. This week two hurricanes hit the US mainland. Their names were Bonnie and Clyde. Yes, it's just like in the movies. Except that Clyde was Charley, instead. Sorry, Charley. Only the best hurricanes … er, we don't want the best hurricanes here. These hurricanes arrived on or about my 58th birthday, 2004 August 13.

On this date 49 years ago, I celebrated my 9th birthday. There was a hurricane that day too, Hurricane Connie. That's right, in 1955, it was Connie, and in 2004, it was Bonnie. Connie and Bonnie. I was in Rochester, New York then, and I remember that it poured rain and was windy all day long. My father took me to swimming lessons at the Y in the morning. Both Bonnie and Connie had devastating follow-on storms after them. In Connie's case, it was Hurricane Diane, which caused major flooding all over the Northeast, when it poured its rain on soil that was saturated with Connie. In Bonnie's case, it was Charley, which pounded Punta Gorda and other Florida communities into the ground.

And yet another storm is coming. This is Tropical Storm Earl. The Global Forecasting System (GFS) shows it fizzling out, or maybe wimping into Mexico, but the Navy Operational Global Atmospheric Prediction System (NOGAPS) shows it increasing in strength and headed towards the oil platforms of Louisiana. If that occurs, the price of crude oil will skyrocket. In fact, it will probably top $50/barrel. It's interesting that this storm will do that, because Earl sounds like Oil. Hurricane Oil. In fact, Earl is pronounced almost the same as the German Öl, which means oil. Let's hope Hurricane Oil stays away from the oil.