Yes, today is Sunday. I’m a day late.
Yesterday morning I was in a hotel room in Houston, Texas… having traveled for work. I got home at 4 PM, and although I considered writing a blog post yesterday evening, I was too tired.
As for the plane flights, I was either looking at the ground we flew over, or reading fiction… no mathematics at all got done on the flight, and almost none during the week.
Well, someone there did ask an interesting question, I think because they were in the presence of a mathematician who appeared to be able to speak English.
Do negative numbers and complex numbers really exist?
Most, if not all, mathematicians would answer with a resounding “Yes!” (Or a bored “Of course.”)
On the other hand, every time I see a discussion of this question on the digital signal processing newsgroup, it appears that most of the engineers who participate in the discussion answer with an equally strong, “No!”
I understand both points of view. After all, that people used the names “negative numbers”, “imaginary numbers”, and “complex numbers” suggests that they weren’t all that comfortable once they left the nonnegative real numbers behind. And just the idea of adding zero to the positive real numbers was a big step. Oh, not to mention the step of adding irrational numbers to the rational numbers to get the real numbers.
(Interesting. Negative, imaginary, and complex are pejorative words used to describe new kinds of numbers; by contrast, irrational is a pejorative word used to describe human behavior – as applied to numbers, it merely asserted that these new numbers were not the ratio of integers. The pejorative use of the word irrational came about because of the strangeness of the numbers.)
In fact, of course, we can find many discussions where people explicitly complained that these strange things were useful fictions – convenient trickery and nothing more. And that, I think, is where many of those signal processing engineers stand.
There is a classic example which began to convince mathematicians that complex numbers were unavoidable – there was no getting along without them… they were necessary, not just useful.
But it looks like that will be Monday’s post.
To change the subject completely… it’s been an interesting week for earthquakes.
First and foremost, of course, is the 5.8 that hit the eastern United States. I know that Californians, and I’m sure the Japanese, were appalled at the reaction to such a minor quake. After all, I successfully predicted at least four magnitude 6 quakes in the month of July… and at least one magnitude 5 quake every single day in June. A 5.8 isn’t that unusual… there were four other quakes of magnitude 5 or higher that day.
If you followed the news, however, you would have been told that the underlying structure of the east coast is different from the west coast (and, in general, different from places that get frequent earthquakes). Under our east coast, the rock is relatively unbroken – it rings like a bell… the energy released by a quake doesn’t dissipate as quickly as it does on the west coast… so that magnitude 5.8 was felt over a much wider area.
I was more interested – and disappointed – in the news coverage. “Oh, I ran straight out of the building,” people were quoted as saying – but that’s not a good idea.
I wish the media would devote more attention to the picture they briefly showed of a car crushed by falling brick… which fell off the wall of a building. If you rush out the doors, you risk being crushed by falling decoration, while the building as a whole survives.
Yes, people have died inside buildings… sometimes they collapse. But falling debris, in massive amounts, is far more likely, and I, personally, try to avoid running into any. In the United States, that is. In most of the buildings I go into.
If possible, stand in a doorway – the frame is additional structural support. If the shaking gets worse, crawl under a desk if there’s one nearby. In the buildings I live and work in, there are desks – but that student desk in 1971… was too small to crawl under. I should have stood inside the front door on the first floor.
If you want to read about east coast earthquakes that were really bad… in two months, between mid-December 1811 and mid-February 1812, there were 4 magnitude 7 quakes near a town called New Madrid, Missouri. They altered the course of the Mississippi River. And rang church bells in Boston.
More generally, the notifications from the USGS have been somewhat erratic. As I commented, there were two magnitude 7 quakes in Vanuatu within an hour and a half, last Saturday, the 20th.
But my notifications arrived much later, and in reverse order. I knew about one of them only because I went out to USGS.GOV and looked.
And then there was a magnitude 7 quake in Peru last Wednesday… and I have yet to be notified of it.
Finally, there was a 3.5 quake near Oakland International Airport at 9:57 AM local time, also on Wednesday. Utterly insignificant… except that I was on a plane preparing to take off… and we were delayed about 15 minutes while the airport visually inspected every runway for cracks. I presume that landings were also suspended during the inspection, and I think it would be fair to say that the airport was shut down for more than several minutes – by a 3.5 earthquake.
(I never felt it… but I looked it up this morning.)
Now let me get to work on the roots of the cubic equation