Brent Meeker <meekerdb@verizon.net> wrote:
Keith F. Lynch wrote:
I like to collect unexpected numbers. For instance how would you guess the heat generated by the sun, per unit time per unit mass, compares to the metabolic heat generated by a person? Check it out for yourself, as you probably wouldn't believe my answer.
Being a physicists I already knew the answer. :-)
You're a physicists? How many? :-) Ironically, given that I'm not a visual thinker, I discovered this surprising fact by plotting mass against power output of a wide variety of things on a log-log chart. I've learned a lot by doing the same with other pairs of physical parameters. Similarly, Randall Monroe pointed out that, per unit mass, a firefly is thousands of times brighter than the sun. See https://what-if.xkcd.com/151/ I discovered that our galaxy has about the same area density, i.e. kilograms per square meter, as a potato chip. In other words a potato chip of the same diameter as our galaxy would have about the same mass. I wonder if anyone else has noticed this -- or gone on to calculate how long it would take for a person to eat such a chip. Of course it would either collapse under its own gravity or fly apart, depending on how fast it was rotating. It could be stable if it consisted of many concentric rings, each with its own rotation rate. That led to the question of how large a solid object could exist in space. Lets replace the chip with a steel cable in a loop, spinning at just such a rate as to counteract gravity. Assuming it's not near anything, I think it could be of cosmological size. I'm not sure what would finally make it fail. Probably frame dragging due to the Hubble expansion. Or maybe whatever mysterious effect is causing the expansion to accelerate. Or maybe differential pressure from the cosmic microwave background, whose rest frame is different in different places due to the expansion.
Ten miles is plenty of distance for a big difference in rain fall. Didn't they nominate it a thousand year flood in Ellicott City based on measured rainfall?? Was it the same as in Baltimore?
Yes, that was the point in my argument. Sorry if I wasn't clear.
The United States could be divided into about 38,000 squares ten miles on a side. So it can be expected that each year about 38 of them have a thousand-year flood.
But in a lot of them a thousand year "flood" might be 6 inches of rain instead of the mean 2 inches. So however statistically unusual it was, it wouldn't get reported beyond the local newspaper and nobody would call it a flood.
Right, which is why newspapers aren't full of such stories. Also, given that official weather records have only been kept for about 150 years in the US, as there are more than twice that many days in a year it's unusual if at least one day each year *doesn't* set a record for highest or lowest temperature, or most rainfall or snowfall, for that date, even if there's no climate change. For instance each of the past 150 July 24ths has the same odds of being the hottest (or coldest, or rainiest, etc.) July 24th in your city in that period. But the newspaper calls it the hottest *ever*, as if time began in 1870. Getting back to the density of galaxies, there are at least three objects in Earth's sky that are about a half a degree across: The sun, the moon, and the Andromeda galaxy. It's easy to show that the volume of an object of given angular size scales with cube of distance, and that the tidal effect of an object scales with the inverse cube of distance, so the two cancel out. As such the tidal effect of spherical objects of the same angular size is proportional to their densities. And indeed the ratio of the moon's to the sun's tidal effect on Earth is about equal to the ratio of their densities. Andromeda must also have a tidal effect on Earth, but since its density is so low, the effect in unnoticeably small. (Also, Andromeda isn't spherical.) This doesn't seem to be widely known, otherwise visitors to my home could answer when I point to my autographed copy of Misner, Thorne, and Wheeler's _Gravitation_, and ask them whether its tidal effect on them exceeds that of the moon. (Okay, that book isn't spherical either, but if it's so close that it would be more than half a degree wide no matter which way it was rotated....) Does anyone else here have any unexpected numbers or little-known scaling laws to share? Thanks. It's only barely mathematical, but I'm also interested in unexpected facts about chronology. For instance the first tyrannosaurs lived closer to the present than to the Jurassic. Cleopatra lived closer to the present than to when the pyramids were built. When the pyramids were built, there were still living mammoths. The Berlin Wall has been down longer than it was up. JFK has been dead longer than he was alive. The movie Gone With the Wind was released closer to the Civil War than to the present. (Plenty of Civil War veterans watched it. But an adult actress in it is still alive today. Ironically, the character she played died in the movie.) When Star Wars was released, Charlie Chaplin was still alive and France was still using the guillotine. Harvard University was founded before calculus was invented. Fax machines were invented before Texas, California, and Florida were states. The TV show The Simpsons has been broadcast for more than a third of the time since TV was invented. There's a TV interview of a witness of the Lincoln assassination. There are photos of veterans of the Revolutionary War. People who weren't born until after the 9/11 attacks will be old enough to vote in the next presidential election. The first manned moon landing was closer to Lindbergh's flight than to the present, and Neil Armstrong got a congratulatory telegram from Lindbergh. Every ex-president born in the past hundred years is still alive. I've been using email for a quarter of the time since the Civil War.