“Tons of rain” was the grossest underestimate I heard of the amount of water accumulating during Hurricane Harvey. A ton of rain is not very much, roughly about 0.02 inches on a moderate sized roof of one house.

What about 11 trillion gallons of water? The media used the number to say how much water fell on southeast Texas. The problem is first, too many don’t know how big a trillion is and second, a trillion is not a term often used with water.

A trillion, 1,000,000,000,000, 1 x 10 ^12, is a term used to describe both the national debt and the Gross National Product. It is roughly the number of days the Earth has existed. It is about the number of seconds in 31,700 years.

The term we use to describe a lot of water here is an acre-foot (1 acre covered with one foot of water), and while perhaps archaic, it is useful. An acre-foot of water is roughly 326,000 gallons, what an average family of 4 uses in a year. Lake Shasta, the largest reservoir in California, has a capacity of 4.5 million acre feet. Eight Shastas would have flooded Houston, or 11 trillion gallons of water would cover all of New York State a foot deep. If the catchment area described were 10,000 sq miles, it would have covered it to a depth of 5 feet, basically what people needed to know and could see from the pictures.

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Per cent is a useful term, but often misleading. I inadvertently misled people before the recent eclipse. What I should have said in the talks I gave prior to the event was that there were two kinds of eclipses (there are more, but I will keep things simpler), partial and total. They are very different experiences. Had I said that, mentioning that where I lived was in the partial zone, I might have persuaded more people to go to see totality.

Instead, I and many others said the eclipse would be 99.4% (or 99%) and most people figured, reasonably enough, that they would see almost the full event from their house. I have since had several people tell me that they wish they had gone to totality. One poignant comment was that 0.6% made all the difference in the world, since it was still sunlight and not totality. If the eclipse isn’t total, it is partial. It may be a little darker, a little more of the Sun will be covered if it is a deeper partial, but it is not total. Next time, if there is a next time for me, I won’t make that mistake.

Per cent shouldn’t be used when counts are a better measure. I have said in 2001 that the per cent of domestic flights not hijacked was 99.999996%. Counts matter, especially when the counts should be zero. When I was medical director of a hospital, we had a surgeon operate on the wrong side of the head. Actually, we had three wrong side cases that I knew about—one was the wrong knee, and the other was the wrong side of the colon. With the craniotomy, the OR head said that 99.9% of the time they did it right. No, I retorted, we did 99.99% of them right, and that wasn’t the issue. There should be zero wrong side cases; 99.9% of landings done right means a plane crash every other day at O’Hare.

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Not every measurement is interval or ratio, meaning that the difference between 10 and 20 is not the same as the distance between 20 and 30. Most of us realize that with temperature, that 110 is not twice as hot as 55. That is because the Fahrenheit scale has an artificial zero that is 459 Fahrenheit degrees above absolute zero. Therefore 55 degrees is 514 above absolute zero and 110 is 569 above absolute zero, a difference of 10.7%. With Celsius, these numbers would be 273 above absolute zero, 13 and 43, respectively, making the temperatures 287 and 316, or 10.1%, really the same, given the rounding in the conversion from one to the other. It’s important to recognize what is ratio data, meaning that multiples make sense, and what isn’t. Money is ratio data, as are height and weight. Others are ratio data, but they are used in ways where one has to be careful. Height is ratio data, but the Body Mass index is a function (depends upon) the square of the height, or the height multiplied by itself.

This concept of squaring something is important in many areas, such as the energy of a moving body, which is proportional to or depends upon the square of the velocity. With hurricanes, velocity of winds increasing from 100 mph to 120 mph, 20%, is a 44% increase in energy, (120/100)(120/100). A car moving at 60 mph has four times the kinetic energy it had at 30 mph.

Cubing something is to the third power or multiplying it by itself 3 times. While 1 yard is 3 feet, 1 cubic yard is 3*3*3 or 27 cubic feet. A meter is almost 10% longer than a yard (9.4%), and a cubic meter is 31% more than a cubic yard. Gravitational attraction is inversely proportional to the square of the distance between objects; tides are inversely proportional to the cube of the distance between objects, which is why the Moon, so much less massive than the Sun, is responsible for 45% of the tidal pull on the Earth.

Fourth power? Yes. The radiation from a star can be considered to be equal to the fourth power of the temperature, useful for determining the temperature of distant stars. And closer to home, the damage large vehicles cause to roads is roughly equivalent to the fourth power of the load equivalent factor, having to do with axle number and weight.

Other relationships? Yes, too. the acidity of a liquid is the negative log of its hydrogen ion concentration (pH), which is a nice way to call 0.0000001 moles/liter of hydrogen ion a pH of 7. Therefore, what seems like a minor fall in the ocean pH from 8.2 to 8.1 represents a 26% increase in acidity.

It’s not always the magnitude of a number that matters—99.99% is not always good, and a pH’s falling from 8.2 to 8.1 will see the end of most coral reefs on Earth.

Tags: MATH AND MIKE, Outdoor writing, Philosophy

September 6, 2017 at 16:22 |

I’ve seen two high partials (98%+), one annular and (now) one total.

That last little bit does matter a lot. I’m glad we drove to Carbondale. I was surprised by how bright the corona is — I didn’t expect to have color vision at totality, but I did. Actually seeing the corona was amazing. It was so amazing I forgot to do the other stuff I intended to do: looking for the planets and stars.

It took us 10 hours to get home (it’s ordinarily 5 or 6 hours). It was worth every aggravation on the route home. That I got to spend the day with family and friends and a small observatory without being among thousands of others made it that much better.

September 6, 2017 at 16:27 |

I’m so glad you got to see totality! Yes, there is plenty of color, especially the chromosphere, which I just stared at before third contact. There was Venus and there was Regulus. I didn’t see any other stars, so you didn’t miss anything. You don’t see stars during an eclipse. And being with a small group of people whom you know is so much better than a big group.