It’s funny to stare at a sentence in a book that says when you fly to the other end of the USA, you become younger than everyone else by a quintillionth of a second — at the moment when you’re sitting on the plane flying to the other end of the USA.
Hello, Seattle!
Have you ever heard of a unit of mass measurement called a slug? In the US, it does exist, even though it’s less common nowadays. American physics and engineering textbooks for students, especially where they want to clearly differentiate between mass (slug) and weight (lbf), tend to use the imperial system with its feet and the like. It simplifies F = ma in the imperial system without introducing extra coefficients.
1 slug is the mass that accelerates by 1 ft/s² under the force of 1 pound-force (lbf). Thus, a slug accelerating at 32.174 ft/s² “weighs” 32.174 pounds-force (lbf). 32.174 ft/s² is our 9.8 m/s², just in feet.
A “slug” is, on one hand, a slug (a slow-moving mollusk without a shell), and on the other hand, a heavy piece of metal or a bullet (like a shotgun slug – a large-caliber cartridge). In the context of the unit of mass, it’s not about mollusks, but rather about a “heavy lump.” But it’s still funny when they write “mass equals 5 slugs.”
12 slugs equal 1 blob (image of blob attached). Blob is a version of slug, but based on inches instead of feet. It has fun slang names – slinch, slugette, snail.
I also read about the British Thermal Unit — the amount of heat needed to heat 1 pound of water by 1°F. Converting BTUs to calories or joules results in a quite awkward number.
How would you measure the water level in a river? A float? A pressure sensor? Something else? Yesterday, I discovered how it’s done here on the Potomac, and it turned out to be not at all what I had imagined. The USGS engineers are great—they educate passersby by posting a diagram of the operation.
A tube is lowered into the river through which air is supplied in bubbles (through a bubble orifice). A special pressure sensor (Pressure Transducer) measures the air pressure in the tube that is necessary to release the bubbles from it. The higher the water level in the river, the more pressure is required to push the air into the water—because the air pressure in the tube is directly related to the depth of the water (according to Pascal’s law). The bubble method works well even if there is floating debris or ice in the river, which may interfere with other sensors (such as ultrasonic ones). Since the sensor does not contact the water, it always remains dry and clean. Additionally, to prevent data distortion, the system includes an air dryer (Air Dryer), which removes moisture from the air and prevents condensation.
The accuracy of such systems is 1-2 cm in water level for rivers with shallow depths.
Interestingly, the readings are transmitted not through the mobile network, but via satellite.
It turns out that the incline (incline, or grade) – the steepness of a road or slope – has quite an obvious definition, but I never really thought about it. It means the ratio of the projection of a line on the terrain to the vertical plane to the projection of the same line on the horizontal. In other words, the magnitude of the incline equals the tangent of the angle between the rise of the slope and the horizontal (the tangent of the angle of inclination).
Thus, a “steep climb” sign of 10% indicates just about 5.71 degrees of inclination. This is arctan(0.1).
It also turned out that formally among specialists when reading the notation, the “%” sign is pronounced as “hundredths.”
Interesting. I learned, for example, that the human retina is not really attached to the vascular tunic, but is held in place only mechanically by intraocular pressure. Because of this, those who jump from heights or engage in diving, and generally anything that increases intraocular pressure, are at risk of retinal detachment.
(By the way, about pressure, I had a slight barotrauma in my left ear today during airplane landing: after landing there was a lingering feeling of stuffiness and muffled sounds, and while in the air it even hurt a bit. That is, some traces of sensation remained several hours later, but probably, by tomorrow morning I will recover fully).
I’m currently re-reading A Short History of Nearly Everything by Bill Bryson. An old book from 2003. For instance, the author celebrates that Pluto was finally recognized as a planet by the IAU. So, there’s this interesting story about scientific startups in the 17th century.
Everyone knows from school that Isaac Newton is the father of classical mechanics and gravity concepts, and authored a fundamental work that underpins all subsequent physical science: “Mathematical Principles of Natural Philosophy,” or simply “Principia.”
There was also Halley—the one after whom the comet was named, and then there was Hooke, who discovered the cell (and Hooke’s law of elasticity and loads of other stuff).
So in 1684, Halley, discussing the problem of planetary orbits with Robert Hooke and Christopher Wren, asked, “What force makes the planets move in elliptical orbits?” Hooke claimed it was a force inversely proportional to the square of the distance, but he could not prove it strictly. Halley went to Cambridge to ask Newton directly—and to his astonishment, Newton said that he had already proven it. Moreover, he promised to send a detailed account. Actually, he got a bit carried away and instead of simply answering the question, he wrote three volumes of “Principia” (and deliberately wrote it in a complicated way to discourage the uninitiated).
As the work on “Principia” was nearly complete, Newton and Hooke disputed over who first discovered the inverse-square law of force, and Newton refused to release the key third volume that made the first two volumes sensible. Thanks only to tense diplomacy and the most generous doses of flattery from Halley, the fussy professor eventually agreed to release the final volume. Without Halley’s interest and prodding, Newton probably would not have formalized his discoveries into a cohesive work.
The Royal Society had promised to publish the work but then declined, citing financial difficulties. The year before, the society had funded a costly flop called “History of Fishes,” and suspected that a book on mathematical principles would hardly stir market excitement.
Halley, whose financial situation was modest, paid for the publication from his own pocket. Newton, as was his habit, contributed nothing. To make matters worse, just then, Halley had taken a position as the society’s clerk, and was informed that the society could no longer pay him the promised salary of 50 pounds a year.
Instead, they decided to pay him with copies of the History of Fishes. The society handed him 50 copies of the same History of Fishes” (apparently intended for fireplace use).
About several hundred copies of “Principia” were released—a rather large print run for such an expensive book, yet the publication aroused no interest from the reading public. The book sold very poorly, and the publishing did not pay off at all. Even in 1739, 53 years after the publication, an inventory check found the Society still had 126 copies left, and these were being sold at huge discounts, given away, or virtually given away for free.
Ironically, one of the most influential texts in the history of humankind was considered virtually a commercial failure at the time.
And it’s funny that since its publication in 1687, there was a calculation error in the text that wasn’t noticed until 1987, 300 years later, by a student, Robert Garisto, a senior at the University of Chicago.
In sentence eight (the book used such numbering) Newton tried to confirm his theory by calculating the mass, the force of gravity at the surface, and the density of known planets. To calculate mass, he needed to know the angle between the line from the center of the Earth to the Sun and the line from a point on the Earth’s surface to the Sun.
Modern measurements give this value as about 8.8 arcseconds (one second is 1/3600 of a degree). Newton thought it was 10.5 seconds, but mysteriously used 11 seconds in the actual equation. This error was discovered by Garisto when he was redoing the calculations as part of a regular class assignment.
This Robert Garisto is now an editor of Physical Review Letters. He recently made headlines a second time when his journal published a scientific paper with 5,154 authors 🙂
Hi, I'm Rauf Aliev. 