Being the occasionally interesting ramblings of a major-league technophile.
Absolute Nonsense
As an engineer, I have occasionally been witness to someone being presented with an engineering estimate which has a range value, and seeing that rejected. "Can't you give me a firm number?"
The problem is that no, you often can't. Instead, an engineer will specify something as "sixty-two to sixty-eight" or "sixty-five plus or minus three." Because just saying "sixty-five" isn't justified. However, some people believe that if you can't give an exact number, you don't know what you're doing.
People like absolutes. The problem is, there may not be any.
Newton's laws of motion were a large part of the "clockwork universe" view which prevailed even among the well-educated for centuries. As we learned more about the universe, though, it began to look less and less like a clock. For most things, Newton was still quite accurate; Einstein didn't replace Newton, he simply explained a few odd corners where Newton's laws became inaccurate. Even Einstein has subsequently been refined. You still get people who don't understand that - as a standout example - the speed of light is not a firm number.
We all know that the speed of light is the fastest velocity possible. Only, which speed? You see, the speed of light varies with the medium through which it passes. As a general rule, the more matter, the slower it goes. Which is why the value for the speed of light is usually given for its passage through a vacuum. Since a vacuum is the least matter we know of light is fastest there.
How slow can light go? Recent experiments have reduced it to the speed of a slow walk.
Einstein himself expected this. He was co-originator of the idea of the Bose-Einstein Condensate. This is a peculiar state of matter, first proposed in 1924 by Albert Einstein and Satyendra Nath Bose, an Indian physicist. According to their theory, atoms crowded close enough in ultra-low temperatures would lock together to form what another physicist called "a single glob of solid matter." One property of such a cloud of matter is that it can slow light by an extreme factor.
Black holes are singularities, point sources of gravity with no dimension. Or maybe not. There is no doubt black holes exist. By plotting the speed of stars orbiting them - and this includes the one at the core of our own galaxy - the mass of a gravity source can be determined. Through other measures we can get firm estimates of the maximum size these dense bodies can be. Some fiddling is required to account for the accretion disk, but even with the known range of error (see first paragraph) there are many bodies where we know enough matter is crowded into a small enough space that the escape velocity is above the speed of light.
That, friends, is a black hole. But is it a singularity? The theory is that so much mass in one place will literally drop out of fourspace, producing a point of infinite density. Whether this actually happens is something we can't yet see because, well, we can't see inside a black hole. However, even if singularities exist, they may be larger than mathematical points. Some analyses say that the actual singularity could have a finite diameter.
Now, there are philosophical and mathematical absolutes. Absolute magnitude is a good example. Getting the apparent magnitude of a star is easy. A trained human eye can do that pretty well for a wide range of brightnesses. This doesn't take distance into account. Neither does it include emissions outside the range of human vision, or dust and gas in the way. Absolute magnitude assumes detecting all the electromagnetic energy from a particular star striking a standard area at a standard distance.
There's a joke in mathematics - especially programming - that constants aren't and variables don't. Physical constants are generally assumed to be, well, constant. As with the speed of light, however, this isn't always true. There are circumstances where time slows and distance compresses. These are unlikely to be encountered by humans - at least humans who survive to see the phenomena - so generally we shouldn't worry about them.
Absolute zero is a condition where all molecular motion has stopped. However, there is both evidence and theory that this can never happen. That as long as there is matter there will be molecular motion. Some have even hypothesized that matter will "evaporate" to release the energy to continue the motion. Once it's all gone, well, since temperature is a measure of the motion of particles, if there aren't any particles there isn't a temperature. So, no absolute zero. (There is no "extreme cold of space." Space is a vacuum. A vacuum has no temperature. Though, as mentioned in the next paragraph, there may be no such thing as a true vacuum.)
Likewise, there are those who think that there can never be an absolute vacuum. That once the density of matter drops below a certain value - perhaps one hydrogen atom every few cubic meters - particles will spontaneously precipitate from the quantum foam. (Could the Medieval Catholic Church have been right, just using the wrong terms?)
Water is incompressible. Except that it isn't. This is an example of the ever-popular "if it's very difficult it must be impossible" school of thought. Water is far denser than air and far more difficult to compress, but it can be compressed. You can bet that a cubic centimeter of water taken from the surface of the ocean to the bottom of the Mariana Trench will subsequently occupy less than a cubic centimeter.
Yet another speed of light exception is quantum entanglement. This is what Einstein referred to as "spooky action at a distance." Particles separated in a certain way will remain somehow connected, each reacting instantaneously to what happens to the other, no matter how much distance lies between them.
All of this is beside the problem of practical accuracy and precision. An engineer has a good idea of what is achievable and acceptable in his field. For certain tasks, stating an acceptable range is the practical solution to the problem of pursuing an ideal unattainable in the real world.
Knowing what you need (and can get away with) is important to engineering. During the construction of the Hale Telescope at Mount Palomar the first person in charge of designing and building the mounting was a naval engineer. He thought in terms of battleship turrets. These were in the right mass range, but the precision of aim required was more than an order of magnitude finer than he was used to. He eventually had to be fired, and someone willing to accept the astronomers' word as to the precision needed hired to replace him.
So, please, learn to value vagueness. It can be absolutely essential. This document is Copyright 2019 Rodford Edmiston Smith. Anyone wishing to repost it must have permission from the author, who can be reached at: stickmaker@usa.net