Many people think that it’s utterly obvious what a number is. In fact, there are languages and societies with very few words for even the low positive integers, let alone higher ones. There are some with no words for zero and for negative numbers. There are ones with no words for fractions. There are some with no words for decimal fractions like 5.328, 730.3561, 0.249701, etc. There are some with no words for infinities. It is not intuitively obvious what numbers are.
That depends: Is it better to have a misleading name that sticks out and is easy to remember, or a more technically accurate and appropriate name that is likely to sound complicated and intimidating to a person encountering it for the first time?
Everybody’s favourite counterexample, Pirahã, proves there are languages with no words for numbers at all.
Counting is definitely a mathematical concept, not built into the brain or anything like that.
I’ve mentioned Pirahã in previous threads on the SDMB. I recalled that on some such thread, somebody started an argument about whether Daniel Everett’s research into the Pirahã was valid. I decided that I would rather not get into that argument again, so I just avoided mentioning them in this thread. In any case, Daniel Everett and his son Caleb Everett (who has also done research into languages that are very different from those that most of us her know) have published books and articles about just how different such languages can be.
I would say transcendental numbers (numbers that aren’t the roots of polynomials with integer or rational coefficients, such as pi or “e”), because it makes me think that it has something to do with Ralph Waldo Emerson and that crowd. Except the mathematicians had claimed the use of “transcendental” first (in 1682), so it’s the New England philosophers who were poaching the name 9first used in 1836).
Wonderful post. A witty and informative mini-essay, really.
The trouble is that conflicts with the use of orthogonal for matrices. A matrix is orthogonal if each of its rows is perpendicular to all the others. For example (1,2;-2,1) is an orthogonal 2 x 2 matrix. And (3/5,4/5;4/5,-3/5) is called orthonormal because, in addition, the rows have length 1.
I would think it would be clear from context whether the term is being applied to a number or a matrix. Many math terms are resued in different domains. Like “orthogonal” itself has a geometric meaning in addition to the application to matrices, and “diameter” has different meanings in geometry, graph theory and group theory.
Speaking of named concepts, that is not what it says here:
The No-Cloning Theorem is a bit confusing as a title. It states that you can’t create exact copies of a quantum state - but you can make one copy (and destroy the original in the process) (if I’ve understood correctly)
I will stick to what I said. An orthognal matrix is one whose rows are orthogonal and an orthonormal matrix is one whose rows are orthogonal and normal (of length 1). If the rows are orthogonal so are the columns. I guess Wiki doesn’t know everything.
Although the term “singularity” is appropriate for describing the mathematics of the interior of a black hole, it is misleading in that physicists are certain that whatever the truth turns out to be, there can’t be a region of zero volume and therefore infinite density containing all the black hole’s mass.
I don’t think the word “singularity” presupposes any particular theory other than “whatever is at the center of a black hole” . If it turns out that a singularity must be of finite size, say exactly one Planck length, or is actually something completely novel and unexpected, it would still be a valid term.
It is frequently used to presume the physical reality of such a dimensionless point since that’s what General Relativity predicts acc. Penrose et al, and G.R. is the best theory we’ve got; only that’s evidence that G.R. can’t be completely correct, we just can’t currently say what else is.
I’m not sure that “center of a black hole” is even a well defined concept. Sure, you can describe a locus of points with an arbitrarily small diameter around the singularity, but there’s no point in space that’s actually at the singularity.
I think you’re right - “GR predicts a singularity” is physics-talk for “GR predicts something impossible so GR must be wrong” (just as Schroedinger invented his cat as a way to show that the interpretation of QM that allowed dor such a strange thing had to be wrong in some way)
“Imaginary number” is both less accurate and more intimidating than “rotational number”.
We are not at all certain about that. I think it’s fair to say that we mostly suspect that’s the case, but we don’t know enough to be able to actually say.
The center of a sphere is certainly a geometrically well-defined concept. If the singularity is of finite size (perhaps one Planck length in diameter) then the geometric center of the black hole will be within it.
But this is getting away from the point I was trying to make. This thread is about badly named or misleadingly named scientific concepts. I don’t think there’s anything wrong or misleading about the word “singularity”. We just don’t really know what that thing the word describes actually is. Sir Arthur Eddington couldn’t bring himself to believe that black holes could exist at all, and publicly ridiculed Subrahmanyan Chandrasekhar for hypothesizing such. The latter was the author of the famous Chandrasekhar limit governing the collapse of stars into neutron stars and black holes. The whole concept is mind-boggling and singularities probably cannot be described by currently known laws of physics.
Breaking the sound barrier
Back in the early days of jet aviation, the aeronautical world commonly used “breaking the sound barrier” to mean ‘supersonic flight’ or ‘flying faster than sound’. It made sense to them. And they understood that doing this leaves a sonic boom trail on the ground.
However, all too often the groundlings interpreted it to mean ‘when you accelerate to faster than sound’ – it happens once, then you’re done. Thus, a sonic boom is an event in just the one spot.
In the 1950s, many of my relatives lived around Tinker AFB in Oklahoma, where the Air Force was flying low and supersonic a lot, treating the locals to lots of sonic booms. My relatives (many of them, anyway) believe(d) that if this happened to them, a fly boy had transitioned to supersonic just to rattle them on that very spot. Arrgh!
Is this confusion still alive? or has it died out in the last half-century? Aeronautical buffs, please share your recent knowledge with us!
But I don’t think the concept of “sound barrier” had much to do with sonic booms, then or now. It had to do with what would happen when you pushed an airplane beyond the speed of sound. From what I’ve read about Chuck Yeager and the first supersonic flight in the Bell X-1, hitting the speed of sound produced enormous vibration and turbulence, but amazingly, once you were past it things smoothed out again if the aircraft was designed for it. So, intentional or not, it turned out that “sound barrier” is actually a thing, a very real transient condition that you have to break through in order to fly supersonic.
But we have real pilots here, some of whom are Air Force veterans, who know far more about this stuff.