Eugene Salamin <gene_salamin@yahoo.com>

Math-fun seems to have garbled up the line feeds in this message, so I'll try again.

I'm pretty sure the problem is at your end, i.e. you're sending each paragraph as one long line. Also, whenever you have two spaces in a row, one of them gets turned into what I assume is a UTF-8 non-breaking space, which math-fun turns into a question mark. I've noticed that the "smarter" software gets, the more mangled messages get. That's why I use very simple software.

Here's a nice one. What is the energy flux = power per unit area F (W m^-2 = kg s^-3) carried by a gravitational wave of strain h?

I solved that one too. Except I too was off by a small factor. After a live talk at the Philosophical Society of Washington on the topic of LIGO, I mentioned to one of the speakers that LIGO wasn't very sensitive at all, given that if the gravitational wave energy had been visible light instead, it would have been bright enough, not just to see with unaided eyes, but to read by, even though the source was more than a billion light years away. He asked me where I found the equation for converting strain into flux. Apparently they don't publicize that equation much, as it makes LIGO look bad. (On double checking, I found that a video of the whole talk is online, at https://www.youtube.com/watch?v=y6_NpIRhoWg That post-meeting discussion isn't on it, but I do ask a question at 1:52:40, if anyone wants to know what I look and sound like.) There is an element of arbitariness in dimensional analysis. For instance notice that the dimensions of electric charge are completely different in SI and in cgs. See https://en.wikipedia.org/wiki/Statcoulomb Is vertical distance the same thing as horizontal distance? In most contexts, yes, but not to interior decorators, since it's against the rules of interior decorating to place a piece of furniture on its side, back, or front. People used to measure the vacuum speed of light, and debate whether it was constant, or whether it might vary slightly with time, direction, or frequency. But in the 1980s, the length of the meter was redefined to depend on the duration of the second, which caused c to be defined as exactly 299792458 meters per second. It feels like sleight of hand to me. Or has SI changed the definition, not just of the *unit* of distance, but also of what's *meant* by distance? They plan to make further changes, which will turn some numbers that were measured into defined constants, and vice versa. See https://en.wikipedia.org/wiki/Proposed_redefinition_of_SI_base_units They're coming perilously close to *defining* General Relativity as correct. I'm most fascinated by dimensionless constants, such as the fine structure constant, alpha. Those can never have defined values; they have to be measured. If alpha turns out not to be constant after all, it's an interesting question whether we can make an arbitrary choice of whether the speed of light (c), Planck's constant (h), the charge of the electron (e), or the permeability of space (mu-0), had changed, or whether there's some non-arbitrary way to determine which had changed. With current SI, c and mu-0 can't change. With the new SI, c, h, and e can't change, but mu-0 can. But that may just mean that either the old or new SI, or both, are inconsistent with a world in which alpha changes.