MigL

I believe I've already told you about the baby tiger that my niece had for about a year. Before she became a magician at the Greg Frewin Theater, she was part of the act and choreographer, and G Frewin included tigers into his stage act. On one occasion I was invited backstage and got to pet Boomer, an 800 lbs tiger, that has since passed. What I found incredible was that if you scratch them behind the ears, they 'purrr' just like household cats, yet the frequency is so low and loud, it actually vibrates the floorboards.

No, AJB was a former, higly respected member of this forum. I havent found that to be the case. While D Lincoln explains when and how the Higgs was found, for example, 'Physics Explained' delves into how the Higgs field/mechanism works, how it gives rise to mass and the detected particle, all with a 'simplified' mathematical model. Check it out ... Just what I needed, another cat video. Like I already don't spend half of my internet time watching cat videos. As a former owner of two cats that I adored, I'm resisting the idea of getting another, as putting the previous ones 'to sleep' after 15 and17 years were two of the most difficult decisions I've had to make.

If you like a little math with your science, try 'Physics Explained' also. When I first started watching him, I thought ( hoped ) it was AJB.

OK. So, in the case of the x co-ordinate line segment, drawn on x-y co-ordinate graph paper, where the intrinsic separation between points doesn't change when curled to a circle, but the extrinsic separation does, which is the manifold that ... Is it the line segment or the graph paper ?

Thanks for the explanation KJW; excellent as always. I still have a few questions ... Consider a line segment 20 units long with point A at x=5 and B at x=15. We now curl that segment such that the two ends identify with each other into a circle. The distance between the points A and B doesn't change; it is still 10 units. This is what I would term intrinsic curvature, and separation. Now draw that same line segment on a sheet of graph paper. When the segment is straight the distance between the points A and B is similarly 10 units. But upon performing the equivalent curling operation as before ( into a circle ), the distance between the points A and B is no longer 10 units, but approx. 20/3.14 units, as it depends on both, x and y co-ordinates. I would term this extrinsic curvature, and separation. What am I missing ?

Maybe I've got it wrong, but 'intrinsic', to me, means that the separation between two points on a manifold is based solely on the parameters of those points. IOW, if two points are specified as ( k1, l1, m1 ) and ( k2, l2, m2 ), then the intrinsic separation is along the manifold defined by k, l, and m. The introduction of the parameter n, to the manifold, would imply you can have an extrinsic separation as there is now an 'embedding' dimension, n . My apologies if I've used incorrect terminology.

Don't usually watch random YouTube videos, but there are some channels I follow. Most are Military aviation related. Some that may be of interest to Forum members are 'Pax Americana' and 'Perun', which deal with Military policy, and for the 'scientists' among us, 'Physics Explained' and 'Veritasium'.

In the US money took the form of gold and silver pieces until private Banks started issuing paper currency, essentially IOUs, to 'represent' the real moneys, during the 1700s. The Federal Reserve itself only started issuing paper 'greenbacks' in 1861, essentially IOUs again, to enable the Government to finance the Civil War. They are now giving us digital IOUs, as money is not based on gold reserves anymore, so they can more easily use our actual money.

I assure you no 'slagging' was intended on my part; String Junky, on the other hand, can be awfully mean 😄.. Just intended as a gentle reminder of something I'm sure you already know 🙂.

Is this a random observation, or are you referring to some specific events ? Could you maybe elaborate ?

I read last week where German politicians have have floated the notion of Canada joining the EU. It makes little sense for countries in Europe to still send Billions to Russia for natural gas ( and to fund their war against Ukraine ) and then send money to Ukraine to fight off the Russians. With a pipeline to the East coast, Canada could possibly supply most of Europe's NG needs, as well as an abundance of other natural resources, while dealing with relatively sane people ( at least until we get invaded by the US ).

A Billion dollars to join the Board of Peace ? When the Mob does it, they have the decency to call it 'protection' money.

Yeah, I know what you meant. It is the use of the instrument that matters, even a 'lowly' Casio.

Particle spin is intrinsic angular momentum, and any momentum is a 'source' of Gravity. Is that what you meant ?

Music is not an instrument; it is a composition. You would be surprised what a former member of Depeche Mode could do with a Casio in 1982, along with Alison Moyet. And then, 40 years later, with an orchestra ...