lancelot

I saw this game played first in the classic 1960's French film 'Last Year in Marienbad'. I learnt how to play it to always win, by trial and error. I believe there is also a simple maths algorithm for winning play but I have neither the skill nor patience to figure it out. Can anyone help? The game: For two players. Lay four rows of mathsticks: 1, 3, 5, 7. I III IIIII IIIIIII The play: A player can take any number of sticks from any one row at a time. The one who has to take the last match loses. Its always fun to play this a few times and let the patsy win, then offer to bet a couple of beers that you can win the next three games straight out. When he loses, offer double or quits. Eventually he twigs and you both enjoy the beers!

SkepticlAnce - yes, colonisation is a possibility. I concede that. Genetic engineering could also come into play in a big way in a small colony. Mr Skeptic : "Studies show that we are evolving (aka changing) at a faster rate than ever before". which studies are those?

LostLabyrinth - to asnwer your origial question: For mankind to evolve in any signficant way three things are neeeded: 1. Environmnental pressure for gene selection 2. Reproduction. 3. Ideally, a gene pool which is relatively small and isolated from the main pool. Pressure for selection may be as a result of any unforseeable situation, The earth could get hotter and drier. Or colder and wetter. A new virus could wipe out half the population. People who are good at art could become more successful than accountants. There a lot of different scenarios! The most likely pressure with increasing use of technolgoy would probably to be that brainpower becomes more useful than muscle power. BUT - any 'brainy ' genes will only tend to dominate if the parents produce more surviving children than others. If they dont - the gene pool might even drift towatds more muscle power. Populations are now so mobile that the world is one gene pool. It is hard to see how any particular genes could become more dominant since there are so many variables. Medicine allows the less fit to survive, and reproduce. Reproduction is not related to basic success of survival as is used to be. Reproduction is aritfiically controlled in many cultures - look at China So barring some massive catastrophe on the planet, I would bet on the human race staying pretty much the same.

NIN. Throw a dice. It comes up six. Was it your free will that caused it to do that?

Janus - I have just opened this - excellent! Thank you so much.

Very good point Iggy. The analogy is only strictly 'correct' if both A and B move away from each other at identical acceleration. Still it's useful to get people over the intial disbelief of time dilation by comparison with an everyday experience. Having got that sorted, I suppose the analogy could be extended to "now imagine, if perspective worked like relativity, if B runs into the distance and back again, she will actually come back smaller!"

Intersting speculation about DNA at the beginning of this htread. The imagined scenario is that some time ago an 'alien' power genetically modified proto-humans to produce a radically higher level of intelligence in humans. Why? A 'lab experiment'? A philanthropic act? All speculation, and a scenario which 20 years ago would have seemed wildly ridiculous. However it is interestiing to look at how our knowledge of DNA had progressed over that period. It is now perfectly possible to modify specific behavioural traits in animals by gene manipulation. DNA was only discovered fifty years ago. What will our knowledge be in a thousand years? If there are other intelligences, which seems statisitcally probable, they could well be a million years ahead of our knowledge. So manipulation of DNA now seems much less ridiculous. I am NOT putting this forward as a probable scenario! But as a hypothesis, it has to be granted a level of possibility. It would certainly provide a neat explanation for certain human abilities such as articulate speech!

ajb: It seems that the observation of distant starlight deflected by the sun in 1919 proved Einstein's GR to be correct. If so it must have been possible even at that time to calculate the predicted deflection and/or path, I would assume. (?)

Thank you Janus. I see my error. A particle could pass on a geodesic into the photon sphere and out the other side if at the right angle of approach. As you point out, only within the event horizon do all geodesics lead back into the BH.

People getting introduced to SR often have a bit of a problem grasping how Anna's time can appear 'frozen' as seen by Betty, but equally Betty's time can appear frozen as seen by Anna. Yet time for Anna and Betty actually carries on at the same rate as far as they are concerned. Eye glaze takes over..... I have found that a useful analogy to help grasp the concept is the familiar one of visual perspective. Anna walks into the distance and Betty sees her as smaller. Anna sees Betty as smaller. But they stay the same size. How is this possible??? Once people ponder on that familiar phenomenon they begin to accept time dilation quite easily!

I understand that the photon sphere, the circular orbit of a photon, would be at R = 3/2 Schwarzchild radius. This is the geodesic path at that location. But this seems odd. It implies (A) if moving tangentially at greater than R, the photon will pass by with mere deflection. Fair enough. But, (B) it equally implies that if moving tangentially at less than R, the photon would be in a less than circular orbit, which I can only imagine as a spiral towards the BH. But this would imply that the photon sphere is effectively a Schwarzchild horizon for the photon! Where am I going wrong in this interpretation?

That exactly what I was looking for. It could be an interesting 'trival pursuit' challenge for someone! I suppose I am right to assume from ajb that it would not be a para/hyperbolic function, as for a mass particle? Pity, that would have been neat, and within my maths capabilities!

ajb thanks, the link on 'notes' does work, it wasnt apparent to me before, as normally the blue text is more prominent on messages. That's an interaction between the forum software and my RGB monitor I guess. I have looked at the link - and I see the maths and terminology is quite complex. I will endeavour to work through the maths but it could take me a while! To deal first with a dense body in space question - that seems to be quite a complicated matter in GR. For a massive particle in Newtonian physics it's easy - an elliptical orbit or other variation of a hyperbolic function. But it would seem perhaps there is not simple equivalent in GR so I will just accept that. To deal with a photon emitted from a torch on earth: A rifle bullet willl have a vertical acceleration vector of g, which defines its trajectory. As any student knows, a = g, because m cancels out in the Newtonian derivation, using f=ma. My curiosity was aroused by wondering what happens if m is made infinitesimally small (but not zero). Even if m were 10^-10000 eV, or whatever, it would still cancel out and a = g. So i wondered how that path calculated in Newtonian fashion for a 'bullet' of infinitesimally small mass at velocity close to c, would compare with the path of a particle of absolute zero mass when calculated correctly in GR. i.e what would be the 'rate of fall' of the photon towards the earth surface? And the resultant trajectory? However, I begin to suspect that using GR, the answer may not be a simple one, at least not for me.

Hi everyone. Maybe there is something odd with my computer or my settings, but I cant see any link appearing in ajb's post. I wondered what he meant by 'these notes'. (?) ajb could you possibly try to post that link again, see if it appears? * Ahah! Have just noticed that 'notes' is a link. It hardly shows up as different from main text on my screen . Will check that out and thanks.

ajb/spock, Not what I am lookng for. To clarify, my first question rephrased is : What is the trajectory of the photon as measured at the earth's surface in cartesian terms. For example a rifle bullet has a parabolic path, the resultant of horizontal velocity vector and vertical acceleration vector (g). What is the path of the photon? Second question - please ignore "black hole" and substitute 'heavy dense body in free space" to make it simpler and avoid getting into photon spheres and Schwarzchild radius. So, what is path of a photon as it passes by a dense body in free space, in cartesian terms?

Two questions: A hand-held torch (on earth) is shone horizontally. What is the path of an emitted photon in earth based coordinates? A photon approaches a black hole, but not head-on. It is deflected and continues past the BH. What is its path?