studiot

Why is that a problem ? We both sprang from a traceable common ancestor so have some common genetic material. But when push came to shove HS proved more adaptable than HN so outcompeted them.

Current thinking in anthropology actually proposes the opposes of this as the reason why H. Sapiens superceeded the more numerous H Neanderthalis. The last episode of the recent BBC series Human made this point most emphatically.

This is actually a very good question +1 and @TheVat has given a good shortform answer +1 If you like to explore this further the mathematics is extremely simple, yet reaches into most corners of the subject from classical mechanics to relativity to geometry to cryptography to error correction codes to statistics to topology to.... This all hinges on what is meant by 'distance' that is what we want from our 'tool'.

Thanks +1

Do you have a quotable source for this information ?

If you are going to quote the originator of the Butterfly Effect, then you should take note of what he actually said and / or wrote in his paper or his book. So read that instead of quoting rubbish garbled up by some experimental program. What was actually said is interesting because Lorenz said that if we are going to consider the scenario that s small sensitivity in the initial conditions such as the disturbance caused by a single flap of a butterfly's wing could cause a tornado, we should also consider that on another occasion a similarly small disturbance could prevent a tornado. As the implications of that are profound because unless you have reason to think that disturbances pushing in one direction are more numerous than disturbances pushing in another such disturbances should balance out and merely change the order of events. So can you control it ? Well the nature of the problem depends upon the deterministic equations involved. For instance autonomous first order differential equations cannot be controlled. But there are other equations that admit a form of control. (Not those to do with weather)

If you want to discuss your claim, then discuss it. But, when presented with a counterexample, please do not pretend you are the sole arbiter of nomenclature in such an offensive way.

Well the op certainly seems to have been frightened away, if that was your objective. As far as I know most students start with the definition a vector is something that requires both a magnitude and a direction. My treatment is linked to that and is designed to develop from there.

OK so you read a short paper which didn't tell you any of the back history leading up to this. Professor Millikan (famous for millikan's experiment with electrons) was a very careful and thorough worker and indeed justly famous for the work he did on the electron and its properties. But he also did a lot of work in Cosmic Rays. Not only was he a careful worker but he also documented his work in papers and in a book what was revised several times, starting in 1917 and called the electron. My 1947 revision is a model of how to report basic research, methods, results and conclusion and is now called electrons (+ and -) , protons, photons, neutrons, mesotrons and comic rays. It is the mesotrons that are the same particles we now call muons. The book also documents and correlates the work of other scientists in this field. The actualy work took place over a period 1917 to the early 1940s. It was published by Chicago University Press (and also by Cambridge University Press in England) On page 519 ff , you will find all the detail you want carefully explained with photographs, graphs, and more.

I liked James Blish and his spindizzy series, very imaginative. I assumed you know about Watership Down since it was a blockbuster film and hit for Art Garfunkel. But I asked because I was thinking about another such novel (actually a series of 3) tracing the semise of the red squirrel under pressure from the invading greys and based on fact, rahter than just being a nice personification story about animal colonies. For instance red squirrels bury nuts, but grey squirrels don't. The Silver Tide Michael Tod I also liked James Blish and his spindizzy series, very imaginative.

See Fleisch A students guide to Vectors and Tensors page 2 Cambridge University Press 2012 You should also note that this thread is only about directed line segments, or 'arrows', not any other type od vectro.

As a biologist you might then just appreciate the science behind the McCaffrey Pern books. Her other books are rather pedestrian and predictable though.

I fully understand virtual or imaginary forces as I prefer to call them (after D'Alembert who invented the method) But my point is that your example was not a good one. The walkers could just as easily stand still, involving no forces, pseudo or otherwise. https://en.wikipedia.org/wiki/Free_fall

I am not sure why you are introducing tensors, when you still have questions about vectors. So I suggest we defer the introduction of tensors till we have dealt with your questions about vectors. It would be helpful to tell us in what connection you wish to use vectors and tensors and if you understand matrices ? OK so your arrow is what is also called a 'directed line segment' I have shown this in Fig 1 as the arrow Op, where 9a,b) are the coordinates of p and V is the length of Op Op is a line segment of the extended line shown dashed. This line makes and angle theta with the x axis. As you say this vector is one of a family of vectors that all start at the origin and are totally determined by their length v = Op and the anticlockwise angle theta they make with the x axis. In other words they are 'bound' to one point (the origin) and indeed are called bound vectors. Yes indeed if these vectors begin somewhere else they are called unbound vectors, as vector W in Fig 2 Now I am going to leave x y coordinates behind for a moment since it is obvious that an unbound vector will, in general, point to some other coordinate than (a, b) - let us choose one and call this point q again as in Fig2. Now to specify a vector in a plane we need two numbers and if we do not want to be stuck with starting at zero we need to use different properties of the vector than its end coordinates. So I am going to introduce the vector V with length v = Op and making an angle ϴ with the x axis as V = (v, ϴ) Similarly we can consider the unbound vector W with length w = O'q and making an angle Φ with the x axis. So W = (w, Φ) So if v = w and simultaneously ϴ = Φ Then we have an unbound vector we can place anywhere on the plane parallel to our bound vector. Does this help with your first question ?

Of course its not irrelevant. A body cannot move itself without external interation. (newton's first law) So there must be The walking involves some real force (probably friction). The exzample is not a good one for gravity. A bodies motion through the curved space is free fall.

A thought experiment question. In a universe with no light at all, but everything else, would these phenomena still occur ?

One definition of force is rate of change of momentum, which is what happens when you bump into someone.

I'm not debating with you an explanation from some armchair of a measurement that has actually been made. Length contraction is a measured observable fact. This was first done in 1941. http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muon.html

Sorry I don't understand your comment.

Not necessarily. Pratchett does nothing for me, but some fantasies can be fun. You generally have to suspend (dis)belief for some aspect of the story in SF, whether it's people magic or technology magic.

Unlike the first number I misquoted, where I made a silly copying mistake 156,423,343 is not prime. 156,423,343 = the product of two primes 22,343 x 7001. I should have constructed this example in the first place as it is beginning to show just how far you might have to go to find any factors. This of course is also beginning to demonstrate the interest in large or very large primes for cryptography. To recap Apologies for the earlier mistake 9,991,991 is not prime and = 2833×3527 9,999,991 is prime .

Gosh yes you are absolutely correct, I miscopied it I should have written 9.999,991 (which is the largest prime number less than 10 million) Thanks +1

I must admit that it is a long time since I last looked at Einstein's train and lightning though experiments and I was thinking about the length contraction one. I no longer have the original text of these experiments, but I have found a reliable explanation online here. https://www.vicphysics.org/documents/teachers/unit3/EinsteinsTrainGedanken.pdf Note the authors' comment that there are a lot of versions about, some quite misinformed. No there is no third, fourth or what ever observer involved and there are only two frames, the frame of the train and the frame of the platform. The referenced article explains quite well what you may be thinking of as a third observer as the point of view that the train is standing still and the platform is moving past it. However, as far as I can see all this is entirely off topic and you have made no response at all to my comments on the actual topic of this thread viz spooky action at a distance. I suggest the relativity issue be further discussed in its own thread as it is entirely off topic to action-at-a-distance, spooky or otherwise.

This seems to be the only actual question here. The point about the Einstein lightening strike is that it marks both the train and the platform with a visible, permanent mark that can be seen and measured at a later time. The act of the strike in such a small space is considered instantaneous and appears in both frames of reference. Do you understand what the two frames of reference are ?

I missed the author of Jurassic Park off my list, Michael Crichton. He has many feasible near future scenarios, a gripping style with plenty of suspense ans suprises. This has led to several successful films.