studiot

Not at all sure what you mean by the last part but the underlined part is refuted by natural example. This is another case where Nature, Reality, what-you-will conspires to offer cases that do not fit human preconceptions or categorisations. I offer you a length of rope of a reel. and ask you to predict its actual breaking strength. True you can do an actual experiment to measure this. But once broken the experiment cannot be repeated. If I took another length off the reel and broke it, the result would be a little different. The best I can do is to take many samples and work out a statistical answer. Despite the fact that I can never predict in advance the exact breaking load of any given piece of rope the concept is not meaningless.

I don't recall mentioning a wave equation. However I (and I expect others) would prefer you used conventional notation when referring to the Laplacian, though I did understand that is what you mean. However the Laplacian is an operator. As such it only has meaning in terms of what it operates on. And that is not E, if you are using E as the standard symbol for Euclidian. You have a missing variable - usually the field variable under consideration. The point I am trying to make to you is that (your) delta is a linear combination of differentials - a linear form in other terminology - whcih is why it is permissible to use it as you are proposing. There are however such forms as non linear forms (ie non linear combinations of differentials). you can't use tensors for these either. This is all meant to help, nothing more.

Quick response. No apology needed. That's the Engineer in you. Engineers have to get all the relevant numbers out of an analysis. In my experience that means solving all the equations neatly bundled up in a matrix or tensor. Only a Physicist can say ohm's law says E = Z I , where E is the circuit voltage vector, Z is the circuit impedance matrix and I is the circuit current vector., leave things at that. An Engineer needs to know what all those voltages and current etc actually are, so has to solve all the equations one way or another. Long term response It will take some time to read through all 6 pages, but thank you for the thread. +1

I agree and I wasn't suggesting that. The mathematics of Euclidian space of any number of dimensions is linear - which brings a host of computational benefits and why we always try it first. But the mathematics of Special Relativity is non linear. The simplest non linear geometry that fits the bill is hyperbolic geometry. But even in non linear geometry the differential components still obey linear maths as I said so your equation (delta presumably refers to these differential components ?) can still be worked with, as can similar Maxwell equations.

How do you define a lightyear ? Please think again if you genuinely think that Special Relativity allows 'matter' to travel at travel at lightspeed or so close that it traverses 5 lightyears in one second.

Actually no I don't mean this at all. Nor do I refer to the fact that gravity is stronger at the poles than the equator due to the shape of the Earth. Acceleration is a vector quantity directed towards the centre of mass of the Earth. This direction line is not usually perpendicular to the surface of the Earth at a general point, so has components perpendicular to and parallel to the Earth's surface at that point. These components vary with latitude and interact with the spin of the Earth to produce the actual acceleration experienced as 'local g'.

So what conclusion do you draw from that ? And in particular how does the above calculation not conflict with what you said correctly earlier ? I repeat the world line is the appropriate measurement. So the next question should be what is the world line comprised of and how do we measure it?

Both your questions are incompatible with balancing or trading off motion through space against motion through time. The solution is that the interval is measured along what is known as a world line, which is a four dimensional space curve. That is a curve like say a spring in 3 dimensions, which is a helix, but in four dimensions 3 space and one of Time. As an aside other combinations of different numbers of space and time dimensions have been considered in the past, by the man who proved relativity experimentally - Eddington.

The wave function of a photon extends over all space and time.

Have you read Einstein's Theory of Relativity by Max Born ? He discusses your question starting at p238, but understandably this is in the middle of Max' development of the subject so you may need to look back a bit as well. A piece of maths you may not know is the difference between finite rotations, which are non commutative and infinitesimal rotations which are commutative. This and the fact that the coordinate infinitesimals go to zero in the limit allow linear mathematics to be employed in differential geometry. All treatments rely heavily on these two facts of maths.

If you want to carry on slinging guesswork around using vague ill defined words carry. Statistics says you will say something in agreement with Physics, as MigL has noted But your statement is so general as to be unusable in any application. If you were to study some Physics you might learn the true significance of this statement. Alternatively you might just ask as I'm sure there are plenty of members (including MigL or myself) who would be happy to explain.

Actually the patterns of gravitational acceleration vary from point to point, as has been known for several centuries. So this is a poor example. A better one might be that an near infinite range of ice crystals exist but all have the famous six point symmetry. Actually there were two articles on the BBC yesterday, one noting the hottest temperature ever recorded (in Somerset about 12 miles from me) and the other noting the residents of Shetland complaining how cold is was.

Here is an interesting story of a creature that changed colour from white to black and back to white again. Darwin's Moth or the peppered Moth. Peppered Moth and natural selectionThe Peppered Moth is widespread in Britain and Ireland and frequently found in ordinary back gardens, yet its amazing story has made it famous all over the world. It is one of the best known examples

Thank you for replying but I'm afraid that adds nothing new to your explanation. You asked and I am trying to tell you it conflicts. Speed is distance divided by time. You cannot get away from defining how you are measuring distance (and time) to specify what you mean by speed in a four dimensional continuum. This inevitably means you have to define how space and time are connected to satisfy your proposals.

Thank you for the response. Like most members I remain unsure as to the scope of the discussion as the OP reverts to repetition every time he is challenged. One of the fascinating things about evolution I have found out in my reading around is that it cannot even be said to have a direction.

Welcome back. Did you come up with any answers to my questions whilst you were thinking ?

You made this claim ( claim emboldened by me ) at the very beginning and I have to thank you for this thread because it caused me to look much further into a subject I had only passing acquaintance with. I have found out much about the subject I did not know as a result. so +1 for that. However I must challenge you original claim by asking. If you are claiming that the Laws of Natural Selection are the most important Laws in Evolution then are you saying that they are more important than The Laws of Mechanics The other Laws of Physics The Laws of Chemistry The Laws of Probability The Laws of Geometry. If so which of these Laws are you claiming can be transcended by Evolution ?

One matter that has not received an airing is the nature of 'Natural Selection'. One important factor is the timescale considered, and whether that time scale is relative to the total time length of evolution of the species being compared, and whether the periods are concurrent or not. Another important factor is that neither natural selection nor evolution itself proceed at a constant even time rate. Both are jerky in manifestation.

I think the whole point of this thread was to establish the technical how this might be achieved, not whether or not there is some source of energy or not, such as nuclear. Just having energy doesn't automatically make it available.

I've mentioned this several times in several ways but the OP seems uninterested in the bald fact that nearly have the human lifespan is beyond the reproductive stage, unlike most other creatures and life forms. So they are only considering the contribution of half an average human's total.

I wonder where the word mammals comes from. There were mammals 66 million years ago, long before there were any humans. Breasts are a spurious argument. Here is a proposal I think worthy of consideration. I suggest the main difference between humans and their evolution and other creatures and their evolution is that humans are generalists and very very adaptable. Many, if not most, other creatures tend to develop (evolve) specialist traits and characterisation not possessed by humans or by many other creatures.

I never said anything like this. I never said "A is imperfect and therefore has a lower chance of survival to reproduce or take one factor in isolation." I never said I measured "'success' by how long has a species survived" I have been ignoring many of your posts because you don't even seem to be paying attention. No you did not say any of this. I said it as your quote clearly shows. Furthermore it was said in response to one of your posts. Which was clearly shown in my post, but not yours. Instead you chose to metaphorically shout a demand that I answer your question, when I had in fact included a lengthy explanation as to why your analysis is not wrong but too simplistic. The part about 'A is imperfect is my paraphrasing' of your word 'disabilities'. Why should I answer you question when you avoid answering mine ? I don't see how you can accuse me of 'not paying attention' when my posts contain your posted text to which I am replying. Furthermore most of my posts contain requests for clarification since you have been so vague about the basis for your claims. Of course the rate of evolution isn't the same for all species. I never said anything similar to that. Yet you keep ignoring the fact that 'rate' can be measured in many different ways, which is why I specified the 'time rate', as opposed to any other rate. I don't know of any theory or rule that says the time rate of evolution has to be same for all species and can't vary greatly between species. I have already mentioned the greatest difference have you forgotten it ? You even agree with me that evolution is multifactorial and claim a particular explanation for the agreed difference between humans and animals.

I don't follow how this is a response to either of my separate points ?

I don't know of any theory or rule that says the time rate of evolution has to be same for all species and can't vary greatly between species. I have already mentioned the greatest difference have you forgotten it ?

Since we have now all agreed that most of us agree with much of what you said, what would be helpful would be if you were to outline what conclusions and implications you draw from your statements. I think swansont has a good point here.