studiot

So what was your point (especially as it apparently warranted an exclamation mark) ? I encounter this problem and worse with the poorly designed entry text box this forum has. My solution is to open quote marks, then copy and paste into the quote box, preceding the paste with an acknowledgement to the true author. Since you may be asking for an answer to a question that was already discussed in detail please restate your question briefly and succinctly. Note In the previous material I gavel some satellite figures which showed that 1000m of raised oceanic crust produces about 2m of change at the surface. I don't know of any shallow water lake that has 1000m lumps on the lake floor. The limits of the word 'flat' were never discussed, but I noted that the change was 1/500 of the vertical size of the bump in the floor. So a 1m bump (a substantial bump in a nominally flat lake floor) would produce less than 2mm of effect. I think this is beyond current technology to measure. Have you read the full preceeding material ? I realise it is more substantial than the average discussion. Points to look for are The difference between 'flat' and 'level' - shown to be less than 20mm ie at least 10 times that of the bottom influence. The discussion of lake hydraulics and its influence on the water surface. The critique of the experimental method.

What energy is transferred to the accelerating body executing constant circular motion?

That's a clever trick an no mistake.

I can't make out what you want from this thread, you have so many ideas mixed up along with not a few gripes. Perhaps this thread would be better in the General Philosophy section, it certainly isn't about modern and theoretical Physics. So I will comment on one point you made. In Science (including Maths) one important way we learn about things by observing the how they interact with other things. To compare two (or more) things we can use this by replacing one thing with the other in these interactions and observing the differences. Numbers are no different in this respect so to tell the difference between two numbers we can put one in place of the other and see what happens. Would you prefer I gave you £1 or £100 ? In fact you are strictly correct. There is no detectable difference between 0.9 recurring and 1. But the 9 must be strictly recurring ie not terminate at some large count of 9s. That is the count is infinite. Note that the number itself 0.9 recurring or 1 are both finite. If the count is finite the that number is less than 1.

I'm glad we have lots of points of agreement and, in fact, I agree that technically your point about R3 [aside] Did you know this site has superscript and subscript, which are very useful? Looka long the top toolbar in the editor for X2 and X2.[/aside] If you regard a function as a map from a set of all ntuples for some n (eg 3 in your case) to R This is, of course, also the definition of a functional. But I think this is somewhat disingenuous since you have to know all n numbers somehow. Further complication comes when the Xs are not numbers so the map cannot be to R. For a simple example a function connecting the strain tensor to the stress tensor. The objects in both the domain and co-domain are ntuples or arrays. It is really nice to chat amicably like this but it would also be nice to know where it is all leading? It certainly goes to show how slippery some definitions are.

Thatcham vehicle test track demonstration that current autopilot driverless car can involve itself in a crash situation. https://www.bbc.co.uk/news/av/business-44460980/this-car-is-on-autopilot-what-happens-next

So what have you found out so far? Surely you should have only one thread per topic.

Is this is a new proposition, if not can you point me to where you enunciated it before please? How can quoting the rules be threatening to any rule abiding member?

I thought I had pointed out that pairs may not be adequate. Nor need a function be analytic or specified by an equation. All that is required is that every time you apply it to a member of the domain set you get the same answer. So it can't be a table of experimental results directly. But it could be a specific table such as a logic truth table (Cayley table) Or it could be a filter for instance one which has all the integers as the domain but selects only odd integers.

A long time ago I was taught that the full specification of a function comprises three things. Specification of the Domain Specification of the Co-domain Definition of the rule of mapping. So it is up to the specifier of the function to specify these and by choosing a different domain / co-domain / rule we can vary the function or choose a different one. You mentioned a hyperbola, which is officially a conic with two branches,(unlike say a parabola that only has one branch) but by restricting the domain we can make it a 'new' function that has only one branch. Would you like to compare the terms injective, surjective and bijective? Note uncool talks of ordered pairs which implies there are only two variables, but of course you can extend this count.

I think we cross posted since When I last looked you had replied to uncool, apparantly but not bothered with my earlier post. However I see that you have since replied. So let's start (again) with some definitions. There is no such thing in general as the co-domain. A valid co-domain is any set that includes all the values of a function. There is no requirement for it not to include any members that are not values of the function. That honour is given to a more restricted set called the range which is the set of values taken on by a function as its argument varies through its domain. Thus the range is the image of the domain in the co-domain. Now if every member of the of the co-domain is the image of at least one member of the domain then the function is said to be surjective. In this case the range and the co-domain are the same or coincident. As an example the mapping from the set of all men to the set of married women is surjective (modern gender relations aside). But there remain men in the domain who are not married, that is their function value is null. It's tricky to get all the definitions to match sweetly, which is why so much thought was put into it by many clever people. How are we doing?

That was not your question, although it would have been addressed, but I note that you don't want a discussion on that subject. Note also that the range is a different thing from the co-domain.

This is a very good subject to consider as it highlights an important property of functions, that of being single valued. Consider the function [math]f(x):x = \sqrt 4 [/math] Now the point about this very simple example is that 4 has two square roots, -2 and +2. So if we allowed the function we call the square root function to have two values then we could justifiably say that for f(x) : x + x = 0, but that f)x): 2x = +4 or -4. We can develop this further if you like and also investigate other properties of functions.

I may be being selfish but I prefer my own frame of reference.

Over a journey distance of 5 light years from Earth? No way.

That is a strange answer to my question. Anyway consider the following. How can the Earth twin measure the speed of the traveller? He can have previously measured the distance to the turnaround point by astronomical means. That is he knows how far the target star is away. He can set his clock to start when the traveller leaves and read it again when the traveller returns. Thus he can calculate the speed as the distance divided by the double time in his system. What about the traveller? Well he can take a clock with him that starts as he leaves and is read again when he returns. He will find this clock reads a different time from that of the Earth twin. His reading however is the transit time in his system. But what about the distance? He has no means of measuring distance. He has no means of directly measuring speed.

Did you not read the very short piece I referred to? The Earth twin doesn't go anywhere so makes no journey at all.

@worlov Since you are not interested in my comments look very carefully at this one. It contains the a most important piece of information.

beecee, It seems a good list, but why would anyone bent on disproving the conventional rules of Physics bother to obey your list?

I can't honestly see anything objectionable in the OP so I have placed a +1 to counter the negative.

I think (from practical experience) that one of the big difficulties is that some members only read the last few posts, as opposed to all the ones new since they last looked. Consequently they often don't see many of the responses. Once again I should like to bring up that hoary old chestnut that failure to number the posts makes referral almost impossible and encourages lazy activity. Also every time I try to post a link to some other thread or post I get that ridiculous little window opening and I have to stop what I am doing and remember to cancel that option. It interrupts my flow of thought and discourages me from bothering. Computers ought to be made to stop and wait for humans, not the other way round.

I think Swansont gave a good answer pointing out that light has a frequency. It's not a big deal.

I picked the arch because it is a particularly good example of your comment about a particular arrangement of component pieces. Arching action shows what is called 'emergent behaviour'. That is the arch behaviour only appears at a critical point when all the components are assembled. Before that the arch ahs no strength whatsoever and has to rely on something else to support it. As to taking photographs there are Roman arches that if you could have taken your photograph when they were constructed and come back every 100 years your could have taken another photo showing much the same for the last 2000 years, so you would have some 20 photos Now you say your method involves deducing from these photographs how the arch system works. That is to deduce the necessary arrangement of component pieces. So I am asking you to do just that. I am also challenging you to show where any energy is involved.

Strictly a photon has one frequency, and cannot change it. Of course, you can have different photons of different frequencies. I'm pretty sure someone else had this discussion recently with swansont in another thread.

Perhaps the photon has had more whisky than the electron? Seriously though, I think you second sentence could give the wrong impression.