studiot

Well our Welshman is not claiming something for nothing, and as we understand the need to protect trade secrets I would suggest that useful discussion could focus on performance characteristics. Does it run on DC or AC, mains or battery? How much current and power does it consume? What speed /torque/power output does it develop? What is its power to weight ratio? Discussion of these could help understand the viability of the project, which I too wish well.

Attitude? Sarcasm? I was actually offering you a compliment that you had made good headway in a broad and difficult subject, without formal training. However you had reached an stumbling block, which I identify as mixing up the fundamental difference between before and after the event. I might warn you that some of the statistics/probability terminology is described as "an unfortunate historical accident" in the main Oxford University Textbook at introductory level. So for example Another term of importance is 'relative', which has a particular meaning in probability, different from the one you have used in this thread. I did ask if you have a working definition of probability, because this is important, as well as offering many relevant areas/subject heading for discussion. As far as I can tell you have not responded to/ignored all of them. This is a particular shame as this is the only thread with any serious technical content in the first twenty on the current/recent list. So instead of feeling insulted and lashing out, why not try some dialog, questions and answers directed at the substance of each others' posts?

But once someone points out the correct terminology surely it is most sensible to adopt that? Your obvious deductive powers have led you to explore a subject that has taken a few hundred years human effort to establish a viable basis for this area of mathematics. By all means extend it further and develop your own terminology there. But please don’t start by introducing unconventional usage as fact, as you did in post#1. You say you would like to be educated in mathematics so I am quite taken aback by your response to my post#21 which was offering the beginnings of some small help towards this goal. Actually, no you weren’t. and the correct phrase is ‘a priori’. Further Strange’s incorrect analysis in post#12 complicates this. The a priori probability cannot ever alter. So for the coin toss it is still 0.5 even after you have looked. What has changed by reporting a probability of 1 is the event the probability is reported for. The actual outcome of an experiment is independent of the probability of any particular possibility. There are other considerations concerning your proposed perfect mechanical universe, and prediction machine. How far are you prepared to analyse? Again referring to the coin experiment. Let us suppose you have set up your perfect coin tosser. At the moment of tossing there is an earth tremor. Or the sun goes nova Or your machine tosses and catches correctly, but you make a mistake when you read the result. How do these possibilities (amongst others) affect you probabilities? I really thought you were interested in how human subjectivity is usefully brought into the evaluation of probabilities. For instance if there have been zero events of a particular nature, an a priori probability cannot be assigned. But it may be very desirable to do so. The Bookies do this all the time. Or what is the probability that a nuclear missile will be fired at New York, by accident? In many branches of engineering practice we operate what is known as ‘limit state theory’. This involves combining probabilities arising from several factors to effect safe and efficient designs and assessments. All of these are interesting subjects in their own right. So over to you if you want to discuss them properly.

I have been watching this discussion with interest. So here are some thoughts. They revolve mainly round the definition of probability or more completely what you understand by the term. Firstly do you know the difference between anterior and posterior probabilities? (Before and after the event) The issue of a probability of 1 or 0 raises special considerations. There are three approaches to probability called, the a priori, the empirical and the subjective approach. I think you are really meaning to discuss the last one so it is important to avoid the trap of mixing up the meaning given to each approach. For example a probability of 1 means 1) In the a priori approach it means the event must always occur. 2) In the empirical approach it means that the event has always occurs but does not imply that it will occur in the future 3) In the subjective approach it means that we think the event will occur but does not imply that it must occur. This summary includes Bayesian probability, which has been the subject of intense and vitriolic argument for about two centuries, despite its many successes.

There is a similar recent thread about this. http://www.scienceforums.net/topic/103089-the-golden-ratio/

It is good to see you coming back to discuss your topic; connecting entropy and order/disorder can be paradoxical and often leads to surprising or even inappropriate conclusions. As noted here modern science is therefoe veering away from offering this connection. https://en.wikipedia.org/wiki/Entropy_(order_and_disorder) This Wikipedia summary is a fair summary, and says nothing actually incorrect unlike many offerings, although it raises some questions it does not properly answer. The connection really hinges on what you mean by order or disorder. The definition of entropy is pretty well specified, swansont has provided a statistical definition, and has bender a physical one. However there is no such convenient definition of either order or disorder. What is meant depends in part on the parameters of interest. You have not discussed these further or indicated you mathematical level but you can't fully consider the question without some mathematics. Going with the statistical approach, since it is in the title, here is a simple introduction. Consider a chessboard : It has 64 squares. Which means there are 64 ways to place a single black pawn on the (otherwise empty) board. There is no reason to assume any of these positions or arrangements is 'better' than any other so we choose one square and call it 'order'. If we place the pawn there the arrangement is 'ordered'. If we place it anywhere else the arrangement is 'disordered'. There is thus 1 possible arrangement called order but there are 63 possible ways of disorder. Now we consider a change of arrangement. If we make a single change to arrangement, i.e. move a disordered pawn to any other square, there are 62 ways of doing this whilst maintaining the disorder and only one way to change to an ordered pawn. For this system a change is 62 times more likely to result in disorder than order. This is only for one single pawn. Now take all 8 black pawns and consider arrangements of them on the board. You can place the first pawn in one of 64 ways i.e.on any square. You can place the second pawn in one of 63 ways i.e.on any remaining square. You can place the third pawn in one of 62 ways i.e.on any remaining square. and so on. In total this means there are 64 x 63 x 62 x 61 x 60 x 59 x 58 x 57 = 178462987637760 different arrangements. So what is order now? Is it perhaps some relationship between the positions of the pawns, say they are all in a straight line? Well there are 2 ways this can be done if they are to remain on the same colour and another 16 ways if the colour does not matter. This simple model can be developed to embody all the important characteristics of Statistical Mechanics which are, in relation to the OP. 1) The pawns are not distinguished. Every pawn is equivalent to every other, so any pawn in the order position constitutes order. 2) The arrangements are not distinguished so any position can be chosen as order. 3) It is changes to the position that offer meaningful properties. 4) When talking about the change, only the beginning and end positions are meaningful. No meaning is attached to the positions during the change. Notes what I have called arrangements or positions are called states in Thermodynamics and Statistical Mechanics.

What you seem to be misunderstanding is the meaning of an axiom. 1) You cannot either prove or disprove and axiom. Axioms are taken as true without proof. 2) Every Field must obey every Field axiom completely or it is not a Field. By way of explanation a simpler algebraic structure is a group which has one binary operation by axiom. Some groups have additional structure such as a second operation or commutatively. We do not add the additional structure as axioms, just as definitions of the special restricted type of groups. It would be the same for Fields if you wished to introduce a special type of Field with some additional structure. Your special fields would then 'inherit' all the standard axioms to which you would add your definitions. But these definitions would not qualify for the elevated status of axioms. In particular none of the standard field axioms deal with numbers since some fields deal with objects other than numbers. Nor could you add an axiom the required numbers for the same reason. I have stated my version of the standard field axioms in my response to wtf, below. Since my use of letters was not clear enough I have redrawn the tables as below. The field contains four geometric shapes and two combining operations which take in any two shapes and output one of the four shapes. I hope you will agree that there is nothing numeric about turning a square and a triangle into an axehead (or the inverse operation for those inverses that are specified in the tables). So, given a set F and two combining operations, # and * the field axioms are 1) # and * are closed operations with unique outputs. 2) # and * both obey the associative law 3) There is a (different) identity element for both # and * in F. Combination of the identity element for either # or * on any element leaves that element unchanged. In my geometric example combination of the square with any element leaves it unchanged under # combination of the triangle with any element leaves it unchanged under * 4) There exists an inverse operation for every element in one of the combining operations and for every element except perhaps one in the second. In my geometric example For the # operation, having combined any pair of shapes to reach a third it is possible this third one with another shape to restore the original element. So if I combine a circle with a triangle under #I get an axehead. To get back to a circle I need to combine the axehead with a triangle and so on. For the * operation inverses work the same way, except for combinations with the square, for which there are no inverses. There is a final optional axiom which states that 5) Both # and * obey the commutative law. Any field also obeying axiom (5) is called a commutative field.

You completely failed to understand my question. I deliberately chose a field, that contains neither zero nor one. In fact I specified a non numeric field and emboldened that fact to help you. So please read my question again reconsider your answer.

To save you getting bogged down in mysticism here is an extract from Ball: The Self-Made Tapestry with a solid reference to Ian Stewart's book at the end.

How would this work for the F4 field, comprising four non numeric elements {A,B,C,D}, defined below by the two binary operations, # and * , which satisfy all the standard Field Axioms?

The point about force might be a good one, Endy. However such calculation does rather assume there is a perfect vacuum on one side of the window. The question needs clarification to answer properly.

You don't say if you are going to experiment with different insulating materials but look at as many packaging materials as you can. There are lots of types for mechanical safety to try. I assume your insulation does not have to hold the water, just the bottle or whatever it is in. Small point but you mean insulation, not isolation that is a different word. Look them both up.

Not needed now.

Testing Testing Testing Luv it Charon Y +10 (I saw that in the gravity thread) But nope, test failed system still only awards +1 Actually I was preparing to answer in the tensor thread and I realised I had to revisit how to post matrices here. SF doesn't parse my MathType output directly.

Perhaps it does, but the first 8 posts wandered around the subject of the accuracy of measurement of G itself, before digressing to a discussion of the measurement of time. I certainly gained the impression that the OP considered the current value of G stated as being a pretty poor quality measurement. I would observe that considering the small magnitude of the G, the question should not have been "Why was it so bad?" but, "How the hell did they get it so damn good?" My analysis was deliberately stopped because it leads into the question of what do we have to measure accurately (and how accurately) to measure G? Does it matter if we get the density wrong say 4.5 or 6.6? What about the radius? As I said a proper mathematical assessment of this should been undertaken at the outset, and I still don't see one. I take my hat off the these guys of old who could not simply ask Google, as I did, what is the size, mass and density of the Earth etc, when attempting such fine measurement.

madmac OK in post#14 I tried to point this thread towards a more scientific footing and was disappointed by your lack of acknowledgement. The latest twaddle in your posts #36 and #38 with no proper analysis make this the last time I will try here. There are more rewarding threads to spend time on. For instance tides do not affect gravity. Gravity affects tides. I did in fact refer you to a reference that offered a summary of the several physical factors that might have affected gravity and the experiments that were made to study this. So I will leave you with a simple example evaluation of the issue, of the type that you should have carried out at the beginning. Newton's Law of Gravitation states [math]F = G\frac{{Mm}}{{{d^2}}}[/math] Where F is the force between two bodies of mass M and m respectively, di is the separation of their centroids and G is a universal constant. If we let M be the mass of the Earth and m be the mass of a 1kg pendulum or other test mass then The force on the mass (at the surface of the Earth) is given by F and using Newton's Second Law we have [math]mg = G\frac{{Mm}}{{{d^2}}}[/math] Since the mass is at the surface, d = the radius, R so this reduces to the relation between little g and big G [math]g = G\frac{M}{{{R^2}}}[/math] Replacing M by volume times density we have [math]g = G\frac{1}{{{R^2}}}4\pi {R^3}\rho [/math] Which reduces to [math]g = 4\pi R\rho G[/math] Where rho is the density. So a change in G referred to a change in g is [math]\Delta G = \frac{{\Delta g}}{{4\pi R\rho }}[/math] That is delta g divided by a very large number. Putting in some numbers The radius of the Earthis [math]R = 6.4x{10^6}metres[/math] and the density is [math]\rho = 5.5x{10^3}kg/{m^3}[/math] So the variation of G measurable as a variation in g is given by [math]\Delta G = \frac{{\Delta g}}{{4\pi *6.4*{{10}^6}*5.5*{{10}^3}}} = 2.3x{10^{ - 12}}(\Delta g)m/{s^2}[/math] You should compare this with the magnitude of other reasons for g varying. It also accounts for the difficulty in making measurements of G.

TEST [latex] \begin{matrix} \alpha & \beta & \gamma & \delta\\ \epsilon & \zeta & \eta & \theta\\ \iota & \kappa & \lambda & \mu\\ \nu & \xi & \pi & \rho \end{matrix} [/latex] Procedure for Mathtype For table create table from drop down list Copy and paste table Remove unneccessary coding Edit 'array' to matrix' Close up to continuous string For matrix create brackets create table and in placeholder and reduce as above Also remove extra 'math' and '/math' tags Post math]\begin{array}{*{20}{c}} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ \end{array}[/math Becomes math]\left[ {\begin{matrix}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ \end{matrix}} \right][/math [math]\left[ {\begin{matrix}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ \end{matrix}} \right][/math] Thanks elfmotat, when are you coming back?

Actually it is what I said. I even posted an excerpt from a renowned textbook describing such a situation, the coincidence two spaces viz momentum space and position space at a particle.(post#88).

A few notes. Firstly Xerxes had confirmed what I said elsewhere, that there is more than one space associated with some fields. He refers to the tensor space and the dual space, although I sis not mean that particular combination for my purposes, I think it proves the point. Secondly all the tensors you will meet can be represented as square matrices, but not all square matrices are tensors. For instance the matrix 0 1 0 0 0 1 1 0 0 is not a tensor. Second order tensors produce square matrices like the above, third order tensors produce cubical matrices and so on. I see a sixth order one was noted.

Pity you dismissed my comment so summarily. On the Lochee Road in Dundee there is an 'environmental monitoring' station, which records weather data and sends it back over the same grid the street lights and houses are connected to. I still think you had a mains borne false triggering from such a device. Perhaps your neighbour has a remote weather station or home automation gadget? Your timescale is a bit vague, and you have not said if the computer is still working and misbehaving?

Put it in a 'spoiler (There is one in the 'special BB code drop down - third icon from the left top row on the input box)

Reminds me of an elecrtical repairman's story I once heard. He had installed an automatic security light outside a property. Shortly after hed was called out because the light kept coming on and staying on during the night. Several tests later there were no faults to be found with the installation. So in desperation he kept watch one night. When the light came on he found a semicircle of local cats sitting facing the light. In your case I would look again (if you can remember it) at the geography. Some street lights are light operated, some are operated from a remote timeclock control signal, sent along the mains. Even early computers had various 'wake on' settings in BIOS. They are never truly off, and can be activated by a suitable remote signal. Perhaps you pc was picking up such a signal from a street lighting or other remote station.

Here is an authoritative reference on the history of Field theory (advertising suppressed) Berkson : Fields of Force: The Development of a World View from Faraday to Einstein. Original hardback 1974

Congratulations, you actually asked a question instead of proclaiming your gospel. And wow, swansont quickly gave you a helpful answer +1 Let me offer you two pieces of advice. Firstly Einstein's clocks and thought experiments all refer to perfect or ideal clocks and other apparatus and perfect observers. Nevertheless secondly, you need to distinguish between practical difficulties and theoretical ones. It is the practicalities that cause difficulties with simple pendulum clocks. However this thread is about the measurement of G and perhaps g, not the measurement of time. I suggest starting another thread if you want to discuss that. Now that you have found out how to get help from swansont ask plenty of questions, he is a real expert in the area of time measurement.

Very good reference Eise. +1 However a word of warning about it. The preferred reference in the page on electronics is to Tony Kuphaldt's monumental work. Unfortunately Tony uses the reverse polarity convention from the rest of the world in his circuit theory. This is not technically incorrect but can make for many difficulties when reading what the rest of the world writes.