studiot

You seem to only have considered two possibilities. Probability v Determinism Nature is more diverse than that, both swansont and I have mentioned situations other than probability where the mathematical equation does not have a nice tidy deterministic output. swansont mentioned the uncertainty principle which is a physics principle that the product of momentum and position or energy and time cannot be known exactly. As a result the more deterministic your calculation about one the less deterministic is your calculation about the other. This is nothing to do with mathematics, but to do with the physics of reality. I mentioned that many equations have no solution in closed form. That means that it is impossible to arrive at a perfect deterministic value for the output Y (given an input X) that the equation is calculating. Bessel's equation is a simple(?) example. Of course we can get as accurate as we wish (unlike with the uncertainty principle). This is inherent in the nature of the mathematics and nothing to do with the physical world that such equations are used to represent.

The physics of projectiles have nothing to to with the physics of airfoils. So please do not claim to be following the laws of physics as here Of course they must be correctly applied, which you have singularly failed to do. This must be your best (or worst?) pronouncement. No. If the one airfoil (as described in post #46) is able to move vertically but not horizontally then it is not friction that keeps it in place. It must be in some sort of track (a frictionless track it is now here so stipulated) that allows it to move vertically but keeps it in place horizontally. So are you really saying that is not physically restrained against the real physical drag force or are you just wasting everyone's time?

Thank you for your references, I will look at them shortly. Meanwhile please look at this discussion about the word 'random' http://www.scienceforums.net/topic/84215-chance-vs-probability/page-2 I extract my post#29 for convenience. Final point let me thank you on conducting an adult and professional discussion without the rancour too often seen here. You are certainly proving up on your original statement. and your points are not easy to answer.

I'm sorry if you did not understand this. It is basically the same point both strange and swansont have made. There is a deterministic equation that will yield a definite probability P(E) of some event E. Hence there is another definite probability of a different event = {1-(P(E)}. Now you started this thread with the proposition So, given P(E) or {1-P(E)} we are all asking what is the deterministic prediction of the outcome?

Not so by Godel's Theorem. You still haven't answered my second point in post#12

OK so geodesics. They have an interesting story. Wikipedia does a fair job of summarising facts. I have picked out some salient points and numbered them. http://en.wikipedia.org/wiki/Geodesic Unfortunately, Wiki gets the history wrong by nearly 2000 years in point (note 3). Geodesic is an Ancient Greek word ‘geodaisia’ which means ‘divides the Earth’ from two Ancient Greek Words geos- the Earth and daiesthai - to divide. To understand this you need to understand that in 2000+ years ago Science, Philosophy and Religion were inextricably linked. The Greeks of that time regarded ‘perfect’ shapes is proper and real and many cultures had a Royal Road that could only be traversed by the ruler-cum-deity. Since to them (some at least) a sphere was the perfect 3D shape, the Earth was a sphere. This road did not deviate to right or left from its path (kept straight on). So if one followed it one would eventually come back to one’s starting point and one’s path would ‘divide the Earth equally’. This accords with the notion in (note 2). They were, of course, talking about great circles on the globe. Moving on nearly 2000 years cartographers realised that the minor arc of a great circle on a sphere is the shortest distance between two points. Unfortunately they also realised that the Earth is not quite a perfect sphere, and the modern idea of a geodesic as the shortest distance on the real shape of the earth was born. So the mathematicians of the time got hold of the issue (which is where the Wiki history starts) and they realised that geodesics had other properties, besides shortest distance. (Note 1) shows that the proved that geodesics on a plane are straight lines and that lead to the mathematics of developable surfaces and ‘ruled’ lines. (Note 6) was the culmination of 100 years of post renaissance maths development, primarily in Europe where the geodesic as the shortest line between two points on a surface dominated. This period, to the mid 19th century, also saw the development of much of the apparatus of modern maths, in particular the idea of manifolds (note4) instead of surfaces. All these were variations on the cartographic idea of a geodesic, where the scale is even on all axes. This brings us to (note5) which introduces the next instalment of the story and provides the link to geodesics as minimisers (or maximisers) of other expressions besides distance.

No so. You are the one who said that X is the input and confirmed that X could be any number. The problem is that you cannot obtain an output although you can indeed write the equation 82 - 4 = 0 Which is what i actually said, written out as an equation. If it is of interest this is because the equals sign in this equation is differnt from the equals sign in the first one I presented. The equation, x + (-x) = 0 is an identity ; That is it holds for all values of X The equation X2 - 4 = 0 is an equality. Perhaps you have heard of and understand the difference? Secondly you have not answered my second example in post#12

So if I choose x = 8 as the input to this equation, what is the output ? x2 - 4 = 0 Your theory is also in difficulty with simple probability. I can state the probability of heads in a fair coin toss is 0.5. X = the probability of heads, output 0.5 Deterministic as you say. But what is the output of the equation X = the result of next toss of the coin? How is that deterministic?

I suppose the inputs to a mathematical equation must be other equations as a substitutions or numeric values. Mathematics as the language only deals with equations and numeric values, physics as an application of that language then adds concepts like types (e.g. cats and dogs). So, just to confirm, are you saying I can freely input any number to an equation and the output is always deterministic?

Billiards, that is a very good question +1

I noted today a question from the originator of a thread about a comment I had made. I had presented this, more than once, in the past so I tried a search on 'zero' first with my name attached and second without, to find my previous replies on the subject. Both searches returned a zero result and I consider this pun by the system most unfortunate.

You didn't (put numbers to it), I did. But variations in speed, acceleration, and distance must all be taken into account in an energy analysis (balance). You have not done this. This is part of what makes energy analyis not as simple as we might like. Here is another reason. Your comparison of bouyancy forces and airflow lift forces is flawed. No the pressure difference is not gravitational potential energy. If the (bouyancy) force leads to movement of the object then it will accelerate the object, imparting the kinetic energy of movement to that object. In addition, once the object has been moved upwards some distance (any distance however small) then it also imparts gravitational potential energy. All this is fine and dandy and leads to the following energy balance. As soon as a net bouyancy force exists (however small) it accelerates the object upwards (however slowly), thus imparting kinetic and potential energy to the object as noted above. However this does not happen with an airfoil lift. It is well known that an aircraft has to achieve a certain minimum speed in order to be able to take off at all. Translated into air motion past a stationary airfoil this means that if you free stand an airfoil on a support and blow air past it, there will be a minimum airstream speed, below which nothing will happen. An aside here to Larry jevens This is why we need friction. The airfoil would simply blow backwards off the support in the absence of friction as we brought the airspeed up above zero. So if we consider any airstream speed in the sub takeoff range, a lift force will be generated, but the airfoil will not rise. This is unlike the bouyancy force situation described above. No one doubts that the airstream imparts energy to an object in its path. But this energy is always initially purely kinetic. Any potential energy transferred comes later. The second question is "What is the form of the energy loss from the airstream?" Again this is complicated since the airstream may possess linear kinetic energy, rotational energy, static head (potential) energy, gravitational potential energy and thermal energy. This is why an energy balance is less than easy for flight calculations.

So are you saying I can input anything I like to an equation and get an output? Please note I mean valid mathematical objects, like numbers not cats, dogs etc, I am not being facetious.

Zet, please note that you have to restrain the object both against the drag and the lift in the restrained case. JC has the right of it +1 However please also note we are talking about the lift and drag of aircraft in the atmosphere. The aircraft has kinetic energy, which is replaced by the engine when under power. When gliding the aircraft looses both gravitational and kinetic energy, eventually coming to rest on the ground. No glider flies forever. You are describing the action in a wind tunnel, where the energy comes from the fan that drives the airflow. In the free atmosphere the energy comes from the natural forces that created the wind, which (I think) are usually temperature differentials. As regards you question comparing the energy in lifting a heavy object v a lighter one. The lift force is determined by geometry so will not be able to lift a heavy object so far or so fast ( as you have shown in your diagrams) so energy conservation is preserved.

I didn't say otherwise, but since that was not a permissible setup I did not consider it. Perhaps didn't make a very full statement, which led to misunderstanding. All three train clocks are specified to be in physical and temporal alignment at rest and side by side with the three platform clocks at the start of the experiment. However this leads directly to the issue Strange and I have been discussing. Two light signals travelling at (obviously) the same speed for different times (measured in the same frame) must perforce have travelled different distances to arrive together at the same point. It would be perverse to measure the times in one frame and the distances in another. Equally clearly if they travelled for different times and arrived at some point together, they cannot have started at the same time in that frame.

The end clocks on the moving train can't be opposite the platform clocks in either frame since the train appears shortened in the platform frame.

If you think that an equation will is deterministic what is the output of this equation? x + (-x) = 0 So what is x?

No. What about do we know of any successful mathematical modelling of the universe? Again No. You need to understand what is meant by an equals sign in mathematics. It often indicates the result of a process (Chemists for instance used to use it for this but now more often use an arrow). That process may or may not produce a predeterministic result. Sometimes an equation may have an infinite number of valid solutions, so any one chosen at radom will hold true. Sometimes we say 'an equation cannot be solved in closed form'. Does that make it deterministic?

I respectfully suggest you go and measure some Hall voltages before you make such sweeping pronouncements. You do not need to be near a black hole or other exotic body to do this, nor do you need exotic substances, copper, gold, magnesium and aluminium will suffice. I await your results and explanation with interest.

Well poisson's equation in cylindrical coordinates is [math]{\nabla ^2}V = \frac{1}{r}\frac{\partial }{{\partial r}}\left( {r\frac{{\partial V}}{{\partial r}}} \right) + \frac{1}{{{r^2}}}\frac{{{\partial ^2}V}}{{\partial {\theta ^2}}} + \frac{{{\partial ^2}V}}{{\partial {z^2}}} = - \frac{\rho }{\varepsilon }[/math] The reference to a long cylinder provides a value for [math]\frac{{{\partial ^2}V}}{{\partial {z^2}}}[/math] and radial symmetry provides a value for [math]\frac{1}{{{r^2}}}\frac{{{\partial ^2}V}}{{\partial {\theta ^2}}}[/math] Leaving only the first term and therefore reducing the equation to a solvable ordinary one. Now the physics is that the potential at the boundary with any conductor is a constant. So if we reckon zero potential at the inner surface of the outer conductor as zero and the potential at the outer of the inner one as v (a constant), we can obtain an expression for V®. This leads to the logarithmic ratio solution. You are then asked to rework with v = 0 in part c. I hope this is enough of a nudge as I'm off out on the town tonight.

How far do you wish to take the concept of a machine? So how about a greenhouse as a machine-building that concentrates solar energy? If you accept this what about modern energy recovery installations or older north light roofs? And what do you mean by a building? Does a wave-wall count in flood defence work? Scientific instruments also come to mind, The camera obscura of old and the modern telescope like Palomar.

"Which is Professor Challenger's room?" Down the corridor. Down the corridor, on the left. Down the corridor, third door on the left. Down the corridor, room 15. Each may be adequate or inadequate, depending upon circumstances.

Trying reading again whatever you misread before, I made no such claim.

Since you were again so hasty in replying perhaps you would like to show how the following system of two particles (mass m1 & m2) and one force (F) is inertially invariant when transformed to a new system whose origin is at (x0 , x0) compared to (in) the original. The Newtonian equations of motion in the original are [math]{m_1}\frac{{{d^2}{x_1}}}{{d{t^2}}} = F({x_1},{x_2})[/math] [math]{m_2}\frac{{{d^2}{x_2}}}{{d{t^2}}} = - F({x_1},{x_2})[/math]

Newton's First, Second and Third Laws. A good background book on this stuff is the University of Sussex student booklet Relativity Physics by R E Turner