studiot

I am angry because DParliviet has been wasting my time. I told you more than once that MY ATOMIC CLOCK DOES NOT WORK LIKE THIS. In fact its function has nothing whatsoever to do with electrons or EM radiation. Yet, as Strange (+1) says, you keep repeating this nonsense, instead of saying "Hey, I've not heard of your type of atomic clock, please tell me more"

Hello, this is really CaptainPanic's field, but I haven't seen him around lately. Perhaps someone can get him on the batphone? For your information, this site accepts superscript and subscript useful for powers and indices without needing TEX. The toolbar has bold, italic, underline, strikeout, subscript, supercript and some. So I have written out you equation again for the benefit of those who don't realise it has powers in it. [math]\frac{{{G^E}}}{{RT}} = {x_1}{x_2}\left\{ {A + B\left( {{x_1} - {x_2}} \right) + C{{\left( {{x_1} - {x_2}} \right)}^2}} \right\}[/math] It is useful realise that in a binary system like yours, x2 = (1-x1) and to obtain the gammas you need to rearrange the xs and take logs. However we do not do homework for you, but can work with you to help you solve the problem. So please show what working you have so far. A useful reference is Redlich, Kister & Turnquist Chem Eng. Progr Symp Ser 48(2): 49, 1952.

If this was a response to my post 7 then try reading it again properly. But you are prepared to pronounce yourself expert anyway? Consider any physical quantity [math]\Psi [/math]. Then if there exists any function such that [math]\frac{{d\Psi }}{{dt}} = f(t)[/math] ; where t is time That is the rate of change of this quantity is a function of time alone, then this equation can be used as the basis of a distance indepedent clock as you originally asked for. A simple quantity is number and I offered this in my atomic clock. [math]\frac{{dN}}{{dt}}[/math] is quite independent of distance (or the motion of counter or material , though that was not actually specified). In fact the progress of many chemical reactions can be measured in this way. The reaction will proceed equally well in a petri dish or a swimming bath or a tall measuring cylinder. The same rate laws apply to all. You also need to understand the difference between the dependent and the independent variable. Some processes can depend on time, but measurement can be most conveniently made as a distance, for example the burning of the candle you mentioned or the reading in a fuel tank sight gauge. In both cases a distance is a convenient (dependent) function of time, which is the independent variable. The actual property changing is a different dependent variable that is more difficult to measure than distance.

I gave several examples in post#7

Can you apply the inverse scattering transform to the correlation (probability) version of Bell's theorem, in the same way that the fourier transform applies to ordinary correlation (probability) version? https://en.wikipedia.org/wiki/Inverse_scattering_transform

My atomic clock counts decayed radioactive atoms. Distance is not involved. My charge clock measures the charge on a capacitor. Again distance is not involved. I'm sure others can think of more clocks which only have to count. Edit Paleontologists use yet more methods of measuring time. For instance. http://www.scienceforums.net/topic/87968-fossil-use-in-calibrating-molecular-dating/

1 comes after 12, of course. Look at a clock. It is an abstract example of what you are asking. In this case it is called modular arithmetic. Modular arithmetic is a counting technique whereby we count the fabric of a continuuum of numbers up to a certain number (12 in this case) and then start again, effectively bringing 13 in coincidence with 1 (or 0 if you include it). This idea also underlies the answer to your second question. 1 are 13 are the separated parts of a number continuum, but since they are both abstract we can only bring them together in the abstract. It is the object of much speculation as to whether this could occur or we could do this for a physical object, ie the 'fabric of spacetime'. The Mobius strip and Klein bottle are famous examples of this in lower dimensions.

No.

It is very easy to create a connection (used in a looser sense than the strict mathematical definition of a 'connection') between two separated parts of a mathematical object. Whether such a connection has any reality, or is just a mathematical curiosity, is another matter. What number comes after 12? Have you heard of a Mobius strip or a Klein bottle?

Yes it is exactly as stark as that. Even in non relativistic physics light plays a fundamental role because it is a result of a form wave motion, as predicted from the physical laws that govern it. If these equations did not result in some form of wave motion would that mean that wave motion was excluded? So water waves, sound waves and all the mechanics associated with wave motion would be lost to our universe. Dislocation theory in solid mechanics would not work, Quantum effects would fails so electronics, chemical reactions, ................ This list of physics that would not hold is mind bogglingly large if the wave equation were not true.

I'm not sure what the american for 'white spirit' is.

Next, you will be asking what would an Englishman have for breakfast with his eggs if bacon did not exist, or what would he eat for lunch with his fish if chips did not exist.

Fiveworlds, it would be interesting to know how you continued your analysis to find the minimum. There are several non mainstream methods that could be used in attacking this whole problem. Yours sounds equivalent to moving the parabola to a new position relative to axes.

Why do so many potential theories loose credibility by going over the top? The deepest ocean is only 11km deep. http://geology.com/records/deepest-part-of-the-ocean.shtml

There are enormous spin-off and long term benefits to be gained for all humanity in changing our way of life for the better in response to the climate change issue. For example as a youth I can remember walking round our towns and cities in the 1950s. Most of the buildings and particularly the railway bridges were black, due to a soot coating. Since the Clean Air Acts, I have watched the brickwork emerging from behind its coating and take great comfort that I am not breathing the shit that my ancestors did for the last couple of hundred years. This is a small example that affects over 80% of folk in the UK. The list of such improvements could go on and on. We must not stop now and say, the job is done. It is not. We still have a long way to go.

Yeay you are getting there. You get three equations connecting a, b and z . But because they refer to the same parabola they are the same a , b and z in each equation. We say the equations are simultaneous. So you can solve these three equations to find a, b and z, as you did back in post 5 In order to help a little bit I will tell you that a = 3 is a good guess, or you can just go ahead and find all three. What do you make a, b and z? So when you have found a,b and z you can write down the equation of your particular parabola, that passes through the given points. So you can find any point on it if you know x or y, you can calculate the other. The point you want to find is the minimum. Now I asked you back in post4 what you know about the parabola as you have two ways to do this. You can either use the calculus to differentiate the equation and se this equal to zero to find the minimum if you know how to do this. Or you can use the geometric properties of the parabola (in this case the symmetries) to find the axis and thus the vertex, which is the geometrical name for the minimum. So we await your next input.

But modern politics has made an amazing leap forward when it was realised that individual citizens no longer have to work hard wasting resources. Their government can do this much more efficiently for them, whilst the citizens take their ease, if they can still afford it.

OK so let's provide some motivation. Pavel has offered the equation of a parabola ax2 + bx + z = y Where a, b and z are constants. This is also known as a quadratic equation. But you are not asked to solve the quadratic, you are given the values of x and y at three points on the curve. x = -2 , y = 0 and x = 4, y = 0 and x = 3, y = -15 So can you write down what happens if you substitute these values into the quadratic equation of the parabola? What do you get?

Let's just keep going with the simultaneous equations in post9 Then we can use our information in pavels equation from post 10 to get the correct answer.

Actually you also need some calculus in theory. As pavel said, there are three constants to find, not one.

So if I wrote ax + by = 7 cx + dy = -1 Would you understand it and what would you need to solve these two equations? If you don't understand I will explain in more detail. This will lead to the more complicated example of your parabola.

So what is the equation for a parabola? Alternatively, what do you know about parabolas? Note we do not do your homework for you, just help you find the way. I do not know what maths you should know, but if you are studying quadratic equations (parabolas) then you should have met simultaneous equations. Can you not solve for instance 3x + 2y = 7 3x - 2y = -1 These are simultaneous equations. Incidentally I agree that the minimum is at x=1, y=-27.

White spirit is probably your best bet. However you would need to test for insolubility of your powder.

I usually ask those who maintain that all reality is amenable to description by mathematical formulae the following question. You are going to build an earth embankment, starting (of course) with the bottom layer and ending up with the road/rail/canal formation surface at a prescribed location, elevation and width. The original ground you are starting from is uneven and sloping. Where do you start?

Have you heard of simultaneous equations? What is the general equation between x and y for the parabola? How many constants does it have? and at how many points do you know both x and y?