studiot

I asked a simple civil question in post 10 and would appreciate a simple civil answer.

Surely there is more to this. Even at the level of a virus there is an attempt to 'direct and control' its environment, as well as react to it. That is what altering DNA/RNA is all about (I'm not sure of the biochemical details). I don't see why not.

There seems to be a full frontal assault on several scientific forums by completely blinkered geocentricists, all posing similar nonsense about the CMB. Can we not say we have now had our fun and close this thread?

I can only take this as your conclusion drawn from from the material you presented. If that is not your conclusion, please say so and tell us what is. However I don't believe the important matter is whose conclusion this is. What I am saying is that in my opinion there is truth in the mechanism, but it falls a long way short of the whole story and that the brain not only responds, but also initiates, observes, measures, recalibrates, and sometimes modifys. The fact that I can so readily produce examples supports this.

That's all very well and thank you for the reply, but it didn't address my comment about your conclusion. Namely I was offering situations where the brain produces what seem to me to be spontaneous independent thoughts. Lot's of musicians report that the tune 'just popped into my head' or words to that effect. Another example occurred to me subsequently, The golf swing, whereby golfers rehearse their shot several (many?) times before the actual event. This is an example of the brain attempting control over external conditions, not just response to them.

Since I had not heard of Libet until you brought it up I know considerably less than you do about it. So I am only commenting on your conclusions in which you seem to be implying, if not explicitly stating, that the brain is incapable of thought or creation that is independent of external stimulus. I am not arguing that external input does not stimulate brain processes, merely observing that some of the output of the brain seems to me to bear no relation to external input. For instance how do you explain the conception of a work of art eg a novel or a symphony? How about explaining a hallucination?

I didn't intend to bother with this thread from past experience, but the OP seems serious this time. Further he has been short changed in answers, even though he was a bit lax in terminology. Firstly the situation of charging a store with large short term current pulses is exactly how a standard rectifier / filter capacitor works after a transformer. So there is nothing wrong or unusual there. Similarly the current and power to lighting if resistive or especially if LED can be dramatically reduced (saved) by pulsing that supply. A superbight LED will still be well visible with a 1% duty cycle. So what is required is a chopper ciercuit driving either thyristors or powerFETS supplying the lights. Without proper details of the requirements I cannot be more specific, but standard off the shelf integrated circuits are cheaply and widely available for this.

At least as important as your definition of uniform is using the correct definition of order. Order does not mean set out in rows and clumns like soldiers at a parade. Since you asking the same question in at least three threads, I have been trying to keep the reply confined to one. Perhaps you missed my last reply there? http://www.scienceforums.net/topic/90143-entropy-at-maximum/

Did you have a question in this? All the normal laws of Physics are obeyed in the mechanics of flight. You can't exclude one. In addition to Newton's and Bernoulli's laws you should also consider The continuity equation The circulation theorem The momentum theorem.

Keeping to this thread, although you have posted the same question in more than one place, I don't know what you have been reading to gain the impression that entropy always increases. It doesn't. Entropy over a complete cycle can never decrease, but may decrease in parts of that cycle or parts of a system. That is not the same thing at all. Your question was pretty specific and to answer it I will have to get a wee bit technical. Consider a sealed cylinder, divided into two compartments by an adiabatic frictionless piston. Each compartment ( a and b) contain some ideal gas. Suppose the piston has an equilibrium position such that the volume of compartment a is Va, and temperature Ta and of compartment b, Vb. and Tb. Now suppose the piston suffers a slight displacement so its volume increases to Va + dVa. Since the piston is adiabatic no heat is transferred so q = 0 and dS = q/Ta = 0 Similarly for compartment b, q = 0 so dS = q/Tb =0 Or TdS = dUa + PadVa So there is no change in entropy as the piston is moved back and fore, compressing one compartment and expanding the other. Mechanically we know that at the equilibrium position the pressure on one side of the piston equals the pressure on the other, whilst any displacement leads to a pressure differential which leads to a restoring force. So if the displaced piston is released it will oscillate about this equilibrium position, in an isentropic process. A plunger connected to this piston can transfer this oscillation as work to say a resistive dashpot outside the cylinder. There was a much more detailed question about this set in homework help a while back. All the full mathematics is available in that thread. I will try to find it.

What about it, go on when you have cleared your throat.

When you say 'time travel' you need to start by explaining exactly what you mean. Here is an example to think about. Say you have a ruler 10 units long. When the ruler is lying still on the bench at time. t =0, all the particles (represented by the numbers 0 to 10) are in the same time zone together. Now say you push it along from the zero end so it travels in space. The push on the piece of ruler from 0 to 1 pushes on the piece of ruler from 1 to 2 and so on. Each push takes a finite time to transmit so the push from 9 to 10 comes a finite time after the push from 0 to 1 . So you are not moving the entire ruler at the same time or each piece of ruler follows its own trajectory in time. If you now turn this argument round to discuss time travel, not space travel, how do you describe 'time travel' ?

Coefficient = cooperating to produce a result, from the Latin. Coefficients mean nothing by themselves but they modify variables in some way, cooperating with them to produce a result that neither could produce by themselves. This is more common in Physics than Maths They can also act a 'filters' selecting a particular set of circumstances from many available ones. This is more common in Maths than in Physics. For example stress = a coefficient x strain. (Hookes Law) This coefficient, called Young's Modulus, converts units of strain to units of stress. also Voltage = a coefficient x current (Ohms Law) This coefficient, called resistance, converts units of current to units of voltage You mentioned first order equations y = ax + b. For any given a, the coefficient b selects a particular straight line from an infinite set of parallel lines covering the xy plane. also For any given b, the coefficient a selects a particular straight line from an infinite starburst of rays passing through b and again all covering the plane.

Yup. My guess (after your responses) is that the original question only asked for the area, but Tom assumed you need to calculate the ( or a) radius and, of course, couldn't do that. So he asked for the radius as well I never considered that possibility in my original response.

Isn't that what I said in post#3

This is pretty clear to me. Perhaps the OP was attempting the wrong problem.

The question requires you to find r and R. The relationship between them is h = R - r and R = h/2 + c2/8h where c is the chord length. You are only given c and require one other of h, R or r to complete the calculation.

Don't forget you entitled this thread curve fitting and interpolation. Pure mathematics only admits one situation and it is deterministic. That is you know the true function and its values at certain data points and want intermediate ones between the points. There is no choice of curve(s) to fit. For example you have sine tables with the sine at every degree and want the sine of 23o 30'. Numerical mathematics adds two more scenarios. Firstly you have a set of data points, but you dont know true function at all. For example you have a set of tide tables with the tide height every 10 minutes and want to correct a set of soundings to mean sea level. You have the soundings at random times in the interval covered by your tables so you need the tide heights at say 11 minutes, 14 minutes, 18 minutes etc. Finally you may know the exact function, but it may be to difficult to handle so you choose a simpler one that is near enough. It is this third method that is the basis of all the finite element computer programs for structural engineering, fluid mechanics, electric and magnetic field plotting and so on. The calculus of variations and Lagrange-Hamiltonian mechanics are ways to choose such simpler functions.

Here is a spread sheet calculating the value of r given various values of h = R - r

I think you need one more piece of infomation to solve this. You need either the rise of the arc over the chord (h), or one of the radii ajb mentions R or r, or the angle subtended at the centre.

Google the Brachistochrone problem.

Dr Dy, please look at post#11 of this thread, to save me a deal of writing. http://www.scienceforums.net/topic/90143-entropy-at-maximum/

OK so someone likes my last post so here is a rough guide to some of these basic terms. You are currently posting similar stuff in three threads about thermodynamics, but I am trying to collect together in one thread (this one). First 'state'. The state of anything is a complete list of the values of properties of interest for the system concerned. The next bit is very important. A state can only be defined if one value for each property can be obtained that represents the whole system (for instance average particle velocity in a gas) If one part of the system is in one state and another is in a different state, you need to divide the system into two subsystems. It may also be that one value cannot be obtained (for instance turbulent motion in a fluid) in which case the state of the system is undefined. For properties of interest that do not change with time (ie are independent of time) then the system is said to be in a state of equilibrium with respect to those properties. A system can be in equilibrium with respect to one property but not with respect to another. For example a system can be in horizontal equilibrium, but not vertical equilibrium in mechanics. Which brings me to note that I have been general in my statements so far since thermodynamic state is not the only state possible. For instance colour. It makes no thermodynamic difference if the working fluid changes colour at some temperature (although this might be useful for other purposes) or through ageing with time. Further thermodynamics and other subjects offer relationships (equations) connecting the properties of interest so it is not necessary to know all of these to complete the list. Each relationship can reduce the number of unknown property values by one. OK so we have our list of properties and we have a list of values so we have a state for some system. The information content is a second list which is a list of all the possible states. plus one piece of additional information - telling us which state the system is in. Since all the possible states are not independent, we can reduce the list by one as this can be deduced from the rest of the list of possible states, as being whatever is not already listed. Relating this to entropy is tractable for systems that have a defineable set of states (this is good in quantum theory) but not so easy where we enter an (infinite) continuum of states. Finally heat and work etc are not properties of the system. They are exchange or interaction variables which relate interactions between the system and that which is not system (its surroundings).

Yes, and as I indicated in your other thread, it would help you enormously if you were to get hold of the proper definitions and meanings for the basic terms you are throwing around. Please take this in the (good) spirit in which it is meant. Information is another such word and has a very specific meaning in statistical thermodynamics that is different from, but also related to, the (also specific) meaning in communications theory or the meuch wider meaning in use in general English. To understand the meaning of information you need to understand the meaning of 'state'.

That's not true. Did you miss my post4? It is not equilibrium within the system that counts.