studiot

All distance measurement is by difference. If you have done any serious hermodynamics you will have met the thermodynamic absolute temperature scale which is defined independently of any thermometer, unlike distance, for which we have no absolute unit.

I've yet to see it in this thread. Nonsense, it's the other way round. Every symbol in maths has a name that can be spelled in English. Every line in maths can therefore be written as a proper english sentence. English is composed of proper english sentences.

I agree, the method of measurement is not a definition. I don't have a complete definition or description but my idea is that there are many phenomena in our observable world that are best modelled or explained by introducing a mathematical variable we call time. I hesitate to suggest this thread about the same subject because it suffered much misdirection but look at my post#62 on page4 http://www.scienceforums.net/topic/82939-explanation-of-time/page-4 The introduction of a new variable to ease the mathematics has other precedents, for example the introduction of entropy in thermodynamics to pair with temperature on an indicator diagram. Of course we do not have the same up close and personal relationship with entropy that we have with time but the maths follows a similar path.

The ancient Greeks did a lot of thinking, some of perhaps due to the peculiar quality of the wine made from the grapes that grew on Mt Olympus. They were particularly fond of paradoxes, Zeno remaining the most famous in modern times, but there were many chroniclers. Most of their 'paradoxes' can be resolved by adding our further knowledge to their less developed state knowledge. But I am not really a classics scholar so I don't know the full story of Zeno. Today we have our own 'paradoxes' to wrestle with such as quantum tunneling and quantum entanglement. Perhaps later generations will have the proper understanding to fully resolve these. For example Proclus has that " Not every triangle is also a trilateral figure", simply because they did not fully understand angles.

Why am I dodging the issue? No one, not even Zeno, pretends that Achilles does not catch and overtake the tortoise. That is not the issue. He just saddles up his trusty kangaroo and hops right past. Zeno's issue is/was "Where is the mistake in my homework, Miss? I can't see it" In order to explain the inadequacy of Zeno's reasoning we need to do something equivalent to that presented in physica's video, and then some, because the good doctor of maths in that video didn't complete his 'proof'. This can be done either mathematically or liguistically, following the same route. What I have not done, but left in the air for the moment, is state what I think is missing from existing explanations in this thread. What do you think that might be?

Like many I have been following this thread with interest and would like to make the following comments. 1) The OP did not contain a question, but since this is the speculations thread I assume that the statements made were a proposed analogy for explaining Zeno, and this is borne out in the Title statement, which is also not phrased as a question. 2) The thread deteriorated into a dispute about mathematics v linguistics. 3) Now since there is nothing that can be said in mathematics that cannot be said linguistically this is or was a pointless diversion. 4) Since there are those who will wish to argue against (3) they should note that this may involve going back to the basic axioms of maths, which are all stated linguistically and developing the necessary mathematics for resolving the problem. Using Maths is of course more concise. So a linguistic answer may be very very long winded but it can be done. 5) The most interesting point is that neither side has actually resolved Zeno. Not even the 12 minute youtube video did that. So far only part of the solution has been presented. 6) No, calculus is not required, but a study of convergence either mathematically or linguistically is. A good textbook for this is the classic by Ferrar at Oxford, suprisingly entitled " A Textbook of Convergence ". I look forward to someone presenting a complete solution.

Well let's hope I have succeeded then.

I have thought long on this topic.......it's still at the back of my mind. I am afraid you won't like my response........... My response is as follows............. I think that proportionality is the result of a choice rule......and.......choices can be many. It is not a question of whether I like or dislike your response - actually neither. I don't understand your response. I have no idea what you mean by a choice rule. The definition of proportionality was set at least four hundred years ago. If you are proposing an alternative, I have pointed out it's arithmetical flaw since we cannot divide by zero. A further arithmetical flaw is that is does not define what happens when the constant is zero. Do you think an alternative definition for a relationship between three quantities that is undefined for two of them in certain important cases is worthwhile?

Yes, it is true that whatever clock ticks measure it is not time and that a ruler directly compares one length with another. But it is also true that neither tells us what space or time are. In fact we cannot measure time itself, only time difference, and that is what the clock tick measures. There are many quantities in Physics that we can only measure by difference, eg voltage. Again in fact the ruler length is a distance difference not a true measure of space either. One of the few absolute quantities that we can measure is absolute temperature (at least in theory). One further note is that for quantities that we account in either absolute or difference terms such as voltage, time etc, both the absolute and difference measurements are made in the same units. go well

This is not a satisfactory definition of proportionality. What happens when x=0? We do not allow division by zero. I have already given you one that works in all cases. Use it! Quoted is your last statement on proportionality, followed by my reply and further explanation. You have not responded to this. Further your last statement was a contradiction of my long post explaining proportionality. I have suggested we discuss forces, masses and energy when we have finished proportionality. Proportionality is a very very important concept in Physics, that we use whenever we can, so it is vital to fully understand it and to be able to get it right.

None of this is necessarily true. It is all, as you said, hypothetical. Further it suggests you have not bothered to work through the material I carefully spent time writing out for you. You started this thread about proportionality. So let us keep on topic and discuss that.

Not at all so long as you have a genuine interest. You are nearly there, but remember that x is the independent variable and y the dependent variable. The idea is that changes in y depend upon changes in x ie they only happen because we change x. This is because we normally know x but not y. We obtain y by calculation from the equation or formula. So an expression of the type y/x or y-x contain an unknown. However you are skirting around the fact that we can sometimes change things (ie find a different x) so that we can recover proportionality. for example The length of a stretched spring is not proportional to the force required to stretch it. but Another variable, the extension, e, is proportional. If we double F we double e and so on e=kF. e, of course is the difference between the current length at force F and the original that is e = (L-L0) This is not a satisfactory definition of proportionality. What happens when x=0? We do not allow division by zero. I have already given you one that works in all cases. Use it! Force fields do not exert forces on each other. They exert forces on material objects placed in the field(s). So what you are asking is how do the effects of the fields combine when they both act on the same object. Do you understand this, this is essential before proceeding.?

In short , no the definition in green does not. But the statement in black is not correct either. A word of friendly advice here. I have noticed in your threads that you bring in far too many ideas far too quickly. The result is that you confuse yourself and possibly others as well. Further you have scattered your subject over several questions, where it is apparent that a difficulty in one also comes out in each thread. So let us stick to proportion in this thread. It will help in the others as well. When two quantities, say B and A are in proportion we say that B is proportional to A. This means that B depends upon A in a particularly specified manner. You should realise that there are many other ways for B to depend upon A where they are not in proportion. What is meant by in proportion is that if we double A we double B, if we triple A we triple B, if we halve A we halve B and so on. We use this as follows: If A is 10 and B is 14, then For A = 20 B = 28 and if A=10 and B = 5 For A = 20 then B = 10 Note I have not needed to employ a constant of any sort in this definition. The above is always true regardless of the constant I shall introduce below. But I can go on pairing values of A and B in the manner above without any constant. We can convert the above to a general equation connecting A and B by introducing a multiplicative constant. We call this the constant of proportionality. So B = pA, where p is the constant of proportionality. In the examples above the first p = 1.4 and the second p = 0.5. Note I have said a multiplicative constant. This is very important. If I do anything else then B is no longer proportional to A In particular if I add anything at all, even a constant, B is not proportional to A. So if I have a second additive constant such that B = pA + D then I loose proportionality. ajb has mentioned 'linear', but I recommend you avoid the term since linear and proportional are not always the same. So we move on to what happens if B is proportional to two quantities, A and C. So B is proportional A and B is proportional to C How can I write an equation to combine A and C so that my definition will hold? Well if I add C to A what happens? That is if I double A but do not alter C for the moment. so if B = p(A+C) I want B2 to be double B1, when I double A Let us work out B1 = p(A+C) and B2 = p(2A+C) B1 = pA+pC and B2 = 2pA+pC This shows that B2 is not double B1 so an equation adding C to A will not work in proportion. OK so what about multiplication? If B = pAC B1 = pAC and B2 = p2AC So B2 = 2B1 as required. So far, I have kept C constant but if the constant of proportionality for C is q then B = pqAC, maintains proportionality. We can then combine p and q into one constant of proportionality r = pq. So B = rAC Finally I have councilled avoiding the term 'linear'. This is because we can extend the concept of proportionality to more complicated (non linear) expressions so that we can say B is proportional to the reciprocal of A, or B is proportional to the square of A. Our equations now become B = p(1/A) and B = p(A2) To cope with this extension we add qualifying words to the original statement. We now call our original simple proportionality direct proportionality, Then we say that being proportional to the reciprocal is inverse proportionality and Being proportional to any other expression is proportional to any other expression so our example with the square of A says that B is proportional to the square of A. We often omit the 'direct' when we mean simple proportionality. Does this help?

This is a better link http://www.power-technology.com/projects/strangford-lough/

Phosphorus, ground state. 1s22s22p63s23p33d0 So phosphorus has 5 electrons in the third shell. This makes the empty 3d orbital available for hybridsation. This is called the expanded octet. In the case of POCl3 the octet is expanded to 10 this way. Note that resonance is possible with alternate partially polar forms of bonding and an octet.

Both of these are inherently inefficient. It's all to do with timing. Although the waves move more or less continuously for longish periods of time, they will only contact the periphery of the wheel for a short time since they are irregularly spaced out in time and distance. It would be much more efficient if you could ge the paddles and the waves to mesh like a worm gear wheel. The tides overtopping your wall will flow continuously but only for about 1/8 of any day, again making the process inefficient. Further the process is capital (£, $) inefficient because you are proposing large structures that must be built before any £return can be made. This is actually what kills most hydro power schemes. The most attractive from an engineering point of view, taking into account geographic, mechanical and financial considerations is to realise that tides not only go up and down the also flow backwards and forwards. And this is a relatively continuous movement 24/7. So if we plant a single turbine generator on the seabed it will 1) Stay submerged and clear of traffic and other installations. 2) Produce continuous power from installation. 3) Not require massive investment in initial support works. 4) Can be added to with a second, third etc turbine as finances allow.

Just to be crystal clear. Velocity is a vector quantity. This is it has both speed and direction. Change either and it is an acceleration. Acceleration is also a vector quantity, with magnitude and direction. It take energy to change the speed but no energy to change the direction. But in both cases a force has to be applied to cause this. Can you see why? Can you see the connection to the definition of work?

It's the same method, just he used u for substitution, then found that u appears in the normal parts formula and regretted it. That was why I suggested t. Have a good exam.

http://www.youtube.com/watch?v=P-o6iFzJLpw

Thank you for this quote Gopher T (Post #622 in this thread here http://forum.allaboutcircuits.com/showthread.php?t=60389)

Substitute t = root(x) Then integrate the resulting integral in t by parts.

Following swansont's Popeye challenge, I challenge anyone who believes that only material things are real to use one of these without a real hole in the middle.

I ran a little spreadsheet to test values. If there was a misprint so that the lefthand chamber pressure was 1.8 bar instead of 8 bar then the equal chamber pressure would be 1.32 and the max right chamber pressure I make 1.45 bar, pretty close to the 1.6 bar stated. A left hand pressure of 0.8 or 2.8 diverges further from that offered.

Don't you mean having too much 'vodka craft'?

I will see what figures I come up with over the weekend. You do not have to arrive at the chamber volumes by trial and error. Boyles law works even better. Because the cylinder must have constant cross section the volume is proportional to the piston displacement. You can easily calculate the piston start position geometrically. Boyles law again will give the equal pressure volumes (or any other) and thus the piston displacement. So calculating the piston position at any moment is easy. If you like you can form an equation for the work done on the piston in terms of the pressure difference force and the displacement, but it is a quadratic fraction that must be integrated. As regards the book answer, perhaps there was an error which is why Endy couldn't find it in his later edition of the book in post#3? One final thought. Say the piston was 0.1 metres long then its volume is (0.1 x 0.1) m3 (note the superscript and subscript icons in the toolbar here) = 0.01m3 So I wonder what the authors think this piston is made of? Gold is heavy stuff of density 19000kg/m3, so my gold piston has a mass of 190kg. Any longer piston would make nonsense of the rest of the calcs since the cylinder is only 2.5 m (plus piston) long.