studiot

The following statement was offered in a recent thread as justification for a point. As this was not really germane to the thread and I can't find it anyway since the forum upgrade, I thought it woudl make a good discussion subject. Well I take'Nature' to mean the real world, both theoretical and observable and I respond "Science sees Nature as rife with discontinuities. In fact so much so that many Sciences have coined specific (often quite colourful) words for their discontinuities." So in Earth Sciences (Geology, Paleontology etc) we have Unconformity Fault (many sub types) Extinction In (Fluid) Mechanics we have The Hydraulic jump In Mathematics and Computer Science we have the terms Concete Mathematics Discrete Mathematics Endpoint Boundarypoint and of course discontinuous.

You can indeed get a practical perspective. Density is mass/volume. So the density at a point is mass / zero. Yet the sum of all these density points over some region, eg the space occupied by a 1kg weight, is finite.

This is why you need the Dirac or impulse functions for the integration, as I noted. I'm sorry I only know how to use them in mechanical situations, but I have seen them in statistical applications, so I can't provide a reference.

No you did not make that clear, quite the reverse. My apologies if you do not, in fact, have a computer science degree, perhaps you call them something different in your part of the world.

Just a couple of points here. When you have a situation where you have an infinite baseline and therefore zero point probabilities, yet the integral must add to something finite, as here (the total probability must sum to 1), you are into dirac or impulse functions for the calculations. We had a long thread a while back discussing the difference between chance and random and the meaning of probability. I observed that mathematicians and physicists mean something different by the words chance and random and in fact mathematicians rarely use the word chance at all. The nub of it is that mathematicians divorce the cause and effect whereas statistical physics is full of chance causes of processes being distinguished as random or partly random. I also noted what computer mathematics calls the 'Kolmogorov definition' of the term random. This allows mathematicians to state (correctly) '1' is a random number. Physicists concentrate more on how one arrives at that number.

Hopefully you have spent (some of) the last seven days reading and fleshing out my last post? I am not a little surprised that you have no questions as a result of that post. And also a little disappointed that you have just ploughed straight on with your use of the word Field as though I my post had never been written. The whole point of that post was to avoid the misunderstanding you seem to have about a Field, since you seem to treat one as though it was some form of mystic substance that emanates from the end of a magician's wand. The other trap to avoid is to try to 'pick 'n mix' topics from classical and modern Physics. It is best to stick with one or the other and employ whichever gives the most convenient and closest match with observation. In general modern Physics applies at very high velocities and /or very small sizes. You have asked about stored energy ( a classical concept) and the Sun ( very large object) So which would you think applies here? Energy in particular is a classical concept so you need to fully understand classical energy before moving on to any modern application.

I see that scherado has a degree in confusion computer science. I dread to think how computers could operate without the number zero, since most have only two numbers to work with and one of those is zero.. I hesitate to use the t- word, but If we are genuinely being ignored I think the best we can do is to ensure that balancing correct statememnts are present in this thread.

Of course, since many equations have more than one solution, scherado could be using a less general interpretation of value to mean "The particular solution we select from the solution set of a given equation" The problem with this is that zero is the only solution to some equations. This means that scherado has to exclude some equations from his definition, as having no solution or no value in his terms. You are correct he also has to exclude zero from all solution sets, which may or may not then then not be empty. But of course he then ends up in a worse position, equation solving wise, than if he had simply done what mathematicians realised over a thousand years ago and was going to be in my post that he rejected out of hand.

I think I now know what scherado means by value. The statement X has the value 7.3, or X = 7.3 as an equation, is specific. There is only one number that X can be. But that is true of only a handful of equations at most. There are many more equations for which the statement is not true. So the 'value of X' is a more general statement than a specific number. It requires a referential statement or condition to define the circumstances when specifity is needed. The statement X has no value does not mean that X = 0. It means that there is no number that satifies the particular condition in question. For instance [math]\sqrt { + 5} [/math] has no integer values and [math]\sqrt { - 5} [/math] has no real values. Of course this does not prevent zero having a value, just as 7.3 does. It just provides rational meaning for the terms.

The number of electrons in a hydrogen atom is absolute. The speed of light is invariant, but not absolute. And yes the rest mass of a particle is also invariant. While we are about this an FYI. The speed of light is both constant and invariant. The interval, s, (as identified by the equation ds2 = dx2 +dy2 + dz2 -dc2t2) is invariant, but not constant or absolute in Relativity.

Butch, What do you think the difference between an invariant and an absolute is?

Strange - you are so right. +1 Easy - My Humble apologies for doubting you. scherado - take note.

Copper is diamagentic. https://www.nde-ed.org/EducationResources/CommunityCollege/MagParticle/Physics/MagneticMatls.htm

Sorry, Dr Krettin you don't get two upvotes because you posted the same thing twice. But you do get a +1 because the Keep it Simple is really good. I would add one alternative / addition to that. Simple depends upon the reader. Try to find some material about a subject you already know in the foreign language. I did very well improving my German and French with cookery books and programs.

Of course, mathematics has meet the difficulty presented by the OP (and it is a difficulty) before, which is (one of the many reasons) why the theoretical structure of mathematics was revised and extended towards the end of the 19th century. The sad thing is that the OP choses to stamp and act in a juvenile manner rather than listen when someone takes the time and trouble to explain.

Thanks uncool, +1 I was coming round to expressing exactly that in less formal language and with longer explanation when I was so rudely interrupted.

You should start by understanding that EM energy is not purely a function of EM frequency. Define evidence. Here is an example of some evidence. If I take a 50 watt monochromatic sodium lamp and shine it on a photocell to measure the energy and compare this with a 500 watt monochromatic sodium lamp I will find that the light energy is of the same frequency but substantially smaller.

Is a great deal a value? If so how much? Are you going to answer my previous question?

Why couldn't you wait till I came back and finished my post as I promised?

I think you have misunderstood what Halls of Ivy said. Putting words he did not say into the quote does not help either. He said that 0/0 is not a specific number. He did not say that either infinity or zero are not numbers or values. I will leave the issue of infinity aside since it is the more complicated of the two and off topic here. Zero on the other hand is most decidedly a perfectly respectable number. Failure to recognise this held back Mathematics for several thousand years. Let us examine the situation more closely. For most of its history mathematics was developed by practical persons needing figures to carry out their daily life. Also throughout history these processes were isolated from the praticality and formalised into the discipline we know call Mathematics. So we start where the ancients started. With arithmetic. They identified four processes as forming a vital basis for arithmetic, long before algebra was invented. These are addition, subtraction, multiplication and division and I am going to use the modern description for these. I will come back and finish this.

A couple of quick points about (scientific) English. A particle is always taken to be of negligable dimensions. So in the calculation of planetary orbits, the radius of the Earth is negligable compared to radius of the orbit and we can consider the Earth as a particle. The word 'punctual' in English means at the correct or appointed time, it is inappropriate to use with particles. If you want to describe something of finite or non-negligable dimensions you would use the word 'body' or even 'rigid body' as appropriate to the situation. I still think you are missing the point and as it is an important one I will try to say it in a different way in my next post. Perhaps it is a language thing as you obviously have a better understanding of electromagnetism than your English allows. Maxwell did not know about electrons, that was Thompson at least 30 years later. Maxwell's equations are classical field theory equations in continuous functions. As regards self interaction with its own field, relativity limits the horizon of this as shown by this animation from NASA.

I have to say that I almost completely with Dan on this, since I can't see the benefit of an essay on that book. Far , far better would be a communication skills course. One that included multiple media that would help far more in both Dan's future career and benefit the people he interacts with far more as well. This might avoid the following poster that I photographed on the noticeboard of a leading Scottish University this year, advertising no less than their language society! The first pic shows the board, the closeup shows the spelling mistakes. It isn't only technologists that make them.

I agree that technical people are not usually philistines who need force feeding some culture and I thought that this hangover from the days of arts softening was dying out. +1 Do you get a choice of liberal studies and does it affect your marks or progress?

Notice it is the women who seem do all the work here. But seriously it is a great project. http://www.bbc.co.uk/news/av/magazine-41391844/why-is-africa-building-a-great-green-wall

Well more modestly I've introduced this. I had been going to cover it more thoroughly. When a molecule has more than one bonding mode or configuration available to it, very often a phenomenon occurs that chemists call 'resonance'. This occurs when the result lowers the internal energy of the molecule compared to any of the modes referred to above. Essentially what happens is that a combination of the different modes actually occurs. When this does occur the energy difference between the non hybrid structure and others is called the 'resonance energy'. In the case of carbon dioxide there are three contender molecular structures which combine to form the actual one. There are no vibrations and therefore no frequency associated with this and the molecule is in this state, whether it is vibrating in sympathy with some other input or not. Since (as I have already indicated) the configuration geometry of the molecule is altered by this chemical resonance, the mechanical vibration modes are also displaced from those of the simpler contributing structures. Since this is a Chemistry question in the Chemistry section, this is what I take the term resonance to mean. It is also true that, just as an conductive aerial provides a conductive path for electrical resonance to occur (in classical terms), So the slight charge separation within the molecule provides a capacitive path for electrical resonance in the bonds of that molecule. (again in classical terms = displacement current) Change of potential can lead to electrical work being done in distorting the bonds and thus energy being transferred to the molecule. I am sorry you do not want to explore this fascinating subject, but rather chose to fight tooth and nail to bend observed phenomena to your own limited viewpoint.