studiot

Doesn't that depend upon your distance function?

Personally I've never been offended by someone calling me 'bro'. All the persons (not many it's true) I've come across using this form of address have not meant it in a derogatory way.

my point exactly but I actually said However do (some?) ruled surfaces not incorporate both straight lines and geodesics?

I can't accept that a geodesic is the 'equivalent' of a straight line, except in very loose terms. You can have 'straight' lines in curved space and geodesics in the same space. Are these equivalent? You can have 'straight' lines in euclidean space and geodesics also in euclidian space. Are these equivalent? Remember also that Newton did not talk about straight lines, in relation to motion. His actual phrase was "In its right line" I think it would be best to explain the difference between the purely geometric statement of geodesic or straight line and the least energy formulation of physics.

Did I waste my time in post#58?

Actually you should study colour receptors more thoroughly. The RGB scheme in colour cameras, television and projectors is no accident. It stems from the fact that not only our eyes, but the eyes of pretty well all life that has eyes, works in the same way. Eyes have triplets of receptors, each single receptor sensitive to one of the primary triplet colours, just as in colour cameras. Yes we have copied nature. And the colours chosen are no accident either, they correspond to available pigment photchemical reactions. Perhaps a biologist could chip in here as I only know the outline details.

My post was for your information not a criticism. go well

There was a long discussion about this recently. http://www.scienceforums.net/topic/72725-is-mathematics-alone-a-safe-medium-for-exploring-the-frontiers-of-science-or-should-observation-and-hypothesis-lead-in-front/ My answer is that yes, there are some technical subjects that cannot be described by mathematics. These are often described by processes. The example I gave was the mixing of concrete, which cannot be prescribed exactly in advance by mathematics. There is an element of 'add water until the consistency is as desired' Another example is the colouring of squares by some cellular automata at successively reducing scales. It is imposiible to state the final colour of a point, it depends upon the scale.

A simple way to test whether anything you 'see ' is inherent in the value of the number or purely coincidence due to the presentation of the number in arabic numerals is to write it out in roman, sanskrit and chinese numerals and see if the 'pattern' stills holds true.

Your question is to abbreviated to understand easily. Does "in H.P." mean in harmonic progression ? Here is a hint : look at the conditions. What other conditions besides a,b,c,d could be stated ?

Most people find it helpful rather than confusing, that is why they do it. No it is not inserting an operator. The + or - is part of the number so -9 is a different number from +9 and can stand alone in an operation that has nothing to do with subtraction or addition. They are not a 'neutral' 9 with an appended sign. The fact that the distance between 0 and - 9 is the same as the distance ebtween 0 and +9 is coincidence. The distance between -18 and -9 is also the same. In the complex domain there are an infinite number of numbers att he same distance from any given (complex) number. That is getting into metric space theory, by the way. There are many different number systems with many different purposes. Some of these do not have positive and negative numbers, For example the complex numbers, and the transfinite numbers. Some do not have a zero For example the natural or counting numbers (this was the first system invented) Some have strange looking numbers that cannot be directly expressed in the decimal system for example [math]\left( {5 - \sqrt 7 } \right)[/math] The expression in brackets is one single number. These are known as surds. I mention the last because in my post#4 I said that you are onto the trail of something much bigger and you should look at certain (?new) ideas. one such is the conjugate, which has many variations. One of these is called the algebraic conjugate. These are the roots of the same algebraic equation. For example the equation [math]{x^2} - 6x + 1 = 0[/math] has two conjugate roots [math]3 - 2\sqrt 2 [/math] and [math]3 + 2\sqrt 2 [/math] neither of which are negative. I didn't say your notation bothers me and it doesn't. But I don't see the point of changing something to introduce a new notation that does not add anything new. This has already been done too many times in maths in my opinion. I seriously suggest you will find much rich food for thought if you follow up my references in post#4

Not 'as if' this is actually the case, we just do not normally write the + by convention. But the + or - are definitely part of the number and not just an 'operator'. for instance what happens if you add -2 to -3? (-2) + (-3) = (-5) The + here is an operator but all the minus signs are part of the number. Strictly we should perhaps write (+2) + (+3) = (+5) where are the plus signs in the brackets are part of the number as before and the connective plus sign is an operator.

SF is an excellent generalist forum, that seems to me to specialise in discussion. For practical help, there is a University of Toronto teaching forum, that shares an administrator (Dave). You will find they are just as friendly there. AllAboutCircuits.com Do bring anything you learn there back here. go well

Think again.

Sure, keep coming back for discussion about stuff.

There is only one being I can think of that has symmetrical hearts and he was on television over Christmas. Agreed. Pairing, rather than real symmetry, is more frequent in the externis of living things than the internal structure. For example you have a left hand and a right hand, they are not symmetrical. They are, however a reflective pair. For true symmetry you have to be able to overlay one part on its symmetric partner part exactly by rotation. But there are plenty of examples of monism (Rhino horns, fish fins, etc), and even a few of trilateration eg the now extinct tricertops.

I agree with ajb your source is spouting nonsense. This again comes from trying to interpret proper scientifically consistent theory in terms of general parlance inexactitude. Consider a matter point at (x1,y1,z1, t1) It is fundamental in our science and maths that his point cannot also occupy (x2,y2,z2) at t1 That is it cannot be in two places at once. That is it is impossible to travel in space without also travelling in time. That is you cannot travel from (x1,y1,z1, t1) to (x2,y2,z2, t1), you can only travel from (x1,y1,z1, t1) to (x2,y2,z2, t2) as the transit takes time (t2 - t1). Populist stories such as by HG Wells have the hero 'travelling' in time, without travelling in space. Incidentally think about what you mean by 'time travel'

Excellent point, +1 Don't forget that what is meant in technical circles by a 'dimension' is a very different animal from what is meant in general parlance.

x, y and z (Yes I know you can embed a plane, but I think this point needs elucidating to the OP)

What happens if you use Internet Explorer (No add ons) version? All Programs > Accessories > System tools > IE(No add ons)

First here is the full quotation. It would have been nice to have been told that this was nearly at the end of the webpage linked to. This is a good example of the difficulties you can encounter when trying to explain electric current by means of the water in a hosepipe model. Electric current is not water in a hosepipe they are different. You are quite right to question this passage, it is unhelpful. I have also underlined a further unhelpful extract which almost implies you can arbitrarily change the voltage across a resistor without changing the current, in conflict with Ohm's Law. What is happening here is the failure to properly explain what is meant by 'voltage'. 'Voltage' has more than one meaning, Side note : This is not unique in Physics : The product force x distance means either work or moment depending upon the context. Firstly a primary source of electrical energy offers electrical energy measured in volts (per coulomb). We do not normally state the coulombs bit because that varies whilst the voltage remains fixed. It is called the EMF (ElectroMotiveForce) of the circuit. This could be a battery, of say 9 volts. It is this EMF which 'drives the charge through the resistance'. A primary source of EMF introduces electrical energy into a circuit. A resistor (or conductor) is not a source, primary or otherwise, of EMF. The resistor has a voltage difference or drop between its end terminals. We call this a potential difference or potential drop. (PD) Energy is dissipated in a potential drop. That is energy leaves the circuit (in the case of a resistor as heat) Does this help so far?

You seem to be feeling your way towards the Yin and Yang of Mathematics. Mathematicians love to generalise, to extend an idea to larger and larger classes of (mathematical) objects. But not all objects can be classed as positive or negative, for example complex numbers, matrices, operators etc. This idea appears many times in many guises, you should investigate the following Adjoint, Conjugate, Dual Transpose Maybe ajb will add to my list.

You cannot build a mechanism that lifts its own weight against gravity without pushing or pulling against something else. Your mechanism appears to be a bit like a Scotsman whirling a hammer in the Highland Games. There is always a reaction force to consider at the centre of the whirling.

OK It's good that you only want hints not answers since we don't provide full answers in this forum. Surely you must have had some thoughts? Here are some hints. 1)What is the relationship between work and energy? [math]Work = \int {F(x)dx} [/math] So can you see what to do to obtain the force from the energy and the function which describes x? 2) The total energy = E What forms may the total take and how does that energy budget compare with the values of U on the graph. Have you, for instance, enough energy if E = 5 to traverse the whole graph? Again your graph shows potential energy as negative for certain values of x. Can PE ever be negative?

These books listed are accessible from middle high school through senior high and onto first degree level, except the last which took me right the way through O level, A level, Degree, Professional Institution and Postgrad and is still going strong. Atkins Molecules. (P W Atkins) a really delightful book described by some as the most beautiful chemistry book ever written. The Mathematical Mechanic (Walter Levi) a brilliant melding of maths and physics. Levi sets out to prove mathematical theorems in as many physics ways as possible. Cats Paws and Catapaults (Steven Vogel). Compares and contrasts the approach by Nature asd Man to the solution of important engineering problems. describes materials science v muscle action and much more. From Calculus to Chaos (Acheson.) The development of non linear dynamics brought to life and a uniquely simple way. The Penguin and Dictionary of Curious and Interesting Geometry. (David Wells) Fascinating reading for a dark winter's night. Did you know Napoleon was responsible for a theorem in Maths? The Day the Earth Nearly Died (Michael J Benton) Wonderful balanced roundup geological study of the five main mass extinctions in the Earth's geological history and more. and finally that piece de resistance A Compendium of Mathematics and Physics (Myler and Sutton)