studiot

For the benefit of those who would like to continue discussing this subject here is my definition of a singularity. In order to have a function you must have a domain, a codomain and a rule which maps the elements of the domain to the elements of tyhe codomain. Once set the domain cannot be altered, although it may be restricted. The domain describes the location of a singularity which occurs in the codomain as a result of the rule. It is not the singularity itself. The singularity occupies some region in the domain, which may be a single point or a line or a curve or an area or a volume or hypersurface or hypervolume etc depending upon the number of dimensions the domain possesses. The singularity occurs where the function is discontinuous or re-entrant or infinite or is of class less than Cn where n refers to the maximum order of derivative required. Some singularities are said to be removable others are permanent. Infinite discontinuities can often be removed and are called poles in electrical engineering, where there is a lot of information to be found under the heading 'poles and zeroes'. Any function with a discontinuity cannot have an inverse. So not quite to those who said a singularity is a point in time. That point is part of the domain and describes the location of the singularity, not the beast itself.

If you really want to explore this I suggest you start with more accessible singularities, such as the Hydraulic Jump or the Acoustic Schock Wave, where we can answer some of these questions. MigL is the perfect Physicist to ask about the latter.

Addressing the issue of imagination further; I often say I distinguish two complementary processes: analysis and synthesis. Analysis is about measuring, describing and explaining what is already there. Synthesis (which I consider more difficult) is about creating something that is not yet there.

I have absolutely no idea. I have said nothing to indicate that I agree or disagree with the 'Big Bang' and I am not very interested in Cosmology or other the study of other unreachable realms. Grow up.

That was a most intriguing and thoughtful answer Thank you. +1 As to the selected quote, I am not sure what you mean by Kurdish text please elaborate. Actually no, I am not sure I have a suitable working definition of imagination. The source of my disagreement was the all embracing part. I don't know why this is but the larger part of scientific work does not involve new discovery, yet all the scientists who participate in the grunt work which is also part of Science seem to for ever remain unsung. As our body of scientific knowledge grows the scope for new discovery compared to the work of verifying, recording and collating becomes less and less. Of course, set against this, the work of imagining new applications and new correlations is expanding, due to the new knowledge. So the balance and direction of that balance is never fully determined. Just a small welcome pointer. Welcome as a new member. I see you have reached your 24 hour post limit. This is in place as a very effective antispam measure, but only lasts the first 24 hours. I look forward to further interesting posts in the future.

Maybe there is some mileage in this but it is too all embracing. What do you mean by imagination ? Fleming for instance nearly threw away the all important penecillin culture as a failure because he was looking for something else. Roengten, likewise, was looking for something else entirely when he discovered X rays.

Where exactly did I say you think you are like Einsrein ? Funny you should accuse me of this, although I did make a post at least in part supporting the sense of a quotation you attributed to Einstein, that was challenged by another member. I said absolutely zero about your intentions. I challenged a flat statement by you that 1+1 = 2 and offered some supporting evidence which you have thrown back in my face as pathetic. Have you any further rude insults you wiah to offer in return ?

I don't see what the good lady has to do with the price of bacon. But if you would like to explain what you mean you might get a better answer. Are you referring to Dirac Delta Functions ?

Oh dear, oh dear, oh dear. Once again you have ignored the questions I did ask Yet offered answers to questions I did not ask. Nowhere did I ask you to explain the mathematical reason why 1 + 1 may not equal 2. What I did say backalong was Instead of asking 'what do I mean ?' or 'how could that be ?' or somesuch You chose to not only preach your guess to me but to challenge my statement as well, without the knowledge of what I was referring to. This is what several other members have been cautioning against. As English is my first language I put a question mark at the end of any question I (unless I forget) and I have asked now on several occasions for clarification of one of your statements. for instance the one you ignored in your last response. . By contrast I cannot recall any time you have actually asked a question of one of mine. Yes your guess would have some merit if we were talking about probability or accuracy but I was not. The answer I was thinking about is 1 + 1 = 1. The electronic chip I was referring to (although the mathematical process can also be implemented in other ways) is called an AND gate. Have you heard of Truth Tables ? Yet again you refer to singularities and infinites indiscriminately. They are not the same, which perhaps is why they have different names, It is true that an infinity is one way for a singularity to occur. But there are many more types of singularity that have nothing to do with infinity. Further your statement that maths cannot handle infinity (or singularity) is just plain wrong, but I will excuse you since you need more knowledge. Once again

I don't understand this question. What does it have to do with the topic ? You have stated that you are guessing (intuition) where mathematics failed. You have also stated that you are not comfortable with mathematics, but wish to learn more. As I see it this has led to a situation where you don't know enough mathematics to actually discern whether and where mathematics has failed. Take a 'singularity'. A very simple example is density. Consider a homogeneous object such a s a ball bearing or a billiard ball. Density is defined as mass divided by volume. Now ask the question what is the density at any individual point in that ball ? An individual point has exactly zero volume. Yet we are taught from a very young age in mathematics that you cannot divide by zero. So what is the density at that point ? Ha smathematics failed ? Is there a singularity at that point ? Yet every day folks all over the world handle this mathematical conundrum ( that stopped the ancient greek philosophers in their tracks) without thinking about it because mathematics that you don't know about, can handle the situation with ease. I have already offered you another example ( 1 + 1 not equal to 2) that you have consistently ignored.

So what do you want to know about either ?

As I honestly do not know what an Orson or a Mork is I am going to do the obvious thing and ask. What is an Orson and a Mork ?

One factor not yet mentioned is that the torque/speed characteristics are very different for electric motors as compared to internal combustion ones. So one consideration is to know where you want maximum power.

Do you honestly find it uninteresting to learn that our whole IT technology rests on devices that do not make 1 + 1 = 2 ? You computer would not work without these devices. As regards infinities and singularities, you whole world is surrouinded by them but since you seem unwilling to discuss them I can only think you don't want to know more about them.

These are much more cojerent thoughts. But what makes you think this hasn't already been done in mathematics? Is this the problem? It is a fact that all members here are communicating using real material electrons chips that can only provide a different answer to that sum.

So let us look at some examples using my definition of a distance function. [math]d:X \times X \to {\Re ^ + } \cup \{ 0\} [/math] So my first example is as follows 1 Let X be the set of all binary words of length 3 characters. Thus there are 8 members of this finite set { 000, 001, 010, 100, 110, 101, 011, 111 } Then if x, y are elements of this set define d(x,y) as the number of digits in which x and y differ. It can easily be seen that for each x there are 3 ys that differ by one character Thus each x has 2 ys at a distance of 1 from it . d = 1 similarly there are 3 words that are at a distance of 2 characters from each. And there is 1 word that is at a distance of 3 characters 2 Let X be the set of all real numbers and d(x,y) be be the modulus or abs function. [math]d(x,y) = \left| {x - y} \right|[/math] 3 [math]d(x,y) = \sqrt {{{(x - y)}^2}} [/math] Again it is easy to see that all three examples satisfy the requirements [math]d(x,y) \ge 0[/math] [math]d(x,y) = 0if\;and\;onlyif\;x = y[/math] [math]d(x,y) = d(y,x)[/math] [math]d(x,z) \le d(x,y) + d(y,z)[/math] The distance function in Example 1 is discrete The distance function in Example 2 is is continuous but it is not differentiable over the entire domain. The distance function in Example 3 is both continuous and differentiable, which is why it is often used to replace the absolute value function. So in order to do calculus with our metric we must further limit allowable distance functions, which has clear implications for relativity.

[math]d:X \times X \to {\Re ^ + } \cup \{ 0\} [/math]

Yes and you are asking us to respect your imagination. Do you think you have shown due respect to the short piece of help I offered ? Only you don't seem to have read it very well.

You could of course see if Euclid's method for finding the HCF can be combined with your proposal, to find factors, as it already seems to be a modification of it.

Before we disappear down an einstinian rabbit squabble hole, I'm pretty sure he did say something like the quote, though I am not sure those were his exact words. Einstein was renouned for his intuitive understanding of Physics, a skill which greatly assisted his progress. He did say something like get the Physics right and the Maths will follow, though I haven't got the exact quote to hand. But then he was also wrong sometimes and had the grace to admit it. indeed (General) Relativity started out without the lambda term, but that is another story.

Thank you, agreed. As to the cautionary tale of the sea mile that no one seems interested in, A few hundred years ago we could determine latitude pretty well but not longitude. At that time we had a properly spherical model of our globe. Maritime nations, in particular England, introduced the 'sea mile' or 'nautical mile' as a measure of distance ... at sea where the surface of the model globe was considered uniformly spherical. The sea mile was defined as 'One minute of arc, measured along a meridion of longitude'. Although they did no know which meridion, they assumed all segments of all meridions were equivalent. They chose meridions of longitude because they were all supposed to be great arcs, whereas the equator is the only parallel of latitude that is a great arc. Mixing these up still leads to some unfortunate descriptions (particularly when AI is asked) about the arc being one of latitude to this day. The point is that they did not know the flattening of the Earth distorts these great arcs of longitude, especially near the poles. This was sufficient for the 'metric' to vary from place to place, a most undesirable requirement. Subsequently an average was agreed internationally, but it still means that the sea mile still does not conform to its original definition anywhere.

There are such things as non stochiometric compounds, https://en.wikipedia.org/wiki/Non-stoichiometric_compound These are still made of atoms and or other particles.

That's the way. Did you notice I did not include either quantum or field in my basic list ? What did you make of the list ? I don't know what you think a field is but in Science it is a name for a region of space in which some property ( or collection of properties) has specific values at every point in that region. The value may be zero and , of course, a field where the value is zero everywhere is not very interesting. The field may be real like an electric field or a magnetic field or it may be totally abstract as in a direction field. Obviously in order to specify values we must have a way of referring to each point and equation(s) telling us the value at that point. If these equations fail at a few points the we say there is a singularity at that point and we cannot then determine the desired values. Now the point of knowing all this is that a field, for example a magnetic field, can interact with other objects, in particular material objects. For example magnetic materials will align themselves with a magnetic field. It may be that the equations that describe these interactions yield discrete or stepped solutions. This is called quantisation. So it is the interaction between the field and something else that is 'quantum' and leads to quantum theory. There is no such thing as a 'quantum field' by itself. I mentioned 'principles' and energy because our understanding of The Principle of Least Energy is what underlies quantum theory and much else of the processes of the universe.

It's a little more than that as it also includes charge conservation, which you need sometimes to gather the right number of equations to complete the set for solving.

It would also be useful to understand the meaning of 'singularity'. But it's rather technical and I don't think the definition as 'a point where a function ceases to be analystic' will help much until you know quite a few more supporting technical terms.