studiot

Yes indeed it was designed to show that you have to be careful. It is not actually nonsense, since all the terms are pure numbers with magnitudes. I can repalce the one in the identity with -eπi since they are both the same type of object - a magnitude. But I can't replace it by c since 1 is a magnitude and c is a velocity. But it is very strange. Similarly c and hbar are different since one is a velocity and the other an action. So I can't just replace one with the other and say (ℏ−c)=1−1=0 Those consequences were designed to show that it is nonsensical No I was not trying to introduce QM or Unification. I have always been happy with the separation. I think it is a very good idea to work from the known to the unknown or to try out ideas on simple, well defined examples before plunging into the complicated. This is why I mentioned number and SI. For various calculations in chemistry it is necessary to work simultaneous equations balancing the number of atoms, the number of charges, and perhaps the number of phases or the energy input. For other calculations in the Gas Laws you need the number of molecules. This discussion of number and dimensions (and circles) is worth reviewing https://scienceforums.net/topic/80023-the-dimensions-of-numbers/ Please note I do not mean different types of numbers that you will find if you ask the question of Google - Natural, integer, rational, fractional, decimal, real, imaginary and so on. What I was referring to is a different viewpoint. I will use the conventional # symbol to denote numbers in this context. Consider a horse race. Horse #52 wins with #19 second and #5 third. Here we have two other uses of numbers. As labels horse # 52 etc As an ordering first, second and third. - The ordinal numbers Neither of these are magnitudes and do not obey the ordinary rules of arithmetic - adding first and third makes no sense any more than adding #52 + #5 Nor does the set of them need to be complete. As symbols for example on car number plates. Again ordinary arithmetic is not followed but some information may be conveyed, nevertheless As magnitudes - the cardinal numbers Which do obey both ordering and the normal rules of arithmetic. These numbers are often used as coefficients to be combined with some quality or property, which may well imply a scale, units and magnitudes. Or they may be specific coefficients of variables in expressions where the variables are also pure numbers (but obviously a range of pure numbers). Finally you can generate the natural numbers from nothing using copies of the empty set.

Which side will Canada be on in the forthcoming second US Civil War ? That's it. the question.

Just as HS2 , the Millenium Dome and other glory projects have diverted money from truly worthwhile projects, some of these in deprived areas so failure to replace Drax (I did say replace) is having the same effect. Those North Sea wind farms, though far better than Drax2, are not as sustainable as say a Severn or Irish sea tidal project. But they could be used to provide the energy to convert Keilder to a pumped storage scheme. Furthermore such schemes would have the added benefit of bringing the country back together rather than driving it further and further apart. We should be thinking at least 100 years ahead.

It's clear you are intent on ignoring anything said to you that is against your gospel so I will leave you happy with the gaderines. Good night.

Actually I am not doing it at all. I agree that not only is Can we say that sin2(x)+cos2(x) is NOT equal to "1 Full Feynman"?" , I have been saying that all along ! If you go back you will find I have been conditionals like ' if 'could' and so on to try to demonstrate the folly of doing so. I claim, as do others such as in my reference and you apparantly now agree with that the 1 in natural units is different from the 1 in say 1+ 1 = 2. The nature of that difference is all importance. As a matter of interest we now teach up to 4 different meaning for the symbols 1, 2, 3 ... etc in primary school. Have you come across these ? It is actually a very difficult subject at the foundations of mathematics. As a matter of interest as a new member, my respect for your mathematical knowledge and ability has grown immensely during this thread. Very few new members come as well equipped. But I had to tease out a lot of it with seemingly trivial questions. This is why is has been so disappointing to only ever have have my comments addressed at a time. So in the case of natural units c is 1 natural velocity unit. And in Physics, equations must agree in both units and numbers. I don't know if you are aware that 'number' as in pure number or count has recently been added to the primary list of SI quantities ? Some equations in physics or chemistry do not make sense without it. You haven't respomded to my construction of the natural unit system where you can indeed choose energy as your one free variable by constraining the other two of the 3 required for mechanics. This does then lead your equation E2 = p2 + m2 but in suitable units. And it comes with a very high price in lack of convenience in the everyday world. Nor have you explained what you mean by emergent, I think of it as a very special term, not applicable to common or garden situations as already explained in an earlier post. But progress has been made. Finally do you need any further help with Latex or MathMl ? I often post various alternative for scientific notation for members.

You are still wrong. By the way scientists don't believe in things - they deduce them - Belief is for religous folk. Did you not re-read what I wrote. Postulate 1 defines a start. In the case of the natural numbers that is 1, yet the natural numbers do indeed go on to infinity. Existence is of course a much less well defined concept. What do you mean by existence / You seem to be entertaining only material objects, but there is much that is immaterial in our universe. For instance the configuration of the solar system is immaterial but since the material solar system exists its configuration must also exist.

Nor was I Read the reply yourself.

There was a BBC programme about mines in Northumberland and Durham being extended under the North Sea and carbon being sunk in them. This has been successfully ongoing for several years now. But I think it is another crying shame waste of billions of public money because our great and good leaders will not pay out for alternatives that will carry on into the indefinite future without the need for carbon sinking. Carbon sinking in any location obviously has a limited life. It has already cost billions to convert Drax and there was indeed a scandal when a huge contract to supply the pellets from cutting down areas of the Brazilian rain forest.

I don't think so. The cardinality of the reals is the greatest known there is. It is also a property of infinite sets that any subset, any interval of the real line in this case, may be matched one-to one with the entire set. Am I gullible ? Here is an endless chain of causality Postulate 1 There is a first natural number Postulate 2 Every number has a successor Result there is an infinite chain of natural numbers each number causing the next number in the chain. Note to MigL The reals have a greater cardinality than the naturals.

So you can't follow the fact that if I replace a 1 in any of your equations (for example the one you are having a love-in with KJW over) by c, or c2 or c3 or... or hbar or eπi or (sin2x + cos2x), where x is any number, you have changes the physics of that eqaution ?

I have to agree that Dundee is rather depressing in parts. I often wondered why they didn't brighten up the old place by painting all that dirty grey render, and is currently in the doldrums with the decline in the offshore oil industry. I also agree that it has some very interesting bright spots. Did you get up the Law or the astronomical observatory ? (Law in scottish mean a conical hill.) Dundee was also famous for children's comics and timex watches.

Well it's your show and I did ask how you would acomplish this. In its complete form N1 also addresses the absence of any forces acting on a body. This is done separately for a good reason. Your answer need to be stated here, I have not watched a video. You could embed the video here and state the timestamp where you explanation occurs. You are going too far before completing the first part I have only gone as far your fig 9 and Newton's laws. These need to be cleared up before proceeding.

You have made four propositions . viz that you only need simple arithmetic that of the three independent variables required for mechanics (normally called mass length and time) two may be fixed (leaving you only one degree of freedom in your equations) by the expedient of defining c= 1 and hbar =1. Here are some interesting consequences of doing this Propositions [math]\hbar = 1[/math] [math]c = 1[/math] Mathematical Identities [math]{e^{\pi i}} = - 1[/math] [math]{\sin ^2}x + {\cos ^2}x - 1 = 0[/math] Consequences [math]c = - ( - 1) = - {e^{\pi i}}[/math] [math]\hbar - c = 1 - 1 = 0[/math] [math]{\sin ^2}x + {\cos ^2}x - 1 = 0 = \hbar - c[/math] [math]{\sin ^2}x + {\cos ^2}x = \hbar = - {e^{\pi i}}[/math]

Sorry I have no idea what you mean by this. Cant see any connections at all. There must be some misunderstanding between us. Have you heard of Euler's identity ? https://en.wikipedia.org/wiki/Euler%27s_identity e, i and π are all pure numbers, 1. That is they have no units at all. So if you are saying that c, etc = 1 as a pure number you are saying that it satisfies what I wrote above. That is why these constants cannot do without units and why you are incorrect to say. That is why marcus at the university of waikato is correct in his statement of the units of c that cannot be left out. My further apologies I did say by mistake it was the university of Otago (where my contact is a professor of geology, not physics). My esxcuse is that it was late here. The link I gave is correct. My concern is that mathematically you have not started at the beginning, but have invoked mathematics which have nothing to do with algebra, whilst claiming this as you 'proof'. You want to talk about a manifold, OK, but you need to start with a basic set. You can turn that set into a manifold by specifying suitable additional structure. Conventionally we go even further by specifying a metric etc but that is not necessary. If you do not specify a metric you cannot use the properties of the disk as is done in complex analysis (since you have the whole plane to play with). However you require a circle, not a disk. This is also why it is taking me so long to unravel what you are doing. It was as though Euclid had started halfway through book 1 instead of at his 5 postulates.

Thanks for reminding me of the terminology +1 That is exactly what I was getting at when I was discussion 'relational geometry'.

So has the book. Wikipedia Note quite, but different yes. Orzel's book is a lot more up to date and tells you a lot more about clocks and time itself, and a lot less about cosmology. But relativity, QM, the double slit, Pound Rebka, are all well explained.

While you are thinking about Markus' questions ( and actually answering mine), and since I am an Applied Mathematician here are a couple of tongue in cheek questions. Are you suggesting that c = -(eπi) ? or any of your natural constants, set to unity ? Since you are listed as living in Brisbane I am suprised you need AI to write English for you. Do you not speak English ? If this latter is true, fair enough, we at SF often need to help folks over a language barrier.

Suit yourself.

This is a much better book. I think the title was inspired by the Hawking book.

My apologies, I forgot to include the link to my quote. https://blog.waikato.ac.nz/physicsstop/2011/08/01/natural-units/

good faith ? something a bit ironic there. 😄

Great summary +1 The only thing I would add is not only is the 'Bible' a folder containing several books from disparate sources, there are different versions with a different selection of books.

Considering the rant from a few days ago I don't see why I should help you but I am not like that. The forum uses Mathjax. Mathjax also allows MathML I use this. The following code appears as [math]{z^2} = \sqrt {{{\left( {\frac{{\Delta y}}{{\Delta x}}} \right)}^2} - {{\left( {\frac{{\Delta p}}{{\Delta q}}} \right)}^2}} [/math] As a model I have removed the leading and trailing square half-bracket math]{z^2} = \sqrt {{{\left( {\frac{{\Delta y}}{{\Delta x}}} \right)}^2} - {{\left( {\frac{{\Delta p}}{{\Delta q}}} \right)}^2}} [/math What is in between the mathml tags is pure Latex others will perhaps offer other methods such as using the backslash, I am not so familiar with that. Due to other vagaries of this forum you may have to either refresh the page or the go to another page and then return. Finally I told you right at the beginning you are hiding some Physics by using natural Units. Here is a useful explanation from the University of Otago Physics blog. I have emboldened the most important part. Finally I amstill waiting for a response to my previous post.

Interesting subject geordief. Is your question asking about the misinterpretation of the flash of light or something else ? There was a most interesting discussion, with plenty of examples, in Stafford Beer's book in the late 1960s of such situations. Unfortunately my copy got lost in one of my many moves and I can't trace it on Wikipedia (he has written quite a few books). This is sad, not only because it contained lots of cogent thinking, but because his books are now fetching hundreds of £s S/H. The book I am thinking of I'm pretty sure was a Pergammon publication.

Thanks for the quick answers folks. The only person I know (and who made a pretty good living out of being one 1975 - 2005) sort of fits CharonY's first definition. But her research was conducted at the Bodliean on a self employed basis, mostly for specific topics on contract.