imatfaal

open bracket c close bracket = © ie it gets rendered as copyright symbol

happens on both preview and post, and when you switch between fast reply and full editor

John - of course you are right that question said "Not the arch curve but the straight line between them." Even now I tend to read the question too quickly - but I still struggle to see how it could easily be done otherwise. The Taylor Series would be accurate to 1 in 10^9 by the second term because of the smallness of the angle. But even restricting to two terms cubing pi/80 (to 7 dp or more) is an awful job. There has to be a trick that I am missing.

I hope the OP posts the intended solution method

Anyone have any idea what sort of aircraft is in the sky at 1:35 of the video. The pilot must have had a pretty spectacular and scary view (unless I have my perspectives wrong)

Skaff - I am not fretting, but thanks for your concern. R, SR, and GR are also not probabilistic as your last comment implies (unless perhaps at some arcane depth I have not reached).

Relativity predated M&M by about 300 years. The opposite of objectivity is subjectivity - which means that the law and even the information are dependent on the individual being measured. velocities being relative doesn't mean that objectivity is lost merely that observations must be understood in a certain frame of reference; as these FORs and the calculations used with them are easily defined and universally agreeable then there is absolutely no loss of objectivity. The same applies to the transformations required to deal with coordinate systems in non-flat space.

Not massively familiar with him - but the fact that Immanuel Kant, Adam Smith, Charles Darwin, Jeremy Bentham, and later Karl Popper thought of him as a great and central influence shows the importance of his work. I used this resource far too much in the past - you might find it interesting http://www.iep.utm.edu/humereli/

Relativity doesn't dismiss objectivity - quite the opposite in fact. AJB called it the demand that "the physics should not depend on the details of how you chose to present it" - which sums up well the idea that it dismisses subjectivity and local variations.

Cannotfind

First off - your Sine Law calcs were getting a bit crazy, I didnt check them but you were taking sin(x) and x is a side length and not taking sin of 87.75 which is an angle (you might want to look through to make sure you are happy with sine law stuff)

Secondly - the problem is more simple than sine law. you have an isoceles triangle with two long equal sides of length R and an angle of theta in between two long sides. Drop a vertical splitting theta and making perpendicular with short side; you now have rightangled triangle with known angle (theta/2) and known hypoteneuse (radius).

Sin(theta/2) = o/h = Unknown/Radius

Radius.sin(theta/2) = Unknown

the length of your desired line is of course twice the unknown in the right-angled triangle

Answer = 2.radius.Sin(theta/2)

Thirdly - I think you can use small angle approximation for a problem like this. the small angle approximation states that for small enough angles in radians Sin(theta) tends to theta.

Your angle is theta 2.pi/(80.2) = pi/80. This is still a pretty vile long division but quite doable with a pen,paper and patience. I make the error through using small angle approximation about 2 parts in 100,000

Jtvd78 - I am not sure what age grade 8 is but I am guessing mid-teens.

Your questions as follows

1) What was the scientific question they were asking?

I think this is best answered by looking at some of the big problems/questions that we want to solve. Maybe start by explaining a little about current/voltage/resistance and make the obvious point that power generation places are geographically distant from consumption areas. Perhaps wiki-ing/googling electricity transmission and looking at losses. On a more scientific need - try googling particle accelerators - most of the sites for particle accelerators will explain why they need superconductors.

2)What did the scientists think before?

there are lots of web resources on the history of superconductivity - and I am sure that you can pick up hints of what was previously thought there. Perhaps pick up some old physic texts books from local/school library - or from google books perhaps. the older the book the more likely that the previous thought will be covered. If you are lucky enough to find a book from 1900ish - that's before they were even discovered

3) How did they make their discovery?

again loads on web. there have been nobel prizes for superconductivity research - the nobel site has some really good - easy to read - write ups. Lots of encyclopedias will concentrate on the history because they fear going into too much scientific depth - so again easy pickings. remember to stress this is ongoing research. perhaps find out if this was a discovery in which the theorists imagined a solution which someone later found the real-world material - or whether someone discovered a strange property of a material and this then had to be explained (do you see the difference?)

4) How did their discovery change what other scientists did or thought?

much more difficult. on the "did" side you can go back to particle accelerators or google uses of superconductors. the "thought" side of the question I suppose means a quick dip into the theory of WHY and HOW superconductivity works; this could rapidly become technical so you will need to search for nice sources that take things slowly. this research will also allow you to fill in some of the gaps in the "what did scientists think before"

Just a few ideas - good luck

Classically, this seems to be the case, under some sensible conditions we have the various energy conditions, which more or less say no negative masses or energies. Note that these conditions are added to the geometric formulation of general relativity to place sensible constraints on what we mean by a physical matter content.

 

Quantum mechanically the situation is far less clear and negative energies arise. See the Casimir effect, for example. Such effects could create "antigravity" at the subatomic scale and support exotic configurations like wormholes.

 

It is also possible that classically the energy conditions do not hold and we have exotic matter.

AJB - in one of Leonard Susskind's lectures he mentioned, as an aside, that dark energy was "merely" the idea that at huge distances gravity could have a repulsive rather than attractive effect. I wasn't sure if he was serious at all - and I havent read up on this - is this current thinking at all or a bit off the wall?

To be honest, I just read your article on the Hatred of Science and I think all it demonstrates is that scientists and rationalists can be as bigoted, insensitive, and unthinking as those they mock for their irrational non-scientific views. I don't think that the argument for scientific rationalism (which I whole-heartedly agree with) is bolstered by parallels/comparisons of those that say science is wrong with "the mongoloid who can't tie their shoes", by the inclusion of a "Depiction of people at an anti-evolution circle jerk", or by seeming to equate native american culture with a refusal to move forward.

Michel - what do you think the CMBR is?

I don't think my post was un-intelligible (but then I wouldn't - its very hard not to understand yourself no matter how confused one's witterings are). I really think we might be able to get the nub of why we disagree - I think your ideas of the actuality of the CMBR are incorrect. The fact that you used the phrase "smaller CMBR", and I think meant just that, makes me sure of it. Sisy's diagram is quite understandable.

And a very young Earth was observing a smaller CMBR. Correct?

Smaller? mmm. The light that was impinging on the earth (i know it didn't exist) would have travelled for a shorter period of time and would have been radiated at a position less physically distant. The portion of the universe wide CMBR that was manifested on earth would come from a smaller spherical locus of points - but the CMBR wasnt smaller (well it was if you take expansion into account, but I think we are ignoring that).

Your question is not clear - "young galaxy" needs clarification. Also CMBR is the evidence of an period 13 billion years ago - do you mean end of epoch when you refer to CMBR or the evidence we see now?

The event that caused the CMBR happened everywhere at roughly the same time. A billion years ago - an observer on earth (and on distant galaxy) would have seen less red-shifted light that had travelled for around 12 billion years.

Moon - you're totally correct. The default position is "it's faked". And every time we do find a fake it positively re-enforces the attitude (the wolf jumping the gate - google wolf photo fake) that something is awry, it's a photoshop, it's staged, or it's massively out of context. Stories the other way round do little to dispel the cynical attitude. Unfo, with the press as it is, and with many "members of the public" quite willing to make false claims with falser evidence this refusal to take things at face value becomes a necessary defence mechanism. I agree with you it's a sad indictment on society that we may render all documentary evidence as worthless and leave only first person witness statements as acceptable (even when every legal practioner knows they are also terribly unreliable!).

Agree with Timo - and perhaps as a pre-indication of the depths of maths yet to come you could try reading some of the pop-sci maths books. Martin Gardner is brilliant in everything he has done, Alex's Adventures in Numberland by Alex Belos, Marcus du Sotoy's stuff is good and readable. For some actual practice at a school level you could try the net resource at places like purplemaths and plus.maths.org has news and puzzles

The CMBR is the red-shifted remnants of the last radiation of the ionised hot universe - so its not instantaneous but a fairly short period in the history of the universe.

The early universe was a sea of white-hot hydrogen plasma - light is not transmitted through this medium as it is re-absorbed. As the universe cooled it reached a point at which some matter was still radiating and other matter had coalesced into neutral atoms (which are much worse at absorbing radiation); a portion of the radiation from this epoch was not absorbed. It is that portion of unabsorbed radiation that we now see as the CMBR.

So the answer to your second question is a qualified yes.

he/it did exactly the same in the linear algebra sub-forum asking about factorisation. I reckon its a bot that takes question and text from another forum and reposts, and then spams; perhaps this method gets past some automated defences.

Michel,

Through reading this thread I can see at least one stumbling block - you seem to be convinced that the event that caused the CMBR happened in a defined and limited part of the universe. This is not the case. The early universe was hot everywhere - and each point gave off radiation, we now see that light after it has been redshifted down. We see the CMBR in a sphere because the sphere is the locus of points in space from which light has taken 13 billion years to reach us.

The distant galaxy is no closer nor further away from the CMBR, as the CMBR is everywhere. An observer there will see the same as us, microwave light coming from every direction. Sisyphus' post #30 displayed the fact that both earth observers and distant observers both see the CMBR in the same way. Spyman's diagram showed the CMBR as everywhere in the universe in the past of 13 bill years ago. Neither shows CMBR as a distinct position in space nor as a defined horizon.

Might steal that for a signature

Genecks - there you go http://download.cell.com/current-biology/pdf/PIIS0960982210012340.pdf?intermediate=true Its not quite so magnetic bracelet as you imply. It might need duplication (but then what original science doesn't) and moreover a second level of blinding. From quick whizz through I couldnt work out whether sham group were identified to those conducting tests and doing statistical analysis; would be a huge missed opportunity if that level wasn't blinded as well. Seems a fairly nicely put together paper and piece of research

Need a bit more an explanation than that Diego. The falling slug will not turn around unless you have a force that will cause it to decelerate and accelerate back upwards - and I am not sure what the horizontal drill holes and probes are doing either

I would go along with the Cap'n about differential safe loads. I saw a fantastic demonstration with pasta bridging a 30cm gap and the masses that various models of bridge could hold. It was the finale for a schools competition to build best pasta bridge; best was defined as lowest ratio of weight of pasta to safe weight of mars bars held at the centre.

I don't think I know of any private dwellings that have lightning rods (possibly quite different in USA) although I guess the big stately homes do. I really do not think it had any major scietal effect in the UK. I never heard of any anti-religious fervour when they were introduced, whereas many scientists had to move from catholic dominated southern europe to protestant nw europe to avoid persecution and gain funding and favour.

AJB / Lemur - how are neutrinos affected by black holes? I presume that they would follow the same path as light and be trapped. Gravitons? If they follow a simple straight geodesic then they are gonna be trapped - but then how do they mediate the force, if they exist?