imatfaal

Nope. -2akh -2mgh DOES NOT equal -4mgkAh You need to take out the common factors and put the rest in a bracket

Agree with that Marat - and also I wonder how many proselytisers would be happy with me turning up on their doorstep to explain the joys of rationalism, why I think the only sexual prohibition should be lack of true informed consent, how good their proscribed comestibles are to consume, and most importantly the way the hidden manipulations of a dominant ideology is used to reinforce patriarchy, repress the unorthodox, and constrain free-thought.

Jenny Olives book is great for self-study as it includes a serious amount of self test questions with quite a lot of worked answers - once the test is mastered you can be fairly sure you have understood the lesson. I recently ran through it to stop my mind atrophying totally and to remind me of the maths I had forgotten since A levels. I would have thought any science degree would quickly go beyond the level in her book - but for prep before university it would be about right.

It is not the aggregation of dark matter particles that give them mass. They have mass individually as much as any particle - to go deeper you are talking about the interactions with the higgs field. The gravitational attraction between dark matter and luminous matter is practically the only thing we know about dark matter.

Light does not interact with dark matter - or does so incredibly weakly - that's one of the reasons we cannot observe it directly.

Alan - are you confusing MW and mW? Unless I have the wrong end of the stick a 300 MEGAwatt laser is required to exert 1 newton (3*10^8 watts/3*10^8M/s = 1 newton) or 2 newtons with perfect reflection. The way you write makes me think you believe this is a normal laser that you can get on the internet - they would be 200 MILLIwatt a factor of 10^9 smaller. BTW I am not saying that 200mW lasers are weak - they can still blind and burn; whereas I think a 300 MW laser would go straight through you)

If you want to solve for h - which I seem to remember you do - I wouldn't divide by h You want a zero at one side of a quadratic in order to solve it - and the obvious way of doing that is to subtract 2mgh from both sides. You will end up with a very complicated h term - but then that was always gonna happen.

Although I am an atheist; from a philosophical point of view, I think I prefer the concept that a child is born pure and unadulterated and is thereafter susceptible to corruption rather than a version that says a child is born already damaged and tainted with an original sin and all human failings.

Penrose wrote a book on these lines as well

Echoing the Captain above - all the best to JohnB and all those in the area.

Not sure what quite what you mean by aggregate property. Dark Matter has mass - its existence was inferred by the gravitational effect it has. It is thought that the majority of dark matter is non-baryonic and does not interact with other matter except through gravity - all that we can be reasonably certain of is that it interacts gravitationally and thus we believe it has mass.

I thought it must be something like that - thanks for setting me straight.

I believe in the universe - but not the Universe. Even though there is much we don't know and may never know about the universe; I believe that nothing in the universe transcends scientific enquiry, nothing requires mystical knowledge or spiritual enlightenment to comprehend, and nothing that depends upon an individual's feelings towards the universe. To define the universe, as I see it, as a god renders one, either, or both of the terms as nonsense.

Not sure if it is the cause - it is an effect. The dark matter has mass that contributes to the gravitational lensing effect. Gravitational lensing means that light from a very distant object is 'lensed' ie bent by the mass of the intervening matter - this can be shown with our own sun and follows from general relativity. We can note from the amount of lensing, that the mass of galaxies is greater than we would expect if we used only the amount of luminous matter to calculate the mass of the intervening galaxy - if we include the dark matter postulated for the intervening galaxy then the lensing effect is correct. Dark matter was originally posited to explain the fact that rotating galaxies and galaxies orbiting in clusters do not seem to have enough mass for their speed of rotation. The evidence for Dark Matter was boosted by the lensing effect above. More evidence was provided by the bullet cluster. The jury is still out; because we do not know what makes up the dark matter - but we are pretty sure it is there.

Swanson - could you elaborate on this bit "Klein bottles are not physically possible in 3-D"? You can't be saying that we cannot have a Klein bottle in our lumpen reality - cos I have one, you can get them on the internet . Are we talking about different Klein Bottles, or are you not referring to the same "in 3-D" as me. I think of a Klein Bottle as a two dimensional surface that has no recognizable inside and outside and looks like a bottle with a handle and a dimple (until you notice that handle and dimple are linked.

How much does k vary with x or ln(k) with v ?

Alien Leader "Do we really want to talk to these people? I mean look at them! Once we show our faces we have got to take some responsibility for setting them straight, we couldn't just leave them like that. Let some other species 'discover' them - and then those dumb schmucks will be the one's landed with the job of teaching humanity how to behave. Come on, just look at how they treat each other; do you really want to get involved with them? " Alien 2-in-C "When you put it like that I can understand. Remain fully cloaked and move out of the Sol System?"

And in the entirely opposite direction; IIRC, a small jurisdiction attempted to remove the entire tortious jurisdiction and replace it with a ramped-up public prosecution of formally private acts of tort and delict combined with guaranteed social provision for the victim. I vaguely seem to remember that it did fairly well till dismembered by opposite political party.

You might want to edit your first sentence for clarity "animals that are invertebrates" I think the system developed along the lines of "we are vertebrates therefore..." Its a question of arbitrary line drawing in the end; our fellow man, other primates, mammals, vertebrates...single-celled thingies - at some point we decide that care and supervision is necessary. We try to make this a rational objective decision based on the test subjects potential for feeling pain, anxiety, stress etc - but let's face it we are far from being to quantify this within ourselves let alone a species with whom we cannot properly communicate.

I had a feeling it might have been - should have checked. Have checked now with the fount of all knowledge: "Equids do not have a gall bladder, so bile flows constantly, an adaptation to a slow but steady supply of food, and another reason for providing fodder to horses in several small feedings." I think we could go around the block many times on the logical/philosphical bit - and I have no intention of starting

Marat Might give that a try - although I would have thought it would raise ethical issues rather than solve clinical. It sounds interesting and most disturbing - is it a good read and accessible? Corollary - it is unethical or at least ethically dubious to use the results of historical highly unethical studies? ie a fruit of the poisoned tree in research ethics. What about when the displacement is in space not time? obligatory qv the stanford experiment

OK Tbird You need to start again from your original formula mgh = k(h-l-L)²/2 - cos you have made a couple of errors (post#3 had no factors of two and post#11 has two ) 1. Are you sure this is the correct starting point - I haven't checked its logic - I presume you are happy with it 2. Multiply through by two 3. multiply out the three way bracket (you have done this already in #11) 4. multiply the contents of your bracket by the k outside 5. group together the h2 terms (should be only one), the h terms (should be three), and the no h terms (should be three) 6. Is there a common factor to the entire equation - if there is factor it out. (good form but doesnt apply here) 7. take the h2 term outside a bracket and put its coefficients within the bracket (good form but doesnt apply here) 8. take the h term outside a bracket and put its coefficients within the bracket You should now have an equation that look like this 0 = something.h2 - 2h(three somethings) + (three other somethings) which is basically your standard quadratic 0 = ax2 +bx +c

1. Whilst I wish the UDofHR was law, it is not. Within EU the EConventionHR can have the power of law within certain states - other states have included HR legislation. 2. In jurisdictions where it is law; Legislation like this acts on the state, on state bodies and other organisation that fulfil a function of the state - the SFN are none of these. 3. You are correct that no contract can be validly made to break criminal/civil law - however it is quite ok to sign away some of your rights within a contractual situation (we all do so regularly)

I think CUNY think of him as a theoretical physicist as well - they employ him as a tenured professor

Presuming that if a unicorn exists it is defined as a white horse with a horn on its head. Q If the Unicorn exists does it have a gall bladder A Yes (I think horses will have gall bladders) Q If the Unicorn exists does it eat rocks A No - we have defined it as very horselike To deny the existence of a Unicorn one must have a fairly clear conception of what a Unicorn is defined as (ie it cannot just be defined as a mammal with a spiral grooved horn on its forehead - qv narwhal). Doesn't the same apply to god?