imatfaal

What's the equation - and what have you tried?

I presume you can write it as ax²+bx+c=0 (if b = 0 it's either really easy or impossible to find real roots).

The next step is to see if you can write it any other way - Do you understand how to factorise a quadratic? - And what you can easily tell from a quadratic written in a factorised form?

So let us know where you started and where you have got to and then we can move on.

Djorde - Oh yeah it is definitely internationally recognized - and I believe every undergrad course will accept it (don't quote me on this) but what might be worth getting a handle on is the relative difficulty of offers. A levels have kinda topped out now - many universities demand straight As for the majority of courses. Could the greater span of grading on the IB benefit or endanger you on this? Perhaps this is a bit cynical but I would want to know if I was putting myself in a position where I might have to way outperform A level students to get on the same course - it could be the other way around of course.

Personally I wish I had been given the choice - my school did A levels and that was it. Good luck whatever path you take

Djorde - I am sure that UCAS or some such organisation can guide you on the hard realities of access to higher education with an IB. Depth of learning and enjoyment are one factor, however we also want to be able to get into the university of our choice. I have no idea what the relative merits are myself - but I would want to know what the Russell Group etc thought the merits were before I took a decision.

Yes, they need cooling water. The sea provides that, which makes it a lot cheaper to build at the coast. This facility is so big that no river in Japan is big enough to provide enough cooling water. It was either the sea, or massive cooling towers.

 

It's also a lot easier to develop a factory on a flat surface. Higher ground is not flat. This facility is enormous. Several hectares of flat ground are hard to come by on higher ground.

 

Both of these arguments are ultimately a matter money. It's possible to make the surface flat, even if it's not flat yet. And it's possible to pipe water to a higher location inland. But both cost money...

And it's not just money that it costs - it uses energy and lowers the efficiency of the whole set up. If we were to make all of our power stations (not just nuclear) as safe and as non-polluting as technically possible we would be in huge global energy debt. Nuclear power plants are built to a standard that would shame any other industry due to the perceived increased risk of nuclear energy. But, in the words of the bard, "shit happens" - we build to a very high tolerance or we build to a lower tolerance, but every action hides a risk reward calculation and sometimes we don't get the payout we were hoping for

The cosmological principle states that we see the same (on large scales) whichever direction we look AND that we would see the same if we were looking from somewhere else in the universe.

The large scale bit can sometimes confuse - as an idea try looking at google satellite maps of London - very high magnification you can see the people and it is clearly not all the same (homogeneous), but if you zoom out it's just a grey blob. When you look at large scales and average out the universe is very boring and uniform - and with this we can make predictions.

I would definitely fall into the category of 'reader of popular mathematics' not 'writer of popular mathematics' but I do have one major bugbear that I think differentiates good popular science writing from bad. I think it is vital to pick a level of sophistication and stick to it - too many books I read start off holding my hand to an annoyingly patronising extent yet later the author seems to forget the non-academic nature of the work and leave me stranded - it's like the cycle lanes that are well marked and separated from the carriage-way on the nice wide open road but disappear as soon as you get to the junction where you might need some help!

Who are the good mathematics communicators and why?

At a mathematical curiosity and recreational level Martin Gardner was a league apart - and his writing is still fresh and engaging. At a less sophisticated and more historical level to yours (I presume) Simon Singh gets fairly complicated ideas across very well, and does manage to be a steady guide for the whole trip. The best short piece I have read recently was the brief introduction to Tensors by Joseph C Kolecki on NASAs website suggested by Ydoaps. I will search out the link.

Hoping that [imath]\phi-4-all[/imath] is right in saying that you mean living human skin for the benefit of the individual concerned - any other alternative is not pleasant.

We can use the skin as a test surface before putting potentially noxious chemicals in our body. Please note I heard the following in a survival context not a scientific context so I must warn you not to take as proven fact - but in a situation where the only things to eat are berries, fungi etc that could be highly toxic, the first stage is merely to smell them (if the smell makes you gag or is very unpleasant then discard) the next is to rub a tiny amount onto the skin (to check for irritation), then onto the lips etc. It's not fool proof but, according to my teachers it does remove some very unpleasant surprises. Of course the first rule is stick to meat, fish and stuff you can positively identify - but after that...

The same idea of testing a substance (that will eventually be taken internally) on the skin first is used in allergy testing http://en.wikipedia....in_allergy_test

Let me try to express my question in a different way:

 

Consider a sphere alpha which expands in radial symmetry about an origin from radius r = 0 to radius r = R

 

So, at any given point in time, the edge of the sphere alpha can be determined by taking a vector radius r(t) and "swinging it around in all directions".

 

Then consider a sphere beta which expands in radial symmetry about the same origin from radius r = 0 to radius r = -R

 

Again, at any given point in time, the edge of the sphere beta can be determined by taking the vector radius r(t) and "swinging it around in all directions", except now the radius r(t) will be 0 or negative.

 

In relation to our original sphere alpha, where does sphere beta exist ?

 

The two spheres are the same. You could define a sphere as the locus of all points a distance R away from a certain point - the same sphere could by convention be defined as the locus of all points -R from a certain point. Each point defined by a +R would be diametrically opposite the point defined by -R, but as you are looking at all points in order to create the sphere that doesn't really matter.

Our sphere alpha covers all positive value for r.

• Where do negative values for r lie.

Or expressed another way:

• Positive values of r are "outwards from our point of origin".
• How do we describe the "space" or "sphere" where r goes "inwards from our point of origin".

In my mind, sphere beta is the inverse of sphere alpha (and not some rotated view of alpha).

It is sphere alpha extruded in the opposite direction.

 

Is there no mathematical term (along the lines of orthogonal or something like that) which expresses the relationship between sphere/space alpha and sphere/space beta ?

It doesn't, in my thoughts, require any concept of a negative / different space and it isn't an inverse. I think you are getting hung up on your definition of what R is (and forgive me if you are not); it is not merely away from the origin, it is away from the origin in a direction specified by the other two components. A negative R is a movement away from the origin in the opposite direction. There is a mathematical expression for -R values - you gave it in your first post. For the sphere - no there is no relationship expression because, if I am right, they are exactly the same. Think of the differences of two lines - one formed by moving +2 in the x-axis from the origin and the other -2 in the x-axis from the point 2,0,0; they are formed differently, but are exactly the same.

Rich - I think you are over complicating matters. To get a negative r flip the elevation over; it's a convention.

You could think of it in these terms; take your 'standard' spherical coordinate - you can envisage simplistically turning to your azimuthal angle, setting your elevation, and proceeding R units along that direction. For -R you proceed R units in the opposite direction - which is the same as flipping over your elevation or adding 180deg ( or [imath]\tau/2[/imath] radians)

Trying to tie this in with the equation of a sphere in spherical coordinates is a little pointless - every minus r can be equally well represented by a positive and vice versa. I don't know which contexts require this - but if you don't why the worry?

Consider Asimov's Three_Laws_of_Robotics

http://en.wikipedia....aws_of_Robotics

1. A robot may not injure a human being or, through inaction, allow a human being to come to harm.
2. A robot must obey any orders given to it by human beings, except where such orders would conflict with the First Law.
3. A robot must protect its own existence as long as such protection does not conflict with the First or Second Law.

Almost all of Asimov's many stories result in very bad things happening to humans by robots following these laws. Note that we haven't agreed on what life, human, person, etc mean (we have threads discussing those definitions), which is part of the problem. And how do you even communicate these concepts to an AI? We don't have an AI that can understand language yet. In any event, an AI that is the moral equivalent of Mother Teresa would be of little value to its creators as it would not want to work for profit. Don't get me wrong, an AI could be the best thing to ever happen to humanity -- but such a powerful thing will be dangerous. And more so because we humans will abuse it first.

It's been a long time since I read any Asimov but "Almost all of Asimov's many stories result in very bad things happening to humans by robots following these laws." reads more like a summary of the films based on Asimov rather than the books themselves

out of topic but I don't understand why would anyone consume gold..?

It shouldn't be tasty..should it?

Needless and wanton consumption basically. Its there for visual effect and to illustrate that the purchaser has money to burn

It's getting silly now - I positive rep'd after ydoaps post a few months ago, but it seems to be getting worse.

Might I suggest a post limit for negative reputation reporting - or remove reputation marks from all but the substantive science sub-fora

I kinda agree with you and the blog quote - one possible reason to keep genetic information in the hands of Doctors only is the legal implications. Doctor patient confidentiality is fairly strong and reasonably well-respected and the Doctor should be able to be relied upon to be an honest intermediary. Without that confidentiality and honest broker I can envisage a new bred of sequence-chasers who persuade any poorly-educated person with a sequence that "this" indicates a propensity for "that" - and I can sell you a nice preventive "medicinal compound".

I am not claiming Doctors are immune from this form of behaviour, but I do think it might make a sensible safety net. But like any safety-net, it should be one you can opt out of, once proper advice has been received.

Personally - I would define the above as realizations based upon a particular perspective of consciousness. It seems to posit a firm barrier between man and bodily-machine; but on what basis do you make this assertion?

To be a bit more explicit.

1. The volume of any standard right prism is area of base x height.

Thus the volume of a triangular prism is area of triangle x height

2. I am presuming that you know how to calculate the area of the triangle that the base is formed from

Calculate this area in units²

3. The volume of a slant prism needs some thinking about

Imagine a right prism that has edges and faces that at are right-angles to the plane upon which the base is formed

Make small slices parallel to the plane (imagine a packet of biscuits for a cyclindrical prism)

Push each slice a little to the side compared to the one below - and what have you got?

Now you should be able to guess what your third element must be and how to calculate it from the vector

4. Wack em all together

Eric - there were many great philosophers and scientists, so much so that a study of their history would preclude a study of the science that they were the progenitors of. I wouldn't recognize Galileo, Maxwell, or Gell-Mann - and I only know Newton and Darwin cos they are/were on our currency. In my opinion it's what they say rather than who said it first and when.

Just found out that if you ever buy super expensive chocolates in Europe you might see the E-number E-175 on the ingredients. Got to be one of the simplest constituents you will find - Au. That's right, it is the e-number for pure gold. Gold leaf is so thin that you can wrap chocolates in it and just eat it!

"Pseudoscience" is a swear. Einstein wouldn't have looked for gravitational bending unless he had thought of it beforehand.

Nobody likes to take a bum rap.

 

"Fantastic ideas" is a swear. There are screwballs everywhere. If you just want to play the odds, its a very safe bet that the next guy you meet will be a real jackass. But stay the rope.

 

Honestly, I was not complaining, but just looking for safer venue than to challenge any mutual admiration society. The only dumbing down I would justify would be to stay inside the lines drawn by consensus if possible. But trying to do that is not so easy. Learning that nobody knows how lightning is formed (although I imagine that I do) would mean that there need be no defender of a consensus to fight me off. Wrong again - the consensus is that nobody knows and there are defenders to be encountered if I go there. My theory for polar jets has practical demonstration within millions of TV sets. It also explains why lightning so often enters open windows. If I told you about it, there would be that "false-scientist" sign hung around my neck. So be it. My only point is to seek out truths unprotected by the masters of all they survey.

 

Am just looking for safe refuge. By the way though, is it not foolhardy to challenge man-made global warming? "The debate is over." for crap sakes. Or cosmic acceleration? My cigarette butt. What flavor is your anti-neutrino? Is that really stuff properly based on observations and experiments that can be repeated? Whatever, that that is is that that is so I will not complain.

 

Shouldn't a forum exist somewhere that fits its definition: a place where anybody can kick an idea around? A little less "king of the hill" would be nice. Control freaks are taking over my favorite nation. The soap box is passing like an old buggy whip.

Mutual admiration society??? They fight like cats in a bag. The whole scientific kit-and-caboodle is about constantly testing and challenging current ideas and responding by explanation and enlargement to other's criticisms of one's own ideas. To depict science as a homogeneous grouping that merely accepts the status quo is completely incorrect. Every accepted scientific theory is only still accepted because no ambitious and aggressive young scientist has been able to provide a better alternative. It's survival of the fittest out there; if a theory cannot stand up to all the tests thrown at it then it does not survive.

You will find great reluctance to accept a new theory that is heuristic and prosaic rather than mathematical and predictive - but if it is good enough people will fill in the gaps. However, if your theory is free from rigour, maths, predictions and logic, yet it contradicts a well-established theory that does have these attributes, then expect it to be given very short shrift.

Is it only not foolhardy to challenge man-made global warming from two standpoints. Firstly, scientific perspective; if you are a climate scientist then feel free to challenge, in fact it is your job to research and test. Secondly, political perspective; if you have been elected on the basis that you will defend the right to burn fossil fuels and increase CO2 emissions rather than take a long-term global view then morally you should keep this view or resign your seat. Otherwise its just bleating and moaning like a two year old for whom 'I want...' is the beginning and end of every argument.

Jill - I think the cool professor knew that well and devised a project that would not only expand your knowledge of chemical structures but would also allow you to connect those abstract formulae to the real world and what you were eating, consuming and relying upon.

And in a tribute to good chemistry teachers - Mr Zablocki, you were, and probably still are, a great and inspiring teacher

I think there is a very laudable and pronounced didactic streak in many of the knowledgeable experts here and this fosters those posters who are not experienced at correspondence on a forum, nor very learned in science. I agree it can be annoying - but the forum would lose a great deal if they were discouraged too much. The mods are quite quick enough in clamping down if a thread is better suited to speculations or to trash. just my two cents

Something like a nasty ready-made meal might be very good pickings - you will get water(very easy); salt (easy); sucrose, glucose and other sugars (again wikieasy) , what we would call E numbers in Europe (ie artificial flavouring and preservatives (more complicated to explain but still traceable on net); if any protein source you can have a stab at explaining what is likely to be there, the same with fat source. I reckon any reasonably unhealthy pre-prepared meal will get you to ten in no time

Sounds like a good task to me

Further to Spyman - I would say that we might be more interested if you actually ask a question rather than merely inviting the forum to explain a complex, poorly understood, and not generally-accepted philosophical interpretation of QM.

I did not see the actual temperature shown although they did say it was cooling faster than normal.

 

At absolute 0 matter does do strange things and I wonder if this is part of that strangeness.

 

Regards

DL

To DL

This is a cooling star - so it has a long way to go to zero kelvin (notleast that it cannot get there per ajb above). The article which I have linked in my first post says the surface temperature is estimated at 2 million kelvin. It is however displaying behaviour that we more normally associate with very cold matter in our laboratory conditions - but in this case it seems to be more todo with the enormous pressure and exotic nature of the stars matter.

To AJB

I never thought to try wikipedia - thanks will read up.

Don't forget that the "edge" pieces would also be curved, having a quarter circle cross section. Since there are 4 of each kind, you can just do it as four cylinders.

 

The answer as I see it would be:

 

2wh + 2wd + 2hd + wπ + hπ + dπ + 4π/3

Of Course! Damn - I missed that.

Mr Skeptik - " Let S be all the points around the box that are, at most, 1 unit away from the box." I think the question precludes just a surface - a point half a unit away from the original box is definitely within the question.

Not sure if DocRoc is right there - I agree with you Trip that the corners would have to be curved (the outside corner is sqrt3 away from inside corner). I would say that you have a collection of shapes

2 @ W*H*1

2 @ W*D*1

2 @ H*W*1

4 @ H*1*1

4 @ W*1*1

4 @ D*1*1*

8 @ unit demi-demi-demi-spheres - ie an eight corner of a sphere -

you could then add these groups together together to get

1 w*h*2

1 h*d*2

1 w*d*2

1 h*1*4

1 w*1*4

1 d*1*4

1 unit sphere

I don't think you can simplify any more

Matthew