Well the play does stop, and I don't know anyone who would claim otherwise. However, the game can't be stopped arbitrarily and the 'stops' are often tactically kept very short. Consider the recent world cup match Germany vs England: A shot hit the crossbar, then the ground, then the crossbar again before returning to the field. If it isn't a goal, play should continue uninterrupted, if it is, then you should stop. Do you stop the game to watch a replay? What if the ball is returned for another goal?

Likewise, throw-ins and free-kicks are often taken quickly to press an attacking advantage - you don't give the defense time to reset particularly if you're counter-attacking. Stopping for a replay would allow defensive players to get back and break an attacking advantage.

Compare it to tennis or cricket, where Hawk-eye aids umpire decisions and you'll see its definitely a way behind. Cricket in particular has a lot of recent tech toys added - 'snickometer' and 'hotspot' being used to see if ball met bat through sound or residual heat. That said, radio communications between players and coaches have been banned - the reason given is that whilst in play, the game should only be decided by the players on the field.

Soccer remains behind a little, it's true, though the English Football Association has recently proposed using a Hawk-eye like system to make line calls. The main reasons cited are that replays etc would interrupt the game, and since it's a free-flowing sport (rather than the stop-start of tennis, american football or cricket say) this would change the game fundamentally.

I think the trick is just practice - I tend to look at the first two digits. If the second digit is 0-3 I round down and add (23 becomes 20+3), if it's 4-6 I go for the nearest 5 (44 becomes 45-1) and 7-9 (87 becomes 90-3) I go above and subtract. One way to break the habit might be to try always going above and subtracting for a while and try to get used to it. You'll find 8s and 9s easy enough, but 2-3s harder so maybe your brain will learn the path of least resistance ;)

Yeah, 2^10 ~ 10^3 is one of the standard ones, along with a few other things like sqrt(2) ~ 1.4 (1.5 at a pinch) sin(30)=1/2, sin(60) = sqrt(3)/2 ~ 0.85 normally is enough to get through an undergrad physics exam without ever using a calculator. Using (A+b)^n ~ A^n + n*A^(n-1)*b for small b/A gets you most powers quick enough that students will think you're the rain man... eg (2.1)^4 ~ 16 + 8*4*0.1 = 19. There's a ton of others, of course, and doing the mental maths is one of the only things that keeps me sane whilst teaching.

True, I would normally just ballpark it, but I was pointing out that this is the way I do mental maths in general. How I do the undergrad exams as a test of their reasonableness - use pi=3, g=10 etc. Generally if I can't do all the questions in 1/10th the time of the exam, it's too hard.

But yeah, reversing the answers for reasonableness is the way to do multiple choice exams quickly, usually you can rule out all but 1 or 2 due to magnitudes (or physics equivalent dimensions).

As someone with a masters in maths and PhD in physics, this is the same way I did the calculation. In fact, I suspect it's the way anyone who knows some more advanced maths would do it: What you've effectively done (in maths language) is:

1) Use the associative property of multiplication and its inverse: (AB)C=A(BC).

2) Rewrite the unknown product 47*3 in terms of two known products, by first rewriting 47=50-3, thus (50-3)*3.

3) Expand the bracket: 47*3=50*3-3*3.

Now this is much akin to the 'normal' method used to teach kids, except they always expand their brackets in terms of positive numbers broken up by powers of 10, ie 47=40+7, however from a mathematical standpoint there's no reason not to use any splitting you like, only the expedience of learning a limited number of multiplications.

The true gift of good mathematicians is not only being able to make these thought processes, but properly explain them so that others can too. Far too often maths as it is taught is just a voodoo recipe for performing calculations rather than a well explained, reasoned setup. This is fine for people who merely have to perform the function (much as you don't need to know the workings of an internal combustion engine to drive a car) but if you want to derive a deeper understanding of what's going on its woefully insufficient.

Linear and quadratic scales aren't the same thing - if you double a length scale, you quadruple the area. Thus 1:1000 in length -> 1:1000000 in area, which is closer to the number you got from the article, modulo rounding (1.5 acre could be anything from 1.25-1.75 if they just rounded to nearest half integer).

To be fair, the flip side to the Neptune story is that of the perihelion advance of Mercury, which until the GR calculations came along, was thought to be the influence of another planet, closer to the sun. Geekgasm trivia: Due to the temperature that the planet would have to endure at such proximity it was named "Vulcan".

Wikipedia actually does a pretty good job of telling the story: http://en.wikipedia.org/wiki/Vulcan_(hypothetical_planet)

Of course, no planet was found, and modifying the theory of gravity Newtonian -> Einstein was what got the right answer in the end.

All that said, you're 100% right - dark matter is the simplest explanation, and we made a prediction from it in the form of gravitational lensing outside colliding galactic nuclei which is realized in the Bullet cluster. This is how science is done! You notice something unusual, come up with a simple, plausible explanation, make a prediction based on that hypothesis and test it. Dark matter fits well within this framework, but sadly outside of cosmology (even within physics) it seems that its name alone ensures it is treated as deus ex machina.

Fair enough - but with the UK version that TFA talked about then UK law would apply, and I believe has much stricter advertising regulations.

It's aimed at the UK - US law doesn't apply. Under UK law the ASA (advertising standards agency) will probably give them a slap on the wrist for it.

Last few jobs I've been involved with had around 400 applicants for a single place. Jobs at the PhD level are like gold dust at the moment.

"When you try to reduce everything to a saying you get nowhere" - let's make this a saying, shall we? ;-)

PS: Agree 100% with what you're actually saying, just found this amusing. Taking care of the pennies is fine when you're not crazy with the pounds (or whatever bastardized version was quoted). But when you've got an open wound, you really don't worry about blood loss from a mosquito bite.

Actually, I really do spend most of my time working pencil to paper. Sure, I do simulations on a computer for some things, and I've used analytic programs for others, but most of the time calculations in my field are done by hand. Sometimes because you're working on a simple enough idea from a new perspective or because you're dealing with mathematical objects for which there is no analytic program.

I'm a theoretical physicists. $40,000 can pay for a LOT of paper and pencils...

I agree - my sample size is merely my own anecdotal evidence from the R1 institution I taught at, and conversations with colleagues who performed the same task at ivy league schools.

Sure, everyone claims to have strong punishments for cheaters, I've just never come across as TA that has reported seeing them enacted, and I've talked to a LOT of people about this - it's a common theme of dinner conversations during conferences for example, since when you get a bunch of grad students together it doesn't take long before the moaning about your job starts!