wrighty

I’ve seen Star Trek and these proposals would be considered somewhat fanciful in the 24th century, never mind in 24 years.

Opposite would be better. I’ve often thought the standing charge should be negative, in effect giving everyone an amount of free electricity, with relatively higher unit charges such that those that waste it or have heated swimming pools get stung. That would not help profits though. Seems a fairly regressive move to put the standing charge up.

Yes, although depending on the landing surface there may be an element of chaotic behavior that comes in rendering predictions impossible. Similar has been done with roulette - I remember reading about some students (usually from MIT for these things) working on a system of video camera measurement of the ball on a roulette wheel and predicting where it will finish up. They had some success if I recall correctly - not necessarily predicting the exact number, but a range of locations such that if you weren't detected by the casino and killed you could profit from it.

Worked out the dropping the needle on the floor problem between cases in theatre. If the needle is the same length as the width of the floorboard the probability it crosses a gap is 2/pi

Not at all. Pondered it while driving. I recognised the pi^2/6 and went from there. If you think about it, any ‘proportion of the total’ has to be a number less than 1. Multiply by 6 and you get a number less than 6, which is less than pi-squared which is about 10. I don’t think there’s much wrong with the text - the author is just quoting an example of how pi appears where you wouldn’t necessarily expect it to. Just like in the dropping needle example - I haven’t worked this one through yet (but it’s not difficult) but again I think the answer is something like 1-1/pi.

I've had a further think about this - it's not quite right. You have to take the reciprocal of the proportion of numbers that don't have any common factors, which can be shown to be pi^2/6. Start with the chance that two numbers selected at random have a common prime factor. There's a 1:4 chance that they have a common factor of 2, a 1:9 chance that they have a common factor of 3, and in general a 1:p^2 chance that they have a common factor of p, where p is any prime. Consequently, there is a 3:4 chance that they don't have a common factor of 2, 8:9 chance that they don't have a common factor of 3, and in general a (p^2-1)/p^2 chance that they don't have a common factor of p. So the chance that they have no common factor at all is the product of these numbers, taken over the infinity of primes: 3/4 x 8/9 x 24/25 x 48/49 x 120/121... This can be shown, with fairly elementary algebra (that I don't have the notation to write out here) to be equal to the reciprocal of (1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/36 ...) which Euler proved to be equal to pi^2/6. https://en.wikipedia.org/wiki/Proof_of_the_Euler_product_formula_for_the_Riemann_zeta_function#The_Euler_product_formula

Maths is everywhere. I haven’t read this book, but I’d guess the method of getting pi from sampling whether two integers have a common factor is connected with the so called Basel problem (sum to infinity of 1/n^2) solved initially by Euler as pi-squared over six. This in turn is one example of the zeta function made famous in the Riemann hypothesis which if correct gives a formula for the number of prime numbers, once thought to be ‘random’. The more you read about it you realise that if there is a god he must be a mathematician.

I recently read a book on forensic linguistics. An interesting, and somewhat surprising fact, is that a string of as few as eight words is likely to be unique. So if you ever want to find out if something has been copied, a google search with such a string in quotation marks will generally turn up the source document. Plagiarists beware.

I find it hard to understand why anyone is prepared to queue up right around the building to get a MacDonalds, let alone block traffic in both directions on Peel road to join the queue. If they have a choice of two outlets surely that’s better?

I agree it’s a complicated area. Another couple of examples may be relevant. There was a case a few years ago of a chap who arranged to meet someone with the wish to be killed and eaten as his ultimate masochistic fantasy. Even though he’d agreed to this his cannibal killer was prosecuted. Rightly in my view. And then there’s labial reduction surgery carried out by some gynaecologists or plastic surgeons. Consent is the only difference between this and female genital mutilation.

This case troubles me a bit: https://www.bbc.co.uk/news/uk-england-birmingham-47198786 In summary, extreme tattooist/piercer/body modifier has pleaded guilty to GBH after the local council prosecuted him following a complaint from some random person about something they'd seen. None of his clients complained, and remain happy with the results of their procedures, and are adamant that they were fully informed about the procedures and offered plenty of opportunities to back out. I can understand that the middle class white males that represent 'the authorities' find his work to be not to their taste, and I can sympathise with them questioning the sanity of anyone that wants to have horns implanted, or their tongue split etc. But that's not the point. I don't really like nose piercings that much, and lips/eyebrows less so. But I have no problem with people having them if they want, and are aware of the risks. So where do we draw the line? Perhaps ear piercing will become illegal, or no-one will do it for fear of being convicted of GBH. What's the difference between what this guy does, and some of the more outlandish jobs carried out by plastic surgeons? For me, consent is everything. If someone wants their nipple removed for some reason, and someone is prepared to do it for them, why is this a problem?

Only if inflation/interest are zero. Without index linking the re-payments and assuming a 2-3% rate which is reasonable, it'll never be re-paid.

There’s a lot of resistance to MOTs here. Reasons include: wouldn’t pick up all faults doesn’t stop faults between tests Can’t trust government to run it Stealth tax that lorry that was tested and still fell apart Mechanics doing the testing might be incompetent. There are probably many others. But, accepting that MOT testing is not a panacea, and that the majority of accidents are driver rather than machine related, is it not the case that they would improve safety on the roads, at least a bit? Great success has come on the back of the accumulation of minor gains in other areas, so why not road safety?

How about a bit of balance here. Since the MOT test was introduced in the UK in 1960, cars have changed a lot, the test itself not so much. Cars are far more reliable, far more complex, and far less amenable to self-service. It's clear that not all faults can be picked up by annual testing, nor can they be picked up by increasingly sophisticated ECUs, although the latter clearly reduces risk and increases the likelihood of picking up faults between tests. So what's the solution? I'd propose something along the lines of an MOT test for cars over 5 years old, from which cars are exempt if they have a service to manufacturer's specifications by a suitably qualified/licensed mechanic. And tests could be every couple of years instead of annually - simply because of reliability improvements.

Nothing, as this is the default. Or it doesn’t start at all. Bit like asking what turns the light off when the bulb blows.