My assumption (perhaps wrong) is that any potential genetic source for intelligence (which I would expect exists) is going to be more prevalent amongst those who have succeeded in a socially mobile (or somewhat socially mobile) society, this while it is possible that there will be exceptions to the rule the general trend will be for inherited levels of intellect.
There certainly is a tendency for ntelligent people to have intelligent children, but such is true for any inheritable trait, and these are all subject to regression to the mean. It is a statistical phenomenon rather than a genetic one.
It is why clever people manipulate the system in benefit to their own progeny. When we talk of social mobility we are very reluctant to talk of downward mobility. Hence coaching for grammar school entry amongst the middle classes. The prospect of our own children going to a Secondary Modern is too awful for words.
But surely there are different means. Assuming that the coupling of individuals will generally be those within the same socio-economic group (for all manner of reasons) then the mean to which the children of intelligent parents regress towards is different to the mean to which children of thicker couples at the bottom of the income scale.
Mathematicians: here's an interesting one for you.
Take an odd number, square it, and then divide it by eight. The remainder is always 1.
That is n^2 mod 8 = 1, where n is odd.
Modulo 8, any odd number has remainder 1, 3, 5, or 7. Or you might say 1, 3, -3, -1.
Squaring those would give 1, 9 (which is 1 again mod 8), and then 9 and 1 again.
Hmmm... I'm not sure I get your post. My observation was that...
1* 1 = 1. Divide by 8. 0, with 1 remainder 3 * 3 = 9. Divide by 8. 1, with 1 remainder 5 * 5 =25: 3, with 1 remainder 7 * 7 = 49: 6, with 1 remainder etc etc
Any odd number is either 1 above, 3 above, 3 below, or 1 below a multiple of 8.
Squaring any of those will always give a number 1 above a multiple of 8.
Ah ha. Now I understand. Thank you MBE!
Modular arithmetic is one of those things on my Big List Of Proper Things They Don't Teach At "O" Level Anymore that I use to demean poor innocent young people with :-)
Anyone who thinks the Govt will cave in is mistaken. They have 4.5 yrs to ride this out.. and they will. Tax credits were a ridiculous idea by McDoom.. hence a bad idea in the first place , and a bribe to the electorate.
[added emphasis]
Actually, tax credits were originally a right wing idea, so Osborne will have intellectual cover for any U-turn. It (or they) can be seen as an instantiation of Milton Friedman's negative income tax.
Edit: the idea is that it makes work more attractive for the poor, and subsidises companies to create wealth.
Really .. so what ideas are ideas .. The Tories dodged a bullet. McDoom put them on the statute book like the idiot he is/was.
Now they have to be removed and that's a hell of a lot harder.. Sort of like the 50 tax rate but infinitely worse..
No, Maggie put them on the statute book, it was called Family Credit.
The idea was that it would incentivise the birthrate. Which it did. Unfortunately it tended to be the wrong people (in general terms) who were most incentivised. So it stayed as a fairly limited top up benefit.
What Brown did was politicise it by making it a fundamental income source for huge swathes of the population (while being quite happy with the prevalence of poor, stupid people popping out lots of poor, stupid children who could grow up to vote Labour).
You neglect the phenomenon of regression to the mean. Fast breeding thick people tend to have broghter children than themselves. Clever people tend to have thicker children than themselves. It is one of the engines of social mobility, and one reason why the clever try to buy advantages for their kids, such as private schools.
Clearly Albert was cleverer than Mr and Mrs Einstein. I do not think there is anything special about your claim. We could hardly expect Alberts children to solve the problems he left behind. But you ignore the debilitating effects of well, culture and brainwashing and the subsequent reversion to type. Abbott bought an education for her children because the BBC money allowed her to afford it and she saw the damage that labour's policies were doing. It's not that the offspring of clever parents are not capable, its that the parents care and can afford.
See my link below. There will always be some that move away from the mean, but these will be outnumbered by those who move towards it. It is the nature of random variation.
PB is one place where statistics are discussed intelligently. It is part of how I got started posting.
I have read today that the EU is thinking of giving Turkey an accelerated accession to the EU as part of the migrant crisis deal. That will entail a crisis of millions of Turks moving West instead.
I just can't see that happening.
So in order to prevent Syrian and other migrants currently in Turkey from coming to the EU the EU wants to allow the Turks in Turkey to come to the EU instead.
Eh??
The discussion was about Turkey joining Schengen, I believe. That does not - of course - give you the right to work in the EU, merely that you don't need to use your passport when travelling between Schengen countries.
The new, kinder more mature politics… an email sent to the 21MPs who abstained. http://t.co/QcKW5A2gmC
Blaming it all on the Jews too. How ugly.
I'm confused by the bit about Osborne adding billions to the debt, because of course he has, but Corbyn wants to as well.
Osborne has not added billions. He has been careful not to cut spending too quickly once the full scale of labour's structural spendthrift ways were realised. Three cheers I would say.
My assumption (perhaps wrong) is that any potential genetic source for intelligence (which I would expect exists) is going to be more prevalent amongst those who have succeeded in a socially mobile (or somewhat socially mobile) society, this while it is possible that there will be exceptions to the rule the general trend will be for inherited levels of intellect.
There certainly is a tendency for ntelligent people to have intelligent children, but such is true for any inheritable trait, and these are all subject to regression to the mean. It is a statistical phenomenon rather than a genetic one.
It is why clever people manipulate the system in benefit to their own progeny. When we talk of social mobility we are very reluctant to talk of downward mobility. Hence coaching for grammar school entry amongst the middle classes. The prospect of our own children going to a Secondary Modern is too awful for words.
But surely there are different means. Assuming that the coupling of individuals will generally be those within the same socio-economic group (for all manner of reasons) then the mean to which the children of intelligent parents regress towards is different to the mean to which children of thicker couples at the bottom of the income scale.
It is a slow phenomenon, but even with assortive mating the phenomenon exists.
On topic, there will be a lot of people - myself included - wanting and expecting Osborne to hold firm. There was always going to be pain for some. Everyone knew that, Osborne more than most. having embarked on the course, you do not then backtrack just because an entirely obvious consequence has come about. This will be the Bedroom Tax all over again (an issue which seems to have disappeared in public debate): a lot of shouting but little meaningful long-term impact.
I'm not sure this is true. I think a lot of us can understand the measures and accept the need for savings, but also have concerns if it reduces the incentive to work. I think most Tories would accept a partial u-turn.
I, for my part, might do so if it left intact the direction of travel on tax credits. The concept is ridiculous, always has been ridiculous and is becoming more ridiculouser by the day.
I have read today that the EU is thinking of giving Turkey an accelerated accession to the EU as part of the migrant crisis deal. That will entail a crisis of millions of Turks moving West instead.
I just can't see that happening.
So in order to prevent Syrian and other migrants currently in Turkey from coming to the EU the EU wants to allow the Turks in Turkey to come to the EU instead.
Eh??
The discussion was about Turkey joining Schengen, I believe. That does not - of course - give you the right to work in the EU, merely that you don't need to use your passport when travelling between Schengen countries.
You don't need a passport?? No ID?? I thought it was just a visa you did not need??
My assumption (perhaps wrong) is that any potential genetic source for intelligence (which I would expect exists) is going to be more prevalent amongst those who have succeeded in a socially mobile (or somewhat socially mobile) society, this while it is possible that there will be exceptions to the rule the general trend will be for inherited levels of intellect.
There certainly is a tendency for ntelligent people to have intelligent children, but such is true for any inheritable trait, and these are all subject to regression to the mean. It is a statistical phenomenon rather than a genetic one.
It is why clever people manipulate the system in benefit to their own progeny. When we talk of social mobility we are very reluctant to talk of downward mobility. Hence coaching for grammar school entry amongst the middle classes. The prospect of our own children going to a Secondary Modern is too awful for words.
But surely there are different means. Assuming that the coupling of individuals will generally be those within the same socio-economic group (for all manner of reasons) then the mean to which the children of intelligent parents regress towards is different to the mean to which children of thicker couples at the bottom of the income scale.
He found that, roughly speaking, on average (in the sense of the conditional mean, i.e. based on the heights of their parents) a child's deviation from the population mean height (i.e. unconditionally: the mean for everyone, irrespective of parental height) is about 2/3 of the parents' deviation from the population mean.
So yes, the conditional mean for the child of tall parents is above the population average. But it is not so tall as the parent's themselves: so tall parents tend to have children who are taller than average, but not so tall as they are themselves (this is why it's called "regressing to the mean").
Conversely, the conditional mean for the child of short parents is below the population average, but not so short as the parents themselves.
Modular arithmetic is one of those things on my Big List Of Proper Things They Don't Teach At "O" Level Anymore that I use to demean poor innocent young people with :-)
In what context did they used to teach it? It seems kind of useless without knowing the algebraic, number theory or algorithmic uses for it.
If anything, it's more likely to crop up naturally in a computing class (as the % operator).
The new, kinder more mature politics… an email sent to the 21MPs who abstained. http://t.co/QcKW5A2gmC
Somehow jew hate got chucked into the middle of that.
It is remarkable just how easily it gets slipped into things sometimes, it's pretty baffling.
Good night all.
Anyone who spent any time on Corbynista facebook groups in the run up to the leadership election will have noticed the startling number of times "Rothschild" or "Zionist" or "Israel" or - subtly ethnically connotated - "financiers" turned up.
I have read today that the EU is thinking of giving Turkey an accelerated accession to the EU as part of the migrant crisis deal. That will entail a crisis of millions of Turks moving West instead.
I just can't see that happening.
So in order to prevent Syrian and other migrants currently in Turkey from coming to the EU the EU wants to allow the Turks in Turkey to come to the EU instead.
Eh??
The discussion was about Turkey joining Schengen, I believe. That does not - of course - give you the right to work in the EU, merely that you don't need to use your passport when travelling between Schengen countries.
You don't need a passport?? No ID?? I thought it was just a visa you did not need??
You do require ID, I believe, but that includes national ID cards and not just passports.
I have read today that the EU is thinking of giving Turkey an accelerated accession to the EU as part of the migrant crisis deal. That will entail a crisis of millions of Turks moving West instead.
The new, kinder more mature politics… an email sent to the 21MPs who abstained. http://t.co/QcKW5A2gmC
Somehow jew hate got chucked into the middle of that.
It is remarkable just how easily it gets slipped into things sometimes, it's pretty baffling.
Good night all.
Anyone who spent any time on Corbynista facebook groups in the run up to the leadership election will have noticed the startling number of times "Rothschild" or "Zionist" or "Israel" or - subtly ethnically connotated - "financiers" turned up.
Gruesome really.
Has "North London" as a euphemism for Jewish been retired now Ed Miliband isn't Labour leader?
Can't say I've any sympathy with that woman at all. She votes Tory because she's only interested in herself so seeing her reap what she sows is almost biblical in it's retribution.
OT Has there ever been a vulgarian like SeanT posting on PB before?
Modular arithmetic is one of those things on my Big List Of Proper Things They Don't Teach At "O" Level Anymore that I use to demean poor innocent young people with :-)
In what context did they used to teach it? It seems kind of useless without knowing the algebraic, number theory or algorithmic uses for it.
If anything, it's more likely to crop up naturally in a computing class (as the % operator).
You don't need to know very much about it to be able to prove fairly useful facts with it, particularly about divisibility. Like rcs's example.
In some A level Further Maths syllabuses it used to be put in to the "Group Theory" section, so students could have some extra examples (together with permutation groups) of small finite groups. That's long gone from most syllabuses now though.
Odd how a concept that was once O level eventually wound up in A-level Further Maths and then off the syllabus altogether.
And a shame because it does make the STEP (formerly, S-level) exams much easier, for students applying to certain high-rank universities.
Tax credits are basically benefits by enough name subsidising low wages, the increased minimum wage and tax cut for the lowest earners are far more sensible policies
My assumption (perhaps wrong) is that any potential genetic source for intelligence (which I would expect exists) is going to be more prevalent amongst those who have succeeded in a socially mobile (or somewhat socially mobile) society, this while it is possible that there will be exceptions to the rule the general trend will be for inherited levels of intellect.
There certainly is a tendency for ntelligent people to have intelligent children, but such is true for any inheritable trait, and these are all subject to regression to the mean. It is a statistical phenomenon rather than a genetic one.
It is why clever people manipulate the system in benefit to their own progeny. When we talk of social mobility we are very reluctant to talk of downward mobility. Hence coaching for grammar school entry amongst the middle classes. The prospect of our own children going to a Secondary Modern is too awful for words.
But surely there are different means. Assuming that the coupling of individuals will generally be those within the same socio-economic group (for all manner of reasons) then the mean to which the children of intelligent parents regress towards is different to the mean to which children of thicker couples at the bottom of the income scale.
It is a slow phenomenon, but even with assortive mating the phenomenon exists.
Are you quite sure, Doc. My own experience and that of friend of mine, who has taught at a school on a sink estate for 30 years, suggests that below a certain level evolution seems to be running backwards.
My assumption (perhaps wrong) is that any potential genetic source for intelligence (which I would expect exists) is going to be more prevalent amongst those who have succeeded in a socially mobile (or somewhat socially mobile) society, this while it is possible that there will be exceptions to the rule the general trend will be for inherited levels of intellect.
There certainly is a tendency for ntelligent people to have intelligent children, but such is true for any inheritable trait, and these are all subject to regression to the mean. It is a statistical phenomenon rather than a genetic one.
It is why clever people manipulate the system in benefit to their own progeny. When we talk of social mobility we are very reluctant to talk of downward mobility. Hence coaching for grammar school entry amongst the middle classes. The prospect of our own children going to a Secondary Modern is too awful for words.
But surely there are different means. Assuming that the coupling of individuals will generally be those within the same socio-economic group (for all manner of reasons) then the mean to which the children of intelligent parents regress towards is different to the mean to which children of thicker couples at the bottom of the income scale.
It is a slow phenomenon, but even with assortive mating the phenomenon exists.
Even with that argument (which I'm fairly sure I don't buy) that the limited inter-coupling between socio-economic groups would eventually lead to a single peak instead of multiple peaks, it is as you say at best a very slow phenomenon.
Meanwhile the incentive is created for lots and lots of offspring to be born to those at the bottom end of the socio-economic (and intellectual) group.
My assumption (perhaps wrong) is that any potential genetic source for intelligence (which I would expect exists) is going to be more prevalent amongst those who have succeeded in a socially mobile (or somewhat socially mobile) society, this while it is possible that there will be exceptions to the rule the general trend will be for inherited levels of intellect.
There certainly is a tendency for ntelligent people to have intelligent children, but such is true for any inheritable trait, and these are all subject to regression to the mean. It is a statistical phenomenon rather than a genetic one.
It is why clever people manipulate the system in benefit to their own progeny. When we talk of social mobility we are very reluctant to talk of downward mobility. Hence coaching for grammar school entry amongst the middle classes. The prospect of our own children going to a Secondary Modern is too awful for words.
But surely there are different means. Assuming that the coupling of individuals will generally be those within the same socio-economic group (for all manner of reasons) then the mean to which the children of intelligent parents regress towards is different to the mean to which children of thicker couples at the bottom of the income scale.
He found that, roughly speaking, on average (in the sense of the conditional mean, i.e. based on the heights of their parents) a child's deviation from the population mean height (i.e. unconditionally: the mean for everyone, irrespective of parental height) is about 2/3 of the parents' deviation from the population mean.
So yes, the conditional mean for the child of tall parents is above the population average. But it is not so tall as the parent's themselves: so tall parents tend to have children who are taller than average, but not so tall as they are themselves (this is why it's called "regressing to the mean").
Conversely, the conditional mean for the child of short parents is below the population average, but not so short as the parents themselves.
There are other factors of course that mitigate the regression to the mean. For example on the issue of height diet makes a difference. While people have a maximal genetic potential it is not always fully expressed. In the context of intelligence (as measured by school attainment) there is major variation with parental education, both parents living with the child, money for additional tutoring etc. These may well drive an intense work ethic that overcomes the fact that the child is not so bright as his/her parents.
I have read today that the EU is thinking of giving Turkey an accelerated accession to the EU as part of the migrant crisis deal. That will entail a crisis of millions of Turks moving West instead.
No one wants the EU to have a border with Syria and Iraq. There will be plenty of vetos. What we are seeing is some support being lobbed to the secularists in Tukey ahead of the 1 Nov election.
Both major parties in the UK support Turkish entry.
I'm at a loss to understand why. I could understand the historical reasons, but now? Just can't see how it benefits the UK's national interests.
It throws the EU into deeper chaos and speeds up its collapse and ultimate destruction.
....perfectly 'benefiting the UK's national interests'.
Tax credits are basically benefits by enough name subsidising low wages, the increased minimum wage and tax cut for the lowest earners are far more sensible policies
Correct - they are a tax subsidy for employers. Given the unemployment rate it's not required,
'When the lights came on the Moore talk, who was there in the audience? Michael Gove and Michael Fallon unsurprisingly, and so too was, somewhat curiously, Peter Mandelson, stony-faced throughout. Perhaps he had more serious concerns. The Londoner bumped into him again at the reception, having a long conversation with George Osborne — so private that an aide firmly told the Londoner that we were standing a bit too close. Probably wise: chinwags between the two in the past have created poisonous fumes.' http://www.standard.co.uk/news/londoners-diary/londoners-diary-george-quizzes-charles-moore-over-leadership-a3092106.html
I have read today that the EU is thinking of giving Turkey an accelerated accession to the EU as part of the migrant crisis deal. That will entail a crisis of millions of Turks moving West instead.
No one wants the EU to have a border with Syria and Iraq. There will be plenty of vetos. What we are seeing is some support being lobbed to the secularists in Tukey ahead of the 1 Nov election.
Both major parties in the UK support Turkish entry.
Anyone who thinks the Govt will cave in is mistaken. They have 4.5 yrs to ride this out.. and they will. Tax credits were a ridiculous idea by McDoom.. hence a bad idea in the first place , and a bribe to the electorate.
[added emphasis]
Edit: the idea is that it makes work more attractive for the poor, and subsidises companies to create wealth.
Really .. so what ideas are ideas .. The Tories dodged a bullet. McDoom put them on the statute book like the idiot he is/was.
Now they have to be removed and that's a hell of a lot harder.. Sort of like the 50 tax rate but infinitely worse..
.
You neglect the phenomenon of regression to the mean. Fast breeding thick people tend to have broghter children than themselves. Clever people tend to have thicker children than themselves. It is one of the engines of social mobility, and one reason why the clever try to buy advantages for their kids, such as private schools.
Clearly Albert was cleverer than Mr and Mrs Einstein. I do not think there is anything special about your claim. We could hardly expect Alberts children to solve the problems he left behind. But you ignore the debilitating effects of well, culture and brainwashing and the subsequent reversion to type. Abbott bought an education for her children because the BBC money allowed her to afford it and she saw the damage that labour's policies were doing. It's not that the offspring of clever parents are not capable, its that the parents care and can afford.
See my link below. There will always be some that move away from the mean, but these will be outnumbered by those who move towards it. It is the nature of random variation.
PB is one place where statistics are discussed intelligently. It is part of how I got started posting.
I do not quibble with the statistics, my extreme example was to show how obvious it was. I suggest other things are also at play in determining the educational outcomes of children, not simply?y that they might be a bit or a lot brighter than their parents. This is the great tragedy of the scrapheap policy of the Labour years.
I am in favour of diversity and opposed to oh what shall I call it... bias to other groups. We need to mix or rather it would not be bad for us, because that is where we stand the best chances of throwing up the people who will have the genius to lead us to educate us and to create for us. I do not know much about eugenics but I view it as the opposite of what I have just said. I think it was a failure.
Tax credits are basically benefits by enough name subsidising low wages, the increased minimum wage and tax cut for the lowest earners are far more sensible policies
Indeed one thing that Osborne should do in the autumn statement is change the name back from "Tax credit" to "Supplementary benefit" and have it paid via the DSS rather than the Inland revenue.
Can't say I've any sympathy with that woman at all. She votes Tory because she's only interested in herself so seeing her reap what she sows is almost biblical in it's retribution.
OT Has there ever been a vulgarian like SeanT posting on PB before?
Rising taxes are rising taxes no matter how do you call it, in 1989 it was called the community charge, in 2015 it's called abolishing tax credits, the result is an increased tax bill under supposedly anti-tax Tory governments.
Abolishing tax credits is not raising taxes, it is reducing a benefit. The aim is to reduce the % of GDP taken by the govt.
Scandanavian levels of bdnefit require Scandanavian levels of tax. The Labour party wants to pretend it can be achieved by a tax on monocles and spats, but really it would require 5-10p on the basic rate of income tax. If they were honest they would make that case, but they do not.
Borrowing to finance current expenditure is just a tax deferred, a tax on children.
The problem is that for your average low-paid worker, they are not really going to be making technical distinctions between "benefits" and "taxes". All they will notice is that they have less money in their pocket.
A reminder that, in most marginal constituencies, the % of people on tax credits (more than 20% of households in some) outstrips the Tory majority.
In 5 years we may well find out if it matters.
A few years ago we were told that the "pasty tax" "granny tax" and "bedroom tax" would propel Labour back to power.
How well did that work out?
I don't remember anyone saying the pasty tax would have an effect (that was just amusing).
Some people did wishfully hope the bedroom tax would have an effect, and it turned out they were wrong - but the difference is that most people who were affected by that never voted Tory in the first place. OTOH, many low-paid workers did vote Tory this year because they were convinced by the Tories' "party of hard-working strivers" rhetoric.
Funnily enough. Someone in my local last night was telling me that they had to move from Potters Bar back to Borehamwood because of the 'bedroom tax' They then went on to tell me that they had found a lovely flat to rent and how much cheaper it would be. After a little gentle questioning from me they agreed that they wanted to move back and the 'bedroom tax' had sod all to do with it, but it saved them a few quid anyway.
I used to have family in Borehamwood!
"Elstree & Borehamwood" station on the line out of St Pancras is actually in Borehamwood.
He found that, roughly speaking, on average (in the sense of the conditional mean, i.e. based on the heights of their parents) a child's deviation from the population mean height (i.e. unconditionally: the mean for everyone, irrespective of parental height) is about 2/3 of the parents' deviation from the population mean.
So yes, the conditional mean for the child of tall parents is above the population average. But it is not so tall as the parent's themselves: so tall parents tend to have children who are taller than average, but not so tall as they are themselves (this is why it's called "regressing to the mean").
Conversely, the conditional mean for the child of short parents is below the population average, but not so short as the parents themselves.
Yes, I understand the argument. My point is that there are societal structures which ensure (or at least promote) coupling within defined parameters for an attribute like intellect which are much less common with something like height.
Many couples will pair off at, for example, University. This group will automatically have a higher mean and therefore a different mean to regress to when they breed. Similarly where you live when growing up will be a factor of your socio-economic group.
The only societal grouping I can think of where height might be a factor would be involvement in elite sport but not only is this a pretty tiny cohort but in many cases won't promote the chance of coupling (most sports are gender separated for example).
On topic, there will be a lot of people - myself included - wanting and expecting Osborne to hold firm. There was always going to be pain for some. Everyone knew that, Osborne more than most. having embarked on the course, you do not then backtrack just because an entirely obvious consequence has come about. This will be the Bedroom Tax all over again (an issue which seems to have disappeared in public debate): a lot of shouting but little meaningful long-term impact.
To be totally unPC, a single mum with four kids?
What's unPC about that, unless you are implying something I'm not getting.
Funnily enough, my mother was a single mum with four kids too.
I don't agree with the rest of your post, but they certainly a name for another type of benefit, carefully named to try and avoid the unfair stigma of being on 'benefits'.
It also tries to avoid the implication that people should be actively seeking to get off them by seeking full-time work when it may not be appropriate - which is a major change in Universal Credit that has mostly gone under the radar by a compliant press.
I have read today that the EU is thinking of giving Turkey an accelerated accession to the EU as part of the migrant crisis deal. That will entail a crisis of millions of Turks moving West instead.
No one wants the EU to have a border with Syria and Iraq. There will be plenty of vetos. What we are seeing is some support being lobbed to the secularists in Tukey ahead of the 1 Nov election.
Both major parties in the UK support Turkish entry.
Really?
Yes, this has been Conservative policy for a long time.
Although, I'm not sure Cameron could carry his party on it now.
'When the lights came on the Moore talk, who was there in the audience? Michael Gove and Michael Fallon unsurprisingly, and so too was, somewhat curiously, Peter Mandelson, stony-faced throughout. Perhaps he had more serious concerns. The Londoner bumped into him again at the reception, having a long conversation with George Osborne — so private that an aide firmly told the Londoner that we were standing a bit too close. Probably wise: chinwags between the two in the past have created poisonous fumes.' http://www.standard.co.uk/news/londoners-diary/londoners-diary-george-quizzes-charles-moore-over-leadership-a3092106.html
I watched the interview of Moore by Osborne. Very Good. An interesting story about Maggie. When her hotel was bombed in Brighton the lights went out. After that event see always carried a torch in her handbag. Sometime later she flew from Asia to Washington stopping off (briefly?) in Hawaii. Maggie asked if she could look around Pearl Harbor which was nearby, but she was told that because it was dark outside she should not. But, she said, I have a torch!. The party duly looked at the harbour.
My assumption (perhaps wrong) is that any potential genetic source for intelligence (which I would expect exists) is going to be more prevalent amongst those who have succeeded in a socially mobile (or somewhat socially mobile) society, this while it is possible that there will be exceptions to the rule the general trend will be for inherited levels of intellect.
There certainly is a tendency for ntelligent people to have intelligent children, but such is true for any inheritable trait, and these are all subject to regression to the mean. It is a statistical phenomenon rather than a genetic one.
It is why clever people manipulate the system in benefit to their own progeny. When we talk of social mobility we are very reluctant to talk of downward mobility. Hence coaching for grammar school entry amongst the middle classes. The prospect of our own children going to a Secondary Modern is too awful for words.
But surely there are different means. Assuming that the coupling of individuals will generally be those within the same socio-economic group (for all manner of reasons) then the mean to which the children of intelligent parents regress towards is different to the mean to which children of thicker couples at the bottom of the income scale.
It is a slow phenomenon, but even with assortive mating the phenomenon exists.
Are you quite sure, Doc. My own experience and that of friend of mine, who has taught at a school on a sink estate for 30 years, suggests that below a certain level evolution seems to be running backwards.
My assumption (perhaps wrong) is that any potential genetic source for intelligence (which I would expect exists) is going to be more prevalent amongst those who have succeeded in a socially mobile (or somewhat socially mobile) society, this while it is possible that there will be exceptions to the rule the general trend will be for inherited levels of intellect.
There certainly is a tendency for ntelligent people to have intelligent children, but such is true for any inheritable trait, and these are all subject to regression to the mean. It is a statistical phenomenon rather than a genetic one.
It is why clever people manipulate the system in benefit to their own progeny. When we talk of social mobility we are very reluctant to talk of downward mobility. Hence coaching for grammar school entry amongst the middle classes. The prospect of our own children going to a Secondary Modern is too awful for words.
But surely there are different means. Assuming that the coupling of individuals will generally be those within the same socio-economic group (for all manner of reasons) then the mean to which the children of intelligent parents regress towards is different to the mean to which children of thicker couples at the bottom of the income scale.
It is a slow phenomenon, but even with assortive mating the phenomenon exists.
Are you quite sure, Doc. My own experience and that of friend of mine, who has taught at a school on a sink estate for 30 years, suggests that below a certain level evolution seems to be running backwards.
I think the penomenon of de-evolution has been discredited (and being overwhelmed by a fast breeding underclass is a perennial middle class fear with a long history) Are we not men?
Dair is correct that various bits of assortive mating and friction to social mobility do tend to mitigate regression to the mean, but they do not eliminate it entirely.
My assumption (perhaps wrong) is that any potential genetic source for intelligence (which I would expect exists) is going to be more prevalent amongst those who have succeeded in a socially mobile (or somewhat socially mobile) society, this while it is possible that there will be exceptions to the rule the general trend will be for inherited levels of intellect.
There certainly is a tendency for ntelligent people to have intelligent children, but such is true for any inheritable trait, and these are all subject to regression to the mean. It is a statistical phenomenon rather than a genetic one.
It is why clever people manipulate the system in benefit to their own progeny. When we talk of social mobility we are very reluctant to talk of downward mobility. Hence coaching for grammar school entry amongst the middle classes. The prospect of our own children going to a Secondary Modern is too awful for words.
But surely there are different means. Assuming that the coupling of individuals will generally be those within the same socio-economic group (for all manner of reasons) then the mean to which the children of intelligent parents regress towards is different to the mean to which children of thicker couples at the bottom of the income scale.
It is a slow phenomenon, but even with assortive mating the phenomenon exists.
Are you quite sure, Doc. My own experience and that of friend of mine, who has taught at a school on a sink estate for 30 years, suggests that below a certain level evolution seems to be running backwards.
Tell me about it, some people don't even understand evolution these days!
I have read today that the EU is thinking of giving Turkey an accelerated accession to the EU as part of the migrant crisis deal. That will entail a crisis of millions of Turks moving West instead.
I just can't see that happening.
It's not going to happen.
I'd estimate the chance of the EU collapsing in the next two decades as, what, 15%.
I'd reckon the chance of Turkey joining in that time period as being at least an order of magnitude less. Firstly, Turks don't want to join the EU. Secondly, it would be vetoed by - at the very least - Greece. Not to mention: North Cyprus, and the fact that large chunks of Turkish law are incompatible with EU membership.
Yes interesting. Here is a black woman sounding of at two muslim women, probably fed up with hearing arabic or a derivative spoken. She is obviously anti muslim but is it racism? Since Islam is a religion and not a race which embraces a multitude of races, the racism charge will not stick.
Can't say I've any sympathy with that woman at all. She votes Tory because she's only interested in herself so seeing her reap what she sows is almost biblical in it's retribution.
OT Has there ever been a vulgarian like SeanT posting on PB before?
I doubt it, given that I joined PB a couple of years after it began, and have gone from obscure, impoverished and little-known drug addict journalist, to SMUG, GLOATING, ANNOYINGLY MILLIONAIRE SUNDAY TIMES NUMBER ONE BESTSELLING NOVELIST within the lifetime of the site.
Incidentally, I hope you don't think the poignant failure of your entire existence and career has gone unappreciated. If you read chapters 19-24 of THE ICE TWINS you will see that the unbearable pathos of the *retired ITV tampon commercials director* has been properly examined.
One of the delicious ironies of life is that your books will eventually be pulped and recycled. Some as bog paper and some as tampons. Time is on roger's side!
I have read today that the EU is thinking of giving Turkey an accelerated accession to the EU as part of the migrant crisis deal. That will entail a crisis of millions of Turks moving West instead.
No one wants the EU to have a border with Syria and Iraq. There will be plenty of vetos. What we are seeing is some support being lobbed to the secularists in Tukey ahead of the 1 Nov election.
Both major parties in the UK support Turkish entry.
Really?
Yes, this has been Conservative policy for a long time.
Although, I'm not sure Cameron could carry his party on it now.
The UK has been te biggest cheerleader of EU expansion down the years deliberately to make the EU go wide rather than deeper. We are probably the biggest cheerleader within the EU for Turkish accession. We would never need to veto Turkish entry as it could never get that far in the near future (Erdogan has taken the nation backwards) and because other nations woild veto it first.
The French have been talking of having a referendum if Turkish membership became a serious question and the French would overwhelmingly vote Non.
I think the penomenon of de-evolution has been discredited (and being overwhelmed by a fast breeding underclass is a perennial middle class fear with a long history) Are we not men?
youtu.be/5JdS-sSKsBc
Dair is correct that various bits of assortive mating and friction to social mobility do tend to mitigate regression to the mean, but they do not eliminate it entirely.
Surely, just by basic statistics, if the entrenchment caused by selective breeding within socio-economic groups outweights the level of cross-group mating, then instead the different peaks on the graph (the different means) actually become more pronounced. There will still be regression to mean but multiple means for each dominant socio-economic group.
In terms of debunking de-evolution, how much of this is based on actual hard science (which as I understand it is limited as much of the potential areas of study are taboo) and how much is based on the anti-scientific, moral-based ways of finding arguments against the principles which underlay eugenics.
The idea that every single child born has the identical potential as every other child with no genetic influence is clearly desirable morally but just because something is desirable does not mean it is actually true.
I have read today that the EU is thinking of giving Turkey an accelerated accession to the EU as part of the migrant crisis deal. That will entail a crisis of millions of Turks moving West instead.
I just can't see that happening.
It's not going to happen.
I'd estimate the chance of the EU collapsing in the next two decades as, what, 15%.
I'd reckon the chance of Turkey joining in that time period as being at least an order of magnitude less. Firstly, Turks don't want to join the EU. Secondly, it would be vetoed by - at the very least - Greece. Not to mention: North Cyprus, and the fact that large chunks of Turkish law are incompatible with EU membership.
But Turkish government wants to join the EU.
Erdogan may want it in theory. He is not willing to make the reforms necessary in practice.
Tax credits are basically benefits by enough name subsidising low wages, the increased minimum wage and tax cut for the lowest earners are far more sensible policies
Correct - they are a tax subsidy for employers. Given the unemployment rate it's not required,
I have read today that the EU is thinking of giving Turkey an accelerated accession to the EU as part of the migrant crisis deal. That will entail a crisis of millions of Turks moving West instead.
No one wants the EU to have a border with Syria and Iraq. There will be plenty of vetos. What we are seeing is some support being lobbed to the secularists in Tukey ahead of the 1 Nov election.
Both major parties in the UK support Turkish entry.
Really?
Yes, this has been Conservative policy for a long time.
Although, I'm not sure Cameron could carry his party on it now.
The UK has been te biggest cheerleader of EU expansion down the years deliberately to make the EU go wide rather than deeper. We are probably the biggest cheerleader within the EU for Turkish accession. We would never need to veto Turkish entry as it could never get that far in the near future (Erdogan has taken the nation backwards) and because other nations woild veto it first.
The French have been talking of having a referendum if Turkish membership became a serious question and the French would overwhelmingly vote Non.
Can't say I've any sympathy with that woman at all. She votes Tory because she's only interested in herself so seeing her reap what she sows is almost biblical in it's retribution.
OT Has there ever been a vulgarian like SeanT posting on PB before?
I doubt it, given that I joined PB a couple of years after it began, and have gone from obscure, impoverished and little-known drug addict journalist, to SMUG, GLOATING, ANNOYINGLY MILLIONAIRE SUNDAY TIMES NUMBER ONE BESTSELLING NOVELIST within the lifetime of the site.
Incidentally, I hope you don't think the poignant failure of your entire existence and career has gone unappreciated. If you read chapters 19-24 of THE ICE TWINS you will see that the unbearable pathos of the *retired ITV tampon commercials director* has been properly examined.
The knife sinks exquisitely between the shoulders blades: SeanT 1, Roger 0.
'When the lights came on the Moore talk, who was there in the audience? Michael Gove and Michael Fallon unsurprisingly, and so too was, somewhat curiously, Peter Mandelson, stony-faced throughout. Perhaps he had more serious concerns. The Londoner bumped into him again at the reception, having a long conversation with George Osborne — so private that an aide firmly told the Londoner that we were standing a bit too close. Probably wise: chinwags between the two in the past have created poisonous fumes.' http://www.standard.co.uk/news/londoners-diary/londoners-diary-george-quizzes-charles-moore-over-leadership-a3092106.html
I watched the interview of Moore by Osborne. Very Good. An interesting story about Maggie. When her hotel was bombed in Brighton the lights went out. After that event see always carried a torch in her handbag. Sometime later she flew from Asia to Washington stopping off (briefly?) in Hawaii. Maggie asked if she could look around Pearl Harbor which was nearby, but she was told that because it was dark outside she should not. But, she said, I have a torch!. The party duly looked at the harbour.
On topic, there will be a lot of people - myself included - wanting and expecting Osborne to hold firm. There was always going to be pain for some. Everyone knew that, Osborne more than most. having embarked on the course, you do not then backtrack just because an entirely obvious consequence has come about. This will be the Bedroom Tax all over again (an issue which seems to have disappeared in public debate): a lot of shouting but little meaningful long-term impact.
To be totally unPC, a single mum with four kids?
What's unPC about that, unless you are implying something I'm not getting.
Funnily enough, my mother was a single mum with four kids too.
I don't get the joke.
It's not a joke for heaven's sake, funnily enough is merely an expression not always to be taken completely literally, I was just struck by the coincidence of my situation being similar to that of the woman in question. Perhaps I should have just said 'coincidentally' instead, but for christ's sake it wasn't that lacking in clarity despite the inelegance of it.
I don't agree with the rest of your post, but they certainly a name for another type of benefit, carefully named to try and avoid the unfair stigma of being on 'benefits'.
It also tries to avoid the implication that people should be actively seeking to get off them by seeking full-time work when it may not be appropriate - which is a major change in Universal Credit that has mostly gone under the radar by a compliant press.
Universal Credit overall does a great deal to ensure work of any form pays
Tax credits are basically benefits by enough name subsidising low wages, the increased minimum wage and tax cut for the lowest earners are far more sensible policies
Indeed one thing that Osborne should do in the autumn statement is change the name back from "Tax credit" to "Supplementary benefit" and have it paid via the DSS rather than the Inland revenue.
Can't say I've any sympathy with that woman at all. She votes Tory because she's only interested in herself so seeing her reap what she sows is almost biblical in it's retribution.
OT Has there ever been a vulgarian like SeanT posting on PB before?
I doubt it, given that I joined PB a couple of years after it began, and have gone from obscure, impoverished and little-known drug addict journalist, to SMUG, GLOATING, ANNOYINGLY MILLIONAIRE SUNDAY TIMES NUMBER ONE BESTSELLING NOVELIST within the lifetime of the site.
Incidentally, I hope you don't think the poignant failure of your entire existence and career has gone unappreciated. If you read chapters 19-24 of THE ICE TWINS you will see that the unbearable pathos of the *retired ITV tampon commercials director* has been properly examined.
"I feel like I'm taking crazy pills! I wrote the ICE TWINS, I wrote it! What have you done, Roger? You've done nothing! NOTHIIIING!"
I think the penomenon of de-evolution has been discredited (and being overwhelmed by a fast breeding underclass is a perennial middle class fear with a long history) Are we not men?
youtu.be/5JdS-sSKsBc
Dair is correct that various bits of assortive mating and friction to social mobility do tend to mitigate regression to the mean, but they do not eliminate it entirely.
Surely, just by basic statistics, if the entrenchment caused by selective breeding within socio-economic groups outweights the level of cross-group mating, then instead the different peaks on the graph (the different means) actually become more pronounced. There will still be regression to mean but multiple means for each dominant socio-economic group.
In terms of debunking de-evolution, how much of this is based on actual hard science (which as I understand it is limited as much of the potential areas of study are taboo) and how much is based on the anti-scientific, moral-based ways of finding arguments against the principles which underlay eugenics.
The idea that every single child born has the identical potential as every other child with no genetic influence is clearly desirable morally but just because something is desirable does not mean it is actually true.
Oops - getting sucked back in!
I have not argued that all children have identical potential. Social rigidities do cause some populations to remain further from the mean, but these are eroded over time, because of random variation. The more the barriers the longer the regression takes, and it does take generations, so pretty quick with fruitflies and Scot Nats but pretty slow elsewhere!
Of course the opposite applies at the other end of the social scale as HL points out. This is why for a population to do well overall it needs to remove the other barriers to upward social mobility. Hence the importance of early years education and support. As Liz Kendall pointed out by time the 11+ comes around much of the opportunity is lost.
Finding the Cayley table for the Klein group was one of the things that was covered in my (rather dated) A-level Further Maths textbook.
I think they introduced it as the symmetry group of a rectangle which is a nice way to think about what RCS found. The four things you can do to a rectangle are "do nothing" (identity), "horizontal reflection", "vertical reflection" and "rotate 180 degrees". If you perform any of these twice, then it's equivalent to "do nothing" (equivalent to RCS's formulation that squaring gets you back to 1 modulo 8).
'When the lights came on the Moore talk, who was there in the audience? Michael Gove and Michael Fallon unsurprisingly, and so too was, somewhat curiously, Peter Mandelson, stony-faced throughout. Perhaps he had more serious concerns. The Londoner bumped into him again at the reception, having a long conversation with George Osborne — so private that an aide firmly told the Londoner that we were standing a bit too close. Probably wise: chinwags between the two in the past have created poisonous fumes.' http://www.standard.co.uk/news/londoners-diary/londoners-diary-george-quizzes-charles-moore-over-leadership-a3092106.html
I watched the interview of Moore by Osborne. Very Good. An interesting story about Maggie. When her hotel was bombed in Brighton the lights went out. After that event see always carried a torch in her handbag. Sometime later she flew from Asia to Washington stopping off (briefly?) in Hawaii. Maggie asked if she could look around Pearl Harbor which was nearby, but she was told that because it was dark outside she should not. But, she said, I have a torch!. The party duly looked at the harbour.
Typical Maggie, always came prepared
"You know, if you just set out to be liked, you would be prepared to compromise on anything, wouldn't you, at any time? And you would achieve nothing!"
I think the penomenon of de-evolution has been discredited (and being overwhelmed by a fast breeding underclass is a perennial middle class fear with a long history) Are we not men?
youtu.be/5JdS-sSKsBc
Dair is correct that various bits of assortive mating and friction to social mobility do tend to mitigate regression to the mean, but they do not eliminate it entirely.
Surely, just by basic statistics, if the entrenchment caused by selective breeding within socio-economic groups outweights the level of cross-group mating, then instead the different peaks on the graph (the different means) actually become more pronounced. There will still be regression to mean but multiple means for each dominant socio-economic group.
In terms of debunking de-evolution, how much of this is based on actual hard science (which as I understand it is limited as much of the potential areas of study are taboo) and how much is based on the anti-scientific, moral-based ways of finding arguments against the principles which underlay eugenics.
The idea that every single child born has the identical potential as every other child with no genetic influence is clearly desirable morally but just because something is desirable does not mean it is actually true.
Oops - getting sucked back in!
I have not argued that all children have identical potential. Social rigidities do cause some populations to remain further from the mean, but these are eroded over time, because of random variation. The more the barriers the longer the regression takes, and it does take generations, so pretty quick with fruitflies and Scot Nats but pretty slow elsewhere!
Of course the opposite applies at the other end of the social scale as HL points out. This is why for a population to do well overall it needs to remove the other barriers to upward social mobility. Hence the importance of early years education and support. As Liz Kendall pointed out by time the 11+ comes around much of the opportunity is lost.
'When the lights came on the Moore talk, who was there in the audience? Michael Gove and Michael Fallon unsurprisingly, and so too was, somewhat curiously, Peter Mandelson, stony-faced throughout. Perhaps he had more serious concerns. The Londoner bumped into him again at the reception, having a long conversation with George Osborne — so private that an aide firmly told the Londoner that we were standing a bit too close. Probably wise: chinwags between the two in the past have created poisonous fumes.' http://www.standard.co.uk/news/londoners-diary/londoners-diary-george-quizzes-charles-moore-over-leadership-a3092106.html
I watched the interview of Moore by Osborne. Very Good. An interesting story about Maggie. When her hotel was bombed in Brighton the lights went out. After that event see always carried a torch in her handbag. Sometime later she flew from Asia to Washington stopping off (briefly?) in Hawaii. Maggie asked if she could look around Pearl Harbor which was nearby, but she was told that because it was dark outside she should not. But, she said, I have a torch!. The party duly looked at the harbour.
Typical Maggie, always came prepared
"You know, if you just set out to be liked, you would be prepared to compromise on anything, wouldn't you, at any time? And you would achieve nothing!"
The discussion was about Turkey joining Schengen, I believe. That does not - of course - give you the right to work in the EU, merely that you don't need to use your passport when travelling between Schengen countries.
You don't need a passport?? No ID?? I thought it was just a visa you did not need??
That's right. There are normally no border officials at all - you just drive or cycle or walk across. Used to be like that from the smaller crossings into Switzerland too and maybe still is - a very Swiss notice said "If you have something to declare, please drive to the next border post".
The unconvincing Tory line - rather Kafkaesque in the way that it was brought out with bravado that dared anyone to contradict it - is that because wages are going to rise in the *future*, they can reduce welfare payments in the *present*. If Tory MPs go along with this it creates the impression that they are either (a) stupid or (b) nefarious.
Comments
Good night all.
PB is one place where statistics are discussed intelligently. It is part of how I got started posting.
Here's the follow up
http://www.standard.co.uk/news/crime/pregnant-woman-subjected-to-isis-bes-bus-rant-why-didnt-anyone-stand-up-for-me-a3092696.html
He found that, roughly speaking, on average (in the sense of the conditional mean, i.e. based on the heights of their parents) a child's deviation from the population mean height (i.e. unconditionally: the mean for everyone, irrespective of parental height) is about 2/3 of the parents' deviation from the population mean.
So yes, the conditional mean for the child of tall parents is above the population average. But it is not so tall as the parent's themselves: so tall parents tend to have children who are taller than average, but not so tall as they are themselves (this is why it's called "regressing to the mean").
Conversely, the conditional mean for the child of short parents is below the population average, but not so short as the parents themselves.
If anything, it's more likely to crop up naturally in a computing class (as the % operator).
Gruesome really.
I said he was talking shit. Was he?
OT Has there ever been a vulgarian like SeanT posting on PB before?
In some A level Further Maths syllabuses it used to be put in to the "Group Theory" section, so students could have some extra examples (together with permutation groups) of small finite groups. That's long gone from most syllabuses now though.
Odd how a concept that was once O level eventually wound up in A-level Further Maths and then off the syllabus altogether.
And a shame because it does make the STEP (formerly, S-level) exams much easier, for students applying to certain high-rank universities.
Meanwhile the incentive is created for lots and lots of offspring to be born to those at the bottom end of the socio-economic (and intellectual) group.
....perfectly 'benefiting the UK's national interests'.
http://www.standard.co.uk/news/londoners-diary/londoners-diary-george-quizzes-charles-moore-over-leadership-a3092106.html
Many couples will pair off at, for example, University. This group will automatically have a higher mean and therefore a different mean to regress to when they breed. Similarly where you live when growing up will be a factor of your socio-economic group.
The only societal grouping I can think of where height might be a factor would be involvement in elite sport but not only is this a pretty tiny cohort but in many cases won't promote the chance of coupling (most sports are gender separated for example).
Square it: 4n^2 + 4n + 1
Group the 'n's: 4(n^2 + n) + 1
But n is odd so n^2 must be odd, so n^2 + n must be even, therefore must also divide by 2.
Hence if n^2 + n divides by 2 then 4(n^2 + n) must divide by 8.
Leaving the +1.
QED.
It also tries to avoid the implication that people should be actively seeking to get off them by seeking full-time work when it may not be appropriate - which is a major change in Universal Credit that has mostly gone under the radar by a compliant press.
Although, I'm not sure Cameron could carry his party on it now.
http://www.eveningtimes.co.uk/news/13848960.Michelle_Mone_QUITS_board_of_controversial_diet_pill_firm/
An interesting story about Maggie. When her hotel was bombed in Brighton the lights went out. After that event see always carried a torch in her handbag. Sometime later she flew from Asia to Washington stopping off (briefly?) in Hawaii. Maggie asked if she could look around Pearl Harbor which was nearby, but she was told that because it was dark outside she should not. But, she said, I have a torch!. The party duly looked at the harbour.
https://en.wikipedia.org/wiki/Idiocracy
https://youtu.be/5JdS-sSKsBc
Dair is correct that various bits of assortive mating and friction to social mobility do tend to mitigate regression to the mean, but they do not eliminate it entirely.
More succinctly:
An odd number is congruent to 1,3,5 or 7 mod 8. The squares of these are 1,9, 25 and 49, all of which are congruent to 1 mod 8
Better still, observe the group (Z/8Z)* is isomorphic to (Z/2Z) X (Z/2Z) so every element is of order 2.
Line 4 n is odd.
That doesn't follow does it? Eg 9 is odd but n would be 4 (2x4 + 1). Though n^2 + n is even regardless of whether n is odd or even.
And so goodnight! :-)
The French have been talking of having a referendum if Turkish membership became a serious question and the French would overwhelmingly vote Non.
In terms of debunking de-evolution, how much of this is based on actual hard science (which as I understand it is limited as much of the potential areas of study are taboo) and how much is based on the anti-scientific, moral-based ways of finding arguments against the principles which underlay eugenics.
The idea that every single child born has the identical potential as every other child with no genetic influence is clearly desirable morally but just because something is desirable does not mean it is actually true.
= 4(n^2 +n) +1
=4n(n+1) +1
If n is odd, then n+1 is even, so replace n+1 with 2p, where p is an integer.
So 4n(n+1) +1
= 4n2p +1
= 8pn + 1
...and if you divide 8pn+1 by 8, you get pn remainder 1
Conversely, if n was even, then replace n with 2p, where p is an integer.
So 4n(n+1) +1
= 4*2p(n+1) +1
= 8p(n+1) + 1
...and if you divide 8p(n+1) +1 by 8, you get p(n+1) remainder 1
QED
And I'm pissed. Still think working-class people are stupid?
I have not argued that all children have identical potential. Social rigidities do cause some populations to remain further from the mean, but these are eroded over time, because of random variation. The more the barriers the longer the regression takes, and it does take generations, so pretty quick with fruitflies and Scot Nats but pretty slow elsewhere!
Of course the opposite applies at the other end of the social scale as HL points out. This is why for a population to do well overall it needs to remove the other barriers to upward social mobility. Hence the importance of early years education and support. As Liz Kendall pointed out by time the 11+ comes around much of the opportunity is lost.
https://twitter.com/leicesterliz/status/654929635612991488
Nice point about using the Klein group though.
Finding the Cayley table for the Klein group was one of the things that was covered in my (rather dated) A-level Further Maths textbook.
I think they introduced it as the symmetry group of a rectangle which is a nice way to think about what RCS found. The four things you can do to a rectangle are "do nothing" (identity), "horizontal reflection", "vertical reflection" and "rotate 180 degrees". If you perform any of these twice, then it's equivalent to "do nothing" (equivalent to RCS's formulation that squaring gets you back to 1 modulo 8).
That's right. There are normally no border officials at all - you just drive or cycle or walk across. Used to be like that from the smaller crossings into Switzerland too and maybe still is - a very Swiss notice said "If you have something to declare, please drive to the next border post".