undergraduates have trouble with is that the

roles of “AND” and “OR” are flipped when

dealing with sets, rather than with individuals.

For instance, let be “the set of cats and

dogs”, and let be an element of . Then it is not true that “ is a cat and a dog”; instead

one has “ is a cat OR a dog”. This subtlety means that one cannot apply

some mindless substitution rule in order to

translate logical connectives into set-

theoretic notation such as unions and

intersections. For instance, the “set of cats

and dogs” is the union of “the set of cats” and “the set of dogs”, but “the set of

numbers that are even and square” is the intersection of “the set of numbers that are even” and “the set of numbers that are

square”. It’s not a problem so long as one is

thinking with the part of the brain that is

capable of comprehending English

sentences, but sometimes this mode of

thinking shuts down when faced with a scary-looking maths problem, and one

instead relies on more dubious formal

substitution rules such as “AND means

UNION”, which can lead to trouble. ]]>

Shockingly, for me (mid-career person), there is a 20% reduction in the annual pension at retirement and I will have to pay 10% more towards my pension per month as well !!

What a joke, a very poor one ,grrrr !!!!

]]>The inequalities discussed above pale into comparison when you consider those who will bear the costs if this petition is upheld: young academics currently struggling to find employment. Salaries and job security have been eroded since the financial collapse. Our generation will work longer and retire on less than those the current changes effect – whether the petition is successful or not. If we ever manage to secure permanent, pensionable jobs at all.

]]>We should all join UCU and support their campaign too.

My wife is a professor enrolled in USS. I work in a University, am also a professor, and earn about the same as my wife, but I am employed by the Medical Research Council and enrolled in the MRC pension scheme. The MRC scheme is essentially identical to the USS scheme in terms of benefits and costs. The MRC scheme is much smaller than the USS one, and so might be expected to have similar problems, if not worse. Is this the case? No.

Although the MRC scheme took a hit around 2007-9, and despite a cautious investment profile, it bounced back well as the stockmarket rose (after all, fluctuation is precisely what stockmarkets are supposed to do and pension funds normally plan for these events). Moreover, I get a clear and concise annual report on the MRC scheme, which shows that the last full actuarial valuation showed it is fully funded and in a strong financial position (assets at 31/12/13 were 118% of liabilities, up from 110% at 31/12/10). There have been no hints of plans to alter the final salary scheme arrangements. My wife does not receive a similar annual report from USS.

One can ask:

1) is the USS scheme really so under-funded as is claimed, or are there vested interests that are eager to use the excuse of the Crash to close out the scheme unnecessarily?

2) if so, what might those interests be?

3) if the USS scheme is indeed underfunded, who made the bad investment decisions that led to the problems?

4) should members have confidence in the USS management/Trustees going forward? If not, how can they act to improve things?

5) why does USS not report its financial position clearly, succinctly and annually to its members?

I have also heard that several top Universities, as institutions, have publicly expressed their opposition to the USS changes, but that several other top Universities have not. Can anyone shed light on why all the employers are not taking the same line?

]]>If one did pursue the continuity criterion (in areas in which there might be no discontinuity in the life of the affected person), I suppose that mere continuity would not be enough. A very steeply increasing or decreasing function can be almost as unpleasant as a discontinuous one. Perhaps we would want some rule that no current or prospective cash inflow should, at any one time, change at more than (say) twice the rate of any other one affecting the same person in relation to the same employment.

(Declaration of non-interest: I have never been, and never expect to be, a member of a defined benefit pension scheme.)

]]>What about those earning over £55000 paying into a pension scheme for their entire salary, but only accruing pension rights up to £55000. How is that right or legal? Or have I missed something? ]]>

If it distracts a student from doing his daily work of attending to the relevant exercises to be done,, it is extremely unhelpful.

Certainly the professor has a lot of good ideas. But he also has a couple of strange ideas which I do not accept..

gowers Says: September 23, 2011 at 11:45 pm

When I was at school, I had a fit of enthusiasm, obtained a copy of the Cambridge schedules, and tried to read up on several of the first-year courses. I certainly didn’t manage to cover any of those courses in full, but nevertheless the result was that I was pretty well prepared for my first year. And the result of that was that I managed to delay the moment where it all got hard to about the beginning of my second year. I’m answering this question in some detail because if I simply say “The beginning of my second year” and you find things tough earlier than that, you should understand that that isn’t necessarily a problem. It just means you are discovering one year earlier than I did what learning mathematics is really like.

It seems clear to me from what gowers says that he found an effective method.of preparing for first year. Why doesn’t he think that this is “what learning mathematics is really like”? Why doesn’t he thin that the same method could be used to prepare for second year and third year?.

Richard Mullins

]]>67A (7) – “At any time when the pensionable service of a member of an occupational pension scheme is continuing, his subsisting rights [i.e. his rights today] are to be determined as if he had opted, immediately before that time, to terminate that service.”

This suggests that the changes are legally correct… which is unsurprising given the expense that will have gone into drafting them. Being morally fair is a different matter.

http://www.legislation.gov.uk/ukpga/2004/35/part/5/crossheading/modification-of-pension-rights

]]>The actuaries advising USS appear to be Mercer, perhaps you can get in touch with them directly (Ali Tayyebi, Four Brindleyplace, Birmingham, B1 2JQ, +44 121 631 3343), or go through the Trustees of the Scheme, who will likely redirect you to the actuaries for any questions regarding benefit calculations.

http://www.uss.co.uk/Actuarial%20Valuation/Actuarial%20Report%20as%20at%20March%202013.pdf

For something more vexing, note the absurdly large volatility in the Scheme’s funding from page 10 – the deficit of 11.5bn (which these proposed changes are supposed to address) shrinks by itself to 7.9bn over the course of the next 3 months. The fixed interest gilt yields used to calculate the net present value of future liabilities are currently even lower than 2013, so the deficit number must be pretty enormous right now. It would seem short-sighted that this number be used as a basis for long-term policy setting, and yet here we are. It clearly does not represent any realistic financial future – only if no new members joined ever again and all old members immediately stopped paying contributions forever would these assets need to be matched against all future liabilities. Also noticably absent are any examples of a pension scheme going the other way and offering to improve future benefits when the market conditions turn in their favour and the fund creates a surplus.

Now in a mathematically continuous universe, the remedy would be to make the terms somewhat less generous for everyone, including those already receiving a pension which is unsustainably high.

But in a world dominated by lawyers, even contracts based on flawed arithmetic have to be honoured. With the likely consequence that USS would become insolvent. If insolvency can already be anticipated, it would not be fair (nor, in my extremely limited understanding of the law, legal) to continue paying everyone at 100% until there is no money left. Thus, USS should be closed now and negotiate with all its creditors, including current pensioners, and might even reach a “continuous” solution.

However, that is also unlikely to happen. Instead, USS would like to continue accepting new money under far less favourable terms and use excess returns (relative to those less favourable promises) to avoid insolvency. Both the USS proposal and modifications along the lines you have sketched will effectively compel younger contributors to subsidize unsustainably generous promises made in the past.

I agree about the desirability of a final-salary pension scheme, though, particularly with a view to the unfairness of salary progression (which in itself is unfair – why didn’t Carl earn most money in his early 30s, but had to wait to become anointed professor and then promoted by virtue of the passage of time?).

If one wanted to retain a final-salary scheme, perhaps it would be easiest to adjust the multiplier: perhaps it would work at 1/100 rather than 1/80?

]]>Your examples however also show other things.

1) A final salary scheme benefits some people hugely (and that necessarily has to come at the expense of others). A career average scheme seems much fairer. Of course instead of “one 80th of your final salary” it shouldn’t become “one 80th of your average salary”. It is possible to do a calculation to determine which number gives an equivalent rate to “one 80th of your final salary” for the “average person”. Apparently the number which USS proposes is worse than that and this is another way in which the new scheme will be worse.

2) Carl should be demoted.

]]>I took out an “added years” contract some years ago. The word was “contract”, which seems legal to me. Under the proposed changes, they will be offering “one off” opportunity to carry this on, but it will be based on the salary at April 2016 ( upgraded for CPI), not my actual final pensionable salary. The cost, however, of the added years contract seems as though it will continue to be based on current salary. Seems to me that the contract is being broken by them. Worth a challenge, I think. ]]>

For the counterexample it sounds like you need two irrational numbers that you convert into two separate continued fractions.

Then you multiply the continued fractions together in order so the smallest continued fraction of both will be multiplied followed by the second largest of both, then the third largest of both, etc…

Then you order this new set of combined fractions with counting numbers so the first combined fraction, then the 2nd, then the 3rd, etc…

Then you multiply the continued fractions by their counting numbers.

Finally you find the counterexample if none of the denominators in the combined fractions from one to infinity cancel with the specific counting numbers.

That’s what I got from the explanation on this page, but I don’t feel like it’s right. Could someone try and explain to me how you are supposed to get the counterexample in the way that I tried to explain it without using math symbols.

]]>The great Nassim Nicholas Taleb author of Antifragile; has decided to ‘uberize’ the publishing business and predicted that the bad guys such as Elsevier, Wiley and Springer will go bust. I am sure you already have, if not; please contact him as he has already taken the steps to demolish these corrupt publishing house. https://www.facebook.com/permalink.php?story_fbid=10152817705893375&id=13012333374 ]]>