Student Loans

 Student Loans

I was lucky. In my day a 3-year undergraduate degree was provided free to those school children who were believed to be able to benefit from it. The state (in my case the UK) provided the university with enough money to put on sufficient courses. And the state (or the county) provided a means-tested grant that provided just enough money for a student to feed and house themself for each academic year of 30 - 40 weeks. Mine was a pretty average family, with one parent writing a book and the other working as a G.P.; but I and five siblings each received the full student maintenance grant.

The state wanted so many doctors each year and got them, so many scientists, so many teachers, so many librarians, artists, etc.;  and they got them. Each year a new cohort of school-leavers found places at university, and a new cohort of graduates found jobs. Firms toured around the better-known universities like wasps round an open jam-jar. 

Then some wretched government, wanting to bribe the electorate by lowering taxes, found that there was no longer enough central government money to pay for the university places; and a short-sighted boffin suggested charging Student Fees. 

It is argued that a university degree confers a benefit on the graduate. Not contested. But it also confers an enormous benefit on the state. With a healthy university system we can staff our hospitals, laboratories, workshops, class-rooms (etc) without needing to bribe people from other countries. I have not heard much about the benefit to the state from a healthy university sector. (On the other hand, I have heard that the university sector in the UK is in an unhappy condition.)

There is some talk about fairness. That it is unfair for the state to give, free to able school-leavers, a means of earning more than less able ones. It is certainly not equal, but it may be fair, if selection is handled fairly and without prejudice. 

The thought of going into considerable debt (e.g. £30,000) at the beginning of a working life may put many able school-leavers off studying for a university degree. 

Suppose the median annual pre-tax salary in the UK in 2025 was £40,000 (actually £39,039), and that of non-graduates was £30,000 (actually £29,500). Suppose, therefore, that the median annual pre-tax salary of graduates is £50,000. (This is a guess.)

There must be many people who realise that graduates would (on these figures) pay more tax than non-graduates, and this might be sufficient to pay for the university course, and to justifying it being free for suitable candidates. So I did some calculating, using data on the salaryaftertax.com  website.

                        Pre-tax(£)   After tax(£)     % tax   Tax p.a.  Tax (30 years)
Non-graduate:        30,000           25,120   16,3        4,880      146,400
Graduate:                50,000          39,520    19.2      10,480     314,400

It is clear that, in a working life, the graduate is indeed paying for her/his tuition, many times over, simply in the already established progressive tax system. He pays £168,000 more tax than the lower earner; more than twice. 

If the government wants the Fees paid up-front, perhaps I would allow a loan scheme. But to charge interest on that loan at greater than RPI seems simply greedy; usury!. (Repayments of the loan should be counted as tax-deductible  expenses.) But I would prefer, as fairer, the system of my youth.

Comments are welcome, direct to cawstein@gmail.com

 Exploring Circles

One of the treats for my 84th birthday just passed was to spend an hour with my brother trying to prove a conjecture, which I do not remember ever having been taught at school. 

(It recalled a similarly enjoyable hour spent 62 years earlier. David, Peter and I, were final-years students each reading for different degrees; David (Greats), Peter (PPP), and I (Botany). We found ourselves meeting regularly on Friday evenings at the "Welsh Pony", a now-vanished pub down by Gloucester Green, Oxford. Conversation roamed; on that occasion we were trying to remember the proof of Pythagoras' famous theorem involving the square on the hypotenuse.)

I had recently noticed that the diameter of a circle subtends an angle (at any point on the circumference) that looks very like 90°. Is it exactly 90°? Why were we never told about this at school? 

Figure 1
In Fig. 1, XZ is a diameter, Y is any point on the circumference, YW is a second diameter. Angle XYW is called a, WYZ is called b. The hypothesis is that angle XYZ (= a+b) = 90°

I showed this to my brother who became equally intrigued. We scribbled away for an hour, occasionally sharing the progress we had made. Success came the next morning. It seemed to us convincing that, by symmetry, we can label four radii as equal, four angles as equal to a, and four equalling b.  Furthermore, in the triangle YCZ, the angle sum (= 180°) is 2a + 2b; so a+b = 90°. Q.E.D. This would be true wherever we placed point Y.
After bathing in the glory of this success for an hour, I wondered if I could prolong this happiness by floating some more hypotheses. What, for example, if the chord was not a diameter but was shorter, as (for example) XW in Fig. 1. That chord clearly subtends angles at Y and Z that are less than 90°, but they are nevertheless patently equal. What is more, the chord XW subtends and angle at the centre that is twice that at the circumference. Of course they are special cases, as the lines XZ and WY are diameters. So I drew Fig. 2. (Below).

Figure 2
In Fig. 2, AB is a diameter, as is CD, passing throught the centre O. AO is therefore the radius, length r. AC is a chord of length r, thus subtending an angle of 60° at the centre and 30° at the circumference. CF and BF are also Chords of length r. 

Once again, AOB and COD are diameters (going through centre O). But the chord AC (likewise CF, FB, and BD) was chosen to be exactly r  because I know (from previous work) that exactly six such chords fit round a circle, forming exactly six equilateral triangles with their tips at the centre. It can be seen from Fig. 2 that chord AC subtends and angle of 60° at the centre and 30° at the circumference. 

In fact, all chords subtends two angles at the circumference. In general one is less 90°, and the other is greater than 90°, unless the chord is a diameter, when both are 90°.  

The chord CB subtends an acute angle (60°) at D, and an obtuse angle (120°?) at F. This example illustrates further property of chords.  The obtuse angle is supplementary to the acute angle (60° + 120° = 180°). For another example, the chord CF subtends an acute angle of (30°) at D, an angle (COF) of 60° at the centre (i.e. twice that at the circumference); and an obtuse angle of 150° at E  (supposing angle-sum quadrilateral is 360°, and you remember that FC and FO are both radii.)

References:

Wikipedia: Chords, Hipparchus,. 

There are many YouTube and other videos on Chords, Tangents and Secants

Apparently chords have been much studied since Babylonian times. The Greek geometer and astronomer, Hipparchus,  wrote a 12-volumed book on Chords around 150 BC, though that book itself is now lost. Tables of chords were used as we have used tables of sines.]

Comments are welcome, direct to cawstein@gmail.com

Happy though Human

How to be happy though Human∗

My father practised as a Freudian psychoanalist. Well, he said he was technically an 'Eclectic'. But the truth is that his training analyst was Freudian; it is just that my dad's training was incomplete. I think the war intervened. I sensed in him a deep respect for Freud's intuitions, with some minor reservations. He had much less time for Jung, and I do not think I  ever hear him mention Adler. My mother, who was usually busy with other aspects of general practice, and house-keeping, respected the more mystical Carl Jung, and summarised Alfred Adler for me as replacing Freud's monomaniacal emphasis on sex, with the more general concept of 'power'. Thus was the house in which I grew up. 

Last week I  paused at the the bookcase on my upstairs landing to enjoy the mere presence of my beloved books. A cluster of early Pelicans caught my eye:  two by A. N. Whitehead, Paul Einzig on monetary policy and Béran Wolfe's familiar title "How to be Happy though Human". Familiar, arresting, haunting; I doubted if I had ever opened  the book in the 60 plus years in which we had shared a house. I wondered who had bought it; I, or my mother, or my father. First published 1932, republished by Penguin Books in 1957. From the back cover I learned that Wolfe had been an 'assistant' to Adler in Vienna between the wars. At last! My chance to glimpse the Adler view of human motivation. 

But ouch! This is going to hurt. Opening the book at random, I found a section titled "The Fine Art of making Presents".  I read: 

"... the giving of gifts for reasons of duty, custom, or the like. ....is the worst... way to make a present.......you give a small boy....... a copy of Marcus Aurelius's Meditations because of some vague hope ....". 

And I wince, for I have made exactly that silly mistake with my oldest grand-daughter, and was about to err again with her younger sister. 

On the other hand, despite Wolfe's rather clunky use of English, Béran offers many pieces of sound advice. For example:

"Peaceful social intercourse can exist only in a society of mentally mature individuals. You can achieve a great deal of happiness and gain an enormous host of friends if you will (sic) incorporate the wisdom of social relativity (?)...... If you wish to convince him of a point, or teach him a new technique, minimise the distance between your superior position of knowledge and his inferior position of ignorance..... Conscious modesty in attitude, quietness in gesture, combined with firmness of purpose and decision, mark the well-adjusted adult. .... The words 'absolutely', 'certainly', 'always', 'never'.. have little place in the vocabulary of the happy man." 

Or his comment on Deferred Living: "One important source of unhappiness is the habit of putting off living to some fictional date in the future.........."

Or: "[The immature man] lives a plan-less life. His strategy consists either in muddling through, or dreaming through, life."  

(Touché!  Though I call it 'going with the flow', and explain my strategy as a result of my fear of making a wrong decision. I am beginning to see developing the theme of this essay; its raison d'être écrit.  Wolfe is forever stripping away the multilayered protective carapace in which I have carefully wrapped myself. I keep pulling it back and re-wrapping.  His therapy is rather brutal; it is like pulling a hermit-crab out of its borrowed shell and telling it to stiffen up.)

Béran Wolfe devotes a significant portion of the book to 'Happiness in Love and Marriage', or more correctly to the unhappiness generated in these area of life. He suggests that there are but few people who could number amongst their acquaintances 10 happy couples. However, he goes on to suggest that the great majority of this widespread unhappiness stems from avoidable causes. There are (he says) certain fundamental prerequisites to a happy marriage:

"Mental maturity, physical health, and psychological independence in outlook, a knowledge of the art of love and the practice of contraception are important premisses of a normal sexual life. A mature sense of social responsibility, the willingness to make concessions to reality, freedom from neurotic traits (including any tendency towards romantic idealism), a wide and catholic range of human interests, and the willingness to grow, to cooperate, to suffer sometimes, and to share always the disappointments and the joys of life – these are the foundations of success in the solution of the love problems of every day life. The willingness to encourage, the ability to identify oneself with the situation of the sexual partner, help one over the usual obstacles, ........"

 Well! That explains that then. In my 15-year marriage I do not think I met a single one of those 12 fundamental prerequisites; unless you would allow me  'psychological independence in outlook', and a 'catholic range of human interests'; which latter I admit would be quite generous, considering my total ignorance of sport and pop music. Contraception clearly defeated us in the second year of our marriage. And the 'Art of Love' defeated me till I was 70 years old. I bristle with a host of neuroses; and I am sure those must include romantic idealism if that means 'foolishly trusting nature as a guide', 'hoping for the best', and 'extreme shyness'.

Surely it is obvious that a neurotic person needs his neuroses. They are his defences against  the pain of facing up to his inadequacies. 

As I put the book back on the shelf, I feel inclined to admit that Life was rather wasted on me. And yet, you know, I just about managed. Bailing, but still afloat.

∗ Wolfe, W. B. (1957) "How to be Happy though Human", Penguin Books Ltd., Harmondsworth, Middlesex

On the Purchase of Greenland

 On the Purchase of Greenland

I do not see the Trump position and the Danish/Greenland/European positions as necessarily incompatible; though our media, and maybe also the principal participants, see the situation as a confrontation.

The sale/purchase of Greenland does not prevent the Greenlanders (with or without the Danes) from having complete control of the question of sovereignty of their island. The way these things normally work is that the would-be purchaser mentions a price. The potential seller then nods or shakes his head. The purchaser then mentions a higher price, and so it goes on until both parties agree that they have found a price at which a transfer of ownership can be mutually agreed. Or the bidder gives up. 

Does anyone know how the purchase of Alaska off the Russians was negotiated? The purchase of California/Texas/Arizona/New Mexico from the Mexicans was negotiated, but not without the threat of continuing a disasterous war. The Hawaiian Islands were merely taken; without (I understand) even so much as a 'by-your-leave'. 

(I believe, that the Hawaiian Islanders had gone so far as to design a flag (in 1848) that incorporates the British Union Jack in a corner as did the Aurtralian and New Zealand flags. Alas, in 1898, we let them down.

https://en.wikipedia.org/wiki/Flag_of_Hawaii)

Ghosts

Ghosts

My house occasionally gives me the impression it is haunted. A fleeting impression which I dispel with a wave of the hand. 

The man who sold me the house a decade ago, was (I understand) a bailiff. I do not know if that was a salaried civic appointment, an Enforcement Officer, like a policeman. Or something you can call yourself, if you have ever tracked down a malefactor and 'served him a writ'. Like a 'bounty hunter' in the wild-west films; perhaps a hard man who likes justice and fancies his chances against most comers, quick on the 'draw', and trained in judo. What I do know is that he made enemies. The house had several safety features which he showed me, as though I also might have enemies who would love to tip-toe round my house at night; sophisticated locks, motion-detectors, an alarm button (red), a black button that must be pressed if you want to exit by the front door (Imagine trapping an angry criminal inside your house! I suppose so that you could approach and put cuffs on him. I think I would rather explain to him from the top of the stairs about the black button, so he could let himself out.) 

My bailiff friend dismantled and removed his c.c.T.V system, but left several holes in the outer wall which moan, on windy nights, if the wind is from the right angle; like organ pipes.

Another feature of the house is the creaking noise made by the copper tubing of the micro-bore central heating as it contracts (or expands) lengthwise and squeezes through holes in the joists. Some minutes after  the central heating switches off (or on) there is  a quiet squeaking noise which moves gently down the corridor like a timid cat-burglar. And I know for a fact that there are mice in the party-wall where my house abuts on John's next door; I have heard them scratching and gnawing.

Last Tuesday I was woken by a different noise – two deliberate taps on the glass pane of the front door. "Must be Denys", I said to myself, "calling about that wiring problem on his way to work." I rolled out of bed, slipped my feet into slippers and fetched down my warmer dressing gown from the back of the bathroom door.  "Gosh", I said as I carefully descended the stairs, "but he starts work early!"  It was pitch dark outside, were it not for the distant street-light; it must be the middle of the night. I pressed the 'black' button (easier using two thumbs together) and opened the door. I just caught sight of a trousered leg as it disappeared round the corner of the house. Had I shoes on I would have gone out to look. I am braver with shoes on. I share the usual male-madness of thinking I could probably cope with a single assailant; but not when I am wearing slippers. I stood on the doormat a-while and listened. I could hear – nothing. Have they fled noiselessly, or are they waiting just round the corner, with a lead pipe? Neither alternative made much sense. It certainly was not Denys. I closed the door and went back upstairs. The clock by my bed said 3.30 a.m. I slipped easily back to sleep. 

Next morning I tried to think up some half-plausible explanations. A vengeful debtor just released after ten years in prison? Or a co-criminal calling for his share of the swag? Or a stalker? A ghost seems as likely as any other explanation.  Knowing that the brain contributes massively to the perceived image of  'optical sense data', can I claim this as a case of the brain similarly trying to make sense of a sound? Am I just waving my hands? I might as well call it a ghost. But is it my ghost or does it belong to the house?

Japan's Debt:GDP ratio

Japan and its Debt-to-GDP ratio 

Introduction
How can we expect the 'propensity to save' to be the same in Japan as in Europe or the USA? History matters.  I am a Scottish 'war baby', and 80 years later I am still hoarding writing paper.  While Europe was evolving the goose-down duvet, Japan was evolving the wooden takamakura pillow. The Japanese temperament, history and  laws are all very different from ours in Britain. Japan struggle to raise its inflation rate to 2%; we in the UK struggle to lower our rate to 2%. 

Japanese regulations and saving propensity
From 1945 - 1990 the average Japanese household saved nearly a quarter of its disposable income. (C.f. 18% in France and 20% in Germany. ) For some reason we in Britain favour investing in stocks and shares. The Japanese psyche (and/or government regulatory preference) seems to prefer the simple, low-interest savings account in a simple bank. I quote Takeo Hoshi (2023): 

"As early as the mid-1990s, the Japanese government realized that various regulations in financial markets made households hold most of their financial assets in the form of cash and deposits." [8].

There is currently "too much money" in such accounts, and banks offer negative interest to try to drive that money away [8]. Managed funds are not favoured in Japan, neither by the public nor the government. Stock brokers would like the Japanese to gamble on the stock market like people do in UK and USA because that is how they make their money, but they cannot get the public enthusiastic [8].  In the period 1950 - 1990 the social security provision in Japan was weak; workers had to save to provide both pensions and 'security against hard times'. (I learn that there is some regulation in Japan that makes low-interest bank-deposits a favourite place for workers to store the money they have saved for their pension. But I do not know what; perhaps rules about interest rates and tax breaks. From [11], I learn that tax breaks for private savings (maruyū) were introduced in 1963, encouraged household savings.)

The 'Bubble' and the 'Burst'.
From the sixties to the eighties, times were good for Japan.  Real Japanese GDP increased fivefold between 1960 and 1990, and with it net household savings increased by the same factor to 45 trillion yen at 1990 [11]. Japan ran a large trade surplus with most developed countries, and in particular with the USA. However, the surging value of the yen eventually depressed sales. In addition, the growth of competition from other Asiatic economies also lowered profitability.  The USA wanted Japan to curb the bubble by raising interest rates, but the Bank of Japan (BOJ) lowered interest rates, trying to "stabilize exchange rates". In 1987 Japanese money supply (M2) was still expanding at 10% p.a. even while inflation dipped to negative values [10]. The BOJ failed to note (in time) the 'overheating' of the economy; and the 'bubble' burst. 

The  'bubble-burst' came in December 1989, with the Nikkei 225 dropping 41%  in 8 months, from 39,000 to 23,000 by August 1990 [12]. But that sudden decline was followed by a persistent slow decline for 18 further years till it bottomed at 7,000 in October 2008, having lost 82% of its maximum value.  The revival of the Nikkei 255 did not really begin till mid 2013, when the BOJ started large scale purchase of Japanese stocks and shares. Since then it has climbed steadily to a new high at the beginning of 2026. 

CPI Inflation

As far as the Japanese themselves are concerned, the Yen has proved to be a very stable currency, since 1991. Between 1956 and 1991 the Yen lost more that 80% of its value, but has remained very steady since then [13]. Conventional wisdom is that it is better to have annual inflation of +2%. Not too much higher, and not too much lower. By 1987 the growth of other Asian economies had created over-production and the need to shed workers. However, in the face of competition Japanese firms tended to hold on to their workforce offering security in place of wages. So wages sank. And prices sank. 

The BOJ saw persistent negative annual inflation (-0.3%) for 15 years from 1998 - 2013, (and again from 2019 - 2026 according to Ian Webster, [13]). That worried them, as every other country had inflation.  So, in 2013 the BOJ instituted a programme of 'Quantitive and Qualitative Monetary Easing', QQE) [14], with the aim of intentionally de-valuing (inflating) the Yen till it achieved the desired 2% inflation rate. They also aimed to lower the risk-aspect of interest rates by underwriting. (Basically, by systematic buying of Japanese government bonds (JGBs) and exchange-traded funds (ETFs) at the rate of some 60 Trillion Yen per annum.).

By the end of 2013 the BOJ had achieved an annual inflation rate of 1.6 %, so in 2014 the board decided to scale up the QQE by some 20% to 80 Trillion Yen per annum. They ended 2014 with an annual inflation of 2.4% [15].  However, the CPI inflation rate again slumped to near zero in 2015 [15]. On the other hand, the economy did start to improve; job vacancies appeared, and wages rose. However, after 15 years of deflation  the expectation that prices would remain static had became deeply embedded in the national psyche. Bank deposits placed at the BOJ were charged with a negative interest rate of (-0.1%) from Jan 2016 till March 2024; only reaching +0.75% in Dec 2025. (Presumably in an attempt to drive the saved money into investments.)

Debt:GDP (as %)

In the 1970 Japan had the lowest ratio of Debt:GDP of all the G7 economies; since 2000 it has had the highest ratio. In 2020 (with COVID) debt reached 250% of GDP. It does seem odd that a relatively wealthy country like Japan should run a fiscal deficit (spending more each year than it raises in tax). But it is relevant to note: [a]  it has (till recently) enjoyed very low interest rates, and [b] 90% of Japan's government debt is owned by Japanese. The benefit of low interest rates needs no explanation. The fact that most of the Japanese debt is held domestically has two benefits.  Institutional Japanese holders are unlikely to attack the Yen in the way that predatory foreign owners can (See Greece in 2011). And the interest paid on the debt is not lost to the country; it could even be viewed as part of GDP.

Diverting Savings to Investment.
From Jan 2016 (till March 2024) deposits placed at the BOJ were charged with a negative interest rate of -0.1%. Presumably this was an attempt to drive the money saved in bank accounts into productive investments. The economy did recover; GDP has maintained a small annual growth from 2013 till 2020 (COVID!). The Silicon Review of 22 Dec 2025 wrote [18]: "The Japanese government is looking to mobilize a portion of the nation's US$ 7 trillion pile of household savings to create fresh demand for its bonds."

The buildup of the 1,324 Trillion Debt.
According to Wikipedia, Japanese debt rose steadily from the bubble-burst of 1990 until COVID: "At the end of March 2025, the general gross debt of the Japanese Government was 1,324 trillion yen, or 234.9% of the country's gross domestic product" [17]. It is now declining. The longer-dated bonds in particular are not selling well; and, as their market price sinks, their apparent 'yield' (or return per annum) rises.

Conclusion.

Japan has struggled to raise its inflation rate to 2% while most other countries have struggled to lower their inflation rate towards 2%. If it ever succeeds, will it have lost something distinctively Japanese?

References:   

[1]  https://notayesmanseconomics.wordpress.com/2025/12/24/2025-and-all-that-the-economics-version/
[2]  https://conversableeconomist.com/2025/12/23/how-does-japan-sustain-such-high-government-debt/
[3] https://worldpopulationreview.com/country-rankings/debt-to-gdp-ratio-by-country 
[4] https://fred.stlouisfed.org/series/IRLTLT01JPM156N 
[5]  https://occidentis.blogspot.com/2014/06/interest-rates_4.html
[6]  https://www.statista.com/statistics/661908/japan-consumer-price-index/
[7]  https://www.bis.org/review/r240527d.pdf    
[8]  https://internationalbanker.com/finance/japans-elusive-goal-of-savings-to-investments/
[9]  https://www.ifo.de/DocDL/cesifo1_wp8927.pdf
[10]  https://en.wikipedia.org/wiki/Japanese_asset_price_bubble
[11] https://www.econstor.eu/bitstream/10419/195770/1/1663195218.pdf
[12]  https://en.wikipedia.org/wiki/Nikkei_225
[13]  https://www.in2013dollars.com/japan/inflation/1956?amount=100
[14]   https://www.boj.or.jp/en/mopo/outline/ref_qqe.htm
[15]  https://www.inflationtool.com/rates/japan/historical
[16]  https://www.reuters.com/business/finance/why-is-boj-tweaking-its-buying-japanese-government-bonds-2025-06-17/
[17]  https://en.wikipedia.org/wiki/National_debt_of_Japan
[18]  https://thesiliconreview.com/2025/12/the-silicon-reviewdec-2025japan-eyes-7t-household-savings-bond-demand

Digital ID cards and the BBC

 Digital ID cards and the BBC

Dear BBC, 

    You have not covered yourselves in glory this morning (14th Jan 2026) over the question of Digital ID cards. I have not heard a single argument either in favour or against. 

    I have many digital ID cards: my passport, my driving licence, my bus-pass, my senior railcard. In addition, I have an identifying number for my social security, and another for my National Health Service. I have no objection to these or any new card in terms of 'privacy' or 'big-brother'. But the issue is not about me. It is about someone who turns up on the beach at Dover without a passport. 

    As far as the BBC is concerned the only story they felt safe with was a question of a 'U'-turn by the government. Are we really so trivial? 

    I can see that a back-bench Labour MP might wonder how ID cards are essential one day but not the next. But why is there a dilemma for such an MP between party loyalty and dignity. Why do they not listen to the arguments for and against and vote for what they think is right for the country? Derrh!

    But perhaps Lord Blunkett is right; the government is seriously weak in communicating with its back benches; and indeed with the media and the public. 

    I can tell you what I think when I have heard the arguments, for and against.