Friday, 31 December 2021

Sentences and Sentencing

 Sentences and Sentencing

Thomas Hughes and Emma Tustin (the father and wicked stepmother of murdered 6-year old Arthur) have been handed sentences of 21 years and 29 years respectively. Those seem stiff enough. But the Right Honourable Suella Braverman, in her capacity as Attorney General, has apparently asked that the sentences be reviewed, as inadequate to the severity of their crimes. 

Another prominent court case this week is the guilty verdict on Ghislaine Maxwell for 5 crimes against under-age girls. Sentence has not yet been passed but she is said to be facing between 40 and 65 years in prison . 

        It is quite possible that the sentencing norms in the USA and the UK are radically different, and any comparison a mistake. And I am ignorant of the details of both cases and unqualified to judge the appropriateness of these sentences. But I do feel that the crimes of these two against the murdered six-year old Arthur are a great deal worse (more beastly, inhuman, unbearable) than the 5 crimes of Ghislaine Maxwell. They are enormously worse; in the way that dying is worse than having a headache. 

I feel that the very real, and decades-long pain, suffered by the girls and young women ‘befriended’ by Maxwell and ‘cuddled’ by Epstein, may be on a par with that suffered by millions upon millions of women around the world and throughout the ages; child-brides, battered-wives, arranged or loveless marriages, under-age daughters of drunken fathers. I am not belittling either pain; just trying to get things into perspective. 

Maybe there is some politics involved in the Maxwell trial. Maybe she is standing surrogate for many other cruelties that have long gone unpunished. 

        But maybe the sentencing of Hughes and Tustin also contains a political element. They may be paying for our guilt, yours and mine,  that this crime was allowed to happen in our country, our town, under our very noses. 

        However, from a restorative point of view, both sentences seem to me to be bizarre.

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Monday, 29 November 2021

The Cough Reflex and its Rôle in Virus Transmission.

The Cough Reflex and its Rôle in Virus Transmission.

(According to the old saw: “Coughs and sneezes spread diseases.”)


The cough reflex involves (a) triggering, or activation of a nociceptor, (b) an afferent signal in C-fibres of the vagus nerve to the brain, (c) efferent signals to the diaphragm and other muscles, and (d) a rapid muscular contraction [1]. 

We can all distinguish between a “dry” cough (when there seems nothing in the trachea or larynx to cough up), and a “wet” or “productive” cough (when phlegm or mucus is moved up by the blast of air travelling, we are told, at ≤ 600 mph.) It is the former that I am interested in. The brain has some (but limited) ability to suppress a cough, as also do placebo drugs [1]. But those who have struggled to suppress a cough during a concert or when sharing a bed, know that it is extremely difficult. 

It has probably occurred to many that virus-infected mucous membranes generate a cough-trigger in some simple or roundabout way [2]. A virus that can trick its host into a cough (or a sneeze) could spread infectious virions widely, and thus increase enormously its chance of finding a new host. But the possibility that the corona viruses target only ACE2 precisely because ACE2 is crucial to the cough-trigger is an hypothesis too good to pass over. Is there a link between ACE2 and the cough reflex? Of all the cell-surface proteins to which the virus could bind, why does it  choose the ACE2?

This led me to wonder what is the cough-trigger, and what part is played by an active viral infection. Dipping into the medical and scientific literature brought up three important areas for further study: Bradykinins, Angiotensins, and ACEs.

Bradykinins, Angiotensins, and ACEs

Bradykinin is a nona-peptide (called Bk(1-9)), which can come with an additional N-terminal Lys residue (here called Bk(0-9)), or lose the C-terminal Arg becoming the more active Bk(1-8) (also called des-Arg9 Bk). Active bradykinins work via two G-protein-coupled receptors called B1 (especially linked to Bk(1-8) and strongly induced during inflammation), and B2 (activated by Bk(1-9) and constitutive, hence the ‘normal’ receptor).[3]

Angiotensins [4] are another small family of peptides, unrelated to the bradykinin sequences other than in size, charge, and having P and F in positions 7 and 8; see Table 1 below.) Angiotensin I is an inactive decapeptide (Ang(1-10)). It is converted to active (vasoconstrictive) angiotensin II (Ang(1-8)) by the removal of the c-terminal dipeptide. [It is probably irrelevant to this story, but angiotensin II raises blood pressure, while bradykinin(1-8) lowers it.]

ACEs, Angiotensin-Converting enzymes [5], are integral-membrane-bound proteolytic enzymes capable of cutting peptide chains. There are two related proteins; ACE1 and ACE2. The former converts angiotensin I (the deca-peptide) to angiotensin II (the octa-peptide), by cutting off the C-terminal dipeptide. [It also converts angiotensin(1-9) to angiotensin(1-7).]

ACE2 has become famous since January 2020 as the unique and highly specific binding site of the SARS-CoV-2 virus. It is present in a wide range of tissue surfaces, but especially in kidney, the endothelium of the gut and blood vessels, the lungs, and in the heart. It converts angiotensin(1-10) to angiotensin(1-9) by cutting off the C-terminal Lys. But it also degrades active Bk(1-8) to inactive Bk(1-7) and other peptides [6]. [It is a quaint irony of history that ACE1 cuts off a dipeptide while ACE2 cuts off a single amino acid residue.]

Table 1 Peptide Sequences (in one-letter code, showing net charge).


Bk(1-9)   RPPGFSPFR ++ Active, vasodilator, B2

(Bk(0-9) LRPPGFSPFR +++ ?B2)

Bk(1-8)   RPPGFSPF + Active, pain, B1

(Bk(0-8) LRPPGFSPF ++ ?B1)

Bk(1-7)   RPPGFSP + Inactive,


AngI(1-10) NRVYIHPFHL +++ Inactive

AngII(1-8) NRVYIHPF ++ Active vasoconstrictor

Ang(1-9) NRVYIHPFH +++ ?

Ang(1-7) NRVYIHP ++ Less active, competes AngII(1-8)

Is Bk(1-8) the Cough-Trigger?

There are three bits of evidence in favour of the hypothesis that the binding of virus to ACE2 might directly trigger cough by allowing the build up of Bk(1-8). 

    (1) A distinct and well documented type of “dry cough” is observed in 15-20% of patients taking ACE inhibitors to counter their high blood pressure [1]. These block the generation of active AngII(1-8), but also block the inactivation of active Bk1-8, which consequently builds up.Though not rigorously confirmed, it is widely assumed that this raised bradykinin level causes the cough. 

    (2) Raised bradykinin levels are found in virally infected mucosae [3]. 

    (3) Cough-Hypersensitivity-Syndrome, especially common in women [1,9] and in patients from south-east asia [1], can be induced in animal models by local application of bradykinin. 

This hypothesis requires that virus binding (and subsequent inversion into the cell) blocks the action of ACE2 in deactivating Bk(1-8) to inactive Bk(1-7). The raised levels of Bk(1-8) suggests that virus has that effect.



[2]  Morice, A.H. Chronic cough hypersensitivity syndrome. Cough 9, 14 (2013).








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Wednesday, 10 November 2021

"Committee on Standards" -- Bad Government

Is the sleazy Tory tail trying to wag the dog?

In the House of Commons, on Wednesday afternoon 3rd. November, there were two divisions, which both went to the Tories (though some rebel Tories voted with the opposition and there were many abstentions). I refer to divisions 99 (Andrea Leadsom’s amendment regarding Owen Patterson) and 100 (On the ‘Committee on Standards’). The amendment was accepted 250:232, and the motion carried by 248 to 221. 

The Speaker of the House declared that the motion was carried, and that is how the news media reported the event. But Hansard lists the party affiliation of the members voting both for and against the motion. And the ‘Commons Library’ has a good article on Turning Votes into seats, which shows that the single Green Party MP represents 866,000 electors  while the single Alba Party MP represents only 21,000 electors. The full results of the December 2019 election are given in Table 1 below, and that information is applied in order to correctively weigh division 100 (in Table 2).

Following this train of thought it is clear that the Tory amendment and motion were defeated by a large margin; the representatives of 9.316 million electors voted for the amended motion, while the representatives of 14.433 million electors voted against the motion. 

In theory, the concept of democracy remains fundamental in British politics. In theory, it is not the army that decides our laws, nor big business, nor the newspapers, nor the Crown, nor the government, nor the Law Courts; it is the people; via their representatives in parliament. 

If there is any vestigial interest in fairly representing, in parliament, the balance of opinion in the United Kingdom, I think this method of assessing the result of parliamentary divisions, which might be called “corrective weighting”, should receive much wider recognition [1-4]. 

What is the relevance of a 248:221 governmental victory in the House, when the government suffers a 9.316 million:14.433 million defeat in the country?

Table 1

Table 2

Thursday, 30 September 2021

"Excluded volume" between close-packed spheres

 "Excluded volume" between close-packed spheres  

I remember reading that the 'theoretical' limit on volume density for close-packed uniform rigid spheres was circa 0.74, (so that in a bucket of marbles the volume of trapped air is 26% of the bucket volume.). Indeed, the Wikipedia article on "Sphere Packing" tells us that Johannes Kepler thought that the densest possible packing would be 0.74048 (i.e. π/(3√2)), a result confirmed by Carl Friedrich Gauss 2 centuries later. Further, that Thomas Callister Hales claimed a "proof" of Kepler's conjecture which a referee found 99% convincing. 

 I thought I ought to be able to calculate that myself, now that I have retired and have the leisure time needed for such an non-essential occupation.


First I considered laying pennies on a flat surface, and was delighted to find that exactly six discs can be fitted round a central disc such that all are touching (Fig. 1).

Next, I considered a football (radius r) closely fitted inside a cubic container (side 2r; Fig. 2). 

The volume of the ball (Vb) is Vb = 4 π r3/3; that of the container (Vc) is Vc = (2r)3 = 8 r3. So the volume density (Vd) of the container filled by the ball is: 

    Vd = Vb/Vc  =  (4 π r3/3)/(8 r3)

Vd = 4 π / 24

Vd = π/6 = 0.5235987756 (when rounded up). 

I concluded that, if many spheres were aligned (touching) in straight Euclidian lines mutually perpendicular in three dimensions, the density would still be 0.5235987756 (and the excluded volume would be 47.64%, or nearly so). This array can be seen as a series of x/y planes stacked one on top of the other in the vertical (z) dimension. Each sphere touches 6 neighbouring balls; 4 in the same plane, plus 1 above, and 1 below. But they can clearly be packed more tightly. 

So I constructed a single plane as follows. First I laid a file of spheres in the x dimension. Then a second file of spheres, but those of the second file do not coincide with those of the first file, but are offset to the right by r, while those of the third file are offset to the left by r (and thus coincide with the first file).  Clearly the centre of a spheres in the second file is equidistant from two spheres in the first file. Indeed, they form an equilateral triangle, side 2r (Fig. 3). 

Drawing a perpendicular (length m in units of r) from the apex to the base, we can use Pythagoras's theorem to calculate m (See Fig. 4 below).

    m2 + r2 = (2r)2 

m2 = (4-1)r2

m = 1.73205081 x r

It is clear that a single layer of this array is more compact than the first array by the factor m/2 (=0.8669254); or more "volume dense" by the factor 2/m (= 1.154700536759). It would be the same if we stacked many layers of the 60º-offset array, such that each sphere touches 6 neighbours in the plane, with one above and one below.

Vd of Loose 3d array = 0.5235987756

Vd of semi-compact 60º-offset array =0.5235987756/0.8669254 = 0.6045997881

But there is more compacting we could do.

Looking down on our single layer of the 60º-offset array (i.e. the marbles in Fig. 3 above), we see that there is a dip formed by 3 contiguous spheres where a sphere of the next layer should lie, touching all three spheres in the lower layer. We can see that there will form a triangular pyramid where every straight line between the apices is of length 2r; indeed a 'regular tetrahedron'. But how high (in the z dimension) is the upper sphere above the 3 lower spheres?

The apex of a vertical equilateral triangle drops a perpendicular of length m to its base, as we calculated above:

m2 + r2 = (2r)2 

m2 = (4-1)r2

m = 1.73205081 x r

But this equilateral triangle is leaning inwards to form one face of the pyramid. The perpendicular line (length p), from the apex to the point on the base equidistant from the three sphere-centres (point e), can be found in the same way; but this was (for me) the most difficult step. I kept getting the wrong answer. It was only after  3½ days that I solved the puzzle. The right triangle we have to solve has hypotenuse 1.73205081 (length in units of r), while the base is not r but Tan(30º) = 0.577350 (in units of r). 

To see this look at the equilateral triangle that forms the base of the pyramid. There is a point (a) midway along one side (so r from either end). A line can be drawn across the triangle to the opposite point. That can be repeated for the other sides. These lines intersect at the point we called e, cutting each line into a shorter and a longer portion. The shorter portion is Tan(30º) while the whole line is Tan(60º). By Pythagoras's theorem:

p2 + (Tan(30º))2 = (1.73205081)2 

p2 =  (1.73205081)2 - (0.577350)2

p = 1.63293936 x r  

If our layers are extended infinitely in the x and y dimensions this compaction in the z dimension will affect the overall volume density of the array:

Vd of compact array = 0.6045997881 x 2/1.63293936 = 0.74048049


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Wednesday, 8 September 2021

Apple versus Google

 Apple versus Google

There is said to be a ‘cold war’ between Apple and Facebook (New Statesman 16-22 July 2021). There may also be a rivalry between Apple and Google. 

I have spent three days trying to get to the bottom of this puzzling problem. My ageing MacBookPro is getting slower and slower. On Monday this week I noticed that it was (in its own words) “Downloading 98,000 emails”. Which is quite daft. And after watching the first 1,000 come down, it was clear that the machine would be out of commission for the whole day. I did not want any of those emails. I do not mind Google storing all my mail (going back 15 years) on its capacious servers; if it wants to do that. But I keep on my MacBook the emails I want to keep, and delete the 2/3 that I do not want.

I found that unplugging the power inlet stopped the nonsense. Then I tried ‘googling’ the problem and found considerable discussion from the period 2017-2019. Thus, an article by Elizabeth Jones from 2019 is titled “Mail App Always Downloading on Mac? How-To Fix” ( She recognised the problem, and tried to meet it, suggesting:

  • Relaunch the Mail app while holding the Shift key on your keyboard;
  • Change your mail account’s setting for storing the Drafts Mailbox Behaviors to “On My Mac”;
  • Take your Mail Account offline temporarily and then take them back online
  • Remove the Mail Account and then add it back;
  • Try rebuilding and reindexing your Mailbox.

Five remedies immediately aroused my suspicions. Why not cut to the chase and use the right fix? But I tried the first 3, setting all my email addresses to “store drafts in a ‘drafts’ folder on the MacBook; with no immediate benefit. (The last two seemed excessively (in medical parlance) "invasive".)

I surfed further, till I came to the suggestion of emptying the Draft Emails box, (easily done but useless), then the deeper suggestion of going to the G-mail site on a web browser and emptying the Draft Emails box there. Now, that was interesting. For there were 2,100 draft emails visible on the browser web-mail site, but none when I used AppleMail’s IMAP approach.

Well, after breakfast, I started to delete these 2,100 drafts. But they only emerged singly, or at best 8 at a time. This was going to be tedious. A draft appeared called “North Downs way”, was selected, deleted, but then up it popped, again; like the Hydra’s head. I seemed not to be gaining on the monster, till I noticed that the number of remaining drafts did reduce each time; 2,000, 1,999, 1998 etc.. Then I twigged! While writing an email, the Apple Mailer records a draft every 20 seconds or so, all under the same name as in the subject line. There may be 20, or 80 drafts of a single email. 

By mid-afternoon I had got rid of 1,100 of my unwanted drafts, but 1,000 remained. 

Some people like “threading” emails into “conversations”, so that if you reply this week to mine of last week they are stored together. I do not. I like my emails to appear in date order, and I had found and unticked the “Please thread my emails” option on AppleMail. With a stroke of genius, I thought to go to the web-mail “settings” and re-tick the threading option there. Now, like ‘Jack-the-Giant-Killer’ each swipe got rid of 50 or 100 drafts all dangling on that silly ’thread’’. In two more minutes the job was done. I had freed up 1 GByte of Google storage space.

But I was now in open country, on my own and ahead of all the boffins and commentators. No one had suggested that the problem was to do with ’threading’ . Could it be that Apple defaults to no-threading, Google to threading? Or did Apple misunderstand Google’s signal for threading? Or, (more sinisterly) did Google deliberately change the signal without telling Apple? They both emerge from the affair a little “muddy”.

I am still bothered by a slow machine. And am highly scornful of the way Apple has messed around with its iCloud (giving me 2, 4, and sometimes 8 copies of each photo). And of its aloof indifference to customers’ problems. And at the way perfectly good hardware becomes obsolete, and needs replacing. 

I hope this train of thought might be useful to some others. 

☆  ☆      

Friday, 3 September 2021

Tom Nairn: Scotland's leading political theorist?

Tom Nairn: Scotland's leading political theorist?

Tom Nairn has been called “Scotland's greatest thinker”, and “Britain’s leading political theorist”, and “by far Scotland’s pre-eminent political intellectual”, all of which sound over-the-top. However, there is no denying that he can claim to be the most prescient prophet of the disintegration of Britain, on the basis of his 1977 book “The Break-Up of Britain”. But who is he, and what has he contributed to political thought in the last 70 years.

Rory Scunthorne’s article in the New Statesman (30 Jul - 19 Aug 2021; from which I take most of my quotes), piqued my interest. But its tedious length and its disjointed stream of inscrutable quotations left me confused and frustrated. So I went to the web. Here below I offer a synthesis; and a conclusion.


    ▪    Born in 1932 in Freuchie, (a small town in Fife, Scotland), where his father was a local head teacher. Nairn attended Edinburgh College of Art, and Edinburgh University where he graduated MA in philosophy in 1956.
    ▪    In 1957, with a British Council scholarship, Nairn enrolled in the Scuola Normale Superiore in Pisa, where he studied politics and encountered the evolving communism of Gramsci, and the strategy of the “long haul”.
    ▪    From 1962, with Perry Anderson in the New Left Review (NLR), he developed a thesis (the "Nairn-Anderson thesis") to explain why Britain did not follow other European nations in their rejection of established religion, and monarchy.
    ▪    He taught at the University of Birmingham (1965-6) and elsewhere.
    ▪    In 1968, Nairn was fired from his teaching job in Hornsey College of Arts, for participation in  a lengthy utopian “sit-in” involving both students and staff. He was clearly shunned by British academic institutions for decades.
    ▪    From 1972–76, with help from a NLR colleague (Anthony Barnett), Nairn was employed in the Transnational Institute, Amsterdam; a non-profit think-tank largely funded by the Dutch Government.
    ▪    He spent 1994-5 at the Central European University (Austria-Hungary) with the sociologist Ernest Gellner, who had argued that Nationalism had helped the development of industrialization.
    ▪    In 1995, he set up and ran (1995-1999) a Masters course on “Nationalism” at the University of Edinburgh .
    ▪    In 2001-2010 he was invited to take up an “Innovation Professorship in Nationalism and Cultural Diversity” at the Royal Melbourne Institute of Technology, Australia,
    ▪    Returning to the UK he became a fellow at the Institute for Advanced Study of Durham University (2009).


He was said to be an excellent cook by a flat-mate in 1970 in Edinburgh. Said also to be “utterly single-minded” yet “resigned”; even “optimistic”. Also “reserved”, and lacking in even the British level of sociability; fiery in writing, but shy in person. He enjoyed Italy, and became proficient in Italian, but also spent time in Amsterdam, Paris and Vienna.


Several ‘periods’ can be discerned, and with each an influencer or colleague.
[1] The Italian period and the romance of communism, Gramsci.
[2] The Perry Anderson period (1962-1965), and the New Left Review. The Nairn-Anderson thesis was that the British state was archaic. The early revolution of 1642-1660 established a consolidated ‘pre-modern’ political structure in England by 1688.  After the Union of 1707 this was inherited by Scotland.
[3] Political period. Nairn was pro-European, and therefore impatient with the UK’s Labour Party which was insular. He joined the Scottish Labour Party (1976) to advocate devolution in a European context (c.f. the 'auld alliance'). His book The Break-Up of Britain (1977, revised 1982) predicted by 45 years the present state of the British union that is ‘Great Britain and Northern Ireland’.
[4] With his coinage “UKania”, Nairn ridiculed the Ruritanian elements that survive in Britain. His anti-monarchical views were concentrated in his book The Enchanted Glass (1988).
[5]  ‘Nationalism’ period. With Ernest Gellner in Vienna, Nairn developed an analysis of Nationalism that extended to post-colonial countries and incorporated the role of myths and artefacts in the creation of national consciousness. He rode this wave in Edinburgh and Melbourne, and is still active in Durham.
[6] All his life Nairn has been a prolific writer. In all, he wrote 14 major books and numerous articles in the New Left Review and the London Review of Books, and elsewhere.


I get the impression of a shy intellectual who benefits from collaboration, but who takes up and develops a thesis with great focus and tenacity. A product of his time and place. So: Scottish; unselfish, indeed actively anti-selfish; anti-privilege, anti-London, anti-Conservative, anti-royalist, pro-Europe; not above using some of the ‘tricks’ of nationalism to further his objectives. Is he Scotland’s pre-eminent political thinker? He maybe the winner, but of an barely contested prize.

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Friday, 27 August 2021

Should we require unanimity of the Supreme Court?


 To the Michael R. Klein Professor of Law, Harvard Law School,

Dear Randall Kennedy,

     I enjoyed your article in the London Review of Books of 21st Jan 2021, and was stimulated by it. You declared yourself to be a ‘Cynical Realist’, believing that the judges of the US Supreme Court are inevitably nothing more than politicians in robes, and are not, in fact, applying 'law' to their judgements.  But I think I am one of the other sort, whatever that is — perhaps a ‘cloud cuckoo idealist’. 
     That is to say, I am inclined to think that, as to the justice of a disputed point, there is indeed a right and a wrong answer, definable in terms of a sufficient number of sufficiently well-trained deep-thinkers. 
     I would suggest that the Supreme Court be required to come to a unanimous decision. (Or at least a 2/3 majority.) If the justices could not discuss their way to a unanimous decision, I would have them sit there hour after hour, like cardinals at a papal election, till hunger drove one side to give way? 
    I do not think that a decision reached in that way would be worse than the predictable and apparently knee-jerk voting of the present Supreme Court? It would reinforce the claim that there exists such as thing as 'Justice'. 
Yours sincerely, 
Ian West

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