Maths Tryout

Here I want to try out mathJax in a blog.

$$\sqrt{\vphantom{I}} n \bigl(\hat\theta_{\text{MLE}}-\theta_0\bigr)~\Rightarrow ~ \mathcal N\,\bigl(\, 0\,, \mathcal I(\theta_0)^{-1}\bigr)$$

That was a test of MathJax: properly displayed (?) mathematical formulas written in standard LaTeX. Please let me know how well it displays - if at all - in your browsers. The html code of the above formula consisted of the following ordinary LaTeX code, between double dollarsigns:

\sqrt{\vphantom{I}} n\bigl(\hat\theta_{\text{MLE}}-\theta_0\bigr)~\Rightarrow ~ \mathcal N\,\bigl(\, 0\,, \mathcal I(\theta_0)^{-1}\bigr).

The results on my MacBook: Safari - appalling; Firefox - excellent; Chrome - appalling; Opera - good ... till I replaced \sqrt{n} with the construction \sqrt{\vphantom{I}} n. That converted "appalling" to "poor". Neither Safari nor Chrome seem to know that text , numerals and Greek symbols are not usually italic, inside of mathematics. Safari on iPad is good.

Here's another example: Dorota Dabrowska's product limit representation of a multivate survival function,

$$

\Pr(T_E\gg t_E)~=~\prod_{A\subseteq E}\,\,\prod_{s_A\in(0_A,t_A]}\, \Biggl(\prod_{B\subseteq A}\Pr\Bigl(T_{A\setminus B}\gg

s_{A\setminus B}\Bigm|T_A\ge s_A\Bigr)^{(-1)^{|B|}}\Biggr)

$$

The whole thing is set up by including the following instructions to run a java script:

< script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">

< /script>

I added a space after the left-angle-bracket so that the html tags would not be recognised as such!

Kevin Sweeney Is Innocent (since not proven guilty)

Here's a draft report I am writing for Sweeney's lawyers. It is all so awfully familiar...

Scientific Conclusions Following from Study of TNO “Experiments” and other “Scientific Evidence” in the Sweeney Case


Richard Gill
Faculty of Natural Sciences
Leiden University

30 May, 2007

Summary: the case must be reopened


Contents

1. Scientific judgements on key scientific evidence in the Sweeney case
2. Proviso
3. My credentials
4. Conclusion





1. Scientific judgements on key scientific evidence in the Sweeney case (especially concerning experimental design and interpretation of statistical evidence and probabilities)

* By the nature of their design, the TNO experiments bear no relevance whatsoever to the question whether or not the fire could have been caused accidentally since no experiments were done simulating the situation in which a fire was accidentally started by a smouldering cigarette unaided by deliberate application of large quantities of liquid fuel.

* The experiments are spectacularly badly designed for answering the question whether or not the fire could have been caused by arson since factors which surely have enormous influence on the course of a fire and the kind of damage it makes were not reproduced (temperature, humidity, ventilation, ....).

* The likely cause of death (CO poisoning) and the position and stance of the body are more consistent with a slowly smouldering fire which only “flashes” into a conflagration later, most probably after the victim was unconscious, than with a major fire started by igniting fuel.

* The fact that witnesses did not notice a raging fire, and the evidence of the time of fire alarms, is more consistent with the scenario of the defence, than with the scenario of a fire caused by deliberate ignition and rapid combustion of 8 l of fuel

* The fact that a witness reports having smelt a fire when questioned again, a year after the accident, but did not report this when questioned immediately after the fire, raises severe doubts into this witness’s reliability and the reliability of the method of interrogation used by police investigators

* The reports of the state of the jerry-can and other fuel containers strongly support the hypothesis that these containers, and especially the jerrycan, were open and empty when the fire started. Others were full and still sealed. This matches exactly the scenario in which a fire starts accidentally in a place where people had been recently been decorating.

* The fact that on autopsy, no trace whatsoever of flammable liquids were found in the body of the victim, further supports the hypothesis that large quantities of flammable liquids were simply not present, let alone deliberately used.

The defendant’s story concerning the likely course of events is completely consistent with all scientific evidence presented to the court with which I am so far familiar. I include here also the results of the TNO experiments.

The scientific evidence contradicts at vital points the scenario put forward by the prosecution. The TNO experiments are essentially irrelevant (they give no support for or against the prosecution’s scenario).

Since not many people murder their wives, while accidental fires (causing deaths) caused by smoking in bed, in particular in combination with drinking or emotional stress, are extremely common, and since Dutch police and public prosecutors have a well established track record of manipulating scientific evidence in order to secure a conviction once they are just a little bit confident that a conviction is possible, the balance of the probabilities points to Sweeney being completely innocent. Moreover, complex scientific evidence is habitually misinterpreted by scientific laymen and in particular by many lawyers and judges.

Since the defence has had three chances (though whether they were fair chances or not, is another issue) the burden of proof now lies, legally speaking, on the defendant. That is why I must emphasize that all the scientific evidence not only supports the case of the defendant, but also discredits the case of the prosecution. (The prosecution is now the “defendant”; Sweeney now has to show beyond reasonable doubt that the prosecution is guilty).

I hereby state that it is scientifically established, beyond any reasonable doubt, that the prosecution in this case is guilty, aided by the police investigation, and in collusion with incompetent and prejudiced “scientists” (employees of state supported “scientific research organisations”) of having misinterpreted and manipulated scientific evidence in order to mislead judges and force an unsafe conviction. To support my case I will mention that it is beyond reasonable scientific doubt that no one was murdered by anyone, let alone by Sweeney. This conclusion was long ago inescapable to any scientist prepared to look beyond the borders of his own narrow discipline and apply his or her scientific outlook and training also to the so-called scientific evidence presented by other witnesses, and in particular, to consider the mismatch between how that evidence has been put into the public domain by police investigators and other agents of the prosecution, and its actual content.

It is also evident to me that a British subject would have been bewildered by the conduct of the trial, which was against all reasonable Anglo-Saxon expectations. The defence were not given a fair opportunity to find decent contra-expertise while the prosecution has all the scientific institutions of the state at their disposal. It is now well documented that scientists in Dutch national “scientific” institutions are extraordinarily (from an Anglo-Saxon point of view) wary to criticise work by colleagues, and that they have a child-like faith in the integrity of the judicial procedures in this country. Experts I have spoken to knew very well that the evidence “from their field” which was presented at the trial was deeply flawed, but they had heard the “propaganda” from the prosecution concerning the strength of evidence of other kinds, as well as the gossip and rumours spread by the prosecution concerning his character, which made them believe that Sweeney was guilty anyway, so no need to get into trouble. “Divide and conquor”. The arrogance, self-righteousness, appalling ignorance, and paternalistic attitude of a board of Dutch judges has become legendary in recent years.

2. Proviso

At this point I have clearly not studied all the scientific material presented at the trial. I have studied the key items (the key items according to the judge’s own summing up). In that summing up I discern major errors of logical reasoning including the infamous “prosecutor’s fallacy”. From a decent, unprejudiced and intelligent person’s point of view, the conviction is evidently “unsafe”. In the Anglo-Saxon world (and I would like to say, the civilized world) this should be sufficient grounds for a re-trial, at the least.


3. My credentials

I am a scientist, mathematician, and statistician, with more than 30 years experience contributing to scientific research, analysis of observational data and experiments, and design of experiments, in engineering, medicine, biology, social sciences, language and literature, and psychology, among many other fields. I have large experience in evaluating and comparing scientific research proposals, applications for research positions, and submitted scientific papers, again across a multitude of disciplines. I am regularly asked to sit on evaluation committees for international, science-wide project application review committees, and scientific evaluations of departments or institutes (again, science wide). I have taught scientific method to non-scientists.

I was elected a fellow of the Institute of Physics though I am not a physicist, though I have collaborated with both experimental and theoretical physicsts. A paper of mine from 1982 contributed to a breakthrough in development of statistical methodology for clinical cancer trials and probably has saved hundreds if not thousands of lives through improvement in development of new cancer treatments. It is one of the most cited papers by a Dutch scientist. I became elected a member of the Royal Dutch Academy of Sciences (I am the only mathematical statistician among the so-called “active” members, and one of only 10 mathematicians in the whole academy. Election is by the combined membership of the natural-sciences sections of the academy). I am currently president of the thousand-strong Dutch Society for Statistics and Operations Research, whose members include people working in industry, business, advertising, management; people who use statistics in biology, medicine, forensic science; as well as academics in all university faculties. My curriculum vitae and publication list are publicly available on my web site at Leiden University. I have published in the Proceedings of the US Academy of Sciences (this comes just after Nature and Science, in the usual rankings) on interpretation of results from experiments in quantum physics, designed to settle the still unresolved controversy between Einstein and Bohr. I have broad cultural interests (can, and do, read half a dozen languages). I am passionately interested in the role of science in society and I become passionate when confronted with abuse of science, whether in a good cause or a bad one. As is well known, the sciences of probability and statistics are especially prone to abuse and misunderstanding, though they are of crucial importance in modern society (finance, medicine, biology, physics, climatology).

Apart from this generalist background, I have deep understanding of the use and meaning of statistics in both experimental and observational studies, in logical reasoning and mathematical modelling, on the distinction between correlation and causation (I have published on causality and participated, on invitation, in multidisciplinary scientific conferences on causation).

4. Conclusion

The case must be reopened.


Richard D. Gill
Faculty of Natural Sciences
Leiden University

30 May, 2007

Lies, damned lies, and legal truths

Lies, damned lies, and legal truths

If there’s one thing which makes me sick it’s having people always quote “Lies, damned lies and statistics” at me. Particularly if they are lawyers. Sometimes they refer to Mark Twain, sometimes to Disraeli. Well, Disraeli is apocryphal; Twain was actually misquoting the famous British Prime Minister George Canning who about 1820 said “you can prove everything with statistics except the truth”. (Canning was probably the best PM Britain ever had, but his term was one of the shortest, since he died “young” from a cold caught while at a funeral in the rain).

I have been looking for a long time for a counter “bon mot”. And I think I have found it. In the Lucia de Berk case, a Dutch judge said at the appeal (and she was not corrected by the supremum court, even though this strange fact was pointed out to its learned members) “it has been scientifically indisputably proven that ...". What this judge actually means is that, of half a dozen so-called scientific experts (one just needs “prof.dr” in front of your name and some professional activity which is vaguely related to the scientific field under issue; your “scientific” advice could have been based on a quick Google search the evening before) one could be found who said that it was their scientific opinion that ... It is quite irrelevant that five possibly better qualified experts thought that it was not scientifically proven at all.

My legal friends say that this is perfectly correct because, of course, notions of legal truth and legal facts are not the same as scientific truth and scientific facts. And, sorry, clearly not the same as man-in-the-street’s truth and fact. I guess this is why it takes so long to study to be a judge or a lawyer, and why lawyers have such big salaries and judges have a job for life.

The judge’s written summing-up, perhaps the longest in Dutch legal history, available on internet but fortunately for Netherland’s international reputation only in Dutch, is stuffed full of similar stupidities, but one can only know that they are stupidities, if one has access to the documents submitted by all the experts and “experts” at the trial, and they are obviously not public. One thing which highly amuses me is that a law professor with a hobby in PC’s (he gives Excel and Word courses to fellow lawyers) was an official expert in statistics and was able to confirm the validity of another “expert’s” statistical computations, a guy who quit statistics two years into his PhD programme, thirty years ago, and is now also a law professor. Of course these guys are very decent fellows who are able to explain their findings to other legal minds very well indeed.

Be that as it may, from now on I want to promote the quotation “lies, damned lies, and legal facts”. It would evidently be a legal fact that this was said by a well known British prime minister, if I (a professor in statistics) say so in a Dutch court. However, I have been heard to say to my friends that I am really worried that this country is in danger of becoming a banana-republic (nonsense – we don’t have widespread corruption yet, do we? Anyway, it’s a monarchy!). This means that I am a Danger to the State and will probably never be allowed to give expert evidence in a Dutch court.

I can tell you that it is now a scientific fact that “lies, damned lies, and legal truths” is a quotation by a well-known Anglo-Dutch scientist which correctly expresses the current state of the use of scientific evidence in Dutch law courts.

The past is particles, the future is a wave

Here are my thoughts on the foundations of quantum mechanics, life, the universe and everything. They are shamelessly stolen from many sources without any guarantee that their original owners would authorize this representation of them.

I think that only detector clicks in the past are real. The future is a wave of possibilities, whose probabilities are determined by quantum mechanics. We and our consciousness reside on the boundary between the past (particles) and the future (a wave of potentiality). As the present moves relentlessly forward the “past” crystallizes out of it, randomly. There is now no measurement problem, no non-locality problem, no problem of interpretation. The probabilities are for real, the past is real, the wave function is objective and non-localized since computed from the whole past. Consciousness resides on the interface and is localizable. (cf. Belavkin; cf. Pirsig [Zen and the art of motor cycle maintenance]).

Why is Nature like that? Reality is discrete, finite. The only way to simultaneously have it invariant under continuous rotations, shifts is to make it random - probabilities can be invariant, continuous, ... This leaves us with QM as the only possibility. (cf. Helland)

Bell's fifth position

Gerard 't Hooft is searching for a deterministic and local theory to underlie quantum mechanics. By Bell's theorem this should not be possible, but the theorem does have some small print. 't Hooft knows this and says: "one does not have the freedom to do arbitrary measurements at the Planck scale". However, this is no escape, because we still appear to have the freedom to do Bell-type experiments at the macroscopic level, and 't Hooft's theory has to accommodate those experiments too. I am not happy with the solution that the photons know in advance how they are going to be measured since the experimenter's choices were predetermined at the time of the big bang!

I propose another reconcilation of 't Hooft's theory-in-spe with the success of quantum mechanics at explaining the real world: a Bell-inequality violating loophole-free Bell-type experiment can never be carried out because quantum mechanics itself prohibits the required initial conditions - the feasibility to create "to order" a bipartite system of two well separated and well localized components, in close to a Bell entangled state. One could think of this as a kind of uncertainty relation.

I call this point of view "Bell's fifth position" since John Bell listed four possible positions to hold in the light of the theoretical violation of his inequality by quantum mechanics. It turns out that several others hold the same or a similar view : Emilio Santos and Iain Perceval, to mention but two. Bell admitted in a letter to Santos that this fifth position is a logical possibility, though Bell said that he did not expect it to be the answer.

To summarize: it could be that quantum mechanics itself prevents us from carrying out a definitive experiment to prove that there cannot be a local and deterministic theory from which QM emerges. So we will never know; 't Hooft's quest is not doomed from the start; a quantum computer may never succeed in factoring large integers, ... .

To physicists who think this is all stupid I would like to say: well, go ahead then, and perform a loophole free and succesful Bell experiment.

Time, Finite Statistics, and Bell's Fifth Position

http://arxiv.org/pdf/quant-ph/0301059

David Anthony Gill 28/9/26 - 5/8/06

Eulogy:
David Anthony Gill
28 September 1926 -- 5 August, 2006

In a few weeks from now my father would celebrate and enjoy his 80’th birthday --- towards the end of a full life in which he played many rôles --- Father, (...-in-law, grand-...), husband, ( lover ), son; scientist, student, teacher; a churchwarden and a churchgoer; a colleague, a friend; a patient in a psychiatric ward ... a man and a human being. Friendly, warm-hearted, rational, passionate, social, private. Anxious to please, humorous, independent. (A man of contradictions?)

Let me outline the facts of this life and then try to weave some threads together.

David Anthony Gill was born on the 28th of September, 1926, in Croydon, Surrey. His young father, Richard Harold Gill, was an up and coming city man with Northern Assurance (his father was a taxi driver). David’s young mother, Marjorie Spicer, had also worked for Northern Assurance but had naturally quit her job when she married.

The Gills moved when David’s sister Jane was born and he was about 4, to Carshalton Beeches. There, the family attended a church called the “Good Shepherd”. Another family --- a large family of 9 children --- came to Carshalton Beeches in 1935; and also attended the Good Shepherd. The youngest daughter was my future mother Pauline Hodgekinson.

David did well at school, though not at sports: he was more the scientific type (shortsighted, glasses...). But he was a social fellow and a handsome young man and he played Joseph in the church nativity play in 1941 when he was fifteen. My mother had already set her sights on him but to her chagrin did not get the rôle of Mary; however, as Anne, she was positioned well enough; they started walking out together, with a first kiss under a holly tree on a hillside field in May 1942.
I said to my mother: May 1942! The battle of Britain? ... air-raid shelters? Well, it was May 1942 and two teenagers were in love and nothing else made much impression on them at the time.

At the age of 17, in 1943, my father would in the course of things have been called up, but England needed scientists and he went up to Cambridge to study physics. It seems that his passion for my mother absorbed more of his energies than his interest in science, and he only obtained third class honours in the finals. In the meantime my mother was in the Wrens doing very hush hush stuff at Bletcheley Park.

In 47 David began two years national service, while Pauline was becoming a chartered physiotherapist at Guy’s; they married in October 1950, living first in a flat in Carshalton. Their first son Richard was born in 1951, and in 1953, more or less simultaneosly with the birth of Nicholas, this young family moved to a new house in Godstone.

Jessica and Caroline, affectionately known as ‘the girls’ were born at two yearly intervals thereafter. In the meantime Father had got a job as physicist in the Paper Research institute at Kenley, moving to Water in Redhill a few years later, where he was the third to be hired at a brand new research centre.

At Redhill he happily burst plastic pipes under carefully controlled experimental situations and he loved to show me his old bath tub in a shed at the back of the big old house (the WRA)filled with measuring apparatus and excitingly contorted and/or shattered pipes.

In 61 the institute, growing still, moved to Medmenham, and my family to Frieth. By 67 my father was deputy director and probably not bursting so many pipes in old bath tubs as before; maybe this explains his move to Wavin around 70.


In the meantime ‘the smalls’ were added to the Gill family: Deborah, born in Spring 63 and Stephen in 65. At one point Frieth school was educating a whole pint of Gills, a staggering 10% (almost) of the school’s population.

At Wavin my father was supposed to be located near a new factory in Dublin but my mother certainly vetoed that move; however, the company so much desired his services that he was allowed to work from an office in London, from which he made frequent business trips all over the world, making long-time and deep friendships in places as far apart as Japan and Holland. (The latter, with unforeseen and far-reaching consequences).

My mother did not quite appreciate these absences (apart from the odd excursion herself) and both were very happy when Father became Deputy Assistant Director at an even bigger Water Research Association back in Medmenham in 1974. However, in 79 water was merged with sewage and clearly there were too many deputy assistant directors around; my father took early retirement under excellent conditions. (He was always more interested in how to optimally distribute water, etc., than in research institute politics).

Against the emphatic advice of all his children he became a science teacher at a Secondary Modern in Amersham in 1979. His predeccesor had had a mental breakdown, there was nobody there to coach him. Not to the surprise of his children, this did not work out ... and Father experienced his own first ‘wobbly’ as it was known in the Gill family (his mother and sister actually also had a number of serious depressive periods). Fortunately he was able to escape to a brick research institute and happily started using his experience in Holland, where people actually pave roads with bricks, to serve society in a new way. But then recession hit the brick business, as everywhere else, and it was ‘last in first out’.


A succession of small jobs followed and a growing interest and passion in personal computing fuelled by his belief that personal computing, and later internet, would lead to a better society. Via computer classes at Finnamore Wood Borstal Camp he eventually became lab technician at Wycombe High School for Girls --- Doyne North was required to write a letter of reference --- where he happily in those early computing days set up a computer lab and became an essential and irreplaceable member of staff.

In 1994, at the age of 68, an unfortunate incident occurred. Badly cutting his hand on some broken glass in the biology department at school the bureaucracy discovered that he was several years past official retirement age. Reluctantly the school had to terminate his employment.

Well, this just gave my father all the more opportunity for fulfilling his mission and satisfying his interests, he became more and more involved in church and parish and synod affairs; and in all these spheres he was appreciated and loved for his lateral out of the box thinking, practicality, knowledge, aimiability, humour, ... [Story about Japanese tourist and standing burials]. He brought these qualities in the same way and was loved for them just as much in the spheres of family (both immediate and extended ...) and hobbies --- whether sailing, camping, footpath preservation ... or whatever.

Time was taking its toll. Mother and Father ‘downgraded’ to Marlow in 92. Still there was a round the world trip, an aerial excursion to view the Aurora Borealis, holidays at their beloved Ravello on the Amalfi coast. Father had some heart trouble and other ailments and coped with these by taking a scientific attitude and producing beautiful graphs of his heart rhythms plotted over many days which surely must have amazed his doctors.


Five years ago a spell of shingles left him with incessant head-aches and difficulty concentrating. A year and a half ago he was ‘switching off’ as my Mother said, retiring from various committees, travelling less, putting his business affairs in order, but still inquisitive, and planning new excursions. One of his last passions was his father’s diary which he dictated into his computer and converted into a splendid web site complete with old and new maps of grandfather’s hike in Dorset in his courting days [there is presently a link to this site from http://gill1109.spaces.live.com].


A bit more than a year ago father amazed my mother by saying to the doctor at a checkup ‘I think I’m in really bad trouble’. She (the doctor) detected symptoms of approaching dementia but a battery of tests seemed to point to a classic and therefore treatable depression. Father was admitted to a psychiatric ward in High Wycombe last September and spent his last year there and at Stoke Mandeville.


[[ Rest of speech was ad libitum. I wonder if Dennis the sound-man made a tape of the whole thing? Anway: I attempted to sum up, using some personal experiences with my Father during the last year. [The broad smile he gave me when I came, for what was to be the last time, to his room; his renewed attempt even then to explain his struggle to rationally understand and then communicate his situation by reference, using his hands, to the Möbius strip --- all twisted up]. A man of contradictions and singular unity and integrity. Complex and simple. Who loved and we loved and we will love and remember. ]]




Richard Gill

Marlow, 2 September 2006