Counts of Meek

Sparrows and starlings

The national Big Garden Birdwatch survey took place on 26 and 27 January this year and is aimed at providing a snapshot of the UK's bird population. Nearly 400,000 people counted more than six million birds in gardens or parks. However, the overall number of birds counted in the survey - held in January - has dropped by 20% since 2004. Milder winters mean food is not as scarce and birds do not have to search in gardens, while some species are in long-term decline, the RSPB says.



BBC News on-line, 27 Mar.

Fish may respond to sound - Call them Pavlov's fish: Scientists are testing a plan to train fish to catch themselves by swimming into a net when they hear a tone that signals feeding time. If it works, the system could eventually allow black sea bass to be released into the open ocean, where they would grow to market size, then swim into an underwater cage to be harvested when they hear the signal.

What's next, teaching them to coat themselves in batter and hop inside a fryer?

Yahoo Website, 27 Mar.

The Simplest Law

We need notice at the moment only that the choice of the simplest law that fits the facts is an essential part of procedure in applied mathematics, and cannot be justified by the method of deductive logic. It is, however, rarely stated, and when it is stated it is usually in manner suggesting that it is something to be ashamed of. We may recall the words of Brutus,

But 'tis a common proof
That lowliness is young ambition's ladder,
Whereto the climber upwards turns his face;
But when he once attains the upmost round,
He then unto the ladder turns his back,
Looks in the clouds, scorning the base degrees
By which he did ascend.

It is asserted, for instance, that the choice of the simplest law is purely a matter of economy of description or thought, and has nothing to do with any reason for believing the law. No reason in deductive logic, certainly; but the question is, Does deductive logic contain the whole of reason? It does give economy of description of past experience, but is it unreasonable to be interested in future experience? Do we make predictions merely because those predictions are the easiest to make?

Jeffreys H., Theory of Probability, Oxford Univ. Press, 1961




Lastly, numbers ae applicable even to such things as seem to e goverened by no rule, I mean such as depend on chance: the quantity of probability and proportion of it in any two proposed cases being subject ot calculation as much as anything else. Upon this depend the principles of game. We find sharpers know enough of this to cheat some men that would take it very ill to be thought bubles; and one gamester exceeds anothe, as he has a greater sagacity and readiness in calculating his probability to win or lose in any particular case. To understand the theory of chance thoroughly, requires a great knowlede of numbers, and apretty competent one of Algebra.

cited in:
Geoffrey Grimmett, Probability and Random Processes, OUP, 2005

Incomplete Knowledge

Incomplete knowledge is the only working material a scientist has!



Anyone who says that “the debate is over” has stepped out of science into irrational dogma. In science, the debate is never over. Any idea, however well established, is open to refutation at any time. We are no longer dealing with science once people start saying “the debate is over.”

idlex

Talking about debates being over (but never in science), I was interested to read in the latest New Scientist that two prominent physicists are challenging Einstein’s Special Relativity. Of course the theory has not been harmonious with Quantum Theory for some time now, but attempts to unite the two have generally not tried to revise either, this time they are.

Einstein himself of course was revising Newtonian mechanics, for which ‘the debate had been over’ for many centuries, the proof was conclusive. If the debate on smoking has so far been over for a few years, and the debate on global warming for a few hours, I shouldn’t imagine that this is a very significant development.

Jack



It’s rather depressing that, with the exception of Jack, everyone seems to have pretty low opinion of Man. It seems that we no longer know what it means to be a human, but have a feeling that it cannot be much. As I have already said, it is not simply intelligence that marks us out as special. Dolphins have a higher intelligence than other animals and some apes may share much of our DNA, but that doesn’t bring them close to mankind in the order of things.

The motive behind these arguments is not their logical coherence, but the desire to knock humans off their pedestal. It occurs to me that the same distaste of human ‘arrogance’ that underlies these attitudes is the same one that motivates other causes, such as environmentalism. It is a plea for humility, designed to prevent the best from leaving the rest behind; a call for us to subjugate ourselves to the will of creatures who have scant awareness of their existence, let alone any comprehension of the ‘rights’ we have bestowed upon them.

What kind of model of man is this? This is the compassion of subservience: we regret causing other beings pain because we feel that we are not worthy. Genuine compassion, by contrast, is based on a fellowship of feeling. Humility is no basis on which to build commonality between human beings, who face each other as equals.

Steven says that dolphins show compassion for other animals, but then states that animals do not have an ethical code. So are their acts of compassion genuine or simply pre-programmed reflexes? This is a red herring. Mankind’s unique status doesn’t hinge on whether other animals possess comparable emotions. It hinges on our achievements and our demonstrable consciousness.

Comments:Tayles

a number of animals use tools, Dolphins and Primates not least. Birds have used tools in the form of dropping rocks to break open things, and more specifically about Dolphins:

Dolphin-human interaction is also employed in a curative sense at places where dolphins work with autistic or otherwise disabled human children.

In May 2005, researchers in Australia discovered a cultural aspect of dolphin behaviour: Some dolphins (Tursiops aduncus) teach their children to use tools. The dolphins break sponges off and cover their snouts with them thus protecting their snouts while foraging. This knowledge of how to use a tool is mostly transferred from mothers to daughters, unlike simian primates, where the knowledge is generally passed onto all the young, irrespective of sex. The technology to use sponges as mouth protection is not genetically inherited but a taught behaviour.

And Primates:
Two Bonobos, Kanzi and Panbanisha have been taught a vocabulary of about 400 words which they can type using a special keyboard of lexigrams (geometric symbols), and can respond to spoken sentences.

Conservation workers have seen the first evidence for tool use in wild gorillas. One instance, caught on film in the Republic of Congo’s Nouabalé-Ndoki National Park, involved a lowland gorilla using a metre-long stick to test the depth of water ahead of her as she cautiously waded into a swampy pool.
In contrast, most examples of tool use in great apes are related to food extraction and preparation. Researchers argue that this new type of tool use may be more widespread, and could hint at abstract reasoning.

Comments: Jack

source: www.boris-johnson.com

Central limit theorem

It was supposed that an archer is shooting at a vertical line drawn on a target, then question how many shots land in various vertical bands on either side of it, concerns with probablity theory. Now is it not self evident that the hits must be assumed to be thicker and more numerous on any given band the nearer this is to the mark? If all the places on the vertical plane, whatever their distance form the mark, were equally liable to be his, the most skilful shot would have no advantage over a blind man. That, however, is the tacit assertion of those who use the common rule(the arithmetic mean) in estimating the value of various discrepant observations, when they treat them all indiscriminately. In this way, therefore the degree of probability of any given deviation could be determined to some extent a posteriori, since there is no doubt that, for a large number of shots, the probability is proportional to the number of shots which hit a band situated at a given distance from the mark. We see Bernoulli (1777) who saw the distinction between probability and frequency, failed completely to understand the basis for taking the arithmetic mean of the observation as an estimate of the true ‘mark’. He takes it for granted (although a short calculation, which he was easily capable of doing, would have taught him otherwise) that , if the observations are given equal weight in calculating the average, then one must be assigning equal probability to all errors, however great. Presumably, others made intuitive guesses like this, unchecked by calculation, making this part of the folklore of the time. Then one can appreciate how astonishing it was when Gauss, 32 years later, proved that the condition
Maximum likelihood estimate = arithmetic mean
Uniquely determines the Gaussian error law, not the uniform one.
In the meantime, Laplace (1783) had investigated this law as a limiting form of the binomial distribution, derived its main properties, and suggested that it was so important that it ought to be tabulated; yet, lacking the above property demonstrated by Gauss, he still failed to see that it was the natural error law Laplace persisted in trying to use the form f(x) exp {-a |x|}, which caused no end of analytical difficulties. But he did understand the qualitative principle that combination of observations improves the accuracy of estimates……………twenty two years later, when Laplace saw the Gauss derivation, he understood it all in a flash and hastened to give the central limit theorem and the full solution to the general problem of reduction of observations, which is still how we analyze it today. Not until the time of Einstein did such a simple mathematical argument again have such a great effect on scientific practice.
Propensity

Behaviour of a discret random variable

The likely behaviour of a discrete random variable X is determined by its probability function pX (also called the probability mass function or pmf), defined, for each possible value x which X can take, as

pX(x) = P(X = x).









Distribution function
The graph of the distribution function of a discrete random variable is flat, except for some upward jumps: the height of the jump at x is pX(x).


Probability function
Any sketch of the probability function should use bars or columns, since pX is equal to 0 everywhere except at the possible values of X.


http://www.staff.city.ac.uk/~sc397/courses/1ps/1ps03_5.htm

Relative measures of effect

Attributable risk measures are not replacements for relative measures of effect; rather, they provide a public health dimension to the appraisal of risks. Identification of a certain exposure with a high rate ratio may yield important clues to disease etiology. Yet, if this same exposure is rare in the population so that the PAR% is small, policy makers and administrators with limited health dollars will probably not rate it as a priority. The PAR% thus provides an important link between causality and public health action. www.ox.ac.uk

The idea of change and comparison : The pear world was the same, only completely different. The remainder of the slush doesn’t look great, but the first snowfall is always magical. The world really does seem remade, so different from what it usually looks like that it almost hard to remember what you think of as normal in the first place. I hope there’s something about that idea of change and comparison that will help us with this passage from 2 Corinthians tonight. It’s all about change; all about comparing what for Paul is the trusted old faith of Moses with the new bright white snowfall that is the Christian faith. We need to do a bit of digging around in the Old Testament to understand what Paul is saying here, but I hope it’ll be worth it as we see what excites him and energises him about being a Christian. So let’s begin by looking at the first passage, from Exodus. This recounts an absolutely central moment in the faith of the Jews: the time when Moses came down the mountain with the tablets of stone, with the commandments engraved on them. Having met face to face with God, Moses came ‘with the two tablets of the covenant in his hand’, the laws of God chiselled out for all to see. This was for them perhaps the high point of the whole of what we call the Old Testament. Moses brought with him a physical token that God had chosen this people and called them to live with a distinctive moral code - they were special. And on top of that, they could see the difference in Moses: his face shone after his encounter with God. He had been changed.
The Freedom of the Spirit
Exodus 34: 29-35, 2 Corinthians 3:7-18, SHC EP Wk 5
live.sthughs.ox.ac.uk/assets/File/Word_Documents/Freedom_of_the_Spirit.doc

On Responsibility

May God, help us take the right measure,
when the responsibility are ours,
May God be behind you, to guide you......

Act of Worship, BBC Radio 4

Oxford Measures

Why is Oxford the Centre of the World?

Its the University stupid!

Oxford Measures

One must be thoroughly overworked - One must be well bred and polite, but without stiffness of ceremony. One must be respectful and assenting, but without being servile and abject. One must be frank, but without indiscretion; and close, without being costive. One must keep up dignity of character, without the least pride of birth or rank. One must be gay within all the bounds of decency and respect; and grave without the affectation of wisdom. You must be essentially secret, without being dark and mysterious. One must be firm, and even bold, but with great seeming modesty.

by Oxon Connoisseur

Binomial distribution

Binomial distribution
A binomial experiment possesses the following properties:

The experiment consists of n identical Bernoulli trials.

Each trial results in one of two outcomes: one outcome is called success, S, and the other failure, F.

The probability of success on a single trial is equal to p and remains the same from one trial to the next. The probability of a failure is equal to q = 1 - p. The trials are independent.

The random variable of interest is Y, which is the number of successes observed during the n trials.

A success is not necessarily good in the everyday sense of the word. As an example, Y could be the total number of heads when two coins are tossed.

www.conted.ox.ac.uk
Statistics for Health Researchers

Binomial Coin Experiment
http://www.math.uah.edu/stat/objects/experiments/
BinomialCoinExperiment.xhtml

Boris Campaign

Donate £2 by text
If you'd like to donate £2 to the campaign by SMS, text BORIS then your email address to 60777. Messages cost £2 and will appear on your next bill.
http://www.backboris.com/news/march/14_03_08_newsletter.php




14th Nov 2006: Smoking will soon be banned in all public places across Britain. Many people believe this is a good thing. Smoking is undoubtedly bad for you, so if banning it means cleaner air and less disease, how could anyone possibly object? Well I object, and I don’t even smoke.

Tayles, Comments, www.borisjohnson.com

Negation Law

- DeMorgan's law: the intersection of any class of sets can be expressed as the complement of the union of the complements of those sets.
http://www.britannica.com/eb/topic-153819/De-Morgan-laws

- Not (A or not B) sounds equivalent to not A or B. But of course the two aren't equivalent; DeMorgan's Law says not (A or not B) is equivalent to not A and B.
http://volokh.com/posts/1205277114.shtml

- Proposition 12 Let a, b ∈ R. If a · b = 0 then either a = 0 or b = 0 (or both).
Proof. If a 6= 0 and b 6= 0 then
0 = (1/a · 1/b) · 0 by Proposition 11
= 0· (1/a · 1/b) by M1
= (a · b) · (1/a · 1/b) by hypothesis
= (b · a) · (1/a · 1/b) by M1
= ((b · a) · 1/a) · 1/b by M2
= (b · (a · 1/a)) · 1/b by M2
= (b · 1) · 1/b by M4
= b · 1/b by M3
= 1 by M4
This contradicts Z and hence a · b = 0 contradicts a and b both being non-zero. By De Morgan’s laws it follows that at least one of a and b is zero.
www.maths.ox.ac.uk/filemanager/active?fid=1075


- DeMorgan Law is quite intuitive once one is able to make the distinction between "or" and "exclusive or" (a distinction that doesn't always exist in common parlance).
- when A is a chain - Many forms of fuzzy logic have a truth-value algebra obtained by equipping the closed unit interval [0, 1] with basic operations of various types; often a De Morgan negation is present. In addition, there will typically be some binary operations meant to model some form of conjunction and disjunction. If these are related via the negation by De Morgan’s laws, then the algebra is referred to as a De Morgan system.
http://www2.maths.ox.ac.uk/~hap/GP3dqalg.pdf



I think not (A or not B) sounds equivalent to not A or not not B, but that's a pointless quibble. My real point is, I think there's a bit of a problem here in the difference between "not" as a logical operator and "not" as an element of how people think. One is strictly "not" means "everything other than", whereas the other allows for "not" to mean "everything other than" or to mean "the opposite of". Likewise, "or" in most people's minds can have an exclusive element that it lacks in formal logic: not so much "A union B" as "A, alternatively B".

Risk of Odds

Studying an ancient earthquake has enabled Oxford University researchers to quantify the likelihood of a tsunami in the Eastern Mediterranean.

They estimate that a ring of faults around the south of Greece and the Aegean Sea generates tsunami earthquakes approximately once every 800 years and, because the last such earthquake took place in 1303, the probability of a tsunami affecting the region is much higher than had been thought.

The Oxford researchers – working with colleagues from the Universities of Cambridge, Nice and Imperial College London – identified the cause of an earthquake that generated a tsunami that destroyed Alexandria on 21 July AD 365.

source: www.ox.ac.uk/media

The Sins of Pride

....No one, so far as I know, puts in a good word for greed or envy. Lust has its practitioners but they do not pretend that it is a virtue. But what of pride? Is it really always a sin?

One of the greatest novels in our language, “Pride and Prejudice”, argues, after all, that we need to be a little more circumspect about how we use the word, and about what we think of those to whom the adjective, proud, is attached. That wise young woman, Elizabeth Bennett, comes to realise that what she originally takes to be a regrettable and dislikeable display of pride by Mr Darcy is in fact something quite else – a sense of loyalty to and identification with ideas, values and institutions that are themselves admirable. Her sister, Mary, early in Jane Austen’s novel, points the way to the conclusion that Elizabeth will later happily reach, “Vanity and pride” Mary notes “are different things, though the words are often used synonymously. A person may be proud without being vain. Pride relates more to our opinion of ourselves, vanity to what we would have others think of us.”

........................Vanity brooked no shadows across the sun.
Vanity, then, we can readily see as a failing of the greatest as well, doubtless, as of the most humble. And the more vaunting the vanity, the higher the mountain of regard, the greater and further the fall and the deeper the pit of humiliation. The descent of the vain is invariably accompanied by cruel laughter. It is a subject for mirth and finger-pointing, The more you pretend for yourself, the more you have to lose. So just as virtue is said to be its own reward, vanity is its own penalty, tracked at a short distance by mockery and even derision. You will not please man for long, better surely to concentrate on pleasing God.

How safe is it to claim, as a politician, divine guidance for what you do for other men, to assert that you simply act as an unworthy agent or instrument of His will? Here I suppose vanity is suffused with pride. Mortal man you may be, but what you do allegedly bears the stamp of God’s grace and authority.

The Epistle of Paul to the Galatians
Chapter 1, Verse 10
“For do I now persuade men, or God? Or do I seek to please men?
For if I yet pleased men, I should not be the servant of Christ.”


Almighty God, have mercy on them, and on all that bear me evil and would do me harm, and their faults and mine together, by such easy, tender, merciful means as thine infinite wisdom best can devise; vouchsafe to amend and redress and make us saved souls in heaven together, where we may ever live and love together with thee and thy blessed saints. O glorious Trinity, for the bitter passion of our sweet saviour. Amen.

University Sermons; The Sin of Pride; Rt Hon Chris Patten


World Book Day

To mark World Book Day 2008 on 6 March, the Bodleian Library held a one-day display featuring the Creation as recorded in three spectacular and historic manuscripts of the sacred books of Judaism, Christianity and Islam – the Torah, the Bible and the Qur’an.

For centuries, religion and the written word have been closely entwined and manuscripts have played a vital role in preserving and transmitting sacred knowledge. The importance and respect accorded to the sacred texts of Judaism, Christianity and Islam is shown in the way they were reverently copied and by the brilliance of their illumination and calligraphy, in the quality of parchment or paper on which they were written, and in their bindings. These texts were designed to be studied and read aloud to an audience of the faithful.

Judaism - The Kennicott Bible, copied in north-west Spain in 1476, is one of the treasures of the Bodleian Library. It was a chance acquisition, named after Benjamin Kennicott, biblical scholar and Radcliffe Librarian, who in 1771, when it was brought into the Library by a young man, recognized its importance and purchased it for 50 guineas.

Christianity - This manuscript is the first volume of a three-volume moralized Latin Bible produced in France in the second quarter of the 13th century. It was given to the Library by Sir Christopher Heydon in 1604; the other two volumes of the set are now in Paris and London.

Islam - This Qur’an is one of a large number of manuscripts purchased in Venice in 1817 by the Bodleian Library from the collection of the Jesuit Matteo Luigi Canonici. It was copied, probably in Cairo, in the year 766 of the Islamic era, which corresponds to 1364-5 AD.

Lesley Forbes, Keeper of Oriental Collections at the Bodleian Library said: ‘Mounting a special display for a public audience to mark World Book Day has become a tradition at the Bodleian Library. In 2008 we invite you to look at the story of the Creation as recorded in three of the Library’s particular treasures’.
Each year the Library celebrates World Book Day by exhibiting one of its great Treasures in the Divinity School, Old Bodleian Library. Past displays included: The Gutenberg Bible (2004), Mary Shelley's Frankenstein,the autograph manuscripts(2005), Shakespeare's first Folio (2006), The original Wind in the Willows: The Centenary of a Children's Masterpiece (2007).


The display was held on 6 March 2008 in the Divinity School, Bodleian Library.

The Rules of Republic of Learned

Oxford is an international university with global research interests and the Bodleian Library has for four centuries served the ‘Republic of the Learned’ - scholars drawn from around the world to consult its unparalleled collections. The plan to recreate the New Bodleian as a contemporary research centre with welcoming public spaces for exhibitions and events, is fundamental to Oxford’s aim to reach out both to the United Kingdom and the world.

Chris Patten, Chancellor of The University of Oxford