## The Moral Activity which Disentangles

Posted in Literature, The Universe and Stuff with tags , , , , , , , on May 22, 2013 by telescoper

I came across this last night and thought I would share it with you. It’s the preamble to Edgar Allan Poe‘s famous short story The Murders in the Rue Morgue, which is arguably the first-ever work in the genre of detective fiction. The piece is a bit dated (especially by the reference to the (now) discredited pseudoscience of phrenology, but Poe nevertheless says some very interesting things about a topic that I have returned to a number of times on this blog: the interplay between analysis and synthesis (and between deductive and inductive reasoning) involved not only in detective stories but also in card games and – I would contend – in the scientific method generally. I  agree with Poe when he says that the most fascinating part of such endeavours is the poorly understood yet vital element of intuition, that creative spark of ingenuity that sets apart a true genius, but am not sure about his contention that it is closely related to the analytic aspect. Anyway, see what you think…

–o–

IT is not improbable that a few farther steps in phrenological science will lead to a belief in the existence, if not to the actual discovery and location, of an organ of analysis. If this power (which may be described, although not defined, as the capacity for resolving thought into its elements) is not, in fact, an essential portion of what late philosophers term ideality, then there are, indeed, many good reasons for supposing it a primitive faculty. That it may be a constituent of ideality is here suggested in opposition to the vulgar dictum (founded, however, upon the assumptions of grave authority) that the calculating and discriminating powers (causality and comparison) are at variance with the imaginative — that the three, in short, can hardly co-exist. But, although thus opposed to received opinion, the idea will not appear ill-founded when we observe that the processes of invention or creation are strictly akin with the processes of resolution — the former being nearly, if not absolutely, the latter conversed.

It cannot be doubted that the mental features discoursed of as the analytical, are, in themselves, but little susceptible of analysis. We appreciate them only in their effects. We know of them, among other things, that they are always to their possessor, when inordinately possessed, a source of the liveliest enjoyment. As the strong man exults in his physical ability, delighting in such exercises as call his muscles into action, so glories the analyst in that moral activity which disentangles.  He derives pleasure from even the most trivial occupations bringing his talent into play. He is fond of enigmas, of conundrums, of hieroglyphics; exhibiting in his solutions of each a degree of acumen which appears to the ordinary apprehension præternatural. His results, brought about by the very soul ­and essence of method, have, in truth, the whole air of intuition.

The faculty in question is possibly much invigorated by mathematical study, and especially by that highest branch of it which, unjustly, and merely on account of its retrograde operations, has been called, as if par excellence, analysis.  Yet to calculate is not in itself to analyse. A chess-player, for example, does the one without effort at the other.  It follows that the game of chess, in its effects upon mental character, is greatly misunderstood. I am not now writing a treatise, but simply prefacing a somewhat peculiar narrative by observations very much at random; I will, therefore, take occasion to assert that the higher powers of the reflective intellect are more decidedly and more usefully tasked by the unostentatious game of draughts than by all the elaborate frivolity of chess. In this latter, where the pieces have different and bizarre motions, with various and variable values, that which is only complex is mistaken (a not unusual error) for that which is profound. The attention is here called powerfully into play. If it flag for an instant, an oversight is committed, resulting in injury or defeat. The possible moves being not only manifold but involute, the chances of such oversights are multiplied; and in nine cases out of ten it is the more concentrative rather than the more acute player who conquers. In draughts, on the contrary, where the moves are unique and have but little variation, the probabilities of inadvertence are diminished, and the mere attention being left comparatively unemployed, what advantages are obtained by either party are obtained by superior acumen. To be less abstract — Let us suppose a game of draughts, where the pieces are reduced to four kings, and where, of course, no oversight is to be expected. It is obvious that here the victory can be decided (the players being at all equal) only by some recherché movement, the result of some strong exertion of the intellect. Deprived of ordinary resources, the analyst throws himself into the spirit of his opponent, identifies himself therewith, and not unfrequently sees thus, at a glance, the sole methods (sometimes indeed absurdly simple ones) by which he may seduce into miscalculation or hurry into error.

Whist has long been noted for its influence upon what is termed the calculating power; and men of the highest order of intellect have been known to take an apparently unaccountable delight in it, while eschewing chess as frivolous. Beyond doubt there is nothing of a similar nature so greatly tasking the faculty of analysis. The best chess-player in Christendom may be little more than the best player of chess; but proficiency ­ in whist implies capacity for success in all those more important undertakings where mind struggles with mind. When I say proficiency, I mean that perfection in the game which includes a comprehension of all the sources (whatever be their character) whence legitimate advantage may be derived. These are not only manifold but multiform, and lie frequently among recesses of thought altogether inaccessible to the ordinary understanding. To observe attentively is to remember distinctly; and, so far, the concentrative chess-player will do very well at whist; while the rules of Hoyle (themselves based upon the mere mechanism of the game) are sufficiently and generally comprehensible. Thus to have a retentive memory, and to proceed by “the book,” are points commonly regarded as the sum total of good playing. But it is in matters beyond the limits of mere rule that the skill of the analyst is evinced. He makes, in silence, a host of observations and inferences. So, perhaps, do his companions; and the difference in the extent of the information obtained, lies not so much in the falsity of the inference as in the quality of the observation. The necessary knowledge is that of what to observe. Our player confines himself not at all; nor, because the game is the object, does he reject deductions from things external to the game. He examines the countenance of his partner, comparing it carefully with that of each of his opponents. He considers the mode of assorting the cards in each hand; often counting trump by trump, and honor by honor, through the glances bestowed by their holders upon each. He notes every variation of face as the play progresses, gathering a fund of thought from the differences in the expression of certainty, of surprise, of triumph or of chagrin. From the manner of gathering up a trick he judges whether the person taking it can make another in the suit. He recognises what is played through feint, by the air with which it is thrown upon the table. A casual or inadvertent word; the accidental dropping or turning of a card, with the accompanying anxiety or carelessness in regard to its concealment; the counting of the tricks, with the order of their arrangement; embarrassment, hesitation, eagerness or trepidation — all afford, to his apparently intuitive perception, indications of the true state of affairs. The first two or three rounds having been played, he is in full possession of the contents of each hand, and thenceforward puts down his cards with as absolute a precision of purpose as if the rest of the party had turned outward the faces of their own.

The analytical power should not be confounded with simple ingenuity; for while the analyst is necessarily ingenious, the  ingenious man is often remarkably incapable of analysis. I have spoken of this latter faculty as that of resolving thought into its elements, and it is only necessary to glance upon this idea to perceive the necessity of the distinction just mentioned. The constructive or combining power, by which ingenuity is usually manifested, and to which the phrenologists (I believe erroneously) have assigned a separate organ, supposing it a primitive faculty, has been so frequently seen in those whose intellect bordered otherwise upon idiocy, as to have attracted general observation among writers on morals. Between ingenuity and the analytic ability there exists a difference far greater indeed than that between the fancy and the imagination, but of a character very strictly analogous. It will be found, in fact, that the ingenious are always fanciful, and the truly imaginative never otherwise than profoundly analytic.

## A Piece on a Paradox

Posted in The Universe and Stuff with tags , , , , , , , , , on March 7, 2012 by telescoper

Not long ago I posted a short piece about the history of cosmology which got some interesting comments, so I thought I’d try again with a little article I wrote a while ago on the subject of Olbers’ Paradox. This is discussed in almost every astronomy or cosmology textbook, but the resolution isn’t always made as clear as it might be. The wikipedia page on this topic is unusually poor by the standards of wikipedia, and appears to have suffered a severe attack of the fractals.

I’d be interested in any comments on the following attempt.

One of the most basic astronomical observations one can make, without even requiring a telescope, is that the night sky is dark. This fact is so familiar to us that we don’t imagine that it is difficult to explain, or that anything important can be deduced from it. But quite the reverse is true. The observed darkness of the sky at night was regarded for centuries by many outstanding intellects as a paradox that defied explanation: the so-called Olbers’ Paradox.

The starting point from which this paradox is developed is the assumption that the Universe is static, infinite, homogeneous, and Euclidean. Prior to twentieth century developments in observation (Hubble’s Law) and theory  (Cosmological Models based on General Relativity), all these assumptions would have appeared quite reasonable to most scientists. In such a Universe, the intensity of light received by an observer from a source falls off as the inverse square of the distance between the two. Consequently, more distant stars or galaxies appear fainter than nearby ones. A star infinitely far away would appear infinitely faint, which suggests that Olbers’ Paradox is avoided by the fact that distant stars (or galaxies) are simply too faint to be seen. But one has to be more careful than this.

Imagine, for simplicity, that all stars shine with the same brightness. Now divide the Universe into a series of narrow concentric spherical shells, in the manner of an onion. The light from each source within a shell of radius $r$  falls off as $r^{-2}$, but the number of sources increases in the same manner. Each shell therefore produces the same amount of light at the observer, regardless of the value of $r$.  Adding up the total light received from all the shells, therefore, produces an infinite answer.

In mathematical form, this is

$I = \int_{0}^{\infty} I(r) n dV = \int_{0}^{\infty} \frac{L}{4\pi r^2} 4\pi r^{2} n dr \rightarrow \infty$

where $L$ is the luminosity of a source, $n$ is the number density of sources and $I(r)$ is the intensity of radiation received from a source at distance $r$.

In fact the answer is not going to be infinite in practice because nearby stars will block out some of the light from stars behind them. But in any case the sky should be as bright as the surface of a star like the Sun, as each line of sight will eventually end on a star. This is emphatically not what is observed.

It might help to think of this in another way, by imagining yourself in a very large forest. You may be able to see some way through the gaps in the nearby trees, but if the forest is infinite every possible line of sight will end with a tree.

As is the case with many other famous names, this puzzle was not actually first discussed by Olbers. His discussion was published relatively recently, in 1826. In fact, Thomas Digges struggled with this problem as early as 1576. At that time, however, the mathematical technique of adding up the light from an infinite set of narrow shells, which relies on the differential calculus, was not known. Digges therefore simply concluded that distant sources must just be too faint to be seen and did not worry about the problem of the number of sources. Johannes Kepler was also interested in this problem, and in 1610 he suggested that the Universe must be finite in spatial extent. Edmund Halley (of cometary fame) also addressed the  issue about a century later, in 1720, but did not make significant progress. The first discussion which would nowadays be regarded as a  correct formulation of the problem was published in 1744, by Loys de Chéseaux. Unfortunately, his resolution was not correct either: he imagined that intervening space somehow absorbed the energy carried by light on its path from source to observer. Olbers himself came to a similar conclusion in the piece that forever associated his name with this cosmological conundrum.

Later students of this puzzle included Lord Kelvin, who speculated that the extra light may be absorbed by dust. This is no solution to the problem either because, while dust may initially simply absorb optical light, it would soon heat up and re-radiate the energy at infra-red wavelengths. There would still be a problem with the total amount of electromagnetic radiation reaching an observer. To be fair to Kelvin, however, at the time of his writing it was not known that heat and light were both forms of the same kind of energy and it was not obvious that they could be transformed into each other in this way.

To show how widely Olbers’ paradox was known in the nineteenth Century, it is worth also mentioning that Friedrich Engels, Manchester factory owner and co-author with Karl Marx of the Communist Manifesto also considered it in his book The Dialectics of Nature. In this discussion he singles out Kelvin for particular criticism, mainly for the reason that Kelvin was a member of the aristocracy.

In fact, probably the first inklings of a correct resolution of the Olbers’ Paradox were contained not in a dry scientific paper, but in a prose poem entitled Eureka published in 1848 by Edgar Allan Poe. Poe’s astonishingly prescient argument is based on the realization that light travels with a finite speed. This in itself was not a new idea, as it was certainly known to Newton almost two centuries earlier. But Poe did understand its relevance to Olbers’ Paradox.  Light just arriving from distant sources must have set out a very long time ago; in order to receive light from them now, therefore, they had to be burning in the distant past. If the Universe has only lasted for a finite time then one can’t add shells out to infinite distances, but only as far as the distance given by the speed of light multiplied by the age of the Universe. In the days before scientific cosmology, many believed that the Universe had to be very young: the biblical account of the creation made it only a few thousand years old, so the problem was definitely avoided.

Of course, we are now familiar with the ideas that the Universe is expanding (and that light is consequently redshifted), that it may not be infinite, and that space may not be Euclidean. All these factors have to be taken into account when one calculates the brightness of the sky in different cosmological models. But the fundamental reason why the paradox is not a paradox does boil down to the finite lifetime, not necessarily of the Universe, but of the individual structures that can produce light. According to the theory Special Relativity, mass and energy are equivalent. If the density of matter is finite, so therefore is the amount of energy it can produce by nuclear reactions. Any object that burns matter to produce light can therefore only burn for a finite time before it fizzles out.

Imagine that the Universe really is infinite. For all the light from all the sources to arrive at an observer at the same time (i.e now) they would have to have been switched on at different times – those furthest away sending their light towards us long before those nearby had switched on. To make this work we would have to be in the centre of a carefully orchestrated series of luminous shells switching on an off in sequence in such a way that their light all reached us at the same time. This would not only put us  in a very special place in the Universe but also require the whole complicated scheme to be contrived to make our past light cone behave in this peculiar way.

With the advent of the Big Bang theory, cosmologists got used to the idea that all of matter was created at a finite time in the past anyway, so  Olber’s Paradox receives a decisive knockout blow, but it was already on the ropes long before the Big Bang came on the scene.

As a final remark, it is worth mentioning that although Olbers’ Paradox no longer stands as a paradox, the ideas behind it still form the basis of important cosmological tests. The brightness of the night sky may no longer be feared infinite, but there is still expected to be a measurable glow of background light produced by distant sources too faint to be seen individually. In principle,  in a given cosmological model and for given assumptions about how structure formation proceeded, one can calculate the integrated flux of light from all the sources that can be observed at the present time, taking into account the effects of redshift, spatial geometry and the formation history of sources. Once this is done, one can compare predicted light levels with observational limits on the background glow in certain wavebands which are now quite strict .

## The Fall of the House of Usher

Posted in Uncategorized with tags , , , on December 17, 2011 by telescoper

It’s a strange tradition that the Christmas season tends to bring with it an appetite for ghost  stories and other tales of supernatural horror. It’s probably a reflection of a much earlier age when the winter was a harsh and dangerous time, during which food was scarce and survival through the winter meant huddling around a fire trying to stay warm. It seems natural to me that the kind of stories that would be told in such an environment would be of fear and foreboding. It’s not really a Christian tradition, therefore, but the legacy of a much older pagan one. Like Christmas itself, as a matter of fact.

Anyway, a few days ago at our little cosmology group Christmas night out the subject of horror films came up.  I’ve never been a particular aficianado of this genre, and I’m afraid most modern horror films are so formulaic that they bore me to tears. I do enjoy the classics enormously, however. James Whale’s 1931 Frankenstein, for example,  has to my mind never been bettered; a great film turned into a masterpiece by an unforgettably moving  performance by Boris Karloff. I think that’s a wonderful film, but I have to say I never found it particularly frightening, even as a child.

The first film I remember seeing that really terrified me was Roger Corman’s The Fall of the House of Usher starring the inimitable Vincent Price, a film based on a short story by Edgar Allan Poe. When I was around 8 or 9 I was once  left home alone on a Friday night by my parents. In those days the BBC used to show horror films late at night on Fridays and, against parental guidance, I decided to watch this one. It scared me witless and when my parents got home they found me a gibbering wreck. I don’t really know why I found it so scary – younger people reared on a diet of slasher movies probably find it very tame, as you don’t actually see anything particularly shocking – but the whole atmosphere of it really got to me. Here’s an example.

This reminds me that I need to get some replastering done in the new year….

Anyway, I’d be interested in hearing other suggestions for the most scariest film through the Comments box…

## Alone

Posted in Poetry with tags , on September 3, 2010 by telescoper

From childhood’s hour I have not been
As others were; I have not seen
As others saw; I could not bring
My passions from a common spring.
From the same source I have not taken
My sorrow; I could not awaken
My heart to joy at the same tone;
And all I loved, I loved alone.
Then – in my childhood, in the dawn
Of a most stormy life – was drawn
From every depth of good and ill
The mystery which binds me still:
From the torrent, or the fountain,
From the red cliff of the mountain,
From the sun that round me rolled
In its autumn tint of gold,
From the lightning in the sky
As it passed me flying by,
From the thunder and the storm,
And the cloud that took the form
(When the rest of Heaven was blue)
Of a demon in my view.

## To look at a star by glances..

Posted in Literature, The Universe and Stuff with tags , , , , , on March 9, 2010 by telescoper

I’ve blogged before about my love of classic detective stories and about the intriguing historical connections between astronomy and forensic science. However, I recently finished reading a book that gave me a few more items to hang on that line of thought so I thought I’d do a quick post about them today.

I picked up a copy of The Suspicions of Mr Whicher by Kate Summerscale when I saw it in a stack of discounted books in Tesco a few monthsa go. I thought it might be mildly diverting, so I bought it. It turned out to be a fascinating read. I won’t spoil it by telling too much about the story, but it is basically an investigation into the circumstances surrounding a real-life murder that happened on 30th June 1860. The case involved a truly shocking crime, the brutal slaying of a young boy, but it also offers great insights into the history of the Criminal Investigation Division (CID) of the Metropolitan Police, which was based at Scotland Yard from about 1842 onwards. Mr Jack Whicher was the Yard’s most celebrated detective at the time, but this crime went unsolved until, about five years later, the perpetrator walked into a police station and confessed to the murder.

In telling the story, Kate Summerscale touches on a lot of fascinating social history. For example, I had never realised that in the early days of the CID people were strongly opposed to the idea that plain clothes policemen might be snooping about so all detectives were required to wear their uniforms even when off duty! It’s also fascinating to note that the rise of the true-life detective coincided with the rise of the detective story in popular fiction.

Edgar Allan Poe’s short story The Murders in the Rue Morgue, generally accepted to have been the first real detective story, was first published in 1841. Even in this first example of the genre, we find a clear parallel being drawn with astronomy by the detective Dupin:

Thus there is such a thing as being too profound. Truth is not always in a well. In fact, as regards the more important knowledge, I do believe that she is invariably superficial. The depth lies in the valleys where we seek her, and not upon the mountain-tops where she is found. The modes and sources of this kind of error are well typified in the contemplation of the heavenly bodies. To look at a star by glances–to view it in a side-long way, by turning toward it the exterior portions of the retina (more susceptible of feeble impressions of light than the interior), is to behold the star distinctly–is to have the best appreciation of its lustre–a lustre which grows dim just in proportion as we turn our vision fully upon it. A greater number of rays actually fall upon the eye in the latter case, but in the former, there is the more refined capacity for comprehension. By undue profundity we perplex and enfeeble thought; and it is possible to make even Venus herself vanish from the firmament by a scrutiny too sustained, too concentrated, or too direct.

No less a figure than Charles Dickens also had thoughts along these lines. In 1850 in a short article called A Detective House Party, he compared detectives with the astronomers Urbain Leverrier and John Couch Adams who in 1846 had simultaneously discovered the planet Neptune. Dickens died in 1870 leaving his own detective story The Mystery of Edwin Drood still unfinished but his good friend Wilkie Collins did a great deal to establish the literary genre of detective fiction with The Moonstone and The Woman in White. Indeed, in the mid-19th Century the idea of detection seems to have imprinted itself on fields as diverse as natural history and journalism as well as astronomy.

The point that strikes me is that astronomy and criminal investigations are primarily observational rather than experimental. One has one Universe and one scene of the crime. In both disciplines the task is to reconstruct what happened from what is seen and what is not.

The detective instinct, brightened by genius, marked unerringly the place of that missing planet which no eye had seen, and whose only register was found in the calculations of astronomy.

I use metaphors like this quite often in popular lectures, and they seem to go down quite well. On the other hand, I’ve often had my leg pulled for admitting to watching TV programmes like CSI: Crime Scene Investigation. Admittedly, the characterisation is very weak and the plots often ridiculously far-fetched. However, these stories do at least attempt to portray something of what the scientific method is about. And that’s something that not many so-called science programmes bother to do these days.