Wind chimes Part I

Fig.1

There is a lot of information online about wind chimes. However, I was unable to find an answer to a natural question: is there a critical wind speed below which the wind chimes will not emit any sound?

The key to answering this question is to first find out the response of a pendulum to a constant horizontal force. This is solved as a question at the website:

http://www.physics.utah.edu/~woolf/2210_ailion/exam3_11.pdf

“A ball of mass m is connected by a strong string of length L to a pivot. A steady wind exerts a constant horizontal force F on the ball as shown. Initially, the ball is held in place with the string vertical. The ball is then released and is observed to swing up and down between it staring point and its maximum height H above its starting point.” - by David Ailion of the University of Utah.

Ailion gives the worked out solution, but does not specifically connect it to the wind-speed v. This is expressed as follows:

                                F = rv²A/2

where r is the density of air and A is the area of the wind-catching surface of the pendulum bob. This assumes that the angle between the normal to the surface and the wind velocity f = 0. If not, this force would be reduced by a cos(f) factor.

                Although Ailion has given the worked-out solution for the equilibrium height and for the maximum height, this is mine; the final equations are the same.

However, the geometry is somewhat different for wind chimes – there is a pendulum bob which catches the wind, but there is also a striker, which is much further up, and is a thin round disk which actually contacts one of the hollow cylindrical chimes, producing the tone that we hear. This geometry is dealt with in the second section, and then applied to the cases of bamboo and iron wind chimes.

Pendulum with constant horizontal force F:

see Fig.1:

a)      Equilibrium height: velocity = maximum

h = L [1 – cos(q)]

Resolve tension T into vertical and horizontal components:

                                T sin(q) = F

                                T cos(q) = mg

                                tan(q) = F/mg

Substituting into equation for h:

h = L{ 1 – [ 1 + (F/mg)²]^-1}

If F = 0, the equilibrium position of the pendulum is the standard h = 0 (pendulum hangs vertically down when there is no wind).

If F = mg, h = L/√2,

And if F = ¥, h = L.

Note: H.Munera & H.R.Maya Lat.Am.J.Phys.Ed. 5 (2011) 22-30: 'method of apparent vertical' applied to the "perturbation of a dynamical system by a constant or nearly constant force, not necessarily small. The basic idea is to rotate the system of coordinates so that the z-axis coincides with an apparent acceleration of gravity".

(Munera & Maya claim that their method is not the same as the equivalence principle. I was unable to understand why, and it is anyway a finer point that is not relevant here). This gives a vector equation:

g' = g + F/m

The upshot is that the equilibrium position is displaced by an angle q, given by: tan(q) =  F/mg. This gives the same position as derived above, as it must.

b) maximum height: velocity = 0

For a constant horizontal force acting over a horizontal distance x:

                                Fx = mgh

This x is related to the length of the pendulum by:

                                x = L sin(q)

The height h is given by:

                                h = L[ 1 – cos(q)]

Eliminating h we get:

F/mg = [1 – cos(q)]/sin(q) = tan (q/2)

Substituting in the equation for h and doing some algebra, using the half-angle formula:

                                tan(q) = 2 tan(q/2)/[1 – tan²(q/2)]

We finally get the maximum height:

                                h = 2L/[1 + (mg/F)²]

If F = mg, h = L.

If F = ¥,  h = 2L.

Fig.2:

Fig.2 shows the wind blowing with velocity v from L to R, displacing the equilibrium position from the vertical dotted line to the line marked 'eq'. The position 1 corresponds to the maximum height calculated above. The position 2 corresponds to the maximum height on the other side as the pendulum swings.

The equilibrium position is a measure of the energy due to the wind because h_eq = 0 when F = 0.

Thus the height corresponding to 2 is given by:

                                mg(h₁ – h₂) = mgh_eq

When there is no wind h_eq = 0 and h₁ = h₂ and the pendulum swings symmetrically about the equilibrium position.

Actually, some of the analysis is not needed for the stated purpose: to find the critical wind speed at which the wind chimes will sound. The only one needed is the one for the maximum height:

                                h = 2L/[1 + (mg/F)²]

However, the actual geometry of the wind chime is somewhat more complicated than a simple pendulum in a wind. There is a bob (which catches the wind) and there is a striker which is higher up, which actually touches the hollow metal cylinders that actually emit the sound on being struck. The actual case is discussed in the second section.

Light & Height

OK, I’m not anywhere near being Flaubert, so I do not seek the mot juste.

I’m also declaring my independence to blog about the nebulous and quite possibly the trite and the obvious – and to do it shamelessly.

The Sun is largely high in the sky, ignoring sunrises, sunsets and high latitudes.

We tend to replicate this in our homes, although lights are more often on walls than ceilings – and rarely on floors.

Trees (almost) always grow upwards, towards the big light in the sky. They are phototropic.

Height is an advantage – the taller trees have unfettered access to sunlight.

For humans, the taller you are, the farther you see. In the savannah that humans are widely supposed to have grown up in, height would allow one to spot both predators and prey in advance. Of course, one could have climbed up a tree to scan the far horizon – if there happened to be a tree nearby.

In the sea also, a tall captain would help – but sailors solved the problem of spotting storms early by putting a lookout on the mast.

Anyway, the area that can be scanned is directly proportional to the height – of the human or the vantage point.

But the point is that the upward direction is associated with more light and increased viewing area. Conversely, if you are shorter or if you are stuck in a pit or a deep valley, you will have a smaller amount of light and a decreased viewing area. So a downward direction is associated with less light.

An extreme example is the concept of building a very high tower at the South Pole that is permanently in sunshine - or a solar collector in low Earth orbit. Either could be used to generate solar energy.

The tower would be 527 kms high on Earth, assuming a perfectly spherical Earth (for R=6400 and q=22.5°). Of course, you would have to add about 18 kms to the height of the tower, since the polar radius (6353 kms) is less than the mean radius (6371 kms). 

Note: The geometry is obtainable from the gif link mentioned below.

http://en.wikipedia.org/wiki/Earth_radius

http://theworld.com/~reinhold/lunarpolar.html

Identity issues

Identity issues

A recent (15^th Aug 2012)issue of the Indian Express carries the story of an upcoming leader of a far-right Hungarian party (Jobbik) named Csanad Szegedi who was (in)famous for his loudly proclaimed anti-Semitic views. By an unkind twist of fate the 30-year old discovered in 2010 from a 'convicted felon' – whom he was unable to silence – that his maternal grandparents were Jews, and that his grandmother was an Auschwitz survivor. Jobbik has just disowned him, although Szegedi is not a practising Jew by any means.

The irony of this story is practically Kafkaesque, and it takes the phrase,” He's his own worst enemy” to a whole new level. One wonders what Szegedi will do: take solace in drink, commit suicide, re-invent himself (as what?), - or emigrate to Israel?

However, the story raises other questions that apply almost universally. One could easily change names and consider a Szegedi clone in the RSS (or the Laskar-e-Teuba) who hates Muslims (or Hindus) viscerally, and belatedly finds out that he has Muslim (or Hindu) ancestors. As Szegedi's story makes clear, it is not enough for Szegedi to denounce Jews – he must be free from any ancestral taint.

All identities are constructed. We share 'markers' with our in-group that differentiate us from all out-groups. But the notion that groups can be exclusive and 'pure' is a difficult one to maintain, at least for humans. The evidence indicates that groups are highly overlapping. The identity constructed (and constricted) by absolute exclusivity is fragile – and flies in the face of evidence. For example, the study of caste in India on the basis of genetics was initially expected to show significant divergences between different groups – considering that caste has been entrenched for at least two millenia. Interestingly, the study showed statistically insignificant differences between the so-called 'upper' and 'lower' castes' - evidence of considerable, and ongoing, miscegenation, by a variety of means [1].

Of course, today we believe that, since cultural evolution is faster than genetic evolution, it determines our future to a greater extent than genetic evolution does. Indubitably the culture you grow up in determines to a large extent the kind of occupation that you will end up in: goat-herder, politician or nuclear physicist. Your culture conditions your expectations and defines your opportunities.

With greater access all over the world to education, one may expect a widening of opportunities. However, the access provided by tools such as the internet may turn out to be illusory or non-existent for people on the wrong side of the digital divide. Also, some may be unable to access certain forms of knowledge because of their own cultural preconceptions: imagine a Taliban anthropologist, almost an oxymoron.

To return to Szegedi, he lived and defended a culture that he felt was under siege from inimical forces, much as the Taliban or Boko Haram fear Western 'contamination' and desire 'decontamination'. However, any culture that repudiates the influences of multiple others is inherently weak. The strongest is the culture that opens its arms to worldwide influences, assimilates and transmogrifies them. To a certain extent, the conservative tendency in a culture that insists on purity and exclusivness allows its identity to survive in a recognizable form. At the same time, no culture can remain static and that means that it must be open. Not completely open, perhaps, but at least partially open.

The irony does not end with Szegedi's quandary. The long-term future of Israel as a 'homeland for Jews' is in doubt, despite its overwhelming military and technological superiority. The problem the Jews face is the desire to acquire and retain as much of the 'Promised Land' as possible while denying Palestinians full citizenship, since they can never be bona fide Jews in a 'Jewish homeland'. Demographics mean that Israel will face a problem in remaining a 'Jewish democracy' in the longer term, even if in the short term they continue to out-maneuver the Palestinians and other Arabs.

But the question that Szegedi's story raises has an another implication. What is the difference between the Jews and the Arabs or Europeans? Some recent genetic studies by Harry Ostrer [2] indicate that both Ashkenazi and Sephardic Jews have common genetic markers, but these are traced back to the Levant, and that these are, in fact, shared with the much-reviled Palestinians. The Jews also have 30-60% non-Middle Eastern genetic markers. That is, Jews also have genes in common with Palestinians and non-Jewish Europeans [2,3]. Does it matter? Or is culture the primary determinant? In that case, an Arab or European child brought up by Jews would be Jewish? Why not?

The attempt by sociobiologists such as E.O.Wilson to explain human behaviour in terms of our evolutionary heritage were widely condemned as sexist, racist and elitist. Nevertheless, we desperately need to understand ourselves, our genes, our cultures, and what they mean for our future. Study of aboriginal tribes in Australia suggested that groups avoid inbreeding when intermarriage occurs at a level of about 7-10% [4] and that there is considerable genetic similarity across tribes.

Today, the metaphor of the 'melting pot' in America has been replaced by the 'salad bowl'. Xenophobia in Europe is undergoing a resurgence - like recurrent malaria - which it does whenever times are hard. The issues of identity are not, in an increasingly globalized world, going away any time soon. The idea of 'multiculturalism' is being touted by the British in the days of the Olympics, alongside ever stricter immigration controls: go figure! A country like Japan which is highly insular but rapidly aging will face a demographic crunch as surely as the Europeans, the problem in both cases being a birth rate that has dropped below the replacement rate.Will demographics and economics ultimately trump the distaste for outsiders, Auslanders?

Even if they do, who will convince Szegidi and Breivik?

1. E.O.Wilson “Sociobiology: the new synthesis” Ch.27, p.11/31.
2. “Legacy: A Genetic History of the Jewish People” (Oxford University Press) by Harry Ostrer
3. “The Chosen Genes” by Josh Fischmann, http://chronicle.com/article/The-Chosen-Genes/131481/
4. E.O.Wilson “Sociobiology: the new synthesis” Ch.27 p. 9/31.

Valleys without rainbows

No rainbows in the valley of Shangri-La

When I went trekking in the Himalayas last month, it rained quite a bit on each day – but mostly after noon. Unfortunately, despite all the rain, we were not lucky enough to see a rainbow. I decided that the blame – as usual – lay in the laws of physics (optics and atmospheric science) and on geometry. After all, the Sun has to be behind you, and the falling rain in front, and the clouds should not obscure the Sun's rays, etc.

Our camp was located in a valley – so that is how I imagined a valley in which rainbows are forevere forbidden to its denizens. Rather depressing, truly, but I was already feeling deprived – so the only solace was to concieve of people even more miserable.

According to wikipedia, if the Sun is more than 42 degrees from the horizontal, you cannot see a rainbow. This refers to the primary bow, which lies between 137.6 degrees (red) and 139.4 degrees (blue). The secondary – which is fainter, and reversed in sequence – bow lies in the range of angles 129.6 (red) and 126.5 degrees (blue). That means that the secondary bow would still be visible if the Sun is as high in the sky as 53.5 degrees.

One does not get into the gory details of trigonometry but it is easy to construct many valleys in which no rainbows - either primary or secondary - could be seen. Of course, in some valleys primary bows will not be visible – but secondary bows can still be seen.

For a valley which is a perfect circle, with a radius of 1000 metres, the encircling mountain range would need to be 916 metres high to forbid all primary rainbows, and 1356 metres high to forbid even seconday rainbows. For more realistic shapes, a little trig would be needed.

The secondary rainbow is about 10% of the total intensity of the primary bow – and its angular range is about 75% greater. Sightings of seconday rainbows are rarer than primary bows, because the size distribution of raindrops needs to be more uniform to get good intensity.

What about higher-order rainbows? They are so faint as to be almost invisible against solar glare.

Tertiary and quaternary rainbows have been seen by the most educated and determined rainbow-chasers in 2011:

http://www.sciencedaily.com/releases/2011/10/111005111001.htm
http://www.atoptics.co.uk/rainbows/ord34.htm
Unfortunately, the third- and fourth-order rainbows will not slake the thirst of our encircled denizens either. Firstly, these two bows are in the direction of the Sun – rather than opposite to the Sun, as are the first- and second-order bows. That makes the glare problem more acute than for the second-order bow. Secondly, although the total intensity of the 3ed order bow is 24% of the 1^st order bow, it is spread over a larger range of angles – so it is fainter. And, lastly, the angle of the 3^rd order is at about 40 degrees – almost the same angle to the horizontal as the 1^st order bow (but in the opposite direction). The 4^th order bow has 15% of the total intensity of the 1^st order bow, and its angle is ~45 degrees to the horizontal. So encircling mountains of a similar height would impose a quarantine on rainbows in the valley.
References:
Photographic evidence for the third-order rainbow, M Grossmann, E Schmidt, & A Haussmann, Applied Optics, Vol. 50, Issue 28, pp. F134-F141 (2011).
Photographic observation of a natural fourth-order rainbow, M Theusner, Applied Optics, Vol. 50, Issue 28, pp. F129-F133 (2011)
All this is somewhat depressing for the dwellers of Shangri-La. Keats in his 1820 poem Lamia lamented Newton's decomposing white light and deconstructing the rainbow, accusing him of (sic) “unweaving the rainbow”.
Richard Dawkins has written a book with exactly that title as a rather belated riposte that “ Science is - or ought to be – the inspiration for great poetry”.
That debate will undoubtedly carry on – but what I think true is that few poets would have the wit or the patience to chase down the tertiary and quaternary rainbows.
Or to do as Jearl Walker did, do an experiment to see a dozen bows in a single drop of water (suspended on a wire and artificially illuminated)!

http://optica.machorro.net/Optica/SciAm/Rainbow/1977-07-body.html

However, the knowledge of rainbows should be more widely known to the general public – especially poets – because even if the vagaries of weather go against you, you can still see, without too much trouble, rainbows in fountains. Providing the sun direction is right and as long as you do not live in an deprived no-rainbow valley!

This is a very short post on the papasan chair.
http://en.wikipedia.org/wiki/Papasan_chair
It is striking that there are two design elements in a papasan chair (ignoring the base and the cushion): the circular outer frame and the 'spiral' inner part.
The circle is important because it is the curve which, for a given length, maximizes the enclosed area (known as Queen Dido's problem, which was proved by the calculus of variations by Newton):


galileo.phys.virginia.edu/classes/321.jvn.fall02/var_meth.pdf


http://mathematicalgarden.wordpress.com/2008/12/21/the-problem-of-dido/

The spiral is the most compact curve in the sense - within a given area - it covers the greatest area for a given length, and thus provides maximum support.

However, there is some ambiguity because there are many possible spiral curves:

http://en.wikipedia.org/wiki/Spiral

Logarithmic spiral search patterns are known to be most efficient in 2-D although mathematicians are still arguing about them:
 "On the Optimality of Spiral Search" Elmar Langetepe
SODA 2010: Proc. 21st Annu. ACM-SIAM Symp. Disc. Algor., 2010, pp. 1-12

www.i1.informatik.uni-bonn.de/publications/l-oss-09.pdf

Yes, these arguments also neglect the 6 radial spokes, and the fact that the spiral is really a helix because it's
in 3-D.
Agreed: these two arguments are not watertight, and the spiral part may even be wrong, but anyway:
The papasan chair design optimally uses material by its combination of circular and spiral elements.

Pronouncements

Almost all of us would have had occasion to smile when somebody else mispronounces some English word or name. Similarly, most of us would have been at the receiving end at least once. The fictional Prof.Higgins claimed to be able to pinpoint – on the basis of your accent - which part of London you belonged to within a street or two. He also lamented the fact that the English a) don’t care about pronunciation unlike the French, and b) use it to reinforce social class. The French certainly do care more – but are hardly exempt from regional and class variations. Of course, it helps that French is more logical in its pronunciation patterns than the eccentric English language.

Additionally, English is spoken by a much larger number of people than is French, because the former had more colonies. Naturally, this leads to increased diversity. This point was driven home to me when I first visited the US as a child. I remember I had an argument in class with the ‘English’ teacher: I was adamant that that the only correct pronunciation was the English one. She countered that a huge number of Americans spoke with a distinctive accent – and this accent would, thus, have to be regarded as equally valid. My argument was in line with Prof.Higgins who said that ‘there are places where English completely disappears: In America they haven’t used it for years!” Higgins also deplored – within England – ‘the cold-blooded murder of the English tongue’. He still has a point if the speech is inarticulate and unclear, since that detracts from communication. But the problem with that argument is that your understanding is partly shaped by your preconceived expectations. Somebody who speaks differently is automatically more difficult to understand – but that cuts both ways, as my American English teacher would have argued.

Today, older if no wiser, I would not be able to so clearly state a preference for the English accent as the only ‘true’ or ‘original’ one. My Fair Lady made the existence of alternatives quite clear – even if Prof.Higgins plumps for the clarity of an upper-class British accent. Much later, I heard the charming duet sung by Louis Armstrong and Ella Fitzgerald: “You say pot-a-to and I say pot-ah-to...” This song implies that two ways exist to say each word, and that a process of negotiation may result to decide which one ‘wins’. Or one could hope for peaceful co-existence... And we haven’t even discussed the shades of various Indian, Pakistani, Australian, Canadian, South African etc accents – and the combinations thereof e.g. the Bihari-American accent to name just one interesting variant. And the Oxford dictionary even prescribes the way a French word should be pronounced by an English speaker...

Restricting ourselves to the so-called English accent, the question remains: is there such a thing as ‘correct’ pronunciation? There must be some common factor: we can’t have everybody saying each word differently, since communication would be impossible. (Although they do: e.g. in Yorkshire and Cornwall accents are distinctly different). Most individuals who have a working knowledge of English have a core vocabulary of around a thousand words, regardless of whether they are non-English speakers or just highly nonverbal, reticent persons. Then there is the age factor: a study showed that the average 40-year old has a vocabulary of around three times that of the average 20-year old. Does that mean that we should revere elders in our society for their mastery of language, if for no other reason? English has also borrowed words from many countries - thanks to its colonial past - many of which are no longer used.

Undoubtedly there are also fashions: words come and go, enjoying a brief currency. Today’s latest invention is tomorrow’s cliché, and is relegated to ancient history the next day. Who cares today about the correct way to say: ‘rattan’? Other than a small minority of people that sit in rattan chairs or sell them to others. Who shall speak long-dead words, their corpses putrefying in unopened dictionaries?

Then there are many words that are specialized jargon that few lay people will – with luck - ever come in touch with e.g. medical or scientific terminology. These words draw upon linguistic heritages from the Greeks and the Romans, like twin backbones, that are no longer required for the large majority of today’s school children.

In the 1950’s, C.P.Snow propounded his Two Cultures theory, in which he argued that scientists/engineers and artists/writers live in two exclusive worlds and don’t talk to each other. I recall that my English teacher in high school – whose name happened to be Mr.Englander – once complained that he had just picked up a science journal and tried to read it: it was definitely in English, but he could not grasp the meaning of the text! Since then, the fragmentation of culture has, if at all, accelerated. Even within science and technology there are many tribes who are happy to be unaware of each other’s existence, let alone thinking. We no longer have a Renaissance Man (or Woman) who can straddle all the fields of knowledge. Instead, we have chieftains who lord it over their respective fiefdoms. And shall these pigmies rule our thoughts?

The substantive point is that there are many words – in fact, the large majority of the million-odd English words - that are not in common use, and are literally unheard-of outside the halls of academe. (A very well-educated adult may know at most 50,000 words). Only a minuscule minority of the population would ever speak these words in a lifetime without stumbling – as though they were foreign exotica. The province of professors, indeed! So, are we to rely upon a few professors in Oxbridge and/or Harvard/Yale to arbitrate the correct pronunciation of the vast majority of words? Or the engineers and scientists who decide, in their own idiosyncratic ways, to name things the way they please?

The lingo of the stockbroker is very different from that of the deep sea driller or the cowboy. The advantage of all this fragmentation, however, is that the people who create new words are everywhere, in every profession, at every social ‘level’. We no longer completely depend upon a priesthood of knowledge creators residing in a handful of universities. Today the whole world is interconnected by the Internet, and English spoken in a myriad of ways. We still manage to communicate with each other. Ideas from one language are adopted by another: in this respect English continues to be the most prolific, if not avaricious, creator and adopter of words and even ideas. However, this dominant position may soon be challenged with the further broadening of the Internet to include widely-spoken languages such as Chinese and Hindi.

The question of comprehension might be more serious than is apparent. What prevented American and English from becoming two different languages? If the Americans and the British had stopped talking to each other and gone their separate ways, English might well have fissioned in two. Partly this did not happen because the language is written and because common historical factors prevailed over fissiparous tendencies. Increasing travel and communication also helped to maintain the status quo. An American who goes to live in the U.K. will suffer mild cultural shock – like having to call an elevator a lift – but nothing like what happens if (s)he were to go to France!

The Internet (via Google) has become the fact-checker of first resort, settling most arguments that would have (in bygone days) meandered on forever. However, even the All-Knowing Internet can only reflect the existing divides in societies. This also extends to matters of controversial pronunciation. One might have thought that homogenized, multinational, mass media would have smoothed out all these linguistic wrinkles, but even the hallowed BBC has succumbed to plurality: it showcases a variety of British accents, other than the fabled (if endangered) Oxbridge accent. People stubbornly hang on to their accents, their imagined (if not imaginary) identity markers, regardless of all the Internet resources that presume to tell them how to say what. But the Internet has helped: it has replaced the bulky multi-volume dictionaries of yore... and just in time, too, since the number of English words has crossed a million long ago (unlike the French Academy which insists only on linguistic purity and has barely reconciled itself to a hundred thousand words).

Despite the growing intercontinental digital rift, the Internet will go on democratizing languages and diversity shall prevail over hegemonistic tendencies. The Internet acts as an agent to resist totalitarianism: no one has a monopoly on the Truth; the best you can hope for is a franchise. While we cannot let loose anarchy and let everyone pronounce every word every which way (‘Who is to be the master?’ asked Humpty Dumpty), we may yet relax the grip of Oxbridge cabals. We do not expect class wars to end forthwith, nor that xenophobia will die, but a multitude of world views and accents will contend noisily while shaping the colo(u)rful mosaic of the future. Meanwhile, go ahead, refuse to spell it as Worcestershire, write is as Woostershire, and say it the same way. As Prof.Higgins may have dimly anticipated, English no longer belongs just to the English - let alone to the Oxbridge professors.

S&T: converting myth into reality

Science and Technology: Converting myth into Reality

This is a theme which has been discussed before, but I want to look at it in the context of three recent developments.
At the outset, of course, one must pay homage to Arthur C.Clarke's 3rd law:

http://tardis.wikia.com/wiki/Clarke%27s_Law

Clarke's Law states that:

Any sufficiently advanced form of technology is indistinguishable from magic.

And since myth is about magic, that just about says it all.

It is a truism that the remote controls that we use so nonchalantly are akin to magic wands. The next step was taken by Prof.Kevin Warwick who, in 1999, embedded a remote control in his body which could control lights, doors, computers, etc... "Look Ma! No wand!"

http://www.salon.com/tech/feature/1999/10/20/cyborg/index2.html

However, the remote control today seems prosaic and quotidian.

Something much more magical is the cloak of invisibility, used by Harry Potter, but probably a lot older. I would have to search out the oldest, but here is the link for "Prince Bairam and the Fairy Bride" which mentions an 'invisible cap"(Charles Swynnerton: Indian Nights' Entertainment. Folk-Tales from the Upper Indus. London 1892, Nr. 82.):

http://www.maerchenlexikon.de/etexte/400/te400-010.htm,

Although H.G.Wells's The Invisible Man is probably the first full-fledged science fiction novel discussing the idea. A few years ago, at Duke University, the 'cloak of invisibility' was first demonstrated in two dimensions and at one wavelength in the microwave region.

http://www.physorg.com/news80488753.html

It was pointed out that you would need much better precision to attain invisibility in the visible wavelength (since wavelengths are much shorter than the microwave), but this too has been recently (Aug.2008) achieved - almost - using metamaterials:

http://www.sciencedaily.com/releases/2008/08/080811092450.htm

Not only that, acoustic cloaking has also been demonstrated:

http://www.technologyreview.com/Nanotech/20912/?a=f

That means, in principle, a cloak that prevents anyone from seeing or hearing you could be made...
Anyway, the details of how these feats are being achieved are best left to those who are developing them...The point I want to make is that scientists and technologists, very systematically, are creating these embodiments of ancient myths, with even add-ons (like acoustic cloaking) that may not have occurred to early dreamers but will certainly appeal to users (spies, thieves, soldiers...)

The second myth I want to discuss is the idea of shape-shifters e.g. werewolves. Apart from the horrific and lunatic elements of these stories, one can envisage that there might be advantages to being able to change your shape at will, in a protean fashion. A recent innovation by BMW is the shape-shifting car. I know: it isn't the same thing, but one has to start somewhere...

http://blog.wired.com/cars/2008/06/bmw-builds-a-ca.html

The hydraulic actuators allow the owner to change the shape of the car e.g. wider fenders, spoiler: yes or no...Of course, it's just a concept car, covered with fabric, that's going to end up in the museum. But it is a demonstration, a proof of concept.

A more radical idea is that of shape-shifting robots, that might be able to reconfigure their modular bodies from a worm-like shape suitable for tunneling through drainage ducts to something like a crane, suited for heavy lifting. The video link is for a robot that "starts from a short tower, changes to a carousel, a walking spider, battle robot and lastly a tank":

http://www.hemmy.net/2006/03/30/shape-shifting-robot-video/

The last thing I want to discuss is the Jack the Beanstalk story. We all know the rest of the story about the giant, but let us stick to the beanstalk: a device for getting higher, way above the clouds. Actually, no known material could sustain its own weight if it got that high, and most certainly no beanstalk. But the concept of the space elevator could well render rockets and space shuttles irrelevant.

http://en.wikipedia.org/wiki/Space_elevator

The space elevator was proposed by the visionary Russian scientist Konstantin Tsiolkosky in 1895. It is a cable that extends from Earth's surface to the geostationary orbit 36,000 kms away. It is theorized that carbon nanotubes are strong enough, but technologically no one yet knows how to make them long enough! Current status: "On February 13, 2006 the LiftPort Group announced that, earlier the same month, they had tested a mile of "space-elevator tether" made of carbon-fiber composite strings and fiberglass tape measuring 5 cm wide and 1 mm (approx. 6 sheets of paper) thick, lifted with balloons." Way to go! Just about 20,000 miles, in fact...

The moral of these three stories is that S&T are well on their way to translating myths into reality: cloaks of invisibility and inaudibility, shape-shifting cars and robots, and space elevators.

Essentially, science and technology are a powerful dynamic duo that systematically make ancient dreams real. Can they do everything? Probably not, but there's an awful lot that they can do.
It is meet that one closes this blog with Clarke's 1st law:

http://en.wikipedia.org/wiki/Clarke%27s_three_laws

1. When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong.
2. The only way of discovering the limits of the possible is to venture a little way past them into the impossible.
3. Any sufficiently advanced technology is indistinguishable from magic.