Wednesday, December 22, 2004

Christmas

At Christmas I no more desire a rose, Than wish a snow in May's
new-fangled shows; But like of each thing that in season grows.
-- William Shakespeare --

Sunday, October 24, 2004

eternity

To see the world in a grain of sand, and to see heaven in a wild flower, hold infinity in the palm of your hands, and eternity in an hour.

-- William Blake --

Sunday, October 17, 2004

Speech recognition

"Human beings' recognition of speech consists of many tasks, ranging from the detection of phonemes from speech waveforms to the high-level understanding of messages. We do not actually hear all speech elements; we realize this easily when we try to decipher foreign or uncommon utterances. Instead, we continuously relate fragmentary sensory stimuli to context familiar from various experiences, and we unconsciously test and reiterate our perceptions at different levels of abstraction. In other words, what we believe we hear, we in fact reconstruct in our minds from pieces of received information.
Even in clear speech from the same speaker, distributions of the spectral samples of different phonemes overlap. Their statistical density function are not Gaussian, so they cannot be approximated analytically. The same phonemes spoken by different persons can be confused too; for example, the /ε/ of one speaker might sound like the /n/ of another. For this reason, absolutely speaker-independent detection of phonemes is possible only with relative low accuracy."

(The Neural Phonetic Typewriter, Teuvo Kohonen - IEEE 1988)

optoelectrical speech transcriber

"In 1930 a Hungarian scientist, Tihamer Nemes, filed a patent application in Germany for the principle of making an optoelectrical system automatically transcribe speech. His idea was to use the optical sound track on a movie film as a grating to produce diffraction patterns (corresponding to speech spectra), which then could be identified and typed out. The application was turned down as “unrealistic.” Since then the problem of automatic speech recognition has occupied the minds of scientists and engineers, both amateur and professional."

(Teuvo Kohonen, IEEE March 1988)

Long hair

Long on hair, short on brains.
- French Proverb -

Balzac

Love is the poetry of the senses.
-- Honoré de Balzac --

Most people of action are inclined to fatalism and most of thought believe in providence.
-- Honore De Balzac --

It is easier to be a lover than a husband for the simple reason that it is more difficult to be witty every day than to say pretty things from time to time.
-- Honore De Balzac --

Tuesday, August 31, 2004

The Role of Phidippides

Phidippides a professional runner of the Athen's army is the one whose tale was immortalized by the Olympic Marathon.
The Athens were fighting the Persas and they were outnumbered, so the Athenian generals send Phidippides to call for Sparta's help. He run 140 miles and another 140 miles back with the disappointing news that the Sparta agreed to help but said they would not take the field until the moon was full due to religious laws. They fought in disadvantage, but they launched a surprise offensive thrust which at the time appeared suicidal and won the battle. Phidippides was again called upon to run from the battlefield in Marathon to Athens (26 miles away) to carry the news of victory and warning about the approaching Persians ships. He reached Athens in 3 hours delivering the message and died thereafter from exhaustion.
When the modern Olympics began in 1896, the tale of Pheidippides' feat was immortalized: A 24.8-mile race would serve as the final event of the Games, covering the route from Marathon Bridge to the Olympic Stadium in Athens.

Thursday, August 19, 2004

Critique of Practical Reason

Zwei Dinge erfüllen das Gemüt mit immer neuer und zunehmender Bewunderung und Ehrfurcht, je öfter und anhaltender sich das Nachdenken damit beschäftigt: Der bestirnte Himmel über mir und das moralische Gesetz in mir.
[Two things fill the mind with ever new and increasing wonder and awe, the more often and the more seriously reflection concentrates upon them: the starry heaven above me and the moral law within me.]
-- Immanuel Kant --

Tuesday, August 17, 2004

words, thoughts and reality

As words miss when they want to express any thought, thoughts also miss when they want to express any reality.
-- Fernando Pessoa --

night and silence

Il ne voit que la nuit, n'entend que le silence.
[He sees only night, and hears only silence.]
-- Jacques Delille --

Conversation between Achilles and Tortoise

"Tortoise: (...) But it is beautiful anyway, is it not?
Achilles: Oh, yes, there is no doubt of its beauty.
Tortoise: I wonder if its beauty is related to its impossibility. (...)"

Introduction - Gödel, Escher, Bach - Douglas Hofstadter - pq. 29

Juana's Dream

Juana's Dream - Eduardo Galeano

She strolled through the market of dreams. The saleswomen settled various dreams over big clothes on the ground.

There arrives Juana's grandfather, deeply sad as it's a long time he doesn't dream. Juana takes him by the hand and helps him to choose dreams, dreams of marzipan or cotton, wings to fly while sleeping, and they go away, both, so full of dreams that there won't be enough night.

(translated by me)

Justice


A personification of the four cardinal virtues (Justice, Prudence, Fortitude and Temperance) represented usually by the scale, the sword, the blindfold and the law books. She symbolizes the fair and equal administration of the law, without corruption, greed, prejudice, or favor.
This figure dates back to the ancient history. The Ancient Egyptians referred to Ma'at, a woman carrying a sword with an ostrich feather in her hair to symbolize truth and justice. The Ancient Greeks believed in Themis, the goddess of divine justice and law. She held a pair of scales upon which she weighs the claims of disputing parties. She was daughter to Uranus and Gaia and was a partner and advisor to Zeus. Themis was a Titan who believed in and taught obedience to laws and peace. "She became known as a goddess of divine justice." The Roman goddess of justice was called Justitia. She’s represented by the constellation Libra, shaped like a heavenly pair of scales.

Thursday, August 12, 2004

mortals

"We are all mortal until the first kiss and the second glass of wine."
-- Eduardo Galeano --

Sunday, August 01, 2004

Measure

"Measure what is measurable, and make measurable what is not so."
-- Galileo Galilei --

Fourier

"Fourier is a mathematical poem."
-- Lord kelvin --

Möbius Strip


In the eighteenth century, Euler observed that for polyhedra the number of vertices minus the number of edges plus the number of faces equals two. But this relations does not states for all polyhedra, as for example, for a polyhedron with a hole. The astronomer and mathematician August Ferdinand Möbius (1790-1868) studied the geometrical theory of polyhedra and identified surfaces in terms of flat polygonal joined pieces. The Möbius strip, a continuous surface named after him, has only one side and one edge. Starting in any point in its surface, one can reach every point on the strip without even crossing an edge. The Möbius strip is a mathematical construction that shows an evolution from a two-dimensional space into a three-dimensional one, by merging inner and outer spaces it creates a single continuously curved surface. The Möbius strip is also a non oriented surface. In order to be an oriented surface it should, for any point on the surface, have normal vectors with opposite directions.

The torus has a parametric equation:
1. x = (R + L*Cos(Alpha)) * Cos(Theta)
2. y = (R + L*Cos(Alpha)) * Sin(Theta)
3. z = L*Sin(Alpha)
Alpha and Theta ranging from 0 to 360 degrees

The strip of Möbius has a very similar parametric equation:
1. x = (R + L*Cos(Alpha/2)) * Cos(Alpha)
2. y = (R + L*Cos(Alpha/2)) * Sin(Alpha)
3. z = L*Sin(Alpha/2)
Alpha ranging from 0 to 360 degrees, L ranging from -Lmax to +Lmax

The Möbius strip has provided inspiration both for sculptures and for graphical art. Maurits C. Escher is one of the artists who was especially fond of it and based several of his lithographs on this mathematical object. It is also a recurrent feature in science fiction stories, such as Arthur C. Clarke's The Wall of Darkness. Science fiction stories sometimes suggest that our universe might be some kind of generalised Möbius strip.
In the short story "A Subway Named Moebius", by A.J. Deutsch, the Boston subway authority builds a new line; the system becomes so tangled that it turns into a Möbius strip, and trains start to disappear.
There have been technical applications; giant Möbius strips have been used as conveyor belts that last longer because the entire surface area of the belt gets the same amount of wear, and as continuous-loop recording tapes (to double the playing time).

Saturday, July 31, 2004

Reason

"Reason is the substance of the universe, the design of the world is absolutely rational."
-- Hegel --

Orchid Flower


Among the most diverse flowering plants are the Orchids. Their name comes from the Greek orchis meaning 'testicle', from the appearance of structures called pseudibulbs. They are monocotyledonous plants and usually found in humid and warm places. Ancient people considered orchids as aphrodisiacs and they were a symbol of fertility. They were ratter used in love spells and it was believed to protect against diseases. In spring patties, the chinese used orchids to frighten evil spirits. It was also consecrated to the german goddess-mother Frija.

Wednesday, July 28, 2004

The Mind's Eye

An Experience of Blindness

"Rain has a way of bringing out the contours of everything; it throws a coloured blanket over previously invisible things; instead of an intermittent and thus fragmented world, the steadily falling rain creates continuity of acoustic experience... presents the fullness of an entire situation all at once... gives a sense of perspective and of the actual relationships of one part of the world to another."

Tuesday, July 20, 2004

dot the i

"A kiss, when all is said, what is it?
A rosy dot placed on the "i" in loving;
'Tis a secret told to the mouth instead of to the ear."
--Edmond Rostand.

The Bastille



The Bastille was a former French prison fortress in the East end of the city of Paris built around 1370. It was despised as a symbol of despotism and royal tyranny. The Bastille was constructed to defend the eastern wall of Paris from hostile forces. With walls over eighty feet high and well stocked and supplied arsenal, the Bastille quickly gathered the reputation of one of France's most secure military stronghold. However, after being defeated several times, the importance of the fortress diminished and by the early seventeen hundreds it had already become a prison. And so it remained during the 17th and 18th centuries being used mainly for housing political prisoners. Among those prisoners there have been famous ones, such as Voltaire, the famous political writer, and Marquis de Sade, a well-known French writer. The most famous and mysterious prisoner of the Bastille, is the legendary man in the iron mask, whose character is in a famous book, written by Alexander Dumas. At the outbreak of the French Revolution in 1789, the Bastille was attacked and stormed by a mob. They found only seven prisoners inside: four forgers, two lunatics and a young noble. The Bastille's fall became a symbol of the end of the Monarchy and the beginning of the First Republic. Two days later the destruction of the stronghold was begun amid great public rejoicings. The site is now an open square, called the Place de la Bastille.


Thursday, July 08, 2004

Finite Element Method

The Finite Element Method (FEM) is a method for solving equations by using approximations of continuous quantities by a set of discrete ones, at discrete points, often displayed into a mesh or a grid. As the FEM can be adapted to problems of great complexity, it can incorporate material properties, anisotropy, boundary conditions, and unusual geometry, it is a extremely powerful tool in the solution of important problems, such as, heat transfer, fluid mechanics, mechanical systems, electromagnetic problems and acoustic problem, as will we will see later. Formulation of problems with the FEM is based on the minimization of the total potential energy of the system via a variational principle. I've written a brief introduction. You may find it at:
http://www.cefala.org/~leoca/acoustics/afem

Tuesday, June 29, 2004

Oliver Cromwell


Oliver Cromwell was born on 25 April 1599 in Huntingdon. Cromwell was a highly visible and volatile member of parliament. In 1626, the King Charles I, dissolved the Parliament. As he had become unable to raise money without it, he had to assembled a new one in 1628. Among the members elected was Oliver Cromwell. The new Parliament drew up the Petition of Right in 1628, and Charles accepted it as a concession to get his subsidy, although it had limited the monarchs power. However, Charles was determined to rule without summoning another Parliament, and this required him to devise new means of raising extraordinary revenue. Charles I managed to avoid a Parliament for a decade, a time known as the "Eleven Years' Tyranny". The English Parliament, having controverted the king's authority, raised an army led by Robert Devereux. The civil war starts in 1642. Oliver Cromwell leaders the parliamentary army. Although Cromwell had some difficulty in finding judges to take part, in 1648, by a 68 to 67 vote, the Parliament found Charles I guilty of treason, being a "tyrant, traitor, murderer and public enemy". He was executed at the Palace of Whitehall in 1649. The Republic is settled in 1649 and in 1653 Cromwell dissolved the Parliament and makes his own dictatorship. In 1658, his health inexorably failed him and he died on 3 September and was buried in Westminster Abbey. Oliver Cromwell had gone from commoner to Lord Protector, the most powerful man in England.

Some quotes from Oliver Cromwell.
"Necessity hath no law. Feigned necessities, imaginary necessities, are the greatest cozenage men can put upon the Providence of God, and make pretences to break known rules by." (Speeches--To Parliament)
"It is not necessary for the public to know whether I am joking or whether I am serious, just as it is not necessary for me to know it myself." (Speeches--To Parliament)
"Paint me as I am. If you leave out the scars and wrinkles, I will not pay you a shilling." (Remark to the Painter, Lely)
"One never rises so high as when one does not know where one is going."(to M. Bellievre, found in "Memoirs" of Cardinal de Retz)
"Put your trust in God, but keep your powder dry."
"He who stops being better stops being good."
"Do not trust to the cheering, for those persons would shout as much if you and I were going to be hanged."
"What is all our histories, but God showing himself, shaking and trampling on everything that he has not planted."
"Make the iron hot by striking it."
"Subtlety may deceive you; integrity never will."

Monday, June 28, 2004

Complex Systems

"As the complexity of a system increases, our ability to make precise and yet significant statements about its behavior diminishes until a threshold is reached beyond which precision and significance become almost mutually exclusive characteristics."
-- L. A. Zadeh --
from: Outline of a new approach to the analysis of complex systems and decision processes. IEEE Transactions on Systems, Man and Cybernetics, January 1973.

Thursday, June 17, 2004

Chi-Square Test

Chi-square test is a test to measure the goodness of a data fitting a given distribution. Suppose you postulated a probability model to a some random experiment and now you want to determine how good this assumption was. What should you do then? The chi-square test is widely used to determine the goodness of fit of a distribution to a set of experimental data.
There are two basic elements in the method. First, a measure is defined between the experimentally observed value and the value that would be expected if the postulated pmf(probability mass function)/pdf (probability density function) were correct. Second, this measure is compared to a threshold to determine if the difference between the observations and expected results is too large. This threshold is defined by the significance level of the test, which is selected by the investigator.
To perform the chi-square method to a set of random data that represents a random variable X, the first step is to partition the sample space Sx into a union of K disjoint intervals. Under the assumption that X has the postulated cdf(cumulative distribution function) we may compute the probability that an outcome falls in the kth interval. Then mk=n.bk is the expected number of outcomes to fall in the kth interval if n repetitions of the random experiment are performed. The chi-square statistic is defined as the weighted difference between the observed number of outcomes, Nk, that fall in the kth interval, and the expected number mk,

Chi-Square Statistic

If the fit is good, then D2 é small. Therefore the hypothesis is rejected id D2 is too large, that is, if 2 ³ tα where tα is a threshold determined by the significance level of the test.
The chi-square test is based on the fact that for large number of repetitions of the experiment, n,then the random variable D2 will have a pdf that is approximately a chi-square pdf with K-1 degrees of freedom. Thus the threshold tα can be computed by finding the point at which

P[X ³ tα] = α,

where X is a chi-square random variable with K-1 degrees of freedom.

K5%1%
13.846.63
25.999.21
37.8111.35
49.4913.28
511.0715.09
612.5916.81
714.0718.48
815.5120.09
916.9221.67
1018.3123.21
1119.6824.76
1221.0326.22

A few values for threshold for the chi-square test.

Sunday, June 13, 2004

Diphthongs

Diphthong is a gliding monosyllabic speech sound that starts at (or near) an articulatory position for one vowel and moves towards a position for another. The diphthong's dynamic quality is in contrast to the vowels which at least in theory are stable segments and can thus be termed monophthongs.
The diphthongs are produced by varying smoothly the vocal tract between one vowel configuration to another's. The figure bellow shows a spectrogram plot for a the diphthong /ay/ spoken by a male talker (myself). In the picture it's possible to see the gliding motion of the formants.
Spectrogram of a diphthong
According to the diphthong's definition given above, there are six diphthongs in American English, namely /ay/ (as in buy), /aw/ (as in down), /ey/ (as in bait), and /cy/ (as in boy), /o/ (as in boat), /ju/ (as in you).

One dollar is missing [riddle]

Three men checked into a hotel room for which they paid $30. The next day, the manager realized that the men had been overcharged. She gave the bellhop $5 to return to the three men. On the way to their room the bellhop decided to keep $2 for himself, and give each of the three men one dollar. The three men had now paid $9 each, or a total of $27. This plus the $2 the bellhop kept makes a total of $29. What happened to the other dollar?

This one is pretty easy!

Friday, June 11, 2004

Taddeo Gaddi

Taddeo Gaddi, son of Gaddo, was born in Florence and was a pupil of Giotto and one of he's majors collaborators. His style is typically giottesque. Gaddi has a simple but at the same time carefully studied composition, with its coherent conception. Gaddi has succeeded in recreating the tri-dimensionality, weight and forms of the figures as well as the expressiveness of their faces.
The painting bellow is one example of Gaddi's great work. The angel on the left seems to be moving toward something outside the panel. Bellow we can see a sheep and a stick which may be a shepherd's crook, suggesting that the scene continues to the left with the episode of the Annunciation to the Shepherds. One characteristic of the school of Giotto is the use of groups of standing figures in the compositions. In "The Nativity" the tow women in the right form a conical shape and together with tower behind closes the composition and provides a vertical counterbalance to the pronounced horizontality of the rest of the scene.

The Nativity by Taddeo Gaddi
The Nativity - Taddeo Gaddi

Chaos Theory

It has been said that something as small as the flutter of a butterfly's wing can ultimately cause a typhoon halfway around the world.
-- Chaos Theory --

Thursday, June 10, 2004

heart

The heart is half a prophet.
-- Yiddish Proverb --

time

The best way to fill time is to waste it.
-- Marguerite Duras --

Maximum Entropy Method

The maximum entropy method is a principle for estimating, make statistical inferences over partial knowledge. It is the least biased estimate possible on the given information, a technique used to estimate input probabilities where little or no information is available.
Specifying probabilities in lack of information is an old world problem. Laplace’s ”Principle of Insufficient Reason” was an attempt to supply a criterion of choice, which says that there is no reason to assign other but equal probabilities when no further information is assumed. However, except in a situation where there is an element of symmetry that clearly renders equal probabilities between events, this assumption is just as arbitrary as any other.
The Principle of Maximum Entropy was originally motivated by Statistical Mechanics, trying to relate macroscopic measured properties of physical systems to microscopic models of the matter. This is a typical situation where there is only little information available and a physical system will be approached with no further assumptions. This principle was pioneered by Edwin T. Janes (1922 - 1998), a professor at Washington University in St. Louis, who first published ”Information Theory and Statistical Mechanics”[1].

[1] Edwin T. Jaynes, Information Theory and Statistical Mechanics, Physical Review, vol. 106, no. 4, pp. 620-630, May 15, 1957. http://bayes.wustl.edu/etj/articles/theory.1.pdf

Where do Emotions come from?

According to the James-Lange theory, provoking stimuli will cause some change in physiological state. Emotion is the cognitive interpretation of these changes. Emotion is the mind's perception of physiological conditions that result from some stimulus. In James' oft-cited example; it is not that we see a bear, fear it, and run. We see a bear and run, consequently we fear the bear. Our mind's perception of the higher adrenaline level, heartbeat, etc., is the emotion.
Here is a passage from his great work, "Principles of Psychology":
"We must immediately insist that aesthetic emotion, pure and simple, the pleasure given us by certain lines and masses, and combinations of colors and sounds, is an absolutely sensational experience, an optical or auricular feeling that is primary, and not due to the repercussion backwards of other sensations elsewhere consecutively aroused. To this simple primary and immediate pleasure in certain pure sensations and harmonious combinations of them, there may, it is true, be added secondary pleasures; and in the practical enjoyment of works of art by the masses of mankind these secondary pleasures play a great part. The more classic one's taste is, however, the less relatively important are the secondary pleasures felt to be, in comparison with those of the primary sensation as it comes in. Classicism and romanticism have their battles over this point. Complex suggestiveness, the awakening of vistas of memory and association, and the stirring of our flesh with picturesque mystery and gloom, make a work of art romantic. The classic taste brands these effects as coarse and tawdry, and prefers the naked beauty of the optical and auditory sensations, unadorned with frippery or foliage. To the romantic mind, on the contrary, the immediate beauty of these sensations seems dry and thin. I am of course not discussing which view is right, but only showing that the discrimination between the primary feeling of beauty, as a pure incoming sensible quality, and the secondary emotions which are grafted thereupon, is one that must be made."

Multimodal Speech Reproduction

Speech is usually understood as an acoustic process, but it has been proved that listeners also acquire visual information during a dialogue [1][2]. Speech perception is a bimodal process, in which both auditory and visual perception play their roles. A striking demonstration of this fact was discovered when Harry McGurk and John MacDonald were studying how infants perceive speech during different stages of development and accidentally created a videotape with the audio syllable /ba/ dubbed onto a visual /ga/. When listeners watched the tape they perceived /da/, which is in articulatory means between these two. This audio-visual illusion has become known as the McGurk effect [3][4].

[1] Q. Summerfield, Use of visual information for phonetic perception, Phonetica, no. 36, pp. 314–331, 1979.
[2] E. Vatikiotis-Bateson, I.M. Eigsti, S. Yano, and K. Munhall, Eye movement of perceivers during audiovisual speech perception, Perception & Psychophysics, 1998.
[3] H. McGurk and J. MacDonald, Hearing lips and seeing voices, Nature, no. 264, pp. 746–748, 1976.
[4] J. MacDonald and H. McGurk, Visual influences on speech perception processes, Perception and Psychophysics, no. 24, pp. 253–257, 1978.

* text extracted from "A System for Multimodal Speech Reproduction" by Nicolau Werneck, Lucas Malta, Leonardo Araujo and Hani Yehia, published in SIBGRAPI 2003.

Thursday, June 03, 2004

Goldberg Variations

"The Goldberg Variations is the last of a series of keyboard music Johann Sebastian Bach published under the title of Clavierübung, and is often regarded as the most serious and ambitious composition ever written for harpsichord. Based on a single ground bass theme, the variations display not only Bach's exceptional knowledge of diverse styles of music of the day but also his exquisite performing techniques. Being also the largest of all clavier pieces published during the Baroque period, the work soars high above others in terms of its encyclopedic character. From this, it is often considered that it sums up the entire history of Baroque variation, the Diabelli Variations by Beethoven being the Classical counterpart.

(...)

The music analyses that explore various possible interpretations of the work, such as multi-layered structural divisions and groupings, may be intellectually satisfying. We cannot always determine, however, the extent to which they are based on Bach's real intentions (which can be justified from historical context) from hypothetical theories based primarily on our subjective invention. It is, indeed, very difficult to sift valid and authentic interpretations from so many speculative approaches which Bach's music attracts. For instance, in his article of 1984, David Humphreys claims that the unifying device of the work is the allegorical scheme of the work, which represents an ascent through the nine spheres of Ptolemaic cosmology, and he discredits the general consensus among listeners and players, that the work represents a purely musical unifying device, as a mistake. Humphreys first divides twenty-seven variations into three cycles, and names them as Canon (3, 6, 9 ... 27), Planet (4, 7, 10 ... 28) and Virtuoso (5, 8, 11 ... 29), then makes various attempts to associate Plato's cosmological philosophy and geometry with Bach's understanding of Affektenlehre seen in his means of expression. Still we are not at all sure whether Bach, who must have been deeply engrossed with his other duties, ever had the intention or inclination to undertake such highly abstract and profound mathematical stuff. It is amazing, to say the least, that the Goldberg Variations can also 'refresh ... spirits' of musicologists who were not able to share such experiences from listening to the work."
-- http://www.pentaone.com/hannibal/goldberg.shtml --


"The Goldberg Variations begin with an Aria Bach had composed in 1725, possibly for his wife This Aria appears in Anna Magdalena's Notebook, where it is written in her own hand. The Sarabande-like Aria becomes theme for a set of 30 variations to follow."

An analysis of each canon may be found at:
http://jan.ucc.nau.edu/~tas3/goldbergcanons.html

magic

One man's "magic" is another man's engineering. "Supernatural" is a null word.
-- Robert Heinlein --

On Acoustc Field

The instantaneous acoustic intensity correspond to the energy flux
density per unit of time, it is the instantaneous rate per unit of
area at which work is done by one element of fluid on an adjacent
element. The acoustic intensity is measured in W/m2 and is
determined by the product of acoustic pressure and the complex
conjugate of the particle velocity (if we're treating those
acoustics variables as complex exponentials).

I = P U*

Let's suppose that both acoustic pressure and particle velocity
are harmonic functions of time (which is quite a suitable
assumption). So they might be expressed as:
P = P0 e- j ω t
U = U0 e- j ω t + θ
so the instantaneous intensity is
I = P0 U0 e- j θ

If we're dealing with real entities we have:
p = P0 cos(ω t)
u = U0 cos(ω t + θ)
i = P0 U0 cos(ω t) cos(ω t + θ)
i = P0 U0 cos2(ω t)cos(θ) - (P0 U0/2) sen(2 ω t)sen(θ)
i = (P0 U0/2) cos(θ) + (P0 U0/2) cos(θ) cos(2 ω
t) - (P0 U0/2) sen(θ) sen(2 ω t)
i = P + P cos(2 ω t) - Q sen(2 ω t)
where
P = (P0 U0/2) cos(θ)
and
Q = (P0 U0/2) sen(θ)

P is called the mean intensity, or the real intensity, and Q the
reactive intensity. The real intensity describes an energy
transfer conveyed by the sound wave. The reactive intensity
corresponds to an oscillation of energy around a fixed point for
which the mean value in time is zero. When pressure and speed are
90o out of phase, the average intensity is zero, the phenomena
is pure reactive and no energy transfer produced by the sound wave
is observed.

The space surround the acoustic source is usually subdivided into
three regions: (a) reactive near-field, (b) radiating near-field
(Fresnel) and (c) far-field (Fraunhofer) regions. These regions
are so designated to identify the field structure in each.
Although no abrupt changes in the field configurations are noted
as the boundaries are crossed, there are distinct differences
among them. The boundaries separating these regions are not
unique, although various criteria have been established and are
commonly used to identify the regions.

Reactive near field is defined as that portion of the near-field
region immediately surrounding the acoustic source wherein the
reactive field predominates. The radiating near-field (Fresnel)
region is defined as that region of the field of the acoustic
source between the reactive near-field and the far-field region
wherein radiation fields predominate and wherein the angular field
distribution is dependent upon the distance from the source. The
far-field (Fraunhofer) region is defined as that region of the
field of the acoustic source where the angular field distribution
is essentially independent of the distance from the source.

Tuesday, June 01, 2004

mistakes

A computer lets you make more mistakes faster than any invention in human history - with the possible exceptions of handguns and tequila.
-- Mitch Ratcliffe --

Canon

Why not start this blog with something really interesting that is Canon.
So here goes a copy of the definition taken from Douglas R. Hofstadter in his delightful book named "Gödel, Escher, Bach: An Eternal Golden Braid".

"The idea of a canon is that one single theme is played against itself. This is done by having "copies" of the theme played by the various participating voices. But there are many ways todo this. The most straight forward of all canons is the round, such as "Three Blind Mice", "Row, Row, Row Your Boar", or "Frére Jacques", Here, the theme enters in the first voice and, after a fixed lime-delay, a "copy" of it enters, in precisely the same key. Alter the same fixed time-delay in the second voice, the third voice enters carrying the theme, and so on. Most themes will not harmonize with themselves in this way. In order for a theme to work as a canon theme, each of its notes must he able to serve in a dual (or triple, or quadruple) role: it must firstly he part of a melody, and secondly it must be part of a harmonization of the same melody. When there are three canonical voices, for instance, each note of the theme must act in two distinct harmonic ways, as well as melodically. Thus, each note in a canon has more than one musical meaning; the listener's ear and brain automatically figure out the appropriate meaning, by referring to context."

--Douglas R. Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid. Copyright © 1979 by Basic Books, Inc.