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.

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."

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.

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

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."

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.

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 m_k=n.b_k 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, N_k, that fall in the kth interval, and the expected number m_k,



If the fit is good, then D² é small. Therefore the hypothesis is rejected id D² is too large, that is, if ² ³ t_α where t_α 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 t_α can be computed by finding the point at which

P[X ³ t_α] = α,

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

K	5%	1%
1	3.84	6.63
2	5.99	9.21
3	7.81	11.35
4	9.49	13.28
5	11.07	15.09
6	12.59	16.81
7	14.07	18.48
8	15.51	20.09
9	16.92	21.67
10	18.31	23.21
11	19.68	24.76
12	21.03	26.22

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

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 /a^y/ spoken by a male talker (myself). In the picture it's possible to see the gliding motion of the formants.

According to the diphthong's definition given above, there are six diphthongs in American English, namely /a^y/ (as in buy), /a^w/ (as in down), /e^y/ (as in bait), and /c^y/ (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!

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 - 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 --

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.

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 --