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(...) [The Problem of the Week] Pyramid numerical

We are approaching the end of the course in our boat school and this is the problem of the week raised:

The graph pyramid consists of bricks, each one with a number. The number of each brick is equal to the sum of the two bricks on which it rests. Find the missing numbers. (Hint: it starts out reasonably the number contained in the brick marked with an "x")

Please ... Still, do not know where is the solution? How is it possible at this point ...! Further down below, after the image!

[In this picture we see the great Pyramid of the Niches at El Tajin, Veracruz, Mexico. Belongs to the Totonac culture, a pre-Columbian civilization that lived in Mexico. If you look in detail, the pyramid is comprised of seven floors, and the number of niches or square holes on each floor in face we see in the picture, is formed, from bottom to top, the sequence 22, 19, 16, 13, 10, 7 and 5. Interestingly, the six lower floors are in arithmetic progression of difference equal -3, ie, each floor in three niches decreases as we ascend. But the top floor, the seventh, breaking the rule decreasing in only two, and instead of having 4 niches has 5. What is the reason for this correction? Referring to wikipedia entry, the total number of niches that decorate the facade matches the number of days in a year: 365. If we add the terms of the sequence, 22 + 19 + 16 + 13 + 10 + 7 + 4 = 91, and multiply by 4-sided pyramid that is, gives us 364 niches. On one side is a staircase, which slightly changes the distribution. The builders had to adapt the sequence and put five niches in the upstairs rather than four to account properly coincide with the number of days a year by adding all the niches of all faces. The image is taken from this site .]

Solution:

Obviously, without the trail of the "x" the problem would be much harder to solve. Look at the two bricks to the left, resting on the bricks indicated respectively with 19, x, 8. Each of these blocks is equal to the sum of the two on which it rests, then these numbers would be 19 + x, x + 8. Adding these two expressions have the brick above, and we get the equation:
(19 + x) + (x + 8) = 53
resolve:
19 + x + x + 8 = 53
x + x = 53 - 19 to 8

2x = 26 x = 26 / 2 = 13.

Once resolved the "x" is very easy to find out the missing numbers. The numbers in the pyramid are:

53 67 120

32 21 46 19 13 August 1938

Notes: This problem is inspired by similar problems listed in the book of David J. Bodycombe, The Riddles of the Sphinx .

Recipes With Rotel And Chicken And Pasta

During all this time could have written the veil, the Gürtel, the Eyjafjallajokull or the fair in April. But what if everyone has already written everything I could?

has also written much of Clegg, smiling young English has been released now vice president of the United Kingdom and still nobody knows what skills will be.

And the hot topic of the day, of course, cuts in government, but I have no desire to do bad blood is still very recent.

Secrets. Today I wanted to talk about secrets. But that can not. Not yet.

Where I Kate From Kates Playground From

relativism and democracy

Among the comments to previous post , one led me to think about so many questions in recent weeks that much I would like to thank the author and so sorry who has remained anonymous. Still, the more I like to be able to express the questions I was asking, but I go through a period of strong alienation, which is not suffering, and contemplative nature of ugliness cold is the cause of restlessness, inertia or rather the reluctance , awareness of the futility (and vain) to the things written, especially if the writing style one realizes the desert of his mind, which is not always unfortunate, as I have already stated twice that the rigor of the argument is rarely useful, and often we need other instruments relating to the vitality that exercising does not confer reasoning.

The reasoning is common in humans, they are as natural as being bipedal and quadrupedal horses, So who could rationally defined, with a hint of malice or ill will if we want to be a supporter obvious which state that human beings are moved on two legs. Another good is common sense not so common attribute, rare as they will know mankind, the basic system of thought by no means elementary, strongly present during childhood and thereafter subject to damage variable.

The reason is inevitable, change requires effort which ignore this function and it is inevitable that hardly differs from the destructive and sterile. The reason, says Kant afflicts us with questions that are beyond our capabilities to resolve. However, despite its inevitability, the destruction of the reason it costs imposed, such as during an earthquake, it is useful to rely on our own two legs and run, and that is what any sensible person would do if you can.

The reason is a tool, not an end, an essential tool for survival but not for the experience. Here's how it works right: in a bunker I carry the canned foods, and as my survival depends on wise use of the contents of the can, try not to overdo their consumption, thus making my estimates rations eating a can a day, I I have been fifty, should be enough for over fifty days. However my desire life and my appetite (related to the experience and not to survival) hint that I can afford another day do not hurt me in the future because maybe my stay forced fifty days but not last twenty-five, and is a challenge not to yield to such temptation against prudence. I have the use of reason, and I have the desire to satisfy my appetite does not agree with my position.

I return to the interesting comment that I referred to and faithfully reproduce it without fear of teasing as its author remains anonymous:

"I came by chance and saw your original message, which is top right. I do not understand something: You say you hate relativism but defend democracy just as democracy promotes relativism. How?. Yes, you heard right. The definition of truth, good and bad (like abortion), are subordinated to the realm of quantity, the majority of votes. Gulp! "

course I'm glad that someone, contrary to current trends, bad judge abortion, trial in which I concur, although it is often a necessary evil.

Now that I defend democracy is because I consider the most acceptable political and social systems, it is an ideal, and ideal work in progress, the democracy is born incomplete and is sensitive enough to debug and refinement. Democracy (which in no way is the government of all) is however subject to the level of society as it is applied, in a democracy governed society itself technically in terms of liability. In a democracy the individual will of man is subordinated to the government of a State in which agreements are being pursued in common, and as encompassing as many people as possible and directly or indirectly goes through their elected representatives, rather said, accepted. The opposite of absolutism in the town is due to the sovereign, and / or a select group and the prince regent, not for the same manner and amount to the people. It is then that all democracy is relativistic and that its opposite is the individual will and it is relativistic absolutism that reflects the will of an individual, to his moods, inclinations, whims, ambitions, and so on.

government say all tantamount to no government, ie government absolutism of an individual, so that morality, justice and truth depend on the willingness of an individual who meets certain powers in excess. The justice of a democratic government and respect for individual freedoms given by the law must protect them and trying to take the roles of referee, technically, "exactly in order to prevent arbitrariness and relativity of the norms of peaceful coexistence so-called laws established in their respective spheres of competence. Infeasible, impossible for any democracy prevarique Law because it would not be the judiciary to the majority of all but the one (s) by majority (exclusivity).

still anonymous commenter's objection that I find plausible:

"I think you got away on a tangent. No if quite understand your comment, but it sounds pretty naive to believe that democracy today has been perfected. Much less that the improvement is due to a system of law because the law itself is being sprayed and replaced by a purely subjective, anthropocentric view of man, become a little god, a creditor of an infinity of pseudo rights (as many as each who want to imagine) and no obligations to his office.

However, we agree with respect to relativism, but ... I disagree, along with CS Lewis, in that that the abolition of man is not possible. The abolishion of man is now happening before our eyes. "

Unfortunately I agree with him with a paradox:

Anthropocentrism encouraging start as emphasis towards humanity and wanting to remove the subject derives for the community, since there is no humanity but human, there is no face of man but of human faces.

While the measure of justice left to the arbitrariness, the alleged anthropocentrism or humanism, relativism ends up confusing, and thoroughly!, The Justice Law and morality with the Good. The community (abstract entity that purports to lay at odds with the community) creates its laws and inventing itself excites the Moral, and that they do their tribunes, the moralists, believing (even worse trying to convince) so manage to preserve the distance, now old, for them, between good and evil. In Los Miserables by Victor Hugo, the inspector pursues Jean Valjean through the sewers of the city, and once trapped, naming Valjean begs God to what the inspector otherwise screaming he does not believe in God but in the laws. The inspector, I have seen in any film adaptation, is no other way to stop the pursuit of Valjean that Quiros life by jumping into the river, as if those laws it is subject were a divine mandate inexorable.

Few things are so pathetic.

The tribunes of the community is self-serving and autocelebran stipulating the measures to prove their definitions of collective truths like called empirical truths whose prerequisite is instructed them not innate or original.

and individuality, the subject, the worst enemy of these fabricators enforcement and collective measures that have been submitted.

As loathe the particular ideas that are developed and respected within the community, the guardians of the collective order police name their opinion, their protectors of mediocrity that are due to other unfortunate artifact of the modern civilization: political ideology.

Ideology and / or political party is nothing but the scattered ideas agreement stipulated under denominators which do not fit or innovative proposals not covered (due to its aspirational character), ergo improponibles. Political ideology, a set of preconceived ideas, not only belonging to the Left, made cheaper, trivialization, flattening and popularisation of the ideals, the mediocratización the ideal and the search and maintenance of such mediocrity. It will nourish and re-creating the ideal all alone. And who adheres to an ideology, without betraying in his heart, pacta giving not only his ideals but also his personal views, unless his authority arrogated or they hold to become a dissident or a reformante.

By contrast, thanks to the invincible unpredictability of the social individual, community disintegration, the cell system and vehicle for individual development, promotes individualism courtier one who by mere convenience willingly abide by the canons and rules of the community and whose wishes are identified by the community, consumerism, and bastard bastard son of our society falsely hedonist is one of its functional manifestations leading to the scheme.

Supported purchasing power, subjectivism courteous, hardworking and tenacious through treaties while leaving consume and consume you purchased the system that has helped to build, he knows intuitively when primitive market conveniences, and opportunistic contempt of the principles, the law is available for sale, and pursues its acquisition, and it actually pursues, with the complicity and connivance of the tribunes of the community, are truly dominant class privileges. And supposed to have been imposed by his individual will.

Decline democratic sense responsible for our current West.

But I've spoken to sufficiency (not exhaustive) and perhaps, if circumstances require, I address the issue, hopefully with the help of contributions, comments, objections of potential readers.