Among the many absurdities that told about math ignorance of their true nature, he is one which is to describe the great captains "Mathematicians of the battlefield." In fact, if we are to avoid catastrophe, it must not exceed their logical calculations the innocent simplicity of the four operations. The sudden need for a deduction also moderately subtle and complex than solving a simple differential equation would cost the lives of thousands. This attack is not the strategy is to defend the uniqueness of mathematics. They say they are for thinking the utmost economy, and without doubt this is true. But the very fact of thinking is a dark matter and problematic. It became a long time (even when it would have been first a simple savings biological) complexity passion to spare, which is not concerned over the postponement of the result that the sparing of his poverty, slowly luxuriously converted into its opposite.
Mathematics permit, under favorable conditions, to complete a transaction in moments such as the addition of an infinite series, we would be unable to ever complete otherwise. They can already make the machine complex logarithmic calculations, integrations and up, the work of modern computer terminal arranging the data of the problem and turning a crank or push a button. Thus, a simple wizard? He able to dispatch problems that his teacher, only two hundred years ago, could have solved without consulting London Newton and Leibniz in Hanover. Even for problems that the machine is still unable to resolve (of course, many more), we can see mathematics as an intellectual ideal device whose purpose, and success are to predict, from first principles, all possible cases.
is the triumph of rational organization. The highways of reason, threatened Bad weather and bandits, have replaced the lines of sleeping cars. From the perspective of the theory of knowledge, that is, without doubt, an economy.
We wondered what proportion of these possible cases actually served. We calculated how much of life, money, fatigue, ambitions have been spent in the history of this huge savings system, how many are still there and need to be invested, even if that not to lose the acquis, and we have tried to be balanced with the profit gained. Again, this device certainly complicated, cumbersome, proved economically incomparable and cleanly. Our entire civilization owes its existence, and we can not by any other means to replace and it fully meets the needs it meets, and the generosity of its operation is to empty one of these unique facts that are beyond the critical.
must therefore look away profits extrinsic apply, even within mathematics, the distribution of elements remained unused, to discover the other face, the true face of this science. So anything less than effective, it is expensive and passionate nature. The average man does not use more than primary school has taught him, the engineer, just enough to find themselves in the columns of formulas technical manuals, that is to say not much, the physicist himself Similarly, ordinary, working with mathematical means relatively poorly differentiated. She needs? It more, it is often limited to himself, mathematicians with little taste for this kind of adaptation. That is how, in many areas of this science (areas of undeniable practical importance), specialists are found to be non-mathematicians. But next door, huge range of areas which exist only for the mathematician, like a vast network of nerves around the attachment points of a few muscles. Somewhere in there that works the mathematician isolated: its windows are not on the outside, but adjacent rooms. He is a specialist: we can not conceive of genius who is still able to dominate the whole. Probably thinks that his work will eventually return one day exploitable advantage, but this is not what stimulates him and he is with the truth, that is to say, his destiny him, not the end of this destiny. The practical result of his activity he would be a miracle of economy, which inhabits it is the extravagance and passion.
Mathematics is now one of the few luxuries rashness of Pure Reason. Perhaps many philologists do they also an activity that themselves do not see the benefit, to say nothing of philatelists and collectors of ties. But these are innocent mannerisms, which are spread very far from the serious business, while there are mathematical penetrate the contrary, few? One of the most fun adventures and boldest of life. A small example: practically, one can say that we live entirely on the results of this science, which it? even completely uninterested. Our bread is cooked, our houses are built, our cars drive through it. With the exception of some manufactured goods: furniture, clothing, shoes, and children, everything is provided by the engagement of mathematical operations. All this life around us running, running or stopped, not only depends on mathematics for its comprehensiveness: it is actually the product, it lies in the infinite variety of its determinations on them. The pioneers of mathematics had done some basic representations used: where followed deductions, computing systems and results that captured physicists to obtain new results, whereupon came the technicians, who often were content to add to these results some further calculations, and machines to make their appearance . But when all this had made the world more beautiful shape, that the mathematicians (theoretical tireless nosy) suddenly discovered in the foundations of the entire company, something irremediable vice: and found by going to the bottom of things that the entire edifice was based on nothing! But the machines worked ... Here we therefore reduced to agree that our existence is pure fantasy, we live it, yes, but only by virtue of an error without which it would not! No man today, not alongside the fantastic more closely than the mathematician. This
intellectual scandal, blamed the mathematician, in an exemplary manner, that is to say with confidence and pride, the diabolically dangerous nature of his intelligence. I could cite other examples, as the fury that physicists have sometimes made to deny the reality of space and time. And this, not at all in the air, as happens to philosophers (we apologize immediately on their occupation) but based on reasons that you suddenly needed with evidence of an automobile, and incredibly reliable. But enough to understand what fine fellows we are dealing.
As for us, since the Enlightenment, we have lost much courage. A small failure was enough to disgust us intelligence, and we let the first come exalted accused of rationalism hollow attempt of a Diderot or D'Alembert. We BRAILLON for sentiment against the intellect, forgetting that without feeling the intellect, with rare exceptions, only blister. We have already so severely corrupted our literature, after he swallowed in rapid succession two German novels, it remains for us to quickly solve an integral, for swelling.
Do not object that the mathematicians out of their specialty, are being banal or stupid, that their logic is useless. Their logic is that there is no place, and they do in their field what we should do in ours. This is the lesson considerable copy of their existence: they are a picture of the future representative of the spirit.
As long as this has seriously drilled in the jokes that we had allowed here about them, the following conclusions do not appear too unexpected. People complain that there is no culture of our time. This can be understood differently, in fact, culture has always been a unit is provided to that religion or society, or even art. We have become too numerous for a company; too many also a religion (that can not be enunciating here, not evidence). And as for art, our era is the first who can not love her artists. Nevertheless, this time not only sees activity such intellectual energy than it ever was, but still experiencing harmony and unity of spirit far unsuspected. Claim that all this concerns only a limited knowledge would be stupid for a long time, the real goal is the thought in general. Without doubt, this form of thought, with its requirements of depth, boldness, novelty, merely does the time domain for IE exclusively rational and scientific. But it is slowly spreading, and when she has earned the feeling, it will deserve the name of spirit. Writers to take that step. To do this, they did not learn any method (psychological, my goodness or otherwise) only to impose requirements. Instead, they just look their situation with perplexity, and console themselves blaspheming. And if contemporary Nor can, by themselves, translate into the human level of thinking, they are nevertheless sensitive to what is still below their level.
Mathematics permit, under favorable conditions, to complete a transaction in moments such as the addition of an infinite series, we would be unable to ever complete otherwise. They can already make the machine complex logarithmic calculations, integrations and up, the work of modern computer terminal arranging the data of the problem and turning a crank or push a button. Thus, a simple wizard? He able to dispatch problems that his teacher, only two hundred years ago, could have solved without consulting London Newton and Leibniz in Hanover. Even for problems that the machine is still unable to resolve (of course, many more), we can see mathematics as an intellectual ideal device whose purpose, and success are to predict, from first principles, all possible cases.
is the triumph of rational organization. The highways of reason, threatened Bad weather and bandits, have replaced the lines of sleeping cars. From the perspective of the theory of knowledge, that is, without doubt, an economy.
We wondered what proportion of these possible cases actually served. We calculated how much of life, money, fatigue, ambitions have been spent in the history of this huge savings system, how many are still there and need to be invested, even if that not to lose the acquis, and we have tried to be balanced with the profit gained. Again, this device certainly complicated, cumbersome, proved economically incomparable and cleanly. Our entire civilization owes its existence, and we can not by any other means to replace and it fully meets the needs it meets, and the generosity of its operation is to empty one of these unique facts that are beyond the critical.
must therefore look away profits extrinsic apply, even within mathematics, the distribution of elements remained unused, to discover the other face, the true face of this science. So anything less than effective, it is expensive and passionate nature. The average man does not use more than primary school has taught him, the engineer, just enough to find themselves in the columns of formulas technical manuals, that is to say not much, the physicist himself Similarly, ordinary, working with mathematical means relatively poorly differentiated. She needs? It more, it is often limited to himself, mathematicians with little taste for this kind of adaptation. That is how, in many areas of this science (areas of undeniable practical importance), specialists are found to be non-mathematicians. But next door, huge range of areas which exist only for the mathematician, like a vast network of nerves around the attachment points of a few muscles. Somewhere in there that works the mathematician isolated: its windows are not on the outside, but adjacent rooms. He is a specialist: we can not conceive of genius who is still able to dominate the whole. Probably thinks that his work will eventually return one day exploitable advantage, but this is not what stimulates him and he is with the truth, that is to say, his destiny him, not the end of this destiny. The practical result of his activity he would be a miracle of economy, which inhabits it is the extravagance and passion.
Mathematics is now one of the few luxuries rashness of Pure Reason. Perhaps many philologists do they also an activity that themselves do not see the benefit, to say nothing of philatelists and collectors of ties. But these are innocent mannerisms, which are spread very far from the serious business, while there are mathematical penetrate the contrary, few? One of the most fun adventures and boldest of life. A small example: practically, one can say that we live entirely on the results of this science, which it? even completely uninterested. Our bread is cooked, our houses are built, our cars drive through it. With the exception of some manufactured goods: furniture, clothing, shoes, and children, everything is provided by the engagement of mathematical operations. All this life around us running, running or stopped, not only depends on mathematics for its comprehensiveness: it is actually the product, it lies in the infinite variety of its determinations on them. The pioneers of mathematics had done some basic representations used: where followed deductions, computing systems and results that captured physicists to obtain new results, whereupon came the technicians, who often were content to add to these results some further calculations, and machines to make their appearance . But when all this had made the world more beautiful shape, that the mathematicians (theoretical tireless nosy) suddenly discovered in the foundations of the entire company, something irremediable vice: and found by going to the bottom of things that the entire edifice was based on nothing! But the machines worked ... Here we therefore reduced to agree that our existence is pure fantasy, we live it, yes, but only by virtue of an error without which it would not! No man today, not alongside the fantastic more closely than the mathematician. This
intellectual scandal, blamed the mathematician, in an exemplary manner, that is to say with confidence and pride, the diabolically dangerous nature of his intelligence. I could cite other examples, as the fury that physicists have sometimes made to deny the reality of space and time. And this, not at all in the air, as happens to philosophers (we apologize immediately on their occupation) but based on reasons that you suddenly needed with evidence of an automobile, and incredibly reliable. But enough to understand what fine fellows we are dealing.
As for us, since the Enlightenment, we have lost much courage. A small failure was enough to disgust us intelligence, and we let the first come exalted accused of rationalism hollow attempt of a Diderot or D'Alembert. We BRAILLON for sentiment against the intellect, forgetting that without feeling the intellect, with rare exceptions, only blister. We have already so severely corrupted our literature, after he swallowed in rapid succession two German novels, it remains for us to quickly solve an integral, for swelling.
Do not object that the mathematicians out of their specialty, are being banal or stupid, that their logic is useless. Their logic is that there is no place, and they do in their field what we should do in ours. This is the lesson considerable copy of their existence: they are a picture of the future representative of the spirit.
As long as this has seriously drilled in the jokes that we had allowed here about them, the following conclusions do not appear too unexpected. People complain that there is no culture of our time. This can be understood differently, in fact, culture has always been a unit is provided to that religion or society, or even art. We have become too numerous for a company; too many also a religion (that can not be enunciating here, not evidence). And as for art, our era is the first who can not love her artists. Nevertheless, this time not only sees activity such intellectual energy than it ever was, but still experiencing harmony and unity of spirit far unsuspected. Claim that all this concerns only a limited knowledge would be stupid for a long time, the real goal is the thought in general. Without doubt, this form of thought, with its requirements of depth, boldness, novelty, merely does the time domain for IE exclusively rational and scientific. But it is slowly spreading, and when she has earned the feeling, it will deserve the name of spirit. Writers to take that step. To do this, they did not learn any method (psychological, my goodness or otherwise) only to impose requirements. Instead, they just look their situation with perplexity, and console themselves blaspheming. And if contemporary Nor can, by themselves, translate into the human level of thinking, they are nevertheless sensitive to what is still below their level.
[Text published in 1913 in the magazine Der Vogel lose; French translation by Philippe Jaccottet, Robert Musil, Essays, Threshold]
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