We distinguish diagrammatic from sentential paper-and-pencil representations of information by developing alternative models of information-processing systems that are informationally equivalent and that can be characterized as sentential or diagrammatic. Sentential representations are sequential, like the propositions in a text. Diagrammatic representations are indexed by location in a plane. Diagrammatic representations also typically display information that is only implicit in sentential representations and that therefore has to be computed, sometimes at great cost, to make it explicit for use. We then contrast the computational efficiency of these representations for solving several.illustrative problems in mathematics and physics.
Herbert SimonRelated topics
alternative contrast cost developing great mathematics plane solving text use representationsRelated quotes
I have a foreboding of an America in my children's or grandchildren's time -- when the United States is a service and information economy; when nearly all the manufacturing industries have slipped away to other countries; when awesome technological powers are in the hands of a very few, and no one representing the public interest can even grasp the issues; when the people have lost the ability to set their own agendas or knowledgeably question those in authority; when, clutching our crystals and nervously consulting our horoscopes, our critical faculties in decline, unable to distinguish between what feels good and what's true, we slide, almost without noticing, back into superstition and darkness.
Carl Sagan
It's true that my initial training was in mathematics. However, almost by accident, I happened to take a course from Kenneth Arrow on "Information Economics,” which was so inspiring that I decided to change direction. It seemed to me that economics combined the best of both worlds: the rigor of mathematics with the immediate relevance of a social science. As for how much math I would recommend, I'd say that basic analysis, including measure theory, is certainly very useful. Also, linear algebra and stochastic processes always helps. But beyond that, I don't think a huge mathematical investment is necessary to do economic theory unless you are planning to work in an extremely technical area.
Eric Maskin
Often we were joined by Maurice Princet. Although very young, he held an important post in an insurance company which he owed to his knowledge of mathematics. But outside his profession it was as an artist that he thought of mathematics, as a specialist in aesthetics that he evoked continuities in n dimensions. He liked to interest painters in the new visions of space that had been opened up by Victor Schlegel and several others. He succeeded. After having heard him by chance, Henri Matisse was caught reading an essay on hyperspace. Oh! it was only a potboiler [un ouvrage de vulgarisation]! but at least that shows that for the great 'fauve' the days of the painter who knows nothing, who runs towards a pretty subject with his beard blowing in the wind, was passed.
Jean Metzinger
Personally, I do not believe that our civilization will fall. I think that on the whole we have grown better and not worse. I think that on the whole the future holds more for us than even the great past has held. But, assuredly, the dreams of golden glory in the future will not come true unless, high of heart and strong of hand, by our own mighty deeds we make them come true. We can not afford to develop any one set of qualities, any one set of activities, at the cost of seeing others, equally necessary, atrophied. Neither the military efficiency of the Mongol, the extraordinary business ability of the Phoenician, nor the subtle and polished intellect of the Greek availed to avert destruction.
Theodore Roosevelt
I am confident that the enactment of the right bill next year will in due course increase our gross national product by several times the amount of taxes actually cut. Profit margins will be improved and both the incentive to invest and the supply of internal funds for investment will be increased. There will be new interest in taking risks, in increasing productivity, in creating new jobs and new products for long-term economic growth. Other national problems, moreover, will be aided by full employment. It will encourage the location of new plants in areas of labor surplus and provide new jobs for workers that we are retraining and facilitate the adjustment which will be necessary under our new trade expansion bill and reduce a number of government expenditures.
John F. Kennedy