Computational Complexity and other fun stuff in math and computer science from Lance Fortnow and Bill Gasarch
An impressive argument for basic research though a bit heavy on the
Lance, that's a fun video taken at face value, but there is another level of meaning behind it, that also is instructive to consider (and highly enjoyable too).Few things in life (IMHO anyway) are more stimulating than reading Jonathan Israel's magisterial two-volume history of the early Enlightenment, Radical Enlightenment and Enlightenment Contested in parallel with reading the (new) 2006 Army/Marine field manual FM 3-24 Counterinsurgency and the (new) 2008 Army field manual FM 3-07 Stability Operations (both of which are freely available on-line).To do so is to renew and sharpen one's appreciation of the centuries-old historical tension between (as Israel calls it) the Radical Enlightenment versus the Moderate Enlightenment; a tension that historically has been mirrored by radical versus moderate attitudes toward science, and by radical versus moderate attitudes toward economics and national security.Nowadays the radical-versus-moderate balance is tending toward radical; the Army-Marine field manuals in particular recognize this trend explicitly ... and embrace it. And this is not surprising, given that most of the officers who write these field manuals have PhDs in history, anthropology, economics, and engineering, and given the severity and the urgency of the challenges that America's military has been tasked with.The point being, that any scientist, mathematician, or engineer who reads these field manuals expecting to find simplistic or unsophisticated levels of understanding will suffer a rude awakening ... regrettably it is the modern academic literature that suffers in comparison.As White House Chief of Staff Rahm Emanuel recently said---and he was only the most recent of a long line of politicians to say it: "You never want a serious crisis to go to waste. And what I mean by that is an opportunity to do things you think you could not do before."That is how the military's strategists have come to understand, early and more deeply than the mathematical and scientific community, that we are faced not only with the opportunity, but the absolute necessity, to evolving mathematics, science and engineering in radical new directions.As for that video ... well ... it's basically a recruiting video. Isn't it?
Sorry, but field manuals for "counter"-insurgency has nothing to do with science, and even less to do with mathematics and theoretical computer science. When mathematicians talk about "radical" ideas and enlightenment, they mean ideas of mathematicians like Euclid, Lobachevsky, Gauss, Hilbert or Grothendieck -- which marked a clear departure from the past and opened up new vistas for the future. They are our guiding lights, not the authors of some "field manuals". Lets not talk about "field manuals" in the same august light -- doing so is a travesty.
Anonymous says: When mathematicians talk about "radical" ideas and enlightenment, they mean ideas of mathematicians like Euclid, Lobachevsky, Gauss, Hilbert or GrothendieckAnonymous ... while I respect your opinion ... it should also be noted that according to Prof. Israel's history of the Enlightenment, that attitude toward mathematics classifies a person---along with Newton---as belonging to the "Moderate Enlightenment" rather than the "Radical Enlightenment." See for example, Ch. 8 of Enlightenment Contested: "Newtonianism and Anti-Newtonianism in the Early Enlightenment: Science, Philosophy, and Religion." Whether you agree with Prof. Israel's conclusions or not, the level of scholarship evident in chapters like this one is pure pleasure ... on that we can all agree! :)The broader values of the Radical Enlightenment (as defined by Prof. Israel, not me) are summarized on page 866 of Enlightenment Contested (for those who have a copy at-hand). But to skip directly to that page, would be to scant Prof. Israel's immense scholarship.Anonymous concludes: "Lets not talk about "field manuals" in the same august light -- doing so is a travesty."Hmmm ... communicating a travesty was certainly not my intent ... although it is true that Prof. Israel's work has aroused a ferment of comment---mostly favorable comment---among historians.Perhaps we may both take comfort in a circumstance that is well-documented in Prof. Israel's works: the history of the Enlightenment is largely the history of moderates who have been offended by the radical!I am curious ... is there anyone other than me on this forum who has read Prof. Israel's works?Students especially (IMHO) can benefit from doing so. That's why we keep this history on the shelves of our laboratory's "Library of Subversive Literature."After all, the Enlightenment is not finished yet. Isn't it therefore a near-certainty that this century's Enlightenment will be just as turbulent and political---and exciting---as that of any previous century? Which is good! :)
Gee, it's very surprising (to me) that Lance's post is not attracting dozens of comments ... As fuel for comment, here's IAS Prof. Israel's eight-point summary of the Radical Enlightenment: ----------------------Radical Enlightenment conceived as a package of basic concepts and values may be summarized in eight cardinal points:(1) adoption of philosophical (mathematical-historical) reason and the only and exclusive criterion of what is true;(2) rejection of all supernatural agency, magic, disembodied spirits, and divine providence;(3) equality of all mankind (racial and sexual);(4) secular 'universalism' in ethics anchored in equality and chiefly stressing equity, justice, and charity;(5) comprehensive toleration and freedom of thought based on independent critical thinking;(6) personal liberty of lifestyle and sexual conduct between consenting adults;(7) freedom of expression, political criticism, and the press, in the public sphere.(8) democratic republicanism as the most legitimate form of politics.----------------------The guidance that Soldiers and Marines receive upon deploying to Iraq is not eight points, but rather the 25 points Counterinsurgency Guidance.If we compare the above two guidances with the video that Lance posted, a great number of points can be made ... here are three.First: how willing is the complexity theory community to embrace the goals of the Commander's Guidance? The ethical alternative being, to follow Grothendieck's path. Second, what about the commonly held point-of-view that (to paraphrase Prof. Israel) "theorem-proving is the most legitimate form of complexity studies"? Is this a desirable distillation of mathematical purity ... or is it an impracticable ivory-tower dream ... or is it an adaptive response to the realities of a harsh academic job market? Or is it all three?Third, the video that Lance posted is (let's face it) intended for children and for recruiting. Is this low level of dialog what the research community---students especially---really wants, and really needs? It is dismaying to think so, but perhaps that is what most people prefer.
The video is totally awful. It fails to mention that the point of armies is destruction, and the army that has sponsored this video has just destructed a far away country for extremely dubious reasons.