Intuition-geometry-computation
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Intuition-geometry-computation
 
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Intuition-geometry-computation-mathematics
The limitations of the mean value theorem are well understood by any carpenter who ever laid out a triangular roof beam. The mean slope is that of the horizontal tie beam; the local slope is that of the rafters. Nowhere does any piece of rafter have the mean slope. Intuition is in the eye of the beholder. The intuition of a test pilot is different from that of a violinist. The fighter jock intuits that a little topstick will sweeten his turn, the fiddler intuits tiny details of bowing will sweeten his melody. Both are true, and learned from years of doing it wrong. Sooo intuition about things with which one has no experience means nothing. Geometry has no place in mathematics. Mathematics cannot be explained graphically -- all math proofs must be for blind men, as me tutor used to say. Pictures are beautiful, but for architects and renaissance draftsmen. Hardy?s great book on pure mathematics, like the Bible contains many transcendental truths, but no prevarications, no illustrations and no jocularities! Computation is, shall we say, counting, very fast, on very many fingers. Pablo Picasso said, ?Computers are useless: they can only give you answers?. Mathematics has been called the Queen of the Sciences and is essentially an abstract and difficult discipline. Consider the ancient puzzlements below, which are answered differently by the four above disciplines, and illustrate their distinction. The length of the hypotenuse of an isosceles right triangle of unit side, which cannot be determined in rational numbers (it?s called root two, but that?s its name, not value) The definition of the interior of a closed curve ( I dunno, nor did Cauchy or my tutor) The perimeter of a circle constructed from infinitely small square tiles laid orthogonally (it?s 4 D) The sum of the infinite series 1/n, compared with that of 1/n squared (it?s infinite in the first case, in t?other not) Peter Lissaman, Da Vinci Ventures Expertise is not knowing everything, but knowing what to look for. 1454 Miracerros Loop South, Santa Fe, New Mexico 87505 TEL: (505) 983-7728 FAX: (505) 983-1694 > [Original Message] > From: <friam-request at redfish.com> > To: <friam at redfish.com> > Date: 7/23/2007 10:03:23 AM > Subject: Friam Digest, Vol 49, Issue 21 > > Send Friam mailing list submissions to > friam at redfish.com > > To subscribe or unsubscribe via the World Wide Web, visit > http://redfish.com/mailman/listinfo/friam_redfish.com > or, via email, send a message with subject or body 'help' to > friam-request at redfish.com > > You can reach the person managing the list at > friam-owner at redfish.com > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of Friam digest..." > > > Today's Topics: > > 1. Re: Why "true" random? (Robert Howard) > 2. Re: Why "true" random? (Russell Standish) > 3. DISREGARD: math and the mother church (Nicholas Thompson) > 4. Re: Why "true" random? (James Steiner) > 5. Re: DISREGARD: math and the mother church (Russell Standish) > 6. Re: Criminalizing Peace (PPARYSKI at aol.com) > 7. Re: Despite the Web, Americans Remain Woefully Ill-Informed > (steve smith) > 8. Re: Why "true" random? (PPARYSKI at aol.com) > 9. Re: Criminalizing Peace (PPARYSKI at aol.com) > 10. Re: DISREGARD: math and the mother church (Nicholas Thompson) > 11. Re: Despite the Web, Americans Remain Woefully Ill-Informed > (Roger Critchlow) > 12. Re: Despite the Web, Americans Remain Woefully Ill-Informed > (Marcus G. Daniels) > 13. It's the Spies, Stupid! (Peter Lissaman) > 14. Re: math and the mother church (G?nther Greindl) > > > ---------------------------------------------------------------------- > > Message: 1 > Date: Sun, 22 Jul 2007 13:52:35 -0700 > From: "Robert Howard" <rob at symmetricobjects.com> > Subject: Re: [FRIAM] Why "true" random? > To: "'The Friday Morning Applied Complexity Coffee Group'" > <friam at redfish.com> > Message-ID: <007501c7cca2$3bd15010$0400a8c0 at Core2Duo> > Content-Type: text/plain; charset="us-ascii" > > How about deleting confidential data from hard disks! > > The solution today is to overwrite it many times with random data. > > But modern mathematics and technology makes it possible to recover the > of the original text given the original random sequence used to delete the > data. Given a long sequence of deleted white space (or zeros on the disk), > then it becomes possible to recover the original pseudo-random sequence (for > example, one based on linear > <http://en.wikipedia.org/wiki/Linear_congruence_theorem> congruence) - even > if a many passes are performed. > > With a true random number generator, only one pass is needed. > > I'm sure hardware random number generators based on quantum effects, which > have been around for decades, would be used instead of hitting a web site, > which compromises the who shebang. > > > > Robert Howard > > Phoenix, Arizona > > > > > > > > -----Original Message----- > From: friam-bounces at redfish.com [mailto:friam-bounces at redfish.com] On > Of Roger Frye > Sent: Sunday, July 22, 2007 6:40 AM > To: The Friday Morning Applied Complexity Coffee Group > Subject: Re: [FRIAM] Why "true" random? > > > > I would argue the opposite. While I agree with Doug that you need good > > RNGs (though not necessarily true RNGs) in order to avoid bias, the > > problem with good pseudo- or true- RNGs is that they have order N^2 > > convergence for Monte Carlo simulations. Quasi-random number generators > > on the other hand (such as multiples of an irrational square root, or a > > Peano tiling) converge in order N. If you can trust the results, faster > > conergence lets you simulate more. > > -Roger > > > > On Sat, 21 Jul 2007 23:18:36 -0600, Douglas Roberts > > wrote: > > > > > Simulations of stochastic processes also require good RN generators, > > > especially for simulations of large systems with (I hate to use this > > > word) > > > emergent behavioral properties. A bad RN generator will introduce > > > emergent > > > behavior that will be "flavored" by a bad random sequences. > > > > > > > > > > > > > > ============================================================ > > FRIAM Applied Complexity Group listserv > > Meets Fridays 9a-11:30 at cafe at St. John's College > > lectures, archives, unsubscribe, maps at http://www.friam.org > > > > -------------- next part -------------- > An HTML attachment was scrubbed... > URL: /attachment-0001.html > > ------------------------------ > > Message: 2 > Date: Sat, 21 Jul 2007 23:39:58 +1000 > From: Russell Standish <r.standish at unsw.edu.au> > Subject: Re: [FRIAM] Why "true" random? > To: The Friday Morning Applied Complexity Coffee Group > <friam at redfish.com> > Message-ID: <20070721133957.GH845 at hells-dell.localdomain> > Content-Type: text/plain; charset=us-ascii > > On Sun, Jul 22, 2007 at 01:52:35PM -0700, Robert Howard wrote: > > How about deleting confidential data from hard disks! > > > > The solution today is to overwrite it many times with random data. > > > > But modern mathematics and technology makes it possible to recover the > > of the original text given the original random sequence used to delete the > > data. Given a long sequence of deleted white space (or zeros on the disk), > > then it becomes possible to recover the original pseudo-random sequence (for > > example, one based on linear > > <http://en.wikipedia.org/wiki/Linear_congruence_theorem> congruence) - even > > if a many passes are performed. > > > > With a true random number generator, only one pass is needed. > > > > I'm sure hardware random number generators based on quantum effects, which > > have been around for decades, would be used instead of hitting a web site, > > which compromises the who shebang. > > > > > > > > Robert Howard > > > > Phoenix, Arizona > > > > > > You don't even need to do that. Entropic sources are available from > considering timings on a system undergoing interrupts from external > sources (eg mouse or keyboard activity). The Linux kernel performs > this analysis and provides a conveniently encapsulated device called > /dev/random. I used used precisely this technique to implement a disk > erasing program a couple of years ago - and offered the possibility > to do it multiple times for the absolutely paranoid. > > Note that /dev/random has rather unpredictable performance - you are > advised to shake you mouse, or something like that when generating a > seed for ssh for instance. To improve its performance, you use the > output of /dev/random to fill a table, which is continually > overwritten as new random bits become available, Then you use a > conventional pseudo RNG to index into the table, so the resulting > bitstream has small chunks of "correlated" numbers, but is by and > large unpredictable. > > The state of the art for doing this is a library called Havege. Look > it up if you're interested. > > Cheers > > -- > > > A/Prof Russell Standish Phone 0425 253119 (mobile) > Mathematics > UNSW SYDNEY 2052 hpcoder at hpcoders.com.au > Australia http://www.hpcoders.com.au > ---------------------------------------------------------------------------- > > > > ------------------------------ > > Message: 3 > Date: Sun, 22 Jul 2007 18:12:58 -0600 > From: "Nicholas Thompson" <nickthompson at earthlink.net> > Subject: [FRIAM] DISREGARD: math and the mother church > To: friam at redfish.com > Message-ID: <380-22007712301258314 at earthlink.net> > Content-Type: text/plain; charset="us-ascii" > > SORRY, i SENT THIS OFF BEFORE IT WAS DONE! THIS VERSION IS COMPLETE > > Dear Friamers -- or Fry-Aimers, however it is that we are pronounced. > > Ever since I first got to santa fe four years ago, the pot has been can or cannot be done with computation. Some have taken the position that some complex processes -- or aspects of complex processes --- can only be understood through computational models while others -- or other aspects --- can only be understoud through maths. I apologize to all for my starting of the isargument in about three different places in the last week, but I have finally decided that the FRIAM list, being the most comprehensive list, is the best place for it. > > What I THOUGHT I understood about this argument was that it was about inference tickets. All deductive arguments give you inference tickets to travel from the premises to the conclusions. How you get to the premises is your own business. Mathematical arguments are deduductive. They tell you that if you can manage to get from Boston to Albany, you can get a train to Chicago. > > In order to get a better idea of what it meant to be mathematically "on a train to Chicago", I decided to read a book for english majors on calculus recommended to me by Mike Agar. I guess I thought this would be helpful because if ever there were some powerful inference tickets lying about, they would be in the calculus, no? And I thought that if I understood, how mathematicians argue for the calculus, I would understand, perhaps, how they argue. > > So, here is my present understanding of the mathematician's argument for the mean value theorem. What I dont understand is why it takes three pages of algebra to get there! > > Let us amagine that ab is a bit of a line. It could be straight, and the argument would still hold, but let us imagine that it is curved.... curved up, curved down, it does not matter. Let's imagine that is an inverted U, except that it doesnt have to be a straight up and down inverted U. In fact, it can be sitting so that somebody wobbled it so that it is, at the instant of being photographed, standing on one leg, about 30 degrees from the verticle. . > > What does matter is that the line be continuous ALL THE WAY FROM a to B. No gaps, not steps. Imagine that no matter how small the steps you are taking, you can walk along the points of the line from a to b and not get your feet wet, NOT AT ALL -- if of course your shoe size is small enough. > > Now draw a line that connects the bottom of the two legs of the inverted U. As we just said, that line will move off to the right, from a through b and beyond, at about a thirty degree angle from the horizontal. Thus the mean slope of the tilted inverted U is 30 degrees, right? > > Here is what that means, as I understand it. Every point on the tilted inverted U has a "slope", the slope of the line that is just tangent to the U at that point. Near point "a" that slope is VERY positive; near point "b", that slope is very negative. Now, imagine you set out to walk along the curve from "a" to "b". If you take tiny enough steps, you MUST step on the point where the slope is the same as the mean slope. That is what the mean value theorem says. > > But I just got there without any of the algebra usually devoted to that proof. So the question is, what is the VALUE of the algebra. If one can estab lish the truth of such an important MATHEMATICAL theorem in other than mathematical means, what is the value of the maths? > > I promise I am not MERELY trying to be a horses ass, here. > > Nick > > > > > > > > > > > > > > . > > > > > Nicholas S. Thompson > Research Associate, Redfish Group, Santa Fe, NM (nick at redfish.com) > Professor of Psychology and Ethology, Clark University > -------------- next part -------------- > An HTML attachment was scrubbed... > URL: http://redfish.com/pipermail/friam_redfish.com/attachments/20070722/43a40c22 /attachment-0001.html > > ------------------------------ > > Message: 4 > Date: Sun, 22 Jul 2007 20:28:48 -0400 > From: "James Steiner" <gregortroll at gmail.com> > Subject: Re: [FRIAM] Why "true" random? > To: "The Friday Morning Applied Complexity Coffee Group" > <friam at redfish.com> > Message-ID: > <5ec674320707221728u77b5b0e7y1405f2ceafa67c80 at mail.gmail.com> > Content-Type: text/plain; charset=WINDOWS-1252; format=flowed > > Robert, > > It's my understanding that there has been no documented case of data > recovered from a hard disk that has been erased by completely > overwriting the contents 3 or more times with your choice of 0s, 1s, > alternating bits, random bits, or whatever, outside of a lab > environment using magnetic electron microscopy. Is that no longer > true? I had thought that one didn't need a particularly good RNG for > it, since anything will do. Or, is that just what the NSA *wants* me > to think? > > ~~James > _____________________ > http://www.turtlezero.com > > > On 7/22/07, Robert Howard <rob at symmetricobjects.com> wrote: > > How about deleting confidential data from hard disks! > > > > The solution today is to overwrite it many times with random data. > > > > But modern mathematics and technology makes it possible to recover the > > of the original text given the original random sequence used to delete the > > data. Given a long sequence of deleted white space (or zeros on the disk), > > then it becomes possible to recover the original pseudo-random sequence (for > > example, one based on linear congruence) ? even if a many passes are > > performed. > > > > With a true random number generator, only one pass is needed. > > > > I'm sure hardware random number generators based on quantum effects, which > > have been around for decades, would be used instead of hitting a web site, > > which compromises the who shebang. > > > > > > > > Robert Howard > > > > Phoenix, Arizona > > > > ------------------------------ > > Message: 5 > Date: Sun, 22 Jul 2007 01:42:01 +1000 > From: Russell Standish <r.standish at unsw.edu.au> > Subject: Re: [FRIAM] DISREGARD: math and the mother church > To: nickthompson at earthlink.net, The Friday Morning Applied Complexity > Coffee Group <friam at redfish.com> > Message-ID: <20070721154201.GJ845 at hells-dell.localdomain> > Content-Type: text/plain; charset=us-ascii > > On Sun, Jul 22, 2007 at 06:12:58PM -0600, Nicholas Thompson wrote: > > > > So, here is my present understanding of the mathematician's argument pages of algebra to get there! > > I don't know where you get the 3 pages from. My analysis book does it > 2 paragraphs of algebra, half a page at most. (That's including all > the necessary lemmas and definitions). > > > > > Let us amagine that ab is a bit of a line. It could be straight, and the argument would still hold, but let us imagine that it is curved.... curved up, curved down, it does not matter. Let's imagine that is an inverted U, except that it doesnt have to be a straight up and down inverted U. In fact, it can be sitting so that somebody wobbled it so that it is, at the instant of being photographed, standing on one leg, about 30 degrees from the verticle. . > > > > What does matter is that the line be continuous ALL THE WAY FROM a to B. No gaps, not steps. Imagine that no matter how small the steps you are taking, you can walk along the points of the line from a to b and not get your feet wet, NOT AT ALL -- if of course your shoe size is small enough. > > > > Now draw a line that connects the bottom of the two legs of the inverted U. As we just said, that line will move off to the right, from a through b and beyond, at about a thirty degree angle from the horizontal. Thus the mean slope of the tilted inverted U is 30 degrees, right? > > > > Here is what that means, as I understand it. Every point on the tilted inverted U has a "slope", the slope of the line that is just tangent to the U at that point. Near point "a" that slope is VERY positive; near point "b", that slope is very negative. Now, imagine you set out to walk along the curve from "a" to "b". If you take tiny enough steps, you MUST step on the point where the slope is the same as the mean slope. That is what the mean value theorem says. > > > > But I just got there without any of the algebra usually devoted to that proof. So the question is, what is the VALUE of the algebra. If one can estab lish the truth of such an important MATHEMATICAL theorem in other than mathematical means, what is the value of the maths? > > > > What you have given is the "handwaving" version of the proof. The > trouble is that human imagination can easily get us into trouble when > dealing with infinities, which is necessarily involved in dealing with > the concept of continuity. In the above example, you mention that > continuity is important, but say nothing about differentiability. Are > you aware that continuous curves that are nowhere differentiable > exist? I fact most continuous curves are not differentiable. By most, > I mean infinitely more continuous curves are not differentiable than > those that are, a concept handled by "sets of measure zero". > > To give an example, consider your interval joined by two line segments > so as to form a single kink in the middle at point c: > > At all points on the interior, except for the c, the slope is either > s1 = (f(c)-f(a))/(c-a) or s2=(f(b)-f(c))/(b-c). At c, the slope is > undefined. But neither s1 nor s2 = (f(b)-f(a))/(b-1), so the mean > value theorem fails. > > > I promise I am not MERELY trying to be a horses ass, here. > > > > Nick > > > > > > Handwaving arguments are good for developing intuition. Great for > teaching during a lecture, and get the students to study the rigorous > proof later. Similarly, they're good for scientific seminars, but not > scientific papers. > > Cheers > > > > > > > > > > > > > > > > > > > > > > > > > . > > > > > > > > > > Nicholas S. Thompson > > Research Associate, Redfish Group, Santa Fe, NM (nick at redfish.com) > > Professor of Psychology and Ethology, Clark University > > ============================================================ > > FRIAM Applied Complexity Group listserv > > Meets Fridays 9a-11:30 at cafe at St. John's College > > lectures, archives, unsubscribe, maps at http://www.friam.org > > -- > > ---------------------------------------------------------------------------- > A/Prof Russell Standish Phone 0425 253119 (mobile) > Mathematics > UNSW SYDNEY 2052 hpcoder at hpcoders.com.au > Australia http://www.hpcoders.com.au > ---------------------------------------------------------------------------- > > > > ------------------------------ > > Message: 6 > Date: Sun, 22 Jul 2007 21:24:34 EDT > From: PPARYSKI at aol.com > Subject: Re: [FRIAM] Criminalizing Peace > To: friam at redfish.com > Message-ID: <cbc.15ce6164.33d55d52 at aol.com> > Content-Type: text/plain; charset="us-ascii" > > I received this from Frank Wimberly and think it deserves distribution > reaction. Bush's executive order is appalling and frightening even more so > because the media have not adequately reported it or reacted. Perhaps we could > apply a RNG to Bush and Cheney? cheers (?) Paul > > > > ************************************** Get a sneak peek of the all-new AOL at > http://discover.aol.com/memed/aolcom30tour > -------------- next part -------------- > An HTML attachment was scrubbed... > URL: http://redfish.com/pipermail/friam_redfish.com/attachments/20070722/d55cff17 /attachment-0001.html > > ------------------------------ > > Message: 7 > Date: Sun, 22 Jul 2007 19:38:41 -0600 > From: steve smith <sasmyth at swcp.com> > Subject: Re: [FRIAM] Despite the Web, Americans Remain Woefully > Ill-Informed > To: The Friday Morning Applied Complexity Coffee Group > <friam at redfish.com> > Message-ID: <4a8d243665c9e2bd940e3b5a5717081b at swcp.com> > Content-Type: text/plain; charset=US-ASCII; format=flowed > > I am disturbed by the non-sequitur inherent in the Subject and Body of > this article: It suggests that the Web inherently *should* make > Americans more well informed. > > 3 points: > > 1) I agree that these are not particularly important questions in their > own right, but they *are* hugely significant indicators of how > uninformed the folks who were "studied" are on this type of details, > and I agree with Owen that is scary that "anyone ALIVE in the US ... > cannot answer these". > > 2) The internet, in my opinion, is still mainly a reference source... > Somewhere between a dictionary or encyclopedia and a newspaper or > magazine subscription. > > If people aren't interested in these kinds of facts, they won't look > them up and they won't "subscribe" (e-mail lists, blogs, podcasts, > news/information web sites) to sources that provide them. Like the > folks I grew up around whose only reading material was their > subscription to GRIT or Nat'l Enquirer. > > 3) If there is a correlation, perhaps it is a negative one... the ratio > of "important" (by some measure) factoids to the "unimportant" (by any > measure) has plummeted, no? > > Even TV (with 182 channels) in it's "ubiquity" has aggravated this. > At 5 or 6 PM and 10 PM each night in my youth, *any* television running > would be showing news... mediated by a local station such that anyone > within earhshot would hear their Gov's name as well as the VP's and > some of the other facts in question fairly frequently. Today > specialized channels like ESPN, MTV, TBS, HBO, Science, Discovery, even > CNN (and all of their competitors/wannabes) mean that you can run your > TV night and day and never hear most of these things (even with CNN you > won't hear your Gov's name often unless he's a bombast like our own). > > At the newsstand there are hundreds of magazines where there were once > tens. Geeks like us maybe all read Byte and now Wired (haven't had a > subscription in a decade myself) and maybe Nature/Science/SciAm and > maybe Fashionistas all read Cosmo (or whatever is equivalent) but the > competition for eyeballs (and ears) is fierce... and a lot that is > being offered up is overly refined (like white sugar, flour, > corn-syrup, textured-vegetable-protein, etc.) to do more than satisfy > (seduce) the most immediate of appetites. > > > Owen said: > I sorta have to agree: Just how IMPORTANT are any of these questions? > > > >> The five questions: > >> Who is the vice president? > >> Who is your state's governor? > >> Does the US have a trade deficit or surplus? > >> Which party controls the House of Representatives? > >> Is the chief justice of the Supreme Court a liberal, moderate, or > >> conservative? > > > > If you were to be able to ask 5 questions that you would LIKE folks > > to know the answer to, would any of these be on it? I think only > > one .. the trade deficit. > > > > But, man, its scary to know that there's anyone ALIVE in the US who > > cannot answer these. > > > > > > > ------------------------------ > > Message: 8 > Date: Sun, 22 Jul 2007 21:47:55 EDT > From: PPARYSKI at aol.com > Subject: Re: [FRIAM] Why "true" random? > To: friam at redfish.com > Message-ID: <cbc.15ceae22.33d562cb at aol.com> > Content-Type: text/plain; charset="us-ascii" > > Logically is true, perfect randomness possible since it is being > by a program designed by a human with a purpose - a thought construct? On one > level is anything in the universe truly random? > > Paul Paryski > > > > ************************************** Get a sneak peek of the all-new AOL at > http://discover.aol.com/memed/aolcom30tour > -------------- next part -------------- > An HTML attachment was scrubbed... > URL: http://redfish.com/pipermail/friam_redfish.com/attachments/20070722/4920991a /attachment-0001.html > > ------------------------------ > > Message: 9 > Date: Sun, 22 Jul 2007 21:52:45 EDT > From: PPARYSKI at aol.com > Subject: Re: [FRIAM] Criminalizing Peace > To: friam at redfish.com > Message-ID: <c02.1b339022.33d563ed at aol.com> > Content-Type: text/plain; charset="us-ascii" > > Somehow the fwd about Bush's exec order didn't work, so I have copied the > text below. Paul Paryski > > > > While the American public...and the world...was being diverted by news > stories of Dubya's colonoscopy scheduled for today, this, his latest executive > order, was signed July 17, 2007... However, blogs, blogging comments have > been numerous...see a sampling below. > > > > Bush Executive Order: Criminalizing the Antiwar Movement > > By Prof. Michel Chossudovsky > > July 20, 2007 > > The Executive Order entitled "Blocking Property of Certain Persons Who > Threaten Stabilization Efforts in Iraq" provides the President with the > to confiscate the assets of whoever opposes the US led war. > A presidential Executive Order issued on July 17th, repeals with the stroke > of a pen the right to dissent and to oppose the Pentagon's military agenda > in Iraq. > The Executive Order entitled "Blocking Property of Certain Persons Who > Threaten Stabilization Efforts in Iraq" provides the President with the authority > to confiscate the assets of "certain persons" who oppose the US led war in > Iraq: > "I have issued an Executive Order blocking property of persons determined to > have committed, or to pose a significant risk of committing, an act or acts > of violence that have the purpose or effect of threatening the peace or > stability of Iraq or the Government of Iraq or undermining efforts to promote > economic reconstruction and political reform in Iraq or to provide humanitarian > assistance to the Iraqi people." > In substance, under this executive order, opposing the war becomes an > illegal act. > > The Executive Order criminalizes the antiwar movement. It is intended to > "blocking property" of US citizens and organizations actively involved in the > peace movement. It allows the Department of Defense to interfere in > financial affairs and instruct the Treasury to "block the property" and/or > confiscate/ freeze the assets of "Certain Persons" involved in antiwar activities. It > targets those "Certain Persons" in America, including civil society > organizatioins, who oppose the Bush Administration's "peace and stability" program in > Iraq, characterized, in plain English, by an illegal occupation and the > continued killing of innocent civilians. > The Executive Order also targets those "Certain Persons" who are > "undermining efforts to promote economic reconstruction", or who, again in plain > English, are opposed to the confiscation and privatization of Iraq's oil resources, > on behalf of the Anglo-American oil giants. > > > > The order is also intended for anybody who opposes Bush's program of > "political reform in Iraq", in other words, who questions the legitimacy of an > Iraqi "government" installed by the occupation forces. > Moreover, those persons or nongovernmental organizations (NGOs), who provide > bona fide humanitarian aid to Iraqi civilians, and who are not approved by > the US Military or its lackeys in the US sponsored Iraqi puppet government are > also liable to have their financial assets confiscated. > The executive order violates the First, Fourth and Fifth Amendments of the > US Constitution. It repeals one of the fundamental tenets of US democracy, > which is the right to free expression and dissent. The order has not been the > object of discussion in the US Congress. Sofar, it has not been addressed by > the US antiwar movement, in terms of a formal statement. > > Apart from a bland Associated Press wire report, which presents the > executive order as "an authority to use financial sanctions", there has been no media > coverage or commentary of a presidential decision which strikes at the heart > of the US Constitution.. > Broader implications > The criminalization of the State is when the sitting President and Vice > President use and abuse their authority through executive orders, presidential > directives or otherwise to define "who are the criminals" when in fact they > they are the criminals. > > This latest executive order criminalizes the peace movement. It must be > viewed in relation to various pieces of "anti-terrorist" legislation, the gamut > of presidential and national security directives, etc., which are ultimately > geared towards repealing constitutional government and installing martial law > in the event of a "national emergency"... > Excerpted from: _http://www.globalresearch.ca/index.php?context=va&aid=6377_ > (http://www.globalresearch.ca/index.php?context=va&aid=6377) > Text of the Executive Order: > _http://www.whitehouse.gov/news/releases/2007/07/20070717-3.html_ > (http://www.whitehouse.gov/news/releases/2007/07/20070717-3.html) > Message to the Congress of the United States Regarding International > Emergency Economic Powers Act _ht > tp://www.whitehouse.gov/news/releases/2007/07/20070717-4.html_ (http://www.whitehouse.gov/news/releases/2007/07/20070717-4.html) > > ---------------------------------------------------------------------------- -- > ----- > Bloggers are alert... > From:_http://digg.com/politics/So_as_of_yesterday_If_you_protest_the_war_the _P > rez_can_take_your_stuff_ > (http://digg.com/politics/So_as_of_yesterday_If_you_protest_the_war_the_Prez _can_take_your_stuff) > > > +357 diggs > by _ajkxxx_ (http://digg.com/users/ajkxxx) on _07/19/2007_ > (http://digg.com/politics/So_as_of_yesterday_If_you_protest_the_war_the_Prez _can_take_your_stuf > f?t=7903154#c7903154) > > > I'm worried that no newspapers have picked up on this story. This is the > White House Website. > This is getting scary. > > _Hide 7 replies to this comment (most popular has 21 diggs)_ > (http://digg.com/politics/So_as_of_yesterday_If_you_protest_the_war_the_Prez _can_take_your_st > uff) > > > > > * +21 diggs > > by _massivity_ (http://digg.com/users/massivity) on _07/19/2007_ > (http://digg.com/politics/So_as_of_yesterday_If_you_protest_the_war_the_Prez _can_take_you > r_stuff?t=7903154#c7905530) > > > Seriously. WHY is this not front page news? > > _View 3 replies to this comment (most popular has 18 diggs)_ > (http://digg.com/politics/So_as_of_yesterday_If_you_protest_the_war_the_Prez _can_take_your_stu > ff) > > > > * +3 diggs > > by _ronaldinho_ (http://digg.com/users/ronaldinho) on _07/19/2007_ > (http://digg.com/politics/So_as_of_yesterday_If_you_protest_the_war_the_Prez _can_take_y > our_stuff?t=7903154#c7907218) > > > it is on Digg, but you know the mainstream media (aside from Jon Stewart and > Stephen Colbert) are controlled by Bush > > _View 2 replies to this comment (most popular has 3 diggs)_ > (http://digg.com/politics/So_as_of_yesterday_If_you_protest_the_war_the_Prez _can_take_your_stuf > f) > > > > > > > > > ************************************** Get a sneak peek of the all-new > http://discover.aol.com/memed/aolcom30tour > -------------- next part -------------- > An HTML attachment was scrubbed... > URL: http://redfish.com/pipermail/friam_redfish.com/attachments/20070722/ba319808 /attachment-0001.html > > ------------------------------ > > Message: 10 > Date: Sun, 22 Jul 2007 21:59:32 -0600 > From: "Nicholas Thompson" <nickthompson at earthlink.net> > Subject: Re: [FRIAM] DISREGARD: math and the mother church > To: "Russell Standish" <r.standish at unsw.edu.au> > Cc: friam <friam at redfish.com> > Message-ID: <380-22007712335932432 at earthlink.net> > Content-Type: text/plain; charset=US-ASCII > > Russell, > > Remember, mine was a book for English Majors, Berlinski's Tour of the > Calculus. > > But thou quibblest! Dothn't thou? Why is the algebra necessary at all. > Doesnt the mean value theorem fall out of the definition of a mean and the > definition of continuity? Full stop. Granting only that the mean falls > between (or is one of) the extremes? > > Nick > > PS. I apologize for my message garblement. In fact I had NOT sent an > incomplete message. So the message saying "disregard the message" was the > only message. "This is not a pipe." > > Nick > > > > > > [Original Message] > > From: Russell Standish <r.standish at unsw.edu.au> > > To: <nickthompson at earthlink.net>; The Friday Morning Applied Complexity > Coffee Group <friam at redfish.com> > > Date: 7/22/2007 7:04:29 PM > > Subject: Re: [FRIAM] DISREGARD: math and the mother church > > > > On Sun, Jul 22, 2007 at 06:12:58PM -0600, Nicholas Thompson wrote: > > > > > > So, here is my present understanding of the mathematician's argument > for the mean value theorem. What I dont understand is why it takes three > pages of algebra to get there! > > > > I don't know where you get the 3 pages from. My analysis book does it > > 2 paragraphs of algebra, half a page at most. (That's including all > > the necessary lemmas and definitions). > > > > > > > > Let us amagine that ab is a bit of a line. It could be straight, and > the argument would still hold, but let us imagine that it is curved.... > curved up, curved down, it does not matter. Let's imagine that is an > inverted U, except that it doesnt have to be a straight up and down > inverted U. In fact, it can be sitting so that somebody wobbled it so > it is, at the instant of being photographed, standing on one leg, about 30 > degrees from the verticle. . > > > > > > What does matter is that the line be continuous ALL THE WAY FROM a to > B. No gaps, not steps. Imagine that no matter how small the steps you > are taking, you can walk along the points of the line from a to b and not > get your feet wet, NOT AT ALL -- if of course your shoe size is small > enough. > > > > > > Now draw a line that connects the bottom of the two legs of the > inverted U. As we just said, that line will move off to the right, from a > through b and beyond, at about a thirty degree angle from the > Thus the mean slope of the tilted inverted U is 30 degrees, right? > > > > > > Here is what that means, as I understand it. Every point on the tilted > inverted U has a "slope", the slope of the line that is just tangent to the > U at that point. Near point "a" that slope is VERY positive; near point > "b", that slope is very negative. Now, imagine you set out to walk along > the curve from "a" to "b". If you take tiny enough steps, you MUST step on > the point where the slope is the same as the mean slope. That is what the > mean value theorem says. > > > > > > But I just got there without any of the algebra usually devoted to that > proof. So the question is, what is the VALUE of the algebra. If one can > estab lish the truth of such an important MATHEMATICAL theorem in other > than mathematical means, what is the value of the maths? > > > > > > > What you have given is the "handwaving" version of the proof. The > > trouble is that human imagination can easily get us into trouble when > > dealing with infinities, which is necessarily involved in dealing with > > the concept of continuity. In the above example, you mention that > > continuity is important, but say nothing about differentiability. Are > > you aware that continuous curves that are nowhere differentiable > > exist? I fact most continuous curves are not differentiable. By most, > > I mean infinitely more continuous curves are not differentiable than > > those that are, a concept handled by "sets of measure zero". > > > > To give an example, consider your interval joined by two line segments > > so as to form a single kink in the middle at point c: > > > > At all points on the interior, except for the c, the slope is either > > s1 = (f(c)-f(a))/(c-a) or s2=(f(b)-f(c))/(b-c). At c, the slope is > > undefined. But neither s1 nor s2 = (f(b)-f(a))/(b-1), so the mean > > value theorem fails. > > > > > I promise I am not MERELY trying to be a horses ass, here. > > > > > > Nick > > > > > > > > > > Handwaving arguments are good for developing intuition. Great for > > teaching during a lecture, and get the students to study the rigorous > > proof later. Similarly, they're good for scientific seminars, but not > > scientific papers. > > > > Cheers > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > . > > > > > > > > > > > > > > > Nicholas S. Thompson > > > Research Associate, Redfish Group, Santa Fe, NM (nick at redfish.com) > > > Professor of Psychology and Ethology, Clark University > (nthompson at clarku.edu) > > > ============================================================ > > > FRIAM Applied Complexity Group listserv > > > Meets Fridays 9a-11:30 at cafe at St. John's College > > > lectures, archives, unsubscribe, maps at http://www.friam.org > > > > -- > > > > > > > A/Prof Russell Standish Phone 0425 253119 (mobile) > > Mathematics > > UNSW SYDNEY 2052 hpcoder at hpcoders.com.au > > Australia http://www.hpcoders.com.au > > > ---------------------------------------------------------------------------- > > > > > > ------------------------------ > > Message: 11 > Date: Sun, 22 Jul 2007 22:22:30 -0600 > From: "Roger Critchlow" <rec at elf.org> > Subject: Re: [FRIAM] Despite the Web, Americans Remain Woefully > Ill-Informed > To: "The Friday Morning Applied Complexity Coffee Group" > <friam at redfish.com> > Message-ID: > <66d1c98f0707222122l7d4160f3p8576dfda03362d89 at mail.gmail.com> > Content-Type: text/plain; charset="iso-8859-1" > > On 7/22/07, steve smith <sasmyth at swcp.com> wrote: > > > > I am disturbed by the non-sequitur inherent in the Subject and Body of > > this article: It suggests that the Web inherently *should* make > > Americans more well informed. > > > Myself, I'm getting a little tired of the pop quizzes demonstrating one > of ignorance or another. > > Given any population, there exists some set of questions which they will get > mostly wrong, and another set they will get mostly right. So what? > > Ability to regurgitate facts on demand measures what? Ability to think? > No. Ability to research? No. Ability to make good decisions? No. > Ability to ask good questions? No. Ability to understand answers? No. > > If you want people to look smart, ask questions they know the answer to. If > you want them to look stupid, ask other questions. In either case, > establish that the questions asked are the ones the people should know by > hand waving, because there is no authority for the questions people should > be able to answer. > > -- rec -- > -------------- next part -------------- > An HTML attachment was scrubbed... > URL: http://redfish.com/pipermail/friam_redfish.com/attachments/20070722/b6d1920a /attachment-0001.html > > ------------------------------ > > Message: 12 > Date: Sun, 22 Jul 2007 22:55:41 -0600 > From: "Marcus G. Daniels" <marcus at snoutfarm.com> > Subject: Re: [FRIAM] Despite the Web, Americans Remain Woefully > Ill-Informed > To: The Friday Morning Applied Complexity Coffee Group > <friam at redfish.com> > Message-ID: <46A434CD.5040101 at snoutfarm.com> > Content-Type: text/plain; charset=ISO-8859-1; format=flowed > > steve smith wrote: > > 2) The internet, in my opinion, is still mainly a reference source... > > Somewhere between a dictionary or encyclopedia and a newspaper or > > magazine subscription. > > > > If people aren't interested in these kinds of facts, they won't look > > them up and they won't "subscribe" (e-mail lists, blogs, podcasts, > > news/information web sites) to sources that provide them. > With more kinds of appealing facts accessible (ranging from gossip blogs > to online academic journals), and assuming fixed available attention by > individuals, then we should expect per-individual knowledge of any > particular topic to be reduced... > > > > > ------------------------------ > > Message: 13 > Date: Sun, 22 Jul 2007 23:48:08 -0600 > From: "Peter Lissaman" <plissaman at earthlink.net> > Subject: [FRIAM] It's the Spies, Stupid! > To: friam at redfish.com > Message-ID: <380-2200771235488891 at earthlink.net> > Content-Type: text/plain; charset=US-ASCII > > Thanks to all who responded in much more courteous terms than my present > title! A'course, it reminded me and well should I have remembered! But > "old men forget" as da Bard had it (Lear). My old tutor (thesis advisor > these parts, (one S.W., for those in the know )) was one of the "Bletchley > Boys" who cracked Enigma in WW II. And, as a math grad student, I well > remember more than 1/2 century ago hearing his tales as we looked out over > the rainy rooftops of Cambridge! A'course, the Enigma Machine was entirely > deterministic, mechanical, but verrray complicated. Wheels within wheels!! > New setting each morning! I can imagine some totally bored Wehrmacht > Feldwebel cranking away at this horizontal axis coffee grinder while he > slurped his ersatz Kaffee and wished he had some sugar! The Brits said, > languidly and typically Englishly, "we usually managed to 'sort out' the > day's code by tea time". Also, being an honorable Englishman, (there were > still a few left then), my tutor said very little of substance because the > Official Secrets Act ran for 50 years. > My remarks are really meant entertain, so thanks to all for putting up with > this BS!!! > > Peter Lissaman, Da Vinci Ventures > > Expertise is not knowing everything, but knowing what to look for. > > 1454 Miracerros Loop South, Santa Fe, New Mexico 87505 > TEL: (505) 983-7728 FAX: (505) 983-1694 > > > > [Original Message] > > From: <friam-request at redfish.com> > > To: <friam at redfish.com> > > Date: 7/22/2007 10:02:51 AM > > Subject: Friam Digest, Vol 49, Issue 20 > > > > Send Friam mailing list submissions to > > friam at redfish.com > > > > To subscribe or unsubscribe via the World Wide Web, visit > > http://redfish.com/mailman/listinfo/friam_redfish.com > > or, via email, send a message with subject or body 'help' to > > friam-request at redfish.com > > > > You can reach the person managing the list at > > friam-owner at redfish.com > > > > When replying, please edit your Subject line so it is more specific > > than "Re: Contents of Friam digest..." > > > > > > Today's Topics: > > > > 1. Why "true" random? (Peter Lissaman) > > 2. Re: Why "true" random? (Robert Holmes) > > 3. Re: Why "true" random? (Russell Standish) > > 4. Re: Why "true" random? (Prof David West) > > 5. Re: Why "true" random? (Phil Henshaw) > > 6. Re: Why "true" random? (Douglas Roberts) > > 7. Re: Why "true" random? (Phil Henshaw) > > 8. Re: Why "true" random? (Roger Frye) > > > > > > ---------------------------------------------------------------------- > > > > Message: 1 > > Date: Sat, 21 Jul 2007 10:24:42 -0600 > > From: "Peter Lissaman" <plissaman at earthlink.net> > > Subject: [FRIAM] Why "true" random? > > To: friam at redfish.com > > Message-ID: <380-220077621162442468 at earthlink.net> > > Content-Type: text/plain; charset="us-ascii" > > > > Why is it important (except intellectually) to have "true" > I very well remember the early, good old, bad old, days of Aerospace, in > the 50's, when we were really doing practical earthshattering things -- > like going to the moon -- sans computers!! The RAND corporation, for whom > I consulted, published a typed book (size of a Manhattan telephone > directory) of "random" numbers for engineering application. Much > entertainment was occasioned when, about three months later, they > distributed a list of "typos" to their original list of random numbers. > Today I use homemade random numbers alla time for real problems, > specifically the actual response of real flight vehicles in real > atmospheric turbulence. Flight tests support analysis, in the sense that > what we predict is not obviously incorrect. We have never found it > necessary to utilize any more "perfectly random" "random" sequences! > > > > > > Peter Lissaman, Da Vinci Ventures > > > > Expertise is not knowing everything, but knowing what to look for. > > > > 1454 Miracerros Loop South, Santa Fe, New Mexico 87505 > > TEL: (505) 983-7728 FAX: (505) 983-1694 > > -------------- next part -------------- > > An HTML attachment was scrubbed... > > URL: > > /attachment-0001.html > > > > ------------------------------ > > > > Message: 2 > > Date: Sat, 21 Jul 2007 13:34:44 -0600 > > From: "Robert Holmes" <robert at holmesacosta.com> > > Subject: Re: [FRIAM] Why "true" random? > > To: plissaman at earthlink.net, "The Friday Morning Applied Complexity > > Coffee Group" <friam at redfish.com> > > Message-ID: > > <857770150707211234h692a7989h5debe46c1b558b3d at mail.gmail.com> > > Content-Type: text/plain; charset="iso-8859-1" > > > > Cryptography. The required robustness of a random generator is highly > > sensitive to the intended application; > > > > - Generating a "thought for the day" for your blog? Required > > randomness = low. > > - Response testing a missile system? Required randomness = medium > > - Stealing above test results, encrypting them and transmitting them > > to Al Quaeda in a form that you hope the NSA won't understand? > > randomness = high > > > > Robert > > > > On 7/21/07, Peter Lissaman <plissaman at earthlink.net> wrote: > > > > > > Why is it important (except intellectually) to have "true" > randomness??? > > > I very well remember the early, good old, bad old, days of Aerospace, > in the > > > 50's, when we were really doing practical earthshattering things -- > > > going to the moon -- sans computers!! The RAND corporation, for whom I > > > consulted, published a typed book (size of a Manhattan telephone > directory) > > > of "random" numbers for engineering application. Much entertainment > was > > > occasioned when, about three months later, they distributed a list of > > > "typos" to their original list of random numbers. Today I use homemade > > > random numbers alla time for real problems, specifically the actual > response > > > of real flight vehicles in real atmospheric turbulence. Flight tests > > > support analysis, in the sense that what we predict is not obviously > > > incorrect. We have never found it necessary to utilize any more > "perfectly > > > random" "random" sequences! > > > > > > > > > Peter Lissaman, Da Vinci Ventures > > > > > > Expertise is not knowing everything, but knowing what to look for. > > > > > > 1454 Miracerros Loop South, Santa Fe, New Mexico 87505 > > > TEL: (505) 983-7728 FAX: (505) 983-1694 > > > > > > > > > > > > ============================================================ > > > FRIAM Applied Complexity Group listserv > > > Meets Fridays 9a-11:30 at cafe at St. John's College > > > lectures, archives, unsubscribe, maps at http://www.friam.org > > > > > -------------- next part -------------- > > An HTML attachment was scrubbed... > > URL: > > /attachment-0001.html > > > > ------------------------------ > > > > Message: 3 > > Date: Sat, 21 Jul 2007 14:27:33 +1000 > > From: Russell Standish <r.standish at unsw.edu.au> > > Subject: Re: [FRIAM] Why "true" random? > > To: plissaman at earthlink.net, The Friday Morning Applied Complexity > > Coffee Group <friam at redfish.com> > > Message-ID: <20070721042733.GG845 at hells-dell.localdomain> > > Content-Type: text/plain; charset=us-ascii > > > > Cryptographic applications require true randomness. If your cipher > > used on a pseudo-random number generator, then a cracker discovering > > your algorithm and key has broken your code. > > > > I also have a hunch that genuine randomness is needed for open-ended > > evolutionary systems. Here, the evol algorithm is in the position of > > the code cracker, and once the code is cracked, the evol algorithm > > stops. I had a workshop paper on this in 2004, which has some problems > > with it. The concept is controversial, to say the least. > > > > Cheers > > > > On Sat, Jul 21, 2007 at 10:24:42AM -0600, Peter Lissaman wrote: > > > Why is it important (except intellectually) to have "true" > randomness??? I very well remember the early, good old, bad old, days of > Aerospace, in the 50's, when we were really doing practical > things -- like going to the moon -- sans computers!! The RAND corporation, > for whom I consulted, published a typed book (size of a Manhattan telephone > directory) of "random" numbers for engineering application. Much > entertainment was occasioned when, about three months later, they > distributed a list of "typos" to their original list of random numbers. > Today I use homemade random numbers alla time for real problems, > specifically the actual response of real flight vehicles in real > atmospheric turbulence. Flight tests support analysis, in the sense that > what we predict is not obviously incorrect. We have never found it > necessary to utilize any more "perfectly random" "random" sequences! > > > > > > > > > Peter Lissaman, Da Vinci Ventures > > > > > > Expertise is not knowing everything, but knowing what to look for. > > > > > > 1454 Miracerros Loop South, Santa Fe, New Mexico 87505 > > > TEL: (505) 983-7728 FAX: (505) 983-1694 > > > ============================================================ > > > FRIAM Applied Complexity Group listserv > > > Meets Fridays 9a-11:30 at cafe at St. John's College > > > lectures, archives, unsubscribe, maps at http://www.friam.org > > > > -- > > > > > > > A/Prof Russell Standish Phone 0425 253119 (mobile) > > Mathematics > > UNSW SYDNEY 2052 hpcoder at hpcoders.com.au > > Australia http://www.hpcoders.com.au > > > ---------------------------------------------------------------------------- > > > > > > > > ------------------------------ > > > > Message: 4 > > Date: Sat, 21 Jul 2007 21:55:30 -0400 > > From: "Prof David West" <profwest at fastmail.fm> > > Subject: Re: [FRIAM] Why "true" random? > > To: "The Friday Morning Applied Complexity Coffee Group" > > <friam at redfish.com> > > Message-ID: <1185069330.26136.1201375009 at webmail.messagingengine.com> > > Content-Type: text/plain; charset="ISO-8859-1" > > > > > > > > > > " cryptography ... missile system ... encrypting ... transmitting ... > > Al Quaeda ... NSA" sequence occurring twice within 7 hours in the same > > mail-list. Somewhere in VA a computer just burped. Expect the black > > helicopters within 24 hours. :) > > > > davew > > > > On Sat, 21 Jul 2007 13:34:44 -0600, "Robert Holmes" > > <robert at holmesacosta.com> said: > > > Cryptography. The required robustness of a random generator is highly > > > sensitive to the intended application; > > > > > > - Generating a "thought for the day" for your blog? Required > > > randomness = low. > > > - Response testing a missile system? Required randomness = medium > > > - Stealing above test results, encrypting them and transmitting > > > to Al Quaeda in a form that you hope the NSA won't understand? > > > Required > > > randomness = high > > > > > > Robert > > > > > > On 7/21/07, Peter Lissaman <plissaman at earthlink.net> wrote: > > > > > > > > Why is it important (except intellectually) to have "true" > randomness??? > > > > I very well remember the early, good old, bad old, days of > in the > > > > 50's, when we were really doing practical earthshattering things -- > like > > > > going to the moon -- sans computers!! The RAND corporation, for whom > I > > > > consulted, published a typed book (size of a Manhattan telephone > directory) > > > > of "random" numbers for engineering application. Much entertainment > was > > > > occasioned when, about three months later, they distributed a list of > > > > "typos" to their original list of random numbers. Today I use > homemade > > > > random numbers alla time for real problems, specifically the actual > response > > > > of real flight vehicles in real atmospheric turbulence. Flight tests > > > > support analysis, in the sense that what we predict is not obviously > > > > incorrect. We have never found it necessary to utilize any more > "perfectly > > > > random" "random" sequences! > > > > > > > > > > > > Peter Lissaman, Da Vinci Ventures > > > > > > > > Expertise is not knowing everything, but knowing what to look for. > > > > > > > > 1454 Miracerros Loop South, Santa Fe, New Mexico 87505 > > > > TEL: (505) 983-7728 FAX: (505) 983-1694 > > > > > > > > > > > > > > > > ============================================================ > > > > FRIAM Applied Complexity Group listserv > > > > Meets Fridays 9a-11:30 at cafe at St. John's College > > > > lectures, archives, unsubscribe, maps at http://www.friam.org > > > > > > > > > > > > ------------------------------ > > > > Message: 5 > > Date: Sat, 21 Jul 2007 23:19:25 -0400 > > From: "Phil Henshaw" <sy at synapse9.com> > > Subject: Re: [FRIAM] Why "true" random? > > To: "'The Friday Morning Applied Complexity Coffee Group'" > > <friam at redfish.com> > > Message-ID: <000001c7cc0f$1b4d1240$2f01a8c0 at SavyII> > > Content-Type: text/plain; charset=iso-8859-1 > > > > Or what about 'decynchronization', rather than random noise..to erase > > inconvenient pattern? Probably has nothing to do with cryptography, > > though, I suppose, as I expect that the sort of lab experiment thing the > > people at the SASO conference were talking about has no mathematical > > representation as yet, just ways of producing them. At least that's > > another property that efficiently hides pattern. It came up that some > > of the work on syncronization, that doing the opposite had valuable > > proprerties in preventing congestion and surges when used to produce > > desynchronized flows. Interesting work though! > > > > > > Phil Henshaw ????.?? ? `?.???? > > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ > > 680 Ft. Washington Ave > > NY NY 10040 > > tel: 212-795-4844 > > e-mail: pfh at synapse9.com > > explorations: www.synapse9.com > > > > > > > -----Original Message----- > > > From: friam-bounces at redfish.com > > > [mailto:friam-bounces at redfish.com] On Behalf Of Russell Standish > > > Sent: Saturday, July 21, 2007 12:28 AM > > > To: plissaman at earthlink.net; The Friday Morning Applied > > > Complexity Coffee Group > > > Subject: Re: [FRIAM] Why "true" random? > > > > > > > > > Cryptographic applications require true randomness. If your > > > cipher used on a pseudo-random number generator, then a > > > cracker discovering your algorithm and key has broken your code. > > > > > > I also have a hunch that genuine randomness is needed for > > > open-ended evolutionary systems. Here, the evol algorithm is > > > in the position of the code cracker, and once the code is > > > cracked, the evol algorithm stops. I had a workshop paper on > > > this in 2004, which has some problems with it. The concept is > > > controversial, to say the least. > > > > > > Cheers > > > > > > On Sat, Jul 21, 2007 at 10:24:42AM -0600, Peter Lissaman wrote: > > > > Why is it important (except intellectually) to have "true" > > > > randomness??? I very well remember the early, good old, > > > bad old, days > > > > of Aerospace, in the 50's, when we were really doing practical > > > > earthshattering things -- like going to the moon -- sans > > > computers!! > > > > The RAND corporation, for whom I consulted, published a typed book > > > > (size of a Manhattan telephone directory) of "random" numbers for > > > > engineering application. Much entertainment was occasioned when, > > > > about three months later, they distributed a list of > > > "typos" to their > > > > original list of random numbers. Today I use homemade > > > random numbers > > > > alla time for real problems, specifically the actual > > > response of real > > > > flight vehicles in real atmospheric turbulence. Flight > > > tests support > > > > analysis, in the sense that what we predict is not obviously > > > > incorrect. We have never found it necessary to utilize any more > > > > "perfectly random" "random" sequences! > > > > > > > > > > > > Peter Lissaman, Da Vinci Ventures > > > > > > > > Expertise is not knowing everything, but knowing what to look for. > > > > > > > > 1454 Miracerros Loop South, Santa Fe, New Mexico 87505 > > > > TEL: (505) 983-7728 FAX: (505) 983-1694 > > > > ============================================================ > > > > FRIAM Applied Complexity Group listserv > > > > Meets Fridays 9a-11:30 at cafe at St. John's College lectures, > > > > archives, unsubscribe, maps at http://www.friam.org > > > > > > -- > > > > > > -------------------------------------------------------------- > > > -------------- > > > A/Prof Russell Standish Phone 0425 253119 (mobile) > > > Mathematics > > > UNSW SYDNEY 2052 hpcoder at hpcoders.com.au > > > Australia http://www.hpcoders.com.au > > > -------------------------------------------------------------- > > > -------------- > > > > > > ============================================================ > > > FRIAM Applied Complexity Group listserv > > > Meets Fridays 9a-11:30 at cafe at St. John's College > > > lectures, archives, unsubscribe, maps at http://www.friam.org > > > > > > > > > > > > > > > > > > ------------------------------ > > > > Message: 6 > > Date: Sat, 21 Jul 2007 23:18:36 -0600 > > From: "Douglas Roberts" <doug at parrot-farm.net> > > Subject: Re: [FRIAM] Why "true" random? > > To: "The Friday Morning Applied Complexity Coffee Group" > > <friam at redfish.com>, plissaman at earthlink.net > > Message-ID: > > <f16528920707212218t5d7a368bk3c81a01bf7b3af63 at mail.gmail.com> > > Content-Type: text/plain; charset="iso-8859-1" > > > > Simulations of stochastic processes also require good RN generators, > > especially for simulations of large systems with (I hate to use this > > emergent behavioral properties. A bad RN generator will introduce > emergent > > behavior that will be "flavored" by a bad random sequences. > > > > > > -- > > Doug Roberts, RTI International > > droberts at rti.org > > doug at parrot-farm.net > > 505-455-7333 - Office > > 505-670-8195 - Cell > > > > > > On 7/20/07, Russell Standish <r.standish at unsw.edu.au> wrote: > > > > > > Cryptographic applications require true randomness. If your cipher > > > used on a pseudo-random number generator, then a cracker discovering > > > your algorithm and key has broken your code. > > > > > > I also have a hunch that genuine randomness is needed for open-ended > > > evolutionary systems. Here, the evol algorithm is in the position of > > > the code cracker, and once the code is cracked, the evol algorithm > > > stops. I had a workshop paper on this in 2004, which has some problems > > > with it. The concept is controversial, to say the least. > > > > > > Cheers > > > > > > On Sat, Jul 21, 2007 at 10:24:42AM -0600, Peter Lissaman wrote: > > > > Why is it important (except intellectually) to have "true" > > > randomness??? I very well remember the early, good old, bad old, days > of > > > Aerospace, in the 50's, when we were really doing practical > earthshattering > > > things -- like going to the moon -- sans computers!! The RAND > corporation, > > > for whom I consulted, published a typed book (size of a Manhattan > telephone > > > directory) of "random" numbers for engineering application. Much > > > entertainment was occasioned when, about three months later, they > > > distributed a list of "typos" to their original list of random > > > numbers. Today I use homemade random numbers alla time for real > problems, > > > specifically the actual response of real flight vehicles in real > atmospheric > > > turbulence. Flight tests support analysis, in the sense that what we > > > predict is not obviously incorrect. We have never found it necessary > > > utilize any more "perfectly random" "random" sequences! > > > > > > > > > > > > Peter Lissaman, Da Vinci Ventures > > > > > > > > Expertise is not knowing everything, but knowing what to look for. > > > > > > > > 1454 Miracerros Loop South, Santa Fe, New Mexico 87505 > > > > TEL: (505) 983-7728 FAX: (505) 983-1694 > > > > ============================================================ > > > > FRIAM Applied Complexity Group listserv > > > > Meets Fridays 9a-11:30 at cafe at St. John's College > > > > lectures, archives, unsubscribe, maps at http://www.friam.org > > > > > > -- > > > > > > > > > > > > > A/Prof Russell Standish Phone 0425 253119 (mobile) > > > Mathematics > > > UNSW SYDNEY 2052 hpcoder at hpcoders.com.au > > > Australia http://www.hpcoders.com.au > > > > > > > ---------------------------------------------------------------------------- > > > > > > ============================================================ > > > FRIAM Applied Complexity Group listserv > > > Meets Fridays 9a-11:30 at cafe at St. John's College > > > lectures, archives, unsubscribe, maps at http://www.friam.org > > > > > -------------- next part -------------- > > An HTML attachment was scrubbed... > > URL: > > /attachment-0001.html > > > > ------------------------------ > > > > Message: 7 > > Date: Sun, 22 Jul 2007 08:31:25 -0400 > > From: "Phil Henshaw" <sy at synapse9.com> > > Subject: Re: [FRIAM] Why "true" random? > > To: "'The Friday Morning Applied Complexity Coffee Group'" > > <friam at redfish.com> > > Message-ID: <000801c7cc5c$38c4fd40$2f01a8c0 at SavyII> > > Content-Type: text/plain; charset="iso-8859-1" > > > > Not sure really what the inputs always used, but I think these Self-org > > & Self-adapt algorithms the SASO engineers were playing with didn't > > always use random generators to produce the systemic effects they were > > getting. Obviously all input effects all output in some sort of way, > > but it was the outcomes that would come from the whole gamete of > > unspecified inputs that seemed to be the 'phase space profile' they were > > most interested in. > > > > Many of the papers were on how the inputs could seriously 'misbehave' > > and still not screw up the control schemes, often discussed in terms of > > 'malicious agent' concepts, of which the real net has plenty real > > examples! I also found them very receptive to considering not only > > what a malicious person would think of doing to defeat someone else's > > operating plan, but also the 'malicious creativity' of natural system > > emergence as a focus of design contingencies. > > > > > > > > Phil Henshaw ????.?? ? `?.???? > > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ > > 680 Ft. Washington Ave > > NY NY 10040 > > tel: 212-795-4844 > > e-mail: pfh at synapse9.com > > explorations: www.synapse9.com <http://www.synapse9.com/> > > > > -----Original Message----- > > From: friam-bounces at redfish.com [mailto:friam-bounces at redfish.com] On > > Behalf Of Douglas Roberts > > Sent: Sunday, July 22, 2007 1:19 AM > > To: The Friday Morning Applied Complexity Coffee Group; > > plissaman at earthlink.net > > Subject: Re: [FRIAM] Why "true" random? > > > > > > Simulations of stochastic processes also require good RN generators, > > especially for simulations of large systems with (I hate to use this > > word) emergent behavioral properties. A bad RN generator will introduce > > emergent behavior that will be "flavored" by a bad random sequences. > > > > > > -- > > Doug Roberts, RTI International > > droberts at rti.org > > doug at parrot-farm.net > > 505-455-7333 - Office > > 505-670-8195 - Cell > > > > > > > > On 7/20/07, Russell Standish <r.standish at unsw.edu.au> wrote: > > > > Cryptographic applications require true randomness. If your cipher > > used on a pseudo-random number generator, then a cracker discovering > > your algorithm and key has broken your code. > > > > I also have a hunch that genuine randomness is needed for open-ended > > evolutionary systems. Here, the evol algorithm is in the position of > > the code cracker, and once the code is cracked, the evol algorithm > > stops. I had a workshop paper on this in 2004, which has some problems > > with it. The concept is controversial, to say the least. > > > > Cheers > > > > On Sat, Jul 21, 2007 at 10:24:42AM -0600, Peter Lissaman wrote: > > > Why is it important (except intellectually) to have "true" > > randomness??? I very well remember the early, good old, bad old, days > > of Aerospace, in the 50's, when we were really doing practical > > earthshattering things -- like going to the moon -- sans computers!! > > The RAND corporation, for whom I consulted, published a typed book (size > > of a Manhattan telephone directory) of "random" numbers for engineering > > application. Much entertainment was occasioned when, about three months > > later, they distributed a list of "typos" to their original list of > > random numbers. Today I use homemade random numbers alla time for real > > problems, specifically the actual response of real flight vehicles in > > real atmospheric turbulence. Flight tests support analysis, in the > > sense that what we predict is not obviously incorrect. We have never > > found it necessary to utilize any more "perfectly random" "random" > > sequences! > > > > > > > > > Peter Lissaman, Da Vinci Ventures > > > > > > Expertise is not knowing everything, but knowing what to look for. > > > > > > 1454 Miracerros Loop South, Santa Fe, New Mexico 87505 > > > TEL: (505) 983-7728 FAX: (505) 983-1694 > > > ============================================================ > > > FRIAM Applied Complexity Group listserv > > > Meets Fridays 9a-11:30 at cafe at St. John's College > > > lectures, archives, unsubscribe, maps at http://www.friam.org > > > > -- > > > > ------------------------------------------------------------------------ > > ---- > > A/Prof Russell Standish Phone 0425 253119 (mobile) > > Mathematics > > UNSW SYDNEY 2052 hpcoder at hpcoders.com.au > > Australia http://www.hpcoders.com.au > > <http://www.hpcoders.com.au> > > ------------------------------------------------------------------------ > > ---- > > > > ============================================================ > > FRIAM Applied Complexity Group listserv > > Meets Fridays 9a-11:30 at cafe at St. John's College > > lectures, archives, unsubscribe, maps at http://www.friam.org > > > > > > > > > > > > -------------- next part -------------- > > An HTML attachment was scrubbed... > > URL: > > /attachment-0001.html > > > > ------------------------------ > > > > Message: 8 > > Date: Sun, 22 Jul 2007 07:40:10 -0600 > > From: "Roger Frye" <rfrye at qforma.com> > > Subject: Re: [FRIAM] Why "true" random? > > To: "The Friday Morning Applied Complexity Coffee Group" > > <friam at redfish.com> > > Message-ID: <op.tvvb880hmlpho7 at vivarini.frye> > > Content-Type: text/plain; format=flowed; delsp=yes; > > charset=iso-8859-15 > > > > I would argue the opposite. While I agree with Doug that you need good > > RNGs (though not necessarily true RNGs) in order to avoid bias, the > > problem with good pseudo- or true- RNGs is that they have order N^2 > > convergence for Monte Carlo simulations. Quasi-random number generators > > on the other hand (such as multiples of an irrational square root, or a > > Peano tiling) converge in order N. If you can trust the results, faster > > conergence lets you simulate more. > > -Roger > > > > On Sat, 21 Jul 2007 23:18:36 -0600, Douglas Roberts > <doug at parrot-farm.net> > > wrote: > > > > > Simulations of stochastic processes also require good RN generators, > > > especially for simulations of large systems with (I hate to use this > > > word) > > > emergent behavioral properties. A bad RN generator will introduce > > > emergent > > > behavior that will be "flavored" by a bad random sequences. > > > > > > > > > > > > > > > > > > ------------------------------ > > > > _______________________________________________ > > Friam mailing list > > Friam at redfish.com > > http://redfish.com/mailman/listinfo/friam_redfish.com > > > > > > End of Friam Digest, Vol 49, Issue 20 > > ************************************* > > > > > > ------------------------------ > > Message: 14 > Date: Mon, 23 Jul 2007 11:02:03 +0200 > From: G?nther Greindl <guenther.greindl at gmail.com> > Subject: Re: [FRIAM] math and the mother church > To: The Friday Morning Applied Complexity Coffee Group > <friam at redfish.com> > Message-ID: <46A46E8B.9040709 at gmail.com> > Content-Type: text/plain; charset=ISO-8859-1; format=flowed > > Hello all, > > > What you have given is the "handwaving" version of the proof. The > > trouble is that human imagination can easily get us into trouble when > > dealing with infinities, which is necessarily involved in dealing with > > I disagree - why was that a handwaving proof? It was exactly the way > someone _understands_ what the proofs are about. Mathematical notation > is only meaningless symbolism unless it is interpreted. It is > interpreted by our intuitions (visualization, relation to other, more > basic concepts etc). > > Mathematical notation is good for a number of things: > > 1) define your concepts exactly (again, somewhere it has to bottom out > intuitively like in the concept of set membership or the rules of > > 2) use a convenient shorthand (=math notation) which let's us reason > more easily about the concepts than in natural language. Good math > notation captures some intuitive reasoning analogy in our brains about > the subject - no platonic reality about the structural relation in itself. > > 3) Mathematics is then used to reason about ever more complex subjects. > The notation has been developed in a way that inferential validity is > preserved when mindless symbol shunting is correctly followed. This > let's us "reason" about things where our intuition _fails_ to preserve > inferential validity. > > > So, actually, there is no _magic_ in math or in the notation: it is just > a very clever way of performing reasoning. > > But in essence, a three page proof in english (if diligently written) > differs not from a two paragraph proof in algebra (which is just more > condensed). > > That is actually the reason (I think) why some people who are very > intelligent fail at math: not because they are to dumb, but because > somewhere in their education they had bad math teachers who failed to > teach the intuition/understanding on a certain essential and basic > formalism. > > As maths will build on this formalism in more complex situations, > everybody who has failed to grasp the grounding "shorthand" will fail to > grasp anything else (or it will appear like magic anyway). > > > Handwaving arguments are good for developing intuition. Great for > > teaching during a lecture, and get the students to study the rigorous > > proof later. Similarly, they're good for scientific seminars, but not > > scientific papers. > > I'm not sure - I think the focus on formalism and the deprecatory > attitude which one regards intuition nowadays is actually bad for > mathematics. > > For a refreshingly different approach read for instance > > Needham: Visual complex analysis > > http://www.usfca.edu/vca/ > > which shows that you do not have to sacrifice rigor by being intuitive > (on the contrary!). > > Cheers, > G?nther > > -- > G?nther Greindl > Department of Philosophy of Science > University of Vienna > guenther.greindl at univie.ac.at > http://www.univie.ac.at/Wissenschaftstheorie/ > > Blog: http://dao.complexitystudies.org/ > Site: http://www.complexitystudies.org > > > > ------------------------------ > > _______________________________________________ > Friam mailing list > Friam at redfish.com > http://redfish.com/mailman/listinfo/friam_redfish.com > > > End of Friam Digest, Vol 49, Issue 21 > ************************************* |
Intuition-geometry-computation
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On Tue, Jul 24, 2007 at 12:39:06PM -0600, Peter Lissaman wrote:
> Geometry has no place in mathematics. Mathematics cannot be explained > graphically -- all math proofs must be for blind men, as me tutor used to > say. I vehemently disagree with this comment. Consider the theorem that the determinant of the product of two matrices is the product of the two determinants. This can be understood geometrically in a trice, as a determinant is simply the ratio of the changed hypervolumes undergo when passed through a linear map (for 2 dimensional hypervolumes, substitute "area", for 3D substitute "volume"). Sign captures whether the volume has undergone a mirror transformation. Obviously applying two linear maps one after the other leads to the desired composition rule. However, to show this theorem algebraicly requires at least a page of algebra, and it is not clear one hasn't made a mistake. One would never get to the theorem in the first place without the geometrical intuition. However, the algebra is needed to ensure one isn't mislead by intuition. I have met mathematicians one cannot talk to in geometry. They are a pain to work with. -- ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 hpcoder at hpcoders.com.au Australia http://www.hpcoders.com.au ---------------------------------------------------------------------------- |
Intuition-geometry-computation
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I agree.
;-} -- Doug Roberts, RTI International droberts at rti.org doug at parrot-farm.net 505-455-7333 - Office 505-670-8195 - Cell On 7/24/07, Russell Standish <r.standish at unsw.edu.au> wrote: > > > > I have met mathematicians. They are a > pain to work with. > > -- > > > ---------------------------------------------------------------------------- > A/Prof Russell Standish Phone 0425 253119 (mobile) > Mathematics > UNSW SYDNEY 2052 hpcoder at hpcoders.com.au > Australia http://www.hpcoders.com.au > > ---------------------------------------------------------------------------- > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org > An HTML attachment was scrubbed... URL: http://redfish.com/pipermail/friam_redfish.com/attachments/20070724/9ec4fed9/attachment.html |
Intuition-geometry-computation
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In reply to this post by Peter Lissaman
-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1 Peter Lissaman wrote: > Geometry has no place in mathematics. [...] > Peter Lissaman, Da Vinci Ventures You cannot possibly expect the joke to go over well without placing your signature in close proximity to the ridiculous statement. For us dumb-asses to get your humour, you have to be simple and state them in close proximity.... something like: "Mathematics cannot be explained graphically! -- Peter Lissaman, Da Vinci Ventures! "da Vinci", indeed. [grin] - -- glen e. p. ropella, 971-219-3846, http://tempusdictum.com There is all the difference in the world between treating people equally and attempting to make them equal. -- F.A. Hayek -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.2.2 (GNU/Linux) Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org iD8DBQFGpse/ZeB+vOTnLkoRAplOAKC57+p64yNsErQYTpBJSIL0srIalwCgxlYR oXDgICGlqTWG1YXxzLYKFTk= =M0c5 -----END PGP SIGNATURE----- |
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