Re: [FRIAM] "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18
Thanks, Tory, great to appreciate http://toryhughes.com/news/ re your art show now at StarBucks on the Plaza this month I've been artistically doing science: Richat Structure, Mauritania -- Cox geoablation via Boslough comet fragment air burst directed 6,000 K high pressure directed jets: Rich Murray 2011.08.17 http://rmforall.blogspot.com/2011_08_01_archive.htm Thursday, August 18, 2011 [ at end of each long page, click on Older Posts ] http://groups.yahoo.com/group/astrodeep/message/93 [ you may have to Copy and Paste URLs into your browser ] 10 m broken rock hill with black glazes, W of Rancho Alegre Road, S of Coyote Trail, W of Hwy 14, S of Santa Fe, New Mexico, tour of 50 photos 1 MB size each via DropBox: Rich Murray 2011.07.28 2011.08.03 http://rmforall.blogspot.com/2011_08_01_archive.htm Wednesday, August 3, 2011 [ at end of each long page, click on Older Posts ] http://groups.yahoo.com/group/astrodeep/message/92 [ you may have to Copy and Paste URLs into your browser ] HUDF center top left, #90 astrodeep200407aab10ada.png 3.68 MB 1244X1243 1 of 4 identical views with different color schemes 2008.12.12 #88-91 on rmforall at flickr.com: Rich Murray 2011.01.09 http://rmforall.blogspot.com/2011_01_01_archive.htm Sunday, January 9, 2011 [ at end of each long page, click on Older Posts ] http://groups.yahoo.com/group/astrodeep/message/80 [you may have to Copy and Paste URLs into your browser] within mutual service, Rich Murray rmfor...@gmail.com 505-819-7388 Skype audio, video rich.murray11 On Fri, Aug 19, 2011 at 4:38 PM, Victoria Hughes wrote: "God is a circle whose center is everywhere and whose circumference is nowhere." attributed to various philosophers, beginning with Empedocles a non-dual rephrase> " ... whose center is everywhere and circumference is now here". or even "be the hologram you are, babe". On Aug 19, 2011, at 5:11 PM, Rich Murray wrote: each of us is all of single entire unified creative fractal hyperinfinity ... . . . . Rich Murray 2011.08.19 > thus, just as with the one-to-one matching of any minute subset of real line continuum with entire continuum, obvious by glancing that concentric circles bigger and bigger around a common center, can have infinite straight radial lines from - to + through the center at 0,0 we see any seemingly individualized "minute" process within the fractal hyperinfinity has the same order of hyperinfinity as the whole we can lose the concepts of inner/outer and small/large in many global multi-dimensional geometries in which the fractal variations can not be used to establish these kind of properties -- not simple or primary, but applicable to limited subsets after a lot of mathematical stage setting the same goes for before/now/after or simple/complex or cause/effect this present moment -- of awareness (somewhere?) of writing, and awareness (for, "my" here, an elsewhere and a hereafter) of seeing, reading, comprehending little crooked black ma r k s this very in s t a n t for all sides, actually inside, highly prejudiced testimony supporting purported sustaining reality of self/world with severely circumscribed templates for communication/collaboration however, actually no ground to describe measure understand limit predict fear control the now moment movement any holding on just more proof of already never is now moment already timelessly locationlessly sizelessly open/vast the shared cocreated self/world simulation already making timeless "quantum" jumps in quality as well as quantity we deliberately openmindedly boldly choose/invite/allow/accept/enjoy/trust/share/celebrate/function/create/serve transformations of self/other simulation here float can do no other God willing within mutual service, Rich Murray rmfor...@gmail.com 505-819-7388 Skype audio, video rich.murray11 On Thu, Aug 18, 2011 at 4:21 PM, Grant Holland wrote: Rich, > Wow. Thanks for passing on such a refreshing and informative article. You get my vote for the most entertaining FRIAM post of the year (so far). Grant On 8/18/11 9:11 AM, Rich Murray wrote: "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18 http://www.newscientist.com/article/mg21128231.400-ultimate-logic-to-infinity-and-beyond.html?full=true Ultimate logic: To infinity and beyond 01 August 2011 by Richard Elwes Magazine issue 2823. The mysteries of infinity could lead us to a fantastic structure above and beyond mathematics as we know it 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
Re: [FRIAM] "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18
"God is a circle whose center is everywhere and whose circumference is nowhere." attributed to various philosophers, beginning with Empedocles a non-dual rephrase> " ... whose center is everywhere and circumference is now here". or even "be the hologram you are, babe". On Aug 19, 2011, at 5:11 PM, Rich Murray wrote: each of us is all of single entire unified creative fractal hyperinfinity ... . ... Rich Murray 2011.08.19 thus, just as with the one-to-one matching of any minute subset of real line continuum with entire continuum, obvious by glancing that concentric circles bigger and bigger around a common center, can have infinite straight radial lines from - to + through the center at 0,0 we see any seemingly individualized "minute" process within the fractal hyperinfinity has the same order of hyperinfinity as the whole we can lose the concepts of inner/outer and small/large in many global multi-dimensional geometries in which the fractal variations can not be used to establish these kind of properties -- not simple or primary, but applicable to limited subsets after a lot of mathematical stage setting the same goes for before/now/after or simple/complex or cause/effect this present moment -- of awareness (somewhere?) of writing, and awareness (for, "my" here, an elsewhere and a hereafter) of seeing, reading, comprehending little crooked black ma r ks this very in s t an t for all sides, actually inside, highly prejudiced testimony supporting purported sustaining reality of self/world with severely circumscribed templates for communication/collaboration however, actually no ground to describe measure understand limit predict fear control the now moment movement any holding on just more proof of already never is now moment already timelessly locationlessly sizelessly open/vast the shared cocreated self/world simulation already making timeless "quantum" jumps in quality as well as quantity we deliberately openmindedly boldly choose/invite/allow/accept/enjoy/trust/share/celebrate/function/ create/serve transformations of self/other simulation here float can do no other God willing within mutual service, Rich Murray rmfor...@gmail.com 505-819-7388 Skype audio, video rich.murray11 On Thu, Aug 18, 2011 at 4:21 PM, Grant Holland wrote: Rich, Wow. Thanks for passing on such a refreshing and informative article. You get my vote for the most entertaining FRIAM post of the year (so far). Grant On 8/18/11 9:11 AM, Rich Murray wrote: "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18 http://www.newscientist.com/article/mg21128231.400-ultimate-logic-to-infinity-and-beyond.html?full=true Ultimate logic: To infinity and beyond 01 August 2011 by Richard Elwes Magazine issue 2823. The mysteries of infinity could lead us to a fantastic structure above and beyond mathematics as we know it 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 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
Re: [FRIAM] "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18
each of us is all of single entire unified creative fractal hyperinfinity ... . ... Rich Murray 2011.08.19 thus, just as with the one-to-one matching of any minute subset of real line continuum with entire continuum, obvious by glancing that concentric circles bigger and bigger around a common center, can have infinite straight radial lines from - to + through the center at 0,0 we see any seemingly individualized "minute" process within the fractal hyperinfinity has the same order of hyperinfinity as the whole we can lose the concepts of inner/outer and small/large in many global multi-dimensional geometries in which the fractal variations can not be used to establish these kind of properties -- not simple or primary, but applicable to limited subsets after a lot of mathematical stage setting the same goes for before/now/after or simple/complex or cause/effect this present moment -- of awareness (somewhere?) of writing, and awareness (for, "my" here, an elsewhere and a hereafter) of seeing, reading, comprehending little crooked black ma r ks this very in s t an t for all sides, actually inside, highly prejudiced testimony supporting purported sustaining reality of self/world with severely circumscribed templates for communication/collaboration however, actually no ground to describe measure understand limit predict fear control the now moment movement any holding on just more proof of already never is now moment already timelessly locationlessly sizelessly open/vast the shared cocreated self/world simulation already making timeless "quantum" jumps in quality as well as quantity we deliberately openmindedly boldly choose/invite/allow/accept/enjoy/trust/share/celebrate/function/create/serve transformations of self/other simulation here float can do no other God willing within mutual service, Rich Murray rmfor...@gmail.com 505-819-7388 Skype audio, video rich.murray11 On Thu, Aug 18, 2011 at 4:21 PM, Grant Holland wrote: Rich, Wow. Thanks for passing on such a refreshing and informative article. You get my vote for the most entertaining FRIAM post of the year (so far). Grant On 8/18/11 9:11 AM, Rich Murray wrote: "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18 http://www.newscientist.com/article/mg21128231.400-ultimate-logic-to-infinity-and-beyond.html?full=true Ultimate logic: To infinity and beyond 01 August 2011 by Richard Elwes Magazine issue 2823. The mysteries of infinity could lead us to a fantastic structure above and beyond mathematics as we know it 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
Re: [FRIAM] "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18
Rich, Wow. Thanks for passing on such a refreshing and informative article. You get my vote for the most entertaining FRIAM post of the year (so far). Grant On 8/18/11 9:11 AM, Rich Murray wrote: "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18 http://www.newscientist.com/article/mg21128231.400-ultimate-logic-to-infinity-and-beyond.html?full=true Ultimate logic: To infinity and beyond 01 August 2011 by Richard Elwes Magazine issue 2823. The mysteries of infinity could lead us to a fantastic structure above and beyond mathematics as we know it WHEN David Hilbert left the podium at the Sorbonne in Paris, France, on 8 August 1900, few of the assembled delegates seemed overly impressed. According to one contemporary report, the discussion following his address to the second International Congress of Mathematicians was "rather desultory". Passions seem to have been more inflamed by a subsequent debate on whether Esperanto should be adopted as mathematics' working language. Yet Hilbert's address set the mathematical agenda for the 20th century. It crystallised into a list of 23 crucial unanswered questions, including how to pack spheres to make best use of the available space, and whether the Riemann hypothesis, which concerns how the prime numbers are distributed, is true. Today many of these problems have been resolved, sphere-packing among them. Others, such as the Riemann hypothesis, have seen little or no progress. But the first item on Hilbert's list stands out for the sheer oddness of the answer supplied by generations of mathematicians since: that mathematics is simply not equipped to provide an answer. This curiously intractable riddle is known as the continuum hypothesis, and it concerns that most enigmatic quantity, infinity. Now, 140 years after the problem was formulated, a respected US mathematician believes he has cracked it. What's more, he claims to have arrived at the solution not by using mathematics as we know it, but by building a new, radically stronger logical structure: a structure he dubs "ultimate L". The journey to this point began in the early 1870s, when the German Georg Cantor was laying the foundations of set theory. Set theory deals with the counting and manipulation of collections of objects, and provides the crucial logical underpinnings of mathematics: because numbers can be associated with the size of sets, the rules for manipulating sets also determine the logic of arithmetic and everything that builds on it. These dry, slightly insipid logical considerations gained a new tang when Cantor asked a critical question: how big can sets get? The obvious answer - infinitely big - turned out to have a shocking twist: infinity is not one entity, but comes in many levels. How so? You can get a flavour of why by counting up the set of whole numbers: 1, 2, 3, 4, 5... How far can you go? Why, infinitely far, of course - there is no biggest whole number. This is one sort of infinity, the smallest, "countable" level, where the action of arithmetic takes place. Now consider the question "how many points are there on a line?" A line is perfectly straight and smooth, with no holes or gaps; it contains infinitely many points. But this is not the countable infinity of the whole numbers, where you bound upwards in a series of defined, well-separated steps. This is a smooth, continuous infinity that describes geometrical objects. It is characterised not by the whole numbers, but by the real numbers: the whole numbers plus all the numbers in between that have as many decimal places as you please - 0.1, 0.01, √2, π and so on. Cantor showed that this "continuum" infinity is in fact infinitely bigger than the countable, whole-number variety. What's more, it is merely a step in a staircase leading to ever-higher levels of infinities stretching up as far as, well, infinity. While the precise structure of these higher infinities remained nebulous, a more immediate question frustrated Cantor. Was there an intermediate level between the countable infinity and the continuum? He suspected not, but was unable to prove it. His hunch about the non-existence of this mathematical mezzanine became known as the continuum hypothesis. Attempts to prove or disprove the continuum hypothesis depend on analysing all possible infinite subsets of the real numbers. If every one is either countable or has the same size as the full continuum, then it is correct. Conversely, even one subset of intermediate size would render it false. A similar technique using subsets of the whole numbers shows that there is no level of infinity below the countable. Tempting as it might be to think that there are half as many even numbers as there are whole numbers in total, the two collections can in fact be paired off exactly. Indeed, every set of whole numbers is either finite or countably infinite. Applied to the real numbers, thoug
Re: [FRIAM] "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18
Yup. Esperanto is rather well known in Brazil (which still means that the number of Brazilian speakers of Esperanto is small). In fact, every week (in 10 minutes in fact) I meet on video Skype with Esperanto-speaking friends I came to know in the Raleigh area when I was at NCSU (I now live in Santa Fe), and a Brazilian group plans to join us. However, it's never been the case that Portuguese has had a major impact on the evolution of Esperanto. Bruce On Thu, Aug 18, 2011 at 3:12 PM, Steve Smith wrote: > Bruce - >> >> Interesting reaction to Esperanto vocabulary, which has no Portuguese >> roots at all except to the extent that there are many Romance-language >> roots in Esperanto, which were borrowed mainly from French or Latin >> forms. > > Bruce- > > Thanks for the correction... > > It has been 30+ years since I studied Esperanto and the reaction is a > vestige of my naivette at the time having only border Spanish and a > smattering of Greek/Latin to draw from then. > > I might not have known French from Portuguese at the time... though I > *think* I would have... I certainly do now! Or maybe it was just an > intuitive affinity alignment for me it is likely that I'd never seen, > or heard any Portuguese until I was introduced to it during my Esperanto > Class as one of the other Romance-languages which I probably held limited to > Italian, Spanish, French at the time... > > Is there a reason I would have associated Esperanto with Brazil? Did they > have a strong interest/influence on it? > > > 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 > 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
Re: [FRIAM] "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18
Bruce - Interesting reaction to Esperanto vocabulary, which has no Portuguese roots at all except to the extent that there are many Romance-language roots in Esperanto, which were borrowed mainly from French or Latin forms. Bruce- Thanks for the correction... It has been 30+ years since I studied Esperanto and the reaction is a vestige of my naivette at the time having only border Spanish and a smattering of Greek/Latin to draw from then. I might not have known French from Portuguese at the time... though I *think* I would have... I certainly do now! Or maybe it was just an intuitive affinity alignment for me it is likely that I'd never seen, or heard any Portuguese until I was introduced to it during my Esperanto Class as one of the other Romance-languages which I probably held limited to Italian, Spanish, French at the time... Is there a reason I would have associated Esperanto with Brazil? Did they have a strong interest/influence on it? 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
Re: [FRIAM] "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18
Interesting reaction to Esperanto vocabulary, which has no Portuguese roots at all except to the extent that there are many Romance-language roots in Esperanto, which were borrowed mainly from French or Latin forms. A large number of constructed languages including Interlingua were simplified Latin/Romance languages designed for immediate passive readability by educated Europeans who already knew some European languages (even speakers of English and German know lots of Romance vocabulary). These Latinate languages however are not easy to master for active use (speaking and writing) due to irregularities and the requirement of a large vocabulary to be expressive. Esperanto is unusual in making it possible to be very expressive even with a rather small vocabulary, thanks to its non-European mechanism for creating new words out of invariant particles which are themselves words. It's rather like making molecules out of invariant atoms, and it contributes to creative linguistic playfulness. Bruce On Thu, Aug 18, 2011 at 12:44 PM, Steve Smith wrote: > I appreciate your post Rich and owen and Bruce's responses. > > 3) Of the several auxiliary languages, I find Interlingua the easiest to > read/understand without any particular training... Esperanto seems to rely > heavily on Portuguese vocabulary/roots which are just (un)familiar enough > for me to find it difficult. In every case, I am not fluent enough to feel > I am able to *think* in these as alternate languages while I do sometimes > think in Spanish, in Mathematics, and in several computer languages (for > very narrow thinking unfortunately). I wish I could think/percieve in > musical structures or holographically, both of which I have a formal > understanding of but only limited intuition. 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
Re: [FRIAM] "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18
I appreciate your post Rich and owen and Bruce's responses. I have a couple of observations: 1) I am always amazed (euphemism for offended) at our use of hyperbole and superlatives in such things. We all know that mathematics and science only has false-summits and that all "ultimates" are perpetual "penultimates", and yet our rhetoric is always laced with absolutes and mega-gigas and supra-ubers. 2) I have long been fascinated at the interplay between language and deep understanding. I studied Esperanto alongside Greek and Latin and Mathematics and Computer Languages in the hopes of finding the right universal tool, or even a toolbox filled with appropriate tools to think/communicate in qualitatively better ways. It was not for naught, and perhaps if I did not have these in my toolbox I would either miss them dearly or not know enough to miss them. But for the most part, my improved thinking/communication feels quantitative, not qualitative. 3) Of the several auxiliary languages, I find Interlingua the easiest to read/understand without any particular training... Esperanto seems to rely heavily on Portuguese vocabulary/roots which are just (un)familiar enough for me to find it difficult. In every case, I am not fluent enough to feel I am able to *think* in these as alternate languages while I do sometimes think in Spanish, in Mathematics, and in several computer languages (for very narrow thinking unfortunately). I wish I could think/percieve in musical structures or holographically, both of which I have a formal understanding of but only limited intuition. 4) I found David Bohm's Rheomode and Dialogue even more compelling because it went deeper than "merely" normalizing somewhat across historical and cultural biases. Esperanto was a great 19th century idea but I felt it did not go nearly far enough. I was (and am still to some extent) enamored of his Holonomics and of course the Rheomode and Dialogue, though the latter two seem under developed and somewhat naive. - Steve Thanks, Rich, for the interesting note. For another kind of completeness, I'll comment that I speak Esperanto. In the period 1900-1905, approximately, there was a lot of interest among French intellectuals in the possible use of a constructed language for the purpose of international communications, with Esperanto the leading contender. This led to a conference of scientific groups that actually picked a language, Ido, which was a modified Esperanto which supposedly "fixed" perceived failings of Esperanto. Roughly speaking, Ido rejected the unusual non-European structure of Esperanto in favor of a more "naturalistic" scheme thought to appeal more to educated Europeans, and possibly easier for Europeans to read at sight (but likely to be more difficult to speak or write). The whole affair was a major schism which damaged the movement to adopt an easy-to-learn second language. Both Esperanto and Ido still exist in globally dispersed communities, but the Esperanto community has by far the largest number of speakers of all the constructed languages. It is difficult to get good numbers, but there are probably 50 to 100 thousand fluent speakers. I've even known a number of native speakers of Esperanto, born to parents who met in the Esperanto-speaking community and continued to speak the language at home. Few educated Americans have ever heard of Esperanto, and what they've heard is in my experience mostly incorrect. Google Esperanto for vast amounts of information, much of it accurate. An interesting math connection: Sometime around 1900 Peano, of mathematical fame, gave a talk in which he started in pure Latin, progressively during the talk introduced various simplifications, and by the end was speaking a much simplified Latin which he proposed for international use. Bruce On Thu, Aug 18, 2011 at 9:41 AM, Owen Densmore wrote: Wow, thanks Rich. And the follow-on conversation on the website is also interesting. I have to admit the Axiom of Choice has been puzzling to me, why its importance, how it is applied and so on. -- Owen On Thu, Aug 18, 2011 at 9:11 AM, Rich Murray wrote: "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18 http://www.newscientist.com/article/mg21128231.400-ultimate-logic-to-infinity-and-beyond.html?full=true Ultimate logic: To infinity and beyond 01 August 2011 by Richard Elwes Magazine issue 2823. The mysteries of infinity could lead us to a fantastic structure above and beyond mathematics as we know it WHEN David Hilbert left the podium at the Sorbonne in Paris, France, on 8 August 1900, few of the assembled delegates seemed overly impressed. According to one contemporary report, the discussion following his address to the second International Congress of Mathematicians was "rather desultory". Passions seem to have been more inflamed by a subsequent debate on w
Re: [FRIAM] "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18
Thanks, Rich, for the interesting note. For another kind of completeness, I'll comment that I speak Esperanto. In the period 1900-1905, approximately, there was a lot of interest among French intellectuals in the possible use of a constructed language for the purpose of international communications, with Esperanto the leading contender. This led to a conference of scientific groups that actually picked a language, Ido, which was a modified Esperanto which supposedly "fixed" perceived failings of Esperanto. Roughly speaking, Ido rejected the unusual non-European structure of Esperanto in favor of a more "naturalistic" scheme thought to appeal more to educated Europeans, and possibly easier for Europeans to read at sight (but likely to be more difficult to speak or write). The whole affair was a major schism which damaged the movement to adopt an easy-to-learn second language. Both Esperanto and Ido still exist in globally dispersed communities, but the Esperanto community has by far the largest number of speakers of all the constructed languages. It is difficult to get good numbers, but there are probably 50 to 100 thousand fluent speakers. I've even known a number of native speakers of Esperanto, born to parents who met in the Esperanto-speaking community and continued to speak the language at home. Few educated Americans have ever heard of Esperanto, and what they've heard is in my experience mostly incorrect. Google Esperanto for vast amounts of information, much of it accurate. An interesting math connection: Sometime around 1900 Peano, of mathematical fame, gave a talk in which he started in pure Latin, progressively during the talk introduced various simplifications, and by the end was speaking a much simplified Latin which he proposed for international use. Bruce On Thu, Aug 18, 2011 at 9:41 AM, Owen Densmore wrote: > Wow, thanks Rich. And the follow-on conversation on the website is also > interesting. > I have to admit the Axiom of Choice has been puzzling to me, why its > importance, how it is applied and so on. > -- Owen > > On Thu, Aug 18, 2011 at 9:11 AM, Rich Murray wrote: >> >> "no one shall expel us from the paradise that Cantor has created", >> Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18 >> >> >> http://www.newscientist.com/article/mg21128231.400-ultimate-logic-to-infinity-and-beyond.html?full=true >> >> Ultimate logic: To infinity and beyond >> >> 01 August 2011 by Richard Elwes >> Magazine issue 2823. >> >> The mysteries of infinity could lead us to a fantastic structure above >> and beyond mathematics as we know it >> >> WHEN David Hilbert left the podium at the Sorbonne in Paris, France, >> on 8 August 1900, few of the assembled delegates seemed overly >> impressed. According to one contemporary report, the discussion >> following his address to the second International Congress of >> Mathematicians was "rather desultory". Passions seem to have been more >> inflamed by a subsequent debate on whether Esperanto should be adopted >> as mathematics' working language. >> >> Yet Hilbert's address set the mathematical agenda for the 20th >> century. It crystallised into a list of 23 crucial unanswered >> questions, including how to pack spheres to make best use of the >> available space, and whether the Riemann hypothesis, which concerns >> how the prime numbers are distributed, is true. >> > > > 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 > 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
Re: [FRIAM] "no one shall expel us from the paradise that Cantor has created", Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18
Wow, thanks Rich. And the follow-on conversation on the website is also interesting. I have to admit the Axiom of Choice has been puzzling to me, why its importance, how it is applied and so on. -- Owen On Thu, Aug 18, 2011 at 9:11 AM, Rich Murray wrote: > "no one shall expel us from the paradise that Cantor has created", > Hugh Woodin's "ultimate L": Richard Elwes: Rich Murray 2011.08.18 > > > http://www.newscientist.com/article/mg21128231.400-ultimate-logic-to-infinity-and-beyond.html?full=true > > Ultimate logic: To infinity and beyond > > 01 August 2011 by Richard Elwes > Magazine issue 2823. > > The mysteries of infinity could lead us to a fantastic structure above > and beyond mathematics as we know it > > WHEN David Hilbert left the podium at the Sorbonne in Paris, France, > on 8 August 1900, few of the assembled delegates seemed overly > impressed. According to one contemporary report, the discussion > following his address to the second International Congress of > Mathematicians was "rather desultory". Passions seem to have been more > inflamed by a subsequent debate on whether Esperanto should be adopted > as mathematics' working language. > > Yet Hilbert's address set the mathematical agenda for the 20th > century. It crystallised into a list of 23 crucial unanswered > questions, including how to pack spheres to make best use of the > available space, and whether the Riemann hypothesis, which concerns > how the prime numbers are distributed, is true. > 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
