[math-fun] California water crisis
Now that Captain Kirk is using Kickstarter to build a water pipeline to California from someplace with "too much" water, I was thinking about what would be cheap ways to get large amounts of desalinated water. One suggestion (Popular Mechanics??) from my childhood: towing an iceberg (assuming we can still find one) to San Diego/Long Beach/San Francisco harbor and harvest it into the water supply. So long as you don't care much about speed, moving stuff through water can be quite energy-efficient. So even if it took a number of weeks to move a large iceberg, the percent lost to melting would be relatively small. Furthermore, if you wanted to reduce the melting, you could wrap the iceberg in bubble-wrap to better insulate it. Another option would be to wrap the iceberg in plastic wrap to catch the melted (desalinated) water & pipe it into a nearby oil tanker. You could presumably use an oil tanker itself to bring fresh water from someplace with "too much", and this would likely be energetically cheaper than using a pipeline, but such a tanker could carry only perhaps 80% (by volume) of the amount of oil it would normally carry. If you were forced to desalinate the seawater locally, it would be best if you could use solar power to do it. Solar panels are becoming cheap enough that they might allow relatively inexpensive desalinators. Even better, solar panels are _distributed power_, so it makes sense to build small, modular desalinators -- perhaps the size of a standard shipping crate. If you made these modules so that they were waterproof & floated, you could hook them together into a floating desalinization plant which required no expensive space on the California coast. Furthermore, if you provided a long enough hose, you could put these (very low profile) modular solar desalinization plants over the horizon so that they wouldn't mess up the view from expensive California real estate (this is a real problem with offshore wind farms). Putting the desal plant far out in the ocean also solves another problem: what to do with the discharge water with higher salt content. If you discharge this close to shore, it messes up the local sea life, whereas if you do it far out to sea, it can get diluted much more in the deeper waters.
Here, from a few years ago, is a decent historical overview: http://www.theatlantic.com/technology/archive/2011/08/the-many-failures-and-...
On Apr 22, 2015, at 11:43 AM, Henry Baker <hbaker1@pipeline.com> wrote:
One suggestion (Popular Mechanics??) from my childhood: towing an iceberg (assuming we can still find one) to San Diego/Long Beach/San Francisco harbor and harvest it into the water supply.
Terrific historical overview. Thanks very much for the link, Hans! But this article doesn't really answer the question about whether such a plan would be feasible today for -- say Santa Barbara -- whose water needs are much more modest than those of San Diego (which is already spending > $1 billion on a desal plant which will cost a bundle to actually operate). You could construct an historical list considerably longer than the Atlantic's about various schemes for getting to the Moon or Mars, but in both of these cases, we finally succeeded because we finally got serious. The Chinese are planning to build a new Atlantic2Pacific canal in Central America, which was contemplated >100 years ago; the only real issue is $$$$$$. Since $1 billion is starting to get serious (Captain Kirk's scheme will cost > $1 billion, as well), it makes sense to dust off some of these older plans to see what has changed & how we could utilize more modern technology to overcome some of the issues. The "rope" problem can be eliminated by not using ropes at all. A number of computer-synchronized "tugboats" _pushing_ (and possibly also pulling with carbon-fiber-based ropes) might be capable of doing the job. So the first new idea is the use of computer-synchronized tugs -- something similar is already in use on long trains for both propulsion & braking to keep the train from flying apart due to non-uniform accelerations. Carbon-fiber ropes are already in use in high-rise building elevators. Due to winds, the tugboats might not be able to keep the iceberg on course. It might be necessary to sculpt the top surface of the iceberg in advance in order to reduce the wind loads. The fact that the vast majority of the iceberg is underwater will help. Currents are another problem, but we have to take a cue from the modern commercial aircraft industry by mapping out these currents, and using sophisticated programming to figure out the optimum feasible path through the various currents. Of course, we don't have the advantage of an airplane which can move to a different altitude to avoid certain headwinds. At 10:54 AM 4/22/2015, Hans Havermann wrote:
Here, from a few years ago, is a decent historical overview:
http://www.theatlantic.com/technology/archive/2011/08/the-many-failures-and-...
On Apr 22, 2015, at 11:43 AM, Henry Baker <hbaker1@pipeline.com> wrote:
One suggestion (Popular Mechanics??) from my childhood: towing an iceberg (assuming we can still find one) to San Diego/Long Beach/San Francisco harbor and harvest it into the water supply.
I have a blue-sky invention, that I have been cherishing in the back of my mind for a decade or so, that is relevant to this discussion. It's a simple nanotech application -- actually within reach with present methods. I call it "black tape" because I imagine that is what it would look like. The tape would be coated with a substance, to be designed that would capture ambient water molecules and transport them preferentially in one direction (probably it would be marked with arrows every few centimeters to show the transport direction). When the tape was wetted anywhere, the downstream end would soon start to drip water. The transported water would be reasonably pure, because the surface coating would not be designed to transport, say, salt. One would dip one end in salt water, and the other end would soon start producing fresh water. Obviously the water transport requires energy. The tape would be black because the required energy would come from absorbed sunlight. "Wait a minute!" you cry. "What the heck is this magic water-transporting surface treatment?" Well, I'm not sure; I only know enough chemistry to guess that it might be possible. The image in my mind is that of a molecule that looks vaguely like a mousetrap, with two positions, "armed" and "released". It would be like a lever-arm, anchored to the substrate; at the outer end would be the "bucket" or water-carrying group, probably a C=C double bond that could be hydrated to CH-COH. In the armed position, the bucket would be a few nanometers upstream from its released position. These molecules would be arranged in a "bucket brigade", so that the released position of one molecule is in just the right place to pass the water molecule to the next molecule in the chain, provided that the next molecule is armed. When the bucket was hydrated, the geometry of the molecule would change in such a way as to snap the "mousetrap", causing the lever to whip over to the released position. Then an energy-neutral reaction would hydrate the next molecule in the chain, causing it also to snap over. A chain reaction could move the water molecule an arbitrary distance. After a while, solar action would restore the molecule to the armed position, ready to pick up another water molecule. How much water could such a tape transport? Let's imagine a meter-wide tape. If the bucket-brigade chains were spaced every nanometer (a water molecule is about a quarter of a nanometer across), then such a tape could carry 10^9 chains. I don't know how fast one could expect the carrier molecules to cycle, but at 10^9 Hz, a meter-wide tape would deliver 10^18 water molecules per second, about a millionth of a mole. This is clearly too slow for practical applications, so the invention as described is probably useless, but the general idea of sunlight-activated selective water transport seems promising. Any other ideas? On Wed, Apr 22, 2015 at 1:54 PM, Hans Havermann <gladhobo@teksavvy.com> wrote:
Here, from a few years ago, is a decent historical overview:
http://www.theatlantic.com/technology/archive/2011/08/the-many-failures-and-...
On Apr 22, 2015, at 11:43 AM, Henry Baker <hbaker1@pipeline.com> wrote:
One suggestion (Popular Mechanics??) from my childhood: towing an iceberg (assuming we can still find one) to San Diego/Long Beach/San Francisco harbor and harvest it into the water supply.
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Ever since we discussed Mark Kac's Statistical Independence in Probability, Analysis and Number Theory, I've thought about other truly great non-recreational* math books. I have not necessarily read all of these books!!! But I have at least spent serious time dipping into each of them extensively, and have found that with most of these, with adequate background, you can dip in almost anywhere and have a very enjoyable read. They are all pellucid, at least most of the time. Here are a few among many: Tom Apostol, Calculus vol. 1 Tom Apostol, Calculus vol. 2 William Feller, An Introduction to Probability Theory and Its Applications, vol. I discrete probability William Feller, An Introduction to Probability Theory and Its Applications, vol. II continuous probability. Covers many subjects a second time in a more advanced way. G.H. Hardy & E.M. Wright, An Introduction to the Theory of Numbers algebraic but not analytic John Conway & Neil Sloane, Sphere Packings, Lattices and Groups Walter Rudin, Principles of Mathematical Analysis George Pólya & Gordon Latta, Complex Variables Tom Apostol, Modular Functions and Dirichlet Series Anthony Knapp, Elliptic Curves pre-FLT, largely based on a lecture series by Don Zagier, but filled with fascinating math James Munkres, Topology ultra-clear William Massey, Algebraic Topology does homotopy, and not homology or cohomology, but has many fascinating nonstandard topics John Milnor, Morse Theory* best to have a background in differential geometry. Explains the amazing Bott Periodicity theorem via geometry. John Milnor & James Stasheff, Characteristic Classes* exquisite introduction to many profound and beautiful results about manifolds that are available with algebraic and differential topology. Based on mimeographed notes Stasheff took on 1957 lectures by Milnor, the book did not appear until 1974, which is probably one reason the writing is so very polished. Although everything is done rigorously, Milnor makes it appear almost effortless. Alexandru Scorpan, The Wild World of 4-Manifolds* Utterly fascinating tour through the topology of dimension 4, which is unlike any other dimension. (For instance, each Euclidean space R^n for n <> 4 has exactly one smooth structure, up to equivalence (diffeomorphism). R^4, on the other hand, has infinitely many inequivalent smooth structures. And the infinity is not aleph_0. It is 2^aleph_0, the continuum.) The author is extremely generous to the reader, explaining virtually everything in detail, often more than one place in the book, with ample cross-references (that save the reader from having to flip back and forth to the index), and with voluminous explanatory footnotes. 0 Dimension 4 is also the only unresolved case of the smooth Poincaré conjecture PC4: PC4: If M is a compact 4-manifold such that every map of a circle S^1 or a sphere S^2 into it can be continuously shrunk to a point, then M is diffeomorphic to the standard 4-sphere S^4. --Dan ________________________________________________________________________________________ * The last three require a solid background in topology, and at least an introduction to homotopy, homology, and cohomology. The 4-manifold book is best read with some background in differential topology. _________________________________________________________________________ * I almost used the word "medical" instead.
Here is another for the truly great list: T W Koerner, The Pleasures of Counting, Cambridge Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Wed, Apr 22, 2015 at 5:13 PM, Dan Asimov <asimov@msri.org> wrote:
Ever since we discussed Mark Kac's Statistical Independence in Probability, Analysis and Number Theory, I've thought about other truly great non-recreational* math books.
I have not necessarily read all of these books!!! But I have at least spent serious time dipping into each of them extensively, and have found that with most of these, with adequate background, you can dip in almost anywhere and have a very enjoyable read. They are all pellucid, at least most of the time.
Here are a few among many:
Tom Apostol, Calculus vol. 1
Tom Apostol, Calculus vol. 2
William Feller, An Introduction to Probability Theory and Its Applications, vol. I discrete probability
William Feller, An Introduction to Probability Theory and Its Applications, vol. II continuous probability. Covers many subjects a second time in a more advanced way.
G.H. Hardy & E.M. Wright, An Introduction to the Theory of Numbers algebraic but not analytic
John Conway & Neil Sloane, Sphere Packings, Lattices and Groups
Walter Rudin, Principles of Mathematical Analysis
George Pólya & Gordon Latta, Complex Variables
Tom Apostol, Modular Functions and Dirichlet Series
Anthony Knapp, Elliptic Curves pre-FLT, largely based on a lecture series by Don Zagier, but filled with fascinating math
James Munkres, Topology ultra-clear
William Massey, Algebraic Topology does homotopy, and not homology or cohomology, but has many fascinating nonstandard topics
John Milnor, Morse Theory* best to have a background in differential geometry. Explains the amazing Bott Periodicity theorem via geometry.
John Milnor & James Stasheff, Characteristic Classes* exquisite introduction to many profound and beautiful results about manifolds that are available with algebraic and differential topology. Based on mimeographed notes Stasheff took on 1957 lectures by Milnor, the book did not appear until 1974, which is probably one reason the writing is so very polished. Although everything is done rigorously, Milnor makes it appear almost effortless.
Alexandru Scorpan, The Wild World of 4-Manifolds* Utterly fascinating tour through the topology of dimension 4, which is unlike any other dimension. (For instance, each Euclidean space R^n for n <> 4 has exactly one smooth structure, up to equivalence (diffeomorphism). R^4, on the other hand, has infinitely many inequivalent smooth structures. And the infinity is not aleph_0. It is 2^aleph_0, the continuum.)
The author is extremely generous to the reader, explaining virtually everything in detail, often more than one place in the book, with ample cross-references (that save the reader from having to flip back and forth to the index), and with voluminous explanatory footnotes. 0
Dimension 4 is also the only unresolved case of the smooth Poincaré conjecture PC4:
PC4: If M is a compact 4-manifold such that every map of a circle S^1 or a sphere S^2 into it can be continuously shrunk to a point, then M is diffeomorphic to the standard 4-sphere S^4.
--Dan
________________________________________________________________________________________ * The last three require a solid background in topology, and at least an introduction to homotopy, homology, and cohomology. The 4-manifold book is best read with some background in differential topology.
_________________________________________________________________________ * I almost used the word "medical" instead.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Another wonderful book: Lester R. Ford, "Automorphic Functions", AMS Chelsea. -- Gene
I found Dan Klain and Gian-Carlo Rota's "Introduction to Geometric Probability" extremely compelling; after I bought it at the Joint Winter Meetings one year, I devoured the whole book in a single sitting (actually, I think I was sitting from 10pm to midnight and lying down from midnight to 2am). I kept thinking "I'm giving a talk tomorrow, I should really stop reading and get some sleep", but I couldn't put it down! Jim Propp On Wed, Apr 22, 2015 at 7:31 PM, Eugene Salamin via math-fun < math-fun@mailman.xmission.com> wrote:
Another wonderful book: Lester R. Ford, "Automorphic Functions", AMS Chelsea. -- Gene _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
From having once been lectured by Körner, I can confirm that this book will be indeed fascinating.
-- Adam P. Goucher
Sent: Wednesday, April 22, 2015 at 10:49 PM From: "Neil Sloane" <njasloane@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Wonderful advanced topology textbook(s)
Here is another for the truly great list:
T W Koerner, The Pleasures of Counting, Cambridge
Best regards Neil
Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
On Wed, Apr 22, 2015 at 5:13 PM, Dan Asimov <asimov@msri.org> wrote:
Ever since we discussed Mark Kac's Statistical Independence in Probability, Analysis and Number Theory, I've thought about other truly great non-recreational* math books.
I have not necessarily read all of these books!!! But I have at least spent serious time dipping into each of them extensively, and have found that with most of these, with adequate background, you can dip in almost anywhere and have a very enjoyable read. They are all pellucid, at least most of the time.
Here are a few among many:
Tom Apostol, Calculus vol. 1
Tom Apostol, Calculus vol. 2
William Feller, An Introduction to Probability Theory and Its Applications, vol. I discrete probability
William Feller, An Introduction to Probability Theory and Its Applications, vol. II continuous probability. Covers many subjects a second time in a more advanced way.
G.H. Hardy & E.M. Wright, An Introduction to the Theory of Numbers algebraic but not analytic
John Conway & Neil Sloane, Sphere Packings, Lattices and Groups
Walter Rudin, Principles of Mathematical Analysis
George Pólya & Gordon Latta, Complex Variables
Tom Apostol, Modular Functions and Dirichlet Series
Anthony Knapp, Elliptic Curves pre-FLT, largely based on a lecture series by Don Zagier, but filled with fascinating math
James Munkres, Topology ultra-clear
William Massey, Algebraic Topology does homotopy, and not homology or cohomology, but has many fascinating nonstandard topics
John Milnor, Morse Theory* best to have a background in differential geometry. Explains the amazing Bott Periodicity theorem via geometry.
John Milnor & James Stasheff, Characteristic Classes* exquisite introduction to many profound and beautiful results about manifolds that are available with algebraic and differential topology. Based on mimeographed notes Stasheff took on 1957 lectures by Milnor, the book did not appear until 1974, which is probably one reason the writing is so very polished. Although everything is done rigorously, Milnor makes it appear almost effortless.
Alexandru Scorpan, The Wild World of 4-Manifolds* Utterly fascinating tour through the topology of dimension 4, which is unlike any other dimension. (For instance, each Euclidean space R^n for n <> 4 has exactly one smooth structure, up to equivalence (diffeomorphism). R^4, on the other hand, has infinitely many inequivalent smooth structures. And the infinity is not aleph_0. It is 2^aleph_0, the continuum.)
The author is extremely generous to the reader, explaining virtually everything in detail, often more than one place in the book, with ample cross-references (that save the reader from having to flip back and forth to the index), and with voluminous explanatory footnotes. 0
Dimension 4 is also the only unresolved case of the smooth Poincaré conjecture PC4:
PC4: If M is a compact 4-manifold such that every map of a circle S^1 or a sphere S^2 into it can be continuously shrunk to a point, then M is diffeomorphic to the standard 4-sphere S^4.
--Dan
________________________________________________________________________________________ * The last three require a solid background in topology, and at least an introduction to homotopy, homology, and cohomology. The 4-manifold book is best read with some background in differential topology.
_________________________________________________________________________ * I almost used the word "medical" instead.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On 22/04/2015 22:13, Dan Asimov wrote:
G.H. Hardy & E.M. Wright, An Introduction to the Theory of Numbers algebraic but not analytic
I'm not sure that's a very accurate description. E.g., on the analytic side they get as far as proving the Prime Number Theorem (but no further; e.g., no Dirichlet) and on the algebraic side they get as far as discussing the primes in quadratic fields with unique factorization (but no further; e.g., no ideal class group). It's always felt to me like quite an "analytic" book, which makes sense given Hardy's work. But I'm not a number theorist; perhaps my idea of what counts as algebraic or analytic is distorted somehow. -- g
Thanks for the correction, Gareth. It was dumb of me to rely on my memory, which went no further than how much of the book I went through by the time I last saw it, many decades ago. --Dan
On Apr 23, 2015, at 1:27 AM, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
On 22/04/2015 22:13, Dan Asimov wrote:
G.H. Hardy & E.M. Wright, An Introduction to the Theory of Numbers algebraic but not analytic
I'm not sure that's a very accurate description. E.g., on the analytic side they get as far as proving the Prime Number Theorem (but no further; e.g., no Dirichlet) and on the algebraic side they get as far as discussing the primes in quadratic fields with unique factorization (but no further; e.g., no ideal class group). It's always felt to me like quite an "analytic" book, which makes sense given Hardy's work.
But I'm not a number theorist; perhaps my idea of what counts as algebraic or analytic is distorted somehow.
-- g
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Hardy & Wright (An Introduction to the Theory of Numbers) is written to minimize the required math background. H&W isn't really 'algebraic' or 'analytic'. There's no mention of homomorphism, groups, or maps. Complex numbers appear, but mostly in algebraic number fields. Ideals of number fields are sampled briefly, discussing how factorization changes. Complex variables do not appear. The zeta function is used, but only with real argument >1. No mention of the zeta functional equation or Riemann Hypothesis. Power series are used extensively in the Partitions chapter, but only as a combinatorial device. They do teach O-notation, and use it extensively. Use of calculus is postponed to the later chapters. The proof of the Prime Number Theorem mostly follows Selberg's elementary proof. The preface mentions that they omit quadratic forms, and are disjoint from Dickson's IttToN (same title, but about Diophantine Equations). I think it's a great book; it's been well worth the $12, even in 1960 $. It's not really aimed at youngsters. I've considered the project of annotating it, to explain the parts that confused me. But it's hard to recreate my younger viewpoint. When I first got H&W, there were entire chapters that made little or no sense -- I could read the theorems, but the proofs were too hard, and often the point of the theorem was a puzzle. I went back many times, and the dark areas have receded. Is it worth doing a math book that makes sense for bright kids, and tries to explain everything? Or is it better to leave some mysteries? Rich ----------- Quoting Gareth McCaughan <gareth.mccaughan@pobox.com>:
On 22/04/2015 22:13, Dan Asimov wrote:
G.H. Hardy & E.M. Wright, An Introduction to the Theory of Numbers algebraic but not analytic
I'm not sure that's a very accurate description. E.g., on the analytic side they get as far as proving the Prime Number Theorem (but no further; e.g., no Dirichlet) and on the algebraic side they get as far as discussing the primes in quadratic fields with unique factorization (but no further; e.g., no ideal class group). It's always felt to me like quite an "analytic" book, which makes sense given Hardy's work.
But I'm not a number theorist; perhaps my idea of what counts as algebraic or analytic is distorted somehow.
-- g
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
I think it's even a good idea to leave some stuff that is tantalizingly abstruse and beyond the reach of younger / less educated folks. On the theory that one's reach should exceed their grasp. But I think the main problems might be the serious decline of brick & mortar bookstores today, plus the absurd pricing for advanced books today. I could not even find (online) that book in the University of Chicago bookstore just now. But in Powell's Books online, it's available for $77.xx — yowch. Back in 1964 many advanced math books were available for $5 or so. (The Internet tells me that $5 in 1964 dollars is $38 today.) --Dan
On Apr 26, 2015, at 11:55 AM, rcs@xmission.com wrote:
Is it worth doing a math book that makes sense for bright kids, and tries to explain everything? Or is it better to leave some mysteries?
P.S. What about this: < http://www.nytimes.com/2015/04/26/opinion/sunday/nicholas-kristof-are-you-sm... > ? --Dan
On Apr 26, 2015, at 6:23 PM, Dan Asimov <dasimov@earthlink.net> wrote:
I think it's even a good idea to leave some stuff that is tantalizingly abstruse and beyond the reach of younger / less educated folks. On the theory that one's reach should exceed their grasp. ... ...
On Apr 26, 2015, at 11:55 AM, rcs@xmission.com wrote:
Is it worth doing a math book that makes sense for bright kids, and tries to explain everything? Or is it better to leave some mysteries?
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