July 2013 - mathfun@mailman.xmission.com

Re: [math-fun] math-fun Digest, Vol 125, Issue 22
by Warren D Smith 20 Jul '13

20 Jul '13

a good solution to the geometry consistency problem is to use exact arithmetic. More precisely, you use ordinary lo-precision arithmetic except when it gets dicey, then you go for more precision... the net effect is, hi-precision calculations are rarely needed, so it is efficient. This is a pain, but it solves everything. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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Re: [math-fun] one crazy idea
by Henry Baker 19 Jul '13

19 Jul '13

I don't know about seek times, but one of the major problems with almost all storage systems is that the time to _process every byte_ continues to go up, because storage density is going up faster than transfer rates. Multiply the fastest transfer rate of your disk drive by its capacity. You'll be astounded at how long it can take to read the whole thing. If you have a large (64GByte) flash drive, calculate how long it will take to _write_ the whole thing. These times are lengthened by another order of magnitude if the data consists of small files (e.g., Unix/Linux). (Actual transfer times are usually considerably slower than advertised, due to the inability of OS's like Windows to do proper write caching for flash drives.) At 05:30 PM 7/17/2013, Bill Gosper wrote: >This reminds me of my dumb idea to reduce disk seek times with >multiple heads per surface. Surface is cheap.

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[math-fun] primes - {2} + {1}? Not.
by Bill Gosper 19 Jul '13

19 Jul '13

What the heck use is A006005, "The odd prime numbers together with 1"? Claim: the presence of 1 and the absence of 2 suggest these are actually "Numbers 2n+1 such that 0=Mod[Binomial[2n,n]-(-1)^n,2n+1]" See Concrete Math (G,K&P) Exercise 5.110 I.e., A065091 ∪ A163209 ∪ {1}, suggesting that A163209 should really be *1,5907*, *1194649*, 12327121, "Catalan pseudoprimes: (odd) nonprime integers n=2*m+1 satisfying A000108<http://oeis.org/A000108>(m) == (-1)^m * 2 (mod n). " A176997, " Odd numbers n such that (2^(n-1) mod n) = (4^(n-1) mod n) = (8^(n-1) mod n)= .. = (k^(n-1) mod n) for k=2, 4, 8, .., smallest power of 2>n" should be extended through 341 to avoid matching A006005. (Is this not equivalent to "Numbers n such that 1 = (2^(n-1) mod n) = (4^(n-1) mod n) = (8^(n-1) mod n)= .. = (k^(n-1) mod n) for k=2, 4, 8, .., smallest power of 2>n "?) Likewise, 0, 1, 2, 3, 5, 6, 8, 9, 11, 14, 15, 18, 20, 21, 23, 26, 29, 30, 33,... A102781 "Number of even numbers less than the n - th prime." is probably less useful than "Numbers n such that 0=Mod[Binomial[2n,n]-(-1)^n,2n+1]" which also include 2953, (1093^2 - 1)/2, and (3511^2 - 1)/2. --rwg

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[math-fun] solar power mirror farms & why not combo water/electricity systems?
by Warren D Smith 18 Jul '13

18 Jul '13

> From: Bill Gosper <billgosper(a)gmail.com> > To: math-fun(a)mailman.xmission.com > Subject: Re: [math-fun] one crazy idea > Message-ID: > <CAA-4O0FQFOA9+hNtR-+=pNNpnuk1F-9FP-UXeQXBZpEWzPE7zQ(a)mail.gmail.com> > Content-Type: text/plain; charset=ISO-8859-1 > > The 43 yr old, 2000m^2 solar furnace at Odeillo, France is still operating: > http://commons.wikimedia.org/wiki/File:Four_solaire_001.jpg > Thermodynamics limits its spot temperature to that of the solar "surface". > The installation is visitor-friendly and probably has personnel who > could enrich this thread. > > Re double duty solar collectors: Unless you're short of real estate, > trying to recover waste heat from a photovoltaic just imposes > engineering constraints that cost more than collecting heat separately. > Also, electrical energy is much more valuable per watt than heat. > > This reminds me of my dumb idea to reduce disk seek times with > multiple heads per surface. Surface is cheap. > --rwg --well, pretty much totally wrong. For use on house rooftops, surface is NOT cheap, and solar panels NOT cheap, and hot water is highly demanded (washing clothes, showers) not just electricity. So I do not see why no combined hot-water and electricity panels for housetops. Incidentally, one thing I learned during Hurricane Sandy -- power out all around here for 2 weeks -- but there were some houses with a ton of solar volt panels on roof, so they were fine, right? Wrong. Actually, essentially every such system REFUSES to generate power when your house stops getting power form the utility company. This is done to protect utility linemen. That means one of the major reasons to buy such a system -- self sufficiency -- is flushed down the toilet. About mirror farms like http://upload.wikimedia.org/wikipedia/commons/a/ac/Four_solaire_001.jpg http://en.wikipedia.org/wiki/Themis_(solar_power_plant) achieving "up to 3500C"; this is well short of solar surface temp, due to inefficiencies. This site (it says) gets 300 sun days/year and is at 1-2km altitude (wasn't precisely stated) and on sloping ground, all positive factors. The power plant generated a (tiny) 2 MW using molten salts heat bath at 450C. Ran for 3 years then closed due to high maintenance expense. The molten salts used were potassium & sodium nitrates mainly, which sounds like safety and corrosion nightmare. The largest in the world is http://en.wikipedia.org/wiki/Solar_Energy_Generating_Systems with 354 MW peak capacity, but annual generation is 662 GW-hours which I compute is on average 75 MW, i.e. averages 21% of that. Also can burn natural gas to generate power at night. 1600 acres of mirrors which is equivalent to a square 2.54 km on a side. The solar power incident on that area (normal to beam, above atmosphere) is 8780 MW, so the efficiency of the entire plant is 354/8780 = 4.0%. It uses tracking parabolic trough mirrors focusing on a black pipe with oil-fluid flow thru, heats to 400C. This site in in Mojave desert, flat, low cloud site (340 sunny days / year), at altitude about 620 meters. I would expect they'd have done a good deal better at higher altitude. About 3000 of their mirrors break per year (0.3%) and one time their oil tank exploded. The company running the place went bankrupt. A 30 MW sub-plant costs about $3 million/year maintenance, plus it cost $90M to build and lasts 20 years which is an additional $4.5M/year cost. The net effect is they produce electricity at 14 cents / kW-hour, which is above the US average price but not hugely above. If their black pipes had magic photovoltaic wrap layer generating electricity directly at 10% efficiency, that'd be maybe 30% extra juice for them... except if the pipe as a consequence got less-black, that'd cost them. Anyway they do not try to do that.

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[math-fun] one crazy idea
by Simon Plouffe 18 Jul '13

18 Jul '13

Hello, I was thinking at how we could procuce energy in a simple way, like having solar ovens with mirrors and such devices. This lead me to Archimedes and the way he used to 'toast' roman warships from the Syracuse citadel, apparently that idea was somewhat validated once, they found a way to toast a pile of plywood resembling a roman ship with plates of metals used at the time. Anyhow which lead me to think : what about today ?, suppose we would hypothetically having the same kind of threat but from space : an alien warship threatening to zap humans from existence. What about doing the same thing ? Billion of people using mirrors directly aimed at (more or less precisely) at this alien ship : what would happen ? More precisely, what would be the effect in energy having let's say 100 miilion mirrors aimed at one point in space toward one of those things, would it do the same thing ? Is this feasible, we would have one shot at it. This may sound naive, well is it ? Can someone calculate what output of energy this represent ? Best regards, Simon PLOUFFFE

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Re: [math-fun] [EXTERNAL] Re: one crazy idea
by Henry Baker 18 Jul '13

18 Jul '13

I don't have a definitive % for transmission losses, but I've attended a number of lectures which talk about these numbers. I believe I've seen figures from LLL/UCSB/DOE that are in the 40-50% range; when I discussed this with someone from PG&E, they didn't dispute the 50% number. I think that there are significant losses going through various transformers along the way. Also, I suspect that the highest voltages are used on the longest distance transmission lines, but these seem to require taller & much more expensive transmission towers, which may not be available to every mom-and-pop solar farm. I think that the whole 'sell-solar-power-back-to-the-utilities' scheme is a complete scam, roughly equivalent to the garbage 'recycling' scam. Here in Los Angeles, a TV crew once followed a 'recycling' garbage truck and found they dumped the contents in exactly the same place that the 'non-recycling' truck dumped its contents. Getting 'solar power' from your electric utility is a way for the politicians & voters to 'feel good' about solar power, but in reality, it is a way for the electric utilities to keep from going out of business: http://grist.org/climate-energy/solar-panels-could-destroy-u-s-utilities-ac… Energy, politics, and more Solar panels could destroy U.S. utilities, according to U.S. utilities By David Roberts Solar power and other distributed renewable energy technologies could lay waste to U.S. power utilities and burn the utility business model, which has remained virtually unchanged for a century, to the ground. That is not wild-eyed hippie talk. It is the assessment of the utilities themselves. Back in January, the Edison Electric Institute Â the (typically stodgy and backward-looking) trade group of U.S. investor-owned utilities Â released a report [PDF] that, as far as I can tell, went almost entirely without notice in the press. ThatÂs a shame. It is one of the most prescient and brutally frank things IÂve ever read about the power sector. It is a rare thing to hear an industry tell the tale of its own incipient obsolescence. http://www.eei.org/ourissues/finance/Documents/disruptivechallenges.pdf IÂve been thinking about how to convey to you, normal people with healthy social lives and no time to ponder the byzantine nature of the power industry, just what a big deal the coming changes are. They are nothing short of revolutionary Â but rather difficult to explain without jargon. So, just a bit of background. You probably know that electricity is provided by utilities. Some utilities both generate electricity at power plants and provide it to customers over power lines. They are Âregulated monopolies,Â which means they have sole responsibility for providing power in their service areas. Some utilities have gone through deregulation; in that case, power generation is split off into its own business, while the utilityÂs job is to purchase power on competitive markets and provide it to customers over the grid it manages. This complexity makes it difficult to generalize about utilities Â or to discuss them without putting people to sleep. But the main thing to know is that the utility business model relies on selling power. ThatÂs how they make their money. HereÂs how it works: A utility makes a case to a public utility commission (PUC), saying Âwe will need to satisfy this level of demand from consumers, which means weÂll need to generate (or purchase) this much power, which means weÂll need to charge these rates.Â If the PUC finds the case persuasive, it approves the rates and guarantees the utility a reasonable return on its investments in power and grid upkeep. Thrilling, I know. The thing to remember is that it is in a utilityÂs financial interest to generate (or buy) and deliver as much power as possible. The higher the demand, the higher the investments, the higher the utility shareholder profits. In short, all things being equal, utilities want to sell more power. (All things are occasionally not equal, but weÂll leave those complications aside for now.) Now, into this cozy business model enters cheap distributed solar PV, which eats away at it like acid. First, the power generated by solar panels on residential or commercial roofs is not utility-owned or utility-purchased. From the utilityÂs point of view, every kilowatt-hour of rooftop solar looks like a kilowatt-hour of reduced demand for the utilityÂs product. Not something any business enjoys. (This is the same reason utilities are instinctively hostile to energy efficiency and demand response programs, and why they must be compelled by regulations or subsidies to create them. Utilities donÂt like reduced demand!) ItÂs worse than that, though. Solar power peaks at midday, which means it is strongest close to the point of highest electricity use Â Âpeak load.Â Problem is, providing power to meet peak load is where utilities make a huge chunk of their money. Peak power is the most expensive power. So when solar panels provide peak power, they arenÂt just reducing demand, theyÂre reducing demand for the utilitiesÂ most valuable product. But wait. Renewables are limited by the fact they are intermittent, right? ÂThe sun doesnÂt always shine,Â etc. Customers will still have to rely on grid power for the most part. Right? This is a widely held article of faith, but EEI (of all places!) puts it to rest. (In this and all quotes that follow, ÂDERÂ means distributed energy resources, which for the most part means solar PV.) Due to the variable nature of renewable DER, there is a perception that customers will always need to remain on the grid. While we would expect customers to remain on the grid until a fully viable and economic distributed non-variable resource is available, one can imagine a day when battery storage technology or micro turbines could allow customers to be electric grid independent. To put this into perspective, who would have believed 10 years ago that traditional wire line telephone customers could economically Âcut the cord?Â [Emphasis mine.] Indeed! Just the other day, Duke Energy CEO Jim Rogers said, ÂIf the cost of solar panels keeps coming down, installation costs come down and if they combine solar with battery technology and a power management system, then we have someone just using [the grid] for backup.Â What happens if a whole bunch of customers start generating their own power and using the grid merely as backup? The EEI report warns of Âirreparable damages to revenues and growth prospectsÂ of utilities. Utility investors are accustomed to large, long-term, reliable investments with a 30-year cost recovery Â fossil fuel plants, basically. The cost of those investments, along with investments in grid maintenance and reliability, are spread by utilities across all ratepayers in a service area. What happens if a bunch of those ratepayers start reducing their demand or opting out of the grid entirely? Well, the same investments must now be spread over a smaller group of ratepayers. In other words: higher rates for those who havenÂt switched to solar. ThatÂs how it starts. These two paragraphs from the EEI report are a remarkable description of the path to obsolescence faced by the industry: The financial implications of these threats are fairly evident. Start with the increased cost of supporting a network capable of managing and integrating distributed generation sources. Next, under most rate structures, add the decline in revenues attributed to revenues lost from sales foregone. These forces lead to increased revenues required from remaining customers Â and sought through rate increases. The result of higher electricity prices and competitive threats will encourage a higher rate of DER additions, or will promote greater use of efficiency or demand-side solutions. Increased uncertainty and risk will not be welcomed by investors, who will seek a higher return on investment and force defensive-minded investors to reduce exposure to the sector. These competitive and financial risks would likely erode credit quality. The decline in credit quality will lead to a higher cost of capital, putting further pressure on customer rates. Ultimately, capital availability will be reduced, and this will affect future investment plans. The cycle of decline has been previously witnessed in technology-disrupted sectors (such as telecommunications) and other deregulated industries (airlines). Did you follow that? As ratepayers opt for solar panels (and other distributed energy resources like micro-turbines, batteries, smart appliances, etc.), it raises costs on other ratepayers and hurts the utilityÂs credit rating. As rates rise on other ratepayers, the attractiveness of solar increases, so more opt for it. Thus costs on remaining ratepayers are even further increased, the utilityÂs credit even further damaged. ItÂs a vicious, self-reinforcing cycle: EEI One implication of all this Â a poorly understood implication Â is that rooftop solar fucks up the utility model even at relatively low penetrations, because it goes straight at utilitiesÂ main profit centers. (ItÂs already happening in Germany.) Right now, distributed solar PV is a relatively tiny slice of U.S. electricity, less than 1 percent. For that reason, utility investors arenÂt paying much attention. ÂDespite the risks that a rapidly growing level of DER penetration and other disruptive challenges may impose,Â EEI writes, Âthey are not currently being discussed by the investment community and factored into the valuation calculus reflected in the capital markets.Â But that 1 percent is concentrated in a small handful of utility districts, so trouble, at least for that first set of utilities, is just over the horizon. Utility investors are sleepwalking into a maelstrom. (ÂDespite all the talk about investors assessing the future in their investment evaluations,Â the report notes dryly, Âit is often not until revenue declines are reported that investors realize that the viability of the business is in question.Â In other words, investors arenÂt that smart and rational financial markets are a myth.) Bloomberg Energy Finance forecasts 22 percent compound annual growth in all solar PV, which means that by 2020 distributed solar (which will account for about 15 percent of total PV) could reach up to 10 percent of load in certain areas. If that happens, well: Assuming a decline in load, and possibly customers served, of 10 percent due to DER with full subsidization of DER participants, the average impact on base electricity prices for non-DER participants will be a 20 percent or more increase in rates, and the ongoing rate of growth in electricity prices will double for non-DER participants (before accounting for the impact of the increased cost of serving distributed resources). So rates would rise by 20 percent for those without solar panels. Can you imagine the political shitstorm that would create? (There are reasons to think EEI is exaggerating this effect, but weÂll get into that in the next post.) If nothing is done to check these trends, the U.S. electric utility as we know it could be utterly upended. The report compares utilitiesÂ possible future to the experience of the airlines during deregulation or to the big monopoly phone companies when faced with upstart cellular technologies. In case the point wasnÂt made, the report also analogizes utilities to the U.S. Postal Service, Kodak, and RIM, the maker of Blackberry devices. These are not meant to be flattering comparisons. Remember, too, that these utilities are not Google or Facebook. They are not accustomed to a state of constant market turmoil and reinvention. This is a venerable old boys network, working very comfortably within a business model that has been around, virtually unchanged, for a century. A frigginÂ century, more or less without innovation, and now theyÂre supposed to scramble and be all hip and new-age? Unlikely. So whatÂs to be done? You wonÂt be surprised to hear that EEIÂs prescription is mainly focused on preserving utilities and their familiar business model. But is that the best thing for electricity consumers? Is that the best thing for the climate? WeÂll dig into those questions in my next post. At 09:26 AM 7/18/2013, Cordwell, William R wrote: >50% loss for that distance seems high. "Transmitting electricity at high voltage reduces the fraction of energy lost to resistance, which varies depending on the specific conductors, the current flowing (measured in kilo-Amperes (kA.)) and the length of the transmission line. For example, a 100 mile 765 kV line carrying 1000 MW of energy can have losses of 1.1% to 0.5%. A 345 kV line carrying the same load across the same distance has losses of 4.2%.[8]" [Wiki, but it does sound plausible] > >Other sources say that California gets some of its electricity from as far away as Alberta and Texas.

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Re: [math-fun] one crazy idea
by Henry Baker 18 Jul '13

18 Jul '13

Google Markus Kayser's 'solar sinter' machine and watch the video on YouTube/Vimeo. This is really cool (I mean hot!). At 07:22 AM 7/18/2013, Simon Plouffe wrote: > Every time there is a neat idea about energy, there is always something >that makes it that : it finaly does not work so well.

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Re: [math-fun] one crazy idea
by Henry Baker 18 Jul '13

18 Jul '13

As Tom Knight & others have already remarked, it is highly unlikely that this story is anything other than some screenwriter's fantasy. Nevertheless, I would think that a use for the Hubble would be something more connected with its different orbit, and possibly with the _generation_ of light -- e.g., using some sort of laser -- rather than the _consuming_ of light. If the fantasy were real, then someone would have also had to mess with the sensor, as well, which would have required a lot of work to make the existing sensor appear to still be there to the researchers on the ground. At 09:52 AM 7/17/2013, Whitfield Diffie wrote: >> After all, the company making the Hubble's lenses was >> the same company that had been making lenses for spy >> satellites since the beginning, and it's hard to see >> how they could have made such an 'error'. > > The story at the time was that they were not allowed to use test >equipment from the classified programs in bulding the Hubble mirror. > > I think the Earth is too bright for Hubble to look at so if they >were doing something secret, it is hard to imagine what it would have >been. > > My devious imagination fails at finding something who's coversion >is so great that the cheapest way to do is was to fly an otherwise >unneeded service mission to the Hubble. > > Whit

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Re: [math-fun] one crazy idea
by Henry Baker 18 Jul '13

18 Jul '13

While we're on the subject of speculation, I saw a TV program last night that suggested that the Hubble Space Telescope's original lens design _wasn't an error_, but a 'cover story' for some nefarious classified tests by the US DoD. After all, the company making the Hubble's lenses was the same company that had been making lenses for spy satellites since the beginning, and it's hard to see how they could have made such an 'error'. After these classified tests were done, the Hubble's new optics were installed (& other stuff removed??), and the Hubble went on to perform its (unclassified) mission. I'm not sure what those classified tests might have involved, but the 'error' in the Hubble's optics has been pretty well documented, so it might be possible to 'reverse engineer' what the original 'design' might have been used for. At 02:07 AM 7/17/2013, Simon Plouffe wrote: >Hello, > > I was thinking at how we could procuce energy in a simple >way, like having solar ovens with mirrors and such devices. >This lead me to Archimedes and the way he used to 'toast' >roman warships from the Syracuse citadel, apparently that >idea was somewhat validated once, they found a way to >toast a pile of plywood resembling a roman ship with plates >of metals used at the time.

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Re: [math-fun] one crazy idea
by Bill Gosper 18 Jul '13

18 Jul '13

The 43 yr old, 2000m^2 solar furnace at Odeillo, France is still operating: http://commons.wikimedia.org/wiki/File:Four_solaire_001.jpg Thermodynamics limits its spot temperature to that of the solar "surface". The installation is visitor-friendly and probably has personnel who could enrich this thread. Re double duty solar collectors: Unless you're short of real estate, trying to recover waste heat from a photovoltaic just imposes engineering constraints that cost more than collecting heat separately. Also, electrical energy is much more valuable per watt than heat. This reminds me of my dumb idea to reduce disk seek times with multiple heads per surface. Surface is cheap. --rwg CG>You may find this interesting (and tangentially related in terms of energy output): http://what-if.xkcd.com/13/ Charles Greathouse Analyst/Programmer Case Western Reserve University On Wed, Jul 17, 2013 at 5:07 AM, Simon Plouffe <simon.plouffe(a)gmail.com>wrote: Hello, I was thinking at how we could pro[d]uce energy in a simple way, like having solar ovens with mirrors and such devices. This lead me to Archimedes and the way he used to 'toast' roman warships from the Syracuse citadel, apparently that idea was somewhat validated once, they found a way to toast a pile of plywood resembling a roman ship with plates of metals used at the time. Anyhow which lead me to think : what about today ?, suppose we would hypothetically having the same kind of threat but from space : an alien warship threatening to zap humans from existence. What about doing the same thing ? Billion of people using mirrors directly aimed at (more or less precisely) at this alien ship : what would happen ? More precisely, what would be the effect in energy having let's say 100 miilion mirrors aimed at one point in space toward one of those things, would it do the same thing ? Is this feasible, we would have one shot at it. This may sound naive, well is it ? Can someone calculate what output of energy this represent ? Best regards, Simon PLOUFF[]E

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