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	<title>Comments for Mathing with Theo</title>
	<link>http://mathing.scroggles.com/wordpress-mu</link>
	<description>A blog about Math, with Applications and Without, Artificial Intelligence, Machine Learning, R, Python and more...</description>
	<pubDate>Sat, 22 Nov 2008 03:05:19 +0000</pubDate>
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		<title>Comment on Hedging your investments&#8230; explained by wildderrick</title>
		<link>http://mathing.scroggles.com/wordpress-mu/2008/11/12/hedging-your-investments-explained/#comment-259</link>
		<dc:creator>wildderrick</dc:creator>
		<pubDate>Thu, 13 Nov 2008 04:33:51 +0000</pubDate>
		<guid>http://mathing.scroggles.com/wordpress-mu/2008/11/12/hedging-your-investments-explained/#comment-259</guid>
		<description>Excellent post!  Why, I was just talking to someone about this today!  His explanation was very incomplete, however, this post TOTALLY makes up for it!  :)</description>
		<content:encoded><![CDATA[<p>Excellent post!  Why, I was just talking to someone about this today!  His explanation was very incomplete, however, this post TOTALLY makes up for it!  <img src='http://mathing.scroggles.com/wordpress-mu/wp-includes/images/smilies/icon_smile.gif' alt=':)' class='wp-smiley' /></p>
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		<title>Comment on Opportunity Cost by greentheo</title>
		<link>http://mathing.scroggles.com/wordpress-mu/2008/04/09/opportunity_cost/#comment-229</link>
		<dc:creator>greentheo</dc:creator>
		<pubDate>Mon, 22 Sep 2008 20:09:30 +0000</pubDate>
		<guid>http://mathing.scroggles.com/wordpress-mu/2008/04/09/opportunity_cost/#comment-229</guid>
		<description>Interesting... yeah decision theories and algorithms that help make decisions are always fun to play with.

What was the solution to the guy at the beach selling slushies?</description>
		<content:encoded><![CDATA[<p>Interesting&#8230; yeah decision theories and algorithms that help make decisions are always fun to play with.</p>
<p>What was the solution to the guy at the beach selling slushies?</p>
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		<title>Comment on Opportunity Cost by chaptor</title>
		<link>http://mathing.scroggles.com/wordpress-mu/2008/04/09/opportunity_cost/#comment-225</link>
		<dc:creator>chaptor</dc:creator>
		<pubDate>Thu, 18 Sep 2008 03:27:18 +0000</pubDate>
		<guid>http://mathing.scroggles.com/wordpress-mu/2008/04/09/opportunity_cost/#comment-225</guid>
		<description>One of the favorite topics I taught in my graduate Statistics classes was the night on Chi Square distributions and Opportunity loss situations. "Decision Making in the Presence of Uncertainty". You start out by saying... I do not know... now with that settled, you ask what do I know that I can use to define the probability that I will loose or gain money if I do "x".  One of my favorite scenarios was a guy who saw a weather forecast each Friday and used it to decide how many icees to take to the beach to sell.  Buy too many and you loose money on the tub of left over slush.  Buy too few and you loose the opportunity to sell more.  It was always a great evening for the students and the instructor!</description>
		<content:encoded><![CDATA[<p>One of the favorite topics I taught in my graduate Statistics classes was the night on Chi Square distributions and Opportunity loss situations. &#8220;Decision Making in the Presence of Uncertainty&#8221;. You start out by saying&#8230; I do not know&#8230; now with that settled, you ask what do I know that I can use to define the probability that I will loose or gain money if I do &#8220;x&#8221;.  One of my favorite scenarios was a guy who saw a weather forecast each Friday and used it to decide how many icees to take to the beach to sell.  Buy too many and you loose money on the tub of left over slush.  Buy too few and you loose the opportunity to sell more.  It was always a great evening for the students and the instructor!</p>
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		<title>Comment on Multi-Agent Algorithms by chaptor</title>
		<link>http://mathing.scroggles.com/wordpress-mu/2008/04/30/multi_agent_algorithms/#comment-224</link>
		<dc:creator>chaptor</dc:creator>
		<pubDate>Thu, 18 Sep 2008 02:45:34 +0000</pubDate>
		<guid>http://mathing.scroggles.com/wordpress-mu/2008/04/30/multi_agent_algorithms/#comment-224</guid>
		<description>Speaking of simply-complex systems... fractal generation is based on exactly this concept, as are the myriads of random-action toys (usually 2 or 3 interacting non-linear motions).  I coded a Mandelbrot set generator for a Commodore 64 in the way-back times.  There were 300 lines of basic code to initialize variables, peak and poke things into memory and reconfiguring to poke into video memory... then there was the algorithm code... one, very short line.  You just take a complex number c(1) = ( ix+y), then iterate: c(n+1) = c(n)^2+c(1), then repeat.  If it's distance from 0,0 gets bigger than 1 (or some other chosen boundary), it is not in the set.  If it doesn't it is in the set.  From that little formula you get all of the complexity of the Mandelbrot set!

Lorentz (I worked with his daughter at Quest!) said that the weather was fractal... well, he didn't have that word... he said that the system was infinatesimally complex with just a few variables... After trying to predict the weather with a building size "super computer" he said that if he had as big and fast a computer as he wanted, and had air temp, pressure, velocity, and humidity at the vertex of every cubic foot of the atmosphere, he could not predict the weather!!!  The tiniest change in any initial condition led to radically different output -- The butterfly effect indeed!!

Check it out:
http://www.math.utah.edu/~pa/math/mandelbrot/mandelbrot.html</description>
		<content:encoded><![CDATA[<p>Speaking of simply-complex systems&#8230; fractal generation is based on exactly this concept, as are the myriads of random-action toys (usually 2 or 3 interacting non-linear motions).  I coded a Mandelbrot set generator for a Commodore 64 in the way-back times.  There were 300 lines of basic code to initialize variables, peak and poke things into memory and reconfiguring to poke into video memory&#8230; then there was the algorithm code&#8230; one, very short line.  You just take a complex number c(1) = ( ix+y), then iterate: c(n+1) = c(n)^2+c(1), then repeat.  If it&#8217;s distance from 0,0 gets bigger than 1 (or some other chosen boundary), it is not in the set.  If it doesn&#8217;t it is in the set.  From that little formula you get all of the complexity of the Mandelbrot set!</p>
<p>Lorentz (I worked with his daughter at Quest!) said that the weather was fractal&#8230; well, he didn&#8217;t have that word&#8230; he said that the system was infinatesimally complex with just a few variables&#8230; After trying to predict the weather with a building size &#8220;super computer&#8221; he said that if he had as big and fast a computer as he wanted, and had air temp, pressure, velocity, and humidity at the vertex of every cubic foot of the atmosphere, he could not predict the weather!!!  The tiniest change in any initial condition led to radically different output &#8212; The butterfly effect indeed!!</p>
<p>Check it out:<br />
<a href="http://www.math.utah.edu/~pa/math/mandelbrot/mandelbrot.html" onclick="javascript:pageTracker._trackPageview('/outbound/comment/www.math.utah.edu');" rel="nofollow">http://www.math.utah.edu/~pa/math/mandelbrot/mandelbrot.html</a></p>
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		<title>Comment on Fun with heliostats by chaptor</title>
		<link>http://mathing.scroggles.com/wordpress-mu/2008/09/03/fun-with-heliostats/#comment-223</link>
		<dc:creator>chaptor</dc:creator>
		<pubDate>Thu, 18 Sep 2008 01:14:45 +0000</pubDate>
		<guid>http://mathing.scroggles.com/wordpress-mu/2008/09/03/fun-with-heliostats/#comment-223</guid>
		<description>Time for the Way-Back machine... Nate was maybe 4 or so ??87??
We lived in a 1200 ft2 home in Aurora, CO with an open basement.  The government declared a $7000 tax credit for solar improvements... by magic several companies came up with $7000 systems right then... go figure...

We got one.  They put 4 "drain down" units on the roof.  There was no water in them until the panels rose above a certain temp, which was every day even in Aurora CO even in the winter.  The units were about 4x8 black metal with a grid of copper tubing and a glass front and insulated back and sides.  The pumps cycled on automatically sending water from and back to a 300 gal closed system in a heavily insulated tank.  The heat built up as long as the water in the panels was hotter than the water in the tank, or if it was too hot in the tank.  

There were 2 sets of heat exchanger tubes inside the tank.  One set pre-heated water into the regular water heater.  most of the time the gas never came on.  There was a mixer that mixed in cold water as needed to keep the water in the household system at non-scalding levels.

The second set of exchanger tubes fed a "solar hearth" in the kitchen.  It had it's own thermostat and hot air distribution fan.  It could draw down the temp in the big tank until it reached a certain minimum, then automatically turned off.  We got heat in the kitchen even in the winter and usually all evening long.  

The team even installed an automatic set-back thermostat.  All in all a very cool and wonderfully effective system... then we moved... no more deals... no more $7000... oh well.  Nice while it lasted!</description>
		<content:encoded><![CDATA[<p>Time for the Way-Back machine&#8230; Nate was maybe 4 or so ??87??<br />
We lived in a 1200 ft2 home in Aurora, CO with an open basement.  The government declared a $7000 tax credit for solar improvements&#8230; by magic several companies came up with $7000 systems right then&#8230; go figure&#8230;</p>
<p>We got one.  They put 4 &#8220;drain down&#8221; units on the roof.  There was no water in them until the panels rose above a certain temp, which was every day even in Aurora CO even in the winter.  The units were about 4&#215;8 black metal with a grid of copper tubing and a glass front and insulated back and sides.  The pumps cycled on automatically sending water from and back to a 300 gal closed system in a heavily insulated tank.  The heat built up as long as the water in the panels was hotter than the water in the tank, or if it was too hot in the tank.  </p>
<p>There were 2 sets of heat exchanger tubes inside the tank.  One set pre-heated water into the regular water heater.  most of the time the gas never came on.  There was a mixer that mixed in cold water as needed to keep the water in the household system at non-scalding levels.</p>
<p>The second set of exchanger tubes fed a &#8220;solar hearth&#8221; in the kitchen.  It had it&#8217;s own thermostat and hot air distribution fan.  It could draw down the temp in the big tank until it reached a certain minimum, then automatically turned off.  We got heat in the kitchen even in the winter and usually all evening long.  </p>
<p>The team even installed an automatic set-back thermostat.  All in all a very cool and wonderfully effective system&#8230; then we moved&#8230; no more deals&#8230; no more $7000&#8230; oh well.  Nice while it lasted!</p>
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		<title>Comment on Fun with heliostats by wildderrick</title>
		<link>http://mathing.scroggles.com/wordpress-mu/2008/09/03/fun-with-heliostats/#comment-221</link>
		<dc:creator>wildderrick</dc:creator>
		<pubDate>Thu, 04 Sep 2008 20:35:11 +0000</pubDate>
		<guid>http://mathing.scroggles.com/wordpress-mu/2008/09/03/fun-with-heliostats/#comment-221</guid>
		<description>Those solar heaters are quite nice indeed, but there is quite a lot of capital to invest initially.  Granted, a couple of the systems on that website qualify for certain tax incentives that could make the system more economical (obviously more research will need to be done to determine the cost effectiveness of going with a system like this).  Furthermore, I don't very much like the idea of having to go shovel off the panels on my roof when it snows.  Thankfully, the snow doesn't stick around for very long in Colorado, so that may not be a serious issue.

In regards to heating your slab, do you have an idea of how you would install such a system?  I'd guess that you'd have to lay the piping on top of the slab and then install some sort of subfloor over that, but I don't think it would provide much heating to the slab.  Ideally, the system would be installed as an integral part of the slab when it is poured, but retrofitting a system like that could be very costly.

I think one of the primary factors in your efficiency will not be the amount of heat that you can direct onto the tank, but minimizing the heat loss through the pipe running from your house to the tank.  I see that the tank is currently located in the North East section of your back yard.  Picturing your yard in my head, I believe this is the ideal location to maximize sun exposure, however, it also places the tank at the farthest location from your house.  Unfortunately, this will require more pipe and more insulation ($$$) and will reduce the efficiency of the overall system.  

I don't mean to be a total kill joy!  I DO think this system will make a difference, I'm just blithering my thoughts about how to optimize the system.  During the winter, for instance, it may be optimal to swap the location of the tank and mirrors to account for the lower arc of the sun, so that may be something to consider as well for the final design.  Either way, I think your roof will be the optimal location.  I'll help you get it up there the next time I come over :)</description>
		<content:encoded><![CDATA[<p>Those solar heaters are quite nice indeed, but there is quite a lot of capital to invest initially.  Granted, a couple of the systems on that website qualify for certain tax incentives that could make the system more economical (obviously more research will need to be done to determine the cost effectiveness of going with a system like this).  Furthermore, I don&#8217;t very much like the idea of having to go shovel off the panels on my roof when it snows.  Thankfully, the snow doesn&#8217;t stick around for very long in Colorado, so that may not be a serious issue.</p>
<p>In regards to heating your slab, do you have an idea of how you would install such a system?  I&#8217;d guess that you&#8217;d have to lay the piping on top of the slab and then install some sort of subfloor over that, but I don&#8217;t think it would provide much heating to the slab.  Ideally, the system would be installed as an integral part of the slab when it is poured, but retrofitting a system like that could be very costly.</p>
<p>I think one of the primary factors in your efficiency will not be the amount of heat that you can direct onto the tank, but minimizing the heat loss through the pipe running from your house to the tank.  I see that the tank is currently located in the North East section of your back yard.  Picturing your yard in my head, I believe this is the ideal location to maximize sun exposure, however, it also places the tank at the farthest location from your house.  Unfortunately, this will require more pipe and more insulation ($$$) and will reduce the efficiency of the overall system.  </p>
<p>I don&#8217;t mean to be a total kill joy!  I DO think this system will make a difference, I&#8217;m just blithering my thoughts about how to optimize the system.  During the winter, for instance, it may be optimal to swap the location of the tank and mirrors to account for the lower arc of the sun, so that may be something to consider as well for the final design.  Either way, I think your roof will be the optimal location.  I&#8217;ll help you get it up there the next time I come over <img src='http://mathing.scroggles.com/wordpress-mu/wp-includes/images/smilies/icon_smile.gif' alt=':)' class='wp-smiley' /></p>
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		<title>Comment on Fun with heliostats by greentheo &#187; Blog Archive &#187; Fun with heliostats</title>
		<link>http://mathing.scroggles.com/wordpress-mu/2008/09/03/fun-with-heliostats/#comment-220</link>
		<dc:creator>greentheo &#187; Blog Archive &#187; Fun with heliostats</dc:creator>
		<pubDate>Thu, 04 Sep 2008 18:56:20 +0000</pubDate>
		<guid>http://mathing.scroggles.com/wordpress-mu/2008/09/03/fun-with-heliostats/#comment-220</guid>
		<description>[...] wrote this post over on my mathing.scroggles.com blog.  You might find this interesting if you&#8217;ve been [...]</description>
		<content:encoded><![CDATA[<p>[&#8230;] wrote this post over on my mathing.scroggles.com blog.  You might find this interesting if you&#8217;ve been [&#8230;]</p>
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		<title>Comment on Fun with heliostats by greentheo</title>
		<link>http://mathing.scroggles.com/wordpress-mu/2008/09/03/fun-with-heliostats/#comment-219</link>
		<dc:creator>greentheo</dc:creator>
		<pubDate>Thu, 04 Sep 2008 18:54:03 +0000</pubDate>
		<guid>http://mathing.scroggles.com/wordpress-mu/2008/09/03/fun-with-heliostats/#comment-219</guid>
		<description>Thanks Derrick!  I like the green thing... but even more.. I like a challenge.  Building a non-conventional solar water heater like this is more fun than anything.

However practically speaking there are two points you bring up:

1.) aesthetics and 

2.) practical usage

For 1.) instead of a raggedy old rusted water heater you could use something like this: http://www.solar-components.com/actvdhw.htm ... these flat panel heaters are both economical and look really nice.

Eventually I plan to add two of these to the round tank and add a horde of mirrors around those as well.  The bonus is you can take those flat panels and stick em up on your roof. 

in Regards to 2.) For any water heating system to be practical it needs to have a few things.

1.) a storage tank that is well insulated.
2.) Heat exchangers that take incomeing hot water and store it in the tank... with the exchangers switched off at night to minimize convective heat loss.
3.) If used for hot water for showers etc. a secondary heating unit will need to be in place for the reasons you mention... no solar heat in the morning.  Though if your hot water storage tank is large enough even this may possibly be omitted.

I plan to use this heater not for the heating of hot water for showers etc. but rather for a radiant heat system in the house.  Ideally it will go in our bottom floor and heat up the slab starting in late summer.  As we go into winter the slab will act as a nice thermal flywheel and ideally lose all of its heat by the end of spring.  Ideally it will be a nice smooth cycle.

As for real calculations?  Simple.

&lt;a&gt;solar BTU per meter square per year:&lt;/a&gt; 484.5 million BTU
heat required to raise 1 gallon of water 1 degree farenheit: 10

In an ideal system which exhanges all the heat in say 300 gallons of water incoming at 60 F we might expect to heat up the water to 484.5 m (BTU)/ 365 days /10 (BTU/gallon/degree / 300 (gallons) + 60 (DF) = 502 (DF).

Because the system may not operate at anything more than about 20% efficiency it's safe to assume that out of a 1 sq. meter system like mine we'd probably acheive a maximum of about 100-120 DF water.  

I have currently about 2 sq. meter of light on the water heater so I might be able to acheive 150-200 DF.

Anyhow, we shall see what I acheive.</description>
		<content:encoded><![CDATA[<p>Thanks Derrick!  I like the green thing&#8230; but even more.. I like a challenge.  Building a non-conventional solar water heater like this is more fun than anything.</p>
<p>However practically speaking there are two points you bring up:</p>
<p>1.) aesthetics and </p>
<p>2.) practical usage</p>
<p>For 1.) instead of a raggedy old rusted water heater you could use something like this: <a href="http://www.solar-components.com/actvdhw.htm" onclick="javascript:pageTracker._trackPageview('/outbound/comment/www.solar-components.com');" rel="nofollow">http://www.solar-components.com/actvdhw.htm</a> &#8230; these flat panel heaters are both economical and look really nice.</p>
<p>Eventually I plan to add two of these to the round tank and add a horde of mirrors around those as well.  The bonus is you can take those flat panels and stick em up on your roof. </p>
<p>in Regards to 2.) For any water heating system to be practical it needs to have a few things.</p>
<p>1.) a storage tank that is well insulated.<br />
2.) Heat exchangers that take incomeing hot water and store it in the tank&#8230; with the exchangers switched off at night to minimize convective heat loss.<br />
3.) If used for hot water for showers etc. a secondary heating unit will need to be in place for the reasons you mention&#8230; no solar heat in the morning.  Though if your hot water storage tank is large enough even this may possibly be omitted.</p>
<p>I plan to use this heater not for the heating of hot water for showers etc. but rather for a radiant heat system in the house.  Ideally it will go in our bottom floor and heat up the slab starting in late summer.  As we go into winter the slab will act as a nice thermal flywheel and ideally lose all of its heat by the end of spring.  Ideally it will be a nice smooth cycle.</p>
<p>As for real calculations?  Simple.</p>
<p><a>solar BTU per meter square per year:</a> 484.5 million BTU<br />
heat required to raise 1 gallon of water 1 degree farenheit: 10</p>
<p>In an ideal system which exhanges all the heat in say 300 gallons of water incoming at 60 F we might expect to heat up the water to 484.5 m (BTU)/ 365 days /10 (BTU/gallon/degree / 300 (gallons) + 60 (DF) = 502 (DF).</p>
<p>Because the system may not operate at anything more than about 20% efficiency it&#8217;s safe to assume that out of a 1 sq. meter system like mine we&#8217;d probably acheive a maximum of about 100-120 DF water.  </p>
<p>I have currently about 2 sq. meter of light on the water heater so I might be able to acheive 150-200 DF.</p>
<p>Anyhow, we shall see what I acheive.</p>
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		<title>Comment on Fun with heliostats by wildderrick</title>
		<link>http://mathing.scroggles.com/wordpress-mu/2008/09/03/fun-with-heliostats/#comment-218</link>
		<dc:creator>wildderrick</dc:creator>
		<pubDate>Thu, 04 Sep 2008 17:53:47 +0000</pubDate>
		<guid>http://mathing.scroggles.com/wordpress-mu/2008/09/03/fun-with-heliostats/#comment-218</guid>
		<description>Theo, I can't help but laugh out of amazement at your experiments.  You have a contagious enthusiasm about being green.  

I really like the idea of using a solar heater to pre-heat water for the house, but I'm curious about the practicality of solar water heating.  For Lesley and me, our primary need for hot water occurs daily at 6AM for our morning showers, which is prior to there being any amount of usable solar heating.  Is there enough insulation/heat capacity to store the heat overnight?  Our secondary need for hot water occurs 2-4 times per week in the evening for a much smaller amount of hot water to wash dishes, hands, and once a month or so - cloths.  

Have you performed any calculations to determine how much, on average (including weather phenomenon that will effect solar heating capability, i.e. clouds, ambient temperature, convective cooling) you will save by implementing the use of solar heating for your water system?

Also, do you have plans for a more permanent location for the solar heater?  I know Lesley would insist that it not be located on our lawn... in fact, unless I could somehow make it very aesthetically pleasing, I don't think I'd be allowed to put something like this ANYwhere around our house :)</description>
		<content:encoded><![CDATA[<p>Theo, I can&#8217;t help but laugh out of amazement at your experiments.  You have a contagious enthusiasm about being green.  </p>
<p>I really like the idea of using a solar heater to pre-heat water for the house, but I&#8217;m curious about the practicality of solar water heating.  For Lesley and me, our primary need for hot water occurs daily at 6AM for our morning showers, which is prior to there being any amount of usable solar heating.  Is there enough insulation/heat capacity to store the heat overnight?  Our secondary need for hot water occurs 2-4 times per week in the evening for a much smaller amount of hot water to wash dishes, hands, and once a month or so - cloths.  </p>
<p>Have you performed any calculations to determine how much, on average (including weather phenomenon that will effect solar heating capability, i.e. clouds, ambient temperature, convective cooling) you will save by implementing the use of solar heating for your water system?</p>
<p>Also, do you have plans for a more permanent location for the solar heater?  I know Lesley would insist that it not be located on our lawn&#8230; in fact, unless I could somehow make it very aesthetically pleasing, I don&#8217;t think I&#8217;d be allowed to put something like this ANYwhere around our house <img src='http://mathing.scroggles.com/wordpress-mu/wp-includes/images/smilies/icon_smile.gif' alt=':)' class='wp-smiley' /></p>
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		<title>Comment on Useful trigonometry by jason</title>
		<link>http://mathing.scroggles.com/wordpress-mu/2008/04/16/useful_trigonometry/#comment-187</link>
		<dc:creator>jason</dc:creator>
		<pubDate>Fri, 25 Apr 2008 17:15:43 +0000</pubDate>
		<guid>http://mathing.scroggles.com/wordpress-mu/2008/04/16/useful_trigonometry/#comment-187</guid>
		<description>good job!</description>
		<content:encoded><![CDATA[<p>good job!</p>
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