tag:blogger.com,1999:blog-37287148823768250562024-02-07T13:52:20.392+10:00My Brain HertzFangor42http://www.blogger.com/profile/15614019534106339132noreply@blogger.comBlogger13125tag:blogger.com,1999:blog-3728714882376825056.post-42111817293379533132014-05-09T18:28:00.000+10:002014-05-09T18:28:49.409+10:00I ... love mathsFor those who say maths only simulates what the universe is.<br />
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Euler’s identity<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkckZBBGcqdDcL-oKIDBquUSTdQ9mzg8E3Q4i1EEJV_H1humVopfuzn9iNsbIeCNgAn4LEwKYQWjFsC_uRYuUkYKOJv6zMQN75UeVd3f5qZEYJWCRxQ_7bMfs33_NDYIgBH7DmMzw5pgJO/s1600/image001.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkckZBBGcqdDcL-oKIDBquUSTdQ9mzg8E3Q4i1EEJV_H1humVopfuzn9iNsbIeCNgAn4LEwKYQWjFsC_uRYuUkYKOJv6zMQN75UeVd3f5qZEYJWCRxQ_7bMfs33_NDYIgBH7DmMzw5pgJO/s1600/image001.png" height="118" width="400" /></a><br />
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An arbitrary and abstract equality but simple, balanced - almost poetic.<br />
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For me it says maths isn’t a self-fulfilling abstraction of the real world but has its own validity.<br />
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Three basic mathematical operations: addition, multiplication and exponentiation<br />
Two transcendental/irrational numbers: pi and e<br />
THE natural number and multiplicative identity: 1<br />
The additive identity: 0<br />
And the imaginary number: i (or j)<br />
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pi derived from the trigonometric proportions of circles<br />
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e derived from exponential growth (compound interest) =<br />
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1 + 1/1 + 1/(1*2) + 1/(1*2*3) …<br />
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Aaah – the life of the mind.Fangor42http://www.blogger.com/profile/15614019534106339132noreply@blogger.com0tag:blogger.com,1999:blog-3728714882376825056.post-2242824870933933562013-05-09T22:12:00.002+10:002013-05-09T23:16:34.376+10:00Beaudesert Balloon<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMXIujcZryFHV5Ot-hO-AnxXTYdHFlw5RAeVFhjUBFIi7MaDTMLYxmYtFuGGv6azi5R2fG6KOEXEKrkvtoVmUEZr0OcZ3MNUZ2O52kqzAS6sQjoTBdeeRJFzZDRqQDRkyWX-rSFoT1lX0b/s1600/20130509_062803.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMXIujcZryFHV5Ot-hO-AnxXTYdHFlw5RAeVFhjUBFIi7MaDTMLYxmYtFuGGv6azi5R2fG6KOEXEKrkvtoVmUEZr0OcZ3MNUZ2O52kqzAS6sQjoTBdeeRJFzZDRqQDRkyWX-rSFoT1lX0b/s320/20130509_062803.jpg" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYpSz8t8EMWlCjKY0sgpESoOGGrTD5udt3z4MZydRvxRzG6ujBYDXnhbmi3igBeXoD1o6cGRW3s-0vnq72QCUD7Z0Hr41yVTZ6xRfeWtQISuef2HhV6OebdbmojH8hZj9w45uzxmc8v0PR/s1600/20130509_061054.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYpSz8t8EMWlCjKY0sgpESoOGGrTD5udt3z4MZydRvxRzG6ujBYDXnhbmi3igBeXoD1o6cGRW3s-0vnq72QCUD7Z0Hr41yVTZ6xRfeWtQISuef2HhV6OebdbmojH8hZj9w45uzxmc8v0PR/s320/20130509_061054.jpg" width="320" /></a></div>
<br />Fangor42http://www.blogger.com/profile/15614019534106339132noreply@blogger.com0tag:blogger.com,1999:blog-3728714882376825056.post-35595878438558022412013-02-14T22:45:00.000+10:002013-02-14T22:45:46.159+10:00Globe trotting<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhY9tTGKI96vduSqE3L5mGABA8LndL25kktOtEwg_2RhqDlBICPBYSH6qQsyU7yzODXRPE_49aY3ipygc5KWCXsiu7-Ix6RFBG4jLIYC_1XrH1pMl66uWAaHNJG5kNfmXA_EbETEPSEBUdL/s1600/20121025_161006.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhY9tTGKI96vduSqE3L5mGABA8LndL25kktOtEwg_2RhqDlBICPBYSH6qQsyU7yzODXRPE_49aY3ipygc5KWCXsiu7-Ix6RFBG4jLIYC_1XrH1pMl66uWAaHNJG5kNfmXA_EbETEPSEBUdL/s320/20121025_161006.jpg" width="320" /></a></div>
<br />The stage of the Globe Theatre with our guide soliloquising in the foreground. The theatre was constructed as close a replica of the original as possible given the lack of historical data. For instance we have no idea if the decoration of the stage is even close...<br /><br />But that's not news...<br />Fangor42http://www.blogger.com/profile/15614019534106339132noreply@blogger.com0tag:blogger.com,1999:blog-3728714882376825056.post-35253395426871458962013-02-13T21:36:00.000+10:002013-02-13T21:36:29.772+10:00Still here...<div class="separator" style="clear: both; text-align: left;">
Not much too say.</div>
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This very cool Citroen H van was part of the international food fair on London's Southbank the night we skated at Somerset House.</div>
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But wait, there will be more.Fangor42http://www.blogger.com/profile/15614019534106339132noreply@blogger.com0tag:blogger.com,1999:blog-3728714882376825056.post-8139253489474481412013-02-12T21:45:00.003+10:002013-02-12T21:45:46.214+10:00Keeping it aliveJust a quick post to keep my blog alive.<br />
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Below is part of Tower Bridge bascule system; steam engines that raise weights that in turn pressurise the hydraulics to raise the two spans. Awesome logic - the spans are not raised often so this buffered system's delay is inconsequential and can use smaller engines...<br />
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Otherwise watch this space...Fangor42http://www.blogger.com/profile/15614019534106339132noreply@blogger.com0tag:blogger.com,1999:blog-3728714882376825056.post-64094388510768771392007-04-11T09:22:00.001+10:002007-04-13T14:09:26.932+10:00A Fractal Fairy TaleOnce upon a time, there was a giant who was fond of strolling the shore of his island each morning as the sun rose. One morning as he strolled he wondered how long his stroll was and asked his fairy godmother how far it was around his island. His fairy godmother gave him a magic, kilometer-long measuring stick and told him to measure it himself.<br /><br />When he had done this, he went back to his fairy godmother and she gave him a magic, meter-long stick, and told him to measure it again. When he had done this, he was given a magic, millimeter-long stick and told to measure one last time.<br /><br />Because the sticks were magic, they were ultimately precise and his measurements ultimately accurate; no errors or tolerances to worry about. However the giant found he recorded a longer distance as the sticks got shorter.<br /><br />Being of a philosophical bent, the giant sat on a large boulder and thought about why. The creatures of the giant's island went about their lifes, tides waxed and waned, the sun sped its daily course across the heavens, seasons came and went, tectonic plates drifted about the planet like the skin on hot milk and the giant's ponderous ponderings finally came to a conclusion.<br /><br />He decided that each stick, although magic, did not measure the distance absolutely, rather they averaged out the "wiggliness"of his island's coastline at its (the stick's) particular scale. So the giant's first stick ignored any coastal feature less the a kilometer in dimension and similarly for the other two measurements at their dimension.<br /><br />The giant decided if he wanted to absolutely know how far he walked he would have to ask his fairy godmother to make his coastline conform to a formula from which the distance could be calculated. He also thought that it would be interesting for his island to have a coastline that was so "wiggly" that it would occupy all space but still have its present finite area.<br /><br />However, deciding he liked his island just as it was, he returned the measuring sticks to his fairy godmother, thanked her for an excellent think, and wandered off down the tideline as the fairy godmother followed his meanderings with a gentle smile.Fangor42http://www.blogger.com/profile/15614019534106339132noreply@blogger.com0tag:blogger.com,1999:blog-3728714882376825056.post-84631885748917048602007-04-02T09:51:00.000+10:002007-04-02T11:17:07.206+10:00Wobbly GenesSay you have a population of frogs in a pond. The number of adult frogs is governed by available froggy food, froggy predators, froggy diseases etc and also governs the size of the new generation of frogs. And these same constraints decide the number of adult frogs in the next generation at reproduction time. So you have a recursive system; the outcome of the previous generation sets the starting condition of the next. I hope you can see that such a system if you track its progress through a host of recursions is sensitive to the condition of the previous incarnation; its initial conditions.<br /><br />This is the basic concept behind Chaos Theory ie does the flap of a butterfly’s wings in Brazil set off a tornado in Texas or <i>sensitive dependence on initial conditions</i>.<br /><br />One of the implications of Chaos Theory is that the systems exhibiting this dependency are sensitive to impulses but after a period of instability as a result of such impulses they standardly find a new point of stability. Like a spinning top on a dimpled surface; a jog will move it from its orginal dimple and make it wobble but with enough spin it will eventually settle in a new dimple.<br /><br />There are biology theorists that are using this characteristic to look at evolution afresh. They suggest that it is valid to look at genetics as one of these systems. A jog from a population’s environment will cause genes to move from a stable morphology, have a wobble-experiment with a bunch of different forms and finally settle to a new solution for survival (with the inference that the jog influences the system towards a successful but still unpredictable result). These theorists explain the potential biological forms available from a genetic set as a convoluted surface of stable dips and valleys (not necessarily three dimensions though ~evil grin~).<br /><br />Apparently this concept does explain some of the more difficult problems with previous theories of evolution with regard to the mechanism of mutation and species differentiation.<br /><br />Maybe there was or will be just such a jog to make humanity to think and act globally...no, not globalisation. <b>>:{(}</b>Fangor42http://www.blogger.com/profile/15614019534106339132noreply@blogger.com0tag:blogger.com,1999:blog-3728714882376825056.post-78204120653871069452007-03-29T07:46:00.000+10:002007-03-29T08:21:27.007+10:00I'm Walking Backwards for ChristmasIf you lie beneath an obelisk and look up to see drifting clouds, the obelisk appears to be moving. This is just one of the side effects of our brain's solution to creating the universe in our heads without having to jam in a representation of each and every particle of the actual cosmos.<br /><br />Anyhoo...Steven Hawking proposed that our universe is just one of a sequence of universes that are created in a Big Bang, expand to a limit, contract to a singularity, which triggers the next Big Bang and universe and so on and so forth. (Like a string of saugages - Hawking's analogy not mine) He also proposed that while the universe is expanding; entropy increases. That is the energy and particles in the universe tend to become more amorphous or randomly and evenly distributed.<br /><br />So our perception of an expanding universe is dependent on our perception of entropy increasing. But what if, like the flying obelisk, it is only a perception and we got it wrong and entropy is decreasing and the universe is contracting. With no external framework to reference how do we know either way.<br /><br />Spike...where are you, Spike? ~sings~ I'm walking backwards for Christmas.Fangor42http://www.blogger.com/profile/15614019534106339132noreply@blogger.com1tag:blogger.com,1999:blog-3728714882376825056.post-43989282591772170402007-03-15T08:12:00.000+10:002007-03-15T08:57:12.004+10:00Freedom's Just Another WordI think I have a border-line mathematical axiom...if something has a bunch of characteristics each of which can vary, and you can show that one of those characteristics is limited in how much it can vary; does that mean the something does not have an infinite capacity to vary?<br /><br />Or is it necessary to show, and this seems a much harder thing to do, the something's number of varying characteristics is also limited? (Is there something vaguely Suess about all this?)<br /><br />So my leap in my previous blog is a little extreme and we are back to life is all a flip of a coin...depression avoided....well, unless you are obsessive/compulsive...Fangor42http://www.blogger.com/profile/15614019534106339132noreply@blogger.com0tag:blogger.com,1999:blog-3728714882376825056.post-63970007429522085992007-03-14T14:33:00.000+10:002007-03-14T14:51:35.511+10:00Settle your Hash<p>So if something is making noise, the noise is saying something about the something. But if the something never repeats itself then you have to listen to all the noise forever to know the something properly.<br /><br />But the noise has limits; it cannot be louder than the something can make it for example. Is it true to say that the noise is predictable because it cannot be random without limit? (I can sense a cosmos full of mathematicians screaming for a stoning for that little generalisation/transgression.)</p><p>Which means that something/anything/everything must be predictable and chance is a myth.</p><p>Therefore fate is actual...wonder how many depressions that will spawn? </p><p> </p>Fangor42http://www.blogger.com/profile/15614019534106339132noreply@blogger.com1tag:blogger.com,1999:blog-3728714882376825056.post-47080256070478009272007-02-19T09:20:00.000+10:002007-02-19T09:30:52.053+10:00Whether you're paranoid or arrogant...Did you realise that you have your back to half the Universe?<br /><br />If you subscribe to the theory that the Universe is a closed loop then you have your back to all of the Universe or none of it ...or both.<br /><br />Whether the Universe is against you or you're against the Universe; this certainly reinforces the egocentric/homocentric world view.Fangor42http://www.blogger.com/profile/15614019534106339132noreply@blogger.com1tag:blogger.com,1999:blog-3728714882376825056.post-26634751470618957602007-02-16T14:59:00.000+10:002007-02-16T15:16:16.556+10:00Trivial deep thoughts<span style="color: rgb(255, 255, 255);font-size:100%;" ><span style="color: rgb(0, 0, 0);font-family:courier new;" ></span></span>When a tree falls in the forest, does its mother come to kiss the boo-boo?<br /><br />Why did the chicken cross the road?<br />DNA? Upbringing? Or was it hatched from a cross-the-road egg?<br /><br />A Pontius decision is letting someone decide for you and take on the risk.<br /><br />Teutonic plates is the crockery that earth-shattering german gods eat from.<br /><br />Given that great minds think alike and fools seldom differ, these are all my own work...sad eh?<br /><span style="font-size:100%;"><br /></span>Fangor42http://www.blogger.com/profile/15614019534106339132noreply@blogger.com0tag:blogger.com,1999:blog-3728714882376825056.post-16643924923718923312007-02-15T13:50:00.000+10:002007-03-14T15:34:06.441+10:00A Hidden Agenda...I have to admit I have what amounts to an obession to conspiracy theories...I would love to believe that there are secret societies that manipulate mankind to their own ends. It is sad and nieve and borders on mysticism but a good conspiracy does brace one's skepticism.<br /><br />I have read Robert Anton William and Robert Shea’s Illuminatus! trilogy, Umberto Eco’s Foucault Pendulum, Holy Blood and Holy Grail, and the Templar Revelation and now see whereof the CIA plagarised its mission statement.<br /><br />I guess part of this obession is that history is an appalling litany of bullies and robber barons and pretending these violators were the poor pawns of some masters of subtlety and secrecy redeems it from bad farce to decent drama.<br /><br />Then again if historians had recorded the churn of culture and science instead politics and conflict I could be sitting here with nothing to occupy me.<br /><br />Anyway back to looking for the fnords...Fangor42http://www.blogger.com/profile/15614019534106339132noreply@blogger.com1