Abundant Michael - Math
http://abundantmichael.com/blog/index.cfm
Abundant Michael Blogen-usMon, 20 Jan 2020 05:41:05 -0500Mon, 11 Feb 2013 10:03:00 -0500BlogCFChttp://blogs.law.harvard.edu/tech/rssmichael@teratech.commichael@teratech.commichael@teratech.comnoRisk, Asteroid, micromorts and the zeitgeist
http://abundantmichael.com/blog/index.cfm/2013/2/11/Risk-Asteroid-micromorts-and-the-zeitgeist
<p>I think that most people don't understand risks and probability and can either over or under react to news stories about risk. The recent anouncement of a an <a href="http://thefuturediaries.com/2013/02/05/asteroid-risk-in-usa-explodes-real-estate-prices-in-new-zealand/">Asteroid Impact Risk in USA Causes New Zealand Real Estate Boom</a></p>
<p><br />
<em> Real Estate prices in parts of New Zealand are reaching atmospheric highs after authorities announced that the risk of Asteroid 1997 XF11 hitting Earth close to New York State on 28 October 2028. What if the risk was 1100:1? Would you seek shelter in another country?</em></p>
<p> </p>
<p>This wikipedia article on <a href="http://en.wikipedia.org/wiki/Micromort">micromorts</a> has a nice list of equally risky behavior and just breathing the pollution in a big city like NYC for 2 days is one micromort so living there for 120 days or 4 months is 60 micromorts just from the air. Let alone other risk factors such as traffic. The asteroid is currently rated at 1 in 1100 in 16 years time so that is approx 60 micromorts (1000000 / 1100 / 16).</p>
<p><br />
I think the other factor going on here is a cultural zeitgeist that knows that the US Empire is in serious decline and there is a likelihood of several dangers in the US. The government-industrial-media complex's Matrix of control is falling apart and people know (at least on the subconscious level) that they are at risk from high inflation, great depression 2.0, food shortages, rising crime, police state/martial law, reduction/elimination of privacy, rising sea levels covering coastal cities.</p>
2012MathMon, 11 Feb 2013 10:03:00 -0500http://abundantmichael.com/blog/index.cfm/2013/2/11/Risk-Asteroid-micromorts-and-the-zeitgeistWhen is a proof not a proof?
http://abundantmichael.com/blog/index.cfm/2012/8/25/When-is-a-proof-not-a-proof
<p> </p>
<p>(To the tune of "As time goes by" from Casablanca)</p>
<p>You must remember this</p>
<p>A proof is not a proof</p>
<p>A conjecture is not a conjecture</p>
<p>The fundamental things apply</p>
<p>As pure math goes by</p>
<p> </p>
<p>The late William Thurston helped bring about “<a href="http:// http://blogs.scientificamerican.com/cross-check/2012/08/24/how-william-thurston-rip-helped-bring-about-the-death-of-proof/">The Death of Proof</a>” (Scientific American Blog). You might say that there is a lot of math that can be proved, and maybe if if can't be proved, its not math!</p>
<p> </p>
<p><img hspace="10" vspace="10" align="left" src="http://www.abundantmichael.com/blog/images/slideshows//userfiles//WebsiteImages/ExperimentalMath.jpg" alt="Experimental Math Journal" />That is true and it depends what you mean by "proved". In Godel's theory most of math can not be formally proved in systems that do not contain contradictions themselves... so are those proofs valid? We act as though they are... And how is this different from physics where it is all conjecture based on experimental evidence and if a new set of experiments comes along that break the old theory we bring in new ones. There is a school of <a href="http://en.wikipedia.org/wiki/Experimental_mathematic">experimental math</a> that works a similar way using computer programs to both create experimental data and to do formal proofs of the conjectures. They even have a journal about experimental math now, so it is getting quiet popular.</p>
<p> </p>
<p>Prof Doron Zeilberger in his provocative essay says that <a href="http://www.math.rutgers.edu/~zeilberg/Opinion37.html">proving by computer programming gives more understanding than proving by hand</a></p>
<p> </p>
<p>Some of the experiments in math even become <a href="http://www.jasoncantarella.com/webpage/index.php?title=Art">art</a></p>
MathSat, 25 Aug 2012 12:56:00 -0500http://abundantmichael.com/blog/index.cfm/2012/8/25/When-is-a-proof-not-a-proofMath resources on the web
http://abundantmichael.com/blog/index.cfm/2012/6/4/Math-resources-on-the-web
<p>When I studied math there wasn't much about it on the internet. You had to go to a college for classes and to the library to read textbooks and papers. Now there are all kinds of math resources online. I think this lessens the need for universities and academic journals. When people can share and solve problems online, publish papers on their blog or arXiv and even put textbooks online then knowledge is liberated!</p>
<p> </p>
<p>Here are some math resources that I have found useful and interesting:</p>
<ul>
<li>Math articles and ebooks
<ul>
<li>wikipedia math <a href="http://en.wikipedia.org/wiki/Portal:Mathematics">portal</a> and <a href="http://en.wikipedia.org/wiki/List_of_mathematics_categories">categories</a></li>
<li>wikiversity math <a href="http://en.wikiversity.org/wiki/Portal:Mathematics">portal</a></li>
<li>Free <a href="http://www.openculture.com/free_textbooks">e-textbooks</a> (search for math in the long list of subjects)</li>
<li>79 online <a href="http://people.math.gatech.edu/~cain/textbooks/onlinebooks.html">math textbooks</a></li>
</ul>
</li>
<li>Shared problem solving and archive of solved problems
<ul>
<li><a href="http://mathoverflow.net/">Math Overflow</a> (for serious students and researchers) </li>
<li><a href="http://math.stackexchange.com/">math.stackexchange.com</a> (for everyone).</li>
<li>there are other stack exchanges for statistics, physics, Spanish and 80 more areas</li>
</ul>
</li>
<li>Math papers
<ul>
<li><a href="http://arxiv.org/archive/math">arXiv</a></li>
</ul>
</li>
<li>Math blogs and personal websites
<ul>
<li><a href="http://gowers.wordpress.com/">Tim Gowers</a> -</li>
<li><a href="http://terrytao.wordpress.com/">Terence Tao</a> - great discussion of topics, open problems and career advice</li>
<li><a href="http://www.dpmms.cam.ac.uk/~twk/">Tom Körner</a> - learning guides, lecture notes and more</li>
<li><a href="http://theoremoftheweek.wordpress.com/2013/01/11/analysis-i-lecture-0/">Vicky Neale</a> - who blogged for everyone of her lectures with background notes and problems</li>
<li><a href="http://vihart.com/">Vi Hart</a> - super fun math videos and math music</li>
</ul>
</li>
<li>Course materials
<ul>
<li><a href="http://www.maths.cam.ac.uk/undergrad/course/">Cambridge</a> - Pure math example sheets, lecture notes
<ul>
<li>(drill down into the <a href="https://www.dpmms.cam.ac.uk/people/">staff person pages</a> to see posted lecture notes)</li>
</ul>
</li>
<li><a href="http://ocw.mit.edu/courses/mathematics/">MIT</a> - math lecture notes and example sheets. Some are full OCW Scholar courses that are designed for independent learners who have few additional resources available to them. These courses include exam solution notes, online study groups, video and simulations.</li>
<li><a href="http://openlearn.open.ac.uk/course/category.php?id=8">Open University</a> - OpenLearn free course materials on pure, applied and statistics</li>
<li><a href="http://www.udacity.com/">Udacity</a> - free video lectures, online tests and learning community mainly related to applied, applicable and computer science topics.</li>
<li>Free math <a href="http://www.openculture.com/math_free_courses">video and audio courses</a></li>
<li>Indian professors' free<a href="http://nptel.iitm.ac.in/"> video lectures</a> along with Lecture Notes and references (Select "Mathematics" from the list of courses available).</li>
<li><a href="https://www.khanacademy.org/math">Kahn Academy</a> - online courses, videos and interactive problems/tests</li>
</ul>
</li>
<li>Books
<ul>
<li><a href="http://www.amazon.com/Princeton-Companion-Mathematics-Timothy-Gowers/dp/0691118809?tag=TeraTechIncA">Princeton Companion to Mathematics</a> - an encyclopedic overview of pure math and some theorical physics with chapters on proof, many areas of math and biographies of famous mathematicians.</li>
</ul>
</li>
</ul>
MathMon, 04 Jun 2012 20:19:00 -0500http://abundantmichael.com/blog/index.cfm/2012/6/4/Math-resources-on-the-web