Gorgonzola's New Writeupshttp://everything2.com/?node=New%20Writeups%20Atom%20Feed&foruser=Gorgonzola2013-06-10T19:55:46ZE2 Bugs (poetry)http://everything2.com/user/Gorgonzola/writeups/E2+BugsGorgonzolahttp://everything2.com/user/Gorgonzola2013-06-10T19:55:46Z2013-06-10T19:55:46Z<p>The Gold star notification message is truncated, or at least needs some tweaking.</p>
<p><a href="/title/Cool+Man+Eddie">Cool Man Eddie</a> <i>says</i> Sweet! <a href="/title/Klaproth">Klaproth</a> just awarded you a <a href="/title/Gold+Star">Gold Star</a>, because <i>superduperbeautifulnode</i></p>
<p>That's all. Not even a link to the superduperbeautifulnode in question. Also, the link to Gold Star is broken and the italic tags around the node title (but not around the word "<i>says</i>"!!?!) render as <i></i> in Message Inbox (but not Chatterlight??!?) <small>(but that might just be my screwy style defacer stuff)</small></p>
Fermat's little theorem (idea)http://everything2.com/user/Gorgonzola/writeups/Fermat%2527s+little+theoremGorgonzolahttp://everything2.com/user/Gorgonzola2013-05-03T20:31:06Z2013-05-03T20:31:06Z<p><a href="/title/Pierre+de+Fermat">Pierre de Fermat</a> has a unique reputation in mathematics. The letters and <a href="/title/marginalia">marginalia</a> of this king of mathematical <a href="/title/dilettante">dilettante</a>s has provided mathematicians with powerful tools, but also <a href="/title/Fermat%2527s+last+theorem">riddle</a>s that took centuries to solve and also outright <a href="/title/Fermat+number">wrong results</a>. And he's remembered 400 years later.</p>
<p>Modern mathematicians like to render Fermat's theorem as</p>
<dl>
<dt></dt>
<dd><tt>a<sup>p</sup> ≡ a (mod p)</tt></dd>
</dl>
<p>but this isn't what he actually propounded back in 1640 in a letter to a colleague, and it obscures the real power of this concept.</p>
<p>What he actually said was that for any number <tt>a</tt> and any <a href="/title/prime+number">prime</a> <tt>p</tt>, there is some <em>minimum</em> exponent <tt>d</tt> such that <tt>p</tt> divides <tt>a<sup>d</sup>-1</tt> without a remainder, and that <tt>d</tt> divides <tt>p-1</tt>. In modern terms of <a href="/title/congruence">congruence</a>, we can render this as</p>
<dl>
<dt></dt>
<dd><tt>a<sup>d</sup>≡1 (mod p)</tt> and</dd></dl>…Convergence (idea)http://everything2.com/user/Gorgonzola/writeups/ConvergenceGorgonzolahttp://everything2.com/user/Gorgonzola2013-01-15T05:03:43Z2013-01-15T05:03:43Z<p><small><i>Fifteen years and they noded some obsolete tech buzzword but NOBODY NODED THIS! OK, well, until someone spends several days addressing this subject thoroughly, this will just have to do.</i></small></p>
<p>Convergence is a concept at the heart of mathematical <a href="/title/analysis">analysis</a>. It's probably the <em>single most important</em> concept. It's the only way you can pin down the value of <em>almost all</em> <a href="/title/real+number">real number</a>s; indeed, it's the only context under which an "actual" value exists for most of them.</p>
<p><a href="/title/Let%2527s+play+a+little+game">Let's play a little game</a>. We're going to chop up the number 2 and accumulate some of the pieces.</p>
<p>Start with <tt>A=0</tt> and <tt>R=2</tt>.
<p>For each integer <tt>N</tt>, we're going to calculate the value of <tt>F(N)=2*A*2<sup>-N</sup>+2<sup>-2N</sup></tt>, and we'll make a note of whether or not it's greater than <tt>R</tt>. If it's too big, we'll just skip it. If it's not too big, we'll subtract <tt>F(N)</tt> from <tt>R</tt> and add <tt>2<sup>-N</sup> to <tt>A</tt>.</tt></p>…Axiom of Continuum (idea)http://everything2.com/user/Gorgonzola/writeups/Axiom+of+ContinuumGorgonzolahttp://everything2.com/user/Gorgonzola2013-01-13T20:06:49Z2013-01-13T20:06:49Z<p>Before you get yourself too exercised here, be aware that there are two vastly different mathematical concepts that could take this moniker when given the status of a <a href="/title/axiom">basic assumption</a> of a <a href="/title/model">logical system</a>.</p>
<p>In the late 1800's, <a href="/title/Georg+Cantor">Cantor</a>'s theory of <a href="/title/transfinite">transfinite</a> <a href="/title/set">set</a>s ignited fierce controversy. The mathematicians supporting him tended to be younger and more flexible thinking, and those opposed tended towards being of the old guard. As a result, Cantor found it impossible to get a job more prestigious than a low-paying lecturer at the <a href="/title/Univerity+of+Halle">Univerity of Halle</a>. This frustrated Cantor to no end, and he became obsessed with proving one concept that he thought would vindicate his ideas, that the (infinite) <a href="/title/cardinality">cardinality</a> of the <a href="/title/real+numbers">real numbers</a> had the next higher (infinite) cardinality from the integers.</p>
<p>This became known as the <a href="/title/Continuum+Hypothesis">Continuum Hypothesis</a>. As mathematicians are wont to do, the concept was eventually abandoned in favor of a broader, more general concept,…Suggestions for E2 (thing)http://everything2.com/user/Gorgonzola/writeups/Suggestions+for+E2Gorgonzolahttp://everything2.com/user/Gorgonzola2013-01-07T02:08:43Z2013-01-07T02:08:43Z<p>Reputation graph should have different time granularity options than just monthly, and a different viewing window than just the last 6 years. When a writeup has been around a long time, the graph that's shown just doesn't provide any useful information.<p>
<p><a href="/title/My+Big+Writeup+List">My Big Writeup List</a> should be in <a href="/title/E2+Tools+and+Toys">E2 Tools and Toys</a>.</p>iron poisoning (event)http://everything2.com/user/Gorgonzola/writeups/iron+poisoningGorgonzolahttp://everything2.com/user/Gorgonzola2013-01-06T21:24:45Z2013-01-06T21:24:45Z<h2><a href="/title/RUST+NEVER+SLEEPS">RUST NEVER SLEEPS</a></h2>
<p><i>Iron poisoning</i> refers to the tendency of <a href="/title/iron">iron</a>-based <a href="/title/fastener">fastener</a>s to slowly destroy the materials they are fastening, as the fasteners corrode.</p>
<p>During the surface corrosion of some <a href="/title/metal">metal</a>s, such as <a href="/title/aluminum">aluminum</a> or <a href="/title/zinc">zinc</a>, the <a href="/title/oxide">oxide</a>s form a protective layer around the <a href="/title/substrate">metal beneath the surface</a>, preventing water penetration and delaying further corrosion.</p>
<p>Not so iron. The principal <a href="/title/oxides+of+iron">oxide of iron</a> in contact with water, <a href="/title/rust">Fe<sub>2</sub>O<sub>3</sub></a>, forms <a href="/title/cubic">cubic</a> <a href="/title/crystal">crystal</a>s that break away from the metal and allow water to penetrate. What's worse, rust crystals are less dense than the metal itself and so the rust comes to occupy more and more space.</p>
<p>This is less of a problem for the outer surfaces of an iron or steel object than it is for a <a href="/title/nail">nail</a> or a <a href="/title/screw">screw</a>. The surfaces can easily be protected by <a href="/title/paint">paint</a> or <a href="/title/electroplating">electroplating</a>, and what crystals do form expand into the coating or the open air, and the surface can…