Chyetanya KuntePersonal log
http://ckunte.net/log/
en-usPhuket
http://ckunte.net/log/2014/phuket
http://ckunte.net/log/2014/phuketTue, 23 Dec 2014 00:00:00 GMT<p>Ten years on, I am on ground zero, and this place barely looks like anything fateful ever happened here. Sharp eyes will however notice evac. routes are now as prominent as road signs around town. But otherwise, it’s business as usual: the hawkers, the bars, the beach.</p>
<p><img alt="Maya bay, the idea of paradise in the film, The Beach." src="/log/images/phuket-mayabay.jpg" /></p>
<p>I was in Kuala Lumpur in December of 2004, glued to screens when the deadly <a href="http://en.wikipedia.org/wiki/2004_Indian_Ocean_earthquake_and_tsunami" title="2004 Indian Ocean earthquake and tsunami">Indian Ocean tsunami</a> first struck parts of Indonesia and Thailand. A day later, I signed-up to join a group of self-organizing <a href="http://tsunamihelp.blogspot.com/" title="The South-East Asia Earthquake and Tsunami Blog">TsunamiHelp</a> volunteers online, after reading about an opportunity to offer assistance. I worked briefly as a wiki editor, combing through the rolling blog, where the latest information first got posted by a larger pool of posters, and organize information by self-contained topical pages. Volunteering time online — gathering (hopefully) useful information to those unfortunate to be in places where the tsunami struck — was a lot like hit or miss, not knowing if it was of any use at all.<sup id="fnref:1"><a class="footnote-ref" href="#fn:1" rel="footnote">1</a></sup> The premise was that cellphone lines would be jammed but not so with the internet, which meant whoever had access could potentially search for information, find the blog and wiki pages. That said, one only needs to look at the exposed electricity and telephone lines, and realize they’d likely never survive the first and second order effects of a tsunami, which uprooted buildings and trees without discretion. Of course, we were not thinking about things like these.<sup id="fnref:2"><a class="footnote-ref" href="#fn:2" rel="footnote">2</a></sup></p>
<p>Also, unlike the blog, the wiki had its share of downtime. At some point, the wiki had to be switched to domain(s) or service(s) from <a href="http://en.wikinews.org/wiki/Portal:2004_Indian_Ocean_Tsunami" title="Portal:2004 Indian Ocean Tsunami">Wikinews</a> — I forget now, but remember SocialText offered a free account to run the TsunamiHelp team. So, I think we spent some time copying over from one site to another twice. I presume other wiki volunteers did something similar. (With the exception of Wikinews, none of the other wiki sites survive today.) </p>
<p>As news began to spread, the TsunamiHelp blog did eventually get some recognition and was even on Google’s dedicated tsunami page for a while. (Some remnants of links can still be found on the web.) And in the following years, some organizations and a conference or two did applaud the effort — perhaps for its novelty, if not for its usefulness, which I think was nice.</p>
<p>The area destroyed by the tsunami could have been an opportunity to plan town and rebuild its streets well beyond its pre-tsunami days, but then this is Asia. Phuket is back on its feet, although day-tour guides still do remind us of the event.</p>
<div class="footnote">
<hr />
<ol>
<li id="fn:1">
<p>I was working mostly on the information but none connecting with whoever human on the other end of the line looking for help (others in the team tried to do that with Skype — a relatively new thing at the time), so it was hard to tell without any sort of feedback or useful stats. I am pretty sure help via the internet was both absurd and useless in areas like Banda Aceh, where the only way to help was to somehow to eject oneself physically there, or alternatively send food, aid material. <a class="footnote-backref" href="#fnref:1" rev="footnote" title="Jump back to footnote 1 in the text">↩</a></p>
</li>
<li id="fn:2">
<p>There is a lot of grief associated in any aftermath, which volunteers tend to internalize, and develop a certain emotional stability — stop hands from shaking. Needless to say, I was not cut out for this, and I did not sign up for other such noble pursuits after. <a class="footnote-backref" href="#fnref:2" rev="footnote" title="Jump back to footnote 2 in the text">↩</a></p>
</li>
</ol>
</div>Square and cube series conjecture
http://ckunte.net/log/2014/square-cube-series-conjecture
http://ckunte.net/log/2014/square-cube-series-conjectureSun, 23 Nov 2014 00:00:00 GMT<p>My ten year old younger daughter has been discovering number series on her own. Today, she said to me that she has developed two conjectures:</p>
<ol>
<li>Square series conjecture: When any two square values in series are known, an entire series can be built.</li>
<li>Cube series conjecture: When any three cube values in series are known, an entire series can be built.</li>
</ol>
<p>Here’s how she explains them:</p>
<h3>Square series conjecture</h3>
<p>Let’s say we have two square values in series:</p>
<pre><code>25, 36
| |
+--+
11
</code></pre>
<p>The difference between square series is always an even number: 2. For instance,</p>
<pre><code>1, 4, 9, 16
| | | |
+---+---+---+
3 5 7
| | |
+---+---+
2 2
</code></pre>
<p>So, you add 2 to the difference plus the last number to get the next in series.</p>
<pre><code>25, 36, 49 (= 36 + 11 + 2)
| | ^
+--+ |
11 + 2--+
</code></pre>
<p>Likewise, one can find the previous in the series as below:</p>
<pre><code>25 - (11 - 2) = 16
</code></pre>
<p>Imagine a series of sequential square values as below:</p>
<p>\begin{aligned}
…, a_{x-1}, a_{x}, a_{x+1}, a_{x+2}, …
\end{aligned}</p>
<p>If you know any <em>two</em> in sequence, then you can build the series. Here’s how:</p>
<p>\begin{aligned}
a_{x-1} = 2 \cdot a_{x} - a_{x+1} + 2 \newline
a_{x+2} = 2 \cdot a_{x+1} - a_{x} + 2
\end{aligned}</p>
<p>This series is built one step at a time, of course, but it can be programmed to whatever iteration required to build the series.</p>
<h3>Cube series conjecture</h3>
<p>Let’s say we have three cube values in series:</p>
<pre><code>27, 64, 125, 216,
| | | |
+----+----+----+
37 61 91
| | |
+----+----+
24 30
| |
+----+
6
</code></pre>
<p>The difference between cube series is always an even number: 6. So, you come up with the next number as follows:</p>
<pre><code> 64 - 61 + 30 - 6 = 27
216 + 91 + 30 + 6 = 343
</code></pre>
<p>Now Let us again imagine a series of sequential cube values as below:</p>
<p>\begin{aligned}
…, b_{x-2}, b_{x-1}, b_{x}, b_{x+1}, b_{x+2}, …
\end{aligned}</p>
<p>If you know any <em>three</em> in sequence, then you can build the series. Here’s how.</p>
<p>\begin{aligned}
b_{x-2} = 3 \cdot (b_{x-1} - b_{x}) + b_{x+1} - 6 \newline
b_{x+2} = 3 \cdot (b_{x+1} - b_{x}) + b_{x-1} + 6
\end{aligned}</p>
<p>Again like the square series, this series too is built one step at a time, of course, but it can be programmed to whatever iteration required to build the series.</p>
<p>She had to explain this whole thing to me <em>twice</em> before I could get my head around the concept and help formalize into equations, since she’s not yet into it herself.</p>Logarithms
http://ckunte.net/log/2014/logarithms
http://ckunte.net/log/2014/logarithmsSat, 22 Nov 2014 00:00:00 GMT<p>My daughter, who is in year 10, came to me with this problem, which she said she’s expected to solve using logarithms:</p>
<p>\begin{aligned}
3^{x} + 10 = 2 \cdot 3^{x + 1}
\end{aligned}</p>
<p>I am conditioned to plain algebra, and because logarithms play by different rules<sup id="fnref:1"><a class="footnote-ref" href="#fn:1" rel="footnote">1</a></sup>, I find them unfamiliar to get my head around complex expressions. The other problem is that I have also forgotten logarithms conveniently, because why not, I’ve never used slide rules, and I’ve got calculators and computers that I do not find multiplication problems difficult anymore. Or do I?</p>
<p>She and I then spent a better part of an hour trying. I looked up two reference books (<a href="http://www.amazon.com/dp/0831133279">Engineering Mathematics by K.A. Stroud</a>, and <a href="http://www.amazon.com/dp/0750681535">Engineering Mathematics Pocket Book by J. Bird</a>), the <a href="https://www.khanacademy.org/math/algebra2/logarithms-tutorial" title="Logarithms: Khan Academy">Khan Academy</a>, and the <a href="http://en.wikipedia.org/wiki/Logarithm" title="Logarithm">Wikipedia</a>. I mean they all did refresh my memory on rules, but none of them helped me solve a complex equation as above — as my failed attempts below show.</p>
<p><img alt="" src="/log/images/logarithms.jpg" /></p>
<p>After numerous run-ins in expanding the above expression into solvable bits, rearranging LHS and RHS, I thought we’d need to know the answer first. I punched the above expression, and <a href="http://calca.io/" title="Calca - The Text Editor that Loves Math">Calca</a> spit the answer out just like that.<sup id="fnref:2"><a class="footnote-ref" href="#fn:2" rel="footnote">2</a></sup></p>
<pre><code>3^x + 10 = 2 * 3^(x + 1)
x => 0.6309
</code></pre>
<p>As I realized, this turned out to be an exercise in humility in which it was my daughter that finally came up with a solution, and she then taught me how to. First, she split the equation (notably the power part of the RHS) as below:</p>
<p>\begin{aligned}
3^{x} + 10 = 2 \cdot (3^{x} \cdot 3)
\end{aligned}</p>
<p>The question suggested using suitable substitution. So, here’s a clever substitution she used:</p>
<p>\begin{aligned}
3^{x} = a \
\end{aligned}</p>
<p>Using it in the expression, she came up with the following:</p>
<p>\begin{aligned}
a + 10 = 2 \cdot a \cdot 3 \newline
10 = 6a - a \newline
a = 2 \newline
\end{aligned}</p>
<p>Substituting the value of <em>a</em> back, she got this:</p>
<p>\begin{aligned}
3^{x} = 2 \newline
\end{aligned}</p>
<p>Now using the first rule of logarithms:</p>
<p>\begin{aligned}
x = log_{3} 2 \newline
x = 0.6309
\end{aligned}</p>
<p>To get a value of log to the base 3 in the last part, she had to use a scientific calculator, since we do not have log tables.</p>
<p>Part of the difficulty dealing with the problem above was because it’s an expression that also has addition in it, while according to the simple definition (I am repeating myself here), logarithms transform multiplication and division problems into addition and subtraction problems. But the rules do not address how to deal with a mixture of these expressions. So, the best way to deal with these is to reduce the problem via plain algebra to simpler expressions first containing only multiplication and division, and then employ logarithms to the problem.</p>
<p>As to the last part of problem, I realize, log to <em>any</em> base (3 in our case), for computational simplicity, and because built-in calculators within our computers do not have the <em>any</em> base option, the above may also be rewritten as:</p>
<p>\begin{aligned}
x = log_{3} 2 \newline
x = \frac{log_{10} 2}{log_{10} 3} \newline
x = 0.6309
\end{aligned}</p>
<p>The common base can be anything. (Those with calculators would find it convenient to use a common base of 2, e, or 10). The answer would be the same. For instance,</p>
<p>\begin{aligned}
x = \frac{log_{e} 2}{log_{e} 3} \newline
x = 0.6309
\end{aligned}</p>
<p><img class="screen" src="/log/images/logcurve.png"></p>
<p>Here’s the curve, and a graphical check — notice the intersection of the curve on x axis. That’s our answer found above.</p>
<div class="footnote">
<hr />
<ol>
<li id="fn:1">
<p>It is a method that converts difficult multiplication and division problems into addition and subtraction problems using tables of logarithms. <a class="footnote-backref" href="#fnref:1" rev="footnote" title="Jump back to footnote 1 in the text">↩</a></p>
</li>
<li id="fn:2">
<p>Just be aware that in a quadratic equation with two solutions, Calca reports only the positive value. <a class="footnote-backref" href="#fnref:2" rev="footnote" title="Jump back to footnote 2 in the text">↩</a></p>
</li>
</ol>
</div>