Hexnet Hexagonal Tag Feed: dozenalA feed of tagged nodes.
https://hexnet.org/blog
Dozenal Pi Day 11B7<p class="quote">
"Ten is doubtless a convenient number of fingers to have, though men have gotten along with less and a few people have been born with more. But as the purely arbitrary unit which determines the form of our numbers, it was a miserable choice." – F. Emerson Andrews
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"Do not disturb my circles." – Archimedes
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<img src='/files/images/hexnet/dozenal-pi-day-b7.png' title='Yes that's right&mdash;Dozenal Pi Day' alt='Dozenal Pi Day' class='image-right'/>
It's that time of year again—time to start thinking about DOZENAL PI DAY.
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<h3>Overview</h3>
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Regardless of its radical prejudices, Pi Day has become, in recent years, an annual cultural event of some magnitude, and the occasion for a certain nominal enthusiasm about "math" that people seem to find meaningful. At the very least, it seems to remind us of our own cleverness, which is something I have nothing against in principle.
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Yet I am more convinced than ever that, unless we remain firmly mindful of what separates the arbitrary and symbolic in mathematics from the truly meaningful, Pi Day will ultimately remain a rather vacuous and misguided holiday. Thus, I once again propose the observation of DOZENAL PI DAY on 18; March (decimal 20th), to raise awareness of the superior dozenal radix, while also bringing attention to the underlying meaninglessness of our present decimal notation.
</p>Thu, 27 Jan 2011 18:43:08 +0000
https://hexnet.org/content/dozenal-pi-day-11b7
https://hexnet.org/content/dozenal-pi-day-11b7Thoughts on the hexagonal zodiac<p>
<img src='/files/images/hexnet/zodiac-hexagons_0.png' title='A hexagonal arrangement of the zodiac' alt='A hexagonal arrangement of the zodiac' class='image-right'/>
I feel something must be said about this astrological "sign shift" business that has set the 'tubes abuzz in recent days. There being twelve astrological signs ("Ophiuchus" notwithstanding) arranged around a central point, the issue is clearly one of both dozenal and hexagonal import. Despite the fact that I'm not all that into astrology (though I've learned enough over the years to inform my general fluency in Western occult symbolism), I feel the hexagonal principles at stake must be defended.
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First of all, this is of course old news. I don't really understand why it keeps popping up in the media every few years, but this is simply the latest incarnation of a story that we've all been well aware of since classical antiquity, and that certainly should not come as news to anyone, anywhere. "Ophiuchus" has always been there, the twelve signs have never been symmetrically arranged in exact 30-degree sections, axial precession has always been going on, we always knew about it, nobody has ever cared, and nobody cares now.
</p>Fri, 14 Jan 2011 17:11:26 +0000
https://hexnet.org/content/thoughts-hexagonal-zodiac
https://hexnet.org/content/thoughts-hexagonal-zodiacDozenal tau unit circle<p>
This is a unit circle diagram using both dozenal notation (as with elsewhere on this site, using "A" and "B" for ten and eleven) and the newly proposed circle constant τ (tau), which is equal to 2π. The advantages of τ over π are numerous and obvious—instead of a full circle of arc being two of anything, it is just one τ. Put another way, τ is simply the number of radians in a circle.
</p>Sun, 25 Jul 2010 00:47:33 +0000
https://hexnet.org/content/dozenal-tau-unit-circle
https://hexnet.org/content/dozenal-tau-unit-circleAn Excursion in Numbers<p><i>This article was transcribed by myself for Hexnet.org from a PDF file hosted on the <a class='ex' href='http://www.dozenal.org/'>Dozenal Society of America</a> site, and originally published in the Atlantic Monthly, presumably some time ago.</i></p>
<h3>I</h3>
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From the Eskimo counting upon his fingers to the mathematical wizard producing split-second answers with a slide rule, we count by tens. In our critical age, such universality is phenomenal; it cannot be claimed for any religion, code of morals, form of government, economic system, principles of art, language, or even alphabet. Counting is one of the very few things which modern man takes for granted.
</p>Sat, 01 May 2010 18:41:00 +0000
https://hexnet.org/content/excursion-numbers
https://hexnet.org/content/excursion-numbersTwelves and Tens<p><i>This article was transcribed from a PDF file originally hosted on the <a class='ex' href='http://www.dozenal.org/'>Dozenal Society of America</a> site, reprinted from </i>The Listener<i>, 25 January 1962.</i></p>
<h3>On the case against the system of decimalization</h3>
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Many people will be wondering why a mathematician should argue against the proposed change-over to decimal currency and the metric system of weights and measures. Surely, they will think, everyone is agreed that the decimal system is the most practicable system in which to carry out both small calculations and large ones? I wish to point out certain reasons why this is not so, and to show that there exists a better system, which in Britain we have in part already, and which, unwisely in my opinion, we are preparing to throw away.
</p>Sat, 01 May 2010 18:15:57 +0000
https://hexnet.org/content/twelves-tens
https://hexnet.org/content/twelves-tensAn Argument For Dozenalism<p>
<b>Note:</b> Writing about dozenalism always presents some semantic complications. When discussing the natural numbers up to twelve, I have opted to spell out the numbers in English, since this is a clear and base-neutral way of representing them. After trying several different systems, I have settled on writing larger numbers in decimal. Unless otherwise specified, "10" means ten, not twelve, et cetera. When I use dozenal notation, and for clarification purposes elsewhere, I have prefixed the radix as an abbreviation before the number. Thus, "dec. 360" means decimal 360, and "doz. 260" means dozenal 260. "360" by itself, unless otherwise specified, refers to the former. Larger numbers spelled out, where it is stylistically appropriate to do so, will always be given in decimal. My first inclination, of course, was to put all numbers here in dozenal, but on further reflection I see no value in confusing people needlessly. (Confusing them for a good reason though is fine.)
</p>Thu, 29 Apr 2010 18:32:37 +0000
https://hexnet.org/content/argument-dozenalism
https://hexnet.org/content/argument-dozenalismDozenal Pi Day 11B6<p><i>The following is a short writeup I did for an event on Facebook celebrating Dozenal Pi Day on March 18, 11B6 (decimal March 20, 2010). As indicated in the text, it includes some borrowed material from the Wikipedia article on duodecimalism.</i>
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<img src='/files/images/hexnet/dozenal_pi_day-3.png' title='Dozenal Pi Day 11B6' alt='Dozenal Pi Day 11B6' class='image-right'/>
I am not sure when exactly this "Pi Day" thing became so fashionable, but for me it has come to symbolize everything that is wrong and unwholesome about modern society's relationship with numbers. You see, of late I find myself more and more perturbed by the extent to which people seem to take the primacy of decimal notation for granted in conceptualizing and comparing numbers. In the case of pi, there is NOTHING particularly universal or ontologically significant in the sequence of digits 3.14159265... except that they represent a certain way of parsing the value of pi by successive fractions of ten. THIS IS MAY BE INTERESTING IF YOU ARE REALLY INTO THE NUMBER TEN FOR SOME REASON. Otherwise it—like the entire decimal radix system—is fairly useless.
</p>Sun, 14 Mar 2010 01:37:47 +0000
https://hexnet.org/content/dozenal-pi-day-11b6
https://hexnet.org/content/dozenal-pi-day-11b6