This "Mathy Stuff and Ternary Logic" category covers mostly mathematical essays, with occasional forays right into ternary logic, which underpins my inquiry into mathematics.
This is one of those things which thoroughly surprises me, because it seems so obvious, yet it has taken me more than a couple decades to learn how to see. I've written about the idea being revealed here from a number of directions, but never before have I seen it with the clarity that I now see. […]
I've written about a certain little-known role of division in mathematics before, so when a friend recently posted an article I enjoyed (having posted a link to it here before), I was pleasantly surprised while re-reading to see that Cohl Furey is also intrigued by division... in a way that sorta […]
This peculiar thought experiment captures the first time I've been able to completely flip the idea of counting, with a rather original approach. Other attempts have been more high-level, with fewer details, and couldn't be pursued very far. But this time I got to the bottom. Please be patient with […]
Well this is going to be fun. Long ago, my thought experiments on dividing by zero detected a bug*, and therefore went in the direction of "you can divide by zero" and of course this left me on the outskirts of mathematics years ago. I set up a tent and made a home there, where I am quite […]
Update again, Sept 2021: Just found this excellent link to R. J. Lipton taking Atiyah seriously. I don't have time to dig in right now, but want to. I'm delighted to see someone doing this, as the binary response to Atiyah's insights left me feeling like more people should be looking into this, just […]
I just encountered this quote from Salomon Maimon, and it expresses the way I have approached mathematics (which is I believe different from the way most people approach it). The reason I learned to study this way is that I believe so intensely what I believe, I must be careful what I believe. For […]
Well, little known to me at least. Had no idea that Galileo was the one who invented mathematical physics. I found this insight fascinating. Emphasis mine: Perhaps the most important move in the scientific revolution was Galileo’s declaration that mathematics is the language of natural science. But […]
Found this article which goes into a little more depth on this obscure mathematical comment by Winston Churchill about a moment when his life changed. I still consider it to be one of the deeper insights into the true nature of infinity. I had a feeling once about Mathematics, that I saw it […]
Introduction This article contains a long list of several dozen quotations centered around the theme "the infinite sphere whose center is everywhere." Many others have gathered similar lists of this quotation over the centuries. As far as I am aware this present list is the most extensive […]
Originally written in fits and starts from 2015-2019 In unexperienced infancy Many a sweet mistake doth lie: Mistake though false, intending true; A seeming somewhat more than view; That doth instruct the mind In things that lie behind, And many secrets to us show Which afterwards we come to know. […]
The Primordial Singularity is clearly very large, for it encompasses our universe, which is very large -- currently unmeasurably so. Yet it has the nature of perfect, instantaneous communication: when something happens on one "end" of its immensity, the information is communicated […]
It took me a long time to figure out the Monty Hall problem. I was relieved to discover it also took Erdos a long time, and most others. After much stumpification, I found this thread and finally got it: The exact wording of the problem can change the answer. For example, in this version There are […]
When moving from the artificially perfect world of (excluded-middle) mathematics back into the real world, we encounter significant changes to our expectations for how things work. Or, as seen from the other directions, pure math feels "liberating" because we don't have to worry about all […]
It required several years of studying ternary logic -- which at that time I still called trinary -- before I began to glimpse a realization that the way we understand ternary is with a profoundly binary lens. In those early glimpses, I began to understand that even the people who discovered ternary […]
I long imagined that the essential flaw of binary logic lay in its foundation axiomsdefinition which exclude middles by asserting everything is EITHER true OR false with no inbetween. (This results in paradoxes which are considered to be unimportant by most people when compared with the overall […]
I assume this is relevant to the ongoing quest to fully understand ternary logic, its strengths and limitations, but do not yet know what to do with it. So here it is: You can't convert a base2 number to a base3 number without loading it into an integer. The reason is that 2 and 3 are coprime - they […]
(Huh, this post was definitely written while still in ephiphanic mode. Have fun parsing it. I added strikethroughs where appropriate to make it hopefully a little more sensible. I've since explored some of these ideas more coherently elsewhere.) Primes cancel out everything following which is […]
Here I find myself in the middle of an example of how hard it can be to learn mathy things without having gone through years of training. You might say "So, go through years of training." And then I would say "No, that training comes embedded with a way of seeing the world that […]
This guy was a student of Lukasiewicz, who famously established ternary (and then later, multivalued) logic as an alternative to the binary which prevailed since Aristotle's time. I didn't know about the three logical systems here, though, and they bear further study: The distinctive and original […]
I always just assumed the link between algebra and geometry was pretty solid, but actually it's two different worlds, similar to Poincare's distinction between logical and intuitive that I've discussed elsewhere (and so has Terence Tao). So it's nice to find that someone found an elegant synthesis […]