(The piece below that on this lazy Sunday I wrote over hours in reaction to Veritasium's video, will hardly make sense if you are not familiar with the stuff of it. And even if you are familiar with it, the video is well worth watching because very well done and smooth)Veritasium: This equation will change how you see the world
What do 3.14 and 14/3 have in common? -- a geek's journey in semiotics
14/3 = 4.666... is a simplest rational approximation -- an arithmetic allusion
-- to Feigenbaum's "spooky" δ = 4.6692... much like 22/7 ≈ 3.143 is to Archimedes's π, the epitome of mathematical constants. To which 3.14 is in turn another minimal mathematical allusion.
I first observed this ~20 years back as I was driving behind a cab with license plate 314. My first reaction was "Ha! 14/3, Feigenbaum's constant!".
Close behind my second reaction was a huge laugh at myself.
Allusions are a matter of balancing terseness with ambiguity over convention called upon. And they are vaguely transitive. 314 alludes to 3.14 which alludes to π = 3.14159... A bit more weakly (to common sense) 314 also alludes to 14/3 which alludes to Feigenbaum's δ = 4.669201...
The reason I'd perceive δ before π in 314 is that playing with approximations to δ (not π) had been a lazy hobby of mine for 15 years. In turn, the reason for that hobby is the "spookiness" of δ that Veritasium describes in the video, and a moral trap I'd put myself in because of it. I summarize this all below.
This happened late '87, just as Gleick's "Chaos" was first published in the US, and before the word became a household name. It would be years before I became aware of Gleick's book. I knew of bifurcation cascades because of Collet & Eckmann 1980's foundational book on the topic, "Iterated Maps on the Interval as Dynamical Systems"
upon which I'd stumbled a few years earlier.
At that time, late 87, I'd gone very deep
into the rabbit hole of an intimate trajectory -- incidentally, that's something vaguely comparable to iterating a "stubbornly identical" function like is central to what the video describes. A consequence was that I'd become overwhelmed by what's commonly called synchronicity.
Very briefly put, this amounted to welcoming the spookiness inherent to putting simplicity of allusion to the task of figuring out alternate intelligent interpretations to what is spontaneously salient according to normal rules -- while suspending both common sense interpretation and the compulsion to obey cognitive dissonance.
My way I described on top, of going from 314 to 14/3 to Feigenbaum's δ instead of the more common sense and straightforward 3.14 and Archimedes' π, is itself like a miniature model of this divergent way to look at things.
The God delusion?
Now my education and cultural background were strictly atheistic. Religion, faith, churches, rituals, priests and believers didn't to me bear any kind of valence, not even negative. Their status was somewhere between "beyond the horizon" and "features of the skyline". Over the decades since, my effort to relate by finding the mindset to pray sincerely only brought fruit once, in a very particular circumstance -- except for occasional half-serious prayers for a parking space.
However at the time, '87, I found myself quickly enough in need of validating in any way the perception from synchronicity -- the perception that was singling me out and talking to me the resulting "voice". A voice at once barely intelligible and booming.
Booming because it was partially channeled by salient tragic events, similar, say, to a friend making jokes on the circumstances of the deceased at the funeral of strangers.
While cognitive dissonance from such experiencing certainly explains why appeared completely unknown the place I was in, this didn't work to make me simply shut it off, simple as closing eyelids on something nobody else appeared seeing.
...I was curious, and I was in particular impressed by the possibility of a vague relationship to an observation sometimes made about evolution by natural selection -- or rather, about the most simplistic model of it that works -- the observation is that individual death
(not conception!) is the channel by which information flows from the environment to the species -- that information manifest in ecological adaptation which is the central issue of the evolution vs creation dispute. That's an observation which provides some plausibility to the idea of individual deaths encoding intelligent messages.
meeting "The Book" and...
Yet I was in need of validation for the perception of the "voice" talking to me, so that I plunged in the idiosyncratic bits of literature I was vaguely aware of that featured salient bits I could relate to my experience. In order, old Greek myths and Lewis Carroll works -- that I think of as the n+1 iteration of Greek myths. The latter in turn led me to John's Book of Revelation whose over-the-top language I was very surprised to discover at the end of the Bible.
A thing though is that coming to it from that angle makes the tone and overall unintelligibility of Revelation similar enough to the experience of the "voice" -- which implies processing input like pandas do bamboo, leaving most of it undigested to metabolize only what your gut microbes can handle.
After a first scan of John's Revelation, because it was the bit in my science background most relatable to the spookiness of it all, I went straight back to fetch the value of Feigenbaum's constant from Collet&Eckmann with the intention of looking for a numerical relationship to the numerical constant that's the last word of chapter 13 of Revelation, handed there as a key, 666.
I was not aware at the time how much that number had over the centuries gained a life and reputation of its own on the basis of this placement in the text; and, to me, the way the text hands it down clearly enjoined to use its value in a manner quite opposite to what common sense did.
The first thing clear in chapter 13 of Revelation is that from beginning to end it pictures (in fiery metaphors) evil diabolical figures. Then, at the end, with the last verse, it calls for wisdom
to interpret the 666 -- apparently as the key to identify those obscure figures of highly negative valence to people or institutions in the reader's environment. To me, this call to wisdom was the most transparent and compelling thing in the whole chapter, as an allusion to the actual unwisdom
of the temptation to finger-point, a temptation invited by literally everything else in the chapter.
...bouncing back to Feigenbaum's δ
In about two minutes with Collet&Eckmann approximation to Feigenbaum's δ in hand, I arrived at δ^δ = 1333 = 2*666 + 1, to the limit of precision given in the book. I later rewrote this, cheating with Feigenbaum's nomenclature by renaming δ as K (for allusion to the word "King"), as
B = 666
K = 4.6692...
K^K = B + 1 + B
A pico-poem which features a vague mimic, both of the word B1Ble and of my complete initials, BJB. It also scintillates in various ways with allusion to half a dozen bits of verses in the text of Revelation -- in chapter 13 and others -- that would be too fastidious to detail here.
Incidentally, it was a lot of fun and also a great learning experience -- on convergent sequences, and specifically on how the whole of a truncated sequence can harbor more information on the limit value than does its ultimate member and best individual approximation to the limit -- it was great fun to probe the bifurcation cascade with code in order to calculate δ with better precision than that given in Collet&Eckmann ...and so establish that δ^δ = 1333 is only approximately true, and not exact.
However, the absence of exactitude wasn't sufficient to dispel my perception that this micro-poem fit the bill of what I'd been looking for, validation. Unfortunately, it was only validation according to my own criteria and not according to those of society.I remained guiltily stuck with it, and the path to freedom was to come up with alternate numerology for the constants involved that would beat it on the scale of meaningfulness according to my own criteria, which included (subjective) originality
This took a long time... and explains how playing with approximations to Feigenbaum's δ, as I evoke in the beginning of this piece, became a hobby of mine. Another side-effect is that I became fairly familiar with the crooks and nannies of John's Book of Revelation.
Breaking free 1
Ultimately, over the years, I was successful in coming up with three further micro-poems involving the numerology of the 666, that fit my personal criteria for meaningfulness at the time, better than did my initial find above. Well the first two of them at least.
The first successor 666-poem captured my original intuition that Rev 13 meant to allude to the unwisdom of finger-pointing at the point it calls to wisdom before the concluding 666; but the poem below does so without involving my identity as did the original one. A presentation is:
"either with us, or against us"
~ the excluded middle
~ le tiers exclu, tertium non datur
~ 1 - 1/3
What in summary makes 666 a symbol for polarization and divisiveness.
Breaking free 2
The second successor poem carried it to the matter of damning sacred books for being more generally the pretext to draw similar finger-pointing accusations from them. Its core is particularly terse:
666₇ = 3 ⋅ 114
But needs supplementing with explanations:
114 is the size of the Qumran measured in chapters a.k.a. Surahs.
3 counts the main branches of the Abrahamic tradition and their respective sacred corpora.
666₇ is standard form for "666, base 7" equal to 7³ - 1
The irony of it is of course that it covers in its accusation the very book and verse that fuels the accusation. Kind-of illustrates the so-called "fallacy fallacy".
An incidental if vague/partial justification for the interplay involved of base 10 and base 7, is that 7 and 10 are the two numerical constants cited in the first verse of that chapter 13 of Revelation that features the 666 as its last word.
Back to basics
Now, the ultimate poem I came up with, is different. It's pretty recent, way more in line with what common sense did of the negative valence of the number, has a good degree of circumstantial relevance, and is closely inspired by the endnote explanations usually provided with the original verse.
These endnotes are to the effect that the number was originally intended as a rumored allusion to the initial great persecutor of the early Christians, the Roman Emperor Nero, a dozen years after his passing, via the operation of a numerological device of the Hebrew tradition going by the name of gematria, which consists in adding up integers obtained from a standard mapping of the letters of a written name.
The main weakness of that explanation to my eyes, is that there are in fact three distinct scripts involved, the Greek in which Revelation was written, the Roman of emperor Nero, and the Hebrew of gematria for which the standard mapping was defined. It's also often raised that the 666 was likely a belated interpolation and that 616 appears in its stead in the earliest manuscripts.
Putting the latter point aside -- "etymological" exactitude is beside the point -- it's striking that gematria admits a straightforward transposition to the most common script and mapping from letters to numbers of contemporary times that's provided by ASCII -- a mapping that's so centrally embedded in our computers that there's no need to refer to it explicitly when using common programming languages -- and that this allows to compute 666 from a natural enough expression of the name of a famously toxic contemporary leader that has independently been compared to the emperor Nero; and is further famed for the divisiveness of his rule. As the following expression in standard Python 2 or 3 demonstrates:
sum(ord(c) - ord(' ') for c in ' DONALD JOHN TRUMP! ')
Which indeed evaluates to 666.
Note that subtracting the code for the space character to that for each letter is a natural thing to do in order to be in line with the gematria of old times that calculated no contribution for the breaks between words; also, the space character is the first in ASCII order to have a graphical significance (if barely). The bang after Trump's name is the immediate successor to the space character in ASCII and therefore contributes just 1 to the total, which, otherwise, would be 665. However, the famous known love of Trump for capitalization and adding bangs at the end of sentences would seem to justify the exact form chosen.
And a cherry on the cake
Incidentally, 45 isn't the first POTUS that could be trolled using a strikingly simple Python expression. 43 admitted a comparable "Python quip". Back in late 2001 and 2002, the following Python expression could pass as a "program" succeeding the Turing test by apparently behaving just like the mass of "patriotic Americans":
filter(lambda W : W not in 'ILLITERATE','BULLSHIT')
The expression evaluates to 'BUSH'. Or rather, used to: it evaluates to 'BUSH' in python 2 which has become obsolete in the meantime, and requires a bit of tweaking to evaluate the same in Python 3 that's now current -- so much tweaking, in fact, that it loses its charm.