Bad Math, BAD!
I have a morbid fascination with bad math — the egregious misuse or erroneous application of mathematics, often draped in delusional/pompous claims of conspiracy. You might think this sounds mean-spirited; something to do with mocking the offenders, but it’s not — at least not for me. It’s finding beauty in the salmon’s attempt to swim a sheer 400-foot rock face “upstream”. It’s the hair on the back of your neck standing on end as the ferocious little Pomeranian chases a garbage truck down the block. We’re all ignorant from time to time, but only through mathematics can we appreciate provable ignorance and the surefooted stubbornness it breeds in the human spirit.
There are many flavors of bad mathematics, some more popular than others. Below are two examples of the sorts one frequently encounters in the wild: ultrafinitism crankery and mathematical mysticism. These aren’t necessarily the best at scratching the itch — that ends up reserved for assertions equal in their confidence, wrongness, but also novelty — but they are probably the most common, and beloved nonetheless.
The style of this post is at least partially inspired by Underwood Dudley’s wonderful What To Do When the Trisector Comes, an absolute must-read for anyone sharing my affliction.
1. The Ultrafinitist Crank
One very popular flavor of abuses stems from finitism and its offshoots. The ultrafinitist crank (hereafter abbreviated to ultrafinitist) conflates the axiomatic nature of math with a nebulous sort of requirement that concepts be physically plausible. The ultrafinitist never attempts to formally tether an axiom to the natural world, but merely urges you to lean on a presumed material “common sense” we all share when considering his handwavey claims.
One common abuse of the ultrafinitist is the argument that 0.999… ≠ 1, “because you can always add another 9”, or some such silliness. Another asserts that “because you can never compute π precisely, it does not exist!”, or “…therefore π must be rational!”. There’re oceans of these sorts of arguments — alongside tons of hilarious pseudoscience — on viXra, a hub for authors whose papers have been removed from arXiv.
The ultrafinitist often develops preposterous conspiracy theories that explain why their truly grandiose and unprecedented works are being kept from their much-deserved recognition. Uberultrafinitist John Gabriel exemplifies this best in literally everything he writes:
“[My work] is the greatest feat of human intellectual accomplishment. It is the first and only rigorous formulation of calculus in human history. Not worth one, but ten Abel prizes, given that no one before me was able to realise it. You can be certain that if the Church Of Academia (mainstream academia) has its way, I shall never receive any prizes, never mind one Abel prize. Mainstream academics hate me passionately and are pathologically jealous of my work.”
Gabriel’s work, “The New Calculus”, is a sort of deification of infinite rejection. There’s a lot more I could say about John Gabriel — the man is an absolute behemoth in the field — but nothing that would top that double entendre, so we’ll move on from him for now.
The ultrafinitist pays no mind to the fact that he’s often objecting to definitions. Any mention of this will be wholly ignored. The ultrafinitist will almost never provide a proof of his theorem, and when he does, no attempt to point to the erroneous step will dissuade him.
Here’s one carrying the banner of the heated 0.999… = 1 controversy:
“.999 repeating forever represents getting close to 1 without reaching it. 9/10n is an attempt to describe that. It is not what .999… is. Anything that says getting really close to 1 without reaching 1 is the same thing as 1 is fundamentally flawed.”
Note the carefree personal redefinition, the wielding of physical intuition in lieu of proof, the cavalier dismissal of limits (see below). In time, the connoisseur learns to appreciate these characteristics as disparate, nuanced notes that have been coaxed into symphonic togetherness by artists of ignorance — no less capable in their craft than Beethoven or Nabokov.
The “9/10n” bit is referencing a definition of 0.999…:
If this notation is unfamiliar, read “:=” as “is defined as”, meaning there’s no equality being asserted here, just a simple, one-line legend:
> “Here’s what I mean when I say 0.999…”
Don’t worry about the right hand side, other than the fact that it provably evaluates to 1. It does not matter how many times or ways you try in earnest to show that this limit evaluates to 1, formal systems just do not stand a chance against a cocksure sense that something’s simply wrong.
The Ultrafinitist is a Poor Sport
The ultrafinitist can appear mathematically savvy to the uninitiated. He employs tactical distractions — both mathematical and linguistic — to better obfuscate his chicanery, but will eventually abandon his cause (temporarily) when painted into a corner. This usually leads to a short little spat of ad hominem or grammatically pedantic attacks on the opposition before disappearing completely into the night.
It is for this reason that the ultrafinitist should never be sought out for mathematical discussion alone. He should only be engaged when the entire performance is likely to provide entertainment.
2. The Mathematical Mystic
Another common field of crackpottery is mathematical mysticism. Here rigor is eschewed in favor of appeals to mystery and beauty. The very existence of some pattern is proof to the mystic that something magical is happening. It’s nearly impossible for the mathematical mystic to avoid asserting that the very nature of the universe itself is revealed in her discoveries.
The mystic will often refer to “energy” the way a horoscope does. She probably holds in high regard “The Ancients” — a handful of civilizations from antiquity (Mayan or Babylonian, e.g.) whose mysteriousness somehow implies their lost knowledge of all the universe’s secrets. The mystic has the entire arsenal of New Age pyrotechnics at her disposal, effortlessly igniting references to anything from Deepak Chopra-esque quantum mechanics to heart chakras in decorative defense.
Fibonacci Mysticism
One particularly frequent victim of the mystic is the Fibonacci sequence. The trait of interest here, usually, is that the ratio of adjacent Fibonacci numbers, F(n+1)/F(n), approaches φ = 1.618033988… as n approaches ∞. This is all but certainly abused (much like the Higgs Boson) for its colloquial name, The Golden Ratio. It just sounds ordained, or something, I guess.
There’s a ton of pseudoscientific nonsense out there about how this is “the most beautiful ratio”. You can see this in the brilliant works of architects and painters throughout history. You can find “golden spirals” everywhere in nature, from the curvature of a nautilus shell to the twisting expanses of galaxies above. Therefore, the mystic contends, a deep truth about the nature of the universe is hiding in the Fibonacci numbers.
There are a few problems with this, however.
Firstly, and most glaringly, absolutely none of it is true. The common thread in nautilus shells and galaxies is how fantastically terrible golden spirals are at modeling them. Architects nor painters prefer this ratio to any other — I’d bet dollars to doughnuts the ratio 2/3 is much more aesthetically prevalent in both professions.
Secondly, and somewhat agonizingly, some of this Fibonacci fervor is all but certainly born of good-faith but low-effort attempts by educators/enthusiasts to illustrate “the beauty of mathematics”. It’s relatively easy to slap a spiral on a picture of a galaxy, kiss your finger tips and exclaim “voila: maths!”. This works really well for “while scrolling through Instagram”-type faux-intellectual stimulation at the unknown cost of cultivating a nontrivial number of people who think that’s what math is.
Further, “good enough” representations of physical phenomena being tethered to a mathematical construction simple enough for a small child to grasp just seems like far too precious a coincidence to ignore for some. This gives rise to the strong creationist undertone one encounters in a lot of Fibonacci sensationalization. Somehow the notion of being able to model the natural world — even awfully — inspires deference to the mystic’s supreme creator of choice.
For good coverage of this particular sub-brand of woo, check out the fantastically named Fibonacci Flim-Flam. For actually interesting aspects of φ, including why it shows up in phyllotaxis, check out this video by Numberphile.
Number Theory Mysticism
Another style of mystic identifies literally any integer pattern and proclaims that the entirety of human potential flows therein.
One great example of this at scale is “Vortex Based Math”, which is formalized worship of the astonishing realization that the hour hand points at 3 every single afternoon at — drumroll — 3. It’s so astonishing that a VBM crank (the same from the above link) succeeded in making it on stage at TedX and presenting “the most advanced mathematics ever known to mankind”.
The idea behind VBM is that you write 1 through 9 (just because) around a circle (very important, something mystical about circles), start with 1 (because something, something), double it (because something, something else), and continue doubling. You draw a line between the location of each result and, perhaps unintuitively to its inventor, you end up with a repeating pattern.
There is literally nothing VBM advocates can’t derive from this. Notice how the black lines in the above diagram “kinda look like infinity”; this of course implies that the secret to a perpetual motion machine — unlimited, clean energy — is revealed in this most important pareidolia.
And no, I’m not kidding. Here is a 100% serious list from VBM inventor, Marko Rodin, on technology he’s theorized is thus possible:
- This technology can provide endless free energy
- It can eradicate all disease
- Food production can be maximized to end world hunger
- It enables unlimited travel… anywhere in the universe
- It renders all existing technology obsolete
All that, just from playing connect the dots!
For a more thorough yet still cheeky look at why VBM is ridiculous, check out this Professor Puzzler.
The Mystic is a Hopeless Romantic
I think the most telling quirk of the mystic is — as we’ve seen — that there’s often a curious amount of importance bestowed to the symbols themselves. The notion that someone once chose to denote infinity as ∞, and that it was over time adopted by the mathematical community, seems to be wholly lost on them.
In this, we learn a little bit about what makes the mystic tick: a willful glorification of things extraordinary only in their ordinariness.
Aesthetics
Both the mystic and the ultrafinitist build delusions of grandeur on the foundations of their misunderstanding, but do so with fundamentally different structural approaches.
The ultrafinitist makes use of, but often misunderstands, the building blocks of mathematical deduction. Her edifice is process. If the ultrafinitist took the time to learn the difference between steel and particleboard, she might make a fine mathematician (or architect, depending on how far I take this analogy).
The mystic on the other hand prefers theatrical facades, artfully impassioned teleportations from observation to conclusion. It’s not a stretch to imagine the mystic’s work doubling as one hell of an astrological column.
Architecturally, they’re both interesting, but just two in a diverse metropolis of mathematical abuses. I took the analogy too h̵i̵g̵h̵ far.
QED
This almost certainly doesn’t do the job of illuminating why I find all of this so fascinating — maybe I’m just not clever enough to articulate that and would have been better off spamming screenshots with a single “lol” at the end instead of erecting this giant billboard that reads “I’m a pretentious fucking asshole”.
But on the off chance that this does inspire you somehow to fall down the rabbit hole, I would appreciate seeing whatever treasures you discover.
