snek_boi

@snek_boi@lemmy.ml

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snek_boi,

The mneumonic major system. Once I learned it by heart, it helped me memorize all kinds of numbers: cards, IDs, passwords, addresses…

snek_boi, (edited )

I think the way to formally prove this is to find the difference between the Fibonacci approximation and the usual conversion, and then to find whether that series is convergent or not. Someone who has taken the appropriate pre-calculus or calculus course could actually carry it out :P

However, I got curious about graphing it for distances “small enough” like from Earth to the sun (150 million km). Turns out, there’s always an error, but the error doesn’t seem to be growing. In other words, except for the first few terms, the Fibonacci approximation works!

This graph grabs each “Fibonacci mile” and converts it to kilometers either with the usual conversion or the Fibonacci-approximation conversion. I also plotted a straight line to see if the points deviated.

https://lemmy.ml/pictrs/image/528b1166-8b5d-481d-a7bc-180947c29520.png

Edit: Here’s another graph

https://lemmy.ml/pictrs/image/003c6f1a-5555-45d3-a4d6-e4b5ddae71ec.png

So it turns out:

  • Fibonacci-approximated kilometers are always higher than the usual-conversion kilometers
  • At most, the difference between both is 25%. That happens early on in the terms.
  • After that, the percentage difference oscillates around a value and comes closer to it.
  • When talking about more than 100 miles, the percentage change approximates 0.54.

TL;DR:

  • Yes, the Fibonacci trick is true forever as you go higher in the sequence if you’re willing to accept a 0.54% error.
snek_boi, (edited )

If someone wants to play around with the code, here it is.

Note that you need RStudio and the Tidyverse package.

snek_boi,

To give an extreme example:

“I solemnly swear that I am up to no good.” vs. “053250411391271”

But to be fair, I never end up with nice sentences. It’s more like “Thank you, rainbow. Clock firework” and I imagine myself thanking a rainbow and telling it to “clock firework”, whatever that means…

As to how long, I think it could’ve been a couple of months doing a dozen or so conversions. In total it’s a very small investment of time, assuming you space it out and don’t cram. It really helps to use the Wikipedia mnemonics (like how 4 is kinda like a mirrored R).

snek_boi,

what if someone is mildly interested in why you use it as a filter technique? :P

snek_boi,

If you drive, the 3-4-8 second tailgating rule

snek_boi,

Checked it out and love that package! Thanks for the recommendation :)

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