Posts Tagged eleven

Arithmancy Pants for macOS and iOS: Because everything’s a magic number if you’re brave enough


TL;DR: I made an app to derive a lot of ‘lucky’ numbers from any text. You can get it on the App Store now, for iOS and macOS.

Many years ago I came across Uri Geller’s page about how he notices the number 11 a lot and it’s somehow a magic number. I didn’t read all of it, because it’s nonsense, but I was intrigued by the list of ‘Names, events and places that add up to 11 letters.’ It contains:

Arithmancy Pants on iOS, showing that 'What do you get if you multiply six by nine?' can be converted to 30706 different numbers in up to 9 steps, with a chart showing how many steps it takes to reach each number. The nuber 42 is selected, which can be reached by converting letters to their positions in the alphabet to get 23, 8, 1, 20, 4, 15, 25, 15, 21, 7, 5, 20, 9, 6, 25, 15, 21, 13, 21, 12, 20, 9, 16, 12, 25, 19, 9, 24, 2, 25, 14, 9, 14, 5, then by adding up the digits until they sum to a single digit (a.k.a. digital root) to get 5, 8, 1, 2, 4, 6, 7, 6, 3, 7, 5, 2, 9, 6, 7, 6, 3, 4, 3, 3, 2, 9, 7, 3, 7, 1, 9, 6, 2, 7, 5, 9, 5, 5, then by adding up groups of up to 2 numbers to get 13, 3, 10, 13, 10, 7, 15, 13, 7, 6, 11, 10, 8, 15, 9, 14, 10, then by converting each number to Roman numerals to get XIII III X XIII X VII XV XIII VII VI XI X VIII XV IX XIV X, then by taking the number of letters in each word to get 4, 3, 1, 4, 1, 3, 2, 4, 3, 2, 2, 1, 4, 2, 2, 3, 1, then by adding up all the numbers to get 42
Final numbers in Arithmancy Pants for iPhone
  • Many words, names, and phrases that happen to have 11 letters
  • The words ‘hell heaven’ that sound a bit like 11
  • Events that happened on the 11th of some month, or in November, or at 11:11
  • The fact that Queen Elizabeth II is often written EIIR, which looks like E11R (of course, if you know Roman numerals, it clearly means E2R, but when I was a little kid I thought the Commodore 64 game Saboteur II was Saboteur 11, so I shouldn’t judge)
  • Numbers whose digits add up to 11, if you keep adding the digits of the result until you get to 11
  • Dates whose digits add up to 22, if you keep adding the digits of the result until you get to 22
  • Phrases that have two consecutive As in them (because A is the first letter of the alphabet)
  • Numbers that have two or more consecutive 1s in them
  • Numbers that have two or more non-consecutive 1s in them, separated by zeroes
  • Numbers that have 2 in them

It was clear to me that if you look hard enough, you can find 11s anywhere. Not only that, but you could find whatever other smallish (under 1000 or so) numbers you’re looking for. So I wrote code to look for a lot of these things automatically, and put it in an iOS and macOS app called Arithmancy Pants. It’s called that because ‘Numerologist’ was taken, arithmancy is an older word for numerology, and I’m a two-time Fancy Pants Parade winner.

I broke down everything into independent steps, so that we can find as many numbers as possible without doing the same thing twice — for instance, instead of converting AA to 11, we first convert it to 1, 1, and then concatenate them in a separate step to make 11.

Here are the things Arithmancy Pants can do in its quest to find numbers:

The 'Divination' tab for Arithmancy Pants on macOS, with checkboxes and examples for all the different strategies it could use to find numbers
Selecting which strategies to use in Arithmancy Pants for macOS
Arithmancy Pants for iOS, with a chart in the top half and a sheet in the bottom half that has options for 'Log scale', 'Snap selection to nearest found number', 'Limit to numbers less than…' and 'Color bars based on step count'
Chart settings in Arithmancy Pants for iOS
  • Convert text into numbers
    • by converting letters to their positions in the alphabet — Uri only uses this one for converting A to 1, but I’ve seen it quite often elsewhere
    • by taking the number of letters in each word — this covers all the 11-letter words, and when combined with ‘adding up all the numbers’, covers other names and phrases with 11 total letters.
    • by finding numbers that are already in the text, and letters that look like numbers — this covers the EIIR example.
  • Convert numbers into other numbers
    • By adding up the digits until they sum to a single digit (also known as digital root, this is equivalent to finding the remainder when dividing the number by 9, except using 9 instead of 0 unless we started at 0.)
    • By converting each number into Roman Numerals — I think I only added this because I’d already written code to do that for something else. However, this covers the ‘numbers that have 2 in them’ case, as we can convert 2 to 11 by converting it first to II, and then to 11 by converting letters that look like numbers. This is a much more manageable way of turning 2 to 11 than adding a generic ‘convert each number into every possible combination of numbers that add to that number’ step.
    • By adding up numbers
      • Adding up all the numbers — this covers most of the adding-up cases on Uri’s page
      • Adding up numbers in groups of up to 2, 3, 5, 7, and 11 numbers. By using prime-sized groups, in multiple steps we can add the numbers in groups of any size — e.g., we can add up groups of 6 numbers by first adding groups of 3 numbers, then adding those results in groups of 2.
    • By concatenating numbers — combined with converting letters to their positions in the alphabet, this covers converting AA to 11
      • Concatenating all the numbers
      • Concatenating numbers in groups of up to 2, 3, 5, 7, and 11 numbers.

I stop at combining groups of 11, because while I could handle even larger numbers internally by using a different data type:

  • I’ve got to stop somewhere, and not many people’s supposed lucky numbers have enough digits for concatenations or sums of multiples of 13 numbers to matter.
  • I show charts of the numbers found, and there seems to be a bug (FB20491693, if you’re at Apple) in Swift Charts when I include more than one result that would convert to the same Double value. So I’m limited to final numbers under 253.
  • 13 is an supposedly an unlucky number anyway.

The app shows the final numbers you get when you complete enough of these steps to get down to a single number. On another tab it shows the intermediate numbers found alongside other numbers partway through the process. You can also explore the results yourself by expanding each intermediate result to see what was derived from it in the next step.

Explore Results screen in Arithmancy Pants for macOS

Note, there were many years between when I saw that page and when I actually wrote the app. So I don’t cover:

  • Words that sound like numbers. I could have easily done something like this, at least on macOS, as I have a lot of experience with the text-to-speech APIs, but I simply forgot that was one of the tactics. Actually, I would probably just have a list of known words (too, to, for, non-rhotic Severn, etc.) that sound like numbers, or perhaps I would derive such a list by searching through a lot of text using the text-to-speech API. Uri’s suggestion of ‘hellheaven’ would not have come up though, since it doesn’t actually sound like eleven.
  • Numbers that have consecutive or non-consecutive ones in them… although, this depends on how we got the numbers. If we obtained 10001 by concatenating 10, 0, 0, and 1, we would also have added those numbers to get 11.
  • Stopping halfway when calculating the digital root — e.g., adding up the digits of 254 to get 11, but not continuing to add up the digits in 11 to get 2. I just take the remainder when dividing by nine to do the whole thing in a single step, so this won’t even be shown in the intermediate values.

I think that’s all I have to say about that… as I mentioned in my last post, this could also be a MathsJam talk some day. You can download the app for free on any device running macOS 26 or iOS 26. You could use it to debunk the claims of numerologists, or to make your own claims for fun — but please don’t use it to take advantage of gullible people.

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