Posts Tagged mathematics

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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Holiday Inn Express Geometry


On our road trip across the USA, Joey Marianer and I stayed at many Holiday Inn Express hotels. I noticed that (at least for the Eastern side of the country) they had a lot of geometrical decor. In particular, some intriguing wallpaper, which I will analyse in the second hald of the post.

But first, some other geometrical art. For instance, this art made of triangles, shown here with a copy of the book I read on the trip, Matt Parker’s ‘Love Triangle‘:

Matt Parker's book held up in front of a framed artwork made up entirely of triangles of different colours, with mostly coloured triangles toward the top right and more white triangles (separated only by light grey borders) toward the bottom.

This art featuring hexagons, and occasional quadrilateral half-hexagons:

A framed abstract artwork made of rings of coloured rings of hexagons each with a white hexagon in the middle. On the top half the hexagons are mostly yellow, and on the bottom half they're mostly grey, but in between there are some red and purple rings. Sometimes, where the rings meet, the hexagons are split in through the middle, with a different colour on each side. There are also occasional lone red or purple hexagons as part of yellow or grey rings.

And this art with triangles inside hexagons!

A framed abstract artwork made up mostly of grey hexagons, though there are some freestanding triangles and some parts that are yellow, blue, green, or orange. Most of the hexagons have triangles drawn inside them (also usually grey) and each triangle has a smaller triangle at each of its corners.

This door decorated in triangles, diamonds, and parallelograms:

A sliding door divided into triangles, diamonds, and parallelograms in various colours

This more abstract collection of overlapping quadrilaterals making the occasional triangle:

Various diamonds and rectangles in different translucent colours, overlapping to form other shapes where they intersect.

Then there are perhaps less-artistic tesselations which I might not have noticed if not for the other decor. For instance, this couch featuring two different kinds of triangle:

A couch patterned with rectangles that are each divided through the centre into either four or two triangles (with the two-triangle rectangles being in groups of four so they could be seen as an eight-triangle square), with most triangles being grey or off-white, but some in pink or green.

This floor which seems to have at least two different lengths of floorboard:

Floorboards, some of which reach all the way across the picture, others of which are only about a third of that width.

This bedspread tesselation of diamonds and parallelograms:

Shiny white fabric with matte white lines making a design of diamonds surrounded by parallelograms, such that it could be interpreted as a lot of square steps viewed from an angle.

Now, onto the wallpaper. This was present in many different Holliday Inn Express hotels. Here’s the photo I took:

Off-white wallpaper with line art of a complicated pattern of various sizes of rectangles, some of which are divided into two triangles, and some of which have diagonal lines going only part of the way across them.

Here it is after I unskewed, cropped, and lightened it in GraphicConverter:

This raises a lot of questions:

  1. What is the repeating unit here?
  2. Which wallpaper group is it?
  3. What’s with all those lines that don’t meet the other side? Would the pattern make any more sense if I completed them?
  4. Is there some kind of pattern to the way the rectangles, the rectangles divided into triangles, and the rectangles with unfinished lines in them are arranged?

Okay, to answer the first question, here I’ve cropped it to show enough of the repeating units to recreate the whole thing, and converted it to black and white so we’re not distracted by the lighting:

At this point I switched from GraphicConverter to OmniGraffle. Here I’ve drawn in the repeating tiles:

A black and white representation of the wallpaper, with purple and orange rectangles surrounding parts of it

There are two kinds of tile, which I’ve outlined in solid purple and dashed orange. Vertically, the two kinds of tile alternate. Each column of tiles is offset vertically by half a tile from the ones next to it, so if you follow across the wallpaper, you’ll be alternating between top and bottom halves of tiles, and they might all be the same kind of tile, or they might be alternating kinds of tile, depending on where you start.

It took me a while to realise (actually, I think Joey pointed it out), but the orange tile is in fact the same as the purple tile, just flipped horizontally. That means we have what’s called a glide symmetry, or glide reflection — it’s like a reflection, but the reflection is moved along. The classic example of a glide symmetry is a trail of footprints — the two feet are mirror images of each other, but since they were walking when they made the footprints, they are never exactly next to each other.

So that means we can answer the question about wallpaper groups. It’s a rectangular lattice with only glide symmetries, no rotations or reflections. That’s called pg, and you can see other examples of it on wikipedia.

Here’s a single tile of it, from which we can construct the whole wallpaper:

One of the outlined rectangles from the image above

It has 43 triangles (mostly in rectangles divided into two triangles, but there’s one divided into three triangles on the bottom left), 24 plain rectangles, and 5 rectangles that have a diagonal line going partway across them.

Okay, so onto question three. What’s with those lines that don’t quite reach the other side? Here, I completed them, and approximately measured the angles using the arc tool in OmniGraffle (I use OmniGraffle for a lot of things that aren’t graphs. For instance, this quark explainer, and the icon of my next app.)

The same tile shown above, but with each partial diagonal lines continued to meet the other side of its rectangle, and the angles drawn in as 41°, 43°, 56.6°, 64°, and 40°.

There. Is that enlightening? No. Is that satisfying? Also, no. Two of the lines pretty much reach the other corner, if you squint, and three of them don’t. But perhaps knowing that you can give up on making any sense of this will give some relief.

Ah, but what about the arrangements of the three kinds of rectangle? Surely there’s something interesting about that. I haven’t found it, but maybe you could. Here’s a single tile, with a purple rectangle pattern for the plain rectangles, a pink zigzag pattern for rectangles divided into triangles, and a green pattern of short lines for rectangles with maddening partial lines in them. I’m not sure how useful the redundant coding is here, but it can’t hurt.

I’m not sure why I didn’t colour the three-triangle rectangle near the bottom left in a different colour from the two-triangle rectangles. I made these a while ago. [Next day edit: This bothered me too much to ignore. See below for a version with a different colour for that rectangle.]

I can imagine the letter P and a dog standing on its hind legs in pink, but I don’t think there’s any kind of hidden message here. Just to be sure, here’s the colourised version extended to show more of the wallpaper:

Well now perhaps there are a bunch of dogs walking past each other doing the can-can. Do you see any interesting geometry or other mathematics that I missed in any of these images?

Next-day edit: Here’s a version with the three-triangle rectangle in checkered orange. I accidentally used a different shade of pink, but the shade of pink had no mathematical value, so it’ll do:

And here’s a larger section of wallpaper using that version:

When I took these photos, I thought they might make a good talk at the MathsJam Annual Gathering. We ended up deciding not to go this year (though we’ll probably join virtually) so I won’t be giving that talk. I have also made a new app which could be the focus of a MathsJam talk. I have submitted it to the App Store, so I hope it will be out very soon.

On the subject of apps, I got a job offer, though I haven’t started work yet. That means I’ve released a new version of Seddit, my text-to-speech-focused Reddit reader, where the only update is that it no longer says I’m looking for work on the ‘Support Seddit’ tab of the settings.

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Sailing off into the sunset toward America


As mentioned previously, I have an idea for a music video I’d like to make about my move to the US. But before I make that, I wanted to publish some of the video I took on the trip, in a fairly raw and unedited way, just to get it out there. I already published hours of 4K video from the ship leaving Hamburg, leaving Southampton, and arriving in New York City, recorded with my Sony ZV1 camera on a tripod.

Well, it was time to put together whatever random video I took with my iPhone. And I was just going to stick it all in a video with fades between clips, but there really wasn’t much going on in terms of sound — it needed music. And of course if there was going to be music, I’d better edit the footage a bit more to fit in with the music. So I ended up making something of an impromptu music video. Probably the coolest part (other than the music) is the sunset I recorded from the front of the ship one evening.

The song is ‘America’ by K’s Choice, as covered by my friend Joseph Camann when I requested it on his Patreon. Joseph is a multifaceted and multitalented individual who is also known as Chromatic Verse (mostly for visual art) CamannWordsmith (mostly for writing) and Joseph and the Bear Hat (for song covers.) It is unclear which parts the bear hat played in this cover.

I initially thought that the song ‘America’ would work better for the road trip across America than the trip across the pond, so I spent some time trying to find something else for this one… but come on, ‘America’ has a line about the sun rising and falling, and most of the video is a sunset. How could I not? Also there’s the double bonus of publicising both my friend Joseph and also one of my favourite bands, K’s Choice.

A day or so after we got to NYC, we visited MoMath, and I recently realised that while I’d put up video of Joey Marianer riding a square-wheeled tricycle there, I had forgotten to edit the other video I took of Joey at MoMath. Here’s Joey changing some benches from a triangle shape to a square and back, set to one of the free jingles that comes with Final Cut Pro:

That’s it for now. Stay tuned for a video of whatever I recorded on my phone during our ensuing road trip across the US, which I will inevitably spend more than the expected amount of effort on!

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Circles (Soul Coughing parody lyrics)


These lyrics are to be sung to the tune of ‘Circles’ by Soul Coughing. They refer to the proposition that we use tau (τ) defined as 2π, instead of pi (π), counterarguments to that, and neverending friendly rivalries about it.

When you were younger you were taught a circle formula
That its perimeter is πd, that is, 2πr
πd gets you all round the circle
All around the circle, all around the circle
All around it
πr’s just halfway round the circle
Halfway round the circle, halfway round the circle
Halfway round it

And now you’re older, there are folks attempting to convince
That 2π’s τ and you should use it for circumference
τr gets you all around the circle
All around the circle, all around the circle
All around it
πr’s just halfway round the circle
Halfway round the circle, halfway round the circle
Halfway round it

Pi-tau-pi-tau-pi
Am I coming or going?
Tau-pi-tau-pi-tau
Am I halving or doubling?
Pi-tau-pi-tau-pi
Am I coming or going?
Tau-pi-tau-pi-tau
Am I halving or doubling?

But I can’t find out what’s the area
It was πr-squared, and now, τr squared on two
τ is now twice, π can do everything
Change it to τr, and complicate the formula

πr-squared is all around the circle
All around the circle, all around the circle
All around it
τr-squared’s twice around the circle
Twice around the circle, twice around the circle
Twice around it.

This row*’s just going round in circles (*with ‘row’ rhyming with ‘cow’, meaning ‘fight’)
Going round in circles, going round in circles
Round and round them…

(repeat entire song indefinitely)

I was not familiar with the original song, but we saw Holy Bongwater perform Nurples at FuMPFest 2024, and when I found out it was a parody of a song about circles, I knew what I had to do. I was motivated to finally finish it by a deadline for a maths music feedback group with a group of people I know from MathsJam. There were a few suggestions, but nothing that stood out as being a definite improvement — it was π of one, half a τ of the other, really. So I’ll put the lyrics here, and you’re welcome to sing them or change them as you see fit. They’ll likely be sung at MathsJamJam this year, perhaps along with This Tiling Never Repeats, which wasn’t sung last year because not enough people were familiar with the tune (and it’s a little harder to get the hang of than this one.)

In other news, after watching Star Trek: The Next Generation, Joey and I watched all of Lower Decks, and have got several seasons through Deep Space Nine. I now know that the combadge I put on my Star-Trek-like dress (which most closely resembles Starfleet cadet uniforms and Deep Space Nine uniforms) is only used for the first two seasons of Deep Space Nine, so the person who told me I had the wrong combadge for the dress was probably thinking of later seasons of DS9.

Since my last post I finished Advent of Code 2024 (which it turns out does not necessarily get more difficult each day, but does continue to be fun and somewhat nerdsnipy), did some more LeetCode exercises, did the final round of interviews for the job that had recommended practising with LeetCode, and did not get the job. So, I’m still looking, but now I feel pretty well prepared for most kinds of interview that could come my way. Meanwhile, I’ve started making a new multiplatform (iOS/macOS) app that a friend of mine always wanted to exist. A very rough, but functional, version of it is on TestFlight already. If you are a big Reddit user, and especially if you are also blind or visually impaired, you might want to try it, but please be aware it is in the early stages and there are many things I already plan to improve.

I have also uploaded a video from when we arrived in New York on the Queen Mary 2. I’m currently doing some light editing on a video from when we left Southampton, which I had forgotten I filmed. As mentioned previously, I still have more videos of my move to edit. On the more practical side, I’ve finished unpacking all my boxes, and filled my shiny new bookcases with books, and my new CD/DVD racks with CDs, DVDs, and also books.

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I swam halfway across the Atlantic Ocean, and now I live in the USA


I keep thinking I shouldn’t post here until I’ve processed more of my photos and videos, updated my apps so I’ll look better for potential future employers, etc, but if I did that, the post would be absurdly long and late. This situation is of course fractal — I keep thinking I shouldn’t release my apps until I’ve fixed all those bugs, got everything working in VoiceOver, etc., but if I did that (as I have, many times in the past) the apps would simply never get released.

So, today I’ll write a blog post, and tomorrow I’ll either put my new macOS app on TestFlight, or submit new versions of NastyWriter and NiceWriter (which don’t work very well in the latest iOS, and also will fail to show ads because I’m halfway through moving my ad accounts to a new country.) Bug me if I don’t, and let me know if you want to test the apps. I should decide which one to release already so that I can focus on one thing at a time, but right now I’m focussing on writing this blog post, not on deciding which apps I can realistically get ready. See what I did there?

First things third: I made it to my new home in the Seattle area! I’m busy se(a)ttling in, changing all my online accounts to the new country (I’ll write a separate post about which hoops have to be jumped through for which accounts), and casually looking for work.

My lovely husband Joey Marianer came to Vienna to help with the moving, and many of my friends helped by taking my furniture and other things I didn’t need to keep. Then Joey and I took a train to Hamburg, the Queen Mary 2 ocean liner to New York City, and a road trip to our home in the Seattle area. It was of course in a pool on the Queen Mary 2 that I swam while we were halfway across the ocean.

Here’s a chart of all the days Joey and I have known each other, with appropriate emojis for the days we were together in person, and black squares for the days we weren’t. It was made by the aforementioned new app, which I started writing in an airport lounge one time when Joey’s flight left several hours before mine. This chart ends on September 6, 2024, because that way it would make a nice 49×56 rectangle. It also shows our first 256 days together, which is a nice round number in binary.

A 49x56 grid, mostly full of black squares, but with some pale pink squares with various country flags, ship, train, and car emoji. There is also a ring emoji and a church emoji.

I’d never been to New York City before, so (after the no-longer-obligatory trip to Ellis Island the day I immigrated) we stayed for a few days before continuing. High on our list was visiting MoMath, the National Museum of Mathematics. I have a few videos from that, but here’s the one I’ve uploaded, of Joey riding a square-wheeled tricycle on a circular track made of inverted catenary curves:

Also in New York, we visited Liberty Island, Central Park, the Oculus, a few Sabrett’s hot dog stands, an annex of the Transit Museum, and the Apple Store on 5th avenue. I tried a rainbow bagel, some poorly-configured hot dogs (a friend from New York had recommended a particular combination of toppings, which neither stand gave us), and an Apple Vision Pro — I’d tried a friend’s one before, but without corrective lenses.

On the way home we stopped to meet friends in Toledo, Chicago, and Minneapolis. We visited Tony Packo’s (which has a large collection of autographed hot dog buns), Portillo’s (which has trays with deep recesses for cups, making it much easier to carry drinks around), American Science and Surplus (which has amusing signs and muzak) and the Minnesota State Fair (which has food on a stick).

Here’s a playlist of videos and podcasts that Joey and I showed each other because of things we saw during the trip:

There’s obviously a lot more to say and show about all of this, but I have to go finish some apps, so here’s a picture of the Statue of Liberty that I took from the Queen Mary 2 (previously posted on X and mathstodon).

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We did a Christmas


I’m visiting Joey Marianer for Christmas, so we sang a slowed-down cover of a Worm Quartet song, as Joey is wont to do.

Worm Quartet is also known as Timothy F. Crist, so we wished everyone a merry Timothy F. Cristmas at the end. I hope you had one of those, whatever it means. I don’t see why anyone wouldn’t celebrate such a talented comedy musician.

I did actually try some of that eggnog (‘milk that have a alcohol and then we put a egg’ except that this one didn’t have a alcohol.) The few times I’ve had eggnog before, I’ve thought that the alcohol ruined what could have been a very nice drink, so I was excited to try some non-alcoholic eggnog. Not only that, but I tried it mixed with orange soda, as recommended on the Judge John Hodgman podcast. I really like it both ways! It’s also good with orange juice.

In unrelated news, we went to the MathsJam Annual Gathering, where Joey gave a talk on the true prisoner’s dilemma, and at MathsJam Jam we sang Symmetry and Seven Bridges (of Königsberg) Road. Ben Sparks taught everyone the harmonies for the Eagles version of Seven Bridges Road to sing Seven Bridges (of Königsberg) Road, and it was fantastic.

We didn’t sing This Tiling Never Repeats, because nobody (not even me) knew the music well enough. But on the Saturday of MathsJam, Joey and I wore Cirque du So What ‘I Want TILE!’ shirts, and I did in fact come away with a few handfuls of 3D-printed spectre aperiodic monotiles. Surprisingly, there were no aperiodic monotile shaped baked goods in the MathsJam BakeOff.

A whole lot of plastic tiles, all in the same complex, curvy shape, tiled together. They fit together in a way that doesn't allow the pattern to repeat.

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This Tiling Never Repeats (Split Enz parody)


I mentioned in a previous post that I was working on a parody of History Never Repeats, by Split Enz, about the aperiodic monotiles that have been found recently. I’ve finished it, so here are the lyrics:

This tiling never repeats
Unending plane the kite and dart complete
We wish to show we can improve
We may assume, there’s always more to prove
It was the best we used to know
From David Smith, a savage blow
Penrose is great, but now we sing
A monotile beats his tiling!
This tiling never repeats
But some might say, reflected tiles are cheats
We wish to show we can improve
We may assume, there’s always more to prove
You say we’ve all been played for fools
We can’t reflect, if that’s the rule
Better to work than make dispute
They made a change and now it’s moot
This tiling never repeats
There’s not a need the Spectre doesn’t meet
And there’s a way to make more and more
Leading us to a space we can explore
This tiling never repeats, this tiling never repeats
Infinite shapes, just turn the dials
Aperiodic monotiles
Pick one and all the plane is spanned  
We think at last we understand
This tiling never repeats
A manifold with manifold defeats
And there’s a way to make more and more
Leading us to a space we can explore
Never repeats!
Never repeats!
Never repeats!

This joins Symmetry and Seven Bridges (of Königsberg) Road in Joey’s and my submissions for this year’s MathsJamJam. Joey Marianer (yes, the one that I’ve somehow ended up married to!) also sang (and sent for inclusion in the Jam) Polygon Pam, a parody of The Beatles’ Polythene Pam written by Chella Quint:

I look forward to seeing Joey at MathsJam (and then Chella afterwards) and singing them together! I also look forward to eating some aperiodic monotile confections which will inevitably be baked for the MathsJam BakeOff.

I mentioned in a different post that Joey had been working on some cover songs which I was excited to share. The one I was most excited about is a slow cover of Entire Dog by Worm Quartet. It lasts almost twice as long as the rather frenetic original, and Joey initially sang it this way completely off-the-cuff one day over FaceTime. After a few slight revisions, I declared it was so good it should be stolen and used on Glee. But Joey kept singing it to me and making it even better.

If you think Joey made a mistake with some SI prefixes, read the video description. To really tie the post together, here’s a slow cover of a frenetic Worm Quartet song that also mentions math — and other kinds of multiplication… let’s just say it’s NSFW — Tired Of Not:

Both of these songs are on Worm Quartet’s new album, Carpe Tedium, which I highly recommend. Joey has been practising genre-benring covers of several more tracks from it, too.

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A few mathematical numbers


My last post had Joey Marianer (to whom I was flabbergasted to be married) singing some lyrics I wrote, and mentioned that we would soon be at the MathsJam Annual Gathering, and that I’d uploaded all my JoCo Cruise footage for that year. Well, in my aperiodic compiling of blog entries, I have reached a familiar local pattern. Joey (to whom I am still gobsmacked to be married) has sung more lyrics I wrote, we are once again planning to go to the MathsJam Annual Gathering, and I have uploaded all my JoCo Cruise footage for 2023.

A Cake of Sets

At my first MathsJam Annual Gathering, I gave a talk involving one poem I wrote and several that I found. At the 2019 Gathering, Joey and I participated in the competition competition with a Hallelujah competition. At last year’s Gathering, we added some set theory to the Bakeoff with this (cheese(cheesecake)cake) Venn diagram:

An edible Venn diagram consisting of most of a circle of cheese on the left, most of a circle of chocolate cake on the right, with a lens shape of cheesecake where they intersect.

It was mentioned in this excellent summary TikTok by Ayliean!

We assembled it on-site from store-bought cheese, cake, and cheesecake. What with travelling internationally to MathsJam, it would have been impractical to (cheesemake(cheesebake)bake) it ourselves.

A Set of Songs

At this year’s MathsJam, we will add to the set list of the MathsJam Jam.

Symmetry

To start with, we noted an existing theme of symmetric relations in the lyrics of The Beatles’ song ‘All You Need is Love’ and made it explicit. Here’s Joey singing our parody, Symmetry:

Here are the lyrics:

Symmetry!
Symmetry!
Symmetry!

There’s nothing that is x that x is not
No ex where you’re not an ex they’ve got
The symmetry says that the relation goes both ways
It’s easy!

If you’re my sibling, I’m your sibling too
You’re married to me and I to you
Each of these relations is the same as its converse
It’s easy!

x relates to y
x relates to y
x relates to y, why? ’cause y relates to x

If one real number’s greater than the other
Or maybe I’m your son and you’re my mother
Such relations exist, but symmetric ones top our list
They’re easier

When x relates to y
x relates to y
x relates to y and y relates to x

x relates to y
x relates to y
x relates to y, why? ’cause y relates to x

Seven Bridges (of Königsberg) Road

I’ve also written a first draft of a parody of the Steve Young song ‘Seven Bridges Road‘ about the Seven Bridges of Königsberg. Joey hasn’t sung this one, but I intend to enter it into the MathsJam Jam songbook (where there is already a parody of ‘Lola’ about the same topic.) Here are the lyrics:

There are rivers in Königsberg
Cross them as you go
Don’t forget one and don’t you repeat
On the Seven Bridges Road
Now each land mass must have odd or even
Bridges to and fro
Arrive but don’t leave in the same way
And Euler’s work did show
Sometimes there’s an odd one out
How to turn from there and go?
No way for a path with these few rules
Down the Seven Bridges Road
There are rivers in Königsberg
And if ever you decide you should go
There is a way by backtracking only
Down the Seven Bridges Road

Note, this is purely based on the way Jonathan Coulton and Paul and Storm sing Seven Bridges Road when they’re not pretending to be tone-deaf. If other artists sing it differently, the prosody might not work out as well.

This Tiling Never Repeats (in progress)

I’m also working on a parody of History Never Repeats by Split Enz called This Tiling Never Repeats, about the recently discovered aperiodic monotiles, which I am sure will be a big feature of this year’s MathsJam. I expect there to be at least three sets of aperiodic monotile cookies entered in the Bakeoff. I’ve only just started with this parody, but figured I’d mention it in case anyone wants to give me ideas for it, encourage me to finish it, or even write their own. I don’t mind who writes it as long as it exists and is sung at MathsJam.

A Song of Cakes

This section title is just for completeness, and because I needed something to separate the last song from the outro. I know too many songs about cakes to pick one.

As many people contemplate the value of X, I’ve created an account at what is obviously the best-named Mastodon server, Mathstodon. Feel free to follow me there! I don’t know yet how frequently I will post on it and/or my Twitter profile, but at least now you know where to find me if you’re on those networks.

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My Poetry Show on JoCo Cruise 2021


I’ve been going on the JoCo Cruise since the ‘shadow cruise‘ was just an iPhone handbell choir. As it developed into something people could book spaces and times for, and have on a schedule that packed 26 days of events into a week, I participated in a few friendsshadow events, but hesitated to run my own in case it conflicted with something else I really wanted to do, or had me nervous or practising instead of enjoying other events.

This year, the cruise went virtual, and my excuses went out the window. I registered to do a poetry show, promising that I would ‘recite some poems that rhyme, some that don’t, and maybe even sing a few things. Topics may include science, love, poop, and life.’ I came to realise I could not only read my poems from my screen to avoid any nervousness about remembering them, but I could also share my screen. There are projectors on the cruise, but they are in short supply, so I wouldn’t request one for just one or two poems in a shadow event. On the virtual cruise, I could share whatever I wanted, including things from the internet, which wouldn’t be reliably available on a ship. And I could use props that I wouldn’t bother to bring on a cruise. So I did! I made slides for poems that worked best with visual aids, I showed off my rhyming dictionary, and I closed with a cover song that requires a video. And of course, I recorded everything. Here’s my show!

I also performed a few poems at the open mic — hastily-adapted versions of a poem I wrote for the Vienna open mic Open Phil, and the one I opened my show with about the differences between the real cruise and the virtual one. Joey Marianer and Phil Conrad (who also hosts Open Phil) hosted the open mic, so the open mic videos are on Joey’s channel.

It sure was weird watching Joey upload videos, when usually I’m spending most of my free time from March to May processing videos from the cruise. On the subject of cruise videos, the videos of the official events will allegedly only be up until May 1, so watch them while you can!

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Things I forgot to blog about, part n+1: NanoRhymo #2


In November 2018 I created NanoRhymo (inspired by NaNoWriMo), in which I wrote and tweeted a very short rhyming poem every day. I did the same thing in April 2019 for Global Poetry Writing Month. I started pretty late with NanoRhymo in 2019, and didn’t end up with a poem for each day of November, but I’ve started it again on January 1 and made up for the missing poems. In November, I mostly stuck to writing something based on a random rhyme from the rhyming dictionary I made, rhyme.science — either a new one I’d found each day, or one generated earlier for the @RhymeScience twitter feed. In January, I’ve often been inspired by other things.

I’ll continue writing a NanoRhymo a day for as long as I can. Here’s what I’ve written so far:

Day 1,  inspired by the rhymes later, translator, and (in non-rhotic accents) convey to:

When you’ve got a thought to convey to
many mortals, sooner or later,
then you ought to get a translator.

Day 2, inspired by the rhyme chunked and bunked, and the folk etymology of ‘chunder’:

Sailors lying in their bunks
would shout “Ahoy there, mate… watch under!”
and then let loose digested chunks
on hapless seamen sleeping under.

That’s why even now, down under,
[I am lying; truth debunks!]
some refer to puke as chunder.
[This is half-digested junk
Please accept my weak apology
and not this doubtful etymology.]

Day 3, inspired by a friend’s experience learning flying trapeze:

My friend Robert Burke tried the flying trapeze.
It meant lots of work mulling hypotheses,
and then much amusement and catching catchees,
to end up all bruised on the backs of the knees.

Day 4, inspired by the rhyme spermicides and germicide’s:

Looking at small things up close and myopically,
one might prevent overgrowth with a germicide.
But looking at large things afar, macroscopically,
one must prevent unchecked growth with a spermicide.

Day 5, inspired by the rhyme explainable and containable:

As soon as the bug is explainable,
we can hope that it might be containable,
and our neural nets will be retrainable,
and our code is so very maintainable
that this progress is surely sustainable!

Day 6, inspired by the rhyme freaking and unspeaking:

Mouth agape, stunned, unspeaking
Eyes wide open, silent freaking,
What could this strange vision be?
a music video, on MTV?!

Day 7, inspired by the rhyme trekked and collect:

Over much terrain they trekked;
specimens they did collect,
to show just how diverse life was
before we killed it off, just ‘cause.

Day 8, inspired by the rhyme interleaved and peeved:

If rhyming couplets leave you peeved,
here, I tried ABAB.
Now the rhymes are interleaved!
This rhyme and rhythm’s reason-free.

Day 9, a rewrite of Day 8 that can be sung to a possibly recognisable tune:

If rhyming couplets leave you peeved,
Then try to make them interleaved
Or don’t, and then just let the hate flow through ya
Just AAB, then CCB
This rhyme and rhythm’s reason-free.
At least it can be sung to Hallelujah.

The most Hallelujest Joey Marianer sang that version:

Day 10, inspired by the rhyme platitudes and latitude’s, and my general dislike of casual hemispherism:

I’m just fine with the end-of-year platitudes —
“Happy Holidays”, nice and generic,
but please, be inclusive of latitudes:
“Happy Winter” is too hemispheric!

Day 11, another Hallelujah, inspired by Joey’s singing of the previous Hallelujah:

A kitchen scale, a petrol gauge,
a cylinder, a final page
will tell you up to what things have amounted.
An abacus, a quipu string,
some tally sticks, to always sing,
are all things on which Joey can be counted.

Day 12, inspired by the rhyme deprecations and lamentations, some deprecated code I was removing from the software I develop at work, and also complaints about macOS Catalina dropping support for 32-bit applications. I imagine it sung to the tune of Camp Bachelor Alma Mater:

Hear the coders’ lamentations
over apps that will not run,
due to years-old deprecations,
updates that they’ve never done.

Day 13, inspired by the rhyme whoop’s and sloop’s, and the tradition on JoCo Cruise of ending the final concert with the song Sloop John B:

Have some more whoops on me,
hearing the Sloop John B
as JoCo Cruise comes to an end.
You still have all night.
Hang loose, or sleep tight.
Well, we feel so broke up
but you’ll stay my friend.

Day 14, to the tune of Morning Has Broken:

Something is broken;
look at that warning!
Unbalanced token.
Unknown keyword.
Raise the exceptions.
Erase all the warnings.
Raze preconceptions wrongly inferred.

Day 15, inspired by Hilbert’s paradox of the Grand Hotel:

The rooms are all full for as far out as they can see;
such a big guest house to fill, but oh well.
What’s this? Nonetheless, there’s a sign saying vacancy!
There’s always more room at the Hilbert hotel.

Day 16, inspired by the rhyme feeling’s and ceilings, and the song Happy, by Pharrell Williams:

Clap along if you feel like a room without a roof. 👏
Please applaud if you think you’re a chamber with no ceiling. 👏
Clap along If you feel like happiness is the truth. 👏
Please applaud if you think there’s veracity in good feelings. 👏

For day 17, I let Pico, emacs, ed, vi count as the NanoRhymo, even though it does not mention the text editor nano.

November ended with no more rhymes, but I started it up again on January 1, simply because I was inspired to, and I continued to get ideas every day since. I’m not promising to keep this up daily all year (indeed, I promise not to keep it up during MarsCon and JoCo Cruise 2020) but I’ll post NanoRhymi whenever I feel inspired to.

Day 18 (on January 1, 2020) was inspired by the rhyme unworthy and incur the:

Don’t worry that you might incur the
sentence, “That person’s unworthy.”
Just try what you wish, and try plenty,
and have a great year twenty-twenty.

Day 19, inspired by the rhyme verb and kerb, but using the North American ‘curb’ spelling because it’s closer to the verb derived from the noun:

If you’d punch down, or kick to the curb
for verbing a noun, or nouning a verb,
researching the past will amount your disturb.

So many of the words we used today, including some in that poem, were once strictly parts of speech other than the ones they’re used as without a second thought today, and people objected to their shifts in usage just as they object to all manner of language change today.

Day 20, inspired by the rhymes occur to, Berta, and (in non-rhotic accents) subverter:

If it were to occur to Berta the subverter to hurt Alberta,
she’d prefer to assert a slur to refer to her to stir internal murder.
(Stones break bones but names make shame — heals more slowly, hurts the same.)

Day 21, inspired by the rhyme unconcealed and unpeeled:

While you’re growing in the field,
all your goodness is concealed,
till some lovely creature picks you,
doesn’t think they have to fix you,
lets you chill, let down your shield;
then, when you are fully peeled,
your sweetest inner self revealed,
that cunning rascal bites and licks you.

Day 22, inspired by the rhymes for fish, dwarfish, and (maybe in some non-rhotic accents with the cot-caught merger) standoffish, the ‘teach a man to fish‘ metaphor, and of course, my own poem, They Might Not Be Giants:

If a person’s always asking for fish,
don’t give them one, and go away, standoffish.
Teach techniques that they’ll expand on.
Be the shoulders they will stand on.
Not a giant — generous and dwarfish.

And then the same thing as a limerick:

There once was a man asking for fish,
who got one from someone standoffish.
Then shoulders to stand on
and tricks to expand on,
were given by someone quite dwarfish.

Day 23, inspired by… certain kinds of transphobic people, I guess:

Some folk seem to be offended
by the thought the queerly gendered
might themselves become offended
when they’re purposely misgendered,
so they’ve boorishly defended
all the hurt that they intended
towards the “easily offended”
who are “wimps” to try to end it.

Day 24, a double dactyl inspired by a conversation with someone who’s considering hormone therapy with one aim being a reduction of schlength, during which we noticed that ‘endocrinologist’ is a double dactyl, and also inspired by Paul and Storm’s habit of calling Jonathan Coulton ‘Dr. Smallpenis‘ (with the ‘e’ unstressed) which began on JoCo Cruise 2013:

Dr. Jon Smallpənis,
Endocrinologist,
helps you to shrink all the
parts that aren’t you.

Piss off, dysphoria!
Spironolactone could
soon make you tinkle the
whole darn day through.

Spironolactone is a medication that blocks the effect of testosterone, which as a side effect can increase urinary frequency.

Day 25, inspired by the rhyme eleven words and heavenwards:

Dear Father, a prayer I remember, amen.
Another, sincere from a vendor, again.
As if by reciting just ten or eleven words
I’ll lift myself quite transcendentally heavenwards.

Day 26, inspired by what I was actually told at my first comprehensive annual checkup:

Sit up straight!
Lose some weight!
Take these pills!
Cure your ills!
Your heart is beating!
You’re good at breathing!
With those two habits kept up,
We’ll see you at the next year’s checkup.

They really did seem impressed by how well I could breathe. I wasn’t too good at it when I started, but I have been practising my whole life, and if I’m good then I may as well continue the habit.

Day 27, inspired by this Smarter Every Day video about activating smart speakers using laser light instead of sound:

Here’s a technique that is quite underhand
to beam gadgets speaking they might understand,
and give an unsound and light-fingered command.

This one works best in accents without the trap-bath split, so that ‘command’ rhymes with ‘understand’ and ‘underhand’.

A small, transparent plastic container with a label saying: 105030064 Bodenträger Safety Safety Trans. 20 Stk.

Day 28, inspired by a container of those little dowel things to hold up shelves, which was labelled ‘Safety trans.’, and the song The Safety Dance, by Men Without Hats. This parody is presumedly to be sung by Women and Nonbinary People Without Hats:

You can trans[ition] iff you want to.
You can leave your assigned gender behind.
‘Cause your assigned gender ain’t trans and if you don’t trans[ition],
Well your assigned gender stays assigned.

Day 29, inspired by a video about Jason Padgett, who survived a vicious beating to end up with (among less attractive brain issues) savant skills and a kind of synaesthesia:

Acquired savants suffer pain,
to wake up with a better brain.
Get a bump, or have a seizure,
then end up with synaesthesia —
not the grapheme-colour kind,
rather, an amazing mind!

Day 30 is a version of day 29’s poem which can be sung to the tune of Hallelujah, with a second verse reminding people that synaesthesia is actually pretty common, affecting about 4.4% of people, (I have the grapheme-colour kind) and doesn’t necessarily confer superpowers:

Acquired savants suffer pain,
to wake up with a better brain
by healing from an injury or seizure.
They sometimes get amazing minds
associating different kinds
of input in a thing called synaesthesia.
Synaesthesia, synaesthesia, synaesthesia, synaesthesia.

But synaesthetes are everywhere,
not magical, or even rare.
It doesn’t make them smart or make things easier.
It just makes Thursday forest green,
or K maroon and 7 mean.
Your ‘the’-tastes-like-vanilla synaesthesia
Synaesthesia, synaesthesia, synaesthesia…

This refers to time-unit-color synaesthesia, grapheme-colour synaesthesia, ordinal linguistic personification (also known as sequence-personality synaesthesia), and lexical-gustatory synaesthesia, but there are many other kinds.

Day 31, a parody of ABBA’s Fernando for which I am deeply sorry:

Did you hear he goes commando?
I remember long ago another starry night like this.
In the firelight, commando,
he was wearing his new kilt and playing bagpipes by the fire.
I could hear his sudden screams
and sounds of mountain oysters sizzling in the fryer.

Day 32, inspired by two tweets I saw, each quoting the same tweet where someone had contrasted pictures of Prince Harry in the army with pictures of him with his wife, and claimed that getting out of the army and getting married was somehow emasculation caused by ‘toxic’ Hollywood feminism:

The two tweets happened to rhyme with each other and follow the same structure, from the ‘fellas, is it gay’ meme, so I put them together, and added a few lines:

Fellas, is is gay to have a wife?
Fellas, is it gay to be a human being with a life?
Fellas, is it gay to wear a suit?
Fellas, is it gay to dress to socialise instead of shoot?
(Fellas, is it toxic to be gay?
Fellas, why frame questions with a word she didn’t say?)

Day 33, another Hallelujah parody, inspired by Joey’s observation that NanoRhymo scans:

You want to practise writing verse.
The secret’s to be very terse.
You don’t have to try hard, just have to try mo’.
You write some dogg’rel every day
and some you’ll toss, but some will stay.
An atom at a time; it’s NanoRhymo.
NanoRhymo, NanoRhymo, NanoRhymo, NanoRhymo.

Day 34, inspired by a Twitter thread which began with my friend Rob Rix expressing frustration with type inference, and one of his followers suggesting the term ‘type deference’:

https://twitter.com/quephird/status/1217968127419416576

I love when it complies,
regards me with deference,
and bravely compiles
my unguarded dereference.

Day 35, inspired by… tea. I feel so rich when I make a pot of tea and top it up all day, having unlimited tea without feeling like maybe it’s wasteful to be using my eighth teabag of the day:

If hot tea’s an oddity,
the tea bag’s your commodity,
but if you drink a lot of tea,
you should make a pot of tea.
(To add some boiling water t’
whenever you want hotter tea.)

Day 36, inspired by my efforts to write an AppleScript to copy all my NanoRhymi and GloPoWriMo poems from Notes into a spreadsheet in Numbers, which initially failed because I had accidentally addressed the script to Pages instead, and Pages don’t know sheet:

👩🏻‍💻Hello there! Your finest Greek corpus, to go!
👩‍🍳The what now? Not understand corpus, no no!
👩🏻‍💻The active Greek corpus, the frontmost, the first, display all the corpora you have; am I cursed?
👩‍🍳I’m sorry? Your question is Greek to me… how?
👩🏻‍💻Okay then, just show me your bookcases, now!
👩‍🍳Bookcases? I have none; you’ve made a mistake.
👩🏻‍💻Ah, frack! You’re no linguist! You’re actually the baker!

The spreadsheet, by the way, shows I’ve written about a hundred of these small poems in total so far, in the course of my NanoRhymo and GloPoWriMo stints. I haven’t gone through it checking for notes that didn’t contain completed poems, so I don’t know the exact number yet. In the next roundup of these things, I’ll probably start numbering them based on that total, rather than the ‘days’ of any particular run of them.

Day 37 (today, as I write this), a parody of Taylor Swift’s ‘Shake it Off‘ inspired by another tweet by Rob Rix, in which he notices that a calculation done in Spotlight Search which should give the result zero does not, and remarks, ‘computers gonna compute’:

’Cause the bugs are are gonna ship, ship, ship, ship, ship
And an on bit is a blip, blip, blip, blip, blip
I’m just gonna flip, flip, flip, flip, flip
I flip it off ⌽, I flip it off 🖕🏻

That’s all of the NanoRhymi I have so far; I’ll post more here occasionally, but follow me on Twitter if you want to see them as they happen.

In other news, please consider buying one or all of the MarsCon Dementia Track Fundraiser albums, which are albums of live comedy music performances from previous MarsCon Dementia Tracks, sold to raise funds for the performers’ hotel costs for the next one. The 2020 fundraiser album (with the concerts from MarsCon 2019) is nearly four hours of live comedy music for $20, and includes my performances of Chicken Monkey Duck and Why I Perform at Open Mics.

For yet more music, Joey and I will be participating in round #16 of SpinTunes, a songwriting competition following in the footsteps of Masters of Song Fu. I’ve been following it since the beginning, but never had the accompaniment to actually enter.

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