## Magic: the Gathering and the axiom of choice

After yesterday’s exertions on the golf course, I took it a bit easier today. Mostly I worked on Darths & Droids story planning, but I took a lunch break to walk up to the local shops and get a chicken burger for lunch.

I also had some interesting discussions with friends in our online chat. Some of it was Darths & Droids story planning, so I won’t go into that further. But somehow we segued into a discussion of the phasing rules in Magic: the Gathering – I think prompted by Mark Rosewater’s latest design article, in which he says:

We’re experimenting with making phasing deciduous.

Okay, this probably makes no sense if you don’t know the early history of Magic: the Gathering, but bear with me. Phasing is a rule that first appeared in the game in 1996, but which was considered too confusing and cumbersome to use again. But now they’re playing with bringing it back, at least in a limited way. (“Deciduous” in the above quote means a rule mechanic that they always consider available to include in new card sets if it makes sense for that set.)

Phasing, in essence, is an effect that makes cards in play behave as though they are not in play – they “phase out” for a turn and then reappear. While phased out, nothing can affect them, nor can the phased out card affect anything else. It’s as if they are briefly shunted to another reality.

In the ensuing discussion, I said they shouldn’t merely have one “alternate reality” – things should be able to phase into specific other realities, of which there could be several… or even infinitely many. Then if you have two infinite sets of alternate realities orthogonal to one another, and you reference them by real numbers (i.e. all the integers, rationals, algebraic irrationals, and transcendental numbers), you could phase all of your creatures in such a way that you could duplicate them using the Banach-Tarski theorem. (For a reminder on why that premise leads to that conclusion, refer to my Irregular Webcomic! annotation on the Banach-Tarski theorem.)

Someone of course immediately pointed out that you can only use the Banach-Tarski theorem if you assume the axiom of choice to be true. (For a simple primer on the axiom of choice, see my annotation on that.)

Then someone else said that rule 722.2a of the Comprehensive Rules of Magic: the Gathering (June 1, 2020 edition) might actually imply the axiom of choice. Rules 722.2a says:

722.2a At any point in the game, the player with priority may suggest a shortcut by describing a sequence of game choices, for all players, that may be legally taken based on the current game state and the predictable results of the sequence of choices. This sequence may be a non-repetitive series of choices, a loop that repeats a specified number of times, multiple loops, or nested loops, and may even cross multiple turns. It can’t include conditional actions, where the outcome of a game event determines the next action a player takes. The ending point of this sequence must be a place where a player has priority, though it need not be the player proposing the shortcut.

Example: A player controls a creature enchanted by Presence of Gond, which grants the creature the ability “{T}: Create a 1/1 green Elf Warrior creature token,” and another player controls Intruder Alarm, which reads, in part, “Whenever a creature enters the battlefield, untap all creatures.” When the player has priority, they may suggest “I’ll create a million tokens,” indicating the sequence of activating the creature’s ability, all players passing priority, letting the creature’s ability resolve and create a token (which causes Intruder Alarm’s ability to trigger), Intruder Alarm’s controller putting that triggered ability on the stack, all players passing priority, Intruder Alarm’s triggered ability resolving, all players passing priority until the player proposing the shortcut has priority, and repeating that sequence 999,999 more times, ending just after the last token-creating ability resolves.

The argument is that it is not only possible within the rules of MtG to produce a loop of actions, but nested loops of actions, and at each loop this rule says you can specify how many times the loop is executed. If the nest of loops is infinitely deep, this means that you are effectively choosing an element from each of an infinite number of sets, where each set contains an infinite number of elements. The rules of the game say you can do this. Therefore the rules of the game say that you can apply the axiom of choice.

This is, in mathematical terms, a rather simplistic case and doesn’t (I believe) in fact rely on the axiom of choice to be doable in an actual game (although I may be wrong), but that didn’t stop us having a fun discussion about it. It was topped off by the original proposer of the example of rule 722.2a saying:

I’m not sure what it says about us that I can say “the Magic: the Gathering comprehensive rules imply the axiom of choice” as a throwaway joke, and the responses are “your rule numbering is out of date”, “no they don’t” and “actually maybe they do” (and not, for example, “ha”, “what the fuck”, or “you nerd”).

This is nowhere near the nerdiest argument we’ve ever had, by the way…

New content today:

## Full metal golf x2

My golfing friend invited me to play today at a new course: North Ryde Golf Club. We planned to play the first 9 holes and then decide if we wanted to continue with the second 9.

It’s a nice course, with a few lakes. Being a large green area with water in the middle of urban Sydney, it seems to attract a lot of birds. In this photo (above), which is from the 2nd hole tee, you can see a group of Australian wood ducks.

Hole 3 (above) is a nice short one. The course was busy, and we often had to wait for groups in front of us to move on before we played our shots. After completing the front 9, we decided to continue on and play the back 9. As soon as we teed off on hole 10, it started raining. Steady but not too heavy. We pressed on.

But after a few holes, my friend said his back was starting to ache, so he pulled the plug and left, but I decided to continue and finish the complete round. I was playing behind a group of four who were pretty slow, but there was no point playing through them as they were being held up by at least two other groups ahead of them. So I went into zen mode and just relaxed and enjoyed being outdoors on this chilly, rainy winter’s day.

The rain eventually eased off and I approached the end of the round (hole 17 above). I actually joined up with the group of four for the last hole, and it turned out they were middle-aged beginners as well. They all teed off on the short par 3, hitting their balls in various skewy places. Then I stepped up and cracked my ball straight onto the green! My first putt almost went in too – it was a good 5 metres long, and it curled around the lip of the hole but didn’t fall in, instead continuing another metre or two (requiring another two putts for a bogey, alas).

Overall, I had a good time, getting some exercise, and also spotting all the birds on the course. I saw: Australian magpie, Australian raven, Australian white ibis, Australian wood duck, Dusky moorhen, Magpie-lark, Rainbow lorikeet, Sulphur-crested cockatoo, Welcome swallow, White-faced heron.

With travel time, I was out of the house over five hours. Throw in cooking dinner and walking Scully and that was pretty much the day.

New content today:

## Scully blech

I didn’t sleep well last night, due to Scully getting up at 2am and being sick. Fortunately I grabbed her in time and took her to a wooden floor so she didn’t vomit on the carpet. She hadn’t eaten any dinner either, so it was all just stomach fluid. Something must have upset her tummy yesterday, putting her off her food, and then causing the vomiting.

I didn’t really get back to sleep properly after that. But fortunately by morning she had her appetite back and seemed bright and cheerful all day today. Hopefully she’s got it out of her system. My wife and I took her for a nice long walk, doing our usual Sunday morning loop, which we’ve skipped for a few weeks because it’s been raining a fair bit lately. Today was dry, but overcast and very cold, quite possibly the coldest day of the year so far.

I just looked it up… close. Sydney recorded a maximum of 15.4°C today, but we had a maximum of just 15.1°C on 2 June. Today was actually the second coldest day of the year so far.

New content today:

## Housecleaning Saturday

You can guess from the title that today wasn’t that exciting. I cleaned the bathroom and the shower stall, and washed the kitchen waste bin, and cleaned up the kitchen. Also cleaned out Scully’s ears with a veterinary ear cleaning solution, and the gave her a bath.

Apart from that, my wife and I went to visit her family this afternoon, just to have a chat and an afternoon tea.

I squeezed in some work constructing new Darths & Droids strips, but that was about it really. Not much more to mention today.

New content today:

## A WordPress mess

I got up this morning and checked my email. There was an automated mail from one of my WordPress installs, saying that it tried to do an automated update but something went wrong.

I checked my various blogs and everything looked okay. Then I checked my professional photography site…

The blog and shop were down, showing error messages. I’m running the shop on the site using the WooCommerce plugin for WordPress. It’s given me grief before, and seems a bit flaky and unstable. It performed fine for the public facing pages, which looked good and loaded fine. But all of the administration pages were unstable and gave me time-out errors and internal server errors maybe 30% of the time. I just put up with it, hoping it would magically be okay.

But it looks like this aborted update has really broken things. I could spend time debugging and (hopefully) fixing it, but I’m highly demotivated to even try, because it just seems like an unstable mess that will probably break again at some point.

I’m thinking I need some other solution. I can fairly easily make my own catalogue pages. The only really hard part is accepting payments, doing all the API work with credit card companies or PayPal or whatever and with secure encryption and stuff. I’ve never done that and it would be very bad to get it buggy or insecure. I’ll have to consider for a while.

In other news, today was Luna’s 2nd birthday (the poodle next door and Scully’s best friend). They both went to doggie daycare today, and they held a birthday party, with a special doggie cake and everything. Here’s a photo from the daycare’s Instagram, showing Scully lower left, Luna right, and the cake in the middle.

New content today:

## Full metal golf

I returned to the local 9-hole golf course today for my first game on a normal length course since cutting my hand. (After playing the par-3 pitch and putt course last week.) And I actually went really well. The hand was fine, and I took a bit more care hitting with the driver off the tee, and I ended up scoring my best ever round on that course: 55 strokes for the 9 holes. So that was good!

I spent most of the rest of the day writing annotations for the latest batch of Irregular Webcomic! strips. I spent a good four hours on one of them, ending up with 2300 words, 5 footnotes, 6 equations, a graph, and a diagram. Hopefully it’s both informative and amusing!

I also made some banana “ice cream”, by blending a couple of overripe bananas and a big spoon of peanut butter, and sticking the resulting mush into the freezer. I’m about to try some to see how it turned out…

Mmm, it’s good. And Scully likes it too!

New content today:

## The hat is back

I accidentally left my Akubra hat at the restaurant where I had lunch yesterday. Now you’d think this is the sort of thing you’d notice, walking around in the early afternoon – but it’s winter and I was mostly walking in shade, so I didn’t notice that I was missing my hat until I was a long way from the restaurant, after finishing the entire Flat Rock Gully walk (as described yesterday), and I was well on my way back home.

So today I had to go back to pick up my hat. I’d called yesterday as soon as I realised it was missing, and they confirmed they had it, and were holding it for me. Rather than walk back there today, I drove over quickly to get it.

I also popped into the hardware store on the way, questing for a light bulb. A very specific light bulb. Philips used to make these SceneSwitch™ bulbs. They are LED bulbs, which have some electronics in them, so that when you switch them off and on again quickly, the light level switches between three different settings: 100% more or less daylight colour temperature, 40% and slightly redder, and 10% and redder still. These bulbs are fantastic, and we have them in every room of the house… except the bedroom.

I recently decided to get one for the bedroom too, but alas they seem not to be in production any more, and so far I haven’t been able to track down any stores that still have them in stock. I should mention that there’s another type SceneSwitch™ bulb, which only has two settings, switching between bright daylight colour temperature, and bright “warm” colour temperature – I don’t want those ones, which do seem to have some stock left in places. Also, I need B22 bayonet fittings.

I checked on eBay, and there is one Australian seller with the bulbs I want, but located in Melbourne, and for some reason refusing to ship them, rather strictly accepting local in-person pick-ups only. There are some sellers located in the UK and US, but I’m not paying \$40 to have an \$8 light bulb shipped overseas and probably end up broken by the time it gets here.

I’m guessing Philips has discontinued these bulbs in an effort to get people to use their Hue™ light bulbs. I think they’re a great idea, but the price is very steep. I’d get them if they were cheaper. Anyway, I’ve put the word out to my friends that if they see any of the bulbs I want, to grab them.

New content today:

## Flat Rock Creek walk

A friend contacted me this morning and suggested we meet up for lunch, at a Japanese place a couple of suburbs over from where I live. I walked there (3.26 km according to Strava).

I got there a bit early and was really hungry, so I ordered some gyoza to eat while I waited.

I would have taken a photo of my main dish too, but I forgot in my hunger to get started when it arrived! After lunch, my plan was to walk home the long way, via a walking track that I noticed a while ago on Google Maps, which I’ve never walked before.

And so I set off to the Flat Rock Gully Walking Track. I had a little bit of a walk to get to the starting point. The first part of the walk was paved, and seemed popular with locals out for some exercise.

After crossing under a main road, the path became more of a bushwalk.

The walk followed Flat Rock Creek downstream, which was beautiful in places.

Eventually the creek spills into this cove on Middle Harbour.

This was the ending point of the walk that I wanted to do, but I still had a long walk back home! All together, the post-lunch walk was 9.12 km, for a total walking distance of 12.38 km. I was fairly worn out by the time I got home!

In other happenings, a friend commented on our group chat that he was watching a YouTube video of “stuff that kids are taught that is wrong”, and told us that it mentioned chameleons, and that—unlike what kids are told—they don’t change colour for camouflage, but rather to communicate and find mates. Someone else pointed out that Wikipedia disagrees, as its article on chameleons says they change colour for camouflage as well as those other purposes.

This began a half hour discussion over whether Wikipedia or a random YouTube video is more reliable. Rather than just haggle over it, I decided to check the literature, and quickly found:

• Stuart-Fox, D., Moussalli, A., Whiting, M. J. “Predator-specific camouflage in chameleons”, Biology Letters (2008) 4, 326–329. doi.org/10.1098/rsbl.2008.0173
• Stuart-Fox, D., Whiting, M. J., Moussalli, A. “Camouflage and colour change: antipredator responses to bird and snake predators across multiple populations in a dwarf chameleon”, Biological Journal of the Linnean Society (2006) 88, 437–446. doi.org/10.1111/j.1095-8312.2006.00631.x

These papers indicate clearly that at least some chameleons do in fact change colour for the purpose of camouflage. I was awarded the win for the conversation. Not only this, but these papers also found another very cool result. The chameleons they studied are hunted by both birds and snakes. Interestingly, when a chameleon sees a bird, it changes colour for camouflage in one way, but when it sees a snake, it changes colour in a different way. It turns out that birds and snakes have different colour vision receptors and see colour in different ways. (Bird vision is very similar to human colour vision, but snakes have less colour discrimination, similar to dogs.) So when a chameleon fears a bird, it changes colour to match its surroundings in a way that makes sense to humans. But when it fears a snake, it changes colour in a different way, which seems less well camouflaged to our human eyes (and to birds), but to a snake’s relatively colour-deficient vision it is actually better camouflaged.

This would be astonishing is it wasn’t actually just a simple consequence of evolution in action. But it’s still very cool.

New content today:

## Un-catching up on sleep

I was hoping for another good night’s sleep last night.

On the weekend I bought a small bottle of chocolate liqueur, to flavour interesting cocktails. I decided to try it last night, duplicating a drink that my wife had a while back at a restaurant, called a “winter negroni”. It’s a standard negroni (equal parts gin, Campari, and red vermouth), with a splash of chocolate liqueur, to give it a chocolate-orange flavour. My wife liked it, and so I thought it would be a good drink to try mixing at home. So last night I had one, and it was indeed delicious.

I went to bed a few hours later. I could not fall asleep. I laid there in bed, unable to switch off my mind, and tossed and turned… all night. Until the sun came up. I did not get a single minute’s sleep. I was trying to figure out why, and went through everything I ate and drank, and there was nothing out of the ordinary… except that chocolate liqueur. And I realised that it probably has some caffeine in it. That would explain it.

I gave up caffeine about 25 years ago. I used to enjoy black tea, and Coca-Cola, but I realised through struggling with disrupted sleep that any caffeine after about 10am would result in me being unable to fall asleep that night. So at one point I decided it wasn’t worth it any more and just quit completely.

Not having had caffeinated drinks for so long, I think I’ve become more sensitive to it. I’ve cut way back on chocolate as well, because some years ago I noticed a strong correlation between eating chocolate in the afternoon and sleeping poorly at night. I love chocolate, but I basically only have it in the mornings now, and much much less than I used to eat.

Over the years, I’ve occasionally accidentally eaten something with caffeine in it, and suffered a restless night. I think that’s what happened last night. I had a yummy chocolate flavoured drink, and lost an entire night’s sleep. So… I guess that’s no more chocolate negronis for me. At least my wife can drink them.

In other news, today I took Scully for a morning play and exercise in the park across the road. At one point she got interested in something in the grass, and I walked over to see what it was. She was sniffing… a huge piece of steak! I gave her the “Leave it!” command and she obediently turned away from it. Thank goodness for training her with that command. I got a poo bag and picked up the meat. It was about the size of a coaster, and a centimetre or two thick – a good cut of meat, like you’d cook for dinner.

Now… A chunk of steak is not the sort of thing that somebody accidentally and innocently drops in a grassy park where dogs hang out. There have been several incidents of people in Sydney laying poisoned baits for dogs over the past few years, with several dogs killed. So I took this suspicious chunk of meat home and called the local council to report it. I asked if they wanted me to bring the meat in for testing. They said as it’s so far an isolated incident, that I should just dispose of the meat, but if I see any more, to report it again and they will launch an investigation.

I contacted my apartment block owners’ corporation and they’re going to notify all residents with dogs. I also posted a warning on a local social media site. And I went back to the park later in the day (without Scully) to look around to see if I could find any more chunks of meat – I didn’t find any.

Anyway, on top of a no-sleep night, that was a pretty crummy day.

New content today:

## Catching up on sleep

So I went to bed early last night, and slept in until about 8am today. With that nice solid sleep, I felt pretty good today!

I took things pretty easy again, although went for a drive with my wife and Scully to get some lunch at a new bakery we hadn’t tried before, about 15 minutes drive from home. While there, we walked Scully around the neighbourhood. It’s a place we’ve never walked before, so it was interesting to look at all the houses, which had a distinct style – it was clearly an older neighbourhood, but perhaps semi-rural when first developed, as many of the older houses were built of stone, which is very unusual for a suburban neighbourhood so far from the historical centre of the city.

New content today: