The introduction goes into the math of if we celebrated Christmas every day. It’s obviously meant to be tongue-in-cheek. If I were in a better mood, I’d probably be chuckling. The part about how much room it would take to have free range turkeys for turkey dinners everyday was actually pretty hysterical, though. It goes pretty far in the joke, too. However, there IS one actually semi-serious point here about the benefits of having 1.8+ billion turkeys:

“Those turkeys are going to generate a lot of poo: 18 billion pounds a year, in fact. As you might expect, this brown gold serves as an excellent fertilizer, but more impressively, it can also be used to fuel power stations… then, all our energy concerns will be sorted…” Never thought about this. We may not even need fusion in that case! We just need 15,300 square miles of free range turkey farms…

This part actually made me laugh out loud and almost stop breathing it’s so funny. Here’s the biggest issue of having christmas every day…

“Granted, our GDP might slip a bit if almost everyone stopped going to work. There’s also the small matter of having nowhere to shop for the presents, 1.8 billion turkeys running amok, and a generation of children growing up with no work ethic or sense of discipline. But let’s not get bogged down by trivialities like that.”

Minus the turkeys, we’re already on the way to this! This is the genius of Hannah Fry, making a joke that is actually betraying an underlying truth. That’s our world in five years, except instead of turkeys it will be stray formerly domestic animals and whatever Gen Alpha grows up into…

“We believe that mathematics is so powerful that it has the potential to offer a new way of looking at anything…” Me, too. Which is why I bought this and all three of the other books authored by Hannah.

Now onto chapter one…

I never thought about this… what actually happens to letters to Santa? They get filtered and go somewhere it seems.. At one time, sometimes there were non profits that would actually reply to them. I’m assuming now they just get tossed as nondeliverable… humanity is ruined.

I love this part about mathematical vs scientific proof:

“In mathematics, proving something ‘beyond all reasonable doubt’ isn’t good enough. You have to prove it beyond all unreasonable doubt as well. Mathematicians aren’t happy unless they have demonstrated the truth of a theory absolutely, irrefutably, irrevocably, categorically, indubitably, unequivocally, and indisputably. In mathematics, proof really means proof, and once something is mathematically true, it is true forever.”

I love how they bring the Liar Paradox into the question if Santa exists. I like the conclusion that perhaps we should see Santa as “an undecidable being. You can’t prove his existence one way or the other, you just have to close your eyes and decide for yourself.”

And she’s aligning this with Descartes’ ontological proof of God existing! Wow, this is going deep. A very good start to this book

…

I’ll be honest, I’m not a fan of cylindrical Christmas trees but I DO agree with Platonic solids as ornaments! Especially the stellated icosahedron! They are a pain to actually make, though…

I love the concept of figuring out the utility of buying presents mathematically, and how it’s different for various people. Some people are never going to be happy regardless of how much you spend on a gift, after all. Me personally, I’m more interested in the utility of a gift for myself or for the person I’m buying it for, not how much was spent on it. Some of the least expensive gifts I’ve bought have gone on to be very useful for people. That’s difficult to quantify, but I’m sure it’s possible, figuring out replacement costs, etc.

Now in some cases, like those people who are impossible to buy for, buying presents moves from the realm of decision theory into game theory… and then you wonder why I don’t observe Christmas anymore and instead decide to celebrate the birthdays of Rickey Henderson (RIP) and Annie Lennox (sweet dreams are made of these…) but it makes sense that people have gift buying strategies, although this is just a clever way of talking about the Prisoner’s Dilemma.

…

Funny enough, we never had Secret Santa where I worked, in the only office job I had, probably because it was a Jewish-owned business. I’m grateful for this.

With Secret Santa: “There’s no need for thought or tact, since any resulting resentment won’t be directed at you but will be diffused across all participants, thus preventing irreparable damage to working relationships and allowing business as usual to resume when everyone manages to stagger back to work in the New Years.” Beautiful description of what I find a silly, although occasionally “fun” business tradition in many places.

I’ll say that when it comes to wrapping presents, Amazon has really made things easier by providing boxes to put irregular shaped gifts into. Some boxes are even ideal for using the least amount of wrapping paper! Amazon will even wrap them for you, but the guarantaee the intended gift is inside? I wouldn’t risk it.

I’ll also say cuboidal presents are typically the best presents to wrap, and I love this line: “There is also a diagonal method for wrapping cuboidal presents, one that smug wrappers claims superior. This alternative technique is often presented as some sort of mystical secret, accessible only to the pure of heart, so powerful that those who master it are able to completely cover a fridge-freezer using only a postage stamp.” So silly. And the method is actually less efficient than the standard way… You canna break the laws of physics, lassie. Unless you’re a chief engineer on Star Trek, like Scotty, ironically.

The absolutely most efficient you would think is a sphere, but making it perfectly neat is actually mathematically impossible. The best is actually a box that has a height that’s half the side length of its base.

This is funny: “using a sufficiently long and thin strip of paper, you could wrap a cuboidal present with essentially no wastage at all by winding the paper round and round like a bandage. However, unless your gift of choice is a 5,000 year old Egyptian pharaoh, this is unlikely to be a very sensible option.

…

The chapter on cooking turkey is quite useful, but unfortunately Emily and I likely will never cook a whole turkey again – we just buy deli turkey these days, especially Boar’s Head in Stamford, because it’s a fair bit cheaper and easier to prepare! Also I’m not spoiling teh advice in this chapter – I want people to buy this book after all!

Dividing dessert is as easy as introducing the Ham Sandwich Theory, if Christmas cake is your jam, at least. BUt wait, it’s only a theorem, so it doesn’t actually solve your problem. SIlly Hannah!

Austin’s Moving Knife Procedure definitely sounds like “a horrific new form of cosmetic surgery…” I’m actually familiar with this cake-cutting strategy; didn’t know that’s what it was “officially” called in the math world. Anyway, my family did pies in a similar fashion, but each person got a turn choosing their piece.

[I like to remember it as starting with the kids… so my brother and I did well in this respect. I might be remembering this incorrectly and I was the only kid around at Christmas for some years; my other cousins on my dad’s side didn’t live close by, and I was an only child for eight years. We spent most Christmases with my mom’s side of the family, so me and my brother got special treatment, I suppose. In any case, I have to have some happy holiday memories, don’t I?]

I do love the idea of cake auctions, though. 

I gotta type up this footnote on Pg 95… “In case you’re wondering why mathematicians seem to have spent so much time thinking about cake, we probably should point out that these methods of fair division can actually be applied to all sorts of things other than baked goods. They have the potential to be used to tackle problems as diverse as dividing possessions between divorcees to resolving territorial disputes between nations. Math is more fun if you do it while eating cake, though. That we can’t deny.”

Also, I’d love to bake a 4D or 5D cake, no matter how tricky. And the Pancake Theorem is a math thing that exists.

…

Got to learn about British Christmas crackers. I also learned about optimal cracker pulling strategies. Neat stuff, especially when it comes to all the unwritten rules of cracker pulling etiquette being written down.

…

For some reason I never knew the Queen (or King now) gave annual Christmas speeches in Britain. One of these random blind spots in my knowledge I suppose. I love how Hannah focuses on the total number of words the Queen has used in these speeches over the years and stacks Queen Elizabeth (RIP) up against hip-hop luminaries, putting her in the same company as the vocabularies of Snoop Dogg (ugh) and Kanye West (double ugh) – not company that has aged well. Nicki Minaj (triple ugh) is significantly ahead, and Jay-Z did well (okay, he’s cool.) funny enough the Wu-Tang Clan blows away Shakespeare in unique words, and the Bard had to make words up! 

What’s really funny is she starts talking about using math to write new speeches for the Queen. This is several years before ChatGPT, mind you. So this is really funny to read now. And she’s doing this to give the Queen a break, which is adorable.

She talks about Markov chains, which if you make them more complex, you just get recycled chunks of previous speeches – and that’s what early LLMs were essentially doing, just plagiarizing shit. (I should double check this honestly, were early LLMs actually using Markov chains? I’m assuming so.)

The two-step chain output is entirely nonsense. We’ve come a long way in ten years… however that method makes very funny Christmas songs at least. I wouldn’t trust it at all for thank you notes, though.

…

Probably the most famous chapter from this book: how to win at Monopoly. There’s a video about it on YouTube. 

“Monopoly, whose sole objective is to have you force your friends and family into poverty, seems, above any other board game, to have the ability to turn the most angelic of us into a monster.”

“… what better way to while away those good winter nights that a session of good old-fashioned arithmetic…” adorable.

Wait, what’s the difference between a Markov chain and a Markov matrix? They are indeed directly related.

I love this footnote: “You have been taking notes, right? What did you think this book was? A frivolous stocking stuffer?” Hannah is clearly a woman after my own heart.

Back to the Markov thing: “You might think we’re cheating a bit, using the same math for two completely different bits of Christmas, but actually this connection precisely illustrates one of the genuinely wonderful things about applied mathematics. Often you’ll discover seemingly unconnected areas of the real world – like royal speeches and tedious board games – that are in fact underpinned by startlingly similar mathematical principles. It’s like building a bridge between two parts of the world. Suddenly – with that mathematical connection – everything you know about one area applies to the other.” (pg 133) 

Generally speaking, knowledge can work this way in a lot of areas, but in math it happens all the time.

I won’t spoil the strategies here except for one – utilities end up worthless.

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Last chapter: watching Santa’s weight.

The days immediately following Christmas: “The decorations may stay up for a few days…” (I need to type this up from page 143)

There was a 1993 court case in San Francisco where they were “asked to rule on whether Santa should ‘present children with a slimmer, healthier image.’” They did rule in Santa’s favor. (For proof you can check out the La times from December 12, 1993, “Jolly Old Court upholds St. Nicholas”)

Yet it seems he’s slimmed down a bit since then in Christmas card images…

This might be the funniest thing in the book: “… Santa doesn’t visit all the children of the world. As a great believer in religious and cultural tolerance, he understands that parents in some areas prefer to make their own arrangements for offering gifts to their children, so he respectfully avoids those homes where Christmas is not celebrated.” (pg 145-46) 

It’s an absurd assumption, but funny nonetheless. 

However, plenty of non-Christians celebrate Christmas, so their assumption here that Santa visits only nominally Christian children is a major stretch. Hannah is doing it to make the math work, and it’s a joke anyway. (But yeah, being the last chapter, the gimmick has definitely worn thin.)

This is funny, though, “Unlike Santa, mathematicians never sleep, so we’ll be heading back to our workshop to sit out the rest of the winter enjoying the simple pleasures of triangulating matrices, rationalizing denominators, and integrating polynomials. Try not to be jealous.”

…

I enjoyed the book, but I don’t see it as a keeper.