# Binti Question 3 - Math

Binti is, like her mother and father, a mathematical genius, and 'trees' mathematically, using math to induce a zen-like meditative state. This doesn't sound too off for me - I have a close friend who dreams entirely in numbers - but what did you think encountering it? Binti is a 'Master Harmonizer' like her father, with an ability to bring two disparate things into harmony, which she does through numbers. This is the key to creating astrolabes, which Binti's father sells to the Khoush. Is understanding numerical relations being the key to everything an interesting choice? Mwinyi is also a Master Harmonizer, but does not use mathematics - and instead communicates to people. Is this an intersting variation? Does it make sense within the book?

## Comments

That said, I did like the idea of treeing, and occasionally wondered how particular formulae or mathematical relationships might lend themselves to meditation... for example maybe attempting to visualise the changing shapes of a parameterised family of curves, or thinking about how perturbations around a curve might reconverge or diverge over time.

I did wonder about the idea of seeking to reconcile _everything_ with maths... part of maths is identifying when things _cannot_ be reconciled, like a sphere vs a torus, or the infinity of the natural numbers vs the infinity of real numbers. But that aside, it's a cool notion.

I wasn't so sure about the introduction of different kinds of harmonisers... on one level it seems sensible, but in the context of the story it felt like an abrupt add-on. Sort of like a retcon maybe.

I had no idea this was aimed at the YA market, but what you say makes sense.

I personally love visualizing curves - particularly multi-dimensional curves, so that I can see. It's an interesting thought and makes sense on the "this equation is too beautiful to be false!" level.

I was thinking that just like mathematics is a powerful toolbox to manipulate the world with, the same can be said for words. Words, like equations, can explode in your mind like grenades.

It totally seemed YA to me, and consequently I found it a bit simplistic in terms of the dialogue and the way people spoke and reacted to one another. This was an aspect of the book I didn't enjoy.

I liked the treeing, though, and my first thought was 'Oh, cool, she's autistic'. Can one boil everything down to mathematics? On some level, everything is just ones and zeroes, isn't it?

My take was not that Binti was a master harmonizer, but rather had a harmonizer birthright - but it was a role that she didn't want and didn't feel particularly able to fulful, which is why she wanted to go to University. Her father is the real master harmonizer. And yet, in the story, Binti was able to bridge the gaps between species and groups. So maybe there was something to that, afterall.

I don't read enough YA stuff to know!

Especially if the universe is a simulation.

Ah! Interesting! I like that take!

“Binti’s player started treeing:. _’Attribute plus skill plus passion, modified by advantage... 75% chance to succeed? Ok, I’ll go for it!’_

Hahahahahaha! Indeed, yes!

I thought that using repetitive or iterative mathematics and algorithms to generate trance was fine. I did wonder why anyone travelling through a utterly hostile and unknown situation would think doing things in a trance would be a good way to go.

I did have doubts about the idea that mastering numbers has something to do with harmony - why not just stick with music? Music as we hear it is both rational (the pitch of the sounds express whole number fractions) and organises time (rhythm), so what's the need for numbers? And a master harmoniser isn't placing disparate things in a relation, but making their relation pleasant, as if there is galactic agreement about what that sounds like. While I see the appeal of this (wouldn't things be wonderful?) it seemed poorly thought out to me. So this is a

Mary-Sueaspect to me.OK... I won't argue.

All things musical are at their root mathematical. Pythagoras showed us this. Music is geometric, and is all about the relations of notes. The numbers are much less important than their relationships, but still mathematical.

Only to some level of approximation. Pi isn't ones and zeros (though you can get arbitrarily close to it with

enoughones and zeros). Hence my point about maths showing you what cannot be reconciled or brought into agreement, as well as what things can.Your comment struck a chord in me (haha) - isn't it interesting that we use the word

harmonyto express both a musical idea and also one of reconciliation and peace.Pi is a ratio, a relationship, which is geometric in nature and thus mathematical.

I agree it's a geometric ratio, and that it's mathematical. But it is not a rational number - it cannot be expressed as a ration a/b where a and b are whole numbers, and cannot be expressed by a non-infinite string of ones and zeros (or base 10 digits for that matter). It's irrational, despite being a geometric ratio. You could probably invent a base-pi number system where pi was rational... but then it would be colossally hard to count real-world objects like trees or fingers!

That's exactly what actual geometry is about - the area of a circle radius 2 is 4(pi), which is 4 base(pi). The utility of geometry is its ability to happily deal with the irrational. And life is irrational.

Ah, but how many fingers do you have in base pi?

10(pi)

I think it's more like 20.010221... (but a non-terminating decimal)

Okorafor has stated that

Bintiisn't a YA book, and seems to get a little frustrated that people categorise it as such. But saying that, it certainlyreadslike a YA book, with characters with simple inner lives, clearly drawn conflicts, and a hero who achieves great things.As for treeing, that sounds like a deep contemplation of mathematical forms, nothing special (though there is the scene at the start of studies at Oomza where most students are trying to tree but fail).

What does seem like magic or similar is the idea of mathematical currents that can affect things, such as the edan. I don't find that when I contemplate a deep theorem or proof that I'm able to affect the world in non-mundane ways.

That surprises me: I had assumed it was intentional on her part.

How disappointing

OK, my nerdiness came to the fore (I blame Binti) - I was bothered earlier by the fact that I had used the integer digits 0, 1 and 2 in a base pi system (ie where the ascending placeholders are 1, pi, pi^2, pi^3 etc instead of 1, 10, 100, 1000, and the descending ones are 1/pi, 1/pi^2 etc instead of 0.1, 0.01). Why would such a system use regular base 10 integers to describe numbers?

So I did some searching and found that back in 1957 a guy called Bergman set out the rules for a number base of the golden ratio phi (which he calls tau for some reason). To do this he goes back to the definition of phi as (1+sqrt(5))/2, and notes that there is a recursion formula for positive powers of phi that looks like the Fibonacci series. Then he generalises this for negative powers of phi and goes on to develop rules for using it as a number base. See https://math.berkeley.edu/~gbergman/papers/base_tau.pdf if interested, but be warned it's nowhere near as straightforward as number bases of positive integers!

There's been a bit of discussion over the years since then - see for example https://math.stackexchange.com/questions/2311541/why-can-bases-of-number-systems-not-be-rational-numbers and one of the general features seems to be that any number which is uniquely defined in base 10 has multiple possible representations in a number system based on irrational numbers (I think this is related to the fact that the infinity of real numbers is bigger than the infinity of natural numbers or rational numbers).

So... I'm sure that a base pi number system is possible, but I'm also sure that it's monumentally hard to work with, and that most numbers which have a simple definition in base 10 have multiple equally-valid representations in base pi. As commented in the maths stack exchange post, "[the study of irrational number bases] remains a niche subject with few people working on it"

</nerdy interlude>

THank you Richard! I found that very interesting!