How Lewis Carroll computed determinants (2023)

167 pointsposted 12 hours ago
by tzury
(johndcook.com)

33 Comments

esafak

11 hours ago

> Arrange the given block, if necessary, so that no ciphers [zeros] occur in its interior.

I forgot that cipher used to have a different meaning: zero, via Arabic. In some languages it means digit.

vee-kay

an hour ago

Fun fact: zero and numerals were not invented by the Arabs. The Arabs learnt the concept & use of mathematical zero, numerals, decimal system, mathematical calculations, etc. from the ancient Hindus/Indians. And from the Arabs, the Europeans learnt it.

https://en.wikipedia.org/wiki/Hindu-Arabic_numeral_system

Persian scholar Al Khwarizmi translated and used the Hindu/Indian numerals (including concept of mathematical zero) and "Sulba Sutras" (Hindu/Indian methods of mathematical problem solving) into the text Al-Jabr, which the Europeans translated as "Algebra" (yup, that branch of mathematics that all schoolkids worldwide learn from kindergarten).

pinkmuffinere

11 hours ago

lol I never made that connection — in Turkish, zero is sıfır, which does sound a lot like cipher. Also, password is şifre, which again sounds similar. Looking online, apparently the path is sifr (Arabic, meaning zero) -> cifre (French, first meaning zero, then any numeral, then coded message) -> şifre (Turkish, code/cipher)

celaleddin

10 hours ago

Nice! Imagine the second meaning going back to Arabic and now it's a full loop! It can even override the original meaning given enough time and popularity (not especially for "zero", but possibly for another full-loop word).

lupire

2 hours ago

0 is a full loop!

cgio

8 hours ago

The Turkish password word may be the same used for signature? I suspect so, because in Greek we have the Greek word for signature but also a Turkish loan word τζίφρα (djifra).

esafak

7 hours ago

imza is signature while şifre is password. I imagine the conflation occurred because signatures are used like passwords for authentication...

pinkmuffinere

7 hours ago

Hmm i don’t think that one is related in Turkish — i only know of “imza” as signature, but there could also be other variants.

sundarurfriend

3 hours ago

In Tamil, it still means a zero. It's usually pronounced like 'cyber' though, because Tamil doesn't have the 'f'/'ph' sound natively.

aiuu

2 hours ago

When someone says "it still means zero" about Tamil when responding to comments about Arabic, two languages which have no shared root and little similarity, what does that mean?

I think it means HN is full of misleading ideas.

gsf_emergency_6

2 hours ago

So is Gemini. but from it I gather there might be something interesting about a word that "loops back" (geographically) but evolutionarily speaking it was a reworking of _independent_ discoveries of "emptiness"

Arabic -> Tamil <- Arabic - Sanskrit

https://en.wikipedia.org/wiki/0#Etymology

Isamu

2 hours ago

Isn’t the implication that cipher is a loanword? So language relatedness is irrelevant?

We use “arabic” numerals around the world. So use of an Arabic loan word is unsurprising.

Razengan

2 hours ago

Buddy English has no "shared root" with Japanese but we still say sushi.

What does it mean when someone creates a new account for posting contradictory comments?

stackghost

2 hours ago

English's superpower is readily absorbing new words from other languages.

Sushi is now an English word. So is hummus, etc.

jacquesm

10 hours ago

Dutch too: "Cijfer", German, "Ziffer", French: "Chifre", Spanish: "Cifra".

BobbyTables2

4 hours ago

Wow, I never realized the cofactor method wasn’t the only one.

I loathed it and it put me off wanting to get into advanced matrix topics.

RossBencina

2 hours ago

I don't think determinants play a central role in modern advanced matrix topics.

Luckily for me I read Axler's "Linear Algebra Done Right" (which uses determinant-free proofs) during my first linear algebra course, and didn't concern myself with determinants for a very long time.

Edit: Beyond cofactor expansion everyone should know of at least one quick method to write down determinants of 3x3 matrices. There is a nice survey in this paper:

Dardan Hajriza, "New Method to Compute the Determinant of a 3x3 Matrix," International Journal of Algebra, Vol. 3, 2009, no. 5, 211 - 219. https://www.m-hikari.com/ija/ija-password-2009/ija-password5...

barbazoo

3 hours ago

And just like back in university I know how how calculate Determinants but have no clue what one would actually use it for.

ComplexSystems

2 hours ago

Suppose you have (let's say) a 3x3 matrix. This is a linear transformation that maps real vectors to real vectors. Now let's say you have a cube as input with volume 1, and you send it into this transformation. The absolute value of the determinant of the matrix tells you what volume the transformed cube will be. The sign tells you if there is a parity reversal or not.

Razengan

2 hours ago

3blue1brown is your friend

RossBencina

2 hours ago

Form a quadratic equation to solve for the eigenvalues x of a 2x2 matrix (|A - xI| = 0). The inverse of a matrix can be calculated as the classical adjugate multiplied by the reciprocal of the determinant. Use Cramer's Rule to solve a system of linear equations by computing determinants. Reason that if x is an eigenvalue of A then A - xI has a non-trivial nullspace (using the mnemonic |A - xI| = 0).

kazinator

10 hours ago

> Dodgson’s original paper from 1867 is quite readable, surprisingly so given that math notation and terminology changes over time.

Given that Jabberwocky is also quite readable, we shouldn't be too astonished.

01jonny01

8 hours ago

When I'm not cognitively depleted from over working and kids I'd really like to sit down and read this properly.

messe

12 hours ago

HN title filter cut off the initial "How".

You can manually edit it back in.

marcusestes

11 hours ago

“Drop the ‘how.’ It’s cleaner.”

vharuck

11 hours ago

It gives it a different implication. As I read it, an article titled "Lewis Carroll Computed Determinates" has three possible subjects:

1. Literally, Carroll would do matrix math. I know, like many on HN, that he was a mathematician. So this would be a dull and therefore unlikely subject.

2. Carroll invented determinates. This doesn't really fit the timeline of math history, so I doubt it.

3. Carroll computed determinates, and this was surprising. Maybe because we thought he was a bad mathematician, or the method had recently been invented and we don't know how he learned of it. This is slightly plausible.

4. (The actual subject). Carroll invented a method for computing determinates. A mathematician inventing a math technique makes sense, but the title doesn't. It'd be like saying "Newton and Leibnitz Used Calculus." Really burying the lede.

Of course, this could've been avoided had the article not gone with a click-bait style title. A clearer one might've been "Lewis Carroll's Method for Calculating Determinates Is Probably How You First Learned to Do It." It's long, but I'm not a pithy writer. I'm sure somebody could do better.

miltonlost

10 hours ago

"How Lewis Carroll Computed Determinates" is fine and not clickbait because it provides all the pertinent information and is an accurate summary of its contents. Clickbait would be "you would never guess how this author/mathematician computed determinants" since it requires a clickthrough to know who the person is. How is perfectly fine IMO to have in the title because I personally would expect the How to be long enough to warrant a necessary clickthrough due to the otherwise required title length.

867-5309

8 hours ago

it's not quite McKean's Law so I'll settle for contagious