@jcastroarnaud@mathstodon.xyz
@jcastroarnaud@mathstodon.xyz avatar

jcastroarnaud

@jcastroarnaud@mathstodon.xyz

A simple person, with some very complicated ideas. Trans woman. Computer programmer. Science and math fan. Amateur writer. Amateur game designer. Curious about too many things.

Uma pessoa simples, com umas ideias muito complicadas. Mulher trans. Programadora de computador. Fã de ciência e matemática. Escritora amadora. Criadora de jogos amadora. Curiosa sobre um bocado de coisas.

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ColinTheMathmo, to random
@ColinTheMathmo@mathstodon.xyz avatar

Does this count as a "Trick Question"? Apparently nearly everyone gets it wrong:

================

If f(x)=x^2-10, find an equation of the tangent to the curve passing through the point (5, 1).

================

I didn't fall into the trap, and now that you've been warned possibly you won't either.

Be honest ... would you have?

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@ColinTheMathmo Since (5, 1) isn't in the graph of f, it must be in the graph of the tangent line. I think this is the trap.

I didn't manage to solve the actual question: too rusty in analytic geometry.

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@ColinTheMathmo It's all on the ambiguous wording.

christianp, to random
@christianp@mathstodon.xyz avatar

Here's a game inspired by @two_star's "reverse the list of integers" game.

Get from one integer to another by a sequence of moves. Valid moves are:

  • EXPAND: replace a number with an equivalent mathematical expression, e.g. 5 → 1+4
  • EVALUATE: replace an expression with its numerical value, e.g. 1+4 → 5.
  • SWAP: swap a mathematical operation for another one, e.g. 1+4 → 1×4.

I'll put an example game in the next toot

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@christianp You should define "valid mathematical expression" better. Is division allowed? Is integer division allowed? Are negative integers allowed? Can one uses factorial, or other non-alphabetic operator?

A short sequence from n from/to n + 1, for every integer n, is:

n
n + 0
n + (1 - 1)
n + (1 * 1)
n + 1

Are these moves valid?

a + (b * c)
(a + b) * c
(a + c) * b
(a * c) + b

futurebird, to random
@futurebird@sauropods.win avatar

Thinking about world building & the consequences of “too much” history. In many sci-fi tales parts of history are forgotten— some cataclysm results in a society with about as much history as we have: some 20k years with the last 2000 being most referenced and the last 100 (living memory) of real consequence.

But what if you had a million years of detailed written history? What about a billion? I think there is a reason so many sci-fi stories have the trope “we forgot the location of earth”

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@futurebird History (with big H) would be much more important and developed than nowadays. As you said, for almost every historical situation in the now, there should be a parallel situation somewhere in the past, in another society, in another planet, to learn from.

An in-character explanation:

An important part of the Historian guild work is to find these situations, translate them to the current language, translate the concepts to the current society, and point out an adequate interpretation; all of it in a reasonable time frame (days to weeks).
Fortunately, the Archivist guild provides all the historical data in the current digital format, having had translated and converted digital formats thousands of times since the first computers, more than a million years ago.
Searches in the Archives are slow, but very accurate: the Programmer guild created, refined (and many times rediscovered) the best possible search algorithms.

jcastroarnaud, to design Portuguese
@jcastroarnaud@mathstodon.xyz avatar

A provocative thought, and a question.

After meeting the (https://www.uiua.org/) programming language, and identifying it as queer (in both gender and style), I started thinking about the intersection of and .

I feel that most programming languages are : the (do this, then do that) matches the stereotype of "man commanding". Object-oriented paradigm, same thing. paradigm resembles an assembly line, also stereotypically male.

I feel that some languages are : SQL and Prolog, both . But I know no language.

Do you see programming languages as gendered? If so, which ones you see as female, and why?

jcastroarnaud, to random Portuguese
@jcastroarnaud@mathstodon.xyz avatar

I completed of !

Part 1:

  • Difficulty: 1/10
  • Workout: 1/10

Part 2:

  • Difficulty: 1/10
  • Workout: 3/10

Done in a bit more than 3 hours. I hit two dead ends on part 2, believing that word -> digit substitution worked. Not so. Make sure that "twone" maps to 21. Loop from both ends of the string.

ColinTheMathmo, to random
@ColinTheMathmo@mathstodon.xyz avatar

Ok peeps, What's this? Some sort of Chinese vegetable?

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@MartinEscardo @ColinTheMathmo I confirm it: it's a chuchu, although somewhat out of shape. Here is a more typical photo:
https://acientistaagricola.pt/wp-content/uploads/2019/06/AdobeStock_87942669.jpeg

julesh, to random
@julesh@mathstodon.xyz avatar

70 years ago, the people who designed languages like Cobol, Algol and Fortran made the questionable choice that the semantics of an argument to a function is determined entirely by its position within an ordered list of arguments. Since their compilers had to run on a potato and grab arguments directly from registers it probably made sense at the time, but it's a language choice that's definitely overstayed its welcome by 50 years. Named arguments are better in every conceivable way, and so many languages that ought to know better are still beholden to the caveman languages.

Meanwhile, type theorists decided that their contexts are lists equipped with explicit commutativity, not bags - and category theorists characterising free symmetric monoidal categories did exactly the same thing. There is an obvious and totally reasonable way of making a selection of variables from a bag-like scope, namely, names. Is there an actually good reason to stick with argument lists, or have type theorists and category theorists also been hyptonised by Algol and Cobol?

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@julesh The ones I can remember right now are: ease to remember, and shorter function calls. A few examples:

new Point(5, -1);
If I know that the argument order is always (x, y), there's no need to name the parameters.

c = map(a, b);
One of the arguments is a list, the other is a function. Which is which? What are the parameters' names? If I know that, say, the function is always the last argument, the above questions are moot.

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@BoydStephenSmithJr @julesh I feel that there are two different issues at play: sophisticated type inference for named/unnamed arguments, and practical syntax and usability for the same. I saw the syntactical issue, when others saw the type inference issue.

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@julesh @BoydStephenSmithJr Hmmm. Thinking aloud here; I know almost nothing of type theory.

So, one can replace a parameter or argument list with a bag of pairs (name, type) - much alike a JavaScript object - and, with suitable syntax, do function calls, currying, composing, returning, and other things.

To have a concrete example: in a geometry app, there's a Point class, with coordinates x, y, z, and a label. The Point type would be, instead of [float, float, float, string], an object { "x" => float, "y" => float, "z" => float, "label" => string }. No actual ordering required, the order of these elements is an artifact of writing.

The harder question could be: what's the type of the above object? Not a JavaScript Map (too general). Not a list of pairs (string, Type), because of implied ordering. Not a pair of lists (string[] and Type[]), also because of implied ordering. Maybe a function string -> Type, but the domain must be very restricted. Maybe this is a new kind of type, and one mappable to all of the above.

That remembers me of relational modeling, where entity elements (rows of a table) are tuples, with associated names for the values (the column names of the table). I don't know if any ideas from that are applicable here.

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@BoydStephenSmithJr @julesh I'm reading the PureScript book by now. Interesting reading, and it appears less impenetrable than Haskell to me.

> It also has polymorphic record tails, which you haven't quite considered in the comment to which I'm replying.

Never heard of them.

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@BoydStephenSmithJr @julesh Yes. Let's see a few details of relational modeling. The whole story is at

https://en.m.wikipedia.org/wiki/Relational_model

A table is composed of rows, which can be seen as tuples (a_1, ..., a_n), where a_1 in D_1, ..., a_n in D_n; D_* are the domains of values, aka sets of values, aka types of columns. A tuple is an element of the cartesian product D_1 x ... x D_n. Each tuple is uniformly labeled by an index or name (the column position or column name).

Now, let's go metaprogramming. How to describe a table's structure? With another table, a metadata table (like user_tab_columns in an Oracle database). The columns of the metadata table, for a given table, are:

  • column_name: String
  • column_type: Type

Tables have no requirement of row ordering.

The similarity is evident: a metadata table is the same as a bag of parameters and the same as a record type definition in PureScript.

Also, via the tuple point of view, all these are the same as a set of (String, Type) tuples: a relation (in the mathematical sense) between String and Type, or a subset of String x Type.

I wonder how functional programming would map to SQL instructions... Currying would become a "select ... where" instruction. Structural typing would use only the "column_type" column, ignoring "column_name".

johncarlosbaez, (edited ) to random
@johncarlosbaez@mathstodon.xyz avatar

Last night Lisa and I went to a Chinese restaurant with the computer scientist Mike Fourman, his partner Jeanne, and her son and his wife. The bill was £98. To add a tip and make the bill divisible by 3, Mike rounded it up to £108. I instantly recognized that this number is divisible by 3, since the digits add up to 9. But to my annoyance I didn't instantly remember what 108 divided by 3 is. That is, I didn't remember thinking about this question before.

Later, in the middle of the night, I realized I had run into this question!

Do you see what I mean?

If not, read on....

(1/2)

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@johncarlosbaez I don't, mainly because I saw 108 = 3 * 36 at once. What's the "Aha!"?

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@johncarlosbaez Oh, nice one!

mcnees, to random
@mcnees@mastodon.social avatar

Mathematician Karl Weierstrass was born #OTD, Halloween, in 1815.

The fools at The Academy all said he was mad, but in 1872 he announced that he had succeeded in creating a monster.

Image: Smithsonian Institution Libraries

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@mcnees And there are the Eldritch Abominations: almost-everywhere discontinuous functions.

Some are subtle: their value at any x is just an epsilon away from their limit, an optical illusion that never goes away.

Some are blatant, like r(x) = (x in Q) ? 1 : 0. Seeing its graph, you start doubting that's a function at all.

And most are truly nonsensical; I cannot even think of them without feeling something slowly chipping away my sanity!

SvenGeier, to random
@SvenGeier@mathstodon.xyz avatar

Until today I did not know that there is a mastodon client for Android that supports mathJax (i.e. latex rendering). I had been resigned to reading math on the desktop and using the app basically for skimming clear text only.
If you are like me, then go to the Android play store and download "mathstodon" (yes, really). Looks and feels like the generic tusky except that suddenly you can read equations!
(Now I just need to find the time to spend online...)

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@SvenGeier Found and installed. Thank you for the tip!

Linux_Is_Best, to microsoft
@Linux_Is_Best@mastodon.social avatar

Microsoft, quietly, has published a guide on how to download and install Linux.

No... Seriously... It is not a joke...

https://learn.microsoft.com/en-us/linux/install

The article was published September 29, 2023 (9 days ago).

The guide provides every option available, too. Starting with using their Windows Subsystem for Linux (WSL), to using a Virtual Machine, and even on "Bare Metal" alongside Windows.

That's right, Microsoft now tells you how to dual-boot Linux. 🤯

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@Linux_Is_Best

Prediction 😈: Windows 13 (alias: "The Unlucky") will be a Linux distro with a Windows VM on top of it. Most end users won't notice the difference.

Further prediction 😈: there won't be a Windows 14.

Viss, (edited ) to random
@Viss@mastodon.social avatar

how many times have you had covid?

(boost for reach! im genuinely curious)

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@Viss Once, mid-2020. Never tested, but the symptom was obvious: a few months without smell. Took my vaccines, all of them, hope to never catch COVID-19 again.

ColinTheMathmo, to random
@ColinTheMathmo@mathstodon.xyz avatar

I recently sold my theremin ... I hadn't touched it in years -- Anon

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@ColinTheMathmo 🤦🏻‍♀️

ColinTheMathmo, to random
@ColinTheMathmo@mathstodon.xyz avatar

I have a challenge for my constraint programming colleagues ...

I believe there is no perfect solution to this, so the question is what's the least bad solution.

I have 6 home players, A-F, and six visitors, 1-6.

There will be six rounds.
Each round will have 3 matches.
Each match will have two pairs.
Each pair will have one visitor and one home player.

We would like:

Each home player to be paired with each visitor at more once;

Each player to play against each other player at most once.

I don't believe this is possible, but how few repetitions can you get away with?

Here's one tournament:

Rnd 1: B2 v E5, C3 v F6, D4 v A1
Rnd 2: A2 v C4, F1 v B3, E6 v D5
Rnd 3: B4 v A3, C5 v D6, F2 v E1
Rnd 4: C6 v D1, E2 v B5, A4 v F3
Rnd 5: F4 v D2, E3 v A5, B6 v C1
Rnd 6: A6 v F5, E4 v B1, D3 v C2

This is not especially good: Player A players against player 4 in the first three rounds, and so on.

How well can you do?

I can get a tournament with 9 clashes. Can you do better?

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@ColinTheMathmo A lower bound.

There are 18 matches and 12 players. In 18 -11 = 7 matches, at least, a player will be against someone he met in another match (a player can't match against himself).

By the pigeonhole principle, there's no better solution.

lowqualityfacts, to random
@lowqualityfacts@mstdn.social avatar

Whats that you say, favoriting a post is functionally useless because there's no algorithm on Mastodon?

Tell that to my instant gratification addicted lizard brain that's getting hit with a tidal wave of dopamine every time my phone vibrates.

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@lowqualityfacts We are Mastodon's algorithm. :proud:

Vergo, to random

My research partners and I have found that many people struggle to understand the fundamental operation that we are studying. Because of this I have been spending time trying to develop better explanatory tools. This animation is something that we think does a good job of providing a purely visual explanation of what we are studying, but we would love your feedback.

Just by watching the animation below, are you able to recognize and describe the operation being repeated here? note: this does not require you to be able to explain the resulting structure (that's what we are working on!)

video/mp4

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@Vergo I see two circles taking a part of their intersection to themselves, borders and all, then rotating. The angle of rotation is such that the borders form two 5-sided symmetric figures, with nice fractal-like shapes within.

Beyond being geometric art, I have no idea of its meaning.

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@Vergo Now that I read your paper, I understand that the video is a showcase of elements of your new GG_5 group.

Could other mechanical puzzles, like Rubik's Cube, be described with the help of such GG groups? I read somewhere that the group of symmetries of the Rubik's Cube is quite large, although finite.

BartoszMilewski, to random
@BartoszMilewski@mathstodon.xyz avatar

This is the conclusion of my upcoming blog post.

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@BartoszMilewski I have a marvelous proof for this theorem, but the margin is too small for the diagram. ;-)

xgranade, to random
@xgranade@wandering.shop avatar

An update added Grammerly to my phone keyboard without my consent. I'm now seeking suggestions on alternative AI-free Android keyboards as a result.

jcastroarnaud,
@jcastroarnaud@mathstodon.xyz avatar

@xgranade Hacker's Keyboard. Advantages: has Ctrl, Alt, Esc and arrows, and multilingual support. Disadvantages: smaller keys (tries to emulate a physical keyboard), and it's old (from 2018).

https://play.google.com/store/apps/details?id=org.pocketworkstation.pckeyboard

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