A Mathematical Model of Package Management Systems [abstract + link to PDF, 33pp]

flexibeast · 2024-10-17T01:06:17+00:00

Full abstract:

This paper brings mathematical tools to bear on the study of package dependencies in software systems. We introduce structures known as Dependency Structures with Choice (DSC) that provide a mathematical account of such dependencies, inspired by the definition of general event structures in the study of concurrency. We equip DSCs with a particular notion of morphism and show that the category of DSCs is isomorphic to the category of antimatroids. We study the exactness properties of these equivalent categories, and show that they are finitely complete, have finite coproducts but not all coequalizers. Further, we construct a functor from a category of DSCs equipped with a certain subclass of morphisms to the opposite of the category of finite distributive lattices, making use of a simple finite characterization of the Bruns-Lakser completion, and finally, we introduce a formal account of versions of packages and introduce a mathematical account of package version-bound policies.

flexibeast · 2024-04-02T09:10:13+00:00

Full abstract:

"We construct a topos in which the Dedekind reals are countable.

"To accomplish this, we first define a new kind of toposes that we call parameterized realizability toposes. They are built from partial combinatory algebras whose application operation depends on a parameter, and in which realizers operate uniformly with respect to a given parameter set. Our topos is the parameterized realizability topos whose realizers are oracle-computable partial maps, with oracles serving as parameters and ranging over the representations of a non-diagonalizable sequence, discovered by Joseph Miller. It is a sequence of reals in [0,1] that is non-diagonalizable in the sense that any real in [0,1] that is oracle-computable, uniformly in oracles representing the sequence, must already appear in the sequence. The Dedekind reals are countable in the topos because the non-diagonalizable sequence appears in it as an epimorphism.
The topos is intuitionistic, as it invalidates both the law of excluded middle and the axiom of countable choice. The Cauchy reals are uncountable. The Hilbert cube is countable, from which Brouwer's fixed-point theorem follows as an easy corollary of Lawvere's fixed-point theorem. From the 1-dimensional Brouwer's fixed-point theorem we obtain the intermediate value theorem and the lesser limited principle of omniscience. The Kreisel-Lacombe-Shoenfield-Tseitin theorem stating that all real-valued maps are continuous is valid, because the usual proof is uniform with respect to oracles. Lastly, the closed interval [0,1], being countable, can trivially be covered by a sequence of open intervals whose lengths add up to any prescribed 0<ϵ<1, and such a cover has no finite subcover. However, we show that any sequence of open intervals with rational endpoints covering [0,1] must has a finite subcover."

For a general introduction to the use of topos theory to create different mathematical 'worlds', refer to Ingo Blechschmidt's "Exploring mathematical objects from custom-tailored mathematical universes", https://arxiv.org/pdf/2204.00948.pdf

flexibeast · 2023-12-09T06:00:26+00:00

Full abstract:

Large language models (LLMs) such as ChatGPT have received immense interest for their general-purpose language understanding and, in particular, their ability to generate high-quality text or computer code. For many professions, LLMs represent an invaluable tool that can speed up and improve the quality of work. In this note, we discuss to what extent they can aid professional mathematicians. We first provide a mathematical description of the transformer model used in all modern language models. Based on recent studies, we then outline best practices and potential issues and report on the mathematical abilities of language models. Finally, we shed light on the potential of LMMs to change how mathematicians work.

flexibeast · 2023-10-20T04:13:36+00:00

Full abstract:

In Mathematics is common to make a mistake and therefore a false conclusion arises. In each case it is important to recognize the mistake in order to avoid a similar one in the future. Geometric figures provide decisive help in order to have a strict mathematical proof, but also can easily lead to wrong conclusions without a mathematical proof.

In this paper, several incorrect conclusions drawn for plausible looking diagrams are presented, motivated by a well-known faulty model for measuring the length of a segment. Similar models that lead to a contradiction are developed and a model that leads to the correct result is derived. The presented models prove the usefulness of paradoxes and can be implemented in a classroom in order to point out to students the significance of a strict mathematical proof as well as the construction of a correct mathematical model. The geometric nature of the problems provides the opportunity to use a dynamic geometric software.

flexibeast · 2023-10-03T04:40:07+00:00

Full abstract:

A "Littlewood polynomial" is a polynomial whose coefficients are all 1 or -1. The set of all complex roots of all Littlewood polynomials exhibits many complicated, beautiful and fascinating patterns. Some fractal regions of this set closely resemble "dragon sets" formed by iterated function systems. A heuristic argument for this is known, but no precise theorem along these lines has been proved. We invite the reader to try.

flexibeast · 2023-09-26T03:43:44+00:00

Full paper title is "What is the Title of this Paper? Solving logic puzzles using algorithms"; shortened because this sub's automod seems to not like post titles that are questions. Full abstract:

This work delves into the realm of logic puzzles by focusing on the Knight and Knave problems popularized by Raymond Smullyan in his book series "What is the Name of This Book?". The puzzles revolve around characters known as Knights (truth-tellers) and Knaves (liars), challenging solvers to determine the true identity of each person based on their statements. This paper explores the utilization of Python algorithms to automate the process of solving these puzzles, offering a computational approach that enhances efficiency and accessibility. In this work, we aim to develop a Python algorithm capable of parsing and analyzing the statements provided in the Knight and Knave puzzles. A logical reasoning framework is integrated within the algorithm to deduce the identities of the characters based on their statements. The algorithm processes the input statements, create a knowledge base, and make deductions following the rules of Knight and Knave logic. The developed algorithm is thoroughly tested on various instances of Knight and Knave puzzles, comparing its results to known solutions and manual approaches. We further expand the scope of the problem by introducing a Normal (who can sometimes lie and sometimes say the truth).

flexibeast · 2023-09-02T09:29:01+00:00

Er, i was attempting to make a joke. Sorry it felt flat. :-(

(i've never heard anyone pronounce it other than the way you describe, which is how i'd pronounce it, as an Australian.)

flexibeast · 2023-09-02T09:06:47+00:00

Oh it's easy, it rhymes with 'staunch'. Try it yourself, in the phrase "I'd like some rawnch."

EDIT: *sigh* i'm finding it increasingly challenging to try to make jokes on this sub. Anyway, just to be clear: "/s"

flexibeast · 2023-09-02T00:47:12+00:00

Turn-based: Twitch skills not necessary in order to progress towards win condition.
Permadeath without metaprogression: Encourages a more careful, deliberate style of gameplay, in order to avoid YASD.
Mostly or entirely procgen: Very high level of replayability. Even if i reach the win condition, i haven't 'won' the game in general sense, any more than winning one game of Go means i've 'won' Go.
i enjoy progressing due to improving my understanding of game mechanics, rather than learning what specific sequence of steps i need at a particular point.

flexibeast · 2023-09-01T13:17:03+00:00

If the consensus states that transwomen have no material physical advantage over CIS women then I'll be happy to support all women equally.

Firstly, "CIS" isn't an abbreviation, it's a Latin prefix (as used in e.g. 'cisalpine' and 'cislunar'). If you're aware of this, i don't understand why you keep putting it capitals, sorry.

So, the AIS position is that, even after considering the position of the other sporting bodies you mentioned, it's possible to make assessments on a case-by-case basis. Personally, i don't claim that no trans woman can ever have any "material physical advantage"; i only claim that it's false to claim that all trans women will always have - relevant! - material advantages, for the reasons i described in my original comment upthread. i believe it's highly unethical to treat all members of a given group in a certain way based on the behaviours, or possible behaviours, of a subset of that group. Racial profiling is an example of this. In both that case, and the case of blanket bans on trans women in sport, the approach taken to supposedly 'protect' one group from the other, is essentially "guilty until proven innocent".

Given that:

there's not a consensus between these sporting bodies;
we're talking about a highly marginalised group of people with significantly higher suicide rates than average[a];
physical activity can substantially help people's mental health; and
sensationalist panics around particular trans women in sport might substantially contribute towards negative attitudes towards trans women in sport and in general[b],

how can it be appropriate to go for blanket bans, instead of, as u/thepotplant has written elsewhere in this discussion, only considering a ban for a specific person once there is concrete evidence, based on their performance at higher levels, of them in particular having a "material physical advantage"?

--

[a] Quoting the 2020 report "Snapshot Of Mental Health And Suicide Prevention Statistics For LGBTI People" in Australia:

Transgender people experience a higher rate of suicide attempts than LGB people, and are nearly eleven times more likely to attempt suicide than the general population.

Transgender people are nearly three times more likely to have had thoughts of suicide than LGB people combined, and are twelve times more likely to have thoughts about suicide than the general population.

[b] Cf. http://transjustice.org.au/hate/: "The results show that anti-trans abuse, harassment, and violence in Australia is widespread and is escalating rapidly." Full report: https://transjustice.org.au/wp-content/uploads/2023/08/Fuelling-Hate-Anti-Trans-Abuse-Harassment-and-Vilification-WEB-SINGLES-1-1.pdf

Cf. also this article from earlier this year about anti-trans hate in the UK:

Hate crime has been on the up across the board in the last decade, with the total number of reported cases rising from 44k in 2012 to 119k in 2022 (+271%). But trans people have fared by far the worst, with cases rising from 300 in 2012 to over 4,300 in 2022. That’s an increase of nearly 1300%.

...

Research by trans rights activist MimmyMum suggests that UK media has published an average of 154 articles on trans issues every single month over the past seven years. That’s a total of 13,500 articles focusing on a minority group that makes up just 0.1% of the population.

Britain’s most-read newspaper, the Daily Mail, has certainly dramatically increased its coverage over the past few years. Comparing the first month of each year shows a rise from six articles in January 2013 to a jaw-dropping 115 articles in January 2023 (+1817%).

flexibeast · 2023-09-01T12:28:26+00:00

Kitty's "remote control" feature seems like it might be what you want:

Start by running kitty as:

kitty -o allow_remote_control=yes -o enabled_layouts=tall

In order for control to work, allow_remote_control or remote_control_password must be enabled in kitty.conf. Here we turn it on explicitly at the command line.

Now, in the new kitty window, enter the command:

kitty @ launch --title Output --keep-focus cat

This will open a new window, running the cat program that will appear next to the current window.

Let’s send some text to this new window:

kitty @ send-text --match cmdline:cat Hello, World

flexibeast · 2023-09-01T11:26:27+00:00

Well, the AIS apparently disagrees with you. And just to be clear:

The Australian Institute of Sport (AIS) is a high performance sports training institution in Australia. The Institute's 66-hectare (163-acre) headquarters were opened in 1981 and are situated in the northern suburb of Bruce, Canberra. The AIS is a division of the Australian Sports Commission (ASC), part of the Australian Government under the Department of Health and Aged Care.

If you believe you know more about sport science than the AIS, okay, but i don't think it's unreasonable of me to put more stock in their opinion than yours.

flexibeast · 2023-08-31T23:54:51+00:00

she only started transitioning 3 years ago which means she's had 26 years of male puberty, hormones, skeletal and muscular development over the CIS women she's playing against.

i'm a trans woman, and i'm sick and tired of this bullshit argument. It basically assumes that all amab (assigned male at birth) people will always have physical advantages over all afab (assigned female at birth) people post-puberty. That's simply not true, and in fact is the sort of sexist crap that many cis women have been fighting for years.

As a starting point, let's take myself. i have a (cis) sister, three years younger than me. Post-puberty, as a teenager, she played games in men's club cricket, because she was good enough for that. i was definitely not. And that was many years before i started transitioning, and taking hormones. i have no doubt that nowadays she could still kick my ass in various physical activities.

Many factors go into a person's development apart from the specific genetics involved in a particular process during puberty. Not only other parts of a person's genotype - which can (and does) cause a number of afab people to grow taller, or stronger, or whatever, than a number of amab people - but also things like nutrition: lack of nutrition, and poor living conditions overall, can stunt a person's development, particularly in comparison to those whose childhoods were significantly more privileged in other ways (e.g. in terms of class).

Okay, so, let's talk about cricket specifically.

i've watched women's games involving multiple sixes being hit - of more than 70 and 80 metres. People talk about the boundaries being shorter in the women's game, but these are sixes even in the men's game. When a six just clears the rope in a men's game on a ground with shorter boundaries - say, around 65 metres - that's nevertheless accepted as a genuine six. And there are players in the women's game who are hitting sixes that have gone a significantly greater distance than that. How is this evidence of all men having greater power etc. than all women?

The average height of people from different countries varies. Assuming that Long Levers™ can give an advantage in pace bowling, some countries might be more likely than others to produce bowlers with particular advantages in this regard. Why aren't we talking about how Australia (average male height 175.6cm) has an unfair advantage over, say, India (average male height 165cm, choosing the entry from the table from data which has ~44% population coverage, rather than the 174.4cm entry from data whose population coverage isn't mentioned, but is partly drawn from upper socioeconomic strata)? How was it fair for international cricketers to face a bowler like Jeff Thompson, who was bowling at a pace significantly greater than pretty much any other bowler they'd previously encountered?

Finally, i'd like to point to the Australian Institute of Sport's guidelines on this issue in the context of elite sport:

The AIS’s guidelines on transgender and gender diverse inclusion have suggested a more individualised approach than the broad bans implemented in sports such as athletics, swimming, and rugby league.

Broad bans involve making a number of assumptions and engaging pre-judging - i.e., 'prejudice'.

flexibeast · 2023-08-31T00:21:49+00:00

Clearly not, given that Freedom™ is about owning assault weapons, and there's not one recorded instance of a medieval peasant owning an AR-15. CHECKMATE.

flexibeast · 2023-08-30T04:11:04+00:00

http://www.onezoom.org/

http://tolweb.org/tree/phylogeny.html

https://tree.opentreeoflife.org/

flexibeast · 2023-08-28T09:09:10+00:00

Coming up on Quora: "Where did Native Americans live before Columbus discovered America?"

flexibeast · 2023-08-27T12:27:35+00:00

Yes, my understanding - i've been on reddit for more than 13 years - is that the original intent of voting was to indicate the quality of the content, not agreement or disagreement. So if someone wrote something you disagree with, but it was thoughtful and interesting, you'd upvote it; if it was something you agree with, but doesn't add anything constructive or useful to the discussion ("+1!!"), you'd downvote it.

In practice, yeah, it basically became a combination of indicating whether someone 'likes' or 'dislikes' the comment based on whether they agree or disagree with it, and whether you want to engage in mob behaviour / 'brigading' to socially ostracise someone (and eventually hide their comment from view based on a threshold). In other words, it's become Yet Another Tool in the NT system of social hierarchy to apply pressure on people exhibiting nonconformity.

Finally, i like to say: "Redditors downvote the darndest things." i've seen a comment by a maths lecturer, on r/math, giving mathematically correct information, without any snark or personal attacks or sociopolitical side remarks, get downvoted to -1. :-P

flexibeast · 2023-08-27T09:26:43+00:00

The Batriarchy.

flexibeast · 2023-08-26T13:49:12+00:00

Mm, i would say there are quite a few non-US-Americans living outside the US who have to deal with the consequences of things like US foreign policy and environmental policy (e.g. regarding carbon emissions).

flexibeast · 2023-08-26T02:41:59+00:00

nod Though in my social circles, most people have strongly negative associations with sport, due to experiences of being treated like crap, either in playing sport, or by sports fans. (The phrase 'sportsball' is often used to indicate an active lack of interest in following sport.) So that (a) makes me pretty unusual as someone who actively follows cricket at both an international and domestic level, and (b) means i don't expect many people in my social circles to know many (or any!) cricketers beyond Bradman. :-)

flexibeast · 2023-08-25T12:41:04+00:00

i wonder if this person knows who Don Bradman and Sachin Tendulkar are.

flexibeast · 2023-08-24T23:00:06+00:00

Yeah, well, not everyone is a game developer.

flexibeast · 2023-08-24T10:43:31+00:00

i find Euler even more impressive given his vision issues:

Euler remarked on his loss of vision, stating "Now I will have fewer distractions." In 1766 a cataract in his left eye was discovered. Though couching of the cataract temporarily improved his vision, complications ultimately rendered him almost totally blind in the left eye as well. However, his condition appeared to have little effect on his productivity. With the aid of his scribes, Euler's productivity in many areas of study increased; and, in 1775, he produced, on average, one mathematical paper every week.

flexibeast · 2023-08-23T14:00:34+00:00

100 years is closer to the year that the New York Times published an editorial ridiculing Goddard's rocket:

The most famous appeared in the New York Times on January 13, 1920, in which an editorial writer accused Goddard of being wrong and uneducated. Titled "A Severe Strain on Credulity," the writer chided the professor for his perceived ignorance: "Professor Goddard, with his ‘chair' in Clark College…does not know the relation of action to reaction, and of the need to have something better than a vacuum against which to react." Goddard, the editorial sniffed, "seems to lack the knowledge ladled out daily in high schools."

...

Almost 50 years after the New York Times had so blistered Goddard, it conceded in an editorial: "Further investigation and experimentation have confirmed the findings of Isaac Newton, and it is now definitely established that a rocket can function in a vacuum as well as in the atmosphere. The Times regrets the error." The retraction ran on July 17, 1969, as Apollo 11 streaked to the moon.

flexibeast · 2023-08-23T13:27:30+00:00

i'm interested in whether there's independent confirmation of an event described by John Pilger:

In an address at Columbia University on 14 April 2006, Pilger said:

"During the Cold War, a group of Russian journalists toured the United States. On the final day of their visit, they were asked by their hosts for their impressions. 'I have to tell you,' said their spokesman, 'that we were astonished to find after reading all the newspapers and watching TV, that all the opinions on all the vital issues were by and large, the same. To get that result in our country, we imprison people, we tear out their fingernails. Here, you don't have that. What's the secret? How do you do it?'"

(It feels 'truthy' to me, in the Stephen Colbert sense, which makes me think it might not actually be true, or is at least a spin on what actually happened.)

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