Ask Math Problems

cross-posted from: https://slrpnk.net/post/24512484

(The pic is sample output for an arbitrary query on “vegan vege pesc”. Irrelevant side note: there is no free-world venue for pescatarians.. just one in L/W that scrolled off the screen)

CF

The federation is not wholly decentralised, obviously, when giant centralised fiefdoms like Facebook “Threads”™ and Cloudflare hook in their technofeudal variety of oppressive infra and abuse their power.

Each post submission begins with finding a relevant venue for the content and it must be consistent with my sense of ethics. Cloudflare is automatically nixed because it’s inherently centralised in a walled garden (regardless of the user count for any given node). CF is a non-starter for an open, free, and fair society (fair implying power balance, equality, transparency, etc).

My script queries the catalog of communities for relevant venues. It still prints the Cloudflare walled garden because it’s useful to see what names match my regex queries, which sometimes helps form a better query. It’s the only thing #LemmyWorld is good for (a shit-ton of community names with redundant variations of the same subject matter). Those results are in red, tagged with a thundercloud (🌩 ), and printed first (because when they scroll off the terminal I don’t typically care to scroll up to see them).

non-CF

CF is not the only issue. Some non-CF nodes are centralized due to uncontrolled growth to disproportionately large sizes. I don’t cancel them hard-and-fast like CF nodes, but they get treated with low “last resort” favorability. They have the warning symbol (⚠) and are in yellow.

Is my math decent?

My script began by filtering on total user count. Then I realised dead or dormant users probably should not count because such users don’t really contribute to a node’s disproportionate power over a population. It’s active users that matter. But if the number of active users in a day are filtered on, that’s too dynamic for deciding where my post can live for a month or however long it is relevant. So I took the users_active_half_year count. Is that sensible?

What constitutes an “active” user, simply logging in, or commenting?

The line is drawn at 2 standard deviations above the average -- after tossing outliers. Nodes with less than 5 active users in ½ a year are likely 1-person nodes which do not influence the average. The average is around 320 active ½yr users per node. The standard deviation is ~702 users. My statistical competence is rusty for sure, but I’m a bit bothered by a standard deviation that’s more than double the mean. Seems like a variation so wild it should perhaps be disregarded. Nonetheless, I opted to flag nodes that exceed ~1724 users_active_half_year.

The pseudocode looks like this:

avg=$(sqlite3 "$db" 'select round(avg([counts.users_active_half_year])) from node_tbl where tags not like "%cloudflare%" and [counts.users_active_half_year] > 4')
variance=$(sqlite3 "$db" 'select avg(([counts.users_active_half_year] - subtbl.aua) * ([counts.users_active_half_year] - subtbl.aua)) as var from node_tbl, (select avg([counts.users_active_half_year]) as aua from node_tbl where tags not like "%cloudflare%" and [counts.users_active_half_year] > 4) as subtbl where tags not like "%cloudflare%" and [counts.users_active_half_year] > 4;')

sqlite3 "$db" "select case when baseurl in (select baseurl from node_tbl where [counts.users_active_half_year] > $avg+sqrt($variance)*2) then '$yellow⚠' else '$cyan' end||baseurl||'$reset',name from community_tbl where (name like '%${1}%' or desc like '%${1}%') and baseurl not in (select baseurl from node_tbl where tags like '%cloudflare%') order by baseurl,name"

Code is ugly because sqlite does not have a stdev builtin function.

My other thought is to cut slack for closed nodes because at least they are expected to shrink. To list the possible figures to filter on, this is a record for lemmy.ml (the biggest non-Cloudflare node):

record for lemmy.ml

url = https://lemmy.ml/ baseurl = lemmy.ml name = Lemmy desc = A community of privacy and FOSS enthusiasts, run by Lemmy’s developers downvotes = 1 nsfw = 1 create_admin = 0 private = 0 fed = 1 version = 0.19.12 open = 1 usage.users.total = 54790 usage.users.activeHalfyear = 4201 usage.users.activeMonth = 2125 usage.localPosts = 167331 usage.localComments = 818559 counts.site_id = 1 counts.users = 54790 counts.posts = 167331 counts.comments = 818559 counts.communities = 4608 counts.users_active_day = 947 counts.users_active_week = 1496 counts.users_active_month = 2125 counts.users_active_half_year = 4201 icon = https://lemmy.ml/pictrs/image/fa6d9660-4f1f-4e90-ac73-b897216db6f3.png banner = langs = ["all"] date = 2019-04-20T18:53:54.608882Z published = 1555786434000 time = 1751974533970 score = uptime.domain = lemmy.ml uptime.latency = 0.034 uptime.countryname = France uptime.uptime_alltime = 99.04 uptime.date_created = uptime.date_updated = 2021-10-29 15:09:21 uptime.date_laststats = 2025-04-11 21:03:25 uptime.score = 100 uptime.status = 1 isSuspicious = 0 metrics.usersTotal = 54790 metrics.usersMonth = 2125 metrics.usersWeek = 1496 metrics.totalActivity = 985890 metrics.localPosts = 167331 metrics.localComments = 818559 metrics.averageUsers = 50720.8825256975 metrics.biggestJump = 225 metrics.averagePerMinute = 0.02475 metrics.userActivityScore = 0.055574151274483 metrics.activityUserScore = 17.9939770031028 metrics.userActiveMonthScore = 25.7835294117647 tags = [] susReason = [] trust.lastCrawled = 1751974533970 trust.baseurl = lemmy.ml trust.metrics.usersTotal = 54790 trust.metrics.usersMonth = 2125 trust.metrics.usersWeek = 1496 trust.metrics.totalActivity = 985890 trust.metrics.localPosts = 167331 trust.metrics.localComments = 818559 trust.metrics.averageUsers = 50720.8825256975 trust.metrics.biggestJump = 225 trust.metrics.averagePerMinute = 0.02475 trust.metrics.userActivityScore = 0.055574151274483 trust.metrics.activityUserScore = 17.9939770031028 trust.metrics.userActiveMonthScore = 25.7835294117647 trust.users = 54790 trust.name = Lemmy trust.base = lemmy.ml trust.actor_id = https://lemmy.ml/ trust.tags = [] trust.guarantor = fediseer.com trust.endorsements = 17 trust.score = 598.1875 trust.reasons = [] blocks.incoming = 0 blocks.outgoing = 0 blocked = []

Some communities missing from the Lemmyverse DB - why?

Anyone know why some slrpnk.net communities are in the Lemmyverse DB, and some are not? E.g. why is !nolawns@slrpnk.net missing, despite many others from the same node that are included?

More importantly, what’s the fix apart from crawling all the nodes (which would probably be unwelcome)? Is there another open DB apart from Lemmyverse? There is fediverse.space and fediverse.observer, but they don’t appear to be sharing their data.

I can't seem to wrap my head around how to calculate this, nor the reasoning behind it.

Say you have 3 10-sided dice. 2 dice have 8 "winning" faces and 2 "losing" faces. So an 80% chance of winning. The third dice has 5 "winning" and 5 "losing" sides, so a 50% chance of winning.

If you roll all three of these dice at the same time:

-What is the probability of at least 1 dice winning.

-What is the probability of at least 2 dice winning.

-What is the probability of all 3 winning.

From what I've seen I can calculate the probability of all 3 winning by doing:

0.8 x 0.8 x 0.5=0.32

A 32% chance of all 3 winning at the same time.

But what about the others, I can't seem to figure it out.

The well-ordering theorem follows only if the AoC is true, which means that otherwise, there are sets with no well-ordering.

Supposedly, the Real numbers is one of such sets. Does that mean the real numbers can't be shown to have a direct bijection to any aleph number? And if that's the case, does that mean 2^Aleph_0 is bigger than any aleph number?

I was watching this video, which was describing the intution behind the second derivative. I understand how the 1-dimmensional result was found, but I am quite at a loss for how to arrive at the n-dimmensional result, where the second derivative is the laplacian (the video provides the 3-dimmensional result, i.e. $f(x,y,z)$, at 00:08:08). The specific part that I'm having trouble with is finding the average of the multivariable function so that it fits the equation stated in the video, which, even more confusingly, has a single variable in it.

• Update (2024-05-08T06:31Z): I found this document, which provides a lot more detail.

Are there any known right triangles that have integer side lengths and rational angles? If not, has it been proven that none exist?

There are certain things whose number is unknown. If we count them by threes, we have two left over; by fives, we have three left over; and by sevens, two are left over. How many things are there?

Definitions

A graph G = (V, E) is a set of nodes V and a set of undirected edges E. An undirected edge is a set of two vertices.

Two graphs G1 = (V1, E1) and G2 = (V2, E2) are isomorph if there is a bijective mapping f from V1 to V2 such that f(E1) = E2. Applying f to E1 means applying it to each node in each edge in E1.

Problem

Is there an algorithm that decides if two arbitrary graphs are isomorphic in polynomial time?