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@ -21,6 +21,7 @@ Here is a comparison of the Creative Commons licenses/waivers, from most free (b
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| Creative Commons Attribution NonCommercial | CC BY-NC | NO! :((( |yes but|yes but|yes but| yes :/ |forced :( | yes :( | [proprietary](proprietary.md) fascist license prohibiting commercial use, DO NOT USE |
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| Creative Commons Attribution NoDerivs | CC BY-ND | NO! :((( |yes but|yes but|NO! :( | yes :/ |forced :( | no but | [proprietary](proprietary.md) fascist license prohibiting modifications, DO NOT USE |
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|Creative Commons Attribution NonCommercial NoDerivs| CC BY-NC-ND| NO! :((( |yes but|yes but|NO! :( | yes :/ |forced :( | yes :( | [proprietary](proprietary.md) fascist license prohibiting commercial use and even modifications, DO NOT USE |
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| Creative Commons Attribution NoValue | CC BY NV | no | yes | yes | no | no |forced | yes | [joke](joke.md) license by Question Copyright :) |
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| none (all rights reserved) | | NO! :((( |NO! :( |NO! :( |NO! :( |FUCK YOU|FUCK YOU | FUCK YOU | [proprietary](proprietary.md) fascist option, prohibits everything, DO NOT USE |
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There Creative Commons "paradox": there seems to be a curious pattern noticeable in the world of Creative Commons licensed works (and possibly [free culture](free_culture.md) and [free software](free_software.md) in general) -- the phenomenon is that **the shittier the [art](art.md), the more restrictive license it will have**. { I noticed this on opengameart but then found it basically applies everywhere. ~drummyfish } Upon closer inspection it doesn't look so surprising after all: more restrictive licenses are used as a slow and careful transition from "all right reserved" world, i.e. they are used by newcomers and noobs who fear that if they don't enforce attribution people will immediately exploit it. More skilled people who have spent some time in the world of free art and published more things already know this doesn't happen and they know that less restrictive licenses are just better in all aspects.
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10
gnu.md
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gnu.md
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@ -1,14 +1,18 @@
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# GNU
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GNU (*"GNU is Not Unix"*, a [recursive](recursion.md) acronym) is a large project started by [Richard Stallman](rms.md), the inventor of [free (as in freedom) software](free_software.md), running since 1983 with the goal of creating a completely free (as in freedom) [operating system](os.md), along with other free [software](software.md) that computer users might need. The project doesn't tolerate any [proprietary](proprietary.md) software (though it sadly tolerates proprietary data). The project achieved its goal of creating a complete operating system when a [kernel](kernel.md) named [Linux](linux.md) became part of it in the 90s as the last piece of the puzzle -- the system is now known as GNU/Linux. However, the GNU project didn't end and continues to further develop the operating system as well as a myriad of other software projects it hosts. GNU gave rise to the [Free Software Foundation](fsf.md) and is one of the most important software projects in history of computing.
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GNU (*"GNU is Not Unix"*, a [recursive](recursion.md) acronym) is a large software project started by [Richard Stallman](rms.md), the inventor of [free (as in freedom) software](free_software.md), running since 1983 with the goal of creating, maintaining and improving a completely free (as in freedom) [operating system](os.md), along with other free [software](software.md) that computer users might need. The project doesn't tolerate any [proprietary](proprietary.md) software (though it sadly tolerates proprietary data). GNU achieved its goal of creating their free operating system when a [kernel](kernel.md) named [Linux](linux.md) became part of it in the 90s as the last piece of the puzzle -- the system should be called just GNU but is now rather known as GNU/Linux (watch out: most so called "Linux systems" nowadays aren't embraced by GNU as they diverge from GNU's strict policies on what the system should look like, only a handful of operating systems are recommended by GNU). However, the GNU project didn't end and continues to further develop the operating system, or rather a myriad of user software that runs under the operating system -- GNU develops a few of its projects itself and also offers hosting and support (such as free legal defense) for GNU projects developed by volunteers who dedicate their work to them. GNU gave rise to the [Free Software Foundation](fsf.md) and is one of the most important software projects in history of computing.
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The mascot of GNU is literally gnu (wildebeest), it is available under a copyleft license. WARNING: ironically GNU is extremely protective of their brand's "intellectual property" and will rape you if you use the name GNU without permission (see the case of GNU boot). It's quite funny and undermines the whole project a bit.
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The GNU/Linux operating system has several variants in a form of a few GNU approved "Linux" [ditributions](distro.md) such as [Guix](guix.md), [Trisquel](trisquel.md) or [Parabola](parabola.md). Most other "Linux" distros don't meet the strict standards of GNU such as not including any proprietary software. In fact the approved distros can't even use the standard version of [Linux](linux.md) because that contains proprietary [blobs](blob.md), a modified variant called [Linux-libre](linux_libre.md) has to be used.
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GNU greatly prefers [GPL](gpl.md) [licenses](license.md), i.e. it strives for [copyleft](copyleft.md), even though it accepts even projects under permissive licenses. GNU also helps with enforcing these licenses legally and advises developers to transfer their [copyright](copyright.md) to GNU so that they can "defend" the software for them.
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**GNU greatly prefers [GPL](gpl.md) [licenses](license.md)**, i.e. it strives for [copyleft](copyleft.md) and largely recommends it, even though it will also accept projects under permissive licenses as those are still free. GNU also helps with enforcing these licenses legally and advises developers to transfer their [copyright](copyright.md) to GNU so that they can "defend" the software for them.
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Although GNU is great and has been one of the best things to happen in software ever, it has many flaws. For example their programs are known to be kind of a [bloat](bloat.md), at least from the strictly [suckless](suckless.md) perspective. **It also doesn't mind proprietary non-functional data** (e.g. assets in video games) and their obsession with copyleft also isn't completely aligned with [LRS](lrs.md). GNU is also generally **NOT supportive of [free culture](free_culture.md) and use copyright to prohibit modifications of their propaganda texts**: the [GFDL](gfdl.md) license they use for texts may contain sections that are prohibited from being modified and so are non-free by definition. This sucks big time and shows some of fascist corruption within the movement.
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**If we still have a bit of freedom in computing nowadays, it is largely to GNU** -- this can't be stressed enough. But although GNU is great and has been one of the best things to happen in software ever, it also has many flaws, for example:
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- **GNU programs are typically [bloated](bloat.md)** -- although compared to [Windows](windows.md) GNU programs are really light as a feather and though GNU programs are also in many cases (but not always) quite optimized, their source code, judged from strictly [suckless](suckless.md) perspective, is mostly huge, which many view as a big issue (it's a common theme, there are [jokes](joke.md) such as GNU actually meaning *Gigantic and Nasty but Unavoidable* and so on). This is likely because GNU chooses to [battle](fight_culture.md) proprietary programs, often by trying to beat them at their own game, so features are preferred over [minimalism](minimalism.md) to stay competitive.
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- **GNU also doesn't mind proprietary non-functional data** (e.g. assets in video games). This goes against [free culture](free_culture.md) and many other free software groups, notably e.g. [Debian](debian.md). Justifications for this range from "data itself can't be harmful" (false), through "we just focus on software" to "we need GNU to be more popular" (i.e. compatible with proprietary games and so on). GNU is also generally **NOT supportive of [free culture](free_culture.md) and even uses copyright to prohibit modifications of their propaganda texts**: the [GFDL](gfdl.md) license they use for texts may contain sections that are prohibited from being modified and so are non-free by definition. They also try to "protect" their names, you can't use the name "GNU" without their permission and so on. This sucks big time and shows some of the movement's darker side.
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- **GNU greatly pushes [copyleft](copyleft.md)**, which we, as well as many others, oppose.
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## History
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@ -2,6 +2,9 @@
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*Not to be confused with [liberalism](liberalism.md).*
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Libertarianism is one of very broad [harmful](harmful.md) political ideologies whose definition isn't at all clear, but which in essence gives highest priority to individual liberty and seeks to minimize the role of state. It is in some ways similar to [anarchism](anarchism.md) -- and just like anarchism it has many branches which frequently greatly diverge and even oppose each other -- it focuses on the people and believes people can form a working, decentralized society by loose associations, however while anarchism opposes state altogether, libertarianism may want to preserve some functions of the state such as courts and justice, protection from criminals etc.; libertarians believe in "equality before law" and they also mostly want to end private property and keep only personal property, i.e. usually opposing "the kind of [capitalism](capitalism.md) we have today" so that we can have "the better capitalism" (lol), however be careful, libertarianism basically embrace the **"law of the jungle"** or **"wild west"** mindset, some of the most retarded ideologies in history, such as ["anarcho" capitalism](ancap.md), are often classified as rightist libertarianism. So don't subscribe to this, it's shit.
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Libertarianism is a [harmful](harmful.md) political ideology whose definition is quite broad and not super clear, but which in essence gives highest priority to individual "liberty" and seeks to minimize the role of state (but typically without wanting to remove it). A bit like [anarchism](anarchism.md), libertarianism has many branches which frequently greatly diverge and even oppose each other, some are called more "leftist", some more "rightist" -- libertarianism usually tries to pretend to be focusing on the people, i.e. their "liberties", pseudoequality ("equality before law", "equality of opportunity", ...), oppose "the kind of corporate [capitalism](capitalism.md) we have today", believing some kind of "saner" version of it can work (which it can't), and claims that people can form a working, decentralized society by loose associations, however, unlike anarchism which opposes state and any kind of hierarchy altogether (with [true anarchism](anpac.md) also opposing any violence), libertarianism typically wants to preserve some functions of the state such as courts and justice for protection against crime, and it acknowledges property as a sacred thing that may even be defended by violence, i.e. libertarianism just replaces the rule of states by rule of private subjects, getting quite close to ["anarcho" capitalism](ancap.md), the stupidest idea yet conceived. Libertarians basically adopts the **"law of the jungle"** or **"wild west"** mindset. So it's [shit](shit.md), do not subscribe.
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[USA](usa.md) is essentially just a land where libertarians [battle](fight_culture.md) with [liberals](liberalism.md). Both camps are similarly stupid.
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{ Some bashing by digdeeper: https://digdeeper.neocities.org/articles/libertarianism. ~drummyfish }
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@ -5,7 +5,7 @@ WORK IN PROGRESS
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{ Most of these I just heard/read somewhere, e.g. on [4chan](4chan.md), in [Jargon File](jargon_file.md) or from [RMS](rms.md), some terms I made myself. ~drummyfish }
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| mainstream | correct/cooler |
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| ------------------------------------------ | -------------------------------------- |
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| ------------------------------------------ | ---------------------------------------------------- |
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| American | Amerifag |
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| [anime](anime.md) | tranime |
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| [Apple](apple.md) user | iToddler |
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@ -36,7 +36,7 @@ WORK IN PROGRESS
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| [global warming](global_warming.md) | global heating |
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| [Google](google.md) | Goolag |
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| Gmail | Gfail |
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| [GNU](gnu.md) | GNUts, freetards |
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| [GNU](gnu.md) | GNUts, freetards, Gigantic and Nasty but Unavoidable |
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| influencer | manipulator |
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| [Intel](intel.md) | [Incel](incel.md) |
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| [Internet Explorer](internet_explorer.md) | Internet Exploder, Internet Exploiter |
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@ -83,7 +83,6 @@ WORK IN PROGRESS
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| [work](work.md) | slavery |
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| [world wide web](www.md) | world wide wait |
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| [YouTube](youtube.md) | JewTube |
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## See Also
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- [acronyms](acronym.md)
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132
number.md
132
number.md
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@ -41,60 +41,86 @@ Here are some [fun](fun.md) facts about numbers:
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*Number lines and some notable numbers -- the horizontal line is real line, the vertical is imaginary line that adds another dimension and reveals complex numbers. Further on we can see quaternion lines projected, hinting on the existence of yet higher dimensional numbers (which however cannot properly be displayed using mere two dimensions here).*
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The following is a table demonstrating just one way of how you can play around with numbers -- here we just examine whole positive numbers (like number theorists would) up to 50, count each one's total number of divisors (excluding 1 and itself, 0 here means the number is [prime](prime.md) except for 1, if the number is highest in the series so far the number is called "highly composite"), unique divisors (excluding itself), sum of total and unique divisors (if the number equal sum of unique divisors, it is said to be a "perfect number"), average "dividing spread" (distance of each tested potential divisor's remainder after division from half of this tested potential divisor, kind of "amount of not dividing the number") in percents, maximum dividing spread and normalized range between smallest and biggest divisor expressed in percents (-1 if there are none). You can make quite interesting graphs from similar data and discover cool and interesting patterns.
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The following is a table demonstrating just one way of how you can play around with numbers -- of course, we have generated it with a program, so we also practice [programming](programming.md) a bit ;) Here we just examine whole positive numbers (like number theorists would) up to 50 and take a look at some of their attributes -- we count each one's total number of divisors (excluding 1 and itself, 0 here means the number is [prime](prime.md) except for 1, if the number is highest in the series so far the number is called "highly composite"), unique divisors (excluding itself), minimum divisor (excluding 1 except for 1), maximum divisor (excluding itself except for 1), sum of total and unique divisors (if the number equal sum of unique divisors, it is said to be a "perfect number"), average "dividing spread" (distance of each tested potential divisor's remainder after division from half of this tested potential divisor, kind of "amount of not dividing the number") in percents, maximum dividing spread and normalized range between smallest and biggest divisor expressed in percents (-1 if there are none). You can make quite interesting graphs from similar data and discover cool and interesting patterns.
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| number | divisors |divisors uniq.|divisor sum|uniq. div. sum|avg. div. spread (%)|max div. spread (%)|div. range (%)|
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| -------- | -------- | ------------ | --------- | ------------ | ------------------ | ----------------- | ------------ |
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| 1 | 0 | 1 | 0 | 1 | 0 | 0 | -1 |
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| 2 | 0 | 1 | 0 | 1 | 0 | 0 | -1 |
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| 3 | 0 | 1 | 0 | 1 | 0 | 0 | -1 |
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| 4 | 2 | 2 | 4 | 3 | 33 | 100 | 0 |
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| 5 | 0 | 1 | 0 | 1 | 16 | 50 | -1 |
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| 6 | 2 | 3 | 5 | 6 | 43 | 100 | 16 |
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| 7 | 0 | 1 | 0 | 1 | 24 | 66 | -1 |
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| 8 | 4 | 3 | 10 | 7 | 44 | 100 | 25 |
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| 9 | 2 | 2 | 6 | 4 | 36 | 100 | 0 |
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| 10 | 2 | 3 | 7 | 8 | 40 | 100 | 30 |
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| 11 | 0 | 1 | 0 | 1 | 34 | 80 | -1 |
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| 12 | 5 | 5 | 17 | 16 | 53 | 100 | 33 |
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| 13 | 0 | 1 | 0 | 1 | 35 | 83 | -1 |
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| 14 | 2 | 3 | 9 | 10 | 43 | 100 | 35 |
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| 15 | 2 | 3 | 8 | 9 | 44 | 100 | 13 |
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| 16 | 7 | 4 | 24 | 15 | 49 | 100 | 37 |
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| 17 | 0 | 1 | 0 | 1 | 38 | 87 | -1 |
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| 18 | 5 | 5 | 23 | 21 | 47 | 100 | 38 |
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| 19 | 0 | 1 | 0 | 1 | 42 | 88 | -1 |
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| 20 | 5 | 5 | 23 | 22 | 51 | 100 | 40 |
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| 21 | 2 | 3 | 10 | 11 | 45 | 100 | 19 |
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| 22 | 2 | 3 | 13 | 14 | 43 | 100 | 40 |
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| 23 | 0 | 1 | 0 | 1 | 42 | 90 | -1 |
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| 24 | 8 | 7 | 39 | 36 | 55 | 100 | 41 |
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| 25 | 2 | 2 | 10 | 6 | 45 | 100 | 0 |
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| 26 | 2 | 3 | 15 | 16 | 45 | 100 | 42 |
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| 27 | 4 | 3 | 18 | 13 | 44 | 100 | 22 |
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| 28 | 5 | 5 | 29 | 28 | 49 | 100 | 42 |
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| 29 | 0 | 1 | 0 | 1 | 45 | 92 | -1 |
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| 30 | 6 | 7 | 41 | 42 | 52 | 100 | 43 |
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| 31 | 0 | 1 | 0 | 1 | 45 | 93 | -1 |
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| 32 | 9 | 5 | 42 | 31 | 48 | 100 | 43 |
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| 33 | 2 | 3 | 14 | 15 | 45 | 100 | 24 |
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| 34 | 2 | 3 | 19 | 20 | 47 | 100 | 44 |
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| 35 | 2 | 3 | 12 | 13 | 48 | 100 | 5 |
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| 36 | 10 | 8 | 65 | 55 | 54 | 100 | 44 |
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| 37 | 0 | 1 | 0 | 1 | 45 | 94 | -1 |
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| 38 | 2 | 3 | 21 | 22 | 45 | 100 | 44 |
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| 39 | 2 | 3 | 16 | 17 | 46 | 100 | 25 |
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| 40 | 8 | 7 | 53 | 50 | 51 | 100 | 45 |
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| 41 | 0 | 1 | 0 | 1 | 47 | 95 | -1 |
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| 42 | 6 | 7 | 53 | 54 | 51 | 100 | 45 |
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| 43 | 0 | 1 | 0 | 1 | 46 | 95 | -1 |
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| 44 | 5 | 5 | 41 | 40 | 49 | 100 | 45 |
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| 45 | 5 | 5 | 35 | 33 | 47 | 100 | 26 |
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| 46 | 2 | 3 | 25 | 26 | 47 | 100 | 45 |
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| 47 | 0 | 1 | 0 | 1 | 47 | 95 | -1 |
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| 48 | 12 | 9 | 85 | 76 | 53 | 100 | 45 |
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| 49 | 2 | 2 | 14 | 8 | 48 | 100 | 0 |
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| 50 | 5 | 5 | 47 | 43 | 49 | 100 | 46 |
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{ Be warned the following is just me making some quick unoriginal antiresearch, I may mess something up, it's just to show the process of playing around with numbers. ~drummyfish }
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| number | divisors |divisors uniq.|min. div.|max. div.|divisor sum|uniq. div. sum|avg. div. spread (%)|max div. spread (%)|div. range (%)|
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| -------- | -------- | ------------ | ------- | ------- | --------- | ------------ | ------------------ | ----------------- | ------------ |
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| 1 | 0 | 1 | 1| 1| 0 | 1 | 0 | 0 | -1 |
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| 2 | 0 | 1 | 2| 1| 0 | 1 | 0 | 0 | -1 |
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| 3 | 0 | 1 | 3| 1| 0 | 1 | 0 | 0 | -1 |
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| 4 | 2 | 2 | 2| 2| 4 | 3 | 33 | 100 | 0 |
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| 5 | 0 | 1 | 5| 1| 0 | 1 | 16 | 50 | -1 |
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| 6 | 2 | 3 | 2| 3| 5 | 6 | 43 | 100 | 16 |
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| 7 | 0 | 1 | 7| 1| 0 | 1 | 24 | 66 | -1 |
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| 8 | 4 | 3 | 2| 4| 10 | 7 | 44 | 100 | 25 |
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| 9 | 2 | 2 | 3| 3| 6 | 4 | 36 | 100 | 0 |
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| 10 | 2 | 3 | 2| 5| 7 | 8 | 40 | 100 | 30 |
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| 11 | 0 | 1 | 11| 1| 0 | 1 | 34 | 80 | -1 |
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| 12 | 5 | 5 | 2| 6| 17 | 16 | 53 | 100 | 33 |
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| 13 | 0 | 1 | 13| 1| 0 | 1 | 35 | 83 | -1 |
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| 14 | 2 | 3 | 2| 7| 9 | 10 | 43 | 100 | 35 |
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| 15 | 2 | 3 | 3| 5| 8 | 9 | 44 | 100 | 13 |
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| 16 | 7 | 4 | 2| 8| 24 | 15 | 49 | 100 | 37 |
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| 17 | 0 | 1 | 17| 1| 0 | 1 | 38 | 87 | -1 |
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| 18 | 5 | 5 | 2| 9| 23 | 21 | 47 | 100 | 38 |
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| 19 | 0 | 1 | 19| 1| 0 | 1 | 42 | 88 | -1 |
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| 20 | 5 | 5 | 2| 10| 23 | 22 | 51 | 100 | 40 |
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| 21 | 2 | 3 | 3| 7| 10 | 11 | 45 | 100 | 19 |
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| 22 | 2 | 3 | 2| 11| 13 | 14 | 43 | 100 | 40 |
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| 23 | 0 | 1 | 23| 1| 0 | 1 | 42 | 90 | -1 |
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| 24 | 8 | 7 | 2| 12| 39 | 36 | 55 | 100 | 41 |
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| 25 | 2 | 2 | 5| 5| 10 | 6 | 45 | 100 | 0 |
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| 26 | 2 | 3 | 2| 13| 15 | 16 | 45 | 100 | 42 |
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| 27 | 4 | 3 | 3| 9| 18 | 13 | 44 | 100 | 22 |
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| 28 | 5 | 5 | 2| 14| 29 | 28 | 49 | 100 | 42 |
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| 29 | 0 | 1 | 29| 1| 0 | 1 | 45 | 92 | -1 |
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| 30 | 6 | 7 | 2| 15| 41 | 42 | 52 | 100 | 43 |
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| 31 | 0 | 1 | 31| 1| 0 | 1 | 45 | 93 | -1 |
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| 32 | 9 | 5 | 2| 16| 42 | 31 | 48 | 100 | 43 |
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| 33 | 2 | 3 | 3| 11| 14 | 15 | 45 | 100 | 24 |
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| 34 | 2 | 3 | 2| 17| 19 | 20 | 47 | 100 | 44 |
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| 35 | 2 | 3 | 5| 7| 12 | 13 | 48 | 100 | 5 |
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| 36 | 10 | 8 | 2| 18| 65 | 55 | 54 | 100 | 44 |
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| 37 | 0 | 1 | 37| 1| 0 | 1 | 45 | 94 | -1 |
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| 38 | 2 | 3 | 2| 19| 21 | 22 | 45 | 100 | 44 |
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| 39 | 2 | 3 | 3| 13| 16 | 17 | 46 | 100 | 25 |
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| 40 | 8 | 7 | 2| 20| 53 | 50 | 51 | 100 | 45 |
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| 41 | 0 | 1 | 41| 1| 0 | 1 | 47 | 95 | -1 |
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| 42 | 6 | 7 | 2| 21| 53 | 54 | 51 | 100 | 45 |
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| 43 | 0 | 1 | 43| 1| 0 | 1 | 46 | 95 | -1 |
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| 44 | 5 | 5 | 2| 22| 41 | 40 | 49 | 100 | 45 |
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| 45 | 5 | 5 | 3| 15| 35 | 33 | 47 | 100 | 26 |
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| 46 | 2 | 3 | 2| 23| 25 | 26 | 47 | 100 | 45 |
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| 47 | 0 | 1 | 47| 1| 0 | 1 | 47 | 95 | -1 |
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| 48 | 12 | 9 | 2| 24| 85 | 76 | 53 | 100 | 45 |
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| 49 | 2 | 2 | 7| 7| 14 | 8 | 48 | 100 | 0 |
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| 50 | 5 | 5 | 2| 25| 47 | 43 | 49 | 100 | 46 |
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Now we may start working with the [data](data.md), let's for example notice we can make a nice [tree](tree.md) of the numbers by assigning each number as its parent its greatest divisor:
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```
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1
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.---.------------.------------.-----'--.-----.---.--.--.--.--.--.--.--.--.
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| | | | | | | | | | | | | | |
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2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 <--- primes
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| | | | | | | | |
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| .'---. .----+----. .---.-'-.--. .-'-. .-'-. | | |
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| | | | | | | | | | | | | | | | |
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4 6 9 10 15 25 14 21 35 49 22 33 26 39 34 38 46
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| | | | | | | | |
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| | .-'-. | .-'-. | | | |
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| | | | | | | | | | |
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8 12 18 27 20 30 45 50 28 42 44
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16 24 36 40
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32 48
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```
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Here patterns start to show, for example the level one of the tree are all prime numbers. Also in this tree we can nicely find the [greatest common divisor](gcd.md) of two numbers as their closest common ancestor. Also if we go from low numbers to high numbers (1, 2, 3, ...) we see we go kind of in a zig-zag direction around the bottom-right diagonal -- what if we make a program that plots this path? Will we see something [interesting](interesting.md)? We could use this tree to encode numbers in an alternative way too, by indicating path to the number, for example *45 = {2,1,1}*. Would this be good for anything? If we write numbers like this, will some operations maybe become easier to perform? You can just keep diving down rabbit holes like this.
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|
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## Numbers In Math
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4
prime.md
4
prime.md
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@ -12,7 +12,7 @@ The largest known prime number as of 2022 is 2^82589933 - 1 (it is so called [Me
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Every natural number greater than 1 has a unique **prime factorization**, i.e. a [set](set.md) of prime numbers whose product it is. For example 75 is a product of three primes: 3 * 5 * 5. This is called the *fundamental theorem of arithmetic*. Naturally, each prime has a factorization consisting of a single number -- itself -- while factorizations of non-primes consist of at least two primes. To mathematicians prime numbers are what chemical elements are to chemists -- a kind of basic building blocks.
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|
||||
**Why is 1 not a prime?** Out of convenience -- if 1 was a prime, the fundamental theorem of arithmetic would not hold because 75's factorization could be 3 * 5 * 5 but also 1 * 3 * 5 * 5, 1 * 1 * 3 * 5 * 5 etc.
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||||
**Why is 1 not a prime?** Out of convenience -- if 1 was a prime, the fundamental theorem of arithmetic would not hold because 75's factorization could be 3 * 5 * 5 but also 1 * 3 * 5 * 5, 1 * 1 * 3 * 5 * 5 etc. It also makes sense under some different definitions -- imagine for example we create a [tree](tree.md) of numbers, assign each number *N* a parent number *M* which is the maximum of all *N*'s divisors that we check from 1 (including) to *N* (excluding); in this tree prime numbers are all numbers in depth 1, i.e. those that are direct children of 1, but 1 itself is not at this level, it's at the root, having no parent (as it would be its own parent), so by this definition 1 is also not a prime.
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||||
The unique factorization can also nicely be used to encode [multisets](multiset.md) as numbers. We can assign each prime number its sequential number (2 is 0, 3 is 1, 5 is 2, 7 is 3 etc.), then any number encodes a set of numbers (i.e. just their presence, without specifying their order) in its factorization. E.g. 75 = 3 * 5 * 5 encodes a multiset {1, 2, 2}. This can be exploited in cool ways in some [cyphers](cypher.md) etc.
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@ -85,7 +85,7 @@ There also exists a term **pseudoprime** -- it stands for a number which is not
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**[Fun](fun.md) with primes**: thanks to their interesting, mysterious and [random](randomness.md) nature, primes can be played around -- of course, you can examine them mathematically, which is always fun, but you can also play sort of [games](game.md) with them. For example the prime race: you make two teams of primes, one that gives 1 modulo 4, the other one that gives 3; then you go prime by prime and add points to each team depending on which one the prime falls in; the interesting thing is that team 3 is almost always in lead just by a tiny amount (this is known as Chebyshev bias, only after 2946 primes team 1 gets in the lead for a while, then at 50378 etc.). Similar thing can be done by evaluating the Mobius function: set total sum to 0, then go number by number and if it only has unique prime factors, add 1 if the number of those factors is even, otherwise subtract 1 -- see how the function behaves. Of course you can go crazy, make primes paint pictures or compose [music](music.md) -- people also like to do this with digits of numbers, e.g. those of [pi](pi.md) or [e](e.md).
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**Can we generalize the concept of prime numbers?** Yeah, sure, why not? The ways are many, we'll rather run into the issue of analysis paralysis -- choosing the interesting generalization of out of the many possible ways. The above mentioned pseudoprimes, superprimes and twin primes are examples of generalizing primes, another one is e.g. defining so called **almost primes** -- a number is *n*-almost-prime if it has *n* prime factors, so 1-almost-primes are just regular primes (they have 1 prime divisor -- themselves) but then there are 2 almost primes like 9 or 15 that are kind of closer to being primes than let's say 5-almost-primes such as 48 or 80. I.e. we took the idea of numbers having either none (primes) or some (non-primes) divisors and generalized it by says a number is more prime like if it has fewer divisors. Similarly we may try to play on this observation: a non-prime is a number that is divisible by something, i.e. there is some number that when dividing the original number gives remainder after division zero; primes are those for which no number gives remainder zero, but some primes might be considered "weaker" by giving very low or very high remainder such as 1, i.e. being "not quite but almost" divisible by something (of course we have to somehow account for the fact that low divisors can only ever give low remainders) -- ideal prime would have remainders after division near the half of the dividing number (it would dodge multiples of other numbers with some margin), which we can formalize and define kind of "prime strength".
|
||||
**Can we generalize the concept of prime numbers?** Yeah, sure, why not? The ways are many, we'll rather run into the issue of analysis paralysis -- choosing the interesting generalization of out of the many possible ways. The above mentioned pseudoprimes, superprimes and twin primes are examples of generalizing primes, another one is e.g. defining so called **almost primes** -- a number is *n*-almost-prime if it has *n* prime factors, so 1-almost-primes are just regular primes (they have 1 prime divisor -- themselves) but then there are 2 almost primes like 9 or 15 that are kind of closer to being primes than let's say 5-almost-primes such as 48 or 80. I.e. we took the idea of numbers having either none (primes) or some (non-primes) divisors and generalized it by says a number is more prime like if it has fewer divisors. Another generalization was hinted on above: construct a [tree](tree.md) of numbers, 1 being the root, assigning each number a parent that's its greatest divisor (exclude the number itself from divisors); in this tree 1 is above prime numbers, prime numbers are on level 1, second level may be seen as the "next best thing" to primes (4, 6, 9, 10, 15, ...), third level the next (8, 12, 18, 27) and so on, i.e. we define the "primeness" as a number of times we have to replace it with its greatest divisor before we get to 1. Similarly we may try to play on this observation: a non-prime is a number that is divisible by something, i.e. there is some number that when dividing the original number gives remainder after division zero; primes are those for which no number gives remainder zero, but some primes might be considered "weaker" by giving very low or very high remainder such as 1, i.e. being "not quite but almost" divisible by something (of course we have to somehow account for the fact that low divisors can only ever give low remainders) -- ideal prime would have remainders after division near the half of the dividing number (it would dodge multiples of other numbers with some margin), which we can formalize and define kind of "prime strength".
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TODO: generalization to non integers? does it exist?
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3358
random_page.md
3358
random_page.md
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@ -3,8 +3,8 @@
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This is an autogenerated article holding stats about this wiki.
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- number of articles: 566
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- number of commits: 739
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- total size of all texts in bytes: 3366093
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- number of commits: 740
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- total size of all texts in bytes: 3375996
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longest articles:
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@ -14,8 +14,8 @@ longest articles:
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56K chess.md
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52K how_to.md
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52K less_retarded_society.md
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44K faq.md
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44K number.md
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44K faq.md
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40K c.md
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36K internet.md
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32K 3d_rendering.md
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@ -24,6 +24,15 @@ longest articles:
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latest changes:
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```
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Date: Sat Mar 16 23:04:04 2024 +0100
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bloat.md
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encyclopedia.md
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flatland.md
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number.md
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random_page.md
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trolling.md
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wiki_pages.md
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wiki_stats.md
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Date: Sat Mar 16 19:49:26 2024 +0100
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3d_model.md
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computer.md
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@ -48,15 +57,6 @@ main.md
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number.md
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random_page.md
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sqrt.md
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trolling.md
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wiki_pages.md
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wiki_stats.md
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woman.md
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wow.md
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Date: Thu Mar 14 23:30:14 2024 +0100
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antivirus_paradox.md
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byte.md
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c.md
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```
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most wanted pages:
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@ -70,6 +70,7 @@ array.md
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quake.md
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irl.md
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gpl.md
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tree.md
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pointer.md
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lisp.md
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html.md
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@ -81,6 +82,5 @@ waiver.md
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syntax.md
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rpi.md
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mcu.md
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log.md
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```
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2
woman.md
2
woman.md
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@ -2,6 +2,8 @@
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A woman (also girl, gril, gurl, femoid, toilet, wimminz, the weaker sex, the dumber sex or succubus; [tranny](tranny.md) girl being called [t-girl](tgirl.md), [trap](trap.md), [femboy](femboy.md), fake girl or [mtf](mtf.md)) is one of two genders ([sexes](sex.md)) of [humans](human.md), the other one being [man](man.md). Women are the weaker sex, they are [cute](cute.md) (sometimes) but notoriously bad at [programming](programming.md), [math](math.md) and [technology](technology.md): in the field they usually "work" on [bullshit](bullshit.md) (and mostly [harmful](harmful.md)) positions such as "diversity department", [marketing](marketing.md), "[HR](human_resources.md)", [UI](ui.md)/[user experience](ux.md), or as a [token](token.md) girl for media. If they get close to actual technology, their highest "skills" are mostly limited to casual "[coding](coding.md)" (which itself is a below-average form of [programming](programming.md)) in a baby language such as [Python](python.md), [Javascript](javascript.md) or [Rust](rust.md). Mostly they are just hired for quotas and make coffee for men who do the real work (until TV cameras appear). Don't let yourself be fooled by the propaganda, women have always been bad with tech.
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The symbol for woman is a circle with cross at its bottom ([Unicode](unicode.md) U+2640). Women mostly like pink [color](color.md) and similar colors like red and purple.
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{ I would like to say there are a few women and girls I hold dear, whom I admire and who are in many aspects much better beings than myself and most men I known. ~drummyfish }
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**Even mainstream science acknowledges women are dumber than men**: even the extremely politically correct [Wikipedia](wikipedia.md) states TODAY in the article on human brain that male brain is on average larger in volume (even when corrected for the overall body size) AND that there is correlation between volume and intelligence: this undeniably implies women are dumber. On average male brain weights 10% more than woman's and has 16% more brain cells. The Guinness book of 1987 states the average male brain weight being 1424 grams and that of a female being 1242 grams; the averages both grow with time quite quickly so nowadays the numbers will be higher in both sexes, though the average of men grows faster. The heaviest recorded brain belonged to a man (2049 grams), while the lightest belonged to a woman (1096 grams). Heaviest woman brain weighted 1565 grams, only a little more than men's average. [IQ](iq.md)/intelligence measured by various tests has been consistently significantly lower for women than for men, e.g. the paper named *Sex differences in intelligence and brain size: A paradox resolved* found a 4 point difference, noting that in some problems such as 3D spatial rotations males score even 11 points higher average.
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Reference in a new issue