Update

number.md

@@ -8,7 +8,7 @@ Numbers (from Latin *numerus* coming from a Greek word meaning "to distribute")
 
 Let's not [confuse](often_confused.md) numbers with digits or figures (numerals) -- a number is a purely abstract entity while digits serve as symbols for numbers so that we can write them down. One number may be written in many ways, using one of many [numeral systems](numeral_system.md) (Roman numerals, tally marks, Arabic numerals of different [bases](base.md) etc.), for example 4 stands for a number than can also be written as IV, four, 8/2, 16:4, 2^2, 4.00 or 0b100. There are also numbers which cannot exactly be captured within our traditional numeral systems, for some of them we have special symbols -- most famous example is of course [pi](pi.md) whose digits we cannot ever completely write down -- and there are even numbers for which we have no symbols at all, ones that are yet not well researched and are only described by equations to which they are the solution. Sure enough, a number by itself isn't too interesting and probably doesn't even make sense, it's only in context, when it's placed in relationship with other numbers (by ordering them, defining operations and properties based on those operations) that patterns and useful attributes emerge.
 
-Humans first started to use positive natural numbers, i.e. 1, 2, 3 ..., so as to be able to trade, count enemies, days and so on -- since then they kept expanding the concept of a number with more [abstraction](abstraction.md) as they encountered more complex problems. First extension was to fractions, initially reciprocals of integers (like one half, one third, ...) and then general ones. Around 6th century BC Pythagoras showed that there even exist numbers that cannot be expressed as fractions ([irrational numbers](irrational_number.md), which in the beginning was a controversial discovery), expanding the set of known numbers further. A bit later negative numbers were discovered/invented, likely in China. Adoption of the number [zero](zero.md) also took some time, with it first just having a limited use as a mere placeholder digit. Since 16th century a highly abstract concept of [complex numbers](complex_number.md) started to appear, which was later (19th century) expanded further to [quaternions](quaternion.md). With more advancement in mathematics -- e.g. with the development of set theory -- more and more concepts of new kinds of numbers appeared and still appear to this day. Nowadays we have greatly abstract numbers, ones existing in many dimensions, capable of counting and measuring infinitely large and infinitely small entities, and it seems we still haven't nearly discovered everything there is to know about numbers.
+Humans first started to use positive natural numbers (it seems as early as 30000 BC), i.e. 1, 2, 3 ..., so as to be able to trade, count enemies, days and so on -- since then they kept expanding the concept of a number with more [abstraction](abstraction.md) as they encountered more complex problems. First extension was to fractions, initially reciprocals of integers (like one half, one third, ...) and then general ones. Around 6th century BC Pythagoras showed that there even exist numbers that cannot be expressed as fractions ([irrational numbers](irrational_number.md), which in the beginning was a controversial discovery), expanding the set of known numbers further. A bit later (around 100 BC) negative numbers started to be used. Adoption of the number [zero](zero.md) also took some time (1st use of true zero seem to be in 4th century BC), with it first just having a limited use as a mere placeholder digit. Since 16th century a highly abstract concept of [complex numbers](complex_number.md) started to appear, which was later (19th century) expanded further to [quaternions](quaternion.md). With more advancement in mathematics -- e.g. with the development of set theory -- more and more concepts of new kinds of numbers appeared and still appear to this day. Nowadays we have greatly abstract numbers, ones existing in many dimensions, capable of counting and measuring infinitely large and infinitely small entities, and it seems we still haven't nearly discovered everything there is to know about numbers.
 
 Basically **anything can be encoded as a number** which makes numbers a universal abstract "medium" -- we can exploit this in both mathematics and programming. Ways of encoding [information](information.md) in numbers may vary, for a mathematician it is natural to see any number as a multiset of its [prime](prime.md) factors (e.g. 12 = 2 * 2 * 3, the three numbers are inherently embedded within number 12) that may carry a message, a programmer will probably rather encode the message in [binary](binary.md) and then interpret the 1s and 0s as a number in direct representation, i.e. he will embed the information in the digits. You can probably come up with many more ways.
 
@@ -163,7 +163,9 @@ One of the most interesting and mysterious number sets are the [prime numbers](p
 
 Of course there are countless other number sets, especially those induced by various number sequences and functions of which there are whole encyclopedias. Another possible division is e.g. to *cardinal* and *ordinal* numbers: ordinal numbers tell the order while cardinals say the size (cardinality) of a set -- when dealing with finite sets the distinction doesn't really have to be made, within natural numbers the order of a number is equal to the size of a set of all numbers up to that number, but with infinite sets this starts to matter -- for example we couldn't tell the size of the set of natural numbers by ordinals as there is no last natural number, but we can assign the set a cardinal number (aleph zero) -- this gives rise to new kind of numbers.
 
-**Numbers are awesome**, just ask any number theorist (or watch a numberphile video for that matter). Normal people see numbers just as boring soulless quantities but the opposite is true for that who studies them -- study of numbers goes extremely deep, possibly as deep as humans can go and once you get a closer look at something, you discover the art of nature. Each number has its own unique set of properties which give it a kind of "personality", different sets of numbers create species and "teams" of numbers. Numbers are intertwined in intricate ways, there are literally infinitely many patterns that are all related in weird ways -- normies think that mathematicians know basically everything about numbers, but in higher math it's the exact opposite, most things about number sequences are mysterious and mathematicians don't even have any clue about why they're so, many things are probably even [unknowable](knowability.md). Numbers are also self referencing which leads to new and new patterns appearing without end -- for example prime numbers are interesting numbers, but you may start counting them and a number that counts numbers is itself a number, you are getting new numbers just by looking at other numbers. The world of numbers is like a whole universe you can explore just in your head, anywhere you go, it's almost like the best, most free video [game](game.md) of all time, embedded right in this [Universe](universe.md), in [logic](logic.md) itself. Numbers are like animals, some are small, some big, some are hardly visible, trying to hide, some can't be overlooked -- they inhabit various areas and interact with each other, just exploring this can make you quite happy. { Pokemon-like game with numbers when? ~drummyfish }
+Worthy of mentioning is also [linear algebra](linear_algebra.md) which treats [vectors](vector.md) and [matrices](matrix.md) like elementary algebra treats numbers -- though vectors and matrices aren't usually seen as numbers, they may be seen as an extension of the concept.
+
+**Numbers are [awesome](awesome.md)**, just ask any number theorist (or watch a numberphile video for that matter). Normal people see numbers just as boring soulless quantities but the opposite is true for that who studies them -- study of numbers goes extremely deep, possibly as deep as humans can go and once you get a closer look at something, you discover the art of nature. Each number has its own unique set of properties which give it a kind of "personality", different sets of numbers create species and "teams" of numbers. Numbers are intertwined in intricate ways, there are literally infinitely many patterns that are all related in weird ways -- normies think that mathematicians know basically everything about numbers, but in higher math it's the exact opposite, most things about number sequences are mysterious and mathematicians don't even have any clue about why they're so, many things are probably even [unknowable](knowability.md). Numbers are also self referencing which leads to new and new patterns appearing without end -- for example prime numbers are interesting numbers, but you may start counting them and a number that counts numbers is itself a number, you are getting new numbers just by looking at other numbers. The world of numbers is like a whole universe you can explore just in your head, anywhere you go, it's almost like the best, most free video [game](game.md) of all time, embedded right in this [Universe](universe.md), in [logic](logic.md) itself. Numbers are like animals, some are small, some big, some are hardly visible, trying to hide, some can't be overlooked -- they inhabit various areas and interact with each other, just exploring this can make you quite happy. { Pokemon-like game with numbers when? ~drummyfish }
 
 There is a famous [encyclopedia](encyclopedia.md) of integer sequences at https://oeis.org/, made by number theorists -- it's quite [minimalist](minimalism.md), now also [free licensed](free_culture.md) (used to be [proprietary](proprietary.md), they seem to enjoy license hopping). At the moment it contains more than 370000 sequences; by browsing it you can get a glimpse of how deep the study of numbers goes. These people are also [funny](fun.md), they give numbers entertaining names like *happy numbers* (adding its squared digits eventually gives 1), *polite numbers*, *friendly numbers*, *cake numbers*, *lucky numbers* or *weird numbers*.
 
@@ -238,6 +240,7 @@ Here is a table of some notable numbers, mostly important in math and programmin
 | thirty one                          | 31                  | 2^5 - 1                                  | maximum unsigned number storable with 5 bits            |
 | [thirty two](thirty_two.md)         | 32                  | 2^5, 0b100000                            |                                                         |
 | thirty six                          | 36                  | 2 * 2 * 3 * 3                            | highly composite number                                 |
+| thirty seven                        | 37                  |                                          | most commonly chosen 1 to 100 "random" number           |
 | [fourty two](42.md)                 | 42                  |                                          | cringe number, answer to some stuff                     |
 | fourty eight                        | 48                  | 2^5 + 2^4, 2 * 2 * 2 * 2 * 3             | highly composite number                                 |
 | sixty three                         | 63                  | 2^6 - 1                                  | maximum unsigned number storable with 6 bits            |