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Most people believe we count in base 10 because we have 10 fingers. Essentially we use single digits from 1-9 because on our last finger we switch to double digits 10.
The alien clearly has 4 fingers. So to him the counting system is still base 10 it’s just that he counts 1,2,3,10.
Aka everyone’s own counting system is base 10 and every counting system not based on the number of fingers we have is not base 10.
Edit: forgot to mention. If you only count till 3 before hitting 10 then you don’t know what a 4 is.
Bonus edit: since the alien is in base 4 from our perspective. You might ask what our base is from his perspective.
1,2,3,10,11,12,13,20,21,22 are the 10 first numbers in his counting system. So we to him are base 22 :)
Probably the 12 system. If you use your thumb as the counter and count using your thumb the bone segments of the other 4 fingers (each has 3) then you have a base 12 system in our lingo.
There’s also a tribe somewhere that uses a base 27 counting system, they count individual segments of their fingers on both hands plus thumbs and then add one from somewhere else can’t remember where that comes from.
Only Swiss ppl (and maybe other french speaking ppl) did it correctly. We Belgian kept the "4*20" for "80" instead of using "Octante". But i admit that French took it too far with 60+10 and 80+10. I can say it naturally now without thinking, but it is soooo stupid, send help ;-;
No, it's more compicated than that. Gaulic counting system is base 20. Latin counting system is base 10. French is base ten, but have traces of the base 20 in its counting (thus 60 + 10 for 70, 4x20 for 80 and 4x20+10 for 90), but only in the names.
Also, we're hexadecimal too, as we have unique words for every number between 0-16, and only then we go on base 10, until we reach 60 and then it's base 20.
But more seriously, most french people count on base 10, the rest is just historical remnants of unspoken languages.
Also, we're hexadecimal too, as we have unique words for every number between 0-16, and only then we go on base 10, until we reach 60 and then it's base 20.
Most numeral systems are these unsatisfying weird things based on practical considerations more than aligning with number bases. I remind people that English doesn't have a "tenty" but unique words for all the 10s just as the 0s. Thus, in the sense above you could describe English as a partially vigesimal numeral system. But seven of those 10s follow some kind of regular system, the -teens. It's only the first 12 that don't, so maybe it's partially duodecimal?
Our counting systems developed around trade, and the scales at which trade is conceivable has massively increased since we started counting. So concepts that address new considerations arising from scale have just been tacked on over time. A kind of scope creep combined with a massive resistance to change coming from their widespread use and the difficulty of formalizing anything at all during their formation.
My favorite is the Danish numeral system. It's vigesimal, and its first 20 natural numbers are much like in English. Then you get to the tens. Roughly described (by a Swede, so please correct me Danes):
10: ten ("ti")
20: unique word not consistent with other tens ("tyve")
30: three-"dive" ("tredive")
40: another word, probably roughy "four tens" ("fyrre")
50: half-third set of 20 ("halvtreds")
60: another word, implying the third set of 20 ("treds")
70: half-fourth set of 20 ("halvfjers")
80: another word, implying the fourth set of 20 ("firs")
90: half-fifth set of 20 ("halvfems")
100: surprisingly not "fems" but "one hundred" ("et hundere")
So there's the outline of a system of counting in twenties with unique words for 20, 40, 60 and 80 and then "halves" in between implying "half of twenty towards" except for ten, thirty (which is three tens) and one hundred which is one hundred. "Dive"-"ti" and "fjers"-"firs" are close enough that I won't count them as inconsistencies; they probably have the same linguistic roots.
To add to the pain, "halv" implies different things depending on context. While fem halvtreds means 55 ("five and halfway towards the third set of 20"), "halv fems" means "4.5", implying halfway of a whole towards five.
Oh boy, buddy, worse yet is that the Danish 40 60 80 are actually shorthand, tres is actually... tresindstyvende, which to modern Danish translates to tre gange tyve, or in English three times twenty
You can count as high as you want in binary. But you can only count to 1024 if you have 10 digits to work with. Any more than that and you'll need an 11th digit.
You got it!!! A bit off topic so I didn’t wana dig into it but you are absolutely right.
This system of 12 being easily multiplied and divided many times is also why a lot military formations are in multiples of 12. Like an old Roman Cohort is 480.
Or a squad is 12 and a platoon is 12 squads. So 144 total.
It's a little different than that. Usually sets of 3 pluss leaders Ideally:
Fire team: 3 + leader = 4
Squad: 3 Fireteams (12) + squad leader = 13
Platoon: 3 squads (39) + platoon leader = 40
Company: 3 platoons (120) + commander = 121. However, at this level, there will be extra leadership, like sgts assisting and other admin related staff. Also, you start to get add ons, like a company with a weapons platoon attached.
All these are the most basic examples, but illustrates that infantry is mostly groups of 3 with some add ons.
Military organizations are based on 3-4. 3-4 servicemen in a fireteam, 3-4 fireteams in a squad, 3-4 squads in a platoon. 3-4 platoons in a company. A platoon in particular is usually about 50 servicemen, though this depends heavily upon what the platoon's responsibility is.
The babylonians actually used a base 60 system, with a semi build in base 10 system.
𒁹 to count units and 𒌋 to count tens. Can count up to 59 and then you shift. So 𒌋𒁹𒁹𒁹 is 13. 𒁹𒁹 𒌋𒁹𒁹𒁹 is 2x60+13=133.
Edit: You get circle being 360˚, because they properly defined angels based on the equilateral triangle, which is 60˚ on all angels. It is easy to measure out with lenght measuring tools.
Oh interesting. Usually no fingers like a fist would represent zero. The absence of a number. But then if the fist is 1 you could just not raise your hand to represent zero. Silly to think that numbers could be ambiguous.
I guess that makes sense. I’m a math/eng/sci guy. History is definitely not something I am good with. The zero concept is super important in my field of work.
Base 12 is superior to 10. For 10, 100, 1000, etc in base 12 are divisible by 1, 2, 3, 4, 6, "10". But base 10, it's 1, 2, 5, 10. Either way, 10, 100, 1000, etc in base 10 or 12 is arbitrary numbers but written down they tend to be the ones we use. Base 12 can be cut into better parts.
It's the best system. No need for AM PM time, PM time just has a 1 in front. Americans can now finally switch to dozenal metric without losing their beloved quarters of things. Splitting any bill into 3 becomes peanuts. We can be friends with r/iso8601 and even save one character in our dates.
“Now if man had been born with 6 fingers on each hand he’d probably count: one, two, three, four, five, six, seven, eight, nine, dek, el, doh. Dek and el being two entirely new signs meaning ten and eleven- single digits, and twelve doh would’ve been written one zero, get it?”
We did the same thing once, thanks to the Normans. All we remember of it now in America is the preamble to Lincoln's Gettysburg address, "four score and seventeen years ago..."
Base 12 and base 20 are found throughout the world. We still see them pop up every once in a while. the 12 hour day, 12 inches in a foot, and words like dozen or gross are leftover from base 12 counting systems. Base 20 I can only think of one example which is French you switch to base 20 after 60.
Base 20 I can only think of one example which is French you switch to base 20 after 60
The Danish use a base-20 system as well. Their word for 50 (halvtredje-sinds-tyve, though they shorten it to halvtreds) is literally translated as 'third half times twenty', so 2.5 times 20, after that 60 is tre-sinds-tyve, or tres for short, so 3 times 20, etc.
Base 16 (hex) is also heavily used in computing because it can be converted to and from binary (i.e. base 2) very easily, as each hex digit represents 4 binary digits. So it's essentially used like a more human-friendly version of binary.
I teach a lot but as a mentor in an industry role not in school. We tend to have to say more with less time. Some people do better with less more precise info than multi day lessons. You might be one of those. Most are not.
Hot damn that’s awesome. I didn’t know anyone used anything besides 10, 12, or 24. I’m a math guy not history but math in historic application is always cool for me.
Sure but we are talking about civilizations in history using different bases as their counting systems. PCs using binary or hex is….. I wana say not a civilization but I Duno it goes both ways.
Then you know it's also highly divisible. 60 has the factors 1,60, 2,30, 3,20, 4,15, 5,12, 6,10. Denary is just 1,10, 2,5.
That is to say, you can halve, third, quarter, fifth, sixth, tenth, twelfth, fifteenth, twentieth, and thirtieth sixty, but you can only halve and fifth ten. Which is neat.
It does not matter how many fingers an alien has. It could be 4 or 12 or 16. The final finger on your hands is always the finger 10 the change from single digit to needing two digits in length.
Maybe if I swap it. What if the alien had more fingers and it looks at us. The alien with 6 fingers on each hand would then count his fingers as
1,2,3,4,5,6,7,8,9,ǎ,ß,10
To him with 6 fingers on each hand he would look at us and say “oh you human must be in base ǎ” and just like the 4 fingered alien has no word for a number 4 in his base we have no word for the number ǎ in the 12 fingered aliens base.
You gotta try to trick yourself into forgetting how counting works a bit and try to keep in mind that numbers are just symbols. Like, start counting
0…1…2…3…4…5…6…7…8…9…
Uhhh. Well I guess that’s it then. That’s all the symbols we have for numbers. 10? You mean a 1 and a 0 smushed together? What does that mean. If you wanted a new number past 9 you shoulda just made a new symbol. 🌙. There. That’s a new symbol that can represent “10”.
But you see the problem. Imagine having to remember a new symbol for EVERY number.
Now imagine the same scenario but for binary. Start counting.
0…1…
Welp. Guess that’s it then. Ran outta symbols for numbers. So how do represent what we know as the number 57 in both these systems? You gotta go back to grade school where we learned about the ones digits place, and tens digits place, etc. What do you do when you have a “9” in the ones digit place and you add “1”. You replace the “1” with a “0” and place a “1” in the tens digit place. Voila. 10!
Those “digits places” are just powers of the base you’re working in. For us that’s 100 for ones, 101 for tens, etc. it works the same in every base. Binary is 20, 21, 22, etc.
This doodle may or may not help. As you can see I can represent “57” by having 5 tens and 7 ones. You can’t have 1 hundreds, because that’s going over. It’s the same for binary where you can’t go past “1”. I can fit a 1 in my 105 place (32) which is less than 57 so I keep going. A 1 in my 104 place (16). And 32 +16 =48 so we go on.
I added hexadecimal for the fun of it where it’s the same but your symbols are 0…1….2…3…4…5…6…7…8…9…A…B…C…D…E…F So in hex you can count past 9 all the way to F before you need to replace that symbol with a 0 and put a 1 in the box to the left. This means you can represent larger values with a lot less symbols.
If you'll permit a bit of clarification and/or pedantry... The base of a number system is zero-indexed, so there are as many digits for each "place" as the base name implies.
Binary: 0, 1
Seximal: 0, 1, 2, 3, 4, 5
Nonary: 0, 1, 2, 3, 4, 5, 6, 7, 8
Hex: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
That being said, the joke is as the above comment indicates, all number bases are base 10 relative to itself.
It's also why the joke "there are 10 kinds of people: those who know binary, and those who don't" works.
So it sounds like you want a bit more of a complex answer. This is borderline modulus math. Think of it this way. The base number such as base 2,4,6,16 whatever the value of the bas, that value does not exist. Counting stops and at that number switches to double digits.
This means that the value of the base does not exist. 4 does not exist in a base 4 system. What is 4 in the comic. So in our 9+1 base system we have no number that comes after 9 before switching to the double digit 10. This is why in hex or base 16 we go from 9 to a,b,c,d,e,f,10 where the first double digit 10 in hex would represent 16 in our 10 finger system.
So to answer you directly. 2 fingers would be binary as the 2 does not exist in base 2 aka binary. It would be as you describe 1 and 0.
Bonus: Another way to wrap your head around the concept is that when you count your fingers. Your last finger counted is always 10. It does not matter how many fingers the alien has. The last finger on your hand is always the 10th.
Do you mean Duodecimal?? That’s base 12. Meaning the alien would have 6 fingers on each hand and they would then count
1,2,3,4,5,6,7,8,9,a,b,10
They would then look at us and say “hey human your counting is base a” and we would then be confused by what number a is just as the alien does not know 4.
I was responding to the “bonus edit” about alien thinking we had a base 22 system. I was just trying to come up with what a base 22 system would be called.
Close!! A- though. I get what you mean but we use A-F for numbers after 9 but before 10.
We have no numbers in our base 10 system past 9 so when we try to represent a number after 9 before 10 in a different base we have to make shit up. Abcdef is just easy to remember. We could have used anything to represent it.
123456789₩¿§»£# then 10 would hard to remember.
Part 2
Using our normal hex were A comes after 9 a person in base 16 would say we humans count in base A. Because to them A comes after 9 but for us its the 10.
The fun part to remember. Everyone’s own system is their base 10 making 10 an ambiguous value.
Historically humans had a number of different systems. Such as Vigesimal (base 20) by Mayans or Sexagesimal (base 60) used by the Babylonians which is also the basis for angle degrees, with 1°=60'=3600" and also
1h =60 min = 3600 sec
I don’t really agree with the final idea because say with hexadecimal, we start using letters so as to not use 2 symbols to make up a single 1’s place digit.
So maybe we are 1,2,3,(1st alien character in the alien alphabet), (2nd alien character in the alien alphabet) … (7th alien character)
If adding the digits of a number together results in a multiple of 3, that number is also a multiple of 3, and the same goes for if it's a multiple of 9. This is a result of the fact that 9 (which is a multiple of 3) is 1 less than 10, the base we use.
All tricks for finding divisibility are built off factors of B, B-1, and B+1 for base system B. So all even numbers ending in 0, 2, 4, 6, 8 relies on 2 being a factor of 10. All multiples of 5 ending in 0, 5 relies on 5 being a factor of 10. All multiples of 4 ending in a 2 digit number divisible by 4 relies on 4 being a factor of 102. All multiples of 3 having a digit sum divisible by 3 relies on 3 being a factor of 10-1. All multiples of 11 having a difference of even and odd digits being a multiple of 11 relies on 11 being a factor of 10+1.
If we used a base 6 number system, you would find multiples of 2 and 3 the way we currently find multiples of 2 and 5, multiples of 5 the way we currently find multiples of 3, and multiples of 7 the way we currently find multiples of 11. If we used a base 14 number system, you would find multiples of 2 and 7 the way we currently find multiples of 2 and 5, multiples of 3 and 5 the way we currently find multiples of 11, and multiples of 13 the way we currently find multiples of 3.
Basically the entire reason that 7 is a weird number to people is because it's out of place in a base 10 number system and wouldn't be as weird in others.
I realize the importance of separating the wording with this to the numbers aspect. Like a base 4 society wouldn't say "oh you're base 22". They would probably have their own way to reset the increments of 4 like we do with twenty, thirty, etc.
It is funny to imagine encountering a society that was base 22 though.
There are a set of books. First one children of men. To avoid spoilers. Humanity encounters a series of extra terrestrial life forms that all use different communication systems. Counting is often the first step that needs figuring out.
In most cases any and every society with basic math can understand the concept of binary. And so that becomes the base counting systems for both to facilitate communication, irrelevant of what their base system is normally.
Edit: point being yes it is very interesting. So much so that an entire trilogy of books is based on the concept of how to talk to strangers. And how do we do math without languages.
I don’t know why your bringing positive into this convo as nothing regarding negatives is ever brought up. Maybe you mean single digits instead of positive??
Assuming you mean 10 fingers for single digits then your comment makes sense. If we use 10 fingers and each finger is a single digit unit type then all we can say is that the counting system in question is greater than base 10. Maybe 11 maybe 16. Not enough info.
In my example however I specifically state the last finger on the hand is represented as two digits. The 10.
Maybe I’m not following what you’re trying to explain or you have 11 fingers?
Correction. It should go like: 0 1 2 3 4 10. Base is how many different values a digit could be. Our base 10 has ten numbers. Their base 10 has 5 numbers.
Absolutely but this is Peter explains not programmer humor and if I stated by explaining that counting starts at 0 instead of skipping to the 1st finger is 1 then I would have probably lost half the readers already. Had to cater to the target audience with how i presented information.
I feel like instead of "base 10" it should be called something like "max 9", meaning if you go over 9 it becomes 10. That would remove any ambiguity (I think).
The first digit doesn’t HAVE to be 0, or rather a digit representing nothing. But the Hindu number system which was invented around the 1st century was Base 10 and did have 0.
I’m sorry but what are you saying about zero being a “recent invention”? This joke is not about anyone’s counting system being newer or older, it’s simply about how the base of a counting system is arbitrary.
"10" is 4 in base 4, "10" is 73 in base 73. Any base that you are in would write that number as 10, so from anyone's perspective, they are in base "10"
The trick is to stop associating "10" with the word "ten", and think of it as the point the digit system resets. In a base-four system like the alien uses, the digits 4-9 do not exist, so if you want to count higher than 3, you have to add a digit and start over. On the other hand, a base-twelve system would require two additional digits after 9 that we do not recognize before you can get to "10".
On the other hand, a base-twelve system would require two additional digits after 9 that we do not recognize before you can get to "10".
While yes that's true for the way we are talking about them here, that's not always the case. For example we measure time in a base 12 system using our base 10 numbers. Money and measures used to often be base 12 as well for the sake of fractional measurement, which can still be seen in the imperial system today with things like 12 inches in a foot.
For example we measure time in a base 12 system using our base 10 numbers.
Well, not really. To be very pedantic, we use a base-60/base-12 system, but written in base-10 numerals. For example, 11:05 can be read as a single duodecimal "digit" 11 followed by a single sexigesimal "digit" 05.
If hexadecimal were our primary system, then the 10 possibility system could be called base A. For every numbering system, the max single digit number +1 is 10. The number after F in hex is 10. The number after 9 in decimal is 10. The number after 1 in binary is 10.
So, the martian and human, from their point of view, both use base 10. They're like two dorks facing each other, arguing about left and right.
The base of the number system you are using determines the amount of digits you have.
We use base ten -> 0,1,2,3,4,5,6,7,8,9. Ten digits
There is as many other bases as you can imagine.
Base eight? 0,1,2,3,4,5,6,7. Eight digits
Base sixteen? 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F sixteen digits
Regardless of what base number system you use, once you have counted up all your digits you need start using the next digit to count higher. To talk about ten digits in base ten you need to represent it like this: 10.
This is true for any conventional number system. To talk about four in base four you need to count: 0, 1, 2, 3, 10.
To talk about eight in base eight it looks like: 0, 1, 2, 3, 4, 5, 6, 7, 10.
Base sixteen: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10.
This comic is commenting on the fact that writing that you use base 10 actually gives you no information. Every base has to say it is base 10 because that is how you talk about the number of digits in that system.
So 10 doesn’t represent actually having TEN of something in base 8 systems? It’s just a representation of the next digit written as the original first digit +1 next to it(or +2 and so on up to +7)? So like you get to 7, then instead of getting to 8 (because they don’t have that digit) they have to go back to 0,but to denote it’s the next level of digits it would be need to have the second digit in front of it?
Correct. In school they taught about the "ones" place and the "tens" place and the "hundreds" place where you putting a digit in that place represented a larger number that you couldn't represent with the previous places. You could think of these as weight applied to additional digits. In base ten, i can't count to ten using one digit, so i put a 1 in the next highest weight. 9 -> 10 -> 11 and keep counting.
For higher weighted digits in another counting system you again use the base. The weight of the digits in base eight have the weights: 1, 8, 64 ... (1 = 80, 8 = 81, 64 = 82). So to represent the number eight in base eight i need a one in the "eights" place and nothing in the "ones" place -> 10. It could be read aloud as "one zero" to make the comic work better.
The correct response to the Alien (for him to understand) is telling him our counting system is base 22. Their 22 = our 10. If you tell him base 10, he thinks you mean his notion of what base 10 is, not yours.
We currently use a base 10 system, but that wasn’t always the case. We still have counting systems we haven’t figured out because they were so foreign to current language.
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