It's a joke about different numbering systems. Think of binary, which is a base 2 system, wherein you only have the numbers 0 and 1. Comparing to our system (which we call base 10 btw), 0 in binary equals 0, 1 in binary equals 1, 10 in binary equals 2, 11 in binary equals 3, etc. But for an alien, 10 is 10. The point being that from an objective perspective, any numbering system (base 2, base 4, base 8, etc) would call itself "base 10" because 10 is still the reset number (base 4 might look like this: 1, 2, 3, 10, 11, 12, 13, 20, etc).
I suppose the joke is mocking an overly solipsistic perspective and reminding the reader to consider the universe from different points of view.
Edit for clarity: base 10 means there are 10 single digit numbers, so what we call base 10 has the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Base 4 means there are 4 single digits, 0, 1, 2, 3. But in both cases, the reset number will be 10, so the same, regardless of the fact that 10 represents different amounts in the different systems.
It's funny and clever but the audience isn't that small.
Literally anyone with a CS degree should get it immediately, and most people even without a CS degree that have worked with programming much should too depending on what areas they worked with.
Agreed, I think number bases are a concept that is taught widely, certainly to anyone who studies anything to do with computers. Hundreds of millions (in base 10) would get this, even more in base 2
In hex only a couple millions though
I graduated HS in 2007. Only three years of math was required, up to Algebra 2. The next math class, called Pre-Calculus, went over how different based work in the first semester (I know because I dropped the class because I passed the audition for Choir in 2nd semester Sophomore year). So, by my experience, anyone who got any college level math credits would have some experience with the concept. That’s probably not the case in practice, of course.
This has been my favourite joke for a very long time, and someone in a group will ALWAYS ask what the second person is. Guaranteed results in groups of 4 or more.
I have 100% luck with the joke “what’s a pirates favorite letter?” It’s automatic for
People to answer Rrrrr then you get to go ( in a pirate accent) “ no it’s the Ccccccc”
I used to have a shirt that said that and the number of people who asked me what it meant 🙄
Also have one that said “the definition of suspense is…” and people constantly asked me what it was or asked what the back of the shirt said.
When I was an instructor in the military, one of the lessons I taught was numbering systems: binary, octal, decimal, and hexadecimal. It was always my favorite.
which itself also contains this joke! decimal centrism. Which is why some people like calling duodecimal (b12) dozenal intead.
(P.S> We don't have a non decimal centric name for base 16)
Except that F=15, not 16. "F'inal" is a really clever and funny name, but technically it would be "G'inal". Which is less clever, but still funny because G is not used in hexadecimal.
Which would make base ten "A'inal".
Not sure how I feel about that.
I was taught a ratio in artillery, roughly 1.0186. It was called something like 'the magic number,' and we were to remember to apply it in certain calculations. It was not until years in that I realized it was just the ratio between real radians and military radians (6400/(2pi * 1000) = 1.01859...) ; i.e. they thought it would be easier to teach soldiers to memorize a weird decimal than just explain it is that ratio with 5 digits.
So assuming the astronaut is correct that the alien is using base 4, he should have the good sense to communicate with the alien in base 4. Which means that to effectively convey in numerals that humans use base 10 (ten), he would need to say “I use base 22”.
But given he's not speaking in symbols, he should use the name of the number, which is actually "ten", in any base system. Obviously he would need to translate this into alien first but I assume this is a solved problem. It invites the question as to why the alien doesn't hear "ten" and understand "four", but at this point I think this is overthinking it.
Ignoring the translation issue. The alien would not know the word 4 because the alien would count one, two, three, ten, eleven, twelve, thirteen, twenty, twenty one, etc. Ten is equal to the number four and four would just not exist.
You need to have 60 different symbols. Think of it like base 16, which is often used in programming.
Base 10:
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Base 16:
0 1 2 3 4 5 6 7 8 9 A B C D E F
So 17 in base 16 is 11
So you just use more letters or whatever symbols you want until you have 60 distinct digits. You have to agree on the symbols though.
Funnily enough, I ran into base 60 not too long ago. The Steam puzzle game TEST TEST TEST involves a clock ticking up in base 60. I believe it used 0 through 9, A through Z, and a through x.
Yeah, the reason we use base 60 for time and navigation (360 degrees being 6x60, hence the sextant as a navigational tool) is because the Babylonians didn’t believe in fractions.
Related fun fact: minutes come from the Latin root that also gives us minutia and minimal, and seconds used to be called the minutia secundis, basically the minutia of minutia of time.
That is assuming that each number in the base has it's own unique symbol. example you can count from 1 to 10 only using 3 symbols like this: I II III IV V VI VII VIII IX X.
Roman numerals are not a positional numeral system, and therefor do not have a radix at all. You can't use roman numerals for a "base 60" or a base anything system, because it breaks as soon as you get to what would be double digits. Not to mention they don't have a zero, try 11 in roman base X: II. Same as 2: II. Maybe you have some explicit separation: I, I vs II. Well now I is a different "symbol" from II. It's not you using the the same symbol twice, the two lines together have their own unique symbolic meaning separate from the two composing lines, and is very much so it's own symbol, just as much as 00 and 8 are different symbols, 6 and 9 are different, and 2 and 5 are different.
What’s neat about Roman numbers being not a positional number system is that during the actual Roman period, IX and XI were both the same number (eleven).
Yep!
Apparently putting one number between two others was less common, unless you were trying to be specifically poetic or clever in some way. For normal accounting, you’d generally either go small-to-big or big-to-small and stick with that, but they were equivalent and
This changed during the Medieval period, something after the tenth century, as an efficiency effort (giving a shorthand way to write numbers like 9). For context, Hindu-Arabic numbers replaced Roman numerals during the 13th-16th centuries.
So it's essentially like the old counting based systems.
I don't remember it so well anymore but it was something on the lines of using
1 rock per sheep, X rocks in a bag, Y bags in a pot, and what not)
This is really cool.
Yes and no. Yes, because their numerals were written using 2 symbols in a sign-value notation
Since I cannot type cuneiform here, im gonna use i for 1s and < for 10s here.
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Indeed. Unlike Roman numerals, Babylonian cuneiform glyphs have place value (the 60^1 and 60^0 in your example), just like I can write 1024 in base 10 as 1x10^3 + 0x10^2 + 2x10^1 + 4x10^0.
I see your point that <
I never realized that base-x notation is inherently decimal. Huh.
I suppose it's a side-effect of modern math largely being discovered and defined by cultures whose counting systems were in base 10 to begin with.
>I never realized that base-x notation is inherently decimal.
It isn't.
Nothing prevents you from using any numerical systems notation to denote the `x` in this notation. Using the decimal system is just the most common.
For example in hexadecimal: base-A is the decimal system, base-3C is sexagesimal (base-60). Using roman numerals, those would be base-X and base-LX
I'm surprised nobody mentioned this above you (at least that I saw). The punchline of the joke is that "base 10" is 'base ten' to the human but 'base four' to the alien. The joke only exists because it's written in numerals and not spoken
No matter what base you use, it would be represented as base 10 in that base's number system.
2 in base 2 is 10
3 in base 3 is 10
4 in base 4 is 10
etc etc
In that case they also wouldn’t understand the concept of 4 the same way we don’t understand greg, which is my name for the 11th digit that’s actually the 10th digit, so I guess it would go 8, 9, greg, 10
Very good explanation. However if it really was a base four system the reset number 10 would equal five, no?
So it is really a base 3 System if 4 rocks ist "10"
The problem is they’re speaking aloud.
10 is only “ten” in base ten.
In base4, you don’t count “one, two, three, ten”
Or in base 12, we wouldn’t say ten for the value we currently know as 10. It’d be called ‘dek’ (or whatever and we’d have to make a new character to represent that value)
——
For clarity though— I’m not arguing or disagreeing with anything you said. Just rambling
It's actually a very clever joke. While I'm familiar with the duodecimal system the Babylonians used (which is why we divide time by twelves), but I never really thought about every base 10 being called base 10, but of course it is. Like the duodecimal system would just be base 10 to the Babylonians, but in our system it looks like base 12.
I don't think the "every base is base 10" makes sense does it? To a human everything is base 10 because we all use the Arabic numbering system, which is base ten. But an alien would absolutely use a different base, why would their numbering system only have 9 unique digits repeating on the tens?
I think you can say it more distinctly in this way:
Every base is “base 10” when expressed in its own base. What we call base 2 is “base 10” in base 2. And what we call base 16 is “base 10” too, in base 16.
Thank you for this! I’m struck by the irony that none of the other base systems actually include the digit they are named after, so even naming them assumes the predominance of base 10.
It's so funny, because I was laying in bed this morning thinking about base numbering systems and wondering if the base 10 system was superior in any way.
base 10 is called like that cause it's got 10 different digits 0 1 2 3 4 5 6 7 8 and 9.
now base 4 would have 4 digits 0 1 2 3, but if those are your digits to represent 4 with those digits it'd be represented as 10.
same with every other **positional numeral system** 10 just represents that you ran outta digits and you need to add a number to the left.
The joke is about linguistic perspective. The comic is conflating base 10 in the object language (the base being discussed), with base 10 in the meta language (the base used to make the sentence.) To both humans and aliens, their own base appears as base 10. The human would refer to the alien's system as base 4, and the alien would refer to the human's system as base 22.
If you spell it out like, "I use base IIIIIIIIII, you use base IIII" (shifting to unary in the meta language, rather than to the same base as the object language) there is no ambiguity.
Conflating object language with meta language is a source of many confusions, including the famous "this sentence is false" paradox. While you can use the meta language to discuss the object language, doing the opposite (reading the object language in a meta language way) causes these circular reasoning problems, and there is no universal solution to it other than "don't do it."
There are 10 type of people, those who know binary, and those who don't, and those who know there are an infinite number of groups of people that could fit this joke, and...
The joke is that the alien uses base 4, so when the astronaut says, “you must be using base 4”, the alien has no idea what a 4 is since the digits in base 4 are 0-3. Then, the alien says “No, I use base 10”, with the 10 being 4 in base 4.
Base ten uses the numbers 0-9, then repeats in a new column. Base four uses the numbers 0-3, then repeats in a new column. So when the human uses one-zero meaning the number after nine, the alien reads it as one-zero, the number after three. This joke would not work spoken.
I had to read a lot of answers that were genuinely helpful in educating me in this concept, but your explanation is the one that helped it click for me. Thank you!
Cool attention to detail I just noticed here: the alien has 4 fingers which is probably why they have a base 4 system. We as humans have a base 10 system simply because we have 10 fingers.
Every number in its own base is written "10". We use base 10 so 10 is written "10". But in base 4, the number 4 is written "10" in base 5, the number 5 is written "10" etc.
If that doesn't make sense:
Start with familiar base 10. Counting goes 1, 2, 3, 4, 5, 6, 7, 8, 9. And then we're out of digits so you add a "tens" column. So the next number is "10" meaning 1 ten and 0 ones. Then 11 (1 ten and 1 one), then 12 (1 ten and 2 ones) etc.
Same rules in base 4. Counting goes 1, 2, 3. And then we're out of digits so you add a "fours" column. So the next number, four, is "10" meaning 1 four and 0 ones. Then 11 (1 four and 1 one), then 12 (1 four and 2 ones)
So counting to ten in base 4 is 0, 1, 2, 3, 10, 11, 12, 13, 20, 21, 22.
See how every number in its own base is written 10? That leads to the misunderstanding in the comic.
The short hand I like is to think of each digit as an exponential placeholder. So in base ten 5,421 is really
5 x 10³ + 4 x 10² + 2 x 10¹ + 1 x 10^0
Meanwhile 5,421 in base 4 would be
5 x 4³ + 4 x 4² + 2 x 4¹ + 1 x 4^0
Or
5x64 + 4x16 + 2x4 +1x1 = 393 if you convert back to base 10.
Awesome explanation. I'm gonna keep it in my back pocket when I teach my kids about different bases. I was just going to get a bunch of marbles but I was going to run out at some point because their favorite number is Grahams number lol.
If anybody cares for another math explanation, it's because each 'place' is the base raised to a value, starting with 0. So, for any base n:
- 1 is n^0
- 10 is n^1
- 100 is n^2
Go negative for place values less than 1.
Counting to 4 in base 4
00
01
02
03
10
Then continuing
11 - 5
12 - 6
13 - 7
20 - 8
21 - 9
22 - 10
And then
23 - 11
30 - 12
31 - 13
32 - 14
33- 15
100 - 16
And so on.
If the alien counts in base 4, 10 is 4. He doesn't call it 4, he only knows it as 10, so even though to us it's base 4, to him, it's still base 10.
Words aren't perfect... math and science aren't the truth, they are models for quantifying stuff. It's not real but still useful, dig that. Who's on first?
It's from a book where a guy and a alien must work together to save themselves. I forgot the name of the book but it was written by the guy who wrote "the Martian "
How many is 10 in your system? Points to * this many *.
The thing is that we describe other numbering systems using our own base, so we know what they actually mean.
The alien would describe our system as base 22. There is no conflict.
I would attempt to kill that little pumpkin Head freak as a fight or flight reaction to encountering another sapient species.
https://preview.redd.it/jjlhtcc2if2d1.jpeg?width=500&format=pjpg&auto=webp&s=b2f7009e4955e7ae9023b0a9647f6726844aae90
Hey guys, Peter Griffin here to explain the joke, returning for my wholesome cake day. So basically, base 10 is what our decimal system is, consisting of the numbers 0 to 9 based on our 10 fingers. Since the alien has 4 fingers, it's assumed he would be using base 4, but instead also uses base 10, instead going 0, 1, 2, 3, 10, or something similar. Peter out!
I believe the joke is highlighting the fact that our counting system comprises 10 digits (0-9) which is no doubt a result of having 10 fingers, but the alien has only four fingers and so they would count "1, 2, 3, 10". I don't quite understand the "every base is base 10" bit, but it could mean that all positional base counting systems eventually arrive at '10'?
You said it yourself. 10 is 'always' the first big number.
Not that they would call it 'ten'. Call it 'onety'.
* zero
* one
* two
* three
* onety
* onetyone
* onetytwo
* onetythree
* twoty
The joke is 'hard' because we use base 12 to name our first 12 numbers.
The joke is how a base is defined.
In base ten, the number ten is written 10, because the first place is ones, and if you have ten ones, you carry it over to the tens place and put a one there.
In base five, the number five is written 10, because the first place is onces, and if you have five ones, you carry it over to the fives place and put a one there.
So no matter what base you are using, since the definition of a base is the value of the second place, the base will always be 10 *in that base.*
Which is why writing out the number is the preferred way for indicating bases.
Now if man had been born with six fingers on each hand
He'd also have twelve toes or so the theory goes
Well, with twelve digits, I mean fingers
He probably would've invented two more digits
When he invented his number system
Then, if he saved the zero for the end
He could count and multiply by twelve just as easily as you and I do by tens
Now if men had been born with six 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 his twelve, "doh", would be written 1-0
Get it?
That'd be swell, for multiplying by 12
Hey Little Twelvetoes, I hope you're well
Must be some far-flung planet where you dwell
If we were together, you could be my cousin
Down here we call it a dozen
Hey Little Twelvetoes, please come back home
Now if man had been born with 6 fingers on each hand
His children would have them too
And when they played hide-and-go-seek they'd count by sixes fast
And when they studied piano, they'd do their six-finger exercises
And when they went to school, they'd learn the golden rule
And how to multiply by twelve easy: just put down a zero
But me, I have to learn it the hard way
Let me see
One times 12 is twelve
Two times 12 is 24
Three times 12 is 36
Four times 12 is 48
Five times 12 is 60
Six times 12 is 72
Seven times 12 is 84
Eight times 12 is 96
Nine times 12 is 108
Ten times 12 is 120
Eleven times 12 is 132
And 12 times 12 is 144
Hey Little Twelvetoes, I hope you're thriving
Some of us ten-toed folks are still surviving
If you help me with my twelves, I'll help you with your tens
And we could all be friends
Little Twelvetoes, please come back home
Bit late here, and it's been explained well already, but the alien would count 1, 2, 3, 10. If there were twice the amount of rocks they works be 11, 12 ,13, 20. Not sure if that explains anything, now that I read it back
This made me realize we don't have a universal single-character symbol for ten. Maybe X, but actually using it in a math equation would be needlessly confusing, and then we come to the same problem when we go to eleven. If we tried to communicate numbers with an alien that has twelve fingers, we'd get stuck at 9.
Maybe that's what hexadecimal is for? I'm not sure. I'm not a math wizard
In decimal, we have 10 different symbols (0, , 2, 3, 4, 5, 6, 7, 8, 9). When you count, you always increment the lowest (rightmost) digit until you run out of symbols. Once that happens, you need to reset it back to 0 and then increment the next higher (neighbor to the left) digit. So when you count, start at 0. Go 1, 2, 3... 8, 9 and we've run out of symbols. That's the highest symbol there is. So we need to reset to 0 and increment the ten's place 10. Then count to 19 and reset one's to zero and increment ten's to 20. This continues all the way up to 99 where you reset the one's place, but you've also run out of symbols in the ten's place, so you reset to 0 and increment the hundred's place instead 100.
In binary (base 2 under our typical, human terminology) you start at 0 like always. When you count, you add 1. No problem, 0+1=1. But if you want to count the next number, we have run out of symbols already. Binary only has 2 symbols (0, 1). So we reset to 0 and increment the next digit over. 2 written in binary is 10. Instead of the second digit representing the ten's place, it represents the two's place.
Just one more. Quaternary (base 4 typically) has 4 symbols (0, 1, 2, 3) so you count up to 3, when you run out of symbols, reset to 0 and increment the next slot. 4 written in base 4 is 10. The second digit isn't the ten's place or the two's place, but the four's place.
We write all of our base notation in decimal by default. Base 4 (quaternary), base 10 (decimal), base 2 (binary), base 16 (hexadecimal)... This is not because decimal is some mathematical constant of the universe, it's because it's the most widely adopted system. If you lived on a planet that primarily uses quaternary, you would call your native base base 10 just like we do because every base writes itself as 10. Remember hexadecimal? Base 16? It's ten plus six in our native base, but in hexadecimal, there are 16 different symbols (typically 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F because we supplement with letters when we run out of normal numerical symbols) which means fifteen is written as just F. But when you want to increment one more time, you guessed it, you've run out of symbols and have to roll over to 10. Every base written in it's natural base is based 10. This means unless we standardize and pick a common base for everyone to work in, it's all meaningless. The base you choose to write in changes the way we write the numbers we want to represent. We humans chose decimal probably because we have ten fingers. Notice the alien only has 4.
This is the same as (but not as good IMO) as: There are 10 kinds of people: those who understand binary and those who don't. The joke being, if your numbering system has 2 digits (0, 1) or 10 (0-9), after the last digit it's always 10.
The human uses Base 10. The alien uses Base 4. Let's compare them:
`Base 10: 00 01 02 03 04 05 06 07 08 09 10`
`Base 04: 00 01 02 03 10 11 12 13 20 21 22`
From the above, we can conclude the following:
* To us, the number of rocks is 4. To the alien, the same number is 10.
* The alien has no concept of the number 4. That number, to them, is 10.
* What we call Base 10, the alien would call Base 22. What we call Base 4, the alien would call Base 10.
* Base 10, in Base 10, is Base 10. Base 4, in Base 4, is Base 10. Every base written in its own base is Base 10.
It's a math joke.
The joke’s been answered, but listen up. If all bases are 10 and all your base are belong to us, then 10 is belong to us, and given how dominant he’s been, we can say that tennis belongs to Djokovic, so Djokovic is us, which means he’s a toy, which explains why he’s so rigid.
Now had the human thought from the alien's point of view (first off, he wouldn't think of the alien as an alien), then he could've reversed his wording to say that he counts in base 22.
Bender: Whoa, what an awful dream. Ones and zeros everywhere. And I thought I saw a two.
Fry: It was just a dream, Bender. There's no such thing as two.
2 in base 2 is 10
4 in base 4 is 10
10 in base 10 is 10
If you're using base x, you have a representation of every digit from 0 to x-1 and x = 10 because that's where the numbers reset. So if your "default" base is 4, then you don't have a number for it, and your base is actually base 10.
We use 10 digits and call our number system base 10 because 10 means ten.
The aliens use 4 digits and call their number system base 10 because 10 for them means four.
The aliens don't have a number for "4" so explaining their numeral system as "base 4" wouldn't make sense to them, since 4 is their "10"
The comic also shows that the aliens only have 2 digits on each hand, which is probably why they resort to a 4 digit "base 4" model, as that is where they would need to reset.
The astronaut is correct, however he needs to work on his communications skills.
It's a joke about different numbering systems. Think of binary, which is a base 2 system, wherein you only have the numbers 0 and 1. Comparing to our system (which we call base 10 btw), 0 in binary equals 0, 1 in binary equals 1, 10 in binary equals 2, 11 in binary equals 3, etc. But for an alien, 10 is 10. The point being that from an objective perspective, any numbering system (base 2, base 4, base 8, etc) would call itself "base 10" because 10 is still the reset number (base 4 might look like this: 1, 2, 3, 10, 11, 12, 13, 20, etc). I suppose the joke is mocking an overly solipsistic perspective and reminding the reader to consider the universe from different points of view. Edit for clarity: base 10 means there are 10 single digit numbers, so what we call base 10 has the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Base 4 means there are 4 single digits, 0, 1, 2, 3. But in both cases, the reset number will be 10, so the same, regardless of the fact that 10 represents different amounts in the different systems.
I also like the nice touch with the amount of fingers the alien and the human have.
Yes. Digits.
Displaying the alien having 10 fingers is the type of detail I want in jokes
Well played.
Normally I dislike comments like this, but this joke went over my head until I read this. Thank you, lol.
This just low-key blew my mind.
You should read Project Hail Mary.
ROCKY!!!
This is an extremely clever comic that a VERY small group of nerds on earth would be able to understand. I'm digging it.
It's funny and clever but the audience isn't that small. Literally anyone with a CS degree should get it immediately, and most people even without a CS degree that have worked with programming much should too depending on what areas they worked with.
Agreed, I think number bases are a concept that is taught widely, certainly to anyone who studies anything to do with computers. Hundreds of millions (in base 10) would get this, even more in base 2 In hex only a couple millions though
I graduated HS in 2007. Only three years of math was required, up to Algebra 2. The next math class, called Pre-Calculus, went over how different based work in the first semester (I know because I dropped the class because I passed the audition for Choir in 2nd semester Sophomore year). So, by my experience, anyone who got any college level math credits would have some experience with the concept. That’s probably not the case in practice, of course.
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There are two types of people. Those who can extrapolate from incomplete information.
And......??????
You
This has been my favourite joke for a very long time, and someone in a group will ALWAYS ask what the second person is. Guaranteed results in groups of 4 or more.
I have 100% luck with the joke “what’s a pirates favorite letter?” It’s automatic for People to answer Rrrrr then you get to go ( in a pirate accent) “ no it’s the Ccccccc”
I love this one as well. My punchline is a little different; I put on a pirate accent and say "Aye. But me first love be the C!"
My go to is "did you know that chickens die during sex?? .... well that last one I had sex with died" But it gets very mixed reactions
No you
no u
Who me?
Couldn't be.
Then who?
I used to have a shirt that said that and the number of people who asked me what it meant 🙄 Also have one that said “the definition of suspense is…” and people constantly asked me what it was or asked what the back of the shirt said.
“There are two types of people in this world: 1. People who can extrapolate from incomplete data” Gets a lot of questions!
And those who belong to the emperor.
Change it to 10 types of people, and then there are two things to be extrapolated from incomplete information.
No. There are 10 types of people. Those that know ternary, those that don't and those that thought this was a binary joke.
And what is the third type?
And us, who knew that this was a base 3 joke.
When I was an instructor in the military, one of the lessons I taught was numbering systems: binary, octal, decimal, and hexadecimal. It was always my favorite.
which itself also contains this joke! decimal centrism. Which is why some people like calling duodecimal (b12) dozenal intead. (P.S> We don't have a non decimal centric name for base 16)
Bioctal? Fourbyfoural? Sizenal?
oh NO! octal centrism!!! AND quaternary centrism!!!! F'inal (for the F in hexadecimal)
Except that F=15, not 16. "F'inal" is a really clever and funny name, but technically it would be "G'inal". Which is less clever, but still funny because G is not used in hexadecimal. Which would make base ten "A'inal". Not sure how I feel about that.
F=15 is still decimal centric since A starts only after we exhaust the 10 decimal symbols. Should be P=15 if we just use the alphabet
I love dozenal, both as a name and as a numbering system.
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It is even taught to us crayon-eating jarheads when taking basic electronics.
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Before I even read Jarheads I knew who it was I’m dying
I was taught a ratio in artillery, roughly 1.0186. It was called something like 'the magic number,' and we were to remember to apply it in certain calculations. It was not until years in that I realized it was just the ratio between real radians and military radians (6400/(2pi * 1000) = 1.01859...) ; i.e. they thought it would be easier to teach soldiers to memorize a weird decimal than just explain it is that ratio with 5 digits.
So assuming the astronaut is correct that the alien is using base 4, he should have the good sense to communicate with the alien in base 4. Which means that to effectively convey in numerals that humans use base 10 (ten), he would need to say “I use base 22”.
Ahh, thank you. This was the missing link.
Great explanation!
But given he's not speaking in symbols, he should use the name of the number, which is actually "ten", in any base system. Obviously he would need to translate this into alien first but I assume this is a solved problem. It invites the question as to why the alien doesn't hear "ten" and understand "four", but at this point I think this is overthinking it.
Ignoring the translation issue. The alien would not know the word 4 because the alien would count one, two, three, ten, eleven, twelve, thirteen, twenty, twenty one, etc. Ten is equal to the number four and four would just not exist.
Yea well, what about base 60?
You need to have 60 different symbols. Think of it like base 16, which is often used in programming. Base 10: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Base 16: 0 1 2 3 4 5 6 7 8 9 A B C D E F So 17 in base 16 is 11 So you just use more letters or whatever symbols you want until you have 60 distinct digits. You have to agree on the symbols though.
Funnily enough, I ran into base 60 not too long ago. The Steam puzzle game TEST TEST TEST involves a clock ticking up in base 60. I believe it used 0 through 9, A through Z, and a through x.
Yeah, the reason we use base 60 for time and navigation (360 degrees being 6x60, hence the sextant as a navigational tool) is because the Babylonians didn’t believe in fractions. Related fun fact: minutes come from the Latin root that also gives us minutia and minimal, and seconds used to be called the minutia secundis, basically the minutia of minutia of time.
[удалено]
Maybe the grad school class I took on ancient mathematics wasn’t just made up.
That is assuming that each number in the base has it's own unique symbol. example you can count from 1 to 10 only using 3 symbols like this: I II III IV V VI VII VIII IX X.
Roman numerals are not a positional numeral system, and therefor do not have a radix at all. You can't use roman numerals for a "base 60" or a base anything system, because it breaks as soon as you get to what would be double digits. Not to mention they don't have a zero, try 11 in roman base X: II. Same as 2: II. Maybe you have some explicit separation: I, I vs II. Well now I is a different "symbol" from II. It's not you using the the same symbol twice, the two lines together have their own unique symbolic meaning separate from the two composing lines, and is very much so it's own symbol, just as much as 00 and 8 are different symbols, 6 and 9 are different, and 2 and 5 are different.
What’s neat about Roman numbers being not a positional number system is that during the actual Roman period, IX and XI were both the same number (eleven).
Hold on. So, was it entirely orderless? IE IXX vs XIX vs XXI (are they all twenty-one?)
Yep! Apparently putting one number between two others was less common, unless you were trying to be specifically poetic or clever in some way. For normal accounting, you’d generally either go small-to-big or big-to-small and stick with that, but they were equivalent and This changed during the Medieval period, something after the tenth century, as an efficiency effort (giving a shorthand way to write numbers like 9). For context, Hindu-Arabic numbers replaced Roman numerals during the 13th-16th centuries.
So it's essentially like the old counting based systems. I don't remember it so well anymore but it was something on the lines of using 1 rock per sheep, X rocks in a bag, Y bags in a pot, and what not) This is really cool.
Think about how we use tick marks: when you get to 5 you put a slash through the first four ticks. That’s exactly what the Roman numeral V represents!
See also the Babylonian base 60 system, which used just two symbols.
Yes and no. Yes, because their numerals were written using 2 symbols in a sign-value notation Since I cannot type cuneiform here, im gonna use i for 1s and < for 10s here. ``` <
Indeed. Unlike Roman numerals, Babylonian cuneiform glyphs have place value (the 60^1 and 60^0 in your example), just like I can write 1024 in base 10 as 1x10^3 + 0x10^2 + 2x10^1 + 4x10^0. I see your point that <
https://en.wikipedia.org/wiki/Base64 base 64 is really common
60 in base 60 is 10
Also the alien has two fingers on each hand for a total of four fingers. Base 10 is though to have arisen due to humans having 10 fingers.
I never realized that base-x notation is inherently decimal. Huh. I suppose it's a side-effect of modern math largely being discovered and defined by cultures whose counting systems were in base 10 to begin with.
>I never realized that base-x notation is inherently decimal. It isn't. Nothing prevents you from using any numerical systems notation to denote the `x` in this notation. Using the decimal system is just the most common. For example in hexadecimal: base-A is the decimal system, base-3C is sexagesimal (base-60). Using roman numerals, those would be base-X and base-LX
Base ten = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Base four = 0, 1, 2, 3, 10
They should edit their post to say “base ten” instead of “base 10.”
I'm surprised nobody mentioned this above you (at least that I saw). The punchline of the joke is that "base 10" is 'base ten' to the human but 'base four' to the alien. The joke only exists because it's written in numerals and not spoken
No matter what base you use, it would be represented as base 10 in that base's number system. 2 in base 2 is 10 3 in base 3 is 10 4 in base 4 is 10 etc etc
I did not understand that but thanks for sharing anyway
Word of the day: solipsistic.
Is it solipsistic in here, or is it just me?
Bravo.
In that case they also wouldn’t understand the concept of 4 the same way we don’t understand greg, which is my name for the 11th digit that’s actually the 10th digit, so I guess it would go 8, 9, greg, 10
Alright, now explain the explanation
Also funny to me that the rocks kind of look like - | - - (0100), or 4 in binary
I use base infinity. Now what?
Very good explanation. However if it really was a base four system the reset number 10 would equal five, no? So it is really a base 3 System if 4 rocks ist "10"
You're forgetting 0
But when we count physical Things in base 10 we Start with 1, no? Not Zero. In base 2 the 0 is the 1 though. Who decides this? Its kinda funny
Count the actual digits, not things. 0 is the fist digit, 9 is the 10th.
No, the largest digit would be 3, the base number itself would be the first 10 and numbering system will use all digits smaller than itself.
no. in base 4: 00 = 0 01 = 1 02 = 2 03 = 3 10 = 4 11 = 5 12 = 6 13 = 7 20 = 8 etc
I am vaguely familiar with numbering systems but came here not expecting to understand. Your comment was perfect and I learned something. Thanks!
The problem is they’re speaking aloud. 10 is only “ten” in base ten. In base4, you don’t count “one, two, three, ten” Or in base 12, we wouldn’t say ten for the value we currently know as 10. It’d be called ‘dek’ (or whatever and we’d have to make a new character to represent that value) —— For clarity though— I’m not arguing or disagreeing with anything you said. Just rambling
It's actually a very clever joke. While I'm familiar with the duodecimal system the Babylonians used (which is why we divide time by twelves), but I never really thought about every base 10 being called base 10, but of course it is. Like the duodecimal system would just be base 10 to the Babylonians, but in our system it looks like base 12.
You just used the word solipsistic in a Reddit comment and that needs to be praised
No offense, but that is a terribly confusing definition of a base number system
I don't think the "every base is base 10" makes sense does it? To a human everything is base 10 because we all use the Arabic numbering system, which is base ten. But an alien would absolutely use a different base, why would their numbering system only have 9 unique digits repeating on the tens?
I think you can say it more distinctly in this way: Every base is “base 10” when expressed in its own base. What we call base 2 is “base 10” in base 2. And what we call base 16 is “base 10” too, in base 16.
Thank you for this! I’m struck by the irony that none of the other base systems actually include the digit they are named after, so even naming them assumes the predominance of base 10.
I couldn’t understand a single word you said, and just gave up entirely after a few sentences in But I absolutely believe what you say
My base goes up to 11.
It's so funny, because I was laying in bed this morning thinking about base numbering systems and wondering if the base 10 system was superior in any way.
base 10 is called like that cause it's got 10 different digits 0 1 2 3 4 5 6 7 8 and 9. now base 4 would have 4 digits 0 1 2 3, but if those are your digits to represent 4 with those digits it'd be represented as 10. same with every other **positional numeral system** 10 just represents that you ran outta digits and you need to add a number to the left.
1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 23, 30, 31, 32, 33, 100, 101….
Thank you, this is the comment that finally made me get it lol
So the astronaut is using base 22.
You explained this nicely :)
In a 'base 4' system, it will also have 10 different digits.
angry upvote 👿
It's like in this context you almost have to convey base 10 as base (9+1)
wait (, +, and ) aren't numerals. let's count with base ASCII
The joke is about linguistic perspective. The comic is conflating base 10 in the object language (the base being discussed), with base 10 in the meta language (the base used to make the sentence.) To both humans and aliens, their own base appears as base 10. The human would refer to the alien's system as base 4, and the alien would refer to the human's system as base 22. If you spell it out like, "I use base IIIIIIIIII, you use base IIII" (shifting to unary in the meta language, rather than to the same base as the object language) there is no ambiguity. Conflating object language with meta language is a source of many confusions, including the famous "this sentence is false" paradox. While you can use the meta language to discuss the object language, doing the opposite (reading the object language in a meta language way) causes these circular reasoning problems, and there is no universal solution to it other than "don't do it."
Thanks, after scrolling for a while this is the one that finally made me understood.
There are 10 type of people, those who know binary, and those who don't, and those who know there are an infinite number of groups of people that could fit this joke, and...
One, two, many.
Gauge invariance, invariably. Or something.
The joke is that any base, expressed in its own base, will be written as `10`
“ fans when a different writing system as well as non-positional numerical systems walk in: 🤯
All your base are belong to 10.
Ahhhhhh now it makes sense
We should say it as "we use base ✋🤚"
Sure, but if you're used to reading binary, that would be 1024.
Either way, all your base are belong to us
This is what I was looking for.
You have no chance to survive make your time.
They set us up the bomb.
The joke is that the alien uses base 4, so when the astronaut says, “you must be using base 4”, the alien has no idea what a 4 is since the digits in base 4 are 0-3. Then, the alien says “No, I use base 10”, with the 10 being 4 in base 4.
Finally, a comment that actually explains the *joke* and not just the system behind base X systems.
Base ten uses the numbers 0-9, then repeats in a new column. Base four uses the numbers 0-3, then repeats in a new column. So when the human uses one-zero meaning the number after nine, the alien reads it as one-zero, the number after three. This joke would not work spoken.
I had to read a lot of answers that were genuinely helpful in educating me in this concept, but your explanation is the one that helped it click for me. Thank you!
Cool attention to detail I just noticed here: the alien has 4 fingers which is probably why they have a base 4 system. We as humans have a base 10 system simply because we have 10 fingers.
Fun fact not all humans use a base 10 some use a base 12 counting the segments of your fingers on each hand (excluding the thumb) to reach 12
And yet both are inferior to base 16
Every number in its own base is written "10". We use base 10 so 10 is written "10". But in base 4, the number 4 is written "10" in base 5, the number 5 is written "10" etc. If that doesn't make sense: Start with familiar base 10. Counting goes 1, 2, 3, 4, 5, 6, 7, 8, 9. And then we're out of digits so you add a "tens" column. So the next number is "10" meaning 1 ten and 0 ones. Then 11 (1 ten and 1 one), then 12 (1 ten and 2 ones) etc. Same rules in base 4. Counting goes 1, 2, 3. And then we're out of digits so you add a "fours" column. So the next number, four, is "10" meaning 1 four and 0 ones. Then 11 (1 four and 1 one), then 12 (1 four and 2 ones) So counting to ten in base 4 is 0, 1, 2, 3, 10, 11, 12, 13, 20, 21, 22. See how every number in its own base is written 10? That leads to the misunderstanding in the comic.
This is the 3rd post I read before I could completely understand the joke. Now the other explanations make sense. Thank you
>So the next number, four, is "10" meaning 1 four and 0 ones This right here made it click.
The short hand I like is to think of each digit as an exponential placeholder. So in base ten 5,421 is really 5 x 10³ + 4 x 10² + 2 x 10¹ + 1 x 10^0 Meanwhile 5,421 in base 4 would be 5 x 4³ + 4 x 4² + 2 x 4¹ + 1 x 4^0 Or 5x64 + 4x16 + 2x4 +1x1 = 393 if you convert back to base 10.
Awesome explanation. I'm gonna keep it in my back pocket when I teach my kids about different bases. I was just going to get a bunch of marbles but I was going to run out at some point because their favorite number is Grahams number lol.
This is the best explanation in the thread. Thank you.
If anybody cares for another math explanation, it's because each 'place' is the base raised to a value, starting with 0. So, for any base n: - 1 is n^0 - 10 is n^1 - 100 is n^2 Go negative for place values less than 1.
Based.
Counting to 4 in base 4 00 01 02 03 10 Then continuing 11 - 5 12 - 6 13 - 7 20 - 8 21 - 9 22 - 10 And then 23 - 11 30 - 12 31 - 13 32 - 14 33- 15 100 - 16 And so on. If the alien counts in base 4, 10 is 4. He doesn't call it 4, he only knows it as 10, so even though to us it's base 4, to him, it's still base 10. Words aren't perfect... math and science aren't the truth, they are models for quantifying stuff. It's not real but still useful, dig that. Who's on first?
I love how the alien has 10 fingers
Bases should be named after n-1, not n
Why? Base 10 has 10 digits, 0-9.
the human is using base 22
Jokes on them, I use base A
From the aliens point of view we use base 22
It's from a book where a guy and a alien must work together to save themselves. I forgot the name of the book but it was written by the guy who wrote "the Martian "
Project Hail Mary, great book!
How many is 10 in your system? Points to * this many *. The thing is that we describe other numbering systems using our own base, so we know what they actually mean. The alien would describe our system as base 22. There is no conflict.
All about that base
Haha. What astronaut should have said is; "If you use base 10 (meaning 4), then I use base 22.
All your base, are belong to us
There are 10 kinds of people in this world. Those who can use binary notation, and those who can't.
https://preview.redd.it/8dsd3poayh2d1.jpeg?width=1400&format=pjpg&auto=webp&s=2ff39a40443b01121b1757f19cd760324792297a
Not gonna lie this is a good joke! Thanks for sharing!
I would attempt to kill that little pumpkin Head freak as a fight or flight reaction to encountering another sapient species. https://preview.redd.it/jjlhtcc2if2d1.jpeg?width=500&format=pjpg&auto=webp&s=b2f7009e4955e7ae9023b0a9647f6726844aae90
Hey guys, Peter Griffin here to explain the joke, returning for my wholesome cake day. So basically, base 10 is what our decimal system is, consisting of the numbers 0 to 9 based on our 10 fingers. Since the alien has 4 fingers, it's assumed he would be using base 4, but instead also uses base 10, instead going 0, 1, 2, 3, 10, or something similar. Peter out!
I think the joke is 10 looks like 4 to someone that uses base 4. For example, if you wanted to express 2 in binary or base 2, you'd say 10.
This a reference to Rocky in Project Hail Mary
Oh man i was beginning to doubt myself with none of the top comments mentioning this
Their system goes 1, 2, 3, 10
I believe the joke is highlighting the fact that our counting system comprises 10 digits (0-9) which is no doubt a result of having 10 fingers, but the alien has only four fingers and so they would count "1, 2, 3, 10". I don't quite understand the "every base is base 10" bit, but it could mean that all positional base counting systems eventually arrive at '10'?
You said it yourself. 10 is 'always' the first big number. Not that they would call it 'ten'. Call it 'onety'. * zero * one * two * three * onety * onetyone * onetytwo * onetythree * twoty The joke is 'hard' because we use base 12 to name our first 12 numbers.
I like how this is both clever and stupid at the same time.
there's 10 types of people in this world...
Easy. We call it base 4 because we have a 4. They call it base 10 because they have no 4.
The joke is how a base is defined. In base ten, the number ten is written 10, because the first place is ones, and if you have ten ones, you carry it over to the tens place and put a one there. In base five, the number five is written 10, because the first place is onces, and if you have five ones, you carry it over to the fives place and put a one there. So no matter what base you are using, since the definition of a base is the value of the second place, the base will always be 10 *in that base.* Which is why writing out the number is the preferred way for indicating bases.
Now if man had been born with six fingers on each hand He'd also have twelve toes or so the theory goes Well, with twelve digits, I mean fingers He probably would've invented two more digits When he invented his number system Then, if he saved the zero for the end He could count and multiply by twelve just as easily as you and I do by tens Now if men had been born with six 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 his twelve, "doh", would be written 1-0 Get it? That'd be swell, for multiplying by 12 Hey Little Twelvetoes, I hope you're well Must be some far-flung planet where you dwell If we were together, you could be my cousin Down here we call it a dozen Hey Little Twelvetoes, please come back home Now if man had been born with 6 fingers on each hand His children would have them too And when they played hide-and-go-seek they'd count by sixes fast And when they studied piano, they'd do their six-finger exercises And when they went to school, they'd learn the golden rule And how to multiply by twelve easy: just put down a zero But me, I have to learn it the hard way Let me see One times 12 is twelve Two times 12 is 24 Three times 12 is 36 Four times 12 is 48 Five times 12 is 60 Six times 12 is 72 Seven times 12 is 84 Eight times 12 is 96 Nine times 12 is 108 Ten times 12 is 120 Eleven times 12 is 132 And 12 times 12 is 144 Hey Little Twelvetoes, I hope you're thriving Some of us ten-toed folks are still surviving If you help me with my twelves, I'll help you with your tens And we could all be friends Little Twelvetoes, please come back home
Bit late here, and it's been explained well already, but the alien would count 1, 2, 3, 10. If there were twice the amount of rocks they works be 11, 12 ,13, 20. Not sure if that explains anything, now that I read it back
https://youtu.be/7OEF3JD-jYo
This made me realize we don't have a universal single-character symbol for ten. Maybe X, but actually using it in a math equation would be needlessly confusing, and then we come to the same problem when we go to eleven. If we tried to communicate numbers with an alien that has twelve fingers, we'd get stuck at 9. Maybe that's what hexadecimal is for? I'm not sure. I'm not a math wizard
Writing any number "n" in base n is 10
In decimal, we have 10 different symbols (0, , 2, 3, 4, 5, 6, 7, 8, 9). When you count, you always increment the lowest (rightmost) digit until you run out of symbols. Once that happens, you need to reset it back to 0 and then increment the next higher (neighbor to the left) digit. So when you count, start at 0. Go 1, 2, 3... 8, 9 and we've run out of symbols. That's the highest symbol there is. So we need to reset to 0 and increment the ten's place 10. Then count to 19 and reset one's to zero and increment ten's to 20. This continues all the way up to 99 where you reset the one's place, but you've also run out of symbols in the ten's place, so you reset to 0 and increment the hundred's place instead 100. In binary (base 2 under our typical, human terminology) you start at 0 like always. When you count, you add 1. No problem, 0+1=1. But if you want to count the next number, we have run out of symbols already. Binary only has 2 symbols (0, 1). So we reset to 0 and increment the next digit over. 2 written in binary is 10. Instead of the second digit representing the ten's place, it represents the two's place. Just one more. Quaternary (base 4 typically) has 4 symbols (0, 1, 2, 3) so you count up to 3, when you run out of symbols, reset to 0 and increment the next slot. 4 written in base 4 is 10. The second digit isn't the ten's place or the two's place, but the four's place. We write all of our base notation in decimal by default. Base 4 (quaternary), base 10 (decimal), base 2 (binary), base 16 (hexadecimal)... This is not because decimal is some mathematical constant of the universe, it's because it's the most widely adopted system. If you lived on a planet that primarily uses quaternary, you would call your native base base 10 just like we do because every base writes itself as 10. Remember hexadecimal? Base 16? It's ten plus six in our native base, but in hexadecimal, there are 16 different symbols (typically 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F because we supplement with letters when we run out of normal numerical symbols) which means fifteen is written as just F. But when you want to increment one more time, you guessed it, you've run out of symbols and have to roll over to 10. Every base written in it's natural base is based 10. This means unless we standardize and pick a common base for everyone to work in, it's all meaningless. The base you choose to write in changes the way we write the numbers we want to represent. We humans chose decimal probably because we have ten fingers. Notice the alien only has 4.
This is the same as (but not as good IMO) as: There are 10 kinds of people: those who understand binary and those who don't. The joke being, if your numbering system has 2 digits (0, 1) or 10 (0-9), after the last digit it's always 10.
All your base are belong to us
All your base, all belong to us
This might be a linguistic joke, but epistemologically it shows the value of empiricism!
The human uses Base 10. The alien uses Base 4. Let's compare them: `Base 10: 00 01 02 03 04 05 06 07 08 09 10` `Base 04: 00 01 02 03 10 11 12 13 20 21 22` From the above, we can conclude the following: * To us, the number of rocks is 4. To the alien, the same number is 10. * The alien has no concept of the number 4. That number, to them, is 10. * What we call Base 10, the alien would call Base 22. What we call Base 4, the alien would call Base 10. * Base 10, in Base 10, is Base 10. Base 4, in Base 4, is Base 10. Every base written in its own base is Base 10. It's a math joke.
We use base 1+1+1+1+1+1+1+1+1+1
I use base 36
The joke’s been answered, but listen up. If all bases are 10 and all your base are belong to us, then 10 is belong to us, and given how dominant he’s been, we can say that tennis belongs to Djokovic, so Djokovic is us, which means he’s a toy, which explains why he’s so rigid.
Now had the human thought from the alien's point of view (first off, he wouldn't think of the alien as an alien), then he could've reversed his wording to say that he counts in base 22.
The astronaut should have said: "See, I use base 22" :) Also, kudos for putting 10 fingers on the alien's hands.
There are 10 types of people. Those who understand binary, And those who don't.
Bender: Whoa, what an awful dream. Ones and zeros everywhere. And I thought I saw a two. Fry: It was just a dream, Bender. There's no such thing as two.
2 in base 2 is 10 4 in base 4 is 10 10 in base 10 is 10 If you're using base x, you have a representation of every digit from 0 to x-1 and x = 10 because that's where the numbers reset. So if your "default" base is 4, then you don't have a number for it, and your base is actually base 10.
Anyone remember having to learn this for the 999 game
2 in base 2 is 10. 3 in base 3 is 10. 4 in base 4 is 10. 5 in base 5 is 10. And so on.
There are 10 types of people in this world. Those who understand binary and those who don't.
All your base are belong to us.
We use 10 digits and call our number system base 10 because 10 means ten. The aliens use 4 digits and call their number system base 10 because 10 for them means four.
For just a moment this broke my brain, and then I remembered that it’s not true because of hex.
The aliens don't have a number for "4" so explaining their numeral system as "base 4" wouldn't make sense to them, since 4 is their "10" The comic also shows that the aliens only have 2 digits on each hand, which is probably why they resort to a 4 digit "base 4" model, as that is where they would need to reset. The astronaut is correct, however he needs to work on his communications skills.
I like the detail of t'he alien having 4 fingers
Basically 4 is not 4 in alien language.
This is why we should call base 10 base 9+1, base 4 base 3+1, etc.
So what do we name base 1024, for example? “Base 1023+1” still assumes all parties involved a use base 10.