i don’t remember where i got this from
Base 1 rules all for nothing exists without 1
Every number system is base 10.
Binary is base 1+1.
Ternary is base 2+1.
Octal is base 7+1.
Decimal is base 9+1.
Duodecimal is base B+1.
Hexadecimal is base F+1.All your base are belong to us
In written English we use base twelve but then switch to base ten after that.
I learned this one from project Hail Mary, sci-fi worth reading
Base successor(successor(successor(successor(zero))))
Can’t argue about bases if you refuse to elaborate beyond Presburger arithmetic. (Guy pointing at head meme)
Holy shit. actual mind blown moment.
I think I had this comic saved like twenty years ago and I also don’t remember where I found it.
I moaned louder than a procreating moose when I finally got it.
This only works because it’s a written/printed meme though, because we don’t say “ten” if were are not counting in base 10, we say “one zero base four”, which you further can specifify as 104 in written language.
I love how the alien has 10 fingers!
And the creature on the left does too.
Could anyone explain this to me? I get why the astronaut would think the alien counts in base 4, but I don’t understand the alien’s response
base 4 has just 4 digits: 0,1,2,3
so counting goes likes this:
0 1 2 3 10 11 12 13 20 and so on.
since what we call 4 is written as 10 to the alien, the alien calls base 4 base 10
Thanks :)
So then we would tell the alien we use base 21?
Yes 22 would make sense to the alien.
The alien only knows base 4. The astronaut says base 4 and that he uses base 10.
Think about: What is “4” in base 4?
The alien says, it uses base 1 0, which is 14 + 01.So the term “base 10” (in base 4) is the same like “base 4” in base 10.
The alien does not know, what base 4 is, because you cannot count to 4 in base 4.
Two possible solutions to this:
- Always use a single digit for the base. Examples: binary is base 2, decimal is base A (because A=10 in bases higher than decimal), hexadecimal is base G.
- Use the highest digit plus one. Examples: binary is base 1+1, decimal is base 9+1, hexadecimal is base F+1.
… or we just continue to agree that bases are always written in base 10 unless specified otherwise. By the way, how does the alien speak English?
Comicjoke aside, none of these are needed - as soon as the alien called the pile of 4 rocks “10” we could deduce his base.
or use the base’s name: quaternary for base 4, decimal for base 10…
there is a video about it, as well as how to handle an infinite number of bases with that system
Or we use binary to write all bases, since binary is the simplest. So English uses base 1010, and the alien is using base 100.
This system does break down when trying to use a base that isn’t a positive integer. I’ve heard of people trying to use base e (yes, as in euler’s number) for maths research.
Just use Roman numerals to throw your baseless assumptions around.
What about base 789432? What letter do we use for that?
What letter do you use for 789431?
7̵̛̝̯̜̱͔̭̙̭̟͚̹8̷̛̦͉͕̺̽̑̍̓͜͝9̷̩̜̩͈̠͕͊͌̎̍̃͂͌̌͘͝ͅ4̶̡̪̼̠̲̠͍̬͔̉̽3̷̟̝̮̫̪̖̹̽́̈͑̂̊̋͝1̴̢̛̱̠̻͍̞͆̊̈́͘
i think the highest digit should be the base. we use base 9, binary is base 1, hex base F
It’s a good idea, but it’s not backwards-compatible with the system already in use.
When has that ever stopped us from making new systems and standards?
Relevant xkcd: https://xkcd.com/927/
As the alien uses base 4, the number 4 does not exist to it. After 3 comes 10, so he usea base 10 and does not understand what 4 is
yeah I got it
I had to look up the joke. Very clever. Nerds.
This made me realize that I am a nerd. Sad.
The joke: In any base X, the Xth number is always the first number to require a second digit. Base 4 goes 1,2,3,10,11,12,13,20,21,etc. Base 7 goes 1,2,3,4,5,6,10,etc.
But the joke would only work written, not spoken first contact? Base five we would still say five just the numerals would show 10.
That alien doesn’t even have a numeral for 4, so it wouldn’t have a word for it either. If it speaks English, uses base 4, and uses the same words we do for numbers, it would sound like this when counting rocks: “One, two, three, ten, eleven, twelve, thirteen, twenty…”. But when it says “twelve”, it means the same thing as when we say “six”.
So the base is always written as base 10 in the native base. So base 2 (in decimal) is base 10 (in base 2)
If you want another example, try counting to 10 in hex (base 16).
Also, base 10 is always base 10, but “10” in base 2 is 2 in all counting systems above base 2 (since base 2 doesn’t actually include 2, just like base 10 doesn’t include “A”). Likewise, 10 in base 10 represented in base 2 would be 1010. ;)
Base 1 is “base 0”.
0 is expressed as .
1 is 0.
2 is 00, and so on.
Base 1 usually uses ones, because it represents summation at that point. Using zero as the numeral would be a bit awkward. Also historically zero is pretty new.
Tally marks are essentially a base 1 system.
Numbering systems all essentially evolved from base 1. People started out keeping track of wheat/barley using tally marks representing a single stalk, then creating different tally marks representing bushels, baskets, etc. More intentionally designed number systems based on things like the number of fingers on our hands came later.
I’ve had my fair share of mini-mind blowns, and that time I realized this was one of them.
right? i can’t believe i never clocked this. how exceptionalist that the base number is base 10 /j
