I think when I first saw this comic, the punchline was "what's a four?" which I find funnier.
Yes this is the better version that I've seen too
Having seen this for the first time, that was my first thought for an improved punchline.
But there’s 5 rocks?
- 1
- 2
- 3
- 10
- 11
- 12
- 13
- 20
- 21
- 22
The astronaut should've told the alien "I use base 22."
I don't understand :(
When you count up the 1's place, you go 0,1,2,3,4,5,6,7,8,9 and then it rolls over into the 10s place.
But in "base 4", it goes: 0,1,2,3,10,11,12,13,20. 3 is the highest value possible in any of the digits place.
Therefore "10" in base 4 = 4 in base 10, but saying it in base 4 is written as 10.
You can change your base to any base and whatever base it is would have to be written as base 10 because the number above the highest one in that base doesnt exist, it's 10.
Lots of good explanations here, but one thing I'd like to clarify. WHY we add digits together to represent larger numbers. Understanding this helped me to count in binary when I was a young IT technician.
In base 10, we have 10 numbers we use to count everything, each represented by a single digit 0-9. There is no single digit to represent the number 10, so we add a digit to the left and start over at 0 on the right. Hence, the number 10. Then 11-19 in serial.
But we've run out of digits to use again. So we add another digit to the left and start over on the right. Thus, 20.
When you get to 100, you're now starting over at the right-most digit and have to fill up both right digits before the left digit moves up one.
Same goes for binary, where the only two digits are 0 and 1. Once you've counted to one, you've run out of digits to use, so you add a 1 to the left and start over on the right. So 2 is written as 10 in binary. Then 3 is 11. Then you've run out of digits again, so you add another one to the far left and start over. 4 is 100. 5 is 101. 6 is 110. 7 is 111. No more space, so add another 1 to the left and start over. 8 is 1000. 9 is 1001. 10 is 1010. 11 is 1011. 12 is 1100. And so on...
With computers, we sometimes use a hexadecimal numbering system, also known as base 16 (hex = 6, deca = 10). In this case, we need 16 unique digits before we start reusing them. So we borrow from the alphabet. We use 0-9, then go through A-F before we add a 1 to the left and start over at 0.
You can literally create a base-anything and use that to count numbers. Once you figure out how we add digits to count, it's super easy!
Good ELI5 of the concept
Really good explanation. Always thought I had a general grasp of both binary and hexadecimal, but never really bothered to truly understand. Now I do from 1 minute of reading a comment. Thanks!
Oh wow, I am a software dev but never really had a reason to understand binary but this makes so much sense
The number to describe a base is always the number 10 in that base
For example binary is base 2, it has only 1 and 0 as digits, and 2 in binary is 10.
Similarly for 4, and base 10.
So no matter what your numbering system is, with that system it is always base “10”
"Base" is the number of distinct integers you have in play. In Base 10, there are ten of them. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. You can think of the numeric representation 10 as "1 ten, and 0 ones."
In Base 2 (binary) the only two digits available are 0 and 1. The first four binary numbers are 0, 1, 10, 11, which represent zero, one, two, and three. In Base 2, "10" means "1 two, and 0 ones." But, "Base 2" can't be written in binary, there's no concept of 2! Indeed, the way we reflect two in binary is 10. Which means, when we're talking in binary, "Base 2" is written as "Base 10."
This holds true for EVERY base. In Base 4, we have the digits 0, 1, 2, and 3. So if we want a value of four, we need to write it as 10. "1 four, 0 ones". So, when we're talking in Base 4, the way to say "Base 4" is ALSO by saying "Base 10"!
The trick behind it is that numbers written don't have context-free meaning. You can't communicate what "10" means without knowing how many distinct digits your conversational partner is working with. Most people have centralized on base 10, but there's no inherent advantage to doing things that way. Indeed, it's kind of awkward in lots of ways. Consider Base 12 (the digits of which are most often 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, as an aside). In Base 12, you can easily divide your base numbers by 1, 2, 3, 4. That's SUPER handy, since we obviously break things up into groups of 3 and 4 pretty often in our daily lives, but that's pretty painful in Base 10 because you immediately run into the need for fractions.
Base 10 means when you count it goes: 1 2 3 4 5 6 7 8 9 10
Base 4 means when you count it goes: 1 2 3 10. 10 would still be equivalent to 4, 11 would be 5, 12 would be 6, and 20 would be 8.
To an alien that counted in base 4, base 4 would be base 10, because 4 is where they start adding 0s to numbers and they don’t have a concept of what 4 is. Probably not really if they were a mathematician alien, but it made me laugh.
If you count in base 10 (from 0 to 19):
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
Base 4 (from 0 to 7):
0 1 2 3
10 11 12 13
Base 16 (from 0 to 31):
0 1 2 3 4 5 6 7 8 9 a b c d e f
10 11 12 13 14 15 16 17 18 19 1a 1b 1c 1d 1e 1f
It's a language issue. We say 10 because we don't have a single digit symbol to represent 10. If a alien with 20 fingers came we wouldn't recognized their symbols for anything bigger than 9. Base 4 creatures don't use 4 because after 3 comes 10 for them.
Base 16 is used all the time in computer science. The symbols for 9+ aren't arcane or unrecognizable it's 0 1 2 3 4 5 6 7 8 9 A B C D E F. It's often written with an 0X in front to indicate hexadecimal or something like 'h for hex and 'd for decimal.
Examples:
- 'h7 = 'd7
- 'hC = 'd12
- 'hF = 'd15
- 'h7CF = 'd(7 × 162) + (12 × 161) + (15 × 160) = 'd1792 + 'd192 + 'd15 = 'd1999
Yeah I know but base16 creatures would use 10 to express 16 not "G"
What do you mean they don't use A B C D E for 10 11 12 13 13 15?
We wouldn't recognize the aliens symbols for 0-9 at first either.
should interstellar contact ever actually happen, maths would be the first (and for a long while, probably the only) thing we'd actually be able to communicate in.
So we should say base 9+1? Or base ✋🤚 this many.
Hey mathematicians, is this a good universal way to communicate number bases? I think y'all would call it 1111111111₁ or something like that
Fun tangent, on my hands that would be 1023 because I count in binary on my fingers
Actually, I saw this meme before and I didn't notice the alien has four fingers. Do we use base 10 because we have that number of fingers??? Is there really a proof of that?
It's a good reason for us to use base 10, but in the past many people have not used base 10. However, the bases a society use often are somehow tied to something about the body. As an example (haven't looked it up for a while, sorry), I think there is/was a group that used base 8, and counted on the gaps between their fingers.
Based
All your base
are belong to us
When I was bored in math class I used to convert my homework into binary to see if it still worked.
Every base is base 10.
What about base 0? Checkmate, mathists.
Wouldn't that be base 1?
it would be 'what's a base?'
I think it's saying you can factor out the zero because it's zero and we're looking for "base sets" which for us 1's? Factoring every number system down to whatever their base set is equivalent to that original 1's relationship with zero?
It seems a little more esoteric than the practical reality that an alien might just count on it's digits which could be any base number, and we should understand that, particularly if it gets so bad on Earth we have to leave soon.
I haven't taken math in a very long time.
Humans use base 0x0A. Beep boop.
all your base are belong to us
somebody set us up the bomb
In Chinese/Japanese, there's 四 rocks in both base 10, and base 4. (8 rocks would be 二四 in base 4).
I think the concept of "base" is easier to understand when you include a numeral for the highest base (10 = 十, 20 =二十).
Of course, arabic numerals are more concise, using position to imply meaning (21 = 二十一).
Doesn't base 4 only go up to 三? Like binary is base 2 and only has 0 and 1. 四 would be base 5.
In Arabic numerals base 2 has 0 and 1, and base 10 has 0 to 9, which is also 10 numeric symbols. Chinese has 10 numeric symbols for base 10, too, just a "10" symbol instead of a 0.
they already said that they have numerals for the base they use. from what I understood, basically imagine we use base 10 but have a numeral for it, let's say X. our numbers go like this:
1, 2, 3, 4, 5, 6, 7, 8, 9, X, X1,X2, X3, X4, X5, X6, X7, X8, X9, 2X, 2X1, 2X2, etc...
so i imagine it's similarwhen they use base 4:
1, 2, 3, 4, 41, 42, 43, 24, 241, 242, 243, 34...
mind that i have no knowledge on this and I'm only interpreting what i understood from the comment above.
8 rocks would be 二四 in base 4
ok but what about 16? there's symbols for powers of 10 but not for powers of 4
16 might break it.. 四四 makes no sense as 十十 makes no sense... you'd write 百 (100) instead.
And you get the same problem each time you go higher.
You'd need base 4 equivalents of 100 = 百, 1,000 = 千, 10,000 = 万, 100,000,000 = 億,.
Hmm, on the other hand you can have 十万 (100,000), so why not 四四 (16)? What's 20, though...
I only see bleem rocks though. Where are people getting 3 and 4 from?
i only recognize bleem as two possible things. dropout.tv's Brennan Lee Mulligan or the company that emulated playstation games on the dreamcast, got sue by sony and won, setting the precedent that emulation is a legal process, but folded under the weight of the lawsuit anyway.
Doesn't matter how many digits you use. The first number after the last possible single digit is 10. If the first digit tier is 0 and the second is 1 it means it's the number after you have used all the possible digits to express a number with a single digit number. Guess it's harder to explain.
I personally like base infinity
Agree! I don't know why other people don't get how convenient it is to have a distinct character for every single number imaginable.
Single digit numbers always
Obligatory Jan misali video:
All bases should be quoted in Base-1, the basedest of bases
