/sci/ - Science & Math

[Anonymous No.4992521]

The decision for most humans to use base 10 is mostly arbitrary, right?

I mean, there's no objective basis to use it over-say-base 12 or base 7239, right?

[Anonymous No.4992525]

seems pretty arbitrary

base 2 seems to be the only base that makes any sort of sense, to me

[Anonymous No.4992530]

>yfw you realize it's because we have 10 fingers

[Anonymous No.4992529]

Yes. Base 7239 would have too many symbols for an average human to memorize. 9 is enough, but perhaps even that is excessive.

The point is to try to find a balance between the number of symbols and the length of numbers written in a place-value system.

[Anonymous No.4992533]

Then stop using it you edgy 15 year olds.

[Anonymous No.4992534]

>>4992529
>9 symbols

>/sci/ is supposed to be smart
>can't even count

[Anonymous No.4992537]

>>4992530
Yeah but if we can count to 10 on only two hands, shouldn't it be a base-11 number system?

[Anonymous No.4992540]

>>4992525
Why not base 1?

[Anonymous No.4992544]

>>4992530
Still arbitrary

[Anonymous No.4992554]

every base is base 10

[Anonymous No.4992558]

>>4992540
Someone can divide 10 by whole numbers and end up with other whole numbers, whereas that is impossible with 1. Other than that, I see it as having aesthetic simplicity.

[Anonymous No.4992564]

How come there is a negative and positive interval value but no North / West / South / East values?

[Anonymous No.4992563]

>>4992554
Not they're not... you retarded son?

[Anonymous No.4992568]

>>4992564

Because numbers don't have a universal geological position?

[Anonymous No.4992569]

>>4992564
How come geography and math aren't the same thing?

[Anonymous No.4992574]

>>4992569

But latitude and longitude have numerical values. That means math and geography are related.

[Anonymous No.4992577]

>>4992563

For any base b, "base 10" describes base b, because "10" in any base b represents b. Jackass.

[Anonymous No.4992579]

>>4992554
>That one xkcd parrot faggot in every math thread

[Anonymous No.4992587]

>>4992577
That doesn't make the bases equivalent... you must be trolling.

[Anonymous No.4992617]

>>4992569
You study maps in both geography and math.

[Anonymous No.4992621]

Bases with many prime factors work well to express numbers in decimal (basimal?) without non-terminating rationals.

Then the best bases are
2, 3, 5, 6, 7, 10, 12, 30, ...

[Anonymous No.4992647]

>The decision for most humans to use base 10 is mostly arbitrary, right?
More or less, yes, though there is a practical tradeoff between how many symbols you need and how long numbers tend to be. Base 7239 would be rather unpractical for that reason.

[Anonymous No.4992662]

>>4992521
base 64 is the perfect mathematical base becasue of the way radians and circles work. However that is too complicated for most people. There was a king who wanted to change to base 64, but he didnt realize the peasants were too stupid to count that high, so his advisers convinced him to use base 8 which was just a derivative of base 64. It survived for awhile but turns out peasants really need to count on their fingers because there were no books, and so base or writing so 10 became standard.

true story

[Anonymous No.4992663]

we have 10 fingers you moronic idiot

[Anonymous No.4992666]

>>4992662

sauce

[Anonymous No.4992668]

we have ten fingers. its kind of obvious. yet another riveting thread on /sci/

[Anonymous No.4992669]

>>4992587
what is 2 in base-2? 10
what is 3 in base-3? 10
what is 4 in base-4? 10
...
what is n in base-n? 10

If you don't get the humor or the mathematical relevance you are stupid.

[Anonymous No.4992680]

>>4992666
In 1716 King Charles XII of Sweden asked Emanuel Swedenborg to elaborate a number system based on 64 instead of 10. Swedenborg however argued that for people with less intelligence than the king such a big base would be too difficult and instead proposed 8 as the base. In 1718 Swedenborg wrote (but did not publish) a manuscript: "En ny räknekonst som omväxlas vid talet 8 istället för det vanliga vid talet 10" ("A new arithmetic (or art of counting) which changes at the Number 8 instead of the usual at the Number 10"). The numbers 1-7 are there denoted by the consonants l, s, n, m, t, f, u (v) and zero by the vowel o. Thus 8 = "lo", 16 = "so", 24 = "no", 64 = "loo", 512 = "looo" etc. Numbers with consecutive consonants are pronounced with vowel sounds between in accordance with a special rule.[3]

http://en.wikipedia.org/wiki/Octal

[Anonymous No.4992677]

>>4992662
Base 64 doesn't help radians or circles because pi is transcendental. Besides, degrees are already measured in base 60 due to Sumerian customs.


Throughout history all across the planet people have used all sorts of crazy number systems. Many of them not even conforming to our modern notions of base n type number systems.

Wanna see something really mindblowing, check out the incas. They used a system where they would take a thread and tie other threads to it of different colors. These other threads would have knots tied into them. The whole thing functioned as a form of record keeping, written language, and number system. It was admissible in "court" to work out disputes between different people when the spaniards first started getting to the new world. Unfortunately, after the europeans started enslaving/wiping out all the indigenous they also destroyed all the libraries, written records, banned people from talking about old customs (under penalty of death), etc.. and now no one really understands how it worked besides really simple shit that we've been able to figure out.

[Anonymous No.4992683]

Niggers gonna nig

http://en.wikipedia.org/wiki/Complex_base_systems

Base -1+i is clearly the best base.

[Anonymous No.4992689]

>>4992683

saw the "i" and started to laugh hard
>not doing it since a b-thread back in 2005

[Anonymous No.4992701]

>>4992689

Are you serious anon? Did you even read the article? Complex bases are well-defined, well-behaved, and well-researched. There is no joke here. I am making an honest suggestion. Your assumption that I was joking makes my butt leak. Makes it leak tears. Tears of feces, lubricant, semen, and saliva. And blood. Tears of sadness, my friend. Tears of anal humiliation.

[None !tX/x/X/y/. No.4992721]

>>4992530
Many universal numbers are relative to our physiology or psychology. Take the number 150 for example, Dumbars number as its referred, its theorized that its the number of 'close' friends a singular human being is capable of both keeping track of and associating emotional attachment. Its observed to be the average size of the average prehistoric and Ice age era communities, the amount of friends you have on facebook (Give or take 10) and many other seemingly trivial connections in the way of social cohesion.

[Anonymous No.4993313]

>>4992701

there was another Anon that tried to tell me Complex Numbers weren't well ordered.

[Anonymous No.4993319]

base 30 or 60 are the best bases

[Anonymous No.4993329]

Skrillex is the best base.

[Anonymous No.4993333]

>>4993313
There are models of ZF where they aren't.

[Anonymous No.4993336]

>>4993333

[Anonymous No.4993362]

>>4992689

lulz I just lrnd about imaginary numb3rs

[Anonymous No.4993371]

It's based off of humans having 10 fingers. Yeah, pretty arbitrary. Base 12 or 16 would be much better suited for human reasoning.

[Anonymous No.4993382]

>>4993333

That sounds ambiguous to me..

It seems to me that either I can specify whether two complex numbers are 'equal' 'less than' 'greater than' or I can't.

[Anonymous No.4993384]

Base phi master base.

http://en.wikipedia.org/wiki/Golden_ratio_base

[4chan Moderator No.4993386]

>>4992521
10 fingers bro. 10 fingers

[Anonymous No.4993394]

All you 10 fingers people. Learn to read and then perhaps you'll understand what OP is actually asking for. Having 10 fingers is NOT an objective reason for having base 10.

You can just as easily count based on the number of knuckles, which will gives you a total of 28.

[Anonymous No.4993398]

While the 10 fingers thing is good in theory, I dont think it explains everything. At the end of the day, we use base 10 because its a simpler method of storing large numbers. When a human thinks of the number 4 million, you dont have an actual concept of a million.. you are storing two smaller numbers. You are using 4, and then how many digits follow it. You dont actually think of 4 million in and of itself, you think of 4 and 7.

If you were using base 8 or something, the numbers would get far too complicated too fast.

[Anonymous No.4993399]

>>4993394
Were you looking for a proof for an arbitrary choice? We have 10 fingers. It's not the only possible choice, but it's what we've chosen, or what's incidentally become commonplace.

[Anonymous No.4993402]

>>4993398
Do you really thing base 10 is fundamentally easier than for example base 8 or base 12?

It's just easier for you since that's what you're used to.

[Anonymous No.4993403]

Base 8 is superior for mathematics.

[Anonymous No.4993422]

It's cultural. In the US, we use a variable base system for measuring length. In time-keeping, we use a base 60 numbering system, based of the Babylonians.

[Anonymous No.4993438]

People have mostly used 5s and 10s due to our fingers, but notice that we've also based systems on 12 and 60 for divisibility, and even before computers, on 2 for simplicity (ounce, cup, pint, quart, gallon).

[Anonymous No.4993455]

we could easily handle base-8, using our thumbs to touch the ends of each of our eight fingers to count

[Anonymous No.4993466]

we use base ten so that this works

http://www.youtube.com/watch?v=OpNJ1r6uD98

[Anonymous No.4993545]

LOL, dude you didn't even put on that most of computing softwares are using base 16.

basically :0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
That's why a computer consider FFFAAA000 as a number.

But the most fundamental system is the binary : 0, 1

The strange part is that 0 been imagined in India only few century ago.

[Anonymous No.4993568]

binary, octal, decimal, hexadecimal, pic related, very useful, got one of these ~20 years ago

[Anonymous No.4993580]

>>4993568
Got one with my fresh W7 install. Oh yeah!

[Anonymous No.4993628]

I read somewhere that the best was base e. I'll try and find the article. Apparently it's the best balance between number of symbols and length of numbers when written in it.

[Anonymous No.4993632]

>>4993628

http://www.burtonmackenzie.com/2007/12/whats-most-optimal-numeric-base.html

Found it.

[Anonymous No.4993641]

best bases:
1) 2
2) 6
3) 30
4) 60
5) 210
/thread

[Anonymous No.4993651]

>>4993641

[Anonymous No.4993677]

>>4993466
>>4993455
>>4993399
>>4993333
>>4992544

[Anonymous No.4994102]

>>4993677

[Anonymous No.4996155]

>>4993677
OH BOY HERE WE GO

[Anonymous No.4996224]

>>4992521
One of my comp sci professors said we use base 10 because we have 10 fingers.

[Anonymous No.4996303]

>>4996224
So Babylonians had 60 fingers and Mesoamericans 20?

[Anonymous No.4996310]

>>4996303
That's not really an apt deduction. The qualification was "we". The Babylonians can do whatever they so please.

[Anonymous No.4996313]

>>4996303

Babylonians used their knuckles of all fingers except the thumb for counting in a special way, which means 12 'counts' for one hand, and then counting the 'hands' with the other hand, resulting in 12 * 5 = 60 'counts'

[Anonymous No.4996342]

>>4992521
for small bases - long numbers and a short table of multiplication needed
for large bases - small numbers and a large table of multiplication

[Anonymous No.4996347]

>arbitrary
>10 fingers

are you really this dense

[Anonymous No.4996382]

Can somone explain how a non-integer base system would work?

[Anonymous No.4997211]

>>4996382
well, this is what I think.

Say you have base-b
Then 1 would be b^0 or 1
10 would be b^1 or b
100 would be b^2 and so on.

So take base-i
1 be 1
10 would be -1
100 would be -i
1000 would be 1 and so on

[Anonymous No.4997240]

>>4997211
>>4997211
>>4997211
>>4997211
>>4997211
>>4997211
>>4997211
>>4997211
>>4997211

[Anonymous No.4997366]

You could say that we use base one-hundred if you consider each of the first hundred numbers of base ten as a separate symbol.

The digits of base one-hundred are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ... 99.

Similarly, you could say we use base one-thousand.

[Anonymous No.4997370]

By the force of human cognitive logic, there is at least one (this case, of Dravidian) natural language that counts its first few numbers in binary:

0: ko
1: ah
2: ah ko
3: ah ah
4: ah ko ko

I have also heard of languages counting around base 3, but I hadn't looked into it. One could also say that English counts its first numbers to base 12 and French counts to base 16 (Parisian French in particular counts its higher numbers in base 20, so that 82 is called "4*20+2").

[Anonymous No.4997371]

what if base 5?

[Anonymous No.4997380]

>>4997371
>base 5?

Tally marks, yeah? Also Roman numerals and Korean numerals work in Base 5. I think there's some languages that use it too, but I can't recall.

[Anonymous No.4997430]

I like to be a dick when people use the phrase "I can count the number of times on one hand."
I say "So up to 31?"
and they're all like "What? I only have 5 fingers on one hand, retard."

And then I teach them to count in binary with their fingers.

[Anonymous No.4997432]

>>4993398

[Anonymous No.4997437]

>>4993641

>arguing about which base to use

[Anonymous No.4997444]

Here's a fun one I saw on a practice SAT test

log (base) 10 of 100 =
A. 2
B 10
C 100

Anyone see the problem?

[Anonymous No.4997453]

>>4997444
B

[Anonymous No.4997461]

>>4997453
Half right....although, the difficult half.

[Anonymous No.4997470]

>>4997370
> French counts to base 16
Not really.
Although 17 is the first number to be spelled as "ten-seven" (dix-sept), numbers from 11 to 16 don't have original names neither, they are derivative from the digits 1 - 6.
1 un - 11 onze
2 deux - 12 douze
3 trois - 13 treize
4 quatre - 14 quatorze
....

> that 82 is called "4*20+2"
Ha, I've heard this give people a hard time to learn the numbers in French
70 to 79 are spelled 60 + [10..19]
80 to 99 are spelled 4 . 20 + [0..19]

so writing 99 is literally 4 . 20 + 10 + 9

Anyway, you found occurrences of base 12 and 20 in many languages (a dozen, half-a dozen....)

[Anonymous No.4997468]

>>4992669
>>4992554
holy shit mind blown

[Anonymous No.4997500]

>>4997470
In Russian you decline words according to cases, and you decline them differently according to what number your number ends in. French is for pussies.

[Anonymous No.4997501]

>>4997500
Did I write words? I mean numbers, sorry.

[Anonymous No.4997555]

>>4997444
the problem is that SATs don't test logarithms and you just made it up. Also there is always more than 3 choices.

[Anonymous No.4997556]

>>4993394
The OP is working on a fundamental misunderstanding. Arbitrary doesn't mean non objective. You can have very good reasons for using something, even if it isn't objectively better than anything else.

[Anonymous No.4997557]

>>4992558 Someone can divide 10 by whole numbers and end up with other whole numbers,

Why is this important? Is there a proof or reasoning for it?

[Anonymous No.4997564]

No you can't. That's like saying 3/6 is somehow different than 1/2

[Anonymous No.4997588]

>>4997564
if you look at them as only symbols with no meaning, then yes.

[Anonymous No.4997625]

>>4997500
>>4997501
feel free to elaborate, I'm curious

[Anonymous No.4997689]

>>4997625
You can see here:
http://www.linguarus.com/ru/program/grammar/5/

[Anonymous No.4997799]

On one hand, each unique symbol generally requires a glyph in your written language, a word in your spoken language, and structures in your brain to recognize these accurately.

On the other hand, when you want to express a value, smaller bases require you to use more digits, which takes longer to express in writing or out loud.

Decimal is a fair balance between number of unique symbols and number of digits required to represent everyday values.

[Anonymous No.4997804]

>>4992579
Wasn't even xkcd, I think. It was from some webcomic I've never heard of.

[Anonymous No.4997808]

I think it was the Mayans, that had a base 20 system. So I'd say yeah, mostly arbitrary. It hasn't given us any significant advantages above all other bases.

[Anonymous No.4997819]

>>4992521

10 fingers and 10 toes, it makes sense.

[Anonymous No.4997849]

>>4997564
In a game of basketball shooting 3/6 from the line is different than 1/2.

[Anonymous No.4997852]

Proposed New Digits For Base 12, 16, 20 Systems
http://stuff.davesfunstuff.com/83pages/831400.htm

[Anonymous No.4997856]

you don't want to use a base that is a prime greater than 2 - that just sucks dick.

6 and 10 are the best choices - base 6 is my personal fave because counting with your hands is so damn easy with it (mess around with it - you'll find a cool way to make it cool)

[Anonymous No.4997865]

Would you need a new set of numbers?

I wouldn't like to be using base 8 with 9 numbers.

[Anonymous No.4997874]

my brain hurts from trying to conceptualize anything but decimal

[Anonymous No.4997875]

Base 10 is good enough, I'm far more interested in the shittiness of the base system used in degrees and time. People would probably find geometry a lot more intuitive if it was base 10, and it would be a lot easier to convert from radians to degrees in your head.

Basically, base 6, 10, 12 is all okay. But we should just be fucking consistent once we've chosen one.

[Anonymous No.4998753]

I thought that for math/compsci base 8 was master base? Or at least, anything that's 2^x ?

[Anonymous No.4998758]

>>4998753
>base 8

On my linux box I have a program called 'HD' for hex dump and OD for octaldump

Why is base 8 useful in compsci

[Anonymous No.4998797]

No.
We have ten fingers that are easy to count on, so a 10 digit system makes sense, for humans.

[Anonymous No.4998809]

>>4998797
if we used base 2, we can count to 1024 on our fingers.

[Anonymous No.4998818]

>>4998809
>if we used base 2, we can count to 1024 on our fingers.

>mfw people think I'm werid for doing this

[Anonymous No.4998820]

>>4998758
because early computers used 24-bit instructions, so they could represent the dump in 8 octal symbols, now we use 4 hexadecimal symbols

[Anonymous No.4998851]

>arbitrary

How many fingers do you have?

That's probably why.

[Anonymous No.4998949]

>>4998753
>>4998758
A few architectures used to have 12, 24 and 36 bit words. A 12 bit binary number converts perfectly into 4 octal numbers as a 16 bit binary number converts into 4 hexadecimal numbers.

Octal and Hex are easier to read than binary. Octal was therefore used for memory dumps on n*12 bit architectures as hex dumps are used for memory dumps on contemproary hardware.

[Anonymous No.4998979]

>>4992540
>>4992558

>yfw base 1 is how we count objects and teach pre-school children how to count.

There are 2 circles => oo
There are 5 circles => ooooo

[Anonymous No.4998987]

Isn't using our fingers actually using base 1?

[Anonymous No.4999020]

If it's because of our fingers, why are angles in multiples of 60 (degree units)

[Anonymous No.4999046]

>>4999020

for the same reason we count 60 seconds in a minute. it was explained in here earlier. lurk more.

[Anonymous No.4999380]

i think it has something to do with the fact we have 10 fingers.
I heard once that a civilization on africa used to count with the holes between fingers, so they counted 4by4