Sciencemadness Discussion Board

Thinking in different number bases...

DubaiAmateurRocketry - 8-10-2015 at 21:26

if a child was raised in a base 2 number system( aka binary), or any number system not base 10, how different would things be ?

crazyboy - 8-10-2015 at 22:04

I imagine it would be rather difficult to deal with a lot of practical matters, you end up needing more digits to express the same value. For example In the US phone numbers have a three digit area code followed by a seven code number for theoretically 9,999,999,999 unique numbers with ten digits phone numbers in binary look like this: 011101001100000001000110111100 I think a lot of things would be more difficult in binary. That said dozenal or base 12 has been suggested as an alternative base by the addition of two new numerals. Although it will likely never happen it has the advantage of being divisible by 2, 3, 4, 6, and 12 unlike base 10 which is only divisible by 2, 5, and 10.

Fulmen - 9-10-2015 at 01:54

But every system IS base 10. Just think about it...

aga - 9-10-2015 at 03:42

Nah. Just that we use the same arabic digits is all.

Hexadecimal also has A thru F added.

deltaH - 9-10-2015 at 03:45

We all use a time system that's base 12 and don't give it a second thought. Mayans used base 12 didn't they? Here's hexadecimal ala SM:

1 2 3 4 5 6 7 8 9 10 :) :( :D ;) :cool: :mad:

Fulmen - 9-10-2015 at 05:33

Aga: What is 2 in binary? What is 16 in hex?

mayko - 9-10-2015 at 16:15

Quote: Originally posted by deltaH  
We all use a time system that's base 12 and don't give it a second thought.


Welllll... I'd say that's a base-10 system under arithmetic mod 12 ... :P

A while back, Brian Hayes made an interesting case for base three as a compromise between string length (crazyboy's phone number example) and character count:
"Third Base" - Brian Hayes

blogfast25 - 9-10-2015 at 16:43

Yeah but what's 512<sup>(170.6666 / 512)</sup> in binary, huh? ;)

[Edited on 10-10-2015 by blogfast25]

aga - 9-10-2015 at 23:54

000000000000000000000000000000000000000000000000000000001000

blogfast25 - 10-10-2015 at 08:01

Quote: Originally posted by aga  
000000000000000000000000000000000000000000000000000000001000


170.6666 divided by 512 is 1/3.

512<sup>1/3</sup> is the cubic root of 512, which is 8.

8 in digital is 100.

aga - 10-10-2015 at 08:05

Digital ? Dunno what that is.

8 is 1000 in Binary (aka base 2)

Edit

Was about to add (base 10) after the 8 then realised that the number base of the 8 doesn't need stating, as it must be base 9 or higher to be able to use the '8' symbol.

[Edited on 10-10-2015 by aga]

deltaH - 10-10-2015 at 08:17

Hmm, nobody picked up that I had one smiley too many in my SM hexadecimal post, I'm disappointed.

aga - 10-10-2015 at 08:31

The smileys were fine.

you had 1 number (the '10') too many in your post.

blogfast25 - 10-10-2015 at 08:37

Quote: Originally posted by aga  
Digital ? Dunno what that is.

8 is 1000 in Binary (aka base 2)

Edit



Yes, 8 = 1000 in base 2, my bad :mad:. 'Digital': vernacular for binary.

aga - 10-10-2015 at 08:42

Quote: Originally posted by Fulmen  
Aga: What is 2 in binary? What is 16 in hex?

The notation for the exact value of any number base in that number base is always '10'.

That is not Decimal, it's just two symbols next to each other.

We could as easily use other symbols, such as z,k,q = 0,1,2

Then 5 in base 3zkq notation would be 'kq'.

3,735,928,559 is said to be amusing in Hex.

(Programmers don't get out a lot)

aga - 10-10-2015 at 09:03

Quote: Originally posted by blogfast25  
Yes, 8 = 1000 in base 2, my bad

If only my Error Rate was as low as yours bloggers.

j_sum1 - 10-10-2015 at 16:33

My favourite strange base is factorial.
For example,
155770= 3×8! + 6×7! + 6×6! + 2×5! + 0×4! + 1×3! + 2×2! + 0×1!
So, in base "factorial", 155770 is represented by 36620120factorial

Addition in this system is fairly straightforward. Multiplication is a special kind of nightmare.
And, no. I have no idea what practical use this system serves, but I am told there is one.

blogfast25 - 10-10-2015 at 17:03

Chinese multiplication:

https://www.youtube.com/watch?v=U2UloHO5Ubc

aga - 10-10-2015 at 22:51

Wow !

That Chinese method is brilliant !

deltaH - 10-10-2015 at 23:07

For aga:

https://www.youtube.com/watch?v=OuF-WB7mD6k

aga - 10-10-2015 at 23:18

Nice trick !

If the volume of beer in the glass = v as a function of time f(t) then i find that table stability is irrelevant as v = 0 for any f(t) where t > 0.

deltaH - 10-10-2015 at 23:45

You forgot to say that with strong German accent ;)

woelen - 11-10-2015 at 08:48

Quote: Originally posted by blogfast25  
Yeah but what's 512<sup>(170.6666 / 512)</sup> in binary, huh? ;)


It's 111.1111111111111111< irregular infinite pattern of zeros and ones > ;)


[Edited on 11-10-15 by woelen]

aga - 11-10-2015 at 10:35

That is likely the most correct answer using the decimal value given.

The way i approached it was to imagine that the Questioner meant :-

170.666 = 170 + 2/3 = (170*3 + 2 )/3 = 512/3

The Devil is always in those .666 fraction-approximations :o

[Edited on 11-10-2015 by aga]

mayko - 11-10-2015 at 13:59

Another interesting fact about ternary: The cantor set can be defined as those real numbers between zero and one, whose ternary representation contains no 1's

DubaiAmateurRocketry - 23-10-2015 at 15:27

sorry to bring this back up again..

but...

If not all, most music are in base 7 form, for example the piano..

0 C
1 D
2 E
3 F
4 G
5 A
6 B
10 C
11 D
12 E
13 F
14 G
15 A
16 B
20 C

and so on.. and for example in a base 7.... 3*3=12 and 10x10 = 100 is equivalant of 3*3=0 and 7x7=49 in base 10...

but why piano, or music in general,is in base 7(or base 12 if you count the black notes ?)... and why does base 7 music sound so good ? i cannot imagine music in like... for example base 10... also... if a child was brought up studying math in base 7... and was taught music theory / instruments since a kid... would he be able to think / memorize equations like a song ? or memorize a song like a chain of numbers ? because do, re, mi, fa, so, la, ti, do, would be same as 1, 2, 3, 4, 5, 6, 10

would math equations in base 7 make sense in music ? what would some repeating decimal in base 7 sound like in music ?

deltaH - 23-10-2015 at 17:19

So you could sing your numbers, but you'd have to have perfect pitch recognition to interpret them, perhaps one would if it was taught this way from early on.

Certainly mathematics and music are much related.

IrC - 23-10-2015 at 22:40

Quote: Originally posted by aga  
3,735,928,559 is said to be amusing in Hex.

(Programmers don't get out a lot)


3 735 928 559 = 0xDEADBEEF

No but they eat a lot of takeout.

The Volatile Chemist - 24-10-2015 at 12:52

A proffessor of mathematics is coming to our highschool to teach on modulu functions (x mod y) for our 'matheletes' club. T'will be fun.

mayko - 25-10-2015 at 07:22

In high school, there was a traditional call and response each class had around their graduating year:
Rando: "Two-oh!"
Crowd: "Oh Four!"

My nerd clique had a countertradition:
"One one one one one!"
"Zero one zero one zero zero!"

franklyn - 25-10-2015 at 09:18

Someone with polydactyly could readily deal with base twelve. Otherwise what can you do with the extra digits.

Chisanbop or finger math would be no different except for the base.

aga - 25-10-2015 at 13:44

Quote: Originally posted by mayko  
In high school, there was a traditional call and response each class had around their graduating year:
Rando: "Two-oh!"
Crowd: "Oh Four!"

My nerd clique had a countertradition:
"One one one one one!"
"Zero one zero one zero zero!"

Oh, the sheer Class of of the nerd class of 2004.

The Volatile Chemist - 25-10-2015 at 14:39

Quote:
Otherwise what can you do with the extra digits

Heh Heh...be a typist...