Question

Isn't base ten a terrible base to do math in? I mean, it slows down computers, it's totally useless for expressing most rational functions, and, it's really freaking hard to convert!

Answer 1

Why 5 fingers? WHY?!

Answer 2

Would you rather use hex? :D

Answer 3

Real world works in base 10 so it's necessary to include in Computers. Even if they get slowed by that. We need Computers for our benefit , no matter they get slow :P

Answer 4

The real world doesn't use base ten. Just our minds.

Answer 5

I imagine that humans would have an easier time with everything if we used base 12 or base 16.

Answer 6

Or, we could just be babylonians.

Answer 7

Base 60 is the best

Answer 8

why not base 20? That was popular in the Americas.

Answer 9

Fingers and toes!

Answer 10

base 20=base 2*2*5. There are too few rational numbers you can easily express.

Answer 11

Let's look at base 12: 1/2 in base ten=0.6 1/3 in base ten=0.4 1/4 in base ten=0.3 THe only disadvantage of base 12 is that you can't write 1/5 easily, but 1/5 is only important to us because we use base ten.

Answer 12

I'm pretty sure I read some article suggesting that base e was the most efficient base to use. If I find the article I'll post a link.

Answer 13

Really?

Answer 14

does it have to do with e^(ipi)?

Answer 15

e is transcendental, so it might be good for pure math? but not for counting 0.o

Answer 16

"I have the natural logarithm of 1 dollar" (in base e)

Answer 17

I was also thinking it sounded ridiculous for counting, but they seemed to be suggesting that. They made some effort to show it was the most efficient base to express larger numbers with.

Or something like that. I read it a while back. :/

Answer 18

Or, I have (-1^(ipi)) dollars! MUAHAHHA

Answer 19

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

Answer 20

So we should have about 2.7182818284590452353602874713526624977572470936999595... symbols to express numbers.

Answer 21

Hm.

Answer 22

I don't understand though, it's the most "optimal base", but it really sucks for counting.

Answer 23

obviously this guy didn't define optimal base very well.

Answer 24

Interesting in theory, but absolutely terrible for application.

Answer 25

Yes. I bet it would be good for pure mathematics, but the number "1" becomes transcendental in base e!

Answer 26

Shouldn't every rational number become transcendental? In fact, wouldn't every algebraic number become transcendental?

Answer 27

Only God could use it

Answer 28

Exactly, it would be terrible.

Answer 29

And many common transcendental numbers would still be transcendental, I'm sure.

Answer 30

Like pi.

Answer 31

I'm not actually sure if pi would remain transcendental or not. It's related to e from Euler's identity.

Answer 32

PI would remain transcendental.

Answer 33

e^(ipi) was used to prove that pi was transcendental

Answer 34

so, I'm pretty sure it would still be transcendental.

Answer 35

But if e were algebraic, it would follow from that formula that pi was algebraic.

Answer 36

wait, we can't prove this question.

Answer 37

what we are looking for is essentially whether pi-e is transcendental.

Answer 38

I remember reading on wikipedia that it's not known whether or not it is.

Answer 39

However, if we're assuming -1 is transcendental, then pi would have to be transcendental for \(e^{i\pi}\) to be transcendental.

Answer 40

"Sums, products, powers, etc. of the number π and the number e, except for eπ, Gelfond's constant, which is known to be transcendental: π + e, π − e, π·e, π/e, ππ, ee, πe"

Answer 41

Wait, I reduced the problem incorrectly.

Answer 42

I will have to pose this question in class tomorrow. If we were to somehow call e algebraic, would pi remain transcendental?

Answer 43

The easiest question would be: Given the field \(\mathbb{Q}(e)\), is \(\pi\) algebraic or transcendental over that field?

Answer 44

But if we instead use the field \(\mathbb{E}\) such that every element in \(\mathbb{E}\) is generated by multiplying by e and adding by e, is pi algebraic in that field.

Answer 45

However, for this to be a field, we would need to include all of the rational numbers anyways. So really we would have to use \(\mathbb{Q}(e)\) for our field no matter what.

Answer 46

Wait, what are we arguing about again?

Answer 47

If pi in base e is transcendental or algebraic.

Answer 48

Now, don't you wonder how we got there?