Is There a Universal "Base" for Numbering Systems?

[DonRocks]

Our numbering system uses Base 10 because we have 10 fingers; yet, because of that, we end up with numbers such as "Pi," which is irrational (infinite and non-repeating) - irrational literally means, "unable to be put into a ratio."

I haven't checked this, but the possibility dawned on me that there is a more universe-based numbering system that conforms with physics instead of our own human bodies. I cannot possibly be the first person to think of this, but has it ever been discovered? Maybe something like "Pi" would end up being a nice, round number in this "Universal Base" numbering system, like 10.

I'm sure we'll always have irrational numbers, but maybe things could be a little "neater" than with our self-centered, Base 10 system. Who knows? Maybe this theoretical "Universal Base" is itself an irrational number, if it even exists.

[The Hersch]

Base 2?

[DonRocks]

3 hours ago, The Hersch said:

Base 2?

I doubt it, because too many things would still require infinite, non-repeating numbers - my guess is that it (if "it" exists at all) would be some very complex number. I can't find where anyone has researched this, but maybe the concept is so outlandish that nobody would bother. I suspect it would be much easier to prove that this didn't exist than that it did.

[DaveO]

I'm a math head.  Way way back in school I recall learning applications for different bases.  Unfortunately I can't remember why!!!   Duh.

Base 2 is a lot of 1's and 0's.  Its used in computers.  All the time.

And there are any applications for different bases of numbers.  The number 17 in base ten would be 25 in base 6 (I think).  and so on and so forth. 

Now I know we were taught about applications or past uses for different bases other than base 10.  But for the life of me I can't recall what they were nor have I used them.  Maybe someone else can enlighten us.

[DonRocks]

27 minutes ago, DaveO said:

I'm a math head.  Way way back in school I recall learning applications for different bases.  Unfortunately I can't remember why!!!   Duh.

Base 2 is a lot of 1's and 0's.  Its used in computers.  All the time.

And there are any applications for different bases of numbers.  The number 17 in base ten would be 25 in base 6 (I think).  and so on and so forth. 

Now I know we were taught about applications or past uses for different bases other than base 10.  But for the life of me I can't recall what they were nor have I used them.  Maybe someone else can enlighten us.

Well I can certainly enlighten you about bases - you can have a numeric system in any base you want, and if we had only eight fingers instead of ten, we'd all be counting in octal - "10" in octal is "8" in decimal.

In Computer Science, the two primary bases are binary and hexadecimal (base 16), and that's because there's 8 bits to a byte, and it takes two bytes to represent a character in systems such as EBCDIC and ASCII (okay, maybe I'm not helping much). 

In hexadecimal, the numbers 10-15 are represented by A-F, so "2B" in hexadecimal is "43" in decimal.

What I'm asking is whether or not anyone has investigated if there's some non-base-10 numeric system that makes a little more sense of the universe, e.g. "base 863.4821894." Maybe using that system, a lot of irrational numbers would become rational, the Pythagorean comma would disappear, etc. I suspect this has been proven false, but I'm just curious if anyone has looked into it before.

[zgast]

1 hour ago, DonRocks said:

Well I can certainly enlighten you about bases - you can have a numeric system in any base you want, and if we had only eight fingers instead of ten, we'd all be counting in octal - "10" in octal is "8" in decimal.

In Computer Science, the two primary bases are binary and hexadecimal (base 16), and that's because there's 8 bits to a byte, and it takes two bytes to represent a character in systems such as EBCDIC and ASCII (okay, maybe I'm not helping much). 

In hexadecimal, the numbers 10-15 are represented by A-F, so "2B" in hexadecimal is "43" in decimal.

What I'm asking is whether or not anyone has investigated if there's some non-base-10 numeric system that makes a little more sense of the universe, e.g. "base 863.4821894." Maybe using that system, a lot of irrational numbers would become rational, the Pythagorean comma would disappear, etc. I suspect this has been proven false, but I'm just curious if anyone has looked into it before.

I wrote a paper on this in college (you can tell the dorks right away, no?).  Base 12 is actually somewhat ideal, according to what I found.  Don got the reason right - it's mostly because it can be divided evenly, which results in less irrational numbers (like pi) which are somewhat of a scourge in math and science.  Only 5 and 7 can't divide it evenly.  Pi is still pi though no matter what the base system is.

[DonRocks]

On 11/16/2016 at 7:27 PM, zgast said:

I wrote a paper on this in college (you can tell the dorks right away, no?).  Base 12 is actually somewhat ideal, according to what I found.  Don got the reason right - it's mostly because it can be divided evenly, which results in less irrational numbers (like pi) which are somewhat of a scourge in math and science.  Only 5 and 7 can't divide it evenly.  Pi is still pi though no matter what the base system is.

Yes, but in a "Base Pi" system, Pi (which is non-computational in decimal) is 10.

[DaveO]

Thank you folks.  Stir the memory.  I forgot about base 16.  great for computation systems.  Base 12.  Oh man you can divide that a lot of ways, 1-9, T, E.  I'm no expert but I recall learning about irrational numbers.  Don't recall a base that rationalized them.  But oh my...I'm exhausting a very ancient and unused source of learning and knowledge.

[zgast]

Just now, DonRocks said:

Yes, but in a "Base Pi" system, Pi is 1.

You're right.  But in a base pi system, wouldn't it be 2?

[zgast]

3 minutes ago, zgast said:

You're right.  But in a base pi system, wouldn't it be 2?

10.  Crap.  And this is why I left mathematics for good.  Clearly not so good once things get theoretical, linear, or imaginary.

[DonRocks]

On 11/16/2016 at 7:35 PM, zgast said:

You're right.  But in a base pi system, wouldn't it be 2?

No, it would be 10 (I'm typing in an airplane).

If you really want to become nauseated, 100 in a Base Pi system is an irrational number times itself. I wonder if there's a term for that, like a "Really Irrational Number." (Mathematicians have very nerdy senses of humor.)

[porcupine]

No answer to your query but perhaps you'd be interested in watching The Man Who Knew Infinity.

Also, are you familiar with tau?

[DonRocks]

4 hours ago, porcupine said:

No answer to your query but perhaps you'd be interested in watching The Man Who Knew Infinity.

Also, are you familiar with tau?

I will watch "The Man who Knew Infinity" blind - I don't want to look up anything about it.

Al Dente is familiar with Taw - in fact, he's the first person to ever break the news about him, and never got so much as a 'thank you' for keeping quiet about it. In retrospect, that was Warning #1 of about 17,000, but I've always been a trusting soul - which is why I have scars all over from being burned.

I actually wasn't familiar with tau, but thanks for bringing it up - that's the kind of stuff I'm interested in learning about. I read that article in passing, and I don't see the fuss if tau is a simple 2-times multiple of pi - so instead of having "2 pi radians," the circumference of a circle has "tau radians" - I don't see the breakthrough, other than that you don't need to multiply by 2. What am I missing? (This could be a separate topic.)

Do you understand what I'm asking? I'm not asking you if you know the answer; I'm just asking you if you understand the question, i.e., is the question coherent enough to be understandable?

[The Hersch]

19 hours ago, DonRocks said:

In Computer Science, the two primary bases are binary and hexadecimal (base 16), and that's because there's 8 bits to a byte, and it takes two bytes to represent a character in systems such as EBCDIC and ASCII (okay, maybe I'm not helping much).

Sorry, this is incorrect. It takes one eight-bit byte to represent one character in EBCDIC. In the original ASCII standard, one character could be expressed in seven bits. These encoding standards share the obvious drawback of a severe limit in the number of characters that can be expressed (255 in EBCDIC and 127 in ASCII, if I remember correctly, not having time at the moment to do the arithmetic). Unicode and its extensions dramatically increase the number of characters that can be expressed by using double bytes or more.

[DonRocks]

On 11/17/2016 at 0:13 PM, The Hersch said:

Sorry, this is incorrect. It takes one eight-bit byte to represent one character in EBCDIC. In the original ASCII standard, one character could be expressed in seven bits. These encoding standards share the obvious drawback of a severe limit in the number of characters that can be expressed (255 in EBCDIC and 127 in ASCII, if I remember correctly, not having time at the moment to do the arithmetic). Unicode and its extensions dramatically increase the number of characters that can be expressed by using double bytes or more.

You're right: one character = one byte, and this is about as basic as it gets (although I don't think I ever knew that the ASCII limit was 127 characters, but that would make sense, since 127 is 2**7-1, and 255 is 2**8-1). I was typing last night hunched over on an airplane, with no food except for two Bloody Marys in my system, and trying both to read a book and carry on a conversation with my neighbor when I was typing. Plus, this hasn't crossed my mind now in seven years. Still, guilty of shoddy thought processes.

For those that care, you can dig in as deeply as you want to here.

Trivia: There is a very arcane, never-used term called a "nibble" - one nibble is 4 bits, or 1/2 byte. (Refer to my comment above about mathematicians having nerdy senses of humor.)

[TedE]

Ah!  This spurred a memory from my linguistics days that I had to look up to confirm: some human societies developed base 8 systems organically and it is reflected in their languages.  Stuff like this leads to research on how linguistic constructs could affect the way we perceive and interact with the world.

[DonRocks]

Has Pi ever been computed (or attempted to be computed) in something other than Base 10? 

Perhaps it would be finite in some other base system; why should it be considered "transcendental" based on the number of fingers we have?

Maybe in base 2,475,974.68294, it would be a very simple number - has anyone proven otherwise?

Instead of computers churning away for days, trying to compute Pi in Base 10, why don't they examine all other bases, from Base .000000000001, going forward by one-trillionth at a time, maybe carrying it out to 100 digits in each, just to see if there's some Base system that will resolve it simply. 

Base 10 is bullshit, and entirely random in the big picture of mathematics.

[DonRocks]

Sexigesimal

[deangold]

Sorry in advance for this....

Did yo hear about the mathematician who thought Christmas was scary? He said Dec 25 is Oct 31.

Ducks and runs.