Numbering Systems

Hi everyone, just found this site a few days ago and I'm hooked.

So I have had this idea/question floating in my head for awhile now...just never had anywhere to post it until now. The "question" part of it is, Why do we use the same numbering system for everything we do? The "idea" part of it is that I think we will be limited in our understanding and advancement unless we break out of using the base 10 numbering system for everything.

We use the base 10 numbering system from everything from geometry to physics...but why? In computer languages we use binary because of hardware limitations...so we were kind of forced to stray from base 10.

I'm not saying we should just switch to some other already known numbering system like hexadecimal...but I think we need to develop a new numbering system based off of the common constants we use. For geometry...we need a "pi" based numbering system. For electricity...we need an "elementary charge" based numbering system. For quantum physics...we need a plank's constant numbering system. You get the idea.

I'm not saying I have the knowledge (or desire) to develop any of these numbering systems...but I think it makes a lot of sense. I am also not suggesting that creating these numbering systems is as easy as trying to substitute these "constants" into our current numbering systems...meaning I know you just can't make a Base pi system like you could easily create a Base 3, Base 4, Base 5, etc numbering systems. I currently don't know how you would make a numbering system out of irrational numbers...but I refuse to think that it is impossible. And maybe we don't have to create a numbering system where "pi" or any other constant is the base...but maybe a numbering system where "pi" is just a rational number and not the actual base of the system.

To wrap it up...I just don't think using the same numbering system for every type of mathematics/physics is logical. Every time I see a "constant" that needs to be used for formulas to work out correctly, I think in my head that there has got to be a better way. We have to use these irrational constants for a reason...I think that reason is because of the numbering system we are using. Like I said...I don't have the knowledge, time, or desire to try to solve this puzzle...but from browsing through this site I know there are some very smart people on here and maybe this will spark an idea in someone else's head.

Be gentle...I'm a newbie

reply to post by OutKast Searcher


Out....I had this question also.

The train of thought for me involved the possiblity that IF we have been visited by bipedal aliens....the story is that they have eight fingers...well, six fingers, and two opposable thumbs.

Since WE have ten fingers, and think in base ten....would these other creatures count in base eight?

Computers use bits (or bytes) of eight....and these are the machines WE invented!!! Of course, it is still binary, regardless.

Mathematics is just assigning a value to something, in general. 2+2, for example is the exact same as saying 4. Any value in our base-10 system is just like saying values in other system (such as 19 in hexadecimal being the exact same as 25 in base-10). The values in the universe are constant and don't change with the different number systems, much like "water" is still the idea of "water" or H20 even if the French call it "l'eau."
Water is still water wether it is l'eau or Wasser.

The way I see it is that since base-10 can be translated to other number systems, and the values are the same. They can be unruly-looking in base-10 and very tidy in another system.

The main idea is that universal values (wether they be numbers, stars, faces, or hot dogs) are constant whatever they may be, but look different in the definitions humans give to them. However many languages there are in the world mean many different words humans have used to describe one thing.

(edit to fix absurd grammatical error)

[edit on 2-3-2009 by Lifthrasir]

Very weird. I just posted the solution to pi less than 5 minutes ago.

Here it is from another post:

"The only thing that makes pi seem odd to us is the decimal number system.

In other number systems the ratio 22/7 can be expressed as an exact number.

In a base 7 number system the decimal ratio 22/7 equates to exactly 3.1.

That number 3.1 is of course not a decimal number. I guess you would call it a septimal number as it is in the base 7 number system.

Magic of pi dispelled.

Vas"

Originally posted by Lifthrasir
The way I see it is that since base-10 can be translated to other number systems, and the values are the same. They can be unruly-looking in base-10 and very tidy in another system.

Exactly. I'm not saying that using a different numbering system based on pi or a system that would make pi rational would in itself solve anything or change the "value" of pi. But it would make the equations and the understanding of the subject easier...and the easier something is to understand the easier it is to make further advancements in it. But then again...if we did create a new numbering system we may just be transfering the complication from the equations themselves to learning a new numbering system.

Originally posted by OutKast Searcher
But then again...if we did create a new numbering system we may just be transfering the complication from the equations themselves to learning a new numbering system.

It wouldn't be at all difficult to use another number system. I'm old enough that when learning to program I learned binary, octal, and hexidecimal. These days I don't think in them much, but at one time it was no big deal at all. I actually do find myself seeing the hex numbers in my head once in a while.

Vas

If you're asking why do we use base10 rather than other systems like Hex, or Binary, it's likely because we naturally settled on 10 due to the number of digits we have to represent it with.

It seems like a natural starting point.

A couple of previous cultures apparently did use number systems other than base10, but I can't remember their names.

Binary is natural for machines due to the nature of the on or off conditions of registers and data lines.

Hex is a good midpoint between machines and humans, as you can turn a byte (8 binary digits) into two digits (0-9 and A-F), which is easier for humans to recognize on the fly than a string of ones and zeros.
Each digit represents 0 to 15, which isn't too large for us to comprehend on the fly as we are typically used to working with numbers 0-9, and is still large enough that we can represent strings of binary that are still useful in size.


But I'm quite sure the reason we use base10 is because it's easily represented on our fingers to others.



[edit on 3-3-2009 by johnsky]

Originally posted by Vasilis Azoth
Very weird. I just posted the solution to pi less than 5 minutes ago.

Here it is from another post:

"The only thing that makes pi seem odd to us is the decimal number system.

In other number systems the ratio 22/7 can be expressed as an exact number.

In a base 7 number system the decimal ratio 22/7 equates to exactly 3.1.

That number 3.1 is of course not a decimal number. I guess you would call it a septimal number as it is in the base 7 number system.

Magic of pi dispelled.

Vas"

As I mentioned in the other thread where you explained that, pi is not equal to 22/7, so your viewpoint is flawed.

22 / 7 = 3.142857 , with the underlined part repeating.
pi = 3.14159....

Originally posted by OutKast Searcher
For geometry...we need a "pi" based numbering system.

Radians are pretty much a pi-based numbering system. As for the rest, look up Planck units, and see if that's what you're trying to come up with. You seem like a smart guy, but it's possible you're trying to reinvent the wheel, so to speak.

Originally posted by DragonsDemesne
You seem like a smart guy, but it's possible you're trying to reinvent the wheel, so to speak.

Something it seems we all manage to get stuck doing now and then.


I can't count the number of times my experimenting led me to create something that already exists...

... it's frustrating to say the least.

reply to post by OutKast Searcher


In the UK we used to use the Base-12 or Duodecimal system. Many, especially tradesmen still use it, and consider it superior. I am not sure but as I recall we had to conform to the European standard, Base-10.

en.wikipedia.org...

The ET Corn Gods Language uses a "base 66" system.

[snip]

It is a hidden language planted in the English Language. Hidden messages about today's world.



Removed link to personal blog

[edit on 16/1/10 by masqua]

Originally posted by OutKast Searcher
For electricity...we need an "elementary charge" based numbering system.

As an electric engineer, I do not support this motion. The reason we don't use hex or binary in calculations is the same reason we don't use any other number system: It makes things more complicated.

In computers we use binary for the reason you mentioned, but if hardware wasn't a limitation, trust me, we would have started using decimal ages ago, heck, that would even get rid of hex numbers since we wouldn't need to map to binary anymore.

I don't understand why we should use a different number system for each different thing we need to do, since no matter what numbering system we use, the number means the same thing. For instance, the universal name for SEVEN is SEVEN. If you want to write it in decimal you write down 7, if you want it in binary you jot down 0111 (true uncomplemented form, since it is positive) and if you like it in hexadecimal, guess what, you still say 7 :p

So, what I'm saying is that using different numbering systems is pointless since they all represent the same numbers just in a different way.

Now, the reason that we use binary for computers is not because it is "easy" for the computer. It is actually because withing the CMOS board (a kind of integrated circuitry board), we can define voltage levels and assign values ON and OFF to them. For example, the CMOS reads voltages from the range of 1 volt to 8. We program it such that, when it reads a voltage between 1v and 3.9v, it registers ''0'' to indicate the OFF state, and when it reads voltages between 6 and 8, it registers a ''1'' to indicate the ON state. The values between 4 and 5.9 are to indicate invalid input (there is a purpose to this but the explanation is not needed here).

Therefore, the computer has 2 states to work on, 0 and 1. There would be no other way for the computer to "understand" numbers if we didn't program it in such a way as mentioned. But this does not mean that we describe computer programs using ones and zeros. When we program we actually input decimal values. Unless of course you were the VERY first programmer who had to write the very first bootstrapper program in machine language (0,1). I'd hate to be in that guy's position.

By the way, if you think about it, ALL numbering systems are base 10

[edit on 4/1/2010 by Alasian]