A very bizarre question came to my mind a long time ago and I'm pretty much unable to get the answer to it.

This is my question:
Have you ever thought that our basic number system might be inappropriate? Like think of some of the values of all the mathematical constants in the world like Gravitational constant, Boltzman constant, mass of elementary particles and many many more constants of such kind. All these have values that are either extremely small or extremely big.
What if there was an alternate set of numbers, different from our decimal number system, that has the values of the fundamental natural constants in "whole numbers". What if we could represent all the quantifiable things in multiples of some parameter or a set of parameters of some elementary particle or force.
Is there a possibility of the existence of such a parallel "number system", which might behave very differently than our usual 0-9 numbers.

 

There would be a problem correlating the new numbers to our existing number set.

If they exactly correlated, you would be wasting your time in conversions.

Variables do this. They tell you that X is .13546324235 of 1 that you are using in the algorithm or computation.

If you used "Kibtufluz" as a number, you would have to relate it to the other numbers in the equation.

"Kibtufluz" is a number in the new number system you are talking about.

 

Well, there are some values that are measured by alternative quantities. For example the energy gap between the layers of electrons in an atom is measured in ElectronVolts, or eV. This is equal to the kinetic energy of an electron accelerated by an electric potential difference of one volt.
Physics and Chemistry have more need of alternative quantities than math, I quess.

 

I doubt there is a direct correlation, but it is an interesting idea. Math is a human concept, and that would make constants also a human concept.

To top it off, not all constants are really constants according to some article I've read, they change so slowly with the universe we'll never know.

 

Something like the energy gap of electrons is exactly what I'm trying to say...

This thought came to me as a result of the botheration I had in solving numericals involving numbers to large decimal places.
We see in articles that nature follows symmetry in its own ways, take for example the Fibonacci series, the Golden Ratio, prime numbers, etc.
All these seem to hint at something of the likes, and I feel its made even more concrete with the fact that scientists have found an uncanny relation between the behaviour of prime numbers and quantum mechanics.

Although its an old article, but take a look at this : http://seedmagazine.com/content/article/prime_numbers_get_hitched/

 

Ever read Contact by Carl Segan? It had an interesting twist in that concept.

Spoiler Alert!





Basically the constants (such as pi) have messages in them. When a technical civilization becomes so advanced they can declare God doesn't exist there is that little boot in the rear waiting.

 

Down with the SI!

"Human" units have been around a long, and for some reason that I don't fully understand, they gave way to SI units.

As for special units, consider the unit of atomic mass, which is 1/12 (exactly) the mass of \(^{12}\)C. That unit, BTW, has changed during my life. Hydrogen and oxygen were both considered. I believe carbon was decided upon for a very simple reason.

John

 

Some physicists like to do calculations in a unit system where the speed of light and Planck's constant are both unity.

Unless you do funky numerical things like develop a number system that deals with logarithmic relationships, you're going to have to deal with large and small numbers. And such a thing would cause problems elsewhere.

In our universe, at least, you're going to have large and small numbers pop up no matter what you do. For example, the ratio of the average galactic mass to the mass of a proton is going to be a big number no matter what unit system you use.

 

Indeed! In fact, I wrote an essay on this very topic in the Opus of Amateur Radio Knowledge and Lore.

We call elegant numbers like PI "irrational" because we cannot reconcile them with our rather arbitrary decimal number system. What identity could be more RATIONAL than the number PI? Same with the Natural Log function. These are built into the universe! The number 10 isn't!

What if we had a number system based on base-PI? I think a lot of things would actually be simpler. Electrical engineers use angular frequency specificallly because of this simple elegance.

Thanks for bringing this topic up.


Eric

 

The number 10 isn't!

ah-hem:

 

If our system was based on Pi, how many wives could we each have?

John

 

Too many...

 

Well, if it was well rounded 6¼ wifes. One of them is pretty chunky, but the others are perfect.

 

If our system was based on Pi, how many wives could we each have?

John

Not sure, but somehow the pi-system seems appropriate given the circles my wife has me running around in.

 

What you are seeking is embodied in the current greatest unsolved question in mathematics viz the proof of the Riemann Hypothesis.

Many hints at underlying links between nature, physics and maths have appeared in attempts at this problem.

Look up the Riemann Zeta Function.

 

We call elegant numbers like PI "irrational" because we cannot reconcile them with our rather arbitrary decimal number system. What identity could be more RATIONAL than the number PI? Same with the Natural Log function. These are built into the universe! The number 10 isn't!
Eric

Well, irrational is just a bad translation or interpretation in my opinion. The greek word for irrational numbers (wich is around since 500BC) like pi is "άρρητος", wich is read "árritos" and means "one that cannot be spoken/expressed". We see that this is a better name for irrational numbers as it describes better their property of having infinite digits, whether they are expressed as decimals or fractions.
See also http://en.wiktionary.org/wiki/irrational
I tried to translate the webpage from the greek wiki but it didn't make much sense through google translate.

 

There are two issues here, one of numbers the other of units. It would clarify the discussion to keep the issues seperate.