Numerics

**Chaigidel** · August 02, 2007, 07:52 AM

this is meant to be a factual discourse about the nature of numbers, and the universality of those numbers--

my basic contention is that the numbers wont change no matter what mind its applied too-- 1 is always 1, 2 is always 2--I think that communication between completely different species would even be possible with numbers.

because if something reveals the world in such a factual way? could it be less than universal?

add thoughts, comments, and any articles-- cmon math people bust out some moves on us.

this was brought on by a conversation between myself and brother eclipse-- about whether or not aliens would be able to communicate with us with numerics.

**Cataclysm** · August 02, 2007, 12:38 PM

Like how the aliens in Contact got our attention by spamming the prime numbers between 1 and 100 on the radio>

**Chaigidel** · August 02, 2007, 01:56 PM

well obviously that would be a key sign of technological life-- because technology is IMPOSSIBLE without a concept of numbers, much like our own--- they may call one- zork, but zork will remain factually the number one, as does one :O

**Shatterer** · August 02, 2007, 06:11 PM

Originally Posted by Chaigidel

because technology is IMPOSSIBLE without a concept of numbers, much like our own

What makes you so sure about that?

**Chaigidel** · August 02, 2007, 06:41 PM

dunno the fact that all our facts are based on numbers? that nothing is observable in an objective sense without the use of calculations?

numbers truly reach past perception and translate reality in the most real way of any representations.--- without this tool I firmly believe that technology and all forms of advancement would be totally impossible.

**Shatterer** · August 02, 2007, 07:32 PM

Originally Posted by Chaigidel

dunno the fact that all our facts are based on numbers?

You will have to specify what you mean here by "facts" because I know some facts that are not based on numbers.

that nothing is observable in an objective sense without the use of calculations?

Maybe I misunderstand you but that's not entirely true. We see animals making objective observations and predictions without the use of numerical calculations all the time.

numbers truly reach past perception and translate reality in the most real way of any representations.

Yes, but just like with various oral languages, there are many ways to express reality. Numerics - is just our language of expression invented by humans and in no way universal.

without this tool I firmly believe that technology and all forms of advancement would be totally impossible.

Ape men didn't use numbers when they invented a sharp stick.

**Chaigidel** · August 02, 2007, 07:41 PM

yes but no chemical process could be reliably done, no complex machinery made , you could form the crudest of objects, but math and numbers are the definition of intelligence and sentience.

still even though the ape man didnt know he made ONE sharp stick-- it was still numerically one--- if an alien approached this ape man- he could likely even reason with a simpler intelligence than our own, that one means one.

1 2 3 4 5 6 7 8 9 0 look upon the foundation of all your thought--- the foundation of all reality expressed in symbols.

F o I K e J M e n p-- these symbols would be understood exactly the same if applied in the same manner as numbers.

so to speak F + F= o n-K=e the same as 1+1= 2 and 9-4=5, these most basic of calculations would be a constant in any thinking and Technological species-- there is no technology without Numbers.

prime numbers, would be the same in all mathematics else none of our calculations about anything would work !--- you cannot master science without numbers, and most here agree that science is definitely the most powerful thing humanity has ever come up with.

and we did it with the foundation of numbers-- a foundation that doesnt shake

**Simetrical** · August 02, 2007, 09:40 PM

The nature of numbers is determined axiomatically, so they are (as far as I'm concerned, leaving aside wishy-washy epistemology and whatnot) independent of the mind used to calculate with them. You can have humans, computers, or trained goldfish calculate with numbers.

Are they necessary for advanced technology? Overall I can't say I can think of any plausible way you could get to modern physics, say, without numbers, or even any plausible way you could state it without numbers. You can always say things like "the stick's length is a meter combined with a halved halved meter" (halving being a physical, not numerical, operation), but it would kind of be a pain to actually figure anything out with that. Possibly there are other ways that I haven't though of, of course.

**Juvenal** · August 04, 2007, 03:52 AM

I don't think that the "Natural" numbers at all universal. They are actually rather abstract - although they do seem to fit nicely with the way we reason. I think we could easily do without them, getting by on a mathematical system based on rational (and irrational) numbers and inequalities.

The closer I look at integers, the less real they seem. Looking out into my garden I see "1 tree", and then a little way off another "1 tree". But this is actually a piece of mathematical modelling on my part - I have defined an mass of vegetation as "1 tree",and another different mass as another "1 tree". If I looked a bit closer I would see that it includes things that aren't tree, and might even be "2" trees that have grown up together to form a single canopy.

Furthermore, if I chopped away half a tree, I still have "1 tree" remaining! In fact I could continue pruning until I chose to recategorise the result as "1 stump".

The point here is that mathematics is a way that we model the universe. Because it is simpler than the actual universe, we can use it make useful predictions.

I think that the question of the universality of mathematics might rest upon whether mathematics is created or discovered. If the universe really is mathematically based, then we are discovering (at least some) mathematics, and maybe it really is universal.

The problem is that mathematics is an abstraction. Even though the universe appears to have a mathematical basis, I don't see how we could ever prove it, because the proof would only apply to the mathematical model of the universe - not the universe itself.

Oh dear - I seem to be wandering into philosophy.

PS. If there are any fallacies in the above - please let me know.

**Shatterer** · August 04, 2007, 03:58 PM

Originally Posted by Simetrical

The nature of numbers is determined axiomatically, so they are (as far as I'm concerned, leaving aside wishy-washy epistemology and whatnot) independent of the mind used to calculate with them. You can have humans, computers, or trained goldfish calculate with numbers.

I disagree. The nature of numbers is not independent of the mind used to calculate them, but rather is dependant on the logic of the mind used to calculate them. You can not teach goldfish to calculate like humans unless they develop the similar logic required for the numerical calculations. As such, as long as different logic exists, I believe alternatives to mathematics also exists.

Originally Posted by Juvenal

The closer I look at integers, the less real they seem. Looking out into my garden I see "1 tree", and then a little way off another "1 tree". But this is actually a piece of mathematical modelling on my part - I have defined an mass of vegetation as "1 tree",and another different mass as another "1 tree". If I looked a bit closer I would see that it includes things that aren't tree, and might even be "2" trees that have grown up together to form a single canopy.

Furthermore, if I chopped away half a tree, I still have "1 tree" remaining! In fact I could continue pruning until I chose to recategorise the result as "1 stump".

Numbers represent concepts such as a “whole tree” or a “whole meter” which is why when applied to the physical world, it is always necessary to specify what you are referring to when you include a number in a calculation, otherwise the math becomes meaningless.

Originally Posted by Chaigidel

the overall accuracy and results of mathematical processes as involved in our calculations and sciences, In my estimation we are discovering numbers( otherwise how could they work so well all the time?)

Like Juvenal said, we could be discovering mathematics or we could be building it to “fit” the universe. Either way, mathematics can have the potential to be as accurate as it is.

**Chaigidel** · August 04, 2007, 07:54 AM

good posts all, and no it didnt seem to philosophical we are talking about the numerics and how they work in the universe the key question does then become.

are we discovering numbers (at least a portion) or are we simply laying out a model?

the overall accuracy and results of mathematical processes as involved in our calculations and sciences, In my estimation we are discovering numbers( otherwise how could they work so well all the time?)

I would also contend that mathematics and numbers are the perfect abstraction, the perfect way to translate our reality.

**Chaigidel** · August 04, 2007, 07:31 PM

well why does the energy= mass (constant of light)2

why would that work unless the numbers themselves were inherent in the universe?

or would you say that E=mc2 is inaccurate?

**Shatterer** · August 04, 2007, 09:11 PM

Originally Posted by Chaigidel

well why does the energy= mass (constant of light)2

why would that work unless the numbers themselves were inherent in the universe?

It works because the math involved is a true representation of a concept that occurs in the universe. That's not to say that math is the only way to express energy. Obviously, I don't know any other method, but again, that's not to say that it doesn't exist.

or would you say that E=mc2 is inaccurate?

Well, I'm still in my early physics days but as far as I know, E = mc^2 is accurate.

**Chaigidel** · August 04, 2007, 09:23 PM

I think numerics and math are the only way to discover the mechanics of the universe--and thus the same to all sentient species, because why would physics work differently for a different sentient species? it would not , not even a little.

the same could be said of mathematics and numerics--- they may seem like invention but they are perfect translation-- discovery of truth through an abstract idea.

I dont think even as we discover higher and higher sciences that numbers will ever become obsolete in our description or manifestations of the universe.

there is no science without numbers.-- doesnt matter where in the universe you are.