How do hidden assumptions affect our understanding of mathematics?

[hello3719]

( For example: 4 is not identical to 1+1+1+1 because by my reasoning each Natural number is an interaction between is integral side (memory=connector=4) and its differential side (objects=1,1,1,1), as we can clearly see in: http://www.geocities.com/complementarytheory/ET.pdf )
QUOTE]

You are saying that 4 is not identical to 1+1+1+1 but do you still agree that 4 is equal to 1+1+1+1?

if not then define your "equality" concept.

 

[WWW]

I'm continually amazed by your ability to not understand basic maths, and?

Please show us how Peano Axioms can define my system as "second-order".

If you can show this then my system is a "second-order" and N members stays as they are.

 

[WWW]

Hi ram2048,

Thank you for not giving up with my system.

The internal changes are series of single steps of addition or subtraction operations, where each step changes the internal symmetrical degree of the given Natural number.

In the external world of N members each - or + operation is changing the quantity.

In the internal world of each given quantity, the quantity itself remains unchanged during a series of single steps of - or + , where each single step changing the internal symmetry of the given quantity.

But the given quantity can be changed by these single steps when:

a) A single subtraction step is operated on the most symmetrical state of the given quantity for example: (1,1,1,1) - (1) = (((1),1),1).

b) A single addition step is operated on the most non-symmetrical state of the given quantity for example: (((1),1),1) + (1) = (1,1,1,1)

The internal operation steps can move only by a one and only one step for each move, which is not the case in the standard external moves that cares only about quantitative changes.

 

[WWW]

Hi hello3719,

You are saying that 4 is not identical to 1+1+1+1 but do you still agree that 4 is equal to 1+1+1+1?

if not then define your "equality" concept.

Through my point of view, any given n has also several internal symmetrical states that can be defined if and only if any n has an internal structure.

I have found this internal structure by distinguishing between our memory and the objects that it remember, and by combining memory/objects we get the internal world of each given n.

In this internal world of symmetrical changes, our memory is represented by a single notation where the objects are represented by several '1' notations.

From this point of view '4' (the memory notation) is not '1','1','1','1' (the objects notation).

The symmetrical changes are the fading transition between the memory side and the objects side (and vise versa) within any given n > 1.

 

[ram2048]

i think the reason we're all having such a hard time with the system is it has very little in common with the current number system for which we can accurately use to describe common everyday events

that your system would be good for describing events of probability and possibility is indeed useful, it's just difficult to retrain our brains to "think" in that mode.

perhaps if you could outline some example cases it would be easier to get a lock on the system, seeing it in use.

 

[WWW]

think the reason we're all having such a hard time with the system is it has very little in common with the current number system for which we can accurately use to describe common everyday events.

Because my number system is based on cognition (memory) / object(s) interactions , all you have to do is to look on yourself and think if Quantitative-only number system can be a non-trivial model of a complex , creative and unpredictable system like you.

In my opinion quantitative-only number system is too trivial to deal with real complexity where concepts like redundancy_AND_uncertainty are its first-order properties.

1) The standard quantitative-only number system is not get off stage, it is only becomes a proper
sub-system of a single information form of my system, which means that we are not limited to 0_redundancy_AND_0_uncertainty information forms.

2) My number system can be a new base for a "Turing-like" machine where probability is a first-order property of it.

 

[WWW]

For clearer picture of my work, please look at:

http://us.share.geocities.com/complementarytheory/ONN.pdf

http://us.share.geocities.com/complementarytheory/ME.pdf

 

[ram2048]

i think in order for your system to gain popularity you must define a clear relation between your numbers and the ones we currently use.

it's very difficult to convey information otherwise.

like:

i have 5, but not a union of 5, in a configuration of one plus one then one and one and one

i can only imagine the nightmare of trying to tell someone you have 283 of something... :O

 

[WWW]

Hi ram2048,

Organic-numbers are too complicated for "bare hands" use.

They can be useful only by Biological, Optical or Quantum computer systems, by using them as "Multi-level Turing-like machines".

No one can draw a Mandelbrot-set without using Computers, and Julia-sets are only a proper sub-set of my Organic number system, so if we use this Organic information forms as "first-order" building-blocks, we get our gateway to a universe of a non-trivial complexity, where cardinality and ordinality are based on cognition/object interactions, which is a paradigm shift in the Natural number concept.

 

[ram2048]

thanks for taking the time to explain it to me

i think i understand now :D

 

[WWW]

Hi ram2048,

Thank you for the dialog, which is, in my opinion, the heart of any language (including Math).