Fibonacci's sequence and Emergence.

1 + 1 = 2. One apple + another is 2 apples. Easy.
This works when we count material reality. Objects. But that logic only goes so far and isn't very useful in the grand scheme of things.

What if we want to count the other parts of reality that we observe also, the other things that exist, such as the interaction between apples (the space, the distance, the motion, etc) and not just the objects themselves?

In that case we require a new formula: where 1 + 1 = 2 + 1
That is to say that in combining them, 1 + 1 = 2 (the sum) plus the addition of a new emergent conferred from the act of combination. A new phenomena or interaction. That the sum is in fact not equal to but greater than the addition of its components, as follows:

1 + 1 = 2 (1 object + 1 object = 2 objects)
2 +1 = 3 (2 objects plus their interaction with one another = 3 (a new existent relationship).
3 + 2 = 5 (the new existent relationship + 2 more of the previous objects = 5 (another existent relationship different in property to the previous) and so on...
5+3 = 8
8 + 5 = 13
13 + 8 = 21 etc.

The Fibonacci sequence. In this way 2 objects can be combined to give rise to 1 new object with new properties.
Just as hydrogen and oxygen have specific, individual properties as atoms, but when combined give rise to water (a new existent with properties that do not match the sum of its components).

And just like how individual grains of sand can be added together to give rise to a new singular object - a heap/pile of sand that has different properties to the components.
For example, a pile of sands properties are: it can be seen at a greater distance, can be stood on, can hold the form of a footprint, has a texture as it runs through your fingers, can be scooped etc. All things a single grain of sand cannot do.

It seems that when something (a grain) becomes too multiplicitous to count, when it becomes uncountable in any reasonable amount of time required to painstakingly deconstruct it grain by grain, it becomes a new existent (a heap). A pile of sand is no less a pile at 10,000 grains than it is at 100,000 or a million. So the phenomena of "pileness/heapness" is removed from the sum of its components (grains).

Water flows. Two water molecules do not flow. They are distinct existents.

Fibonacci sequence does something other counting methods do not, it does not exclude emergent phenomenon from its summation like regular object counting does. Which is why both systems start out the same: 1 +1 =2, 2+ 1= 3, but then depart from one another:

Material accountancy: 3 +1 = 4, 4 +1 =5, 6, 7, 8, 9, 10 etc

Material and phenomenological accountancy - fibonacci counting: 3 +2 =5, 5 +3 = 8, 13, 21, 34, 55 etc

It stands to reason that counting systems that consider material and behaviors/interaction both as assumed existents (previous sums) will increase in magnitude/size much faster than ones that only consider material things (as they exclude half of the reality of things - actions/behaviours).

Fibonacci sequence is seen throughout nature and can be found in virtually any system. And is tied to the golden ratio: which concerns everything from sunflower seed heads, to seashells, to the vitruvian proportions of man, to the shape of galaxies.

It is emergence as a number sequence. Not strict static objectivity as a number sequence. It is an irrational sequence (never repeating itself exactly - due to the influence of emergent phenomena, but constructed by rational numbers - finite/real objects)