In the first part what I only wrote about the section after Creation was that the weighted sum of the somethings is constant in the whole period, and I also justified the weighting.

In this part I will deal with that part.

The mathematical formula for permanence is the following:

n

s = Σ a_{i}s_{i} = const.

i = 1

where “i” is one type of the somethings, “a_{i}“ is the weighting factor, “s_{i}“ is the amount of the ith something measured in some unit (mass, number, etc.), and “n” is the sum of the types of the somethings.

A constant, unchanged weighting factor belongs to each given something. (From the examples of the previous article, e.g. one helium nucleus always forms from two deuterium nuclei.)

The fact that for example the amount of directed mass may change, seemingly contradicts this. This will be dealt with later, when the simple and complex somethings are discussed.

In time

– both the amount of the individual types of something,

– and their total number

change but new types were created and existing types disappeared.

In the formula the value of “n” grows as new types are created but when some disappear, “n” does not decrease, but for the disappearing type the following is true:

s_{i} = 0

At the same time, in order for the value of “s” not to change, the value of one or more si’s increase or new si’s are created. (For example when dinosaurs became extinct – if it was really caused by a meteor – the amount of dead animals suddenly increased. And the disappearance of dinosaurs resulted in the emergence of a great number of new species. It made it possible for other animal groups to fill the “vacancies” left by the big herbivores and carnivores.)

If “m” is the number of si’s existing at a given point in time, we get the image in the figure. Here before point 1 the value of “n” and “m” moved together from Creation but because of the disappearance that happened in point 1, “m” suddenly became less than “n”, then the two lines were parallel up to point 2, then, because of the emergence of new ones both lines jumped up. The value of “n”, however, jumped less because there were ones that reappeared.

Quantitative changes are the result of evolutionary (mathematically speaking continuous) processes, while qualitative changes are the result of revolutionary processes (finite discontinuities). The latter can be smaller or bigger depending on

– how many new ones appear or how many old ones disappear,

– how big the difference between the new and the old is. (As opposed to mathematical discontinuities, here the jump is not infinite, but very fast compared to evolutionary changes). Revolutionary processes are discussed in the article “Development” on http://www.europeanscience.net. They were also covered in the “Indices” series, in the part about the modification of the Hegel theorem, where I discussed the relationship between quantitative and qualitative changes.)

I would like to stress that not even the greatest qualitative change so far was another Creation because with the creation (or building) of certain groups, however large and wide, and the possible disappearance (i.e. destruction) of others, the s = const. condition remained true.

So far I have treated the somethings as a uniform whole. I have not discussed the difference between the somethings.

Now I divide them into two groups based on one aspect.

The two groups are the

– simple, and

– the complex

somethings.

A simple something is something that cannot be divided into other somethings.

Complex is everything else. Combination is also carried out by weighted adding of simpler somethings perhaps on numerous levels. (For example atoms combine into molecules, molecules into living beings and people into society. I would like to stress that this deduction refers strictly to compositional levels only and not some process of creation! Another example is the building of houses from bricks, streets from houses and a town from streets. This latter example is a three-level composition.) This explains why in the individual cases the ratio of leaders and the led may be very different because the composition of the two groups can also be very different qualitatively in the different cases.

Simonyi Endre