Zero sum

The world we live in is full of zero-sum events. Maybe law of conservation of energy can be one of the foundation stones in that direction. Even in fields like economics or market share or anything, taking a larger or a more holistic view it often is a zero sum.

Consider a economic system in which various parameters (say prices, or purchasing power parity of different people or sets of people etc.) are x1, x2 etc.

So we have,

x1 + x2 + x3 + ... + xn= 0, for all transactions in a fairly large system.

Now if we say that economy is growing at some rate say r.

[r can be dependent upon rate of inflation or GDP growth rate or some parameter which can be calculated as a weighted average of various factors]

So, for the bigger economy, we have

r * [x1 + x2 + x3 + ... + xn ]= 0.

Thus, economy still remains a zero sum game.

Various changes be it social, political or technological, it effects r, but the variables within the bracket may not be effected.

Qualitatively, economy is growing, but on one hand rich are getting richer, and poor are getting poorer. Both qualitative and quantitative appear to be in sync somewhere. So it doesn't matter in the system as whole, and it remains a zero sum game. Same may hold true for other fields also.