Back in time

All dimensions in spacetime are without a direction except time. We can go back and forth in space, but not in time. According to many physicists this is a strange phenomenon, because in their formulas time can go forwards or backwards. Thus they can calculate backwards about the state of the universe and eventually end up in the BigBang. For a biologist this seems much more complicated. Let us take a simple model of population growth: xn+1 = f·xn·(1-xn), where 0 < x < 1 and 0 < f < 4. For f < 3 this model will reach a steady state, f > 3 can lead to oscillations and f > 3.8 can cause seemingly chaotic numbers. xn plot The red line in the figure shows 10 consecutive generations, starting with x0 = 0.5 and f = 3.97. Now we try to go back in time. After these 10 steps we have: x10 = 0.4267..... and x9 = 0.1225..... However, x9 = 0.8774..... (1 - 0.1225.....) would yield the same x10. Two steps backward there are already 22 = 4 possibilities and 10 steps backward there are thus 210 = 1024 starting positions that would all after 10 steps yield 0.2467..... See my attempt to sketch this in the figure (to be honest, in reality there where about 800 starting points, the others disappeared below 0 or above 1). Even when I know the formula, never can I calculate the past from the present. Formulas in biology are really never linear and by the way, the formulas to calculate the influence of planets on the course of other planets are not linear too. If we do not even know what exactly the positions of the planets of our planetary system 65 million years ago, how do we reach the Big Bang?