Logarithmic Time Hypothesis

People once believed that the Earth is flat and that the Sun orbited the Earth, to finally come to the conclusion that the Earth orbits the Sun. I like to believe that Logarithmic Time Hypothesis is equivalent to believing that the Earth is the centre of the Universe – obviously wrong, but still better than believing it is flat.

Introduction to Logarithmic Time Hypothesis

We are used to measuring time in days, months and years. It is very natural and convenient. Are days and years good time periods to describe people's behaviour, especially when strong emotions are involved?

Figure 1a shows how we measure time in an equal, standard manner. Every time period shown is equal with any other. What if I judge first time period (1950-1980) more important than others? If so, I would have to draw it larger to emphasize the importance, just like in the figure 1b (not drawn in any particular scale). Following this way of thinking, every considered time period would be different.

Figure 1. Perception of time.

In my opinion, equal time periods composed of natural time intervals (days, lunar months and years) are not equal when taking their importance into consideration, as well as their influence on people and the way people will remember them. My intention is to transform the time axis in such a way that time intervals will appropriately take importance and influence on people into consideration. This transformation I will call Logarithmic Time Hypothesis (closely related to Logarithmic Timeline).

Let's see how it would work in real life situations.

Arguments for Logarithmic Time Hypothesis

There is a natural phenomenon called 'Perception of Time with Ageing'. It is well described in expert circles, and there are even a few books on this subject. Following some of its concepts will lead us to Logarithmic Time.

Instead of basically rewriting mostly the same thing I will focus here on another aspect – human memory of certain events over time.

On 1st September 1939 Nazi Germany invaded Poland beginning World War II in Europe. In the following years millions of people died and the lives of those who managed to stay alive were changed forever.

Let's take a closer look how people remembered the Second World War.

Figure 2. Memories from World War II.

In 1945 all people older than three years had perfect memories of many nightmarish events that happened during the preceding six years.

In 1980, 35 years since Nazi Germany signed unconditional surrender, the way people remembered WWII has changed. Some of its participants have died. But still the memories of it were vivid and widely accessible. In my country, in the 1980's it was quite common that WWII veterans attended anniversaries in schools – kids could ask questions and hear stories. Moreover almost every grandmother and grandfather could share stories of their lives during WWII.

Twenty-five years from now, there will be no WWII veterans alive, and our knowledge about WWII will be likely constrained to films, written history books and what we will manage to learn in schools.

Area of the squares in upper part of figure 2 reflects the amount and availability of human memory on World War II. For example, if I would like to study the influence of WWII over time, my idea would be to divide boxes from the upper part to obtain even sized squares in the lower part of the figure.

By this operation, the first time period in the upper part of the picture that occupies just 1/5 of the overall period, would be transformed into a full half of the analysed time period.

Let's do some recapitulation. First of all, I am making the assumption that the influence of some events are positively correlated with people's memory of such events, and secondly, I am transforming the time axis to obtain an even, or relative, influence of a given event over time.

Now I will add some simple mathematics to be able to apply it to formulate more strict rules than by dividing boxes.

Time Transformation

Basically we need to find a way to assign equal numbers to non-equal time periods. In most simple case there will be two time periods.

Figure 3. Time Transformation.

I have chosen the first time span of 90 years, from 10 to 100 years (figure 3a), and second of 900 years, from 100 to 1000 years. In figure 3b I just redrew both segments for clarity. In figure 3c I have changed the numbers to products of 10, and then in 3d I have rewritten them once again as 10 to appropriate exponent. Finally, exponents are the numbers we need in this case to form time periods of equal lengths (figure 3e). In this example, from time periods of length of 90 and 900 years we obtain two segments of length equal to 1.

I must mention two things here. The transformation in the above examples is logarithmic transformation, but not everybody likes logarithms, so I decided to omit them. Secondly, I am not saying that this is an ultimate and final transformation – but it is merely a convenient manner to demonstrate dependence.

Conclusions

There is an obvious task of proving Logarithmic Time Hypothesis right or wrong. I will be glad to hear from people interested in this subject. There is of course lot more to the subject than mentioned above, but I hope that this is more than enough to clearly specify my field of interest.