A non-linear clock

Inception

How would you plan your day if you had every say in it? This is a question that was asked to me recently. This project certainly is not the answer to it. It is however an answer to how possibly a personal clock would work when you don't have to care about anyone else or be very precise about matters concerning time durations, meaning without having to be on time at meetings or cooking an egg for exactly 8 minutes.

With my personal clock, I want a clear idea of where I am in the day without and it should have some meaning. Other than that I had no real requirements. However, soon I realized I could make a clock that would be everything that a regular clock or our perception of time is not; or conversely, everything that time is, but a regular clock cannot convey.

Features

By thinking about what time is and isn't, I ended up with the following features:

Non-linearity

We measure time as going forward in a steady even pace. Every second lasts just as long as the next. Sure, in relativity theory we find that things become a bit more complex if things start to travel at great speeds, but in daily life this is not very much the case. However, in our perception time can fly or creep forward and our regular clocks do not seem to convey this perception. The proposed clock will be non-linear, it will move faster at some times in the day and slower at other times.

Duodecimal system

For most things in most people's lives we use a base-10 system. We have 10 fingers and toes so it makes sense to count things in amount of tens. However, a clock divides a day into 2 times 12 hours, and each hour into 12 times 5 minutes, and every minute into 60 seconds. There are people some of which are mathematicians who advocate using a base-12 or duocecimal system for everything. By adding a symbol for 10 and 11 to our arsenal, we could write time more clearly in the duodecimal system.

Cyclic

On the one hand, we associate time as a long line going forward from Big Bang until the end of time. On the other hand, we experience time as being cyclic due to how life is supported in our planetary system giving rise to days, months and years. Maybe the cyclic nature can be made even more clear in the clock.

Non-monotonic

Even though a clock shows the cyclic nature of how we perceive a day, the idea that times flows only forward might make sense considering the laws of physics, but that does not mean that our clock cannot move backwards.

Personal

Because we use time and the clock for meetings and arrangements it is more social than personal. Can we make a personal clock, or at least use the persons location in a more clever way?