A Fixed-Point Life

There are two ways to fill an empty basket with apples. You search from the mountain of apples in-front of you, one by one, looking for the ones you prefer. Alternatively, you can put more than you need without checking into your basket, and remove the bad ones. The different is in the first you search and add to the basket, and in the second you start with the full set of apples and reduce. The first approach ends once you have the minimum amount of apples to satisfy you.

This is analogous to what is called fixed-point algorithms in computer science and program analysis, but as well this phenomena is used in mathematics and in every day life. A fixed-point system is one where a process is repeated over and over until there is no change in the outcome in the last repetition. There are two ways to achieve this – the least and greatest fixed-point.

In the least fixed point you start with nothing, and every time you perform the task, it produces a result. The next time you perform the task, you enter it with the previous result to perform better. Again it produces a result, again you gather the results, this time combining it with the results from the first try, and retry the task a third time. This goes on until there is no added result by completing the task. That is when you have reached the “fixed point.”

In the greatest fixed point you start with “more” of something than you need, and shed away what isn’t needed. Sometimes you cant remove everything in the first try, so you go on removing again, several times, and as you do, the initial amount is reduced until you’ve removed all the undesirable items. This filtration process is much quicker because removing is faster than searching and combining.

Depending on the problem you’re trying to solve in life, you’d employ one of the two techniques. Sometimes you naturally pick the correct one, other times you pick the opposite in ignorance.

When learning a song you’d use least fixed point, as you start with no ability to play, and must repeat the task of practicing just until you can play it perfectly, then the practice phase is over — then it becomes playing.

With love you’d use the greatest fixed point; start by loving everyone, and slowly avoid those who do not.

With the ego we use the greatest fixed point; start with a large ego, and should end without its trace.

With time we do the greatest fixed point; we start with all of it and destroy it until there’s none left.

With the evolution of the body both occur, first there is a least fixed point from sperm to peak adult, then greatest fixed point, from the height of our lives, to the grave, where the body is no longer ours.

When we speak about fulfilled desires, it is best to start with the greatest fixed point — though we often perform the opposite; the least fixed point.

Start with a sense of desires fulfilled, and from there reduce them to just the ones you must fight for. Do not start with none of your desires fulfilled and try and search for ways to satisfy them. That creates a nearly infinite search, and in that search, new and unnecessary desires are created in you. This sense of satisfaction is one of life’s longest struggles.

With money we start poor, with nothing, and slowly acquire until the time is up. Our wealth least fixed-point is satisfied at death — only we are not around to witness it. Only then do we stop the wretched tendency of accumulating new items. That is how long the process of acquisition can extend in humans. Get out of it quick.