As you might know, fractal structures appear in a variety of natural situations and have found many technical applications (see Wikipedia for more information and examples). In this short article I want to ask the question, whether it makes sense to structure various activities according to a 'fractal timetable'?

Cleaning rota

When you have to clean a flat or a house you probably you have seen a list like this before. There are some tasks that one needs to do every day, others come along only once a week or once a month. Aside from those main cleaning tasks, there will be many small things you do several times during a day, like throwing something into the trash bin or washing your hands.

If you analyse the structure of this behaviour, you will find that it looks similar to a one dimensional fractal (compare with the various layers in the construction of the Cantor set, for example).

School Timetables

Most schools that I am familiar with use periodic arrangements for the teaching. You have a weekly timetable and at the same time every week you have the same subject for a whole year. This makes sense from the point of view of teacher and room allocation, but is this the best structure for optimal learning?

My own experience suggests that the quality of my memory strongly depends on my understanding. If I take the time to understand everything, I will remember those things for years and can even reconstruct lost knowledge by using intuition and logical deduction. If I learned something poorly, on the other hand, I sometimes forget it completely in a matter of hours.

Understanding is usually gained by a deep involvement with the topic for a longer period of time. I also find it much easier to learn something if I can focus on it for a certain period of time and examine the object/concept in detail without being disturbed by other matters.

What if the best way of teaching school mathematics (for example) would be to have a 3 week long intense workshop once a year with some other 10 one day sessions allocated once a month and small homework problems evenly distributed throughout the year? The same could be done with the other subjects to fill the full school year.

Other Areas

Our motivation, health and available time fluctuate widely, but most jobs require a periodic commitment. This might be OK for mechanical jobs, but for professions with a substantial amount of creativity and cognitive demand one certainly can do better by playing around with the time/work distribution. (Here is an interesting TED talk about a 'year off'.)

Similar problems/opportunities arise in fitness, personal development and relationships. 

Questions

I don't know, whether there are any existing studies on this topic. A superficial Google search didn't reveal anything interesting. I also would like to know, whether you had similar or contradictory experiences? Maybe I am an exception when it comes to this type of learning.

Do you think that adding the mathematical model of a 'fractal' makes this approach more intuitive/useful or whether 'flexible time management' captures enough of the structure of the problem?

Thanks!

Introduction

When people on LW want to explain a bias, they often turn to Evolutionary psychology. For example, Lukeprog writes

Human reasoning is subject to a long list of biases. Why did we evolve such faulty thinking processes? Aren't false beliefs bad for survival and reproduction?

I think that ''evolved faulty thinking processes'' is the wrong way to look at it and I will argue that some biases are the consequence of structural properties of the brain, which 'cannot' be affected by evolution.

Brain structure and the halo effect

I want to introduce a simple model, which relates the halo effect to a structural property of the brain. My hope is that this approach will be useful to understand the halo effect more systematically and shows that thinking in evolutionary terms is not always the best way to think about certain biases.

One crucial property of the brain is that it has to map a (essentially infinite) high-dimensional reality onto a finite low-dimensional internal representation. (If you know some Linear Algebra, you can think of this as a projection from a high-dimensional space into a low-dimensional space.) This is done more or less automatically by the limitation of our senses and brain's structure as a neural network.

An immediate consequence of this observation is that there will be many states of the world, which are mapped to an almost identical inner representation. In terms of computational efficiency it makes sense to use overlapping set of neurons with similar activation level to represent similar concepts. (This is also a consequence of how the brain actually builds representations from sense inputs.)

Now compare this to the following passage from here.

The halo effect is that perceptions of all positive traits are correlated. Profiles rated higher on scales of attractiveness, are also rated higher on scales of talent, kindness, honesty, and intelligence.

This shouldn't be a surprise, since 'positive' ('feels good') seems to be one of the evolutionary hard-wired concepts. Other concepts that we acquire during our life and associate with positive emotions, like kindness and honesty are mapped to 'nearby' neural structures. When one of those mental structures is activated, the 'closed ones' will be activated to a certain degree as well.

Since we differentiate concepts more when we are learning about a subject, the above reasoning should imply that children and people with less education in a certain area should be more influenced by this (generalized) halo effect in that area.

Conclusion

Since evolution can only modify the existing brain structure but cannot get away from the neural network 'design', the halo effect is a necessary by-product of human thinking. But the degree of 'throwing things in one pot' will depend on how much we learn about those things and increase our representation dimensionality.

My hope is that we can relief evolution from the burden of having to explain so many things and focus more on structural explanations, which provide a working model for possible applications and a better understanding.

PS: I am always grateful for feedback!