Here's a quote from Einstein:
Do not worry about your difficulties in mathematics. I can assure you mine are still greater.
Although I'm no Einstein I think my undergraduate studies in math can explain his difficulties. Most people who have some success studying math get it by looking for and extrapolating patterns while doing problems. I ignored the problems, except for the unusually difficult ones. Instead I looked at the equations and asked myself where they came from, how I might have discovered them, and what could make them wrong. This is a slow and arduous way of learning and it left me with plenty of ongoing difficulties. Seldom, if ever, did I come close to studying everything that was assigned for an exam. But the process gave me a pretty good understanding of some things and also helped me continue my math studies through a postdoc.
I believe Einstein must have worked in a similar way--only more successfully than I. I think of this approach as multiplex thinking.
The concepts of simplex and multiplex can help us understand the Einstein within us. They come from sci fi writer Samuel Delany. Simplex is the kind of explanation you would give a child. I don’t mean the pseudo explanations you might give to hide difficult concepts like rape and cosmology, but simplified explanations of any any all topics which satisfy a child's current curiosity. Multiplex explanations on the ohter hand involve complex juxtapositions that create a meaning beyond their component parts—like you might find in poetry.
I’ve just given you a rather simplex way of looking at the concepts of simplex and multiplex. Delany provides a more multiplex view by creating a protagonist, Comet Jo, who come from a simplex society and then slowly meets up with all kinds of beings, each with a different view of the multiplex mindset.
Let’s try for our own way of understanding the difference. Imagine a quite evening with friends in which you have been asking each other how you picked your career or college major. The explanations will all be simplex. Now think of everything that might be related to your own explanation. Ready? If this isn't somewhat overwhelming, you are not there yet. Take your time. Once you are finished go back to your first explanation and give it some of the color you have just discovered within yourself.
This colorized explanation of your career choice will help both you and your friends understand what you are about but it is only a snapshot taken at one period in time. Think of it as a river carrying your explanation to a sea containing the explanations of everybody else.
Of course the channel to the sea carrying your explanation is a simplification of how your really decided on a career. The real explanation looks something like an Alaskan braided river.
The channels of an Alaskan braided river are not carved into a stone canyon. They are forever rearranging themselves. So it is with your understanding of your career decision. The snapshot was a bit out of date as soon as it was created.
This is a multiplex point of view. It reflects the fact that our brains require certainty in a complicated world of flux. Any certainty we fixate on is somewhat arbitrary.
In simplex mode we recognize and extrapolate patterns. In multiplex mode we synthesize multiple patterns.
Daily life requires enough certainty to know how to behave from one minute to the next. So even a multiplex mind will work in simplex mode most of the time.
Education is mostly a simplex affair and this created some difficulty for me when I started teaching. A third of my student evaluations were negative. Some would complain that the way to succeed in my classes was to do exactly what I said, nothing else would produce a good grade. Others would complain that I never explained what was wanted and so they had no clue how obtain a good grade.
It took me a long time to understand what was going on. My students had been taught discipline and creativity as if they were unrelated. My computer programming assignments required both together. Students who saw them as asking for creativity complained about the discipline required. Students who saw them as asking for discipline complained about the freedom they were given.
Both points of view were simplex. Without consciously realizing it I was asking for a multiplex point of view that synthesized both requirements. Once I was able to explain that to my classes we got along much, much better.
Multiplex thinking involves not only synthesizing points of view but also testing points of view by asking "what if" questions. These abilities seem to have been added to our brains at a recent stage in our evolution. Making use of them is hard work.
In the past daily life required very little multiplex thinking but that is changing. Advancing technology and contact with diverse ways of thinking are increasingly forcing us to synthesize points of view. This is never more apparent than in group decision making. Coming to a consensus when there are disparate views is is hard.
The Quakers have been seeking better ways of doing this for centuries. One offshoot of their thinking, called sociocracy, seems to be attracting increasing interest. I tested this assertion by doing two google searches for “sociocracy”, one for the past year (from March 2021) and another for the year of 2010. I found more references in the recent search.
One thing sociocracy does is to compartmentalize group decision making so that the amount of multiplex thinking needed at any one time is not overwhelming. The process of making a decision is broken into three parts: understanding, exploring, and deciding.
The understanding phase is devoted simply to understanding all the issues involved. Committee members help each other acquire simplex understandings of these issues.
In the exploring phase committee members extrapolate issues to see where they might lead. This is a simplex exercise. They also will sometimes create new issues by synthesizing old ones. This brings the need for multiplexing into play.
In the decision phase synthesis must happen--until a single consensus point of view is arrived at. Of course a decision is not always possible in this phase. It may be that the decision will have to be put off or that the committee will have to return to an earlier phase. The better the earlier phases are accomplished the less likely this will happen.
There are tricks to minimize setbacks in the decision phase. Multiplex thinking doesn't just involve reasoning about stuff, emotions are involved too. Many times a decision will need to be put off because a committee member feels unprepared to make or accept a decision for reasons that are not so very important in the long run. This situation can be handled with "lazy consent". This means that if no objection is raised by a certain date, consent will be assumed. This gives committee members time to cool down and reflect. Many objections will fade away before the deadline and when objections do not fade away they will be more carefully thought out before they are raised.
To summarize mutiplex thinking puts things in a wide context from which we can understand existing opinions or synthesize new ones. This wide context is as close as we humans can get to reality. The multiplex mind understands the fragile nature of our understanding within that reality. Here is how Einstein explained mathematical underrstanding
As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.
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https://cogitamus.substack.com/p/thinking-like-einstein