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Problem-Solving

I want to talk about problem solving , and make some connections to art appreciation. Specifically, the single process that has the ability to solve all possible problems.

You might know it by different names:

Trial and Error
Guess and Check
Variation and Selection
Conjecture and Criticism
Blind Variation and Selective Retention

These all just about mean the same thing, describing the necessary process for the growth of knowledge in all domains.

This is our interest: knowledge creation. In biology, in science, in art, in relationships, in all domains.

But beyond just knowledge creation, we want to specifically solve any possible problem in all domains, so we have to expand this process.

We know we need an expansion because biological evolution and human thought both involve variation and selection, but human knowledge creation is much more powerful than biological creation.

One big difference is that for the growth of knowledge in biology, every variation must be in an organism that can survive and reproduce. In human knowledge creation, not every idea has to be individually viable to progress the growth of knowledge.

So it must involve something more than just variation and selection.

I am starting mostly with ideas from David Deutsch’s The Fabric of Reality (Chapter 3: Problem Solving), and I am expanding and translating it to fit my thinking on the subject.

I’ll give you the full 5-Step Process and then fill in the details.

The 5-Step Process

Attention
Guess
Alternatives
Selection
Progress

To have a mind that is able to solve all possible problems, it is important for each step in this process to be present, and for the criteria of each to be open-ended. None of these should be fixed.

By open-ended, I do not mean “anything goes.” It just means no criteria is final. Each criteria is always subject to replacement.

If any step is removed, you come to very special errors and inefficiencies. With each step present, it is possible to begin the unbounded growth of knowledge, without the need for ultimate justifications or foundations.

I will describe each step in detail.

1. Attention

Attention is where we typically think of “finding problems.” Really, this is where we notice any inadequacy of any theory or idea. You can think of this as a conflict between two ideas. But really, it can be any reason to have your attention directed somewhere.

This is highly personal and based on the context of your life. What you think is a problem is up to you. Problems are always personal. David Deutsch likes to say all problems are parochial.

It is fine to just think of this step as the identification of a problem. Attention is just a little more broad.

If you have no attention, then all of your guesses are totally random.

It also makes other things more difficult. Like, how could you determine what is an alternative guess if there is no problem? How do you select the best of the alternatives if you have nothing to address? You cannot.

If you do not have attention, problems will be solved very inefficiently.

An example here is biological evolution. There is no systematic way to direct which DNA strand mutates. This all just happens randomly and accidentally. Many problems are solved, indeed, but they are solved without any problem being identified.

This act of solving a problem before it is identified will commonly happen for people too, but for a different reason: Because the definition of the problem is open-ended, it could be defined after the solution exists.

If the criteria for identifying a problem is fixed, there are also problems. When fixed, we will only be able to notice a narrow range of things, meaning we would not be able to solve any possible problem. If our criteria for attention is fixed, there will be some potential for progress that always lies outside of our attention.

Our attention must be free to roam.

What is considered a conflict of ideas—and what is considered a synthesis of ideas—may be more subtle than you have seen in the past. This is why the criteria for a problem must be open-ended.

For art appreciation specifically, you want to be able to focus on any aspect of a work of art to appreciate the beauty. You do not want to be stuck only able to notice the lyrics of a song, or only the emotional component of a narrative.

You need to be able to look at anything to be free to guess the beauty that fits.

Any two elements may be conflicting or synthesized. You should be free to notice if the harmony aligns with the lyrics, or if the background visuals of a movie align with the emotion of the scene. You have the ability to notice that each of these elements of a work of art convey some information, and that information can be conflicting such that you need a theory to understand why they are what they are.

To have a mind that is able to solve all possible problems, the ability to direct attention and identify problems needs to exist, and the criteria for directing attention needs to be open-ended.

2. Guess

A guess is a potential solution to your problem. This potentially resolves the conflict between ideas.

All problems are personal, but sometimes solutions are universal. However, there is no way to confirm that a solution is universal; you just attempt to use it in a new context and see if it works. This is why it is called a guess—because you never know if it will fit in a new context.

A guess is novelty. A guess is creation. A guess is newness.

This is where something genuinely new can be introduced into the world. We may call it trials, variations, or conjectures.

This can be directly thinking of something new, or it could be mixing previously existing ideas (some form of hybridization). It could be randomly changing an idea or systematically varying an idea.

It could also come from an accidental mutation, a mistaken error-prone replication. Just misunderstanding an idea is a form of creating a new variation.

The methods to create guesses are open-ended. So a guess could literally be any idea from the space of all possible ideas—the space which must include the solution to every possible problem.

If you cannot make guesses, you have no novelty. So automatically you get nothing new. Without guesses, you could not solve new problems.

Without a new guess you may be able to see what problems you have, and you may be able to choose from the best available options to address it. But with no new guesses, you can only address a narrow range of problems. You’re just handicapped by not being able to make anything new.

Surely you have depressed friends who cannot create new guesses—maybe it’s been you. But you know the situation: no new ideas, just looping on the existing possible solutions. You can do fine if you already have access to a wide set of alternatives, but that can only go so far without the addition of something new.

Because you will always have new problems.

If your system of making new guesses is fixed, then you only have a limited type of novelty. A system that cannot create new guesses, or cannot create new ways to create new guesses, will be predictable.

An example of this is our current LLMs (Large Language Models). They are lacking in many ways, but this is one that is quite obvious. They are great at combining the things that are known, but are severely limited in novelty creation. And so, we do not see the creation of new types of art, nor scientific breakthroughs coming from them.

To have a mind that is able to solve all possible problems, the ability to create guesses needs to exist and be open-ended.

3. Alternatives

Alternatives are alternative guesses. This may seem like it is redundant with the last step, but this is about the categorization of various guesses.

We need criteria for determining when guesses are variations of each other. We need criteria to determine if the same guess is being presented in different words. We need criteria for when different guesses are actually addressing the same problem, and are thus rival theories.

This allows us to properly compare how well rival theories address a particular problem.

Determining the applicability of various guesses is helpful here. Some solutions have universal applicability. Some are narrowly applicable. Some may be logically inadequate to the point that they are totally inapplicable.

If multiple solutions have the same applicability, they are likely the same solutions reformulated in different words.
If two solutions have mostly overlapping applicability except for a small few differences, one has wider reach compared to the other.

This process of categorization is highly valuable and often overlooked. Where these guesses are stored, how they are stored, and their extended implications all become highly relevant in this step.

If you cannot categorize alternatives, you cannot compare two rival theories. When you cannot compare theories, your only option for a standard is: “Is this guess ultimately certifiably true?”

You are stuck with only selecting based on some ultimate justification, rather than successively creating guesses that are better than all previous. Without categorizing, you are stuck with impossible standards.

If you cannot categorize alternatives, you cannot remove multiple guesses in the selection phase.

You may end up looping, always re-guessing and re-selecting exact copies of the same guess. One simple thing would be to equate all guesses that have internal logical contradictions—due to the fact that any contradiction can imply everything. And so there is no way to prefer one contradiction over another.

Without alternatives you indeed can select, but you cannot select the best. You must always select an immediately viable option.

If you only have a fixed criteria for what guesses are similar to others, you’re in trouble. Presumably, as you progress with problem solving, your problems become more subtle and the differences between your guesses also become more subtle. If your standard for distinguishing or equating guesses is fixed, you will not be able to accommodate higher precision. Thus you come to an end of progress.

For example, you need something to say that Newtonian Mechanics and Relativistic Mechanics are related, that they are alternatives to be compared to each other. But you need very sophisticated criteria to consider them similar, because really they are quite different physically and computationally.

Another example of where we need criteria for categorizing alternatives is the overlap of language. For example:

One may say, “Freewill is being able to do anything you want.”
Another person may say, “Determinism is the fact that the motion of fundamental particles is perfectly described by classical physics equations.”
And another may say, “Freewill is when the explanation of a person’s actions terminates at the person.”

You need sophisticated criteria to determine if each of these concepts are addressing the same problem. Are these even alternatives at all? Do they overlap or contradict in any form? Or do they just have similar sounding labels?

Of course, for my purposes of art appreciation, it sometimes becomes quite the puzzle to determine what is an alternative solution in a work of art.

However, when this isn’t such a puzzle, the audience should be able to create alternative solutions, and in the best case, they cannot find better alternatives than presented in the work of art.

It is best when the solutions within the work feel inevitable.

4. Selection

Selection is the process of removing alternative guesses. In a typical situation this involves removing the guesses that do not adequately solve the problem, or removing the guesses with less applicability than others.

The process leaves you with the best of the available options.

When only a few guesses are left, specialized tests create new subtle contexts to help decide between rival theories. This is a special case of comparing the range of applicability of two theories. Experimental tests comparing two rival theories is an example of this.

After a selection process, it is sufficient to use the best known theory as the basis of action and judgment. You should also use the best known theory as the base for future, more subtle problems to solve.

It is very important that there are different types of selection:

In Biology: Individual replicators die with an individual. That is selection, and it compounds over many instances.
In Coding: We may keep a record of the inadequate alternatives, while also systematically replacing them from all existing instances. You do not wait for a user to discover an error and delete the program; you systematically remove the error by pushing an update.
In Art: We may keep a record of older alternatives, yet we may also return to them and iterate on them. Obsolete styles may be reborn and progress can restart from there.

These are all different types of selection. The proper approach to this is open-ended; it must not be stuck in one form.

If there is no selection, you just are stuck with a flood of guesses. There is no removal of guesses that are not useful. This leads to total chaos. Perhaps you can create the right things, but if you cannot remove or ignore the wrong things, progress is muted.

Carlos gives a funny example of a Lion playing touch football with a Gazelle. Yes, it can determine which is the slowest, but if it does not eliminate, if it does not select, then they will eventually all become slow. There is no optimization to remove errors and allow for the best knowledge to progress.

For art appreciation, this is a matter of throwing out inadequate solutions, replacing them with better alternatives. If you are left with the best possible solution, the beauty becomes inevitable. While if it is easily replaceable, it feels arbitrary.

If we could not select in art, we as the audience would not be able to determine if the artist created the best version of their work or if our own immediate imagination were better.

To have a mind that can solve all possible problems, the ability to select and the criteria to select need to exist and both be open-ended.

5. Progress

The final step is Progress.

This should allow for newer, more subtle, better problems. Perhaps also the creation of new transformations that were not previously possible. However, as with all the other steps, the criteria for this is open-ended.

After selection we need to determine if we have moved forward. We need criteria for what progress is, and what type of new problems are appropriate (if any). Spoiler: There are problems. You have to have problems. They are inevitable.

A lot of people think that progress needs to have no problems. This leads to more issues.

This step helps direct our attention to either continue the whole process, or continue to something new. If we do not have a criteria for progress, then we cannot determine if our new problems are better than our old problems. We may even fall into the error of expecting our solutions to have no problems at all!

Having no criteria for progress will throw off our attention, and may keep the process of generating new guesses going longer than necessary.

If we do not know that our new problems are better than the old problems, we may continue to remove guesses. This is the common problem of needing ultimate justification, and thus not accepting any progress, and thus spinning your wheels on the same problems.

If the criteria for progress is fixed, then we come to a dead end.

This is because our problems will become more and more subtle. So our criteria for progress should also become more subtle, or we will no longer be able to identify progress.

This error happens in social commentary often. Someone may dismiss a new, better and more subtle problem as a “first world problem.” They think being sensitive to the particular firmness and temperature of their beds is not a valid problem, because the standards of what is progress are fixed at the survival level.

Or maybe they call kids “snowflakes” because of the kid’s sensitivity to subtle social behaviors. The brute then cannot see that these kids have progressed beyond the social problems of cavemen. We should have more subtle problems. That is the marker of progress.

For art appreciation, we have to recognize when new art is doing something more subtle than we are used to. We have to watch out for the error of dulling our senses, and praising insensitivity. This error will fix our criteria for progress and stagnate our problem solving.

To have a mind that can solve all possible problems, the ability to determine what is progress and what are acceptable new problems needs to exist and both need to be open-ended.

The Nested Loop

When each of these steps are present together and open-ended, there is the possibility of open-ended progress. If any step is removed, unbounded progress cannot happen. If any is fixed, progress is limited and will eventually come to a dead end.

The way to create the criteria for any one of these steps follows the same overall process. This becomes a nested loop.

You need the full 5-step process to determine what the problem is.

You need the full 5-step process to determine what progress is.

You can only guess a new criteria for alternatives after an inadequacy comes to your attention.

The criteria for each step is created by the 5-step process.

If at any point you are having trouble solving a problem in your life, you can see if any of these steps have been neglected, or if the criteria have been fixed.

I hope this is helpful for you to see how these errors show up, so that you may more easily identify these mistakes in your own life.