There is a philosophical assumption, inspired by educational didactics, which consists of thinking that any concept, no matter how intricate, can be presented in simple words and easily understood if it is adequately exemplified. The title of the question is in fact inspired by a book written under that belief: something as complicated as string theory can be simplified to the level that an elementary school child can understand it, supposedly.

However, there is another opposite current of thought, which we could call the "irreducibility of complexity", there is a hierarchy of complexity or even a measure of complexity (e.g. Kolmogorov complexity), we should say that something is complex when it scores high on the complexity scale. If something is indeed complex, and not just apparently complex or simply poorly explained, then it can NOT be reduced to something simple without losing information or descriptiveness. According to this position, something simple can be explained in an abstruse or twisted, artificial way (a bad explanation), but something genuinely complex could not be simplified without partly falsifying it.

My question is: Which of these two positions seems the more accurate (depending on the context)? That is, in which contexts is the first position reasonable and in which contexts is the second position the more reasonable?

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    In the case of Kolmogorov complexity of strings (or possibly including data structures, math objects), when it's scored high it's merely like assigning a complexity level of a 1st-order arithmetic formula in the arithmetic hierarchy, nothing intrinsically complex here so long as it's decidable. But the famous undecidable halting problem can quickly show non-computability of Kolmogorov complexity and Chaitin's incompleteness theorem, so a hard part here is non-computability and incompleteness. Of course on the algo complexity theory side you have P?=NP hard stuff there which is another story... Jul 9, 2022 at 6:26
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    Your "String theory for dummies" case just focuses on some critical concepts and skips the computable steps and details. Your another recent post discussed the right features of this kind of conceptual analysis. As stated in the poem Faith in Mind or A Trustful Mind translated by Suzuki: The Perfect Way knows no difficulties; Except that it refuses to make preferences; Only when freed from hate and love; It reveals itself fully and without disguise... Jul 9, 2022 at 6:49
  • It's a falsifiable proposition. Someone show us a five year old who can understand string theory like a PhD and we'll know it's true.
    – armand
    Jul 9, 2022 at 9:31
  • @armand i doubt this is what is meant, by explaining in lay person terms. If we judge by the success of books on popularized science, it is not that far fetched
    – Nikos M.
    Jul 9, 2022 at 10:59
  • @NikosM. Commercial success do not mean success in teaching science properly. What is more, "something as complicated as string theory can be simplified to the level that an elementary school child can understand it" is pretty straightforward. One has to define "understanding", and judging by the knowledge of lay people people who think they understand, for example, QM, the bar can be set pretty low. Of course any five year old can repeat a sentence or two grossly summarizing the theory, but it can hardly be considered "understanding". But yeah, by setting the bar low enough anything goes.
    – armand
    Jul 9, 2022 at 11:26

4 Answers 4


Even if a concept is sufficiently "algorithmically random" (ie in Kolmogorov complexity sense, cannot be compressed or "explained" further) it is still possible to approximate it with simpler systems up to some desired accuracy (for example see universal approximation theorems for neural networks).

Assuming natural neural networks share this characteristic of universal approximation (a quite plausibe assumption), then almost any concept can be approximated up to some desired accuracy, and in many cases this is just enough (provided that what is missed is irrelevant "noise" and not the main defining features).

PS: Note that both kolmogorov complexity and universal approximation depend on the underlying computing system/model. So they might differ (although difference might be up to some constant) for different underlying computing models.


I will first focus on the OP's leading paragraph: the claim that any concept, no matter how intricate, can be presented in simple words and easily understood. First, assuming a ground language, it is indeed true that every concept can be presented in simple words. For every proper new concept is merely a well-defined extension of the ground langauge. Otherwise it is not well-defined- and hence not likely coherent; although that is a matter of debate, or it is not an extension and hence part of the ground langauge. Moreover, the assumption of a ground language is fairly innocuous, as most humans share a ground language (for their field).

However, this idea, and your introduction of Kolmogorov complexity are not necessarily opposed. For example, consider some mathematical statement, and take our ground language to be the type theory of some popular proof verification software. A statement that involves 4 or 5 well-defined extensions can still be broken down to the ground language, however, the program ( proof, by Curry - Howard!) will of course increase in length. So its KC will be higher than it otherwise would have been, ie its complexity is "high" but it can still be "presented in simple words".

Does this make things easily understood? Since understanding is presumably agent relative, in particular relativized to agent motivation, intelligence, etc, I'll remain agnostic on that question.

  • The first paragraphs are really how education actually works! And since there are educated people that were once uneducated it really produces results.
    – Nikos M.
    Jul 11, 2022 at 20:06

It probably depends on what you count as "understanding" and what kind of "complexity" you're dealing with.

Like if you have the sequence 14563241653246216435 then trying to write a program to recreate that sequence is probably more complex to do and describe than realizing that's essentially rolling a dice for 20 times. Not only is it more complex, it might even lead you down the wrong path of assuming that the concrete sequence matters in the first place and that predicting the next number is possible and not just a matter of probability.

Though it might be possible that the more complex model also gets you to the realization that you're dealing with a homogeneous random distribution between 1 and 6 and by comparison to experience you might suspect a dice. Now what of the two things would you consider "understanding"? Like a child watching the experimenter throw the dice and write down the numbers could get the same understanding as the more complex detective work. Is it the same level of understanding though or has the detective work revealed properties of a dice throw that are not immediately obvious to the child? Or are these further information irrelevant to the problem itself and thus only add unnecessary complexity?

So it would be about the demarcation of a concepts and what is necessary to fully describe and comprehend them. As well as what it means to fully comprehend them.

Also if you'd have ever played with a dice, then just mentioning "dice" would trigger the word cloud associated with that thing, like idk cube shaped, numbered sides, opposite sides adding up to 7, 1/6 probability for each side. And so on.

While if I had to explain to you what a "cube" is, what a "shape" is, what "numbers" are, what an "opposite" is and how probability works. Without any visual aid or prior knowledge and in their full and unabridged glory then you can easily produce something no child is able to comprehend and not necessarily out of a mean spirited attempt to confuse them.

But what if we don't speak about a dice but idk an automobile (a car). Like what do you count as knowledge about cars and what do you consider "the essence" of a car. Like the object/concept that would let you comprehend what is happening beyond seeing part of it or result of it interacting with the environment. Like if I showed you a car, pointed at it and said car and then showed you a different own, would you also identify it as a car, despite being different then the first? What if I took out the engine? Everything looks the same but a major part is missing? Still a car? I mean it's no longer an automobile as it can move itself anymore.

What if I just removed a piston from the engine or an internal part that is crucial for the function but not perceivable from the outside? Is it still the same? Do I understand a car without being able to strip it down to it's vital functionality or is "thing that can be driven" already the essence of that thing?

So even for the most complex subjects you could probably find an abstraction of cutting out some lesser important features, wrapping it in a black box and give it a name and just let people look at the inputs outputs and its appearance, which would be simple, does that mean they understand it? Is what they understand even really what is happening? Or even really what they see?

  • According to the car example one cannot know what a car is unless one is the manufacturer itself. And since manufacturing is divided in separate units with different people working on each unit, really no one can know what a car is. On the other hand I think one does not need intricate details of a car's engine to know what a car is. And in fact this is how learning and education happen. One introduces simpler examples and sufficient outlines of a new or difficult concept..
    – Nikos M.
    Jul 11, 2022 at 20:00
  • Really i can adapt my argument in other cases. So a physics Phd does not know what string theory is, since he might miss the latest theorem on some intricate details of string theory by some colleague on the other side of the planet. He certainly can miss the latest revelation another colleague had on string theory but did not publish it yet.
    – Nikos M.
    Jul 11, 2022 at 20:22
  • @NikosM. That's why I said it depends on what is meant by "understanding". Like almost anybody with a computer is able to use it, but the amount of people how know how the things "they do" are actually done is far smaller. So there are different degrees of knowledge about a thing. And as absurd as as it sounds to say "you don't know what a car is unless you built it". Look at it the other way around do you know what a car is? If I gave you the parts could you build it? Or is that knowledge more or less superficial?
    – haxor789
    Jul 11, 2022 at 22:02
  • It seems you appeal to "exactness" to define understanding, but this rapidly becomes meaningless as my previous arguments demonstrate. So since we don't know (nor ever know) the digits of pi, we don't know pi. But this is not the case, since we can uniquely outline pi as "proportion of circumferance to diameter" and this uniquely fixes pi and a lay person can understand this. In any practical situtation we need the digits of pi we only need them up to some accuracy. And we are done.
    – Nikos M.
    Jul 12, 2022 at 8:40
  • It's not necessarily exactness but rather the question of what is the, so to say "essence" of the thing that you're talking about. Like take your example of pi, would you say knowing the first 10 digits of pi is enough to understand pi? I mean for many practical implications it actually might be. Though not only are there infinitely more digits that you don't know, the whole "proportion of ..." angle to it, opens a whole different field of application that you might have never considered having just memorized a number with 10 digits. So at what point have you understood "the thing"?
    – haxor789
    Jul 12, 2022 at 10:44

Notice this is not only related to language.

The Theory of Systems is the rational answer to complexity.

A system is not only a set of interrelated parts, but much more than that. Any problem can be approached as a system (in fact, such is the central goal of it), because a complex problem (complex = that can't be understood, so, it can't be solved) can be divided, with some theoretical and technical background, in many simple (easy to understand) and solvable problems.

Probably this approach is the one to be taken as the natural human tendency, to seek and effectively find simplicity.

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