# Self-Similarity Some parts of physical reality (such as symbols, pictures or human thoughts) resemble other parts. The resemblance may be concrete, as when the images in a planetarium resemble the night sky; more importantly, it may be abstract, as when a statement in quantum theory printed in a book correctly explains an aspect of the structure of the multiverse. To the extent that the symbols, images and theories are true - that is, they resemble in appropriate respects the concrete or abstract things they refer to - their existence gives reality a new sort of self-similarity, the self-similarity we call [Knowledge](Knowledge.md). To be clear, self-similarity is not merely saying that all of reality follows a consistent set of [Laws of Physics](The%20Laws%20of%20Physics.md) - which it does. It is saying that certain parts of reality can represent other parts arbitrarily accurately. ## Mr Witt's Argument Against Self-Similarity Suppose that [Mr Witt](Mr%20Witt.md) was trying to put forth an argument that reality is *not* self-similar. He proclaims "Reality is not self-similar. Convince me of other wise!" ### A Counter Argument That Begs the Question An initial counter argument that we may be tempted to propose is as follows: if reality was not self-similar then the constructs of language and communication would not be possible, for they rely on self-similarity[^1]. And if language and communication aren't possible, then [Mr Witt](Mr%20Witt.md) couldn't even be making his argument that reality is not self-similar. [Mr Witt](Mr%20Witt.md) would respond by saying: "Ahah! That argument is entirely [Circular](Circular%20Argument.md)! You are assuming self-similarity in order to prove self-similarity. You effectively just said 'we couldn't be having this argument unless self-similarity exists, thus self similarity-exists'. Better luck next time." ### A Proper Counter Argument At this point we can pause and think for a moment. In order to effectively reason with [Mr Witt](Mr%20Witt.md), we are going to need to construct a water tight argument. First things first, why do we want to argue for self-similarity? Because self-similarity is not some arbitrary principle, but rather it plays an integral explanatory role for why the universe is comprehensible and why knowledge is possible. It is the foundation on which biological [Evolution](Evolution.md), language, [Computation](Computation.md), and [Virtual Reality](Virtual%20Reality.md) all stand. The [Turing Principle](Turing%20Principle.md) states that it is possible to build a [Universal](Universality.md) [Virtual Reality](Virtual%20Reality.md) generator. The [Universality](Universality.md) of [Computation](Computation.md) asserts that any physical system can mimic any other physical system given enough time and memory. In other words, self-similarity is part of several of our deepest known explanations and while it can certainly be incorrect - we are [Fallible](Fallibilism.md) and all [Knowledge](Knowledge.md) is conjectural - we shouldn't simply throw it away. For in [Problem Driven Epistemology](Problem%20Driven%20Epistemology.md) we must start with a [Problem](Problem.md), and from there [Explanations Are Justified By Their Superior Ability to Solve Problems They Address](Explanations%20Are%20Justified%20By%20Their%20Superior%20Ability%20to%20Solve%20Problems%20They%20Address.md). What was [Mr Witt](Mr%20Witt.md)'s problem? He never actually said! Suppose we ask him and he tries to worm his way out by saying "My problem was that I just didn't like the idea of self-similarity. It just seemed too convenient." Fair enough. But we can respond by [Taking His Theory Seriously On Its Own Terms](Take%20Theories%20Seriously%20on%20Their%20Own%20Terms.md). If we take [Mr Witt](Mr%20Witt.md)'s theory seriously, it immediately presents a [Problem](Problem.md). By claiming that self-similarity does not exist, many of our deepest explanations - *including that of language* - have been crushed. If he doesn't propose an alternative explanation that details how language and communication, and thus his argument, can exist *without* a self-similar reality, then he is holding an [Inconsistent](Inconsistent.md) position. Notice that we didn't argue that self-similarity *must exist* due to the presence of language. We've already shown that is circular. But we pointed out that our best explanations of language rely on self similarity. By claiming that reality is not self-similar, [Mr Witt](Mr%20Witt.md) *must* propose an alternate theory of language, or else his position is one of [Contradiction](Contradiction.md). We have effectively [Forced him To Take a Position](Forced%20To%20Take%20a%20Position.md), for [Logical Consistency Forces Taking a Position](Logical%20Consistency%20Forces%20Taking%20a%20Position.md). But slippery as he is, we can expect [Mr Witt](Mr%20Witt.md) to try and escape yet again. He may say: "I was expecting you to bring this up! I do indeed have an alternative theory. While reality is not at its core self-similar, it *appears* to us [as if](As%20If.md) it is because there is a [compassionate angel](Descartes%20Evil%20Demon.md) who takes pure chaos and packages it up nicely into the self-similar world we inhabit. Yes I will concede that all of our best explanations are consistent with a self-similar reality. But make no mistake, what is *really* out there in reality is pure chaos" Do you see what [Mr Witt](Mr%20Witt.md) did there? He effectively took an explanation, that self-similarity is real, and added a heaping spoonful of convoluted detritus onto it. His updated explanation introduced an inexplicable angel, and this angel didn't improve the explanation in any way! This makes it a far worse explanation[^3] and thus we are [Justified](Justification.md) to reject it. At this point we have blocked off all the exits, closed the escape hatches and locked the doors. [Mr Witt](Mr%20Witt.md) has been cornered[^2]. It's worth noting that this argument suffers from the same flaws as the argument in favor of [Solipsism](Solipsism.md), and it can be shot down by the same arguments used to [Defend Science by Arguing Against Arbitrary Boundaries](Defend%20Science%20by%20Arguing%20Against%20Arbitrary%20Boundaries.md)[^4]. Self-Similarity is the only way to explain certain regularities of the universe and of our [Knowledge](Knowledge.md) of the universe. To deny this self-similarity, is to create a more complex theory that is inconsistent with our knowledge. ## Self-Similarity is a Feature of Reality So we managed to definitively shut down [Mr Witt](Mr%20Witt.md) and his argument that self-similarity is *not* real. But can we really infer that self-similarity is *real*? That it is an objective feature of of reality? ### Logic Forces Taking A Position Yes, we can. There are two ways to approach this. The first is that there is indeed a genuine dichotomy between real and not real. An entity *must* be one or the other, by definition. This is a matter of [Logic](Logic.md) and the [Law of the Excluded Middle](Law%20of%20the%20Excluded%20Middle.md) prevents self-similarity from falling in some awkward purgatory zone. If the entity is *not* not-real, then it *must* be real. But wait, one may argue "surely there must be a third option! Perhaps an entity can be real, not real, and semi-real?". Let's explore this gripe. Imagine that we are talking about large pine tree and say it must be a "fish" or "not a fish". Now say someone pipes up and tells us "well it could also be a tree". This is of course true, and it is indeed a tree. But this has not changed that fact that as a matter of [Logic](Logic.md) our pine tree must still be either a "fish" or "not a fish". The same thing applies when we are thinking about "not real", "real" and "semi-real". In this case "semi-real" takes the role of a "tree" (assuming that we had a way of defining semi-real that is consistent with real and not-real). Now you may wonder if this is a matter of language - instead of "real", "not real" and "semi-real", what if we had the classification "real 1", "real 0" and "real 2". Now, from a linguistic perspective, it doesn't immediately appear that we are [Forced To Take a Position](Forced%20To%20Take%20a%20Position.md) anymore. An entity could be "real 2" and not "real 1" or "real 0". But is that actually correct? We have used a [Renaming Scheme](Renaming%20Scheme.md), but if the underlying concepts remain the same, then the logic remains the same! If "real 1" corresponds to "real" and "real 0" corresponds to "not real", then, in this renamed system an entity must be "real 1" or "real 0". It cannot be both or neither. Notice that this all stems from the fact that [Rational Inquiry Requires Pursuing Good Explanations](Rational%20Inquiry%20Requires%20Pursuing%20Good%20Explanations.md). [We Must Seek Good Explanations](We%20Must%20Seek%20Good%20Explanations.md) and a good explanation must be logically sound. As we have seen, [Logical Consistency Forces Taking a Position](Logical%20Consistency%20Forces%20Taking%20a%20Position.md). Thus in order to come up with the best explanation of self-similarity we must regard it as real! ### Dr Johnsons Criteria Now we can also use [Dr Johnsons Criteria](Dr%20Johnsons%20Criteria.md), that which provides a [Criterion for Reality](Criterion%20for%20Reality.md), to help us here. It states that something is real if it is complex and autonomous - in other words, if it ["kicks back" and requires an independent explanation](Kicking%20Back%20Requires%20an%20Independent%20Explanation.md). Does self-similarity meet this criterion? Does it require an independent explanation? How does it "kick back"? Self-similarity most definitely does meet this criteria. The very fact that there exist general, explanatory theories implies that disparate objects and events are physically alike in some ways. Likewise [Knowledge](Knowledge.md) is in some way about information that represents other parts of reality. Both of these phenomena reference the idea of self-similarity, which then requires an [Explanation](Explanations.md)! We cannot just take it for granted, it must be explained. We then *do* explain it, via the [Turing Principle](Turing%20Principle.md). Thus it is an independent explanation that fits into our best explanations and we are right to regard it as real. Now what about Dr Johnsons criteria as defined by computations: "If an entity factors into our best explanation, and a substantial amount of [Computation](Computation.md) would be required to give us the illusion that a certain entity is real, then that entity is real". How exactly does self-similarity satisfy *that* criterion? In this case, we already have argued that self-similarity factors into our best explanations, so we would be considering how much computation would be required to [Simulate](Simulation.md) a self-similar universe. This amount of computation would be our measure of complexity. The answer is quite clear in this case: an immense amount of computation would be required. However, the amount of computation required to simulate a non self-similar universe would also be immense. In fact, simulating a non self-similar universe would be far more complex. This is because there would be no way to reuse sub routines of the program - after all no portion of the simulation should be self-similar. But wait, in this case it appears that the [Turing Principle](Turing%20Principle.md) is used to both explain self-similarity and measure the computational complexity of simulating a self-similar universe. Put another way, it may appear that we are saying "self-similarity is possible due to the Turing Principle, and self-similarity is real because the Turing principle says it is". If we slightly tweak this, we are roughly saying: "Our universe follows the Turing Principle, and the Turing Principle is real because the Turing Principle says it is". In other words we roughly have the Turing Principle referencing the Turing Principle - a [Self-Reference](Self-Referential.md). Is this a problem? No, for not all self-reference is [Bad Self-Reference](Self-Referential.md#Bad%20Self-Reference). There is [Good Self-Reference](Self-Referential.md#Good%20Self-Reference) as well. A great example of that is shown in [We Must Seek Good Explanations](We%20Must%20Seek%20Good%20Explanations.md#Self-Reference). ## Relationship to Knowledge TODO: Fill this out when working on [8 - The Significance of Life](8%20-%20The%20Significance%20of%20Life.md) --- Date: 20241114 Links to: [Fabric of Reality](Fabric%20of%20Reality.md) pg 95 Tags: References: * []() [^1]: Specifically, when we communicate we use language. This language may be instantiated via ink on a page, or sound waves having been produced via vocal cords. But we know that if we read the words "dog" or speak the word "dog", that it refers to some abstract concept of a dog (not one particular dog). Thus there is a self similarity between ink on a page, sound waves being uttered through vocal cords producing different accents, and some abstract entity that doesn't physically exist - some [Platonic](Platonic.md) dog. [^2]: There is technically one more way out that [Mr Witt](Mr%20Witt.md) could take. Because [Rational Inquiry Requires Pursuing Good Explanations](Rational%20Inquiry%20Requires%20Pursuing%20Good%20Explanations.md), if he claimed that he didn't care about finding a *good explanation*, but only wanted a flowery, exciting explanation, we would be at a standstill. At that point we would need to *persuade* him of the benefits of rational inquiry and good explanations. [^3]: Why is it a worse explanation? For starters, it is easy to vary! Why an angel? What not a demon, or a titan, or a god, or an alien? Introducing extraneous baggage into a explanation will always make it worse. It will then have inexplicable elements to it. [^4]: Which more generally can be seen as specific instances of [Taking Theories Seriously on Their Own Terms](Take%20Theories%20Seriously%20on%20Their%20Own%20Terms.md)