A good question. I would think that while the story doesn’t have much to offer regarding conscious mental calculation and systems, it still includes a set of powerful allegories (in my article I did mention one of them: Algernon seems to stand for the somatic part, with the person turning into a purely mental entity; another allegory seems to be about the need to stop extrapolating thoughts to prevent an overload) which can, consciously or not, bring about changes to the reader’s rationality.
I don’t think the story has much to do with youth and experience. After all, as we all know (unless we are youths ;) ) while some knowledge only can be had by experience and thus only be gotten in time, the more theoretical types of knowledge are available to highly intelligent youths as well, eg an elementary school pupil can be already exceptionally good at math.
I entirely agree with you. The story isn’t hard scifi at all, and this much is clear :)
It still is one of the gloomiest pieces of literature ever written, and it does manage to move the reader...
While “yes requires the possibility of no” is correct, one should also establish whether or not either yes or no is meaningful itself in the context of the examination. For example, usually one is not up against a real authority, so whether the view of the other person is in favor or against his/her own the answer cannot be final for reasons other than just the internal conflict of the one who poses (or fears to pose) the question.
Often (in the internet age) we see this issue of bias and fear of asking framed in regards to hybrid matters, both scientific and political. However, one would have to suppose that the paradigmatic anxiety before getting an answer exists only in matters which are more personal. And in personal matters there is usually no clear authority, despite the fact that often there is a clear (when honest) consensus.
An example, from life. A very beautiful girl happens to have a disability—for example paralysis or atrophy of some part of her body. There is clear contrast between her pretty features (face, upper body etc) and the disabled/distorted one. The girl cannot accept this, yet—as is perfectly human—wishes to get some reassurance from others. Others may react in a number of different ways. The answer, however, to any question posed on this, can never be regarded as some final say, and in a way it happens that what is being juxtaposed here is not a question with an answer, but an entire mental life with some nearly nameless input of some other human.
In essence, while yes requires the possibility of no, I think that the most anxiety-causing matters really do not lend themselves well to asking a question in the first place.
There is a nice quote by Socrates (iirc it is in the dialogue with the geometrician Theaetetos*) where Socrates mentions one of the views about the origin of philosophical thinking, namely that it is born from the sense of dazzle (thamvos, in Greek). He meant (in context) that when a thinker senses something impressive and unknown, he/she is bound to examine it.
Thamvos is, of course, distinct from anxiety, such as when the sense is negative or even horrific.
In essence I agree that one of the prerequisites for intricate thought is the ability (and chance) to be impressed by something you come across, a trigger, whether external or internal.
*you should check the dialogue for other reasons too. For example it includes the (possibly) first ever reference to the Spiral of Theodoros of Cyrene.
″ Well, here is the point where we disagree. In my view, equations for e.g. gravity or quantum physics are given by nature. Different species may use different syntax to describe them, but the freedom to do so would be quite limited. ”
Yet differences of syntax connote relative uniformity in the observers as well as presupposing science being cosmic (also math being cosmic, where it relates to scientific examination). In my view supposing that indeed the cosmos (something clearly external to our mind) is examined and accounted for in a way which allows some hypothesized own (cosmic) rules to be picked up albeit in a slightly or somewhat particular manner by each observer, is a little like assuming that current AI in computer games actually identifies a sprite as a horseman and merely picks up the horseman as what the code translates it as. When (at least in this example; ie the fault may lie in the analogy) the game AI is obviously entirely incapable of identifying any “horseman” or any other form or trait, and just runs a code which has “horseman” only arbitrarily and in-code be tied to anything the AI can pick up. Likewise, it seems to me, a human runs (as well as reacts to; cause contrary to a current game AI we also have the ability to self-reflect) a human code which inevitably turns anything external into something anthropic. In the end, much like that AI, us humans also only deal with our own code and nothing else, regardless of the fact that the code is applied to specific and distinct phenomena (move the horseman, check if it is good to use a low HP unit against a rebel, etc).
″ The fact that Kepler tried to have it one way, but it turned out to be other way, is an evidence for “the universe having its own mind about the equations”, isn’t it? ”
My point is that it is a bit suspect (granted, this is just intuitive) that so simple and distinct a 2d geometrical form as an ellipse, is actually for us humans front and center in phenomena including the movement of heavenly bodies. Sure, by itself it isn’t against math being cosmic, but I really doubt humans are so important OR that the ellipse is not a human concept but something cosmic. I’d need to elaborate on this, but yes, it is impressive in my view.
″ Of course an alternative explanation is that the scientists—mostly men, at least in history—unconsciously prefer shapes that remind them of boobs. ”
I thought these forums were meant for discussing things which aren’t perfectly clear :D
″ If the hypothetical aliens live in the same universe, they will probably develop natural numbers, some version of calculus, probably complex numbers, etc. Because those are things that describe the universe. ”
I think that they might not. Of course I cannot be certain, but at least in the hypothetical I meant aliens which indeed do not have even the concept of a natural number or other similar concept. And in my view the notion of a sum (a oneness, something specific and easy to contrast to other objects or qualities) is quite possibly (tied to) the most crucial human mental characteristic. The basis of any thought is that it is sensed as distinct from any other thought, regardless of its baggage of unconscious elements.
I can imagine (as an idea) an intelligent alien species which does not have a notion of a sum or a oneness. To that hypothetical alien species there isn’t really an external and an internal. This by itself does not have to prevent those aliens from having advanced science, but I personally doubt it would be mutually intelligible to our own.
In my view nothing describes the actual universe, but there are many possible (species-dependent) translations of the universe. Those are always tied to a phenomenon (what is picked up by sensory or mental organs) and not the actual thing.
That said, another interesting question might be (assuming math and science aren’t cosmic) just why we identify quite a lot of significant patterns as relatively simple forms. For example the elliptic and parabolic trajectories of heavenly bodies, or the (near) spheroid form of some others. Again my suspicion is that has to do with human perception, but it is a good question why so specific a form would be picked up. Recall how even Kepler was originally regarding the ellipsis as way too easy and convenient a form to account for movement in space, and was considering complicated arrangements of the platonic solids :)
I will try to offer my reflection on the two matters you mentioned.
1)First of all whether this development may have been social. It would—to a degree—but if so then it would be a peculiar and prehistoric event:
If I was to guess, at some point (in deep prehistory) our ancestors could not yet be able to communicate using anything resembling a language, or even words. Prior to using words (or anything similar to words) prehistoric humans would only tenuously tie their inner world (thinking & feeling) to formulated or isolated notions. It is highly likely that logical thinking (by which I mean the basis of later formalization of logic, starting -at the latest- with Aristotle) wasn’t yet so prominent a part in the human mentality. It is not at all impossible, or even (in my view) that improbable that some degree of proto- rationalization had to occur so that prehistoric humans would manage to think and sense less of something less organized, and move towards becoming able to establish stable notions and consequently words and a language.
2) Secondly, this would be also inherited. I do suppose that ultimately math (by which I mean more complicated math than the one we currently are aware of) serves somewhat as a dna-to-consciousness interface. But even if this is so, due to point 1 it wouldn’t really connote mathematical parameters as being more important than other parameters in the human mind or overall organism.
But there is another point, regarding your post. I think that a non-mental object (for example any external object) cannot be identified as it actually is by the observer/the one who senses it. In philosophy there is a famous term, the so-called “thing-in-itself”. That term (used since ancient times) generally means that any object is picked up as having qualities depending on the observer’s own ability and means to identify qualities, and not because the actual object has to have those qualities or anything like them. The actual object is just there, but is not in singularity with the observer; the observer translates it through his/her own means (senses and thought). Your point about the object possibly having math inherently is interesting (I do understand you mean that its form is shaped due to actual, real properties, and those are just picked up by us), yet it should be supplemented with the note that even if the object (for example one of those shells) had properties itself which create that spiral and then we notice it, it would have to follow that either we noticed the spiral without distorting the thing-in-itself as an observer of it, or that we picked up some property which didn’t actually have any mathematical value but was (in some strange way) isomorphic to the spiral when translated for a human observer’s sensory organs. If the latter somehow was true then the external object had no mathematical property, and we picked up some math property because we seem to project math even in more ways than one. If the former was true then we are in singularity with the observed object and nothing is actually distinct in the cosmos (certainly anyone senses their own self as distinct from something external). And in both cases it would not connote that math are cosmic, given the case where math were part of the observed object would present a case where we are so full of illusions that we think (incorrectly in that case) ourselves distinct from a shell, when in “reality” we would not have been.
I do realize this may seem way too “philosophical” (and in a bad way). Philosophy has had problems since ancient times (this itself is already examined by Plato himself: how philosophy may seem very alienating and problematic). Yet the gist of the matter is that (in virtually all serious philosophers’ view) there is no reason to think that we as observers pick up any actual non-anthropic reality. We do pick up a translation of something, and this translation is enough to allow us to advance in various ways, including being able to build space-traveling rockets. This is so because we always stay within the translation, and to us the cosmos is witnessed in translation. But a translation of something is not in tautology with the thing itself. My own suspicion is that different intelligent species will not have compatible translations (because they would likely even lack fundamental notions we have; for example they may not sense space or movement or other parameters, and sense ones we cannot imagine. Intuitively I suspect even so alien a species could develop tech and science of a very high level).
Hi, yes, I do not mean why the Fibonacci spiral approximates the Golden Spiral. I mean why we happen to see something very close to this pattern in some external objects (for example some shells of creatures) when it is a mathematical formation based on a specific sequence.
I referred to it to note that perhaps we project math onto the external world, including cases where we literally see a fully fledged math spiral.
There are other famous examples. Another is The Vitruvian Man (proportions of man by Vitruvius, as presented by DaVinci). One would be tempted to account for this by saying math is cosmic, yet it may just be it is anthropic and the result is a projection of patterns. That math is very important for us (both consciously and even more so unconsciously) seems certain; yet maybe it is not cosmic at all.
Thank you. Intuitively I would hazard the guess that even non-obvious systems (such as your example of the story which rests on axioms) may be in the future presented in a mathematical way. There is a very considerable added hurdle there, however:
When we communicate about math (let’s use a simple and famous example: the Pythagorean theorem in Euclidean space) we never focus on parameters that go outside the system. Not only parameters which are outside the set axioms which define the system mathematically (in this case Euclidean space) but more importantly the many more which define the terms we use: I do not communicate to you how I sense the terms for A, B, squared, equality or any other, regardless of the likelihood of myself sensing them in my mind in a very different way to you. It’s the same relative communication which is used in every-day matters: if one says “I am happy” you do not sense what is very specifically/fully meant, although the term is a fossil of specific connotations, so some communication is possible, and often no more is needed. Likewise no more is needed to present a math system like that, but certainly far more will be needed to present a story or the subconscious in math terms (and within a given level; outside of that set the terms will remain less defined).
If you mean my example using people who were born blind, I meant that much like they develop their own system and theory to identify what they cannot sense (visible space), so do all humans in regards to identifying how the external world/the cosmos functions. It isn’t about which one is “less real”, unless we claim that there is one being (or one group of beings etc) which witness an actual reality. That itself is highly debatable (eg Descartes, and some other thinkers, usually reversed such a role for a deity).
If those aliens are able to understand notions such as momentum, it would be because they can (in whatever way; sense or other) understand more fundamental notions which may be non-cosmic. Some good examples of such notions, from Eleatic philosophy (Parmenides, Zeno etc) are size, form, position, movement (change) and time. To a human, those ideas tie to something evident. An alien may not have them at all. An alien closely resembling humans may have them (as well as math).
Indeed, crows are a good example of non-human creatures that use something which may be identified as math (crows have been observed to effectively even notice the -its practical manifestation, obviously—law of displacement of liquids :) )
I used human as a synecdoche here, that is chose the most prominent creature we know that uses math, to stand for all that (to some degree) do. Even if we accept that crows or other creatures have a similar link (itself debatable) it still would link math to dna found on our planet. My suspicion is that what we identify as math is a manifestation of relations, sequences or outcomes of dna, more easily observable in human self-reflection and sense (which is why I mentioned the shells we see in the form approximating the golden ratio spiral).
In essence my suspicion is that math is tied to specific dna-to-conscious animal logistics, and serves as a kind of interface between the deep mind and consciousness, parts of which are occasionally brought up and examined more rigorously. (humans being the species which is more apt to self-reflection, makes us likely the main one here to be conscious of math concepts). I am not of the view that math is cosmic. Approaching this philosophically, it basically connotes that the external world is not mathematical, but because human examination of phenomena in scientific manner presupposes use of the human mind it inevitably is examined through math. One could hypothesize the existence of some other field, non-human, which is equally applicable to the study of the cosmos, and possibly some intelligent species of alien uses that, with compatibility with math being probably non existent.
Thanks for the reply. I think that it does matter, because if math is indeed anthropic then it should follow that humans are in effect bringing to light parts of our own mental world. It isn’t a discovery of principles of the cosmos, but of how any principles (to the degree they exist in parts of the cosmos) are translated by our mentality. I do find it a little poetic, in that if true it is a bit like using parts of yourself so as to “move” about, and special kind of “movement” requires special knowledge of something still only human.
To use another common metaphor: people who are born blind have no sense of how the world looks. They do come up with theories. To a degree those theories, coupled with sensory routines (counting steps to known routes, hearing and noticing smells) provide a personal model of some environment, translated in their own way. Yet the actual phenomenon, the visible world, is not available. Likewise, it seems that math is not part of anything external, and is an own, human tool, composed of particularly human ingredients and enough to model something of the world that it may allow quite complicated movement through it (including space travel).
The thing-in-itself indeed ties somewhat more clearly to the HPL mythos beings, in that they are (by majority; or at least the major ones in the pantheon) supposed to not be three-dimensional in the first place. The thing-in-itself is the object without having to be rendered by any specific observer’s point of view.
While in (most) philosophy one doesn’t examine a topic which is able to cause anxiety, the notions themselves do negate a possible anxiety which would be caused by any examination, in my view. Again, even the notion of the thing-in-itself is formulated as a singular point in a plane: you cannot analyze it to anything, because by definition it connotes impossibility to analyze or attribute qualities to it. It exists only as an idea of difference.
To use a simple example (not for you, who obviously are familiar with the notion), and to tie this to Parmenides (and Plato) which I mentioned in passing in my article:
While a desk gets picked up as something in 3D space, with form, size and other qualities, theoretically one can assume that the same object (desk) still would exist as something, even if its observer had no ability to sense space, position, movement or the other core qualities humans pick up with the senses. So the desk, assuming it exists for any observer regardless of what abilities that observer has, will have some unknown qualities that aren’t dependent on observation; in this sense it is a thing as it is, a thing-in-itself, not to be known and distinct from any view we have of it.
Useful to note that while Kant made the term more popular, the thing-in-itself was already a known term in Plato’s time and is mentioned frequently (eg) in the dialogue between Socrates and Parmenides.