I have liked intuitionism from the very moment I first heard about it.
I often entertain the idea that all the patterns we observe are merely things that match our capability of understanding. This could explain the "unreasonable effectiveness of mathematics in the natural sciences".
It may also help to guide us away from the "why is there something rather than nothing" problem. If existence is total chaos, then we as humans could be limited to the hyperplane of our own observable patterns, which fools us into thinking there is some inherent order -- which there isn't. This leaves us with "why is there chaos rather than nothing", so I doubt it's of any help :)
Great ideas to ponder, but rather hard to reason about.
(Edit: To avoid thinking that I'm a crackpot, with "capability of understanding", I am referring to the physical processes that lead to the existence and dynamics of neurons, not to the platonic world of ideas on top of that. If someone could point out how unoriginal or nonsensical this idea is, it would save me from writing a blog post about it.)
To paraphrase Wittgenstein, is it more likely that we “discovered” chess or that we invented it? He suggests all of mathematics should be thought of in this way, as more and more complex ways of stating tautologies.
> fools us into thinking there is some inherent order -- which there isn't.
Bold claim :)
Even while maintaining a willful agnosticism about Platonic realism, it seems clear that the business of doing mathematics - intuitionistic or otherwise - depends on the ability to state and follow unambiguous rules, or else how to establish a proof within some axiomatic system or other?
But if mathematicians have this ability, even as an asymptotic ideal, and are able to make judgments as to when rules are not being followed correctly, mustn't this in turn depend on some pre-existing regularity (i.e. order) in the universe? Ineluctable physical law seems a natural candidate for this order.
In other words, the Cartesian principle extended to two parties?
Cogito sicut tu cogitas, ergo sum sicut structus es: I think as you think (at least for a moment); therefore, I am, at some level, structured as you are (at least for a moment); and therefore, there is order in the universe, at least in the temporary alignment of our structures that enables us to think along these same lines?
(Saying nothing, of course, of whether you "exist." I may be a brain in a vat, and your thoughts may be the emission of an evil demon running a simulation — but that still means that my thoughts and the evil demon's simulation share structure that implies an underlying shared set of computational axioms!)
I noticed that in nature (i.e. in the physical universe) there appears to be no logic. There are not even two things exactly the same, as far as I can tell. So that lead me to believe that "counting" (or abstraction) is not even a property of the universe, but possibly only a human (or animal, or Turing machine) construct. To me, logic only starts to occur when a very complex amalgam of matter comes together [1] to realize a discrete switch. Using these discrete switches, organisms build memory and abstraction mechanisms, start counting, and do mathematics.
So my thesis is that things that are considered to be "basic" by most, such as logic or mathematics, are in fact quite specific systems built on top of chaos. From there, it remains to be proven that all physical laws that we observe are no more than projections of the chaos onto such a system.
Perhaps a metaphor that helps to take on my perspective, is to look at a screen filled with random noise, and then observe some patterns in there. Now replace the screen with an infinite dimensional set of chaos, and then observe a pattern that is our universe. With the added twist that we are part of this chaos, and observing the pattern, possibly in the form of physical laws.
Of course, there are many problems with this theory. What does the chaos reside in? How can there be discernible parts in the chaos? Is time an emergent property inside the chaos? How can it be that the patterns that we observe are so consistent?
However, to me this theory seems more fruitful than merely accepting that we cannot say anything about things that science cannot observe, or that some deity created all this.
[1] With "comes together" I do not refer to a dynamic process, but to the accidental occurrence of stuff in such a shape or form. Obviously, my ridiculous theory asserts a chaos chock full of dimensions, where time and space are but supporting actors.
I don't think you've taken on the full force of the argument that regularity in human activity (such as building systems) requires a source of order for it not to simply dissolve into chaos itself.
> How can it be that the patterns that we observe are so consistent?
How can we claim to discern consistency (or inconsistency) without the ability to follow a rule correctly? And how can we follow a rule without a source of order or regularity in the cosmos? Wouldn't it be like trying to build a the Eiffel tower out of live slugs?
If you insist on an absence of order in the physical universe, the onus is on you to explain how regularity in human activity (required for mathematics of any kind) can be achieved without it.
This is not an argument for Platonic realism, BTW, or against intuitionism, roughly construed as the view that "mathematics is a creation of the mind" as per [1], or in your formulation that 'mathematical abstractions are not part of the physical universe' (if I understand what you're saying). You can perfectly well believe that mathematics is a mental construct and at the same time acknowledge that it's possible to observe regularities and order in the cosmos. If you want to insist that the regularity doesn't come from physical law, then I find it hard to see how you'll escape from some kind of Platonic belief in a non-physical realm that serves as the source of order :)
In your TV screen dots analogy, isn't it usually thought that patterns appear only because of the structured, generative activity of law-observing physical components, specifically the neurons comprising your grey matter?
This argument completely ignores the observer which is bound by the same limits of our processing - indeed they are paired together.
Entering purely theoretical space here: On the timescale of eternity this might be a local pocket of some logical organization but there is no fundamental logic governing everything. Our observation is limited so we can’t perceive chaos, instead evolved to only recognize patterns. Over infinity, pure chaos does not preclude long pockets of what looks like order. What we consider fundamental rules could very well be local phenomenon, which we are a product of.
Of course this purely theoretical - all I’m saying is that intuitism could be true while also math being useful to predict things right now. We could also only exist for an instant and all our memories just construct, but that’s not very useful. It’s more useful to believe in scientific method because what’s repeatable is provable, whereas chaos is by its nature unprovable - which doesn’t make it impossible.
Well, not a possibility I considered, but nothing in the argument depends on the regularity being a permanent feature of the cosmos, just that systematic human endeavours, such as mathematics or indeed meaningful debate, depend on it, so when it goes they go. In that sense, if you wish to consider this conversation meaningful you are kind of ceding the point that for now chaos doesn't, in fact, reign. If you don't consider it meaningful, then why are you having it? :)
Not arguing anything - it's more an interesting thought experiment. This view doesn't change much other than never finding the "true unified theory of everything", which I'm not sure how many people think is truly possible (at least anytime soon) anyway.
It is useful to focus on repeating things, and useless to focus on randomness. But I don't think it's necessarily true that randomness (probably a better word than chaotic since chaotic systems are complex mathematical interactions) doesn't reign. We evolved to take advantage of repeatable things, our sense organs and perception are all focused on things that are repeatable. Our definition of usefulness (what is useful/what isn't) depends on repeatable things. I believe there's a pretty high likelihood that we are blind to anything outside of that, such as true randomness. IE, we literally cannot conceive of true randomness since we are products of an environment that rewarded it.
To your point, I guess this isn't exactly Intuitionism, since Intuitionism says it's a totally human construct, and mathematics has provenly predicted things in nature from purely theoretical models, whereas I just find the part that supposes mathematics isn't a fundamental part of objective reality possible.
Either way, I don't think it changes anything about how we do math or science or anything - how could you even study this? By definition understanding and using things depends on repeatability. If there truly were cracks in it, they by definition couldn't be repeatable. It certainly won't help us get food.
EDIT
> If you don't consider it meaningful, then why are you having it?
I just find it interesting since I've had this thought before and seeing what other people think of it.
Something to consider in the context of "repetition", is that it requires abstraction, and possibly memory. As noted before, I do not see any kind of repetition (identical things, counting) in nature. I think abstraction and memory are both emergent properties from human brains (or machines, brains in other mammals, octopuses, etc.) My pet theory also initially discards "things", because that again requires abstraction.
For reference, my views are somewhat related to "emergentism", "connectionism", and "realism", but I haven't found a school of philosophy that I feel comfortable with.
> how could you even study this?
This is indeed the biggest challenge. I am currently studying this from a conceptual art perspective, because philosophy and science do not seem adequately equipped for this kind of problem.
Thanks again for taking the time for a thoughtful reply. I am aware that I'm using terminology very loosely, and I omit many details that may be required for a full understanding.
With respect to the full force of the argument: I assume that the "regularity" stems from the physical systems that make up our brain. Just as replication through DNA offers some stability in life, the shape of our neurons (and perhaps the dynamics of space-time, and the laws of physics) offer some regularity in the chaotic universe.
In my view, this regularity is but an accidental blip in the totality of existence, but to us, who cannot observe the rest of the chaos, it seems fundamental -- which from the universal context, it isn't.
The biggest problem that I cannot get around is that I somehow assume this chaos exists, and allows for things to exist inside of it. I do not know how to provide arguments for that, other than the negative one that it seems highly unlikely that "there is something rather than nothing". Likeliness, and the fact that I can define these abstract concepts, only make sense in the realm of human thought, so I am sort of stuck in a recursive loop there.
With regards to the second part of your reply, again it is us humans who do the discerning. It is an emergent property of our brain (or possibly of slightly simpler, but still rather complex "discrete switches") that we can discern things. In the underlying universe of total chaos, there is no context, no logic, no measure to discern things.
So, the source of order does arise through physical constructs, that happen to have a certain structure that allows observation. It is humans, mammals, octopuses, computers, that can use this universal form of observation to process input, and then do observation as we know it. So I suppose my idea is some kind of realism, but my reality is nothing more than pure and utter, unbounded chaos. And we live in some corner of that.
The grand claim is that mathematics is nothing more than the result of some self-observing shapes in the chaos that is existence.
Again, I feel sorry for all the readers who try to make sense of all my overloaded concepts. I wish I had the skills to write down my thoughts more rigorously. Or perhaps someone can save me a lot of time [1].
The first link is an article that explains that all electrons are exactly identical, suggesting that there are indeed things in the universe that are exactly the same. However, the second link discusses the one-electron idea by Wheeler, which suggests the exact opposite :)
> There are not even two things exactly the same, as far as I can tell
Aren’t all basic particles defined by the fact that they are exactly the same? And countable things rely on some difference, such as different spatial locations — or else they wouldn’t be countable, they’d just be the same.
While two neutron stars are distinguishable they are also classifiable as a real type of star in a manner that seems to go beyond human perceptual idiosyncrasy.
But I'm a deep Platonist/Pythagorean — so my bias is that "all is number" and the world is made of math. Math is real :)
If the world is made of math, do new physical objects pop into being whenever a mathematician writes down or thinks of a structure or a proof? Or does only some math get to become physical?
In general, your view seems like a definitional issue to me. If you want to call what the world is made of “math”, then what you and I mean by math are two different things, and using the same word to describe them only leads to confusion.
> "mathematics is not a body of propositions representing an abstract sector of reality but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than ludo or chess."
I take the brevity and lack of commitment to a position in your reply as an indication that you're not really willing or able to defend your position. That's fine, it's a complex topic, as the many articles on the SEP linked above attest. But if you want to claim "the world is made of math", then the onus is on you to define what you mean by that. To me, it looks a little incoherent.
Take the brevity as a lack of hubris. The notion that “the world is made of math” is one of the oldest and most influential ideas of all time. If you find Pythagoras, Plato and Newton a little incoherent, that’s not unusual. But the onus doesn’t lie with them (or me). In any case, I remain interested in your ideas!
None of Pythagoras, Plato, or Newton claimed that the “world is made of math”. Also, Aristotle’s philosophy of mathematics is considered an alternative to Plato’s, so trying to seek solace in both at the same time seems inconsistent.
Plato described math as a realm distinct from both the physical world and the world of consciousness. This doesn’t support the idea the “the world is made of math”.
Newton described the world as operating in accordance with the rules of math, but that’s not the same as being “made of math.” Plato’s view is compatible with this: what Frege described as the “third realm”, the realm of abstract objects, can have a relationship with the physical realm without requiring that the latter be “made of” the former.
Aristotle explicitly distinguished between physics and mathematics, saying in his Metaphysics that physics is concerned with things that change, whereas mathematics encompasses things that are eternal, do not change, and are not substances. So Aristotle seems to explicitly reject your view.
As such, I don’t accept your claim that your position is “one of the oldest and most influential ideas of all time.”
> But the onus doesn’t lie with them (or me).
If you make a claim, the onus certainly lies on you to support that claim.
Pythagoras said “all is number.” So, where some claimed that “fire” was the primary constituent of all things and others “earth,” Pythagoreanism held that numbers were the underlying principle. Do you accept this claim?
Newton was a Pythagorean. He even attributed the inverse square law to Pythagoras.
Plato is always hard to pin down, but he describes the immaterial world as crafted by number, prior to the material world.
There are not even two things exactly the same, as far as I can tell.
That is a common definition of identity, two things are the same if all their properties are the same. So by definition there can not be two different things with all their properties the same as this would make them indistinguishable and therefore the same thing. But if you relax this a bit, then for example elementary particles like electrons are - as far as we know - all completely identical up to their position, momentum and spin.
I've seen statistics proposed as the force that makes reality, that would be fundamentally random, coherent. But statistics laws are themselves very strong when numbers get big.
> mustn't this in turn depend on some pre-existing regularity
Consider the set of all things, including the ordered and disordered. Consider the operation of taking subsets of that set. Consider that conscious entities such as us only arise in ordered subsets (for some definition of ordered).
Those conscious entities would see their proximal environment as ordered. They might assume that the only things in the set of all things are those things that are ordered in the same way as the proximal environment from which they arose.
Our universe may be just a subset of a subset. That is, our universe might be one kind of universe that has some apparent quantum-field or relativity-geometry based regularity. There might be some number of universes that share that kind of ordering and perhaps not in all of them conscious entities arise.
It is still an interesting question to ask: why would conscious entities arise within this particular kind of ordered universe? But it no longer remains the question of whether or not regularity is a fundamental property of all possible states of existence. And in fact it leaves open the question as to whether or not some kind of consciousness (perhaps very different from our own) could arise in what would appear to us as chaotic universes.
I spent quite some time thinking along these lines, but then I realized that it is very unlikely to be the case in our universe.
If our world would be an "accidental" subset of the universe, with ordering, then how can it be that this ordering is so consistent? Would it not be more likely that we'd live in a world that has only some order, or varying order depending on one's position in space and time? For example, I would expect a lot more miracles to happen, but every physics experiment turns out to be extremely consistent.
This led me to believe that there is another process at play. My thought experiment now assumes that observation enforces a certain kind of consistency in the laws of physics. That is, the systems that we use to observe something, must by their very existence result in very consistent patterns in the chaos. What this precisely looks like and how it operates is left as an exercise to the reader.
> observation enforces a certain kind of consistency in the laws of physics.
That sounds like a typical chicken-and-egg problem.
> how can it be that this ordering is so consistent?
One thing that I didn't explicitly state is that the universe only needs to seem ordered. You are making an assumption that isn't necessarily founded. 99.9% of the time we aren't checking on the ordered state of the universe. It is the exceedingly rare case that we measure with sufficient granularity to expect to see quantum effect, for example.
> I would expect a lot more miracles to happen
I totally understand this. You might expect a table upon which your keyboard rests to change color as we pass through a chaotic portion of some multi-verse. But that assumes order can't exist at the time-scales of universes.
Imagine it like a picture. The set of all possible pictures at 640x480 is massive but finite. The vast majority of images in that space are like white noise. But you've probably seen millions of images at that resolution that are totally coherent. You don't expect the middle block of some specific image to randomly be a different color. Same with a movie. The set of all sequences of 640x480 images at 30 fps with 1 minute duration is finite. It is full of total chaos. But when you watch a movie you don't expect chaos to ensue at any moment.
If you consider our entire universe like a single image from the set of all images or a movie from the set of all movies, it isn't surprising that it is entirely ordered from beginning to end. It just feels weird because the scale in both time and space is so large in the case of the universe. But given the scale of the entire set, such a large subset having internal consistency isn't totally unreasonable.
> mustn't this in turn depend on some pre-existing regularity (i.e. order) in the universe?
Yes. And such order exists within the observer, the mediators. We are measuring instruments. Scales are bound to the ruler and not to what’s being ruled. So mathematics represents order only in as much as there are people to validate it. Should all rulers be broken and forgotten, then there’s no measure at all. This is the same for those orders not yet established, that is, the future of science. Nevertheless, I do believe there’s a principle which allows order, but it’s not order itself, but a foundation of order, which I believe to be Unit. Unit is not mere duality, because duality implies two, Unit would be more like Cause-Effect, wherein one is the same as the other (either Cause-Cause, or Effect-Effect, doesn’t really matter). This is also different than yin-yang, since each is discrete, and discreetness itself cannot exist prior to Unit. I like to think that all numbers are qualities of Unit, and the whole of mathematical theories are different theories of Unit, so they will be consistent every time Unit is maintained consistently, when something “follows” from what has already “followed”, following some definition of “following”, whatever it may be. It would explain the effectiveness of mathematics in the sense that the whole Universe is Unit out of self-similar Unit. The fact that all of information can be encoded in 0s and 1s is a great illustration of the power of Unit, and the fact that binary streams only makes “sense” upon interpretation is a great illustration of consciousness, which is an expression of Bias. Even if the Universe would change so all of the physical “laws” would mutate, Unit would still persist unchanged. New things would still “follow”. I haven’t come across anyone realizing that a theory of “everything” can exist but be useless, just like the concept of “everything” is useless as a particularity, and theories aim to be particularly applicable, so a theory which really applies to every thing applies to no thing. This would be the utmost conclusion of Gödel‘s incompleteness. How would a theory of absolutely everything be different than an infinitely long ruler without any subdivisions, or even with infinitely many zero-spaced subdivisions? One wouldn’t be able to measure any particular thing with such universal ruler.
Does your "principle which allows order" presume the existence of space and time, and more specifically the ordering of time? I would say that in a universe without time, "cause and effect" have little meaning.
I think I lost your train of thought when you say that numbers are qualities of Unit. Does your universe involve only "Unit", or are there other principles at play as well?
The Peano arithmetic hints at the proposition that numbers are gradations within a unified principle, in this case the principle of “succession”. If you start with nothing (zero) and recursively apply the same quality (succession) you get all integers. So we can rationally assume that all numbers are different qualifications of some primitive. As for time and space, they do not fundamentally exist and they do not configure a necessity within the universe. It takes a being able to record and internally persist events for time to appear. Space is similar, being also a referentiality. In essence, time and space are different framings of the same phenomenon. The length distance between two points is also a temporal ratio between the points. It is just two perceptions, two expediences, not grounded in singular reality. I believe “beings” are Unit juxtaposed over Unit, in the spirit of Wheeler ideas [1]. I don’t think there are fundamental necessities other than Unit. Unit is not causality, I have just used the terms for illustration. If there are other fundamental necessities other than Unit then one would need to explain how they came into being, and it would eventually recurse into Unit. From nucleosynthesis to procreation, it’s Unit all over. The way I grasp it, mathematics is a coloring of Unit, just like for seeing wind one need to sprinkle something over it. It boils down to the ascription of Parts within Wholes. Parts are mere subjections.
The physical world is a persistent system that exhibits highly consistent behaviour. Because the behaviour is consistent we can describe it in a highly consistent formal language, mathematics.
What Plato called forms are just descriptions. We have a description of what a circle is, and anything that matches that description is a circle.
Highly consistent!? Not really. Some things are, but like OP just said, those are the ones we glom onto. But don't mistake some things for every things, there's a whole big wide world out there. We can hardly describe a ripple in a stream let alone why I've had the 5th argument in five weeks about the order I have to fix the kitchen with me wife, yet my intuition told me it was a comin.
So you consistently perceive streams, the world, have a body, a life, a wife, a kitchen with a flaw that has persisted over time, an order in to fix it. Also the world is consistent enough that you could predict that argument in advance. That sounds like an awful lot of consistency :)
Yes, I've already conceded that some things are consistent. Will you concede that we tend to glom onto them or will I interpret your reply where you once again glommed onto them as a concession? ;)
> The physical world is a persistent system that exhibits highly consistent behaviour.
Thats because chemicals shape/influence our personalities and emotions. You'll see the same consistent behaviours in animals as you do in humans, when given the same chemicals.
I often entertain the idea that all the patterns we observe are merely things that match our capability of understanding. This could explain the "unreasonable effectiveness of mathematics in the natural sciences".
I have a similar but somewhat different take on this. The universe comes first, it behaves - for what ever reasons - in the way it does. Than we humans show up and invent logic, a set of rules that is useful to reason about our universe. It either rains or it doesn't makes sense in our universe. But the universe could potentially have been different, for example something like the many-worlds interpretation but where the inhabitants of that universe can experience all the branches. Their logic might say it rains and it doesn't.
Other ideas like objects, properties, space, time, causation or countability might also be influenced by the way our universe works and how we perceive it and they might be far from universal or useful across different possible universes. On top of that we than construct mathematics and explore what all the things are that we can build from those ideas and our laws of logic. It should probably not be especially surprising that we can on the one hand construct things that are not realized in our universe and on the other hand find structures that are useful for describing and understanding our universe.
I suspect something opposite, that math comes before the universe because the universe needs math but math doesn't need the universe. Math only calls for internal consistency which radically does not depend upon the universe. It describe perfectly self-consistent realities that do not exist. Math could model say for instance a world of continuous matter as opposed to our mostly empty matter for instance. We have calculated numbers larger than the universe itself could render after all.
I beg to differ. Math typically requires abstract thought, symbols, and humans to produce and enjoy it. Especially the latter is quite a dependency.
We could reduce the requirements down to an implementation of a Turing machine, or something similar. (For the argument I simply ignore whether the machine is conscious -- that seems irrelevant in this context.)
That still requires some kind of discrete switch, which may seem fairly minimal to a human observer, but in reality consists of tens of thousands of atoms to operate. Atoms used to be simple, but turn out to be quite complex as well.
Representing, say, a circle in a fairly minimal system such as this would probably require the cooperation of millions of atoms.
If universe was total chaos, then we would observe it, because absence of chaos isn't required by anthropic principle, but instead we observe universe to have at most pseudorandom processes, therefore universe isn't total chaos.
My point is that we as humans can observe only a (highly structured) part of the chaos. I am merely assuming a chaotic universe, because that seems more reasonable than an empty universe or an ordered universe.
(Yes I know that one cannot use "reasonable" as an argument for a context in which human arguments do not apply. The entire thing is a thought experiment, nothing more.)
I get the appeal, it's a minimalism thing. The thinking mind makes up patterns and checks them against each other, there is no ultimate reality, blah blah blah. Besides, a mathematical ground truth would be a kind of transcendence, in that it's prior to human thought, which makes it uncomfortably close to ideas of God.
Still, I've come around basically to mathematical platonism. The structure is out there, we just happen to be smart enough to tease some of it out.
I have two arguments for this. The first is the very existence of long-standing problems, and their eventual resolution either way. For centuries we were able to wonder whether Fermat's last "theorem" (which was really a conjecture at the time) was actually true, and eventually Wiles came around with an extremely complicated proof and it was settled. And we do believe that math/logic is consistent enough that someone else couldn't just have followed a different train of thought and come up with a proof of the opposite. How does a strict intuitionist account for this kind of situation?
The second, and possibly deeper argument, has to do with structural equivalences. I've been out of the field for decades, but I know that a standard trick in academic math is to develop structural equivalences between disparate fields. You want to prove something in an area of math, but it's hard, so you prove that the whole structure of that subfield has a one-to-one correspondence with the structure of another subfield, and then prove the corresponding theorem in the other subfield, which happens to be easier (see: analytic number theory). Again, this sounds like exploring an existing territory, not like arbitrarily building thought-bridges here and there. The bridges are where they are, and if you try to build one where reality didn't put it, your proof will get nowhere.
An even stronger form of this is that, in advanced mathematics, all kinds of notions of universality appear all the time. One of the most famous is probably computability theory. Just using a few basic symbols (say, integers, first order logic and some additive operations), you get theories of varying power. But as soon as you hit a certain level of richness, bang, all of a sudden, you've hit computability. Your theory is rich enough to embed a Turing machine, and therefore is exactly as rich and expressive as any other computable - even if one is based on numbers and multiplication, and the other on graphs or some such other weird thing.
Universality shows up in lots of places. I'm too far out of the field to remember them, but it starts with the very integer numbers - there are plenty of ways to formalize their initial construction, but the eventual result is exactly the same.
At this point my general thinking is that the bulk of the structure is pre-given. I have no special conjecture to make about how that comes to be - it's all a logical structure, prior to matter or thought, so unlike physics, it's not like there could be another universe out there with different basic mathematics.
The system began at chaos and is seeking order, though the existence of inherently unpredictable quantum effects means that there's plenty of chaos to go around.
I often entertain the idea that all the patterns we observe are merely things that match our capability of understanding. This could explain the "unreasonable effectiveness of mathematics in the natural sciences".
It may also help to guide us away from the "why is there something rather than nothing" problem. If existence is total chaos, then we as humans could be limited to the hyperplane of our own observable patterns, which fools us into thinking there is some inherent order -- which there isn't. This leaves us with "why is there chaos rather than nothing", so I doubt it's of any help :)
Great ideas to ponder, but rather hard to reason about.
(Edit: To avoid thinking that I'm a crackpot, with "capability of understanding", I am referring to the physical processes that lead to the existence and dynamics of neurons, not to the platonic world of ideas on top of that. If someone could point out how unoriginal or nonsensical this idea is, it would save me from writing a blog post about it.)