Geometry (a useful fiction)

[Nicomedes]

Geometry doesn't exist in an objective sense, as in, there are spheres, pyramids, cubes and so on out there, nor in a, transcendental sense, if you will, like Plato's forms are supposed to exist.
There are no cubes out there, no one has ever seen a cube, or even anything resembling a cube, nor is anyone ever likely to see one.
We can't draw one, either, not even with a computer.
A cube shape isn't anymore special than an 'amorphic'' shape.

What a cube is, is a concept that exists solely in the mind, a concept given to us by geometricians.
We are able to create and process this concept, because of our human cognition.
Some 'objects' out there may resemble this idea of a cube in our minds more than other objects, but that is all, they're not cubes.
As cube like as an object is, it could always be infinitely more or less cube like.
From the POV of a universe that was significantly more sphere like, planet earth would resemble a cube, more than a sphere.
Furthermore, a cube is a concept, a concept is not a 'thing' that exists out there, concepts are a grid we impose upon a dynamic and ephemeral world, which has features but no borders.
Concepts can be useful for orienting ourselves in this dynamic world, and they can be useful for the purposes of communication, but they're unreal, or rather they're subjective, they are imaginary.

If we encounter extraterrestrials, with radically differing neurology than us, but with equal or superior processing power, that evolved in a radically different environment, we shouldn't be surprised to find them playing with concepts that'll confound us, baffle the best and brightest, we may never be able to make heads or tails of them, but they'll be perfectly sensible to them.
There's nothing necessarily universal about our human concepts.
There's nothing necessarily universal about anything, period.
Anything's possible, but not everything's probable, some things are experientially more probable than others.

So there's nothing more objective about geometry than say, poetry, or Han Solo from star wars, we made it up, and we may be able to come up with something more useful, or else do away with it altogether, it's up to us, as a collective and as individuals.

[Nicomedes]

A triangle is thought to be the simplest straight lined, symmetrical shape we can see, draw or imagine.
Thing is, not only has no one ever seen or drawn an objective, that is, a physical triangle, but it's doubtful we're capable of imagining one either.
We can't see one or draw one in nature, because whatever we see or draw, will have 'imperfections'.
That is to say, nothing is completely simple, straight and symmetrical in nature, things only appear to be symmetrical, straight and simple at first glance, upon closer inspection and reflection, we realize they're anything but.
It's doubtful we can imagine one either, because our imaginations are imprecise, because our brains are imprecise.
Can we even conceive of one?
Well, if we can't, then what is it that we're talking about, I suppose we can conceive of one, or maybe our conception of precision is imprecise, too.
So the whole thing becomes questionable, we certainly can't see or draw a triangle, we might not even be able to imagine one, or conceive of one either...which seems paradoxical, hmmm?

What's so special about that which is simple, straight and symmetrical?
Are these qualities, which don't exist absolutely in nature and possibly even our imaginations and conceptions, intrinsically preferable, or real, in some transcendental sense?
No, they are not, humans prefer things like triangles, or what passes for them, simply because they're easier to mentally digest, to wrap our heads around, that which is more curved, asymmetrical and complicated, is not.
So you see, we prefer them, in some senses, not in all, because they're easier to comprehend.
But if the world was made up of pyramids, cubes and so on, why it wouldn't be the world, all the things that we love and cherish, would vanish, so in that sense we don't prefer them.
Is there anything more transcendental, or universal, about a triangle or a square, then say a tree like shape, or a snake like shape, an organic shape we'd find in nature?
I don't see how.

All triangles have three sides, and three points, right?
Wrong, triangles don't exist, they are figments of our imagination at best, at worst, they're mere noise produced by human vocal cords, meaningless gibberish, there are no sides in nature, or points.
As 3 sided and 3 pointed as a thing could be, it could always conceivably be infinitely more 3 sided and 3 pointed.
So at the very best it could be said, a triangle like shape is more 3 sided and 3 pointed, from our vantage point, than a more contrary like shape.

What is a shape anyway, are there any shapes in nature?
It's human nature to abstract qualities from other qualities...in fact, there are no qualities in nature, nature is a blur, a haze.
No shape without matter and energy has ever been apprehended, and for that matter no matter without energy or energy without matter has.
Energy seems to imply matter and matter shape, it's really one thing, we try to compartmentalize this thing, but much is lost in this process.
Even saying it's one thing is wrongheaded, nature is both one and many, it is everything you can say about it and nothing you can say, in actuality, so you see, whatever we can utter about it, is at best, relative, not what it is or isn't, but these thoughts and utterances serve as bread crumbs, or guiding posts, to make our way through what would otherwise be a fog, garble or bungle, it's all very relative and imprecise.

The mind has limited processing power, so it can't swallow nature whole, it must break it down into bits and pieces, and that is what concepts and generalizations are, and language.
We can psychically consume nature and regurgitate it to others more holistically, that is what we call intuition, and nonverbal, nonmathematical communication, like gesturing, singing and dancing.
Both these forms of comprehension and communication seem to have their advantages and disadvantages.

So in conclusion, not only can we not see, draw, or even imagine or conceive perhaps, of a triangle, or a square, or a pentagon and so on, but even the broader concept these things are all a part of, shape, and size and so on, are suspect, all concepts are suspect, they're not what nature is, you could even say they're inferior to it (if they were to be actualized), not superior.
So from particulars, triangles and so on, we come to the general, what it means to conceive, and its antithesis, existence.
Existence is absolute, but it isn't absolutely this or that, this or that is relative.
Even existence and nonexistence are part and parcel, all dualistic, and monistic and pluralistic conceptions are dissolved when we really see and hear things, as they are, and not as we imagine them to be.

There is a kind of pure, or purer awareness of things as they are, without labeling them, that's an important component of consciousness, to see things as they really, truly are, without comparing, contrasting, speculating, or drawing borders.
Are humans more aware of things both as they were, could, should, would, probably will be, and as they are than other species, or when our minds become cluttered with labels, do we lose some capacity to be grounded in the here, now?
I'm thinking the latter.
So human consciousness kind of exists on a spectrum, from pure awareness, or purer, since nothing is actually absolutely anything, to filtered or crystalized awareness.
Somewhere in between perhaps, or perhaps existing parallel to simpler thoughts like language and mathematics, is our intuition, which has its own concepts, and language, a dark and mysterious language, that the more refined mind can't fully grasp, and vice versa.

It's in our nature to put things into boxes, our cities are just a series of wooden, stone, concrete and glass boxes, and our minds are full of boxes too, but nature has no borders, or at least its borders are substantially more imprecise.
I guess if I'm making an overall point here, it's not to conflate the container with its contents.
As our natural intellect is nurtured to become increasingly refined, and sophisticated, we just might lose something invaluable in the process.

[Obvious Leo]

Nicomedes. As a philosopher of physics I completely agree with what you're saying about the ontological status of mere mathematical abstractions but I'm struggling to see what point you're trying to make. Is there some conclusion hidden in your message which can be drawn about the nature of physical reality or are your fatuous statements of the bloody obvious nothing more than that.

[Hobbes' Choice]

Geometry doesn't exist in an objective sense, as in, there are spheres, pyramids, cubes and so on out there, nor in a, transcendental sense, if you will, like Plato's forms are supposed to exist.

Presumable you accept they exist in some way?
In an Ideal way, maybe?

Such things are analytically true, so must have a virtual existence.

[Hobbes' Choice]

Nicomedes. As a philosopher of physics I completely agree with what you're saying about the ontological status of mere mathematical abstractions but I'm struggling to see what point you're trying to make. Is there some conclusion hidden in your message which can be drawn about the nature of physical reality or are your fatuous statements of the bloody obvious nothing more than that.

What he is saying is a thing not recognised by the some of the most important people that need to know this: namely mathematicians. Some mathematical philosophers think that the Universe is a thing "written in the language of Maths" (Marcus DeSotoi), for example.

[Obvious Leo]

Nicomedes. As a philosopher of physics I completely agree with what you're saying about the ontological status of mere mathematical abstractions but I'm struggling to see what point you're trying to make. Is there some conclusion hidden in your message which can be drawn about the nature of physical reality or are your fatuous statements of the bloody obvious nothing more than that.

What he is saying is a thing not recognised by the some of the most important people that need to know this: namely mathematicians. Some mathematical philosophers think that the Universe is a thing "written in the language of Maths" (Marcus DeSotoi), for example.

You're quite right, Hobbes. In fact it remains the prevailing view in physics that the universe can only be understood in the language of mathematics, a statement of such sublime absurdity that any philosopher who buys it should reach for his hemlock without delay.

[Hobbes' Choice]

Nicomedes. As a philosopher of physics I completely agree with what you're saying about the ontological status of mere mathematical abstractions but I'm struggling to see what point you're trying to make. Is there some conclusion hidden in your message which can be drawn about the nature of physical reality or are your fatuous statements of the bloody obvious nothing more than that.

What he is saying is a thing not recognised by the some of the most important people that need to know this: namely mathematicians. Some mathematical philosophers think that the Universe is a thing "written in the language of Maths" (Marcus DeSotoi), for example.

You're quite right, Hobbes. In fact it remains the prevailing view in physics that the universe can only be understood in the language of mathematics, a statement of such sublime absurdity that any philosopher who buys it should reach for his hemlock without delay.

Agreed. Mistaking the model for reality, they might as well shut themselves in a box and upload themselves into a "matrix' computer.

[Obvious Leo]

Mistaking the model for reality,

I call it mistaking the map for the territory and as I see it physics has fallen for this trap since Newton. However the model-building methodology has a far more ancient pedigree than this, dating all the way back to Ptolemy. Ptolemy set the standard for propping up absurd hypotheses with supplementary hypotheses of escalating absurdity but modern physics has elevated this noble tradition into a high art form. We are now offered a mathematical extravaganza of such spectacular virtuosity that even the geeks themselves haven't got a hope in hell of understanding it. The fact that it is riddled with internal contradictions and can be used to define an infinite number of universes other than the one we live in is regarded as irrelevant. The fact that physics makes no sense has never been regarded as anything more than a trivial inconvenience by its own priesthood but philosophers are expected to set a higher benchmark for truth.

[Hobbes' Choice]

Mistaking the model for reality,

I call it mistaking the map for the territory and as I see it physics has fallen for this trap since Newton. However the model-building methodology has a far more ancient pedigree than this, dating all the way back to Ptolemy. Ptolemy set the standard for propping up absurd hypotheses with supplementary hypotheses of escalating absurdity but modern physics has elevated this noble tradition into a high art form. We are now offered a mathematical extravaganza of such spectacular virtuosity that even the geeks themselves haven't got a hope in hell of understanding it. The fact that it is riddled with internal contradictions and can be used to define an infinite number of universes other than the one we live in is regarded as irrelevant. The fact that physics makes no sense has never been regarded as anything more than a trivial inconvenience by its own priesthood but philosophers are expected to set a higher benchmark for truth.

I think we talked about this before. Newton mistook nothing. Hypothesis non fingo.. He was well aware that what he was trying to do was DESCRIBE the phenomena with maths, NOT offer hypotheses.

What is good about the history of science (and ought to be studied by ALL science students) is that it is a list of working models being shown to be wrong, again and again. Ptolemy's model worked perfectly well, and served astrologers' predictions for 100s of years, and helped navigation and time keeping. Copurnicus' system was actually far more complicated, requiring 14 more epicycles to accommodate the Aristotelean circles that the god-botherers thought had to be necessary, and the potential consequences for parallax (making the universe huge) was just too scary.
Nonetheless the various models all work, more or less, and have various other consequences for adopting them. Smart scientists: history savvy scientists know this stuff, and are better equipped from knowing it.

[Obvious Leo]

I think we talked about this before. Newton mistook nothing. Hypothesis non fingo.. He was well aware that what he was trying to do was DESCRIBE the phenomena with maths, NOT offer hypotheses.

I didn't dispute this then and neither do I dispute it now. Newton had a very precise and clear idea about what he believed physics was because he defined the universe as an artefact of the mind of god. In our secular world of today it's not easy for people to fully understand this but Newton quite literally believed that he was modelling an entity which was the figment of a supernatural mind and the significance of this has completely escaped the illuminati of modern physics because in the modern parlance such an entity would be defined as a Virtual Reality. Instead of modelling a real world physics is merely modelling a timeless mathematical representation of a real world because Newton's god was a timeless being.

What is good about the history of science (and ought to be studied by ALL science students) is that it is a list of working models being shown to be wrong, again and again. Ptolemy's model worked perfectly well, and served astrologers' predictions for 100s of years, and helped navigation and time keeping. Copurnicus' system was actually far more complicated, requiring 14 more epicycles to accommodate the Aristotelean circles that the god-botherers thought had to be necessary, and the potential consequences for parallax (making the universe huge) was just too scary.
Nonetheless the various models all work, more or less, and have various other consequences for adopting them. Smart scientists: history savvy scientists know this stuff, and are better equipped from knowing it.

I couldn't agree more. Every scientific theory in the history of human knowledge has eventually been proven WRONG, but modern physics has an even more serious problem. SR, GR and QM, the three pillars of modern physics, are all mutually exclusive and thus all three of them are assumed to be fundamentally wrong. However the spacetime paradigm on which all three of these theories are predicated remains revered as canonical and holy doctrine. Ptolemy would be delighted to discover that his model-building methodology has survived unscathed for two millennia.

[Nicomedes]

Geometry doesn't exist in an objective sense, as in, there are spheres, pyramids, cubes and so on out there, nor in a, transcendental sense, if you will, like Plato's forms are supposed to exist.

Presumable you accept they exist in some way?
In an Ideal way, maybe?

Such things are analytically true, so must have a virtual existence.

They exist in an imaginary, ideal way.
They have no more real, true existence than a unicorn.
Just as the Unicorn has 1 horn, 2 eyes and so on, but doesn't objectively exist, so to does the Triangle have three points, three sides and so on, but doesn't objectively exist.
The Triangle is a more useful ideal than the Unicorn, only because the Horse is always superior at describing some things than the Unicorn, but nothing is superior at describing some things than the Triangle.
Other than that, there's nothing more special about the Triangle than the Unicorn, and there's nothing more special about the Triangle than the Horse, at all, other than it is a simpler, ideal, and it is a property rather than a collective of properties, but that doesn't make it anymore special, real, or whatever, ideal, transcendental, universal and so on.
Neither the Triangle, nor the Horse is real, objective things are at best more and at worse less like them than other objective things, nothing objective is absolutely like or unlike them, and you can't be nearly absolute, infinite, you either are, or you are not, and nothing in this world is, or appears to be.

You might say, the Triangle has three points and so on, because we define it as having three points, and this is called, a deductive as opposed to an inductive claim?
However, the image we get in our head of the Triangle, isn't even perfectly 3 pointed.
Your image is going to slightly (relatively) differ from my image, and as perfectly 3 pointed as your image of a triangle is, it could always be more 3 pointed.

Therefore, to say a triangle, even the ideal Triangle has 3 points, is only approximately true, not absolutely true, because humans can't imagine, perhaps can't even conceive of perfection, because our brains are imperfect, we can only conceive of things being more or less perfect than they are, or some things are more or less like each other than other things are, so the absolute eludes us at every level, not only objectively in the physical world, but subjectively even in our thoughts.
Therefore, there is no ideal Triangle, not in the world, out there, and not in our heads, in here, there is only a more perfect triangle in our heads, than out there.

So you could say, my philosophy does away with metaphysical idealism, in the sense that I'm using idealism here, as much as one could, I'd imagine.
So in other words, what we think of as the Triangle, is in fact, a triangle, my triangle at this point in time, or yours at that point in time, there is no the Triangle, there is only, a triangle, whether it's a triangle in your head, or out of your head, the world of ideals in our heads, is essentially the same as the world of things out of our heads, I'm doing away with a fundamental distinction and division of the two.

[Obvious Leo]

I'm doing away with a fundamental distinction and division of the two.

What you're saying is hardly breaking news in philosophy, Nicomedes, because this is simply Kant 101. My own field is in the philosophy of science, of which the philosophy of mathematics is a significant subset, and most philosophers of science do not share the Platonist perspective of the physicists. The underpinning ideology of physics, inasmuch as physics has such a thing, is logical positivism. This is a chilling doctrine which denies the role of human reason in the conduct of human affairs because it makes no metaphysical distinction between a subjective and an objective reality. If it is possible to model the orderly patterns of organisation in nature by using the tools of mathematics then physics leaps to the unwarranted Platonist assumption that the tools themselves must have some sort of ontological status.

Interestingly the earlier pioneers of 20th century physics, such as Planck, Einstein and Bohr had a far better grounding in metaphysics than those who were to come along later and these guys wanted nothing to do with logical positivism. They knew bloody well that a distinction needed to be maintained between reality and the tools used to model it and the 1927 Solvay conference was entirely devoted to thrashing out what came to be known as the "problem of the observer". This problem has never been resolved although it has since been re-named as the "measurement problem", or even sometimes the "consciousness problem", a label which sails impressively close to the truth. In a nutshell what the observer problem means is that physics is simply unable to model what's going on in the real world because physics can only model observations and an observation is a construct of the human mind. Physics can therefore only model what the physicist THINKS is going on in the real world, a methodology which has led to a century of endless conclusion and tautologous discoveries. We now have as many theories of the universe as there are physicists with the imagination to dream them up.

[Nicomedes]

I'm doing away with a fundamental distinction and division of the two.

What you're saying is hardly breaking news in philosophy, Nicomedes, because this is simply Kant 101. My own field is in the philosophy of science, of which the philosophy of mathematics is a significant subset, and most philosophers of science do not share the Platonist perspective of the physicists. The underpinning ideology of physics, inasmuch as physics has such a thing, is logical positivism. This is a chilling doctrine which denies the role of human reason in the conduct of human affairs because it makes no metaphysical distinction between a subjective and an objective reality. If it is possible to model the orderly patterns of organisation in nature by using the tools of mathematics then physics leaps to the unwarranted Platonist assumption that the tools themselves must have some sort of ontological status.

Interestingly the earlier pioneers of 20th century physics, such as Planck, Einstein and Bohr had a far better grounding in metaphysics than those who were to come along later and these guys wanted nothing to do with logical positivism. They knew bloody well that a distinction needed to be maintained between reality and the tools used to model it and the 1927 Solvay conference was entirely devoted to thrashing out what came to be known as the "problem of the observer". This problem has never been resolved although it has since been re-named as the "measurement problem", or even sometimes the "consciousness problem", a label which sails impressively close to the truth. In a nutshell what the observer problem means is that physics is simply unable to model what's going on in the real world because physics can only model observations and an observation is a construct of the human mind. Physics can therefore only model what the physicist THINKS is going on in the real world, a methodology which has led to a century of endless conclusion and tautologous discoveries. We now have as many theories of the universe as there are physicists with the imagination to dream them up.

It's unfortunate modern physicists have gone down that road.
I'm not at all surprised other thinkers came to the same conclusion about the ontological status of mathematics, in fact, I expected at least a few of them to have done so, just wasn't sure which ones.
Still, each generation of individuals must rediscover these principles in their own way, either on their own, or by reading the classics, as well as debate/discuss them.
And as Hobbes pointed out, modern physicists believe mathematics has some special, transcendental status I'm sure it doesn't deserve, so it's worth mentioning.

[Obvious Leo]

It's unfortunate modern physicists have gone down that road.

They left themselves with no option once they accepted a logical absurdity as a fact of nature. They assumed that because the speed of light was OBSERVED TO BE a constant irrespective of the relative motions of the observer and his observation that the speed of light must therefore actually BE a constant, an assumption which defies human reason. Unfortunately nothing in physics has made a lick of sense ever since because this dereliction of logic led directly to Minkowski's 4D manifold and the representation of time as a spatial dimension, which it is manifestly NOT.

And as Hobbes pointed out, modern physicists believe mathematics has some special, transcendental status I'm sure it doesn't deserve, so it's worth mentioning.

It is very much well worth mentioning because it goes to one of the foundational metaphysical assumptions of physics which is a load of Platonist bullshit and therefore fucking WRONG. It is quite true that reality proceeds in an orderly and causal fashion but it is so very not true that it does so according to a suite of laws which originate from beyond the universe. This was Newton's a priori creationist assumption and modern physics has merely tried to put lipstick on a pig with its extravagant embellishments.

[Nicomedes]

It's unfortunate modern physicists have gone down that road.

They left themselves with no option once they accepted a logical absurdity as a fact of nature. They assumed that because the speed of light was OBSERVED TO BE a constant irrespective of the relative motions of the observer and his observation that the speed of light must therefore actually BE a constant, an assumption which defies human reason. Unfortunately nothing in physics has made a lick of sense ever since because this dereliction of logic led directly to Minkowski's 4D manifold and the representation of time as a spatial dimension, which it is manifestly NOT.

And as Hobbes pointed out, modern physicists believe mathematics has some special, transcendental status I'm sure it doesn't deserve, so it's worth mentioning.

It is very much well worth mentioning because it goes to one of the foundational metaphysical assumptions of physics which is a load of Platonist bullshit and therefore fucking WRONG. It is quite true that reality proceeds in an orderly and causal fashion but it is so very not true that it does so according to a suite of laws which originate from beyond the universe. This was Newton's a priori creationist assumption and modern physics has merely tried to put lipstick on a pig with its extravagant embellishments.

I know what you mean, it's like absolute zero, just because we can't detect any movement with our present observations and instruments, doesn't mean we ought to conclude there is no movement, it just means our current observations and instruments aren't fine enough, in all likelihood.
Though I can't be certain, there's probably always some movement and variability going on, that's the way nature seems to operate.

I believe spatial dimensions are completely arbitrary concepts, though perhaps useful, there is simply a spectrum of movement, and no, I don't think time ought to be considered the 4th dimension.
Time is history, the idea that everything collectively and individually has a past, present and future, and causality, if x and y then z, existence is sequential, a spectrum of sequence.

Life has a way of simplifying complexity, sensory perception is a simplification of the external world, and thought is a further simplification.
Sensations are largely confined to the surface of things, which are further simplified and put together by thought to form a completer picture.
Sensation is narrower than thought in one sense and broader in another, it's only in touch with the present moment, not the past, nor the future, it doesn't compare or contrast, but the present moment is infinitely more vivid and varied than thought can think.
What we call intuition operates somewhere between sensation and thought, I believe, and has concepts and language of its own.
We simplify, simply because the world is infinitely more complicated than the brain can comprehend in its entirety, so it has to process it, refine it, break it down, chew it up so it can be swallowed, digested.
In other words, where we draw the line between or around things, says as much about our collective or individual sensations and thoughts as it does about the external, and internal, for that matter, world (introspection senses the inner world, which is also processed by thought, we can sense and think about our sensations and thoughts).
Dimensions are a way of doing this spatially, so are inches, feet and so on.
Seconds, minutes and so forth are a way of doing this temporally.
Experience is always degrees of subjectivity, or objectivity, it's more or less.

Yeah reality seems orderly, but this can only be grasped so much, and we should be careful not to conflate what's going on internally with what's going on externally, like Plato, and modern physicists seem to be doing, but that being said, there's always going to be some overlap between the two.