Sections 60 (last updated 03.29.2021)
-the Impartiality of the nature of consciousness, ultimate observer
The universal nature of consciousness is not the same as its particular nature. In the particular nature it remains passive and impartial from the nature of the whole and this maintains the particular forms that it encompasses. For example, she does not demand attention because she is beautiful, but because she demands attention she took on the properties of beauty. Yet this finitude itself possess the universal nature, which is the actively all things, the rational relation of differences. And in this universal way consciousness is impartial and external from the particular thing, yet in the particular thing it is impartial to the whole of the relation. If the particular consciousness is somehow given universal control than everything would collapse as parts of its very universally logical relation, it’s determination would be what is deemed universal and the fact that it can be detested over wise, is part of the objective beyond merely making it subjective.
in the particular lies the potential, which is the potential for the otherwise, and so it cannot both be and not be at once, in order for this contradiction to be maintained not to even eliminate itself because the inverse is that there is no relation, which is contradictory by the fact that it is itself the something in relation to a nothing, involves the universal consciousness impartial from the particular because in the universal something must “be” even though that being is the relation between what is and what is not, the universal is that, even “that” must still be. The universal therefore involves what is and what is not as distinct and in relation, whereas the particular involves what is not as either distinct or in relation.
The edge is at the same time whole with the centre.
The edge is where the centre conceives the object of this relation. The relation between the edge and the centre is the conception where the object contains the edge and the centre. For example, the perception that the earth is spherical is taken from outside of it such that the conception contains the circumference against the area. A conception positioned inside the earth cannot derive it as spherical. The conception of edge and centre must contain the whole of that relation. (Add here Allan watts, what is behind your eyes)
Consciousness is the center as the middle point, the point being the duration of spectrum.
In our explanation that the center of a sphere is any point on it, a further addition must be made to this ideas demonstrating the nature of consciousness. Stating that the centre of the sphere is any point on it does not explain how consciousness is the central point on the sphere that is any point. In the latter case what consciousness means as the centre point of a sphere is that it is the point from which the sphere possess a centre point. Consciousness is therefore the “middle point” of the sphere which explains the form of consciousness is the activity that remains moderate between extremes, that it being the moderate just simply illicit that the alteration between the extreme points is the factor that they extremes. Diameter of sphere
In Buddhism this meditative practice is called “satori”. In Arabic the word “satter”, which is also found informally in English, means gages or board line in the middle distinguishing two aspects from each other. Like the town gate separating the city from the wilderness, cloths separating the naked body from the gaze etc. Satter and satori are rooted in each other with the latter meaning the mental state of consciousness that mediates in the middle of two aspects of the relation. Satter also meaning spectrum with the emphasis on the middle, is explained by satori as the conscious state aware of its external happenings in conjunction with its internal operations such that the distinction is the same spectrum.
If for example we enter a meditative state and simply develop the consciousness that watches the natural functioning of its own mechanism and the environment as the same activity, breathing, hearing etc. The meditative state provides an approximate experience of consciousness as centre point. For example in a closed eye position, the focused consciousness conceiving say breathing and sound, it is placed between the darkness that the eyelids provides and the darkness behind the perception of the eyes. This particular example shows that the meditative state, in order to be detached from the breathing, hearing and so on, so as to be aware of them, stands in a middle point where these happenings including the shutting of the eyelids and the darkness behind the eyes, are occurring spherically around. If you turn your focus to the darkness alone, or your breathing alone, the focused consciousness becomes that which it is focused on and everything else happening around what is focused on, if your breathing, the darkness, the sound etc all operate around the activity of breathing. (Alan watts watch meditation)
Vision operates in this manner. When you look at something you see the object of focus as the middle point between the farthest point of vision and the nearest point of vision. When percpetions picks out an object the objects have behind it some farther plan and a closer plan, of which if you were to focus on that farther point it would also have behind it some farther plan. Vision is te focus on the middle point of the perception. The individual mind which is the point from which perception discloses the perceptual sphere is the circumferences of the perceptual sphere.
let dc be the observation disclosing the perception, circumference of the circle, and r be the line of vision toward the object of focus, that is the center. The point is that vision is always the radius toward a center point of which the diameter is the nearest and farthest of a given point on the circumference, that point being the individual disclosing the entire perception.
uncertainty inherent principle in the thing
Horizon
Where vision ends on a plain and where the plain continues beyond that vision constitutes a dimensional limit. We assume that when we look out into the distance and see a horizon, we assume that the limit of that plain is the extent of vision otherwise the plain is a continuity towards an indefinite point. So that if vision was perfect someone could still see further and further as far as the horizon continues. While this is somewhat true given the latitude of the plain, an important limit of a plain is overlooked and this is what modern “flat earthers” erroneously intuit.
The limit of a plain is fundamentally curvature so that even if vision was perfect and can see the full extent of a plain, as part of that plain is its fundamental limit, which so being curved, motion is required to maintain a flat surface, a motion that follows the curvature of the plain, and in that motion along the plain, there is the abstraction of a latitude. The flat earthers forget that even a flatter surface like a disk still has a very acute curvature at the edge. This means that anything with density is curved.
A disk has a vending acute angle approaching a limit of 0.
Desert from a distance
If you look at an object from a long enough distance, it is not clear whether it is moving towards or away from the observer. This ambiguity is defined best by the “mirage phenomenon”
Mirage
The phenomenon of mirage
“an optical phenomenon, especially in the desert or at sea, by which the image of some object appears displaced above, below, or to one side of its true position as a result of spatial variations of the index of refraction of air.”
In order for a “mirage” to be an optical phenomenon, it first has to be a phenomenon because optics are sense organs that do not independently exists without the phenomenon. Perception is always receptive to some external phenomena which it is depicting, either inaccurately or accurately. The question of accuracy does not change the question about the true nature of the phenomenon that the sense percept is receiving. In other words, something may “appear” like an illusion from a certain distance in space away from the observer, but also, that distance “away” itself may contribute to the nature of reality that object is operating in that level. In other words, what your seeing in a “mirage” is not an “illusion” or some inaccuracy of the sense object, but rather your brain is witnessing the limits of the information it can process when two separate dimensions meet at a focal point in space. In other words, the limits of human observation is the distance where the 2-dimensional plain field intersects with the 3-dimensional. The 3rd dimension begins when depth towards the observer is received by the mind.
“optical illusion caused by atmospheric conditions, especially the appearance of a sheet of water in a desert or on a hot road caused by the refraction of light from the sky by heated air.”
“Mirages happen when the ground is very hot and the air is cool. The hot ground warms a layer of air just above the ground. When the light moves through the cold air and into the layer of hot air it is refracted (bent). A layer of very warm air near the ground refracts the light from the sky nearly into a U-shaped bend.”
“But, in fact, a mirage is not an illusion. … Our atmosphere can cause some distant images to undergo a similar effect called ‘refraction. Close to the ground, refraction is strongly affected by variations in temperature. If the temperature goes up as you get higher above the ground, you might see what’s known as a ‘superior mirage.’ That means an object looks higher above the ground than it really is. But if the temperature goes down as you go up in the atmosphere, you might get an inferior mirage – an object looks closer to the ground than it really is.
When you see a highway mirage – it looks like water on the road ahead of you – you’re seeing an inferior mirage. That’s because an asphalt surface is much hotter than the air above it, as you’ll realize if you try to walk across it barefoot. The very hot road and the cooler air above creates a mirage. The image of something higher up is refracted downward onto a road surface – to create what looks like a pool of water on the road ahead. This mirage is really an image of blue sky on the horizon.”
These refractions or displacement of images are the capturing of one of the many potential moments in time of a thing, water does this because it is a conductor, and it can transmit a potential moment in time abstracted from an object and reflect it outside of that object, we think this is what mirrors do, mirrors captures exactly the the light reflection from the object, so you get an exact image reflected outside of the object conducted by the piece of matter the mirror is, but when there is enough distance and therefore enough time between the object and the conductor that can reflect an image of the object for the observer, we see that the reflection is less exact and certain, the images appears to have different locations, displaced in position, and appear wanky for the eyes, as if something else is there other than the object. We have to ask, if it is a reflection, why is it not an exact reflection like mirrors do?
Between any two conceptions of different things, or in other words, between two different moments in time, is a voice space containing all possibilities of that object, and all possibilities generally beyond that object.
Laws of motion as the mechanics of intention
In mathematics and physics the intention and the action or the reason why something happens and how it happens are never separate questions. the concept of gravity describes the physical mechanics of intent. In physics an “inertial frame of reference” is when there are no objects around to exert forces. Inertia however itself must be a form of motion, even more specifically. In physics inertia possess velocity because it is the continued state of uniform motion or rest unless otherwise changed.
Even though inertia is the condition of no object around to exert force does not mean that inertia itself is no force: inertia as an unchanging state of motion is a vector because remaining in one constant state, whether at rest or active, is an energy state . Or that in order to be nothing, you have to remain nothing, and the very activity of remaining as the same thing means that what is remaining is constantly changing into the same object. The object is constantly changing to remain the same. The state of Nothing must be constantly changing itself into nothing and that is how it can remain nothing and also this is its direction. (Aristotle, rest must also come to be that which makes it at rest)
(Maybe add before Whitehead evolution, only change is progress, the qualitative of this)
The nature of change is introduced by the notion of a “Vector”, which is defined as “a quantity having direction and therefore having magnitude and components.” Change is still itself a constant state of motion. The first law of motion states that something at rest stays at rest and something in motion stays in motion unless acted upon. The implications of this is that inertia and motion are not opposed, and that the “acted upon” factor captures the moment where no motion and uniform motion meet in an instantaneous conception of them, point of change. This is shown by the second law which explains how the velocity of an object changes when it is subjected to a different force. Bear in mind that change is not necessarily brought about from an external source as many people seem to confuse the first law of motion as suggesting, but that the difference brought about by a change is also inherent in the same phenomena, that no change and the same change have their moment of distinction when the movement is directed in a definite manner and is recognizably distinguished from the state before.
Newtons laws are limited when the acting upon something to bring about change is assumed only as externally derived instead of presupposing that the change is found in the moment the stable inertial condition is conceived as such. When focusing on a plain for example, the plain as it appears does not appear like a circle, but when the focus conceives itself as focusing on a plain, then the conception of the plain is invariably circular because it discloses every point at the extent of the plain
when you look around everywhere in a plain, that motion is invariably circular towards an infinite point, like a warp pool.
The moment of change from the plain to a circle is found invariably in the conception of a plain alone distinct from a circle and circle alone distinct from a circle, we only exclude the other from the other because these constitutes abstractions that makes it the only way where you can have something as seen in itself not convolute by an other. Change brought about by differences in force is inherent in inertia itself. This means that the insistence on no activity, is still itself an activity of change because that is equally what it means to remain in the same direction.
Radius means the distance between the change and its original cause. Radius seems to suggest that the change is prior to the original cause, for example when you draw a circle, you can either first draw the circumference then the line cutting across it to the centre, or draw the line reaching from the central point into the circumference of the circle. Either method seems to say that any original cause of an activity first requires the notion of change to bring it about.
Acceleration is the vector made up out of the derivatives of change. In the basic sense, between no change and the change to remain inertia.
which means the components are equal to the second derivative state of coordinates with respect to time.
The first derivative is velocity, the second is acceleration. The relationship between velocity and acceleration is explained by the famous third law, which is for every action there is an equal opposite reaction. In this case, if we apply velocity to inertia and say that the direction of nothing is unchanging so as to remain the same, then the opposite force against this, is the direction of change, which is being, is to always remain different from nothing. And so being is constantly changing into differences only because remaining unchanged is this consistency maintained by that change.
In order for being to remain something different from nothing and that is how it remains itself, nothing must remain itself as that which being is the difference from. This very distinction sets off acceleration, which occurs when the equality is same to the derivative of change; in other words, what is always changing is correspondingly remaining the same insofar as its change is to maintain the same state.
The direction of velocity is therefore necessarily acceleration because to go in one direction requires the activity of constantly changing into that same direction, but in order to remain this way, each time something changes to remain the same, it remaining the same is added with the constant derivatives brought from the change. Change therefore supposes speed because the rate at which something happens or is done assumes measure between each time differences occur in the same activity.
Inertia constitutes one of the first principles of order. Inertia describes the mechanics of focus necessary for thinking activity. Focus is basically the mode of reason that allows for change in thinking to occur while thought remains itself. In other words it is the state of reason where activities of change occur while all conforming to the same principles. If we take the term focus across all disciplines, we have the same idea.
In geology focus is the point of origin of an earthquake. In medicine, focus is the principle site of infection or other disease. In linguistic, focus is the part of the sentence given prominence either by emphasis or contrast. In perception, focus is the quality of the sense producing clear visual definition by picking out focal points, that is, points of interest. The notion of focus brings is to the nature of gravity. Gravity is fundamental force of focus.
F=ma
The x component of force is equal to the mass of the object times the x component of acceleration. The word component is important here because any change of motion, even inertia, is a component.
Mass is conserved only when it is exchanged
Galileo gravity 11:00
Force is proportional to mass
The rule of gravity is that the force itself is proportional to the mass, this characterizes gravity entirely. The mass of thought is proportional to the force of its intent. The mass is not however proportional to its motion, for example, cannon ball and feather fall in same way in a vacuum. This means that mass does not determine motion but that motion determines mass.
In our ordinary language the meaning or words connect to each other such that they portray an essential fact. Reason in the sense of aim and goal, is by definition what matters, in the sense of having importance and significance.
A reason is to matter. Having a reason is what matters and this alone constitutes the physicality of form. reason just like matter, they both have the meaning of “a reason” and “that matters”, in fact what is a reason is what matters, matter is reason).
For something to be a “reason” means that it be felt objectively as a phenomena of experience
(Video “Einstein’s general theory of relativity lecture 11 before 10 min in your likes)
In mathematics, “pie” or 3.14… means the infinity of particulars. It is the equation of difference or the abstraction of diversity. the sequence of particularization.
This whole thing about physics should be used to show that from mind are created natural objects.
Innumerable
The term “innumerable” means both too many quantities to count and something without a number. A number is a measure in terms of “unit” that defines a relation of distinct variables that are themselves units of measure. A unit is a measure of itself, or itself is a unit of variables that are units that group together variables of units. A “unit” is therefore defined as a single and complete thing that at the same time forms a part of a more greater and complex system than itself. For example, 2 is a unit of two units of 1,i.e, 1 unit + 1 unit, but 2 is also a unit part of 4, which is composed of 2 units of 2 and 4 units of 1, and 1 unit of 3, and what other combination may find.
The idea is that the process is cumulative, a unit can be a measure of an infinite variables that are themselves units. The idea of innumerable as “without a number” is said to be a result of “too many numbers”, that the limitation in having too much quantities results in them lacking a number, when there is too much to count that lacks a number. However it is entirely possible for a quantity to have a number even with the limitation of not being able to count it, just because we did not count to a million does not mean there is no millionth of a number.
the idea here is not whether something is not there because we lack knowledge of it, but rather there seems to be an inherent limitation or an uncertainty principle built into the very nature of quantity itself. In arithmetic we see this in the capacity to count to infinity, or there be an innumerable amount of numbers without end. In geometry we see more of the limitation we are talking about in the fact that any shape and figure has within it the incapacity to be fully observed, in other words, no figure is seen fully from a certain position it occupies, or that any shape is only partially viewed. In 1 dimensional view, a point is only a partial view of a line, it is face front view of a line
A line on the other hand is a vector of a point, “direction” of the vector is from its tail to its head, and this develops length. The specific geometric definition of position is the way shape is, or the orientation of the figure, whether it has 4 equal sides, or involves a curve etc., unlike the other more general mathematical definition of position which means the space occupied by an object with respect to another object. If two different positions in space is occupied by two different components of the same figure, or from the same figure we abstract two distinct parts and give them different positions, than any single figure, like a point, line, circle, square etc., are just abstracted units from a more general shape, or in other words, they are partial view of a more general figure.
However when we say that a line belongs to a different figure like a square, it is not a component limited to the figure it is derived from, but changing its orientation derives a more complicated figure, that a line is also universal to all figures, therefore a line belonging as the partial view of another figure, means that it is not a single figure it belongs to but it belongs to figures in general, it belongs to an innumerable amount of figures. A straight line is a partial view of a curve or an angle in a 2 dimensional figure. When a shape changes, when you turn a shape there is always a new part that is seen but another part goes out of view, there is always a “blind-spot”. You can have a shape, change it, and maintain both the old and the new shape, and do that over and over again, and eventually, the shapes will overlap each other to such a a degree where there is a convulsion if angles, sides, etc.,
This is most explicitly in a sphere because ultimately a sphere is simply a circle in motion because if you just look at a still conception of a sphere, it just simply looks like a circle, the only way to discern it is a sphere is when it rotates and then you can discern a tilt in position at the axis, which in other words means that the curvature is itself curved. The reason why there is always a blind spot built into the very structure of objects is because things are constantly in flux, or in other words, they are always changing. However this change is not happening to the object itself, like a circle is turning into a square, but it is rather the difference in the rage of frame, which is the object moving, that is always happening.
And it is this part that is innumerable, in other words, there is an innumerable amount of possibilities that the object can move and behave, and this is because the very figure of the object itself has this element of uncertainty built in, that there is this gape which the object can infinitely move into, or fill in. And this so called “gap” is not physical space somewhere on the object because the object is put together but also has space around it, within it, etc., space is potentially anywhere in relation to it such that any part of it can move or that the object itself as a whole can move in part, and so it is the motion into that, it is the innumerable possibilities for an object to change its form.
Curved surface is the same distance to the centre as all of its points, means that all the points meet at the same point, and the place from where they come from is equally distant away from their meeting point, which is the centre.
A sphere is ultimately defined by this feature where all the conception of discernible points is tracked to the same single point that they begin equally away from. The back point of the sphere, what is “behind” it, spatially is just more roundness of it continuing, but also is its element of time, it’s movement, that there is rotation, spin comes from the back to the front. The question is where does this rotation come from because a sphere is just a circle with a vector and therefore is in motion.
The rotation of a sphere is the originating point from where the roundness comes from, but we do not think of the rotating as coming from anywhere because the cause of the rotation is said to come from external force, a planet rotates because of gravity or a ball spins because someone kicks it etc, also it is assumed that the sphere as a whole is in motion when it spins, however the whole of it is in motion in a given direction of spin when it is coming from one side to the other, this momentum is derived from the velocity of coming from one direction to the other, say from left to right or right to left. This direction in motion is the unequal distribution that although the whole object is in motion it has a an unequal distribution of motion across its surface and this is how it can move in a specific way, like rotating clock-wise or whatever. This specific direction in motion originates from somewhere.
However this is only discernible from what is directly observed, but that roundness observed ordinates from the rotation which involves the unobserved element, the possibility for it to rotate, because they extend back to an uncertainty point, a blind spot, where there is innumerable amount of quantity, or rather amount of possible ways of being. So that when we look at a static sphere and that part of it that is unseen, is the movement of a circle into a sphere, so that the sphere from one dimension appears static, but from a different dimension it is sustained as the result of the circle in motion.
Behind the sphere are all the ways it can be positioned and changed while still remaining a sphere. The reason why not everything can be the possible of anything is because there are instances where a possibility can not be while that thing still remains itself. For example ice is not the possibility of fire because if it is than fire would just be ice and therefore no longer remains fire, it would completely change, however it is the possibility of fire to be smoke, as smoke comes out simultaneously out of fire. And so there are an approximate set of possibilities to any reality, and therefore this is where the idea comes in of things as numbered. There are a set of distinct variables happening in the event of fire, like smoke, combustions, carbon dioxide etc.,
Even in 3-dimensional objects if you have a 360 degree panoramic view of the environment, there is a limitation in distance, that the point beyond the furthest point from the observer becomes imperceptible, also at any furthest point there is curvature which hides any point behind the curved horizon.
Superposition of sphere (qbit)
(Add here locus, bird flying together example) Geometrically the superposition is constructed in three steps:
First, two distinct and inverse points (+) and (-) lead into the same neutral point (0).
The neutral is the vertex of the positive and the negative.
Second, the vertex or the same point where the two lines meet discloses the two lines within a circle, as the same figure.
Third, each point (+) and (-) stand outside the disclosure of the circle as a point in the circumference of a sphere.
+
( ÷ > 0 )
–
This diagram demonstrates the three steps all together
The most important aspect to pay attention to is the red point on the circumference of the sphere, which is the centre of the sphere, is any single potential body that contains the relation of which it is only a component of.
(Add to how infinity is disclosed as one finite thing infinitely) The superposition states that the many are as a group one thing.
For equation describing a physical phenomenon the superposition principle states that a combination of solutions to a linear equation is also one solution of it, in other words having many solution for one equation is still a solution.
In quantum mechanics superposition is a state like waves in classical physics, any two or more states can be added together (superposed or in philosophy presupposed) and the result will be another valid state. Every quantum state can be represented as a sum of two or more other distinct states. If a physical system may be in one of many arrangements of particles or fields, then the most general state is a combination of all these possibilities disclosed into one state, or specified by a complex number (it is equation of the variables and their solution all expressed as a unit)
quantum bits, peaces of information as a unit, Qubits contains all the possible relation of a bit into one unit.
This relates to point extending to form a line and a line into a circle
Superposition how one body forms other bodies or body produces itself into other bodies because it contains the relation of which it is one part of, implicit within it, so that its movement in one determination has the presupposition of itself as a body not moving that way, and moving every other way. These must be distinguished as separate entities and so when body moves away the other body remaining still away from the initial one moved away.
If we take one classical bit, it has within it a qubit as its capacity for motion and change because the qubit is the disclosure of all the possibilities of a bit, the totality of its relation within it as its avenue for determination. Unlike classical motion where the movement of an object means that it is in one position and simultaneously not in another, in the quantum realm the determination of one objects motion reproduces itself as another body taking that movement.
Quantum entanglement
The entanglement of two inverse determinations is that wherever one determinations moves its entanglement is the presupposition disclosing it.
Any sum set of relations are disclosed by each single. component acting as a part in those relations.
(Add locus here) The many bodies combine together to becomes the capabilities of one body, like the organs each with a function becomes the whole functioning of the same body.
Th conception or mind is the superposition of its object because the conception discloses all the possibilities of the objects.
How much of a sphere can you see at once? On some level it appears as if the there is a point of the sphere, its “back side” facing away from the perception that is inconceivable. First reason is that the sphere is not a static object but is the substrate of pure motion. Since the sphere is in constant motion there is an aspect of it that always escapes perception. Motion is by definition movement beyond its conception. Secondly, the inconceivable part of the sphere is not an object because at any one point during the rotation of a sphere each part of it is perceivable but not all parts, all at the same time. For example the “back” and the “front” of the sphere are identical such that the conception determines whether what is perceived has the feature of being the back or front. Or that when the front is being perceived the back is not (Add Peirce) so that looking at the front is the same object as the back at any given moment.
The inconceivable point is a matter of the fact that the back and the front cannot be seen at the same time, the law of non contradiction. As an object it makes no difference whether what is perceived is back or front because both sides are identical with each other. As an activity or motion the inconceivability of one causes the conception of the other. The perception of one causes a rotation away from the other.
For example in mirror sphere no matter of its revolving motion the facing side conceives the same thing. (Add to the Higgs boson) the side facing the observer remains constant capturing the same scene.
If the sphere is hollow and all sides of the circumference is conceivable, there is still the point of the radius that constitutes the circle of the sphere that remains with no measurable quantities, period has no angles sides etc.
Likewise if the point is a sphere from a distance, no matter of the distance away, the quantity of the point does not change only the conception which is a plain, is one possibility of the point, the line and the circle are other possibilities these qualities form around the point.
This abstract fractal demonstrates that to look at a point only expands the scope of the conception. The aspect of the point that is inconceivable is the unchanging feature, the point is the reference point for the aspect of the conception that remains inconceivable to itself. The conception is a superposition of itself which means that all change is the conception pointing out the possibilities of what it is not, all of which become figures the conception is not limited to as it goes beyond them to point out other objects. The point is the infinite distance away from the conception.
The point is the abstract principle of the inconceivable part of a sphere. Which is just the same as a sphere in motion, the circle. (Add before above qbit) the point is a sphere at a distance shows that it is one sided at one time. (Law of non contradiction, you cannot both see its front and back at the same time, the circle is the law of identity of the sphere, its shows its motion, which is starting at one point and back to itself)
(Add to spacetime curvature)
How to make a sphere
In order to understand curvature of spacetime it is important to understand how sphere is the primary form. Sphere is the most primary form because it is the capacity that enables other forms to be functions of system. (Add how sphere is the form of the self existing circuit. How the conceptions goes farthest away from the source, wraps around connecting back to the source. Like looking inside a sphere.)
We normally say that the plain, point, line relate together to form sphere. Yet the sphere so far as their whole is their presupposition.
The plane is the simplest of two-dimensional surfaces – like a sheet of paper, but infinitely extended in all directions. This infinite expansion into all directions is limited by straight line, the shortest connection between two points is a straight line. Straight line so far as determined by the nature of the plain is capable of being connected in all directions enabling the use to construct more complicated geometric objects, such as triangles:
Part of the infinite directions of a plain is the line to find connection with itself forming circle, which structures the plain as sphere. There are no straight lines on sphere but straightest lines. ( add to symmetry and asymmetry sphere is form of to be in motion)
The shortest connection between two points on a sphere will always correspond to part of the circumference of circle.
Def of sphere
A spherical surface is a simple example for a curvedsurface. It is easily pictured as a surface embedded in three-dimensional space: in space, a spherical surface is the set of all points at a certain fixed distance from a given point (the point being the centre of the sphere). Mathematically, a spherical surface can be described without recourse to three-dimensional space – when mathematicians talk of the geometry of such a surface, they (almost) always mean the “inner geometry”: Those properties of the surface noticeable to two-dimensional beings, living and working in that surface, capable of measuring distances and angles in it.
Sphere is regularly used as a synonym for spherical surface (instead of describing a solid, three-dimensional ball). And not only for the two-dimensional spherical surface described above, but also for its analogues in lower and higher dimensions. A one-sphere, for instance, is the same as a circle, a two-sphere is the spherical surface defined above, a three-sphere its three-dimensional analogue.
Order of shapes- inscribe
Hegel exemplifies the triangle as “the first rectilinear figure, that all other figures must, to be determined, be reduced to it or to the square, and so on.-The principle of these figures is the identity of the understanding, which determines the figurations as regular, and in this way grounds the relationships and sets them in place, which it now becomes the purpose of science to know” (199).
Height, width and length are conceptually different but are not yet differences in space (198 nature). Hegel states for example that Geometry measures the precise height to distance from the centre of the earth; but this measurement of height makes no difference in space as it is also equally length, depth etc.
Consciousness inscribed in object (maybe put after atomism) (black hole central point)
The concept of “generality” involves certain difficulties. The term “general” is normally defined as to concern all the main features or elements of something, and the word is often understood synonymously with overall or widespread, for example, the plane holding, disclosing or containing things together. In elementary geometry, there is a fundamental difference between the concepts of Inscribed and circumscribed.
When a polygon is “inside” a circle, every vertex must lie on the circle:
In this diagram, the irregular pentagon ABCDE is inscribed in the circle, and the circle is circumscribed around the pentagon. In other words, the circle circumscribes the pentagon. The word “inscribed” describes the inside shape, and the word “circumscribed” describes the outside shape. Here’s another diagram with the polygon on the outside.
Each side of this irregular pentagon is tangent to the circle. The pentagon is circumscribed around the circle, and the circle is inscribed in the pentagon. In both cases, the outer shape circumscribes, and the inner shape is inscribed.
We have to ask: in what sense can we assign the notion of generality and particularity to the concepts of inscribe and circumscribe?
The relation of the circumscribed circle does not define the notion of generality because of the minimum covering circle problem, which is the mathematical problem of computing the smallest circle that contains all of a given set of points in the Euclidean plane. The Minimal Enclosing Circle Problem is, simply stated, the problem of finding the smallest circle that completely contains a set of points.
It is a minimum bounding circle, which is the smallest circle that completely contains the polygon within it.In this way the circumscribed circle is restricted by the vertices of the polygon. It is always determined by the set of points it contains.
The center of this circle is called the circumcenter and its radius is called the circumradius. In the above image, the circumcenter, O, intersects with the dimeter of cyclic polygon, P, and bounding the circumference of circumcircle C into given angle measures (summing of course to 180°).
Explain how the minimum circle problem does not apply to inscribed circle because it is already the minimum circle because if the circle circumscribes the points, it results in the need for the minimum circle to inscribe it.
The notion of generality is actually informed by “universality” which is understood as the quality of being involved or shared by all things such that to constitute them together. For example, the inscribed circle constitutes various polygons on the grounds of tangibility of their sides.
The inscribed circle, or “incircle” is the inverse geometric property of the circumscribed circle. The inscribed planar shape or solid is one that is enclosed by and “fits snugly” inside another geometric shape or solid. The incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle’s incenter. A circle or ellipse inscribed in a convex polygon (or a sphere or ellipsoid inscribed in a convex polyhedron) is tangent to every side or face of the outer figure. The excircle or escribed circle[2] of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two.
A triangle (black) with incircle (blue), incenter (I), excircles (orange), excenters (JA,JB,JC), internal angle bisectors (red) and external angle bisectors (green). The green triangle is the excentral triangle.
The incircle defines the notion of universality as it is shared by all shapes.
Triangles (dialectic)
As is the case repeatedly in discussions of polygons, triangles are a special case in the discussion of inscribed & circumscribed. Every single possible triangle can both be inscribed in one circle and circumscribe another circle. That “universal dual membership” is true for no other higher order polygons —– it’s only true for triangles. Here’s a small gallery of triangles, each one both inscribed in one circle and circumscribing another circle.
Generality is activity, function, and particularity is result and object. When the circle is inscribed that acts as function or activity, because the points are external. When the circle is circumscribed, that is the object, the result, as the points are internal. The circle is fundamentally always inscribed due to the minimum circle problem, that any points inside can be used to form an even smaller circle. While when the circle circumscribes, it is limited to the shape.
The way consciousness maintains itself inside all objects operates precisely in this geometric way. Consciousness inscribed is the function of the object, its inherent activity, the change. Whereas consciousness circumscribed is the maintenance of the of the particular object and the studying of it deriving knowledge of it. the inscribed and circumscribed process happens simultaneously.
The point of this describes precisely the nature of consciousness inscribed in its object and circumscribed by the object. consciousness described as infinity operates as universality, in other words, infinity operates as universality. The sequence of this (i) consciousness is equal with itself, the circle, (ii) it contradicts its self-identity producing its object, circumscribed circle in triangle. (iii) the idea of itself, the object is
Consciousness as dialectical sequence: 1) Consciousness procures the object, it is equal with that object, is one form. 2) the consciousness critiques the object, is another form, 3) the consciousness that conceives the object and its critique is another form. This unfolding is the sequence of development in the generation of the varying objects. This is simply an abstraction of the process because the critique of the object is found in the very generation of the object, and the synthetization, the overlooking of the generation and its critique, is the whole of that.
water structure, showing that the charge distribution is concentrated around the oxygen atom. Is this organic manifest of the geometric minimal enclosing circle problem? The so called contradiction is actually a real life structure.
Touch in geometry is to be tangent to at a certain point. Tangent is a straight line or plane that touches a curved surface at a point. The curve is the line deviations from its length.
Touch always involves the deviation of the length in the contact due to the curve. The curve is the motion of the intersection. Intersection. From Latin: inter – “between” , secare “to cut,” means the point where two lines meet or cross.
This does not only mean that the point is where the two lines meet is the intersection. But that the point itself insofar as it contains, deviates from itself as the line and the line curves to the circle, (picture with circle line through it)
Objectivity cannot wholly depend on sensations because sense alone is unable to reconcile opposing principles of change. Objectivity moreover deals not only with the indication that the fact exists as is but also what the fact actually is, which may involve what it is not, a fact that cannot be derived by mere sensation. According to sensation, what one object-is-not is just its extension, which simply points to the object as an other.
The concept of what it means to be in contact actually points to a very fundamental problem in the nature of consciousness. Why is there a distinction between internal and external relations? What maintains the object as something distinct from thought? Why are thought and object held separately by consciousness? Before we answer these questions, let us first derive a clearer understanding of objectivity. (put this on top before the geometry)
Tangent as discussed above involves the touch, but not intersecting, a curve surface. Tangible as an adjective means “perceptible by touch” and “clear and definite: real”.
Touch is however defined as to come so close to so as to come into contact with. To be in contact in electromagnetism is a connection for the passage of an electric current from one thing to another. Contact is communication of information. Touch insofar as contact is the mechanism deriving information. The information itself however is something prior to the mechanism.
The trigonometric function that is equal to the ratio of the sides opposite and adjacent to an angle of a right triangle.
The dialectic is the logical relations of the triangle and the triangle is the mathematical structure of the dialectic.
Adjacent= having common vertex (each angular point) and sides.
hypotenuse= the longest side of a right angle, opposite right angle.
opposite
Sine
Cosine
Tangent
universe is circle
This shows that the universe constituted by the infinite possess a form. The universe is spherical, why? Because that is the shape where every aspect in the infinite can relate with one another. Supposing that the infinite possess no shape is supposing that the infinite is going in a particular direction. Any direction however presupposes a shape so that it is directed in. The infinite is usually understood by the initial understanding of the Big Bang, as a direction that is outwards, that the universe expands outwards and is in fact speeding faster rather than slowing down. The reason why it is going faster rather than slower is because in its motion there is the greater immediacy to become. This is characterized by time, which is the motion disclosed within any self contained individual form, whereas space is the motion outside of the thing, where it falls into where it exhibit change for an external observer.
Aristotle calls time the “affection” of motion in the particular cause that causes that which does not cause, which presupposes the caused that is uncaused, unmoved.
When we state that the circle is the universal form, we are not limiting that idea to the shape of the universe. Whereas it is true that orbital systems in the universe take on spherical motion we intend a deeper meaning to the idea that the universe takes on a circular form. The universe is not the shape of a circle rather the circle is the universal form enabling any form and that marks the necessity of the thought as contradiction. The circle is the shape that takes on all shape, the shape in which all shape exists. The circles as a form poises a contradiction between the universal and the particular. On the one hand, what is contained in the circle is limited to the relation between anything else in the same circle and limited in relation to the circle itself.
What exists outside the circle is unlimited. But immiedate idea that comes to mind is that what is unlimited outside the circle exists in every direction away from the circle. This thinking however is mistaken and in fact the opposite of what is true. What exists outside the circle is in fact infinite in relation to the circle. Otherwise the circle would not be contained in the void that holds it. If the very void where the circle lies is present away from the circle, then the circle will be not contained and ceases to be a circle. If my laptop is floating in space, we still say that space is present against the laptop so that the laptop even exists somewhere.
It is also mistaken to say that what exists outside the circle is limited, say for example a single line is holding the circle. This cannot be true, first, because what exists outside the line, and now the circle, is still infinite so as to contain both, even if the line is containing the circle, secondly, the line can only contain a particular part in the circle, that is the point to which it is connected, and so the circle will be that which is containing the line not the other way around. If then it is logically true that what exists outside the circle is pressing infinitely onto the circle so as to contain it, the circle serves as a contradiction to that which is outside of it by limiting it, that the circle itself contains some part of that which is containing it. This not only includes but it is in fact a three dimensional process.
If we substitute the infinite void outside of the circle that is containing it with the principle of reason, we begin to see the working of thought by way of the contradiction. Every idea potentially exists outside circle, but this potentiality is the pressing void that necessitates the actuality of the circle, in this unlimited pressing against the circle, the circle limits the potential into the actual, and so the potential become contained in the circle, that circle being the form of the idea itself. And here we have the first of the abstract into the concrete. This contradiction we identify as the physical, as the sufficient condition for thought as the necessary condition
Squaring the circle
Ex. Squaring the circle is a paradox in geometry since ancient mathematics. It supposes that the circle is infinite. Define the concept; … What is usually said of this paradox is that not the circle is the infinite rather the steps that takes to produce a square that is a circle is infinite. This understanding is however excluding the very ground for all these steps taking by the square, that is, the circle. What is causing the steps of the square being infinite is the circle, that if one can square the circle, that just means it reverts to a circle. This is the law of non contradiction, if you can make a square into a circle, it becomes now a circle and ceases to be a square, and vice versa if a circle can be squared it no longer is a circle but is identical with a square.