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Is there any perfect circle, precisely right angle or pair of truly parallel lines, in reality?

Take parallelism. There are many lines in reality which seem parallel, at first glance. And if one were to measure the distance between them with a tape measure, I have no doubt that the distance between them would remain constant at any point one could measure it at. However, I am equally certain that if one were to measure those same distances with a microscope, in micrometers or nanometers, one would probably find some deviation at some level.

The precision with which we can compare these concepts to any given existent depends so significantly on the tools and procedures by which we obtain our measurements. The very concept of a "perfect" geometric form omits any specification of measurement, though; it means that the measurements will remain indistinguishable, regardless of their precision. It abstracts the observer.

So to say that "there is no such thing as a perfect [whatever]" is to make a sweeping generalization about any measurement that can ever be made (of anything), and so to also generalize about existence, consciousness and the relation between them.

Either answer to that question, then, would have massive implications for basically everything.

Which one is consistent with Objectivism?

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Are there any perfect circles, right angles, or parallel lines inn reality?

 

To say there is no such thing as a perfect circle, what is being referenced as "the perfect circle" that no existential entity can meet? The issue is with the epistemological term of "perfect".

I lay a straight edge down and draw a line. Using a compass, I select two points close enough together on the line that the arcs drawn intersect equidistant on either side of the line. aligning the straightedge on the two intersections, I draw a perpendicular bisector. Examining the arcs made by the compass with a magnifying glass, the start of the arc is thinner than the end of the arc, because the wedge formed by the sharpened lead wore while marking on the medium drawn upon. Repeat the process using aluminum flattened to a uniform thickness, resharpening the point after each arc segment, and recalibrating the compass to ensure constant distance. Instead of a magnifying glass, use a microscope - and note that the topology of the medium is such that the arc varies where the compass interacts with the medium directly. Examine it with an electron microscope. Note that the arcs still vary in thickness due to wear.

 

Replace the aluminum point with a high tech marker that emits a constant thickness arc. Develop a machine that strikes the arc eliminating the slight arbitrary angle to the compass induced by striking it by hand. Examining the process now, it is discovered that machining variance in the equipment used to mechanically draw the arc has tolerance built into it that influences the curve of that arc that can only be observed using a quantum-scope that hasn't been manufactured yet that allows viewing a deviation of a plank unit as if it were a millimeter reveals a 0.25 plank deviation from "perfection" diminish in any way that it is most perfect circle drawn yet? Or consider a plank unit as the smallest unit for a moment. A circle drawn of one plank unit in diameter would have a circumference of 3.1415... plank units in length.

 

Consider the metaphysically-given versus the man-made. Circles, right angles and parallel lines are man-made conceptions, derived from the metaphysically-given. To suggest that the metaphysically-given is not perfect implies that it should be something other than what it is.

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HD

 

You are mixing/confusing abstractions and entities.  Entities are what they are, abstractions are used to deal with thinking about entities, entities do not and need not conform to abstractions, the very reverse is the case.

 

 

Geometry is a specific part of mathematics.  Mathematics in general is a field of abstractions which may or may not apply directly to existents, properties of existents, or relationships between existents.  Certainly integer "number" can directly be a property of a group of existents such as a pile of marbles.  Volume in general can also be applied when properly defined.  Abstractions also can be useful to "approximately" deal with entities.

 

Take the example of an abstract shape like a "perfect" circle.  It is a curved line in a two dimensional plane.  The line of the circle is infinitely thin or better put, it has no thickness whatever, only tangential curved length.  This is directly applicable when thinking about the path a point on the edge of a real object traces when it rotates in free space, but is only approximately applicable when thinking about, for example, a cookie.

 

What extended shape in matter could have no thickness whatever?  Nothing.  This does not mean the abstraction "circle" and its properties like radius and area, are not useful when thinking about cookies, in fact they can be very useful. What we conclude here is only that entities do not actually come in circles.

 

It is clear that abstractions are not the same as entities.  You can abstract away the 3rd dimension to get a 2d shape in your mind. You also can abstract away the variations of a real cookie to get the curved line of a circle.  You can calculate the approximate area of the cookie using the area of the circle and by multiplying by the approximate thickness you can determine approximately "how much" (volume of) cookie you are eating.

 

 

What you define as "perfect" is simply equivalent to the "abstraction" of something from reality, all other things abstracted away.  Real "circles" are made of entities, entities are 3D, if you refer to some "perfect" circle which is 2D you are referring directly to only what ever can "be" 2D, an abstraction.

 

 

Since reality is the given, I would refrain from thinking in terms of "perfect" this or that, all you are doing is thinking of the abstraction and feeling short changed that the entity is not the same.  It shouldn't be, and your abstraction is still quite perfectly valid.  It's simply that these two kinds of things are different and that's all.

 

Not really a big deal.

Edited by StrictlyLogical
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For some reason this thread always shows up in my listing as having 0 replies....

 

anyone know why?

My guess is that it had something to do with messages getting posted during time-outs shortly after switching servers. Your reply synchronized the post count, as it is displaying correctly now. I noticed it on a couple of threads.

Edited by dream_weaver
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  • 1 month later...

Circles, right angles and parallel lines are man-made conceptions, derived from the metaphysically-given. To suggest that the metaphysically-given is not perfect implies that it should be something other than what it is.

And that would be very, very, very wrong. (!!!)

The evaluative side of "perfection" isn't what I meant to ask about, though (and I'm sorry for any ambiguity on that point); only whether or not our concepts must necessarily be 'close enough' approximations, which inherently deviate in one way or another from every single concrete that can ever be.

The issue is with the epistemological term of "perfect".

Exactly.

A circle drawn of one plank unit in diameter would have a circumference of 3.1415... plank units in length.

And if Plank units are the smallest amounts we could possibly measure anything by (I'm skeptical of that point, but for the sake of argument) then this hypothetical instrument would measure a circumference of 3*Diameter - which would seem to deviate from a perfect circle, even if it metaphysically wasn't the case!

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Since reality is the given, I would refrain from thinking in terms of "perfect" this or that, all you are doing is thinking of the abstraction and feeling short changed that the entity is not the same.

Thank you, but I really don't resent existence. There are a few people IN existence who should be a little bit closer to "perfect" (and sometimes I do find that frustrating) but, as far as circles go, I'm good.

Entities are what they are, abstractions are used to deal with thinking about entities, entities do not and need not conform to abstractions, the very reverse is the case.

That's the point. If all of our abstractions are approximations and none of them can ever literally apply to any thing (ie. a "true" circle) then all we can ever know about reality are such fuzzy approximations; that would be the best sort of adherence that would ever be possible to us.

For example, pi is a property of that abstract "perfect" circle. The ratio of a cookie's circumference to its diameter would be something else- perhaps close, but never identical.

I'm not arguing against that; I'm still chewing on it, right now. However, if that is the case then it has serious implications for what "knowledge" means, which have not (as far as I know; I have not yet read "Mathematics is About the World") been laid out before.

I think that's the key, though: "as far as I know".

Edited by Harrison Danneskjold
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