Lessons on Causality

Sorry I’m late to the discussion (I know you were all waiting for me), but I’m very intrigued by this question of whether circles have sides or not. I think I’m partial to the infinite sides faction of the debate. A circle has infinite sides. Yet at the same time, I see how this is equivalent to the notion of a circle having no sides. It makes me wonder if this is a sign that infinity = zero (or everythingness = nothingness). Though paradoxical sounding, it makes sense when you think about this mathematically: as you approach infinity, the elements which you are counting (those that tend towards infinity in their quantity) tend towards zero (like the sides of a polygon–the more numerous, the smaller they must appear in order to apprehend the whole polygon, tending towards zero size and the polygon towards a circle).

So is saying that a circle has infinite sides the same as saying it has no sides? I think these are two “sides” of the same coin. To say that a circle has infinite sides is to focus on the sides themselves, recognizing not only their existence but their numerousness, so numerous that the whole (the infinite) must be said to stand beyond the scope of your focus. But to say that a circle has no sides is to focus on the whole (the circle itself) and to say that any sides that exist can only be said to exist beyond the scope of your focus (but this time in the opposite direction–too small to see, to small to be said to exist). So I think we can say two things, but neither simultaneously: we either have the whole (the infinite) without the elements that amount to the whole (zero sides), or we have the elements (the sides) but without the whole that an impossible amount of them make up (the infinite).

Notice how autistic James is? He’s focusing too much on differences and too little on similarities. That’s autism.

What’s happening here is that UrWrong is telling us that our intuition interprets this shape as being a form of circle. Most people will tell you, independently from any dictionary definitions, that this shape is a circle. That would be intuition at work. And let us not forget that inuition precedes dictionary definitions. James, on the other hand, is telling us that our dictionaries do not allow us to interpret such a shape as being a form of circle.

James is, of course, wrong. What he’s doing here is he’s HIDING the work of his own intuition. In other words, he’s removing himself – his own intuition – from the equation in an attempt to pretend to be purely “objective”, or more precisely, to be a blind follower of instructions. This is evident from the fact that our dictionary definitions of the word “circle” contain certain ambiguities. For example, Google definition that a circle is “a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the centre)” has a problem in that the number of points that the boundary of a circle consists of is not specified. This makes it difficult for us to take a ruler and test any given shape simply by following instructions i.e. without doing any thinking on our own. We simply do not know many measurements we have to take . . . because we do not know how many points there are on the boundary of a circle. Thus, we need to use our own judgment. We need to decide for ourselves how many points there are. And depending on how many points we choose, the above shape can be tested positive. The fact is that James does not see the above shape as a circle, not because of any dictionary definitions, but because of his method of judgment.

That’s what happens if you focus too much on differences and too little on similarities. You become preoccupied with nuances and unable to see “the big picture”. Which is exactly what autism is about.

The hatred of ambiguities, the idea that ambiguities necessarily confuse, is the hallmark of autism.

That’s called intuition. Intuition is not a product of a lack of education. It is a product of evolution. In other words, intuition is far older than any dictionary definition. It is people like you who are attempting to REPLACE this intuition with another mechanism. And the reason is because you have a pathological obsession with precision.

Note that noone here denies the fact that the above circle is not a perfect circle. We know that. What we’re denying is your attempt to make us unnecessarily rigid, formal, precise, etc.
Stop pretending people don’t know how mathematicians define circles.
And stop defending autistic people.

Circles are first and foremost objects of our experience. They are shapes that we can SEE in our everyday life. That’s what they are. And we know what they are thanks to our intuition. We need no dictionary definitions.
When you say something like “circles are a set of points equidistant from some fixed point” you are providing an alterantive way of judging whether any given shape is a circle or not.
This method of judgment involves a ruler that is anchored in the center of the shape. It also involves choosing a number of points on the boundary of the shape you are measuring. And it involves rotating the ruler so that one of its ends passes through one of the selected points on the boundary. What you have to do is to measure the distance between the center and each one of the selected points. If all of the distances are equal you declare that the shape is a circle.
The other approach is polygon approximation but this approach has a weakness in that it involves the redundant concept of side. Sides cannot help us to determine any given shape is a circle or not. They are quite simply useless in this regard. Where they are useful is in measuring the circumference of a circle. That is when describing circles in terms of polygons is useful.
The polygon approximation approach gives us a more complete view of circles.

ukessays.com/essays/philoso … -essay.php

Firstly, we need to look at what perception and reality mean, the definition of perception is the act or faculty of apprehending by means of the senses or of the mind; cognition; understanding. This means that perception is what we sense in our environment from what our senses and mind tells us. The definition of reality is the state or quality of being real (dictionary.com) but if we know what is real because of our perceptions and senses, how do we know our senses can be trusted to tell us the truth, and thus how do we know what is real? Every philosopher has searched within themselves for the answer to what is reality, and how we know what is real, but every philosopher has their own views on reality, to begin idealist Renee Descartes argued that sensations and experience can be doubted, so it is pure reason, not the senses, that must form the basis of Truth and what reality is. Next, an Idealist, Plato who claimed that the world of ideas, for example the ideal nature or essence of a tree or a circle or a color, was more fundamental, more “real,” than physical reality, and that physical reality, a tree for instance, comes into being as an imperfect instance of the ideal. John Locke an empiricist said that the mind starts out without any knowledge and everything one knows is built up from experience through the senses. So who is right? Is there any one way to know what reality really is?

In Descartes his first and second meditations he claims that all our beliefs can be doubted because our senses could simply be just an illusion, he goes on to say that although all our beliefs cannot be certain, because we think and experience, our minds must exist. Descartes argued that our ordinary experiences and views of the world cannot give us the kind of affirmed foundation on which all other knowledge and beliefs can be based. We are often dismayed to acknowledge that what we have learned is simply detriment, or that what our senses tell us is not certain. That should make us wonder about whether all the other things we believe might also be uncertain. So is there anything that we can know for certain without a doubt? We can doubt whether there is a physical world and whether we have a physical body. We can doubt whether our own reasoning can be trusted, so then what can we absolutely know for certain? Descartes gives an example that even if a higher power deceives us about all our other beliefs, there is one belief that we can be certain about, which is that we are thinking. Even to doubt this belief is proving that we are thinking. And since thinking cannot occur without there being something that does the thinking, this proves that we exist. When we think, it proves we have a mind, regardless of whether we have bodies. The body we experience as our own is not an essential part of our self because we can doubt its existence in a way that we cannot doubt the existence of our mind.

Plato believed that reality was in the form of two separate worlds, he believed that something was an individual object, but could be put together into a larger group. For example there are multiple breeds of cats, but they all fall under a larger group, which is cats, or felines.

Another analogy that Plato came up with was the allegory of the cave. Here the physical world is in the form of a cave, in which the humans are trapped from the beginnings of our life, where we are stationary and cannot move our heads, so we perceive only shadows and sounds. Without reason, one of us is released and is encouraged to travel upward to the entrance of the cave. This revelation is very confusing to the person. Then he is pulled to the entrance of the cave, where the light is hurting his eyes that are accustomed to the dark, which threatens the only security his life has known. The world of daylight represents the realm of Ideas. His eyes grow accustomed to the light and he can look up to the sun, and understand what the ultimate source of light and life is. This is symbolic of the Idea of the Good in the Realm. This gradual process is a metaphor of education, and enlightenment. Yet the real lesson of Plato is that the enlightened person now has a moral responsibility to the unfortunate people, still in the cave, to rescue them and bring them into the light. This lesson brings about Socrates’ famous quote, “As for the man who tried to free them and lead them upward, if they could somehow lay their hands on him and kill him, they would do so.” This is ironic in nature. The fact that this man is trying to help these people and they are so uneducated masses will resent him and threaten his life.

Lastly, John Locke stated that we define objects by primary and secondary properties; primary properties being undeniably objective features such as size and shape, and secondary properties being subjective such as colour and taste. (youtube.com/watch?v=7dQpDNtsIAE) Locke’s theory on reality is called Representative Realism, it is the view that sense data (an immediate object of perception, which is not a material object; a sense impression) somehow represents the objects and that these objects are causally involved in our production of the sense data. Our perception of objects is thus indirect; hence, representative realism is a kind of indirect realism. (An Introduction to Epistemology, second edition, 277) This view argues that we experience reality indirectly by perceptions that represent the real world. So, if we see a brown table, what we are actually seeing is not the table itself but a representation of it. In this way, differences of perception which occur due to changes in light conditions, position of viewer, etc., can be easily explained: it is not the object which is changing, only the perception of it. As an example, a man is standing on the corner of a busy road and witnesses two cars collide. Neither driver is hurt, but both step out of their cars to inspect the damage. Driver A is a young mother with a young child in the back of the car; driver B is a business executive in a hurry; the witness is an old man wearing glasses. As the two drivers argue about whose fault it was, the man approaches them and offers to confirm what he saw happening. What does each of them see? Whose is the correct view?

It is evident that the mind knows not things immediately, but only by the intervention of the ideas it has of them. Our knowledge therefore, is real, only so far as there is conformity between our ideas and the reality of things. But what shall be here the criterion? How shall the mind, when it perceives nothing but its own ideas, know they agree with things themselves? (John Locke, 452)

So who is right? These are just three different views on reality out of hundreds, and possibly even thousands from other philosophers, but is there any one way to know if one philosopher’s theory is right over another? One thing most of these theories have in common is that our perceptions of reality, how we view things through our senses and the different objects we see, may not be what is certainly real, they suggest that what our perceptions of reality are, are not really what reality is. What this means is that for the average person living, their reality is based upon ignorance towards other truths.

As humans we struggle to know why we exist and what reality is, but many of us are too afraid to give up the comfort of believing what we see to be true to discover the answers to what reality is, because of this there are select few individuals who question their life and what it means, these individuals give insight to others and are able to teach other individuals about what it means to question our existence and perceptions. Although for many of us the theories of philosophers such as Descartes, Plato, and Locke may seem wildly unlikely, the more we question what reality is, the more we ourselves create new theories about reality, and they themselves may seem far-fetched to other individuals. We may look at what other philosophers have theorized in the past, but for us, as individuals, to discover what reality means to us personally, we must think deeply ourselves, we must theorize and question ourselves until we are so confused by our questions we no longer know what it means to exist. We cannot rely on other theories of reality because everyone perceives reality differently, what one person may perceive is different than what another person may perceive, and because of this not everyone can have the same views and theories on what reality and existence means. Some of us may see God as an important part and influence in our reality, while others may not. Some people may say nothing truly exists, and that we are just an illusion and others may say everything they see is real. No one is wrong; our individual views on reality are personal, our perceptions are not the same as other individual’s perceptions, and that does not mean one is wrong or right. What it means is that we as humans have the responsibly to question ourselves, to question what it means to live. In order for any of us to achieve true happiness we must question reality, existence, and our perceptions. If we live in ignorance, we are not truly being happy; we are letting ourselves be satisfied with not understanding the world. Thinking deeply about reality inspires growth, it inspires us to realize there is more to the world then what we can see, the world is a limitless place of our desires.

So it sounds like you’re saying there are at least 3 approaches to defining circles: intuition (we know a circle when we see it), point geometry (all points on the circumference are equidistant to the center), and polygon geometry (a polygon with infinite sides all at equal angles to each other).

You also say that the polygon geometry approach has the drawback of holding onto the redundant concept of side, yet you also say that it gives us a more complete view of circles. Would you say that this redundancy is a good thing then? That it allows for a more complete view of circles?

Four steps:

1. Perception - based on the sense organs (subjective) and signs (objective). Pre-Knowledge (semiotic language).
2. Knowledge through linguistic skills - based on perception and semiotic language (=> 1) and on linguistic language.
3. Knowledge through the pure logic of language - based on perception and semiotic language (=> 1), on linguistic language (=> 2) and on pure logical language.
4. Knowledge through mathematical language - based on perception and semiotic language (=> 1), on linguistic language (=> 2), on pure logical language (=> 3) and on mathematical language.

Now, we want to know what a circle philosophically means. Right?
For this we do not need “high” mathematics, because we do not know for sure whether mathematics is more right than philosophy or other disciplines. But we want to talk about it in a philosophical sense. Right?

If we know how and wherefore mathematicians use certain definitions, then this does not necessarily mean that they use it in order to get the truth. They are just searching for consistent statements (in their mathematical language).

The “higher” Occidental mathematics has much more to do with functions than with numbers. Its geometry has mainly become a functional theory too. But what does that tell you about the circle when it comes to the first three steps I mentioned above? No mathematician denies the meaning or/and definition of a circle giving in a currently valid dictionary. We already had a similar discussion in another thread: “Is 1 = 0.999…~?”. 1 and 0.999…~ are never identical, but according to the Occidental mathematics functions have become more important than numbers, because functions do work (just: function) much better than pure numbers.

And what about the physicists? Do they say that sunrise and sunset do not exist according to your perception? Do they deny that the Sun is going up and down according to an observer? Do they insist that you have to always say that sunrise and sunset are caused by the Earth rotation? No.

In other words: Does the answer to the question whether a circle is just circular (without sides) or has sides just in order to calculate in a better, the Occidental way of mathematics not also depend on perspectives?

I mean: Would you say that sunrise and sunset do not exist, namely in the world of your perception? Certainly not.

So do we at last not have the same discussion here as almost always: subjectivity versus objectivity?

The argument concerning whether “circle” should be defined this way or that, is an entirely different topic.

Currently a circle is defined in a very exact and ancient way, even in mathematics. If someone wants to call a 12 sided polygon a “circle” merely because it is more circular than a square, he really should specify that he isn’t being precise and certainly shouldn’t be telling others that they are wrong when they explain the difference. They are not wrong (but children will be children).

Defining a circle as having every point on the circumference equidistant from its centre is sufficiently rigorous for no
other information to be required. So while it can also be defined in terms of infinite sides it is not actually necessary
to do so. The first definition is way simpler and easier to understand which is why it has survived for as long as it has

It is redundant if all you want to do is determine whether any given shape is a circle or not. We can do that without the concept of side. The concept of side does not help us in any way. That’s Occam’s Razor. However, if you want to do something more with these shapes, say measure their circumference, then it is certainly not redundant. The polygon approach is more complete in the sense that everything you need is there, in one place. Note that polygon approach builds on top of point approach. Polygon approach is simply point approach with points being connected by lines.

Yes. There is also trigonemtric approach which involves sine waves. And finally, there is my favorite approach, which involves easing functions ← that approach is the most analytical approach of all.

Normal brains process information synthetically (a.k.a. holistically.) This means they focus on the big picture – they don’t focus on the details. Or more precisely, they focus on the details but the amount of time they spend focusing on the details is minimal. They spend more time shifting their attention than they spend maintaining it. You can say they “glance over the details”. You cannot see the whole if you are focusing on the parts for too long – you will only see a lot of parts. You cannot see the forest if you are focusing on the trees for too long – you will only see a lot of trees. So a global thinker will see a circle where a local thinker won’t see a circle (e.g. UrWrong’s picture.)

When you focus on the big picture you lose the sight of the details and vice versa. When we look at UrWrong’s picture we see a circle. We don’t see its details, and hence, we don’t see the imperfections. If we switch out attention away from the big picture and towards the details, then yes, we would be able to see the imperfections, but this won’t make us abandon our earlier claim. If we did abandon the claim and if we adopted the attitude of spending disproportionately long time looking for imperfections then our understanding of circles would become so strict that most, if not all, of the shapes that we normally consider to be circles would no longer be seen as circles. That’s horribly counter-inuitive.

The problem is that there are times when the data that we possess regarding the world around us does not have what is necessary in order to be able to guide us in choosing what to assume regarding the unknown. This is the situation when every choice is as good as any other a.k.a. equi-probability. You cannot approximate (i.e. choose the closest relative) in such a situation because every candidate is equally similar to the original.

Paraphrasing what I said in another thread:

Intelligence is the search for the closest relative of some data set d within some set of data sets S.

In effect, the task of intelligence is to approximate.

(Of course, pedants will be quick to say that this is not intelligence but intuition. And not even intuition but induction. And not even induction but something else – something I made up.

My point will be that if you want to understand intelligence then you have to understand intuition. And if you want to understand intuition then you have to understand induction. In fact, you have to understand whatever is fundamental to the process. You need to understand the foundation of intelligence. Any other approach will be horribly superficial.)

When a data set has more than one closest relative then we’re speaking of randomness.

If we have a data set such as {A, A, B, B} that represents “2 occurences of A and 2 occurences of B” and if we want to find out how many occurences of A and how many occurences of B there will be at 5 occurences of either-A-or-B we will have no choice but to conclude either {A, A, B, B, B} or {A, A, B, B, A}. This is because the two data sets are equally similar to the original data set. That’s randomness. The greater the number of closest relatives, the greater the degree of randomness. On the other hand, if what we want to find out is how many A’s and how many B’s there are at, say, 6 occurences of either-A-or-B then we will be able to give a definite answer: 3 A’s and 3 B’s. This is because this data set is more similar to the original data set than all others. That’s order. The lower the number of closest relatives, the greater the degree of order.

12-side polygons look like this:

Squares look like this:

Circles look like this:

We can easily see, using our intuition, that the 12-side polygon has more in common with the circle than it does with the square. So the right way to call it is certainly not “circular square” but “square-ish circle”.
Your claim that this shape – the 12-sided polygon – is merely more circular than a square quite simply wrong.
It is A LOT MORE circular than a square.

Note that I narrowed the context. The 12-sided polygon is allowed only two relations: one with circles and one with squares. This is why I had to conclude that the best way to describe the polygon is as “squarish circle”. That’s true but only within that limited context. And that is sufficient to make my point – all I wanted to say is that describing it as “circular square” is very bad. Inuitively, however, describing the 12-sided polygon as “squarish circle” sounds rather strange. This is because intuitively we consider a broader context. The best way to describe the shape is as “spiky circle”. Even describing it as “triangular circle” sounds better. But we’ll notice that the similarity with triangles is only in the details.

The argument isn’t that a circle is a 12 sided polygon anyway. It’s an infinite sided polygon.

In order to test whether any given shape is a circle (or not) we need to decide how many points there are on the boundary. This is not an objective parameter. The boundary of the shape under the test does not have a finite number of points. Instead, it is us who has to decide, entirely subjectively, how many points there are. What this means is that testing whether any given shape is a circle or not is in actuality a test of how circular that shape is. No shape is inherently a circle. Instead, shapes are MORE OR LESS circular. When we choose a smaller number of points, we are testing for a lower degree of circularity. When we choose a larger number of points, we are testing for a higher degree of circularity. This is perfectly in line with the holistic stance that there are no absolutes, only degrees.

Sure, we can run binary true/false tests. Any given shape either passes the test or it fails the test. But what we are testing for can never be “the perfect circle”. Why? Because there is no such a thing. Can anyone here define what a perfect circle is? But without taking things out of context. Don’t just say “a perfect circle is every point in the plane that is equidistant from some fixed point”. Such a definition does not specify the number of points that have to be tested. If you say that the number of points does not matter, then the test becomes too lax . . . nearly every shape can pass it. The 12-sided polygon? It’s a perfect circle and James is wrong! On the other hand, if you say that the number of points is, say, quadrillion, then it becomes too strict . . . no shape can pass it. And the problem is not only strictness but the arbitrariness of choosing a number of points that defines the perfect circle. It’s entirely subjective. Why quadrillion and not, say, quintillion? The question cannot be answered without taking context into account. The problem is that analytical thinkers, such as James, don’t want to take context into consideration. They are absolutists.

When someone says that a circle is “an infinite sided polygon” what is meant is that the greater the number of sides a circular polygon (i.e. a shape with its key points being equidistant from the center) has, the more circular it is. That’s all it means. Pentagon is less circular than hexagon which is less circular than octagon which is less circular than 12-sided polygon which is less circular than 24-sided polygon and so on and so forth.

The problem is that with his interpretation of “side”, every polygon and every shape is infinite sided.

That’s the point though, Absolutism.

Some people are too absolute to admit mistakes in definitions and meaning. Like how James refuses to admit that a Chiliagon, 1000-sided shape, is a circle. He is too proud to admit a weakness in his position, his meanings. But James and Arc are missing the points. There will be many different approaches to definition, interpretation. Accuracy is important but there are gray areas wherein which some will say “this is a circle” and others will disagree and say it is not. This gray area, area of conflict, is when each side offers superior definition and increases the stringent requirements, leading to the perfect, absolute circle.

“My definition is the absolute perfect circle and YOURS ISN’T!!!”

That’s not what I’m talking about. But it was necessary to show a few people here they were wrong to completely reject my, ARBITRARY definition. As if a brief definition of a circle has to do with the greater topic at hand? How about a square? A square has 4-sides and 4 right angles. Are people here going to argue with that definition as well? In order to do what? In order to dispute that if I define a cause as this or that, that those definitions must also be absolute and perfect?

That’s the point, isn’t it?

That for there to be “cause” of anything at all, in existence, then those causes must be defined absolutely and perfectly? Nope, that was never my implication or intention, James.

Causes, like these definitions of shapes, require lots of effort and sophistication to apprehend and understand.

Like how an offshore earthquake keeps causing a coastal tidal wave. It keeps happening, everytime, one after the other. So ought we not then deduce, and operate from the premise, that offshore earthquakes cause coastal tidal waves???

My opposition has few directions to travel, to dispute, to doubt this. And you could even say “well so what, it doesn’t matter”. It doesn’t matter to you, but knowing the causes of things, can save lives, and to those who are swept away by coastal tidal waves, will absolutely know the difference of importance, and whether it was the ‘good’ thing to do, to attribute causes to natural phenomenon.

It’s not imaginary, a matter of the mind only. Some humans, a few at least, attempt to find, locate, and identify causes in existence. The patterns of reality, of existence. And in so doing, they gain advantages that other people do not have. The scientist who creates a device to detect offshore earthquakes, can save countless lives, whereas those other places and people who do not, will not save lives. If you are fine with that then so be it. But cause, as a general matter, is much larger than merely offshore earthquakes and chiliagon circles.

Yes, it is true, every polygon and every shape can be said to be infinite sided. Where I disagree is that this is a problem. I ask: what exactly is the problem? Why is it a problem?
We don’t see squares and other shapes as infinite sided simply because there is no need to. There is, on the other hand, very good reason to see circles as infinite sided.
Circles have sides that are related to each other in a very specific manner.

The only way that every polygon or shape could be described as infinite sided would be if a straight line was also described as such
But anything with edges cannot be infinite sided because they are the points where two sides converge and therefore begin or end