The circle drew itself, this is the conclusion I draw from it, meaning it was self caused. — invicta

Bravo invicta! I applaud you for this determination.

Infinity and finitude are two sides of the same dynamic. They require one another as mutual existants.

The circle is the perfect elementary geometric example of the relationship between infinite irrationality and A-B linear or finite rationality.

A circle has 3 features. The circumference, The radius and the focus/central point.

The relationship between these 3 things represents the whole spectrum, the relationship or "triad" between infinity and finitude (the two poles at either extreme).

The central axis is static. Unmoving. Unchanging. A single point. A singularity. It is finite, fixed. It is highly rational. Located. Consistent. Constant. Objective.

The radius is a midway between the circumference and the central axis. It is the link between them and thus shares both properties, it exemplifies balance: half fixed, half dynamic/changing: in the sense a radius is fixed in length, but dynamic in angle of relationship to the center. The radius can assume any projection/vector or rotation in 360 degrees of the central focus. So it represents the interim relationship between the other one 2.

Finally we have the circumference. Purely irrational in vector/direction and length. Never is it moving in the same direction to the previous point along it's course.

The angle or relationship with the center is constantly changing, a state of pure flux, as it revolves around it. It's length is also arbitrary in that it flows directly into itself endlessly. Arbitrarily, we can assign a start point and an end point such that we could make the circumference linear (to unravel it/straighten it up) and assign it a finite length in relationship to the length of the radius from the center, but in doing so we violate it's circumferential nature. We disengage it from the central focus when we examine it's arbitrary finite length.

Ultimately the beginning and end are the same point on any circumference.

Pi determines the relationship (thus naturally using the radius or diameter - double radius) between the center and circumference. It is irrational and endless. But can be made finite to any decimal place for convenience, at the disposal of accuracy.

When this comes to linear vs circular arguments. They are inseparable from one another, and biased in their individual favouring of either infinity or the finite as a satisfactory explanation. But in either case they're both equally correct and incorrect. Neither can be taken in isolation, as an absolute and final account. The only truth in linear vs circular argument lies in understanding their relationship to one another. And their innate non-rectifiability. The relationship itself is the real unifying factor.

But hang on a second, if it was self caused then there can’t be an infinite regression of causes. — invicta

The "infinite regress" is the circumference. As it tracks into itself or infinitely regresses into itself ie "loops" or "revolves".

Everything "infinite" revolves around something "finite". Just as everything that is in a permanent state of change (falsity, transformation or flux) revolves around something permanently unchanging (fundamental truth/constancy/law/rule).

My advice in your quest for answers, is to read into/research the significance, symbolism or role of the circle, cycle, wheel, revolution, circumpunct, sphere, dome, etc as well as triads, trinities, triangles and pyramids in ancient texts, religions, spiritual teachings/mysticisms, philosophies and science (biology, chemistry and physics especially) through the ages and make links between them as geometry demonstrates fundamental relationships and truths about the universe through all ages (because they are the innate structural and relative/relationship basis for all existants).

Yet this never satisfied the philosopher, namely Aristotle. Hence the proposal of first cause or the uncaused cause. — invicta

For Aristotle, the problem with infinite regression is that we would not be able to learn anything theoretical in such a universe:

At the same time, however, it is also impossible that the first [cause], since it is eternal, should pass away. For since coming to be is not without a limit in the upward direction, [a] the first thing from (ek) whose passing away something came to be must be non-eternal. And since the for-the-sake-of-which is an end, and the sort of end that is not for the sake of other things but rather other things are for its sake, it follows that if there is to be a last thing of this sort, the series will not be without a limit, but if there is no such thing, there will be no for-the-sake-of-which. Those who make it unlimited are unwittingly getting rid of the nature of the good (and yet no one would try to do anything if he were not going to come to a limit). Nor would there be any understanding present in beings. For someone who has understanding, at any rate, always does the actions he does for the sake of something, and this is a limit, since the end is a limit. — Aristotle. Metaphysics, 994b5, translated by C.D.C. Reeve

Anyone wanna trash this theory? — invicta

I'm with you. It ties in with the question of whether or not something can come out of nothing for which I have two possible answers, depending on my mood - 1) Of course 2) It depends on what you mean by "nothing."

At the same time, however, it is also impossible that the first [cause], since it is eternal, should pass away — Aristotle. Metaphysics, 994b5, translated by C.D.C. Reeve

I could understand up to this point, after that I seem to have got lost in translation.

But back to the circle, this self-drawing circle. How could a circle draw itself ? This doesn’t make sense when looking at it from this line of reasoning as it’s metaphorical at best. If it did indeed cause itself then why not a straight line ? Simpler, easier.

This is a non-issue because as you will see the circle answers the question more succinctly then a straight line as logical explanation, it’s our best understanding of infinity as a circle does not have a starting point. Yet when we do draw circles we have a starting point or two starting points to be precise if we wish to draw a near perfect circle the centre and circumference.

there could be more esoteric explanations as to infinity but they’re beyond my understanding.

Yet the simple yet complex circle which in itself contains Pi (itself an infinite) points us in such a direction in our inquiry. An irrational number that stretches forever, a hint there of the nature of infinity.

This apparently random number that has conjured the circle stretching forever yet producing the most simple of shapes, a circle ⭕️

If I elaborate further it will sound like bullshit so I must stop here.

If I elaborate further it will sound like bullshit so I must stop here. — invicta

I applaud your perspicacity. There are mathematical ways of avoiding circles, but not now, I think. :chin:

I only say that because if I was to carry on I’d be going in circles

I find his dissatisfaction with infinite regression unsatisfactory for if infinite causes are the chain of sequences ad infinitum does such a chain not imply a closed loop, like that primordial snake ouroboros eating it’s own tail. — invicta

Closed deductive loops are quite valid.

They just do not get you very far - no further than where you started.

Here, though, you seem to be claiming that a "sequences ad infinitum" implies a closed loop. It doesn't.

The trouble with making use of "first cause" is that the notion of causation is problematic.

Russell (1912: 1) famously denied that there are any causal relations at all, quipping that causation is “a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm” — SEP: The Metaphysics of Causation

At the very least, causation causes more philosophical problems than it solves.

I applaud your perspicacity. — jgill

Just so.

Here, though, you seem to be claiming that a "sequences ad infinitum" implies a closed loop. It doesn't. — Banno

Funnily enough I was aware of the same objection upon writing, well spotted Banno. Still it might be defensible, and quite possible, so, but If it isn’t I will concede.

Here we go. And please bear with me here.

Ad Infinitum of course latin for infinity. The circle of course being dictated by the circumference/diameter produces Pi. Now assume you only know Pi

Let’s simplify

X/y = Pi.

If you only knew Pi, which you obviously can’t as it’s irrational and infinite …could you draw a circle?

Of course not.

Thus, infinity, taking Pi as a currently known example is non-repeating and unpredictable

Pi, draws a straight line in a circle, and since no we can’t square a circle the implication of this is that not only is PI not self-recurring (non-repeating pattern) but that the relations of circumference/radius can never be calculated.

If you only knew Pi, which you obviously can’t as it’s irrational and infinite — invicta

Of course we can know Pi: it's the ratio of circumference to diameter. I can draw a reasonable circle of any diameter up to a 20cm or so; after that the paper is too small.

I don't see that your argument works.

It’s an example of circular logic in Action. The full Pi is non-repeating and goes on forever. You will draw a very good circle but it won’t be a perfect circle sorry, because you can’t determine Pi

It’s an example of circular logic in Action. — invicta

No it isn't. The methods used to calculate Pi are iterative, not circular.

The implication being of course that a perfect circle is not physically possible only in the realms of mathematics.

I don't see how that has anything to do with attempting to show that infinite linear arguments are actually circular, nor with your OP.

I don’t blame you Banno, where did this infinite irrational Pi come from, it’s definitely not something physical as a how could a perfect circle exist in the physical world when it can’t be drawn, a perfect circle is only abstract and unable to be represented or drawn because Pi is non-repeating and goes on forever

Is it not purely abstract?

I find his dissatisfaction with infinite regression unsatisfactory for if infinite causes are the chain of sequences ad infinitum does such a chain not imply a closed loop, like that primordial snake ouroboros eating it’s own tail. — invicta

No. A closed loop does not answer Aristotle's quest for an explanation of Causation itself. Note that in the Ouroboros symbol, the snake that seems to be recreating itself, actually has a head and tail, a beginning and end. A true infinite loop would have no head or tail. :smile:

You are not making any sense.

You’re saying im being irrational just like Pi. If pi was rational and predictable yet infinate would it not make a linear straight line rather than a circle ?

Point being, even Isolating Pi to 3 decimal places could you draw a non-perfect circle ?

A closed loop does not answer Aristotle's quest for an explanation of Causation itself. Note that in the Ouroboros symbol, the snake that seems to be recreating itself, actually has a head and tail, a beginning and end. A true infinite loop would have no head or tail. — Gnomon

That's actually a good point I have sometimes mused over. Perhaps the symbol is eternity as devourer of itself.

You’re saying im being irrational just like Pi. — invicta

Hmm. Well, it seems you both go on forever.

No. A closed loop does not answer Aristotle's quest for an explanation of Causation itself — Gnomon

I don't think Aristotle would have described his work that way. He was surrounded by those who rejected the idea of an intelligible whole. He fought them tooth and nail.

Thus, infinity, taking Pi as a currently known example is non-repeating and unpredictable — invicta

Not quite unpredictable, as the first 100 trillion digits in its expansion are now known. Why on Earth someone would make that their life's work is beyond me.

At the very least, causation causes more philosophical problems than it solves — Banno

I suppose so. But when context is specified it's not so problematic. I put a kettle on the stove and turn on the burner. The kettle boils over. Because I turned on the burner - just don't go down the rabbithole. I can set up a causal chain in math using iterations or compositions of functions, basic in dynamical systems.

A circle is a very close approximation of Pi which is infinity itself.

It doesn’t exist in the real world by the fact that in its close approximation it comes in on itself demonstrates the circularity of such an infinity.

The fact that PI remaining abstract yet embedded, but not fully, by fact of impossibility in the real world in the form of the circle highlights a very profound idea of such an abstraction namely that of a never ending non-repeating number.

In a sense, whilst Pi was known to the Greeks, it is actually a Greek letter in their alphabet, they never truly realised the implications of such a number, even Archimedean approaches never went more than two decimal places, so it’s real infinite nature was not readily apparent.

Though PI itself remaining an abstract with imperfect manifestation of itself in the form of a circle perhaps only comes to our understanding by fact of producing the approximation of such a shape.

PI even has a starting value. 3.14 somewhat implying that if it does have a starting value does infinity too?

I believe, again, that this line of reasoning is incorrect, even though by granting it such a concrete starting value (which is always an approximation), by the fact that this value itself never finishes, let’s it remain in the realm of the abstract and pure mathematics.

A circle is a very close approximation of Pi which is infinity itself. — invicta

That sentence is nonsense. A circle is not Pi. Pi is not infinity.

if it’s not infinity why haven’t we been able to calculate it’s finite value.

Of course it’s a circle, even though the approximate value is derived from circumference/diameter

if it’s not infinity why haven’t we been able to calculate it’s finite value. — invicta

You are far too casual with your terms. Pi is exactly the ratio of circumference to diameter. It is not infinite. It cannot be express with a finite number of digits in decimal notation.

Pi is not a circle.

Pi is exactly the ratio of circumference to diameter. It is not infinite — Banno

Ok then mister, please give me the exact value of Pi :rofl:

Pi is not a circle — Banno

Of course it’s a circle what is the value of the line when you’ve performed the calculation circumference/diameter…it’s Pi of course.