Is there a mathematic or geometric construct of an Infinite radius?

Im not sure an infinite circle is logical. A circle is by definition an enclosure of space and puts finite restrictions on the measurements.

Perhaps, but truly, the line composing the circle is just connected points having no dimension, as noted in my initiating post. So the line, itself, even one in a closed arc of a complete circle, is, itself, connected points of no dimension, so, what real "enclosure" in a strict EG realm? Sure, in reality, we can draw circles and squares, and other shapes, but in a srtrict geometric realm, is there such an enclosure?

As a concept it can be anything you want it to be.

As a symbolic representation it is limited by it's medium.

Though it would seem logical to suggest that a radius is limited by, and a factor of, a circle.

And a circle is limited by the necessity of the circle.

Therefore, if either are to occur, then they must have limitations.

Of course this is all theoretical, because an infinite cannot exist in reality, and even if it did, we could not know it.

So theoretically, I don't think so, first a radius is a measurement of distance and infinite is not a mathematical distance, you really can't apply mathematical concepts to it (Georg Cantor tried to but that's why he ended up in an insane asylum)

Second, the radius of circle is geometrically associated with an arc, but if the radius is infinite, then the arc is zero, making it a straight line, and an infinite straight line can't be extended into a circle.

infinite cannot exist in reality?

life is infinite.

infinite cannot exist in reality?

Aristotle first established it, and in the modern era, David Hilbert and Henri Poincaré demonstrated it, all three distinguished between an actual infinity and a potential infinity. Time can't extend infinitely into the past, because we could never arrive at the present, it could only "potentially" extend into the future infinitely, but there is no way for us to know that. A potential infinity can be an abstract repeating process, but even theoretically, an actual infinity can't be observed. Hilbert and Poincaré proved a completed, infinite set can't physically exist, if it is completed, it is finite, if it's not completed, it is only potentially infinite.

life is infinite.

The point being, you can believe that "potentially", but you can't actually know it to be true.

Life is not infinite, it is a blip.

What if Hilbert and Poincaré, sincere in their beliefs, brut misguided, like folks who thought, or still think, that the universe is geocentric? EWe had "proof" of it a few centuries ago, and people still believe it today. But, again, that's the distinction of belief and faith, and faith is how things, like eternal life, can be known to be true, because true faith only leads to truth. Now, faith is a bit like humility; as soon as you declare it for yourself, you're not. It is not a matter of personal pride.

Remember that your soul needs an eyeball to see anything.

What if Hilbert and Poincaré, sincere in their beliefs, brut misguided

Yeah, David Hilbert was a lightweight in the field of mathematics LOL.

You started out talking about Euclidean Geometry, but I suppose that Euclid guy didn't know shit about geometry either.

faith is how things, like eternal life, can be known to be true,

If it's known to be true, it isn't faith.

But hey, if you are a science denier, you may as well also be a mathematics denier, and a logic denier.

BTW, you forgot to tell us about how that Aristotle guy didn't understand logic.

Is it reasonable to suggest that matter in it's most basic state must have infinite potential.

Though if matter cannot be reduced to zero, is it not then both potentially infinite whilst remaining finitely reduceable.

Which would be to say that potential cannot cease to be.

And of course the same conundrum also applies to A GOD...(The magical floaty about or scarecrow in a fedora type).

Though if potential can be lost, this would therefore give credence to the GOD principle. (That which reinitiates or maintains material potential).

The point being, you can believe that "potentially", but you can't actually know it to be true.

Some people sometimes believe illogical non-sense, for various reasons unknown to others.

When science exposes and infinite occupied space, I hope Faux will share with us.

Only two kinds of infinite I believe in.

1} meta-space concept of infinite this that or the other ex life, rocks, numbers, local universes, etc

2} the eternally existent, macro-infinite, truly non-occupied space, that, embraces the finite, occupied space Universe { @ }. Simple

...> Finite has inherent integrity, all sub-catagories of integral Universe decay{ come apart } and transform into another kind of occupied space intergrity.

...> Infinite lacks integrity since integrity is defined as a whole. Obviously infinite is not a whole. Simple.

Is it reasonable to suggest that matter in it's most basic state must have infinite potential.

I guess it depends on what you mean by “infinite potential”, if you are talking about energy, no, it is not reasonable to suggest matter must have infinite potential energy, both classical physics and relativity say that is impossible.

Though if matter cannot be reduced to zero, is it not then both potentially infinite whilst remaining finitely reduceable.

I’m not sure if I follow what you mean by that, please explain further.

Which would be to say that potential cannot cease to be.

Again, if we are talking about energy, then the potential energy of matter can certainly reduce to zero, if you are talking about something else, please explain further.

And of course the same conundrum also applies to A GOD...(The magical floaty about or scarecrow in a fedora type).

No, I don’t think it does, anytime you see the word “infinite” on the internet, people start talking about God, but the OP was about geometry, and I don’t see how this or any other physical conundrum that transfers to the spiritual realm.   Mathematically, infinity tends to apply to limits, and in theology, associating God and the word infinity is meant to signifies that God's being, attributes, and existence are without limit, as opposed to the finite nature of the physical world. It is a matter of God’s transcendence, which would be a matter of transcending physical conundrums, the implication is beyond our finite human intellectual capacity to know, Isaiah 55:8-9 comes to mind:

“For my thoughts are not your thoughts, neither are your ways my ways, saith the LORD. For as the heavens are higher than the earth, so are my ways higher than your ways, and my thoughts than your thoughts.”

((I recognize your "magical floaty about" thing, it's on the tip of my tongue but can't quite remember, what was your screen name at debate.org?))

Though if potential can be lost, this would therefore give credence to the GOD principle. (That which reinitiates or maintains material potential).

I don’t follow the reasoning here, what do you mean?

Previous usernames have been Sonofcharl and Fredsnephew, and I think the former was with debate.org.

"Potential", in this case simply refers to the possibility for material existence, without the need for what we understand to be physical laws.

Is it possible for emptiness to become full...Or can fullness never be empty.

And the dilemma for me is that this conundrum cannot be reconciled...Potential can neither be finite nor infinite.

And whilst out walking yesterday, I was suddenly struck with the notion that a circle cannot be infinite, so therefore neither can it's radius.

And then struck with the notion that the circle might be infinitely expandable.

Just another irreconcilable mind game.

Previous usernames have been Sonofcharl and Fredsnephew, and I think the former was with debate.org.

OK, then it wasn’t you, his exact phrase for God was “floaty about bloke”, pretty close, but no “Scarecrow in a fedora”, that’s unique.

"Potential", in this case simply refers to the possibility for material existence, without the need for what we understand to be physical laws.

You mean, the probable just becomes actual when you look at it?

Is it possible for emptiness to become full...Or can fullness never be empty.

I think I hear the sound of one hand clapping.

And the dilemma for me is that this conundrum cannot be reconciled...Potential can neither be finite nor infinite.

I don’t know about that, according to quantum physics, that’s exactly where physical reality comes from, it is a potential that becomes actual through observation.

Quantum physics tells us reality is made of waves that behave as particles, or particles that act as waves – and not waves of some underlying stuff, but waves of “probability”, reality a halo of pure possibility that goes unrealized until it is “collapsed” by an observer, who almost seems to conjure the particle into existence out of a mathematical haze.

And whilst out walking yesterday, I was suddenly struck with the notion that a circle cannot be infinite, so therefore neither can it's radius.

And then struck with the notion that the circle might be infinitely expandable.

Hey, Einstein used to take walks like that.

What made Einstein great was not some intellectual ability to resolve conflict by determining which side was right, that simply is not what he did to completely revolutionize understanding in physics. Only one representative example would be the battle between wave theory and particle theory of light that had vehemently raged between two "sides" for decades before Einstein took a walk and resolved it all.

He did not determine which side was right, he said both sides were right, and both sides were wrong. He allowed two mutually exclusive theories, two irreconcilable "sides" full freedom to exist simultaneously in his mind with the implicit understanding that perhaps both were expressions of a higher truth and then worked it all out to achieve a higher and more comprehensive understanding of the underlying truth, and in so doing he completely revolutionized physics. Again and again, he engaged in this type of mental process and astounded the scientific world with his insights into the true nature of physical reality. That was his brilliance and the key to his genius.

So keep on walking and let me know when you have figured out the answer to the Ultimate Question of Life, the Universe, and Everything.

Just another irreconcilable mind game.

Mind Games (Remastered 2010)

How do you get something – in this case, everything - from nothing?

In generall, there are two schools of thought on the subject.

There are the “magical floaty about” believers who want to reject science in favor of some transcendent reality, many call it God, but many others use different words, the One, the Void, the Primordial Deep, my grandmother used to call it Unetlanvhi. This transcendent reality was described as dimensionless and infinite.

Of course, that’s just silly and unscientific. Science says everything has a cause, so what caused God? And don’t give me any of that “God just is”, or “God is uncreated”, or that “God is a necessary being that must exist”, because that just isn’t science. Those guys always want to invoke some transcendent existence that precedes or lies outside the physical universe, that just has to be the way it is, to which there is no alternative, they want to tell us that underlying our present universe there is something beyond space and time, something very mysterious, but that is all just nonsense, the universe is everything, and science explains it.

Now let me explain it to you scientifically, to show how foolish those people are.

In the beginning there was a primordial mass we call a singularity, it was infinitesimally small, infinitely hot, and infinitely dense, in it all the matter/energy in the universe was squeezed into a single dimensionless point, don’t ask where it came from, it just was, it was uncaused and uncreated, it just is, a necessity that must exist. In addition to that, there was a deep mathematical structure that necessarily existed, it preceded or lay outside of the physical universe, it just had to be what it was because there was no alternative.

Now, within this deep mathematical structure, if you apply relativity and quantum theory to this pre-existing primordial mystery, you get a cosmic loophole big enough for all creation to jump through. In the end, the universe is a quantum fluctuation that can be described as either a particle or a wave, and n a special kind of mathematical transubstantiation, the numbers took on substance and became the universe.

There, we don’t need all that belief and mystery and supernatural God stuff, because now we have science to explain things.

Yep, B sounds a lot like A.

Just different terminology.

And the scarecrow in the fedora holding a frog was Fauxlaw's idea.

And I'm pretty sure that magical floaty about bloke was mine.

So, were you Sidewalker on DDO?

An "infinite radius" describes a curve whose radius grows so large that it becomes indistinguishable from a straight line at any local level. This concept can be understood by imagining a sequence of circles with increasing radii all tangent to a point; the circles appear flatter and more line-like as the radius approaches infinity. Formally, a straight line can be defined as a circle with an infinite radius, representing the limit of the circle's curvature as the radius tends to infinity.