Clarifying Infinity

[Reg_Prescott]

To keep this on topic I will note that the surface of a wax cylinder is, in one sense, infinite.

Gosh, that was clever.

Tee hee :-)

[Brent696]

>>>>>>To keep this on topic I will note that the surface of a wax cylinder is, in one sense, infinite. A bug on its surface can keep walking forever. But only if its walk is circumferential. It has only one degree of unbounded travel. <<<<<<<

The wax cylinder, by its infinite possibilities, represents a negative infinity of 0, being also indicative of its geometric 2 dimensional form. The needle, as the infinity of 1 and Being, also indicative by its geometric shape (needle) is that which writes upon the infinity depth of possibilities transmitting the information of one form (the divine mind of the needle) into the sound and noise of the universe, the poor quality of which producing what we know today as the background radiation. The Big Bang of course was the drop of the needle.

The bug scientist/philosopher walks continuously in one logical direction around the cylinder, the scientist walking against the spin while the philosopher walks in the direction of the spin, the theologian experiences vertigo as he turns at a right angle to the spin and walks to the edge of the cylinder to look over the side into the vortex of the radial singularity.

[scientificphilosophe]

Wow - quite a lot to read after my period away!

Part of the original problem with the original debate was the confusion between the theoretical extent of a set of numbers (my loose definition) and how well it was deemed to be populated.

Most people would assume that that if you define a set of numbers (such as integers running forwards to infinity), then it is full populated because you haven't included any limitation in your definition. If you then change the definition to impose limits on the population (eg. positive integers except for the number 6) then you have changed your definition. The population factor rather than the abstract concept is important.

Perhaps that is where we begin to reconcile physics (closer to real world) with abstract maths - both of which have their valid place.

To return to some specifics, then re: cylinder, we should differentiate between the finite cylinder, and the potentially infinite length of walk that a bug could make around its surface - given an unlimited lifetime.

I do not agree that the real universe has no examples of infinity - I gave two examples in my earlier posts:-

1. the size of the universe is potentially unlimited (unlimited space) because we cannot see any limit to it, and the 9year findings findings of the WMAP survey concluded that space is not curved and that Euclidean geometry applies.
2. the basis of the bang-crunch theory of physical origin is that the last Big Bang was not a start point (which would break the principle of strict causality) but merely the last in an eternal sequence of Big Bangs. As time is only seen to move forwards, we have a potentially eternal sequence of time prior to the current moment.

Admittedly the finding that the expansion of the universe is accelerating, means that 'Bang-Crunch' is dead and therefore materialist scientists have resorted to other other theories which seek to reinstate the infinity of time in order to preserve the principle of causality.

[phyti]

scientificphilosphe;

Most people would assume that that if you define a set of numbers (such as integers running forwards to infinity), then it is full populated because you haven't included any limitation in your definition.

---
The limitation is: 'the set cannot end'! Thus cannot be made manifest, thus no proof it exists.

[someguy1]

The limitation is: 'the set cannot end'! Thus cannot be made manifest, thus no proof it exists.

What does that mean?

[TheVat]

Am guessing "made manifest" means an infinite series cannot be found and identified as such in the physical world?

[phyti]

That is what I meant, per the dictionary definition.
Any 'contructivist' method of an infinite list, could never be complete.
The mind can only comprehend a complete list (a finite entity) by identifying boundaries, a beginning and an end.
Time is also relevant to the method, when would it be complete?
Any Peano type method allows the formation of larger integers, but not the largest integer.
I.e., you can only extend a list.
Infinite llterally means 'without end', so an 'infinite list' is actually a contradiction of terms.

[someguy1]

That is what I meant, per the dictionary definition.
Any 'contructivist' method of an infinite list, could never be complete.
The mind can only comprehend a complete list (a finite entity) by identifying boundaries, a beginning and an end.
Time is also relevant to the method, when would it be complete?
Any Peano type method allows the formation of larger integers, but not the largest integer.
I.e., you can only extend a list.
Infinite llterally means 'without end', so an 'infinite list' is actually a contradiction of terms.

What's non-constructive about the Peano axioms?

[ronjanec]

I personally define ‘infinity/infinite’, as the particular way in which someone or something is said to have absolutely no end or possible limit to the same.

[Brent696]

For something to be truly infinite, without boundaries of any kind, it would have to be the Only thing of reality. There is no "beside" it for something else.

Within this universe there are no actual infinites existing.

The definition is one of "Potentiality" verse "Actuality", which is why Peano axioms are also known as The Peano Postulates. A postulate "assumes" the existence of something to aide in discussion or reasoning, but they never reach the level of actuality.

BTW, I believe SP is out of town for a few days so it might be a while before he gets back to his thread.

[someguy1]

I personally define ‘infinity/infinite’, as the particular way in which someone or something is said to have absolutely no end or possible limit to the same.

Isn't the set of real numbers between 0 and 1 inclusive, an infinite set? And aren't 0 and 1 the ends? And aren't they limit points of the set? In fact isn't every point of the closed unit interval a limit point?

Reason I mention this is that math has a well-developed theory of infinity, 144 years old at this point. You're not entirely entitled to make up your own without supplying justification, background, and context. We don't believe in the phlogiston theory of heat anymore. Science and knowledge move forward.

[someguy1]

BTW, I believe SP is out of town for a few days so it might be a while before he gets back to his thread.

He went someplace where there's no internet? When I go out of town the first thing I do when I get to my destination is get connected to motel internet. How about you?

[ronjanec]

I personally define ‘infinity/infinite’, as the particular way in which someone or something is said to have absolutely no end or possible limit to the same.

Isn't the set of real numbers between 0 and 1 inclusive, an infinite set? And aren't 0 and 1 the ends? And aren't they limit points of the set? In fact isn't every point of the closed unit interval a limit point?

Reason I mention this is that math has a well-developed theory of infinity, 144 years old at this point. You're not entirely entitled to make up your own without supplying justification, background, and context. We don't believe in the phlogiston theory of heat anymore. Science and knowledge move forward.

Mathematicians can call this an infinite set that has an end(s) and is limited in some way, but this does not actually represent a true infinite state of being existing here ontologically or in the real world.

Some of them will also call a number you can always add to an infinite number, when this cannot exist in the real world in an again infinite state of being.

But I agree with some of what you are saying about my definition here, and will have to figure out a way to include mathematical infinity in my definition, despite this again not being infinity in the truest and most important sense of the word.

someguy, what is your personal definition for the concept of infinity/infinite?

[Brent696]

someguy1 » August 30th, 2018, 4:34 pm

He went someplace where there's no internet? When I go out of town the first thing I do when I get to my destination is get connected to motel internet. How about you?

Could be no laptop, I have answered posts on my phone but it suxs to do that. Could be camping deep, digging up mushrooms in the rain forest, visiting a shaman in the Yucatan, deep sea fishing, or taking a cruise with his wife and not willing to pay the extortion for internet.

He just told me he would be incommunicado for a few days.

[someguy1]

He just told me he would be incommunicado for a few days.

Ah! "Out of town" and "incommunicado" are not the same thing!! One could be one or the other, neither, or both. Thanks for the clarification.

[DragonFly]

We can let the fractions between 0 and 1 be potentially infinite, for math purposes, but we cannot list them all.

Plus, we can call convergences to 1 in math to have gotten to 1.

[someguy1]

We can let the fractions between 0 and 1 be potentially infinite, for math purposes, but we cannot list them all.

The rationals are easily listed. Here's a visual proof intended for high school students. Surely most here have made it through high school.

https://www.homeschoolmath.net/teaching ... ntable.php

Plus, we can call convergences to 1 in math to have gotten to 1.

That doesn't parse. What do you mean?


May I remind the assembled multitudes that this is the math section of this website. Discussions of infinity should be grounded in the mathematical theory of infinity. Or at least show some nodding familiarity with the subject before disagreeing with it.

[TheVat]

SG, Want to be a moderator? I'm tired.

[someguy1]

SG, Want to be a moderator? I'm tired.

Thank you for the compliment BIV but I'm sure you know I haven't got a moderator type personality. The first thing I'd do is ban Toucana.

[DragonFly]

The rationals are easily listed. Here's a visual proof intended for high school students. Surely most here have made it through high school.

The list was only potentially complete.

That doesn't parse. What do you mean?

.999999… or in calculus when a function 'infinitely' converges to 1.

I can't be waiting around forever for these potentials, so I'll grant them for math.

[Brent696]

I found the bold lettering and smiley face extremely disturbing and unprofessional on a tutorial.

[someguy1]

I found the bold lettering and smiley face extremely disturbing and unprofessional on a tutorial.

I chose the most simple-minded presentation I could find for our resident finitists. But actually I find it a very nice picture. It's my go-to page for this particular proof.

[Brent696]

Are we distinguishing between within the dimensions of time and space? I find no infinite within the universe but a certain one transcendent to it.

[someguy1]

Are we distinguishing between within the dimensions of time and space? I find no infinite within the universe but a certain one transcendent to it.

That's beyond my pay grade.

[Brent696]

Science stops at the door of the universe, that which is finite, it utilized "potential" infinities in conceptual ways but the universe does not allow for any actual infinities.

But Mathematics, in theory or philosophically can contemplate an Infinity beyond the limits of the universe. Since this thread is "Clarifying Infinity", it would seem to cover both Potential and Actual as they are contrasted from one another.

[davidm]

Science stops at the door of the universe, that which is finite, it utilized "potential" infinities in conceptual ways but the universe does not allow for any actual infinities.

Had this discussion before. It is possible that the universe is infinite in space and time. Since this is possible, it is wrong to say that that the universe does not allow for actual infinities.

[Brent696]

davidm » August 31st, 2018, 1:18 pm

Had this discussion before. It is possible that the universe is infinite in space and time. Since this is possible, it is wrong to say that that the universe does not allow for actual infinities.

Its also possible a God created the universe, or that consciousness is a fundamental component in the structuring of the universe. Since such theoreticals are possible, it is wrong to say they are magical or fanciful.

You see David, on a discussion forum, there are many points of view bantered about, and generally they are understood as opinion, unless some type of consequence is added thereon like an inference to prove someone dishonest, unintelligent, or the like.

As to the possibility of infinite time or space, they are strongly, strongly contested.

So is time endless as infinity would suggest, how then does it stop at the speed of light. Are we throwing Relativity aside as dysfunctional. Is space actually infinite or does it just seem so, is it two dimensional and folds back in on itself like the donut or some such shape, and if it is infinite are there infinite planets, infinite stars, infinite amount of energy and matter.

Are you actually proposing that the universe, specifically Time and Space are infinite, are you setting for some theory here.

Or is your only point is I CAN"T SAY THERE ARE NO INFINITIES, because people say this all the time, the most commonly accepted model for the universe is a finite one and physicists do not walk around prefacing every statement with "I believe" or "It's possible"

But just so we are clear, I will state my logic again, A true actual Infinity, that which is truly boundless and without limited, cannot share its existence with multiplicity. You CANNOT have and infinite amount of odd numbers in actual existence, because for any other number to be real, so would the boundaries between them.

Mathematics makes use of such Potential subsets, but to "clarify", they cannot possess actual being.

That is my logic, and I would think my opinion.

[scientificphilosophe]

To those of you who have missed my contributions - I thank you.

Sadly the urgent medical needs of my dying mother are not conducive to scientific and philosophical debate, so you may find that I dip in and out of the forum over the next couple of months.

[scientificphilosophe]

Returning to the debate - in general terms we do seem to be recognising the concept of infinity and in various ways & various disciplines, are trying to balance it with our perceived reality.

At its core, mathematics is a manifestation of pure causality, where a precise set of opening conditions can only lead to one inevitable outcome. It is also generally based in the finite which is why it is hard to accommodate concepts of the infinite within it. Mathematics is not designed for that purpose. It is primarily there to 'give voice' to strict causality and the finite.

Mathematics works fine until you break its boundaries, either through the infinite, or through true spontaneity or randomness. I have only seen this discussed in one book (Our Existence Part 1 by C.Finipolscie) so I haven't been able to fully consider the robustness of that premise - but it doesn't seem unreasonable to me.

On that basis, if we find bona-fide examples of infinity, whether theoretical or in reality, maths may not be the best tool to handle it.

The infinity of space, as opposed to any physical matter within it, seems a distinct possibility, even if it doesn't suit some philosophies. Attempts to prove that the universe is finite have all failed so far, so as there is evidence to show that the universe extends beyond the point that we can see, and it is not curved, it seems scientifically wrong to deny the possibility of infinite space just because you prefer one philosophy.

There is some evidence for the infinity of space even if it is not conclusive.

If you do not believe in the eternity of physical matter/energy then it must have an origin... and an origin, as Finipolscie points out, must imply either spontaneity or randomness.

As mathematics cannot cope with 0 = 1 advocates of a start point to existence invented the idea of an origin that created balanced opposites, so that the positives balanced the negatives - ie. 0 = 1+ (-1).

The alternative is to believe in the truly infinite.

[BadgerJelly]

Can anybody explain how mathematical infinities can be added together?