Infinite Regress

[Clizby Wampuscat]

I think what you mean is that a foot can be infinitely divided into smaller segments. Which is true. But a foot is a finite length. So you can actually reach the end of it. You can never reach the end of a ruler of infinite length.

I agree. But you can locate a place on an infinite ruler.

 

[Clizby Wampuscat]

I'd say an infinite regress is not impossible. I defend against the idea taking an "infinite time to reach the preset so we'd never reach now" this way: I did not, in fact, traverse an infinite amount of time to get here even if there were an infinite number of event preceding now. I came into the universe at a time and I will exit at a time. No infinite traversal required.

When people thought the universe was infinite in space, no one imagined that one had to traverse that infinite space to reach Earth. You were born here. Likewise, you were born now-ish.

If anything is traversing, it may be protons (and other massless particles). But they travel at the speed of light and thus don't experience time at all. I believe it was Feynman that proposed the thought experiment that there is just one electron; it's just everywhere, every-time.

ETA: Likewise the universe is time. It does no traversing.

Time is a property of this universe. This universe had a beginning so time as we are experiencing it had a beginning. We do not know if there is time outside our universe or if that is a coherent statement.

 

[Clizby Wampuscat]

There are many arguments that show the incoherence of an infinite number of stuff which would also apply to an ininite regress.

Then one that I like the most is that it leads to the conclusion that “events with zero probability can happen”

If there if an infinite number of balls in room, the probability of me picking randomly a specific ball is zero

But nothing can stop me from picking a ball, so these leads to the conclusion that

1 ether events with zero probability can happen

2 or that an infinite number of things can’t exist.

Since “1” is absurd you have to take “2”

There is a third alternative, which is

3 deny the possibility of a random event, (it´s impossible to randomly pick a ball) but that seems the high price to pay in order to keep the coherence of infinity.

All of this requires time. I am not sure how you rule out an infinite regress of universes since time is only part of our universe. We have no idea if outside the universe is even possible so how can we rule out a regression outside of time? I am not saying I am right I don't know.

 

[rational experiences]

Time is a clock.

Man on eArth in conscious presence inside two forms...light gas burning...clear night gas. Who said time is a shifting experience in light through space.

Earth wandering.

12/12.

So one cycle around a gas alight mass a sun was 12 as proof.

 

[Clizby Wampuscat]

I would deny that claim

A foot is made out of “fine” units otherwise you would have big paradoxes

I agree. I was thinking we can break down the distances with numbers that are infinite but space is not infinite between two points. Why is time different and why do we need to start at the beginning of time and not just pop up somewhere on the timeline?

 

[Left Coast]

I agree. But you can locate a place on an infinite ruler.

But in this analogy, to reach that place you have to traverse an infinite length to get there. But you can't.

 

[RestlessSoul]

I agree. I was thinking we can break down the distances with numbers that are infinite but space is not infinite between two points. Why is time different and why do we need to start at the beginning of time and not just pop up somewhere on the timeline?

Who says time is linear? Maybe that’s just the way we experience it, from our perspective. Time, in an observation attributed to Einstein, is what prevents everything from happening all at once. Each given moment is a unique co-ordinate, but the flow of time could be linear, it could be cyclical, or it could be something else entirely, in a higher dimensional reality than we are able to conceive of.

Then if the flow of time is cyclical, it is in a sense without beginning or end, as the circumference of a circle is without beginning or end. Is a thing without beginning or end, either finite or eternal? Another paradox; I’m pretty confident the universe is built on those.

 

[Tinker Grey]

Time is a property of this universe. This universe had a beginning so time as we are experiencing it had a beginning. We do not know if there is time outside our universe or if that is a coherent statement.

Sure. I get that. The position I was arguing against was time based that asserted if there were an infinite past, we'd never get here. First, "we" don't traverse all of time to get to now. And indeed the universe doesn't either since it *is* time (among other things).

Even if time did exist in some way "outside" the universe, this wouldn't entail the impossibility of infinite regress.

 

[leroy]

All of this requires time. I am not sure how you rule out an infinite regress of universes since time is only part of our universe. We have no idea if outside the universe is even possible so how can we rule out a regression outside of time? I am not saying I am right I don't know.

You don’t need time.

If you have infinite regress of universes, then the probability that you live in this universe is ZERO.

But given that you do exist in this universe, then the probability has to be greater than zero. Therefore there can not be an infinite regress of universes

 

[crossfire]

The absurdity of linear cycles depicted pictorially:

 

[Clizby Wampuscat]

Sure. I get that. The position I was arguing against was time based that asserted if there were an infinite past, we'd never get here. First, "we" don't traverse all of time to get to now. And indeed the universe doesn't either since it *is* time (among other things).

Even if time did exist in some way "outside" the universe, this wouldn't entail the impossibility of infinite regress.

Got it.

 

[Clizby Wampuscat]

You don’t need time.

If you have infinite regress of universes, then the probability that you live in this universe is ZERO.

But given that you do exist in this universe, then the probability has to be greater than zero. Therefore there can not be an infinite regress of universes

1/infinity is not zero. If this were the case then infinity*0 = 1. Infinity is not a number. lim x-->infinity (1/x) = 0.

 

[leroy]

1/infinity is not zero. If this were the case then infinity*0 = 1. Infinity is not a number. lim x-->infinity (1/x) = 0.

Well if infinity is not a number, then you can have an infinite number of seconds nor infinite number of universes.

 

[Clizby Wampuscat]

Well if infinity is not a number, then you can have an infinite number of seconds nor infinite number of universes.

Sure you can. It is a concept that means something is endless. If infinity is a number then (infinity + 1 = what?) If it equals infinity then you have to deal with (infinity - infinity = 1). That is nonsense.

If the probability of randomly choosing the number 5 out of all the numbers possible is zero (1/infinity), I can still choose 5. So if there is an infinite number of universes and the probability of being in any one of them is zero (1/infinity), I can still be in one of the universes.

I am not saying there is an infinite regress of universes, it just does not makes sense to me that it is impossible.

 

[leroy]

Sure you can. It is a concept that means something is endless. If infinity is a number then (infinity + 1 = what?) If it equals infinity then you have to deal with (infinity - infinity = 1). That is nonsense.

If the probability of randomly choosing the number 5 out of all the numbers possible is zero (1/infinity), I can still choose 5. So if there is an infinite number of universes and the probability of being in any one of them is zero (1/infinity), I can still be in one of the universes.

I am not saying there is an infinite regress of universes, it just does not makes sense to me that it is impossible.

If the probability of randomly choosing the number 5 out of all the numbers possible is zero (1/infinity), I can still choose 5.

But in reality you didn’t choose 5 out of and infinite pool of possibilities.

You choose 5 out of all the numbers that you had in mind in that moment

Any computer (or brain) that could select a random number out an infinite pool of possibilities would have to be a computer with infinite power and infinite memory (which is impossible)

 

[LIIA]

Before we discuss whether Infinite regress is possible, we must first agree on the definition of Infinite regress.

Infinite regress is an Infinite chain of cause/effect. Each entity in the series depends on or is produced by its predecessor. It’s a causal relationship between entities that take place within the realm of spacetime where all entities are governed by physical laws. Every predecessor (cause) must exist at a point in time preceding the caused entity; otherwise, nothing would give rise to the effect. Every effect is a cause for a subsequent effect.

Every entity in the chain is caused, no exception. Being caused means that every entity is a possible or contingent being (not a necessary being). Regardless of how long the chain of possible beings is, the entire chain itself always remains a contingent being and its instantiation in reality cannot be explained.

The first effect known is the Big Bang about 14 billion years ago. The Big Bang is a beginning point, beyond which there is no time space, matter, radiation or any physical entity of any kind. It’s a point of instantiation of the universe in reality beyond this point, all laws of physics, as we know it break down and cease to have any meaning. Infinite regression demands no beginning; there is always a predecessor then another predecessor with no end, if time stops the chain breaks. It can no longer continue.

The Big Bang itself is a contingent entity (has a beginning/didn’t always exist). As a contingent being, the instantiation of the Big Bang in reality is necessarily dependent on a cause. The nature of that cause is totally different than anything we may understand or imagine, the cause is not subject to the limitation of time, space or any physical law of any kind. The typical question “what was the preceding cause before that unique cause” doesn’t apply; the word “preceding” itself has no meaning given the absence of time (time is a contingent being). It’s a first cause of an unknown/non-physical nature that exists by virtue of its mere essence without any dependence on causality (no preceding cause). The first cause is a necessary being that always exists without any dependency of any kind on any other entity. The necessary being is not subject to causality, as we understand it within our physical realm, yet must exist to give rise to all (observable/unobservable) contingent beings of all kinds.

The nature of the necessary being is beyond any possible knowledge that can be attained from within the physical realm simply because the first cause is beyond that realm and not subject to its laws.

Infinite regress is a logical fallacy. The argument proposes an explanation, but the mechanism proposed stands just as much in need of explanation as the original fact to be explained. The explanation simply moves the question back into infinite regress rather than answering it. The question remains without an answer.

To summarize, since all items in the entire chain of causally dependent entities of known existence (within our realm) are contingent beings (i.e., “things which do not exist necessarily by their own nature”), then the entire chain itself remains a contingent being, and there must be a reason that explains its instantiation in reality. The ultimate reason for the instantiation of such a chain of contingent beings must be a being whose existence is not contingent (for otherwise, the chain will remain contingent and its instantiation in reality would not be explained). The existence of the chain of causes and effects is only possible as long as the entire chain is grounded in a being, which exists by virtue of its mere essence, i.e., a necessary being.

 

[LegionOnomaMoi]

you have to deal with (infinity - infinity = 1). That is nonsense.

It's a fairly common and very useful component of mathematical analysis, set-theoretical approaches to the real number line, etc. The most common version of algebraic treatment of ∞ as a "number" that can be negative or positive and to which algebraic properties are applied goes under the name "extended real numbers" or "extended real number line" or similar names. As an example:

(from appendix A.1 of Rana, I. K. (2002). An Introduction to Measure and Integration (Graduate studies in Mathematics Vol. 45) (2nd Ed.). American Mathematical Society.)

More compactly (from Beals, R. (2004). Analysis: An Introduction. Cambridge University Press, p. 40).

Also keep in mind that almost all real numbers (in both the everyday sense of "almost all" and the measure-theoretic) require manipulations of infinite sequences or series by which almost all real number must necessarily be defined. This is because the set of rational numbers, while dense, has measure 0 and more importantly isn't complete (i.e., every irrational number is the limit of a sequence of rational numbers converging to that unique irrational number, which means that unless one embeds ℚ in ℝ one cannot even talk about 2*π). Since the set of irrational numbers is a greater/larger infinity than that of the rationals, most of any interval in ℝ is made up of irrational numbers. In fact, one can remove every single rational number from a given non-empty interval in ℝ and the measure (or length) of the interval would remain unchanged.

So we kind of half to deal with a variety of infinities and procedures that require infinitely many "steps" of one sort of another just to get to the point where we can reasonably define pi in order to attempt to define what the product 2*π means, if anything.

 

[LegionOnomaMoi]

1/infinity is not zero. If this were the case then infinity*0 = 1. Infinity is not a number. lim x-->infinity (1/x) = 0.

Division by 0 isn't defined. In order to get to a point where you can do calculus on the real or complex numbers you first have to build up the set theoretic and algebraic structures. But the required axioms don't allow for division by 0, because for ANY number a, if a|b iff there exists a number c s.t. a*c=b
Thus, if a=0, then c=0 and b=0 and the necessary structure doesn't hold. This structure is required for the necessary inverse properties.

Also keep in mind that it was widely believed for a long time that 0 wasn't a number, and that negative numbers were nonsense. What is or isn't a number, practically speaking, is a matter of definitions. More philosophically, but still mathematically, it has more to do with preferences and the philosophical prejudices one has.

Finally, I'm not sure what your point is when you include this: lim x-->infinity (1/x) = 0
After, all, as you know, lim x-->0 (1/x) = infinity. So it isn't just a limiting process but also the limit point itself, which is a bit of a problem (from a rigorous approach) if this point can't even be approached in the reals let alone be fined as the unique limit. These and similar issues are one thing that motivates the extension of R to to R* (the extended reals) and the associated algebraic properties of -infinity and infinity.

 

[LegionOnomaMoi]

If you have infinite regress of universes, then the probability that you live in this universe is ZERO.

Take any continuous probability whatever; say, for example, the distribution of errors in measurements in space or of time, or even just the probability that a particular process that will end within a fixed interval of time but at a random point in this interval given by some pdf.
Since, for any such probability (which, in practice, is most of them), the probability of any particular "event" happening (e.g., a process stopping at an exact point in time) is always 0, it isn't saying much to assert that the probability of event is 0 unless you can at least show that this means something about it occuring.
If, instead, you are imagining a countably infinite set of universes, then you have a big problem asserting that the probability one of them has some property due to being a member of this infinite set (e.g., asserting that the probability of living in one particular universe is 0). This is because it is in general difficult to satisfy the necessary axioms of probability with countably infinite sets (but by no means impossible, as it is indeed rather common in certain special cases). You can't, however, have infinitely many members of a set you wish to treat as a probability space and with a probability measure that e.g., assigns equal probability to each universe because you must have that probabilities are greater than or equal to 0 but also that the probability of the whole set is 1.

 

[Clizby Wampuscat]

It's a fairly common and very useful component of mathematical analysis, set-theoretical approaches to the real number line, etc. The most common version of algebraic treatment of ∞ as a "number" that can be negative or positive and to which algebraic properties are applied goes under the name "extended real numbers" or "extended real number line" or similar names. As an example:

(from appendix A.1 of Rana, I. K. (2002). An Introduction to Measure and Integration (Graduate studies in Mathematics Vol. 45) (2nd Ed.). American Mathematical Society.)

More compactly (from Beals, R. (2004). Analysis: An Introduction. Cambridge University Press, p. 40).

Also keep in mind that almost all real numbers (in both the everyday sense of "almost all" and the measure-theoretic) require manipulations of infinite sequences or series by which almost all real number must necessarily be defined. This is because the set of rational numbers, while dense, has measure 0 and more importantly isn't complete (i.e., every irrational number is the limit of a sequence of rational numbers converging to that unique irrational number, which means that unless one embeds ℚ in ℝ one cannot even talk about 2*π). Since the set of irrational numbers is a greater/larger infinity than that of the rationals, most of any interval in ℝ is made up of irrational numbers. In fact, one can remove every single rational number from a given non-empty interval in ℝ and the measure (or length) of the interval would remain unchanged.

So we kind of half to deal with a variety of infinities and procedures that require infinitely many "steps" of one sort of another just to get to the point where we can reasonably define pi in order to attempt to define what the product 2*π means, if anything.

Ok, so how does this relate to my comment.