# Can loops/cycles (in a temporal sense) exist without beginnings?

I know this might seem like a question that might belong in a Computer Science forum but I wanted a more philosophical explanation and example.

When programming, I sometimes write poor implementations and I get a never ending while loop, in the case of my code there were necessary steps and a beginning for the loop to occur but for some reason I questioned myself is there anyway a loop might exist without any beginning or causation and so I thought this would be a great place to ask. It seems to be very unintuitive and even illogical to think that a loop might exist without a beginning. An end is not necessary because of definition but is a beginning a definitional piece of a loop.

Is it logical to say that a loop has no beginning? (Spatiotemporal abstraction)

If anyone has an explanative answer with an example, I would prefer any possible example and possibly something that draws from other disciplines.

• Its beginning is the point at which you conceive it. Commented Jul 17 at 21:34
• I guess if you thought it as endless then it would have no beginning. But in existential infinity, since there is a now it is grounded and definite. Commented Jul 17 at 22:16
• Is it "logical" to say that a loop has a beginning? If it does it is not, strictly speaking, a loop, and "loop" in programming is used loosely for something that is more like a spiral. Mathematically, a loop is a closed curve with no endpoints, and such curves can, of course, 'exist'. The trajectory of a pendulum in the phase space is a loop, as are all limit cycles. Commented Jul 17 at 22:20
• If time didn't exist until the Big Bang what does before thay mean? What is time? We aren't sure. The Conformal Cyclic Cosmology model seems to indicate a possibly eternal cycle, with the universe decaying into nothing but photons which literally don't experience time, then that being conformally equivalent to the Big Bang, & time 'restarting'. Hawking Points would suggest some information can 'carry over', in large scale cosmic structure Commented Jul 17 at 23:23
• IMO a time loop (not a spatial loop) need not have any definite beginning and certainly we cannot define one unambiguously (this is what a time loop means anyway). n reality there is no definite entry point for a time loop, or, in other words, any point is equally a beginning, and thus there is no (fixed, definite) beginning. Commented Jul 18 at 8:05

All loops which exists or had existed must have had a beginning. There is no loop , mathematical or real, which has no beginning. Mathematical ones take birth in the mind. Real ones start somewhere in time. If we talk about the Universe itself ,then in my opinion, an unconditional cyclical universe is not possible because it would create a perpetual system.

• this is not a "good answer"; it is an assertion of belief, one without any given reason, and which it is safe to assume there is more likely to be a consensus on in the opposite sense Commented Jul 18 at 6:46
• "Unconditional perpetual system would mean perpetual suffering." that is another unsupported assertion - it could equally mean perpetual bliss or perpetual apathy. Energy is conserved (first law of thermodynamics) so there is no problem with perpetual cycles from that perspective AFAICS. Commented Jul 18 at 10:07
• "Real [time] loops start somewhere in time." Er ... no. The very definition of a loop is that it is a closed shape without beginning or end. A loop in time does not begin somewhere in time; it simply is. Commented Jul 18 at 10:11
• " Unconditional perpetual system would mean perpetual suffering" I should add, finding an idea unpalatable does not mean that it isn't true or can't be true. The quote (as does the avatar) is suggestive of Buddhist philosophy, but I don't think that rejecting truth on aesthetic grounds is actually consistent with that? Commented Jul 18 at 10:41

It depends on whether you mean beginning and end in a purely spatial sense, or in a spatiotemporal sense. A loop or circle has no beginning or end by virtue of its spatial existence, but the processes of constructing a loop or circle starting with a definitive time does. Your question might best be answered with a mathematical projection.

Consider the unit circle and a comprehension which represents it. {∃(x,y)∀x,y∈R : x^2 + y^2 = 1}. We can can see that the domain of x will be [1,-1]. If we start at (1,0), we can move into either the first or fourth quadrants and move around the circle and eventually return to (1,0). Whether we move clockwise or counterclockwise, we will find that our points will be periodic and repetitive. Now, we can map that process to a third variable t for time.

This new mathematical structure has a comprehension that is similar. {∃(x,y,t)∀x,y∈R∀t∈N : x^2 + y^2 = 1}. Now we can see that while (x,y) repeats, (x,y,t) never does because at every new point we construct, we will have a new t.

Thus, independent of time, there is no start and end geometrically speaking. A circle is a set of points where no point is privileged (due to radial symmetry), and no matter how many points are calculated, one will find no point that differentiates itself as a start or end value in the same geometric sense a line segment has an initial point and final point. However, the construction over time will have a start and end point because there will be both an infimum and supremum for t. Therefore, it depends on the comprehension or, if you prefer, intension of the abstraction.

EDIT

Give your comment regarding the start of a loop, all loops on a computer will have a start time, and therefore a beginning. In fact, on a modern electronic computer, there's a manufacture date, and it would make no sense to say that a loop could exist prior to the existence of the physical system which generates it. This is in accordance with an abstraction of computation in a physical system.

This, of course, is a constructivist approach to mathematics, where objects are not real, but are constructions of the thinker's mind. In this way, loops are not real, but are mathematical constructions (SEP) of a sort. For instance, you could consider an implementation of an iterating construct in a programing language in terms of its algebraic semantics. By rejecting the actuality of the loop, you would be accepting that it is merely a construct that manifests the property of potential infinity. From WP:

Actual infinity is to be contrasted with potential infinity, in which a non-terminating process (such as "add 1 to the previous number") produces a sequence with no last element, and where each individual result is finite and is achieved in a finite number of steps. This type of process occurs in mathematics, for instance, in standard formalizations of the notions of an infinite series, infinite product, or limit.

Under this understanding, all loops have both beginnings and ends, because they must be constructed and executed, and execution cannot continue indefinitely in any practical physical sense. (Of course, metaphysical speculation regarding the nature of time and the universe itself could lead you into a conversation about whether or not time and the universe itself has a start and end, but for any practical discussion, potential infinity applies.)

• Of course, you can apply the comprehension to a stack and runtime in an application through an obvious extension of the abstraction.
– J D
Commented Jul 17 at 22:25
• +1 Great explanation, but I guess my question is actually in a spatiotemporal sense is there anything that is a loop in a spatiotemporal sense and doesn't have a beginning you see that is why i used my program as an example from a temporal abstraction, is there anything that has no beginning. Commented Jul 17 at 22:29
• I've tried to address your preceding comment in the edit to the original response. Hope this helps.
– J D
Commented Jul 18 at 14:59

Consider a circle that is parameterized by time, for example the set of points

(x(t), y(t))

for all real-number values of t. Since the circle has (in this case infinite) rotational symmetry, I would say that this qualifies as a cycle with no beginning.

If one were tempted to retort, “But it does have a beginning, at the point (x(0), y(0)),” then we’d have to acknowledge that no, by a simple change of coordinate systems we can see that there is nothing special about that point, or about any other point on that circle: simply rotate the axes—which amounts essentially to reparameterizing to

(x(t + c), y(t + c))

for some constant (temporal offset) c. This would amount to switching from measuring time before or since, say, my birth to measuring it before or since yours.

And even if one were tempted to retort, “But that can only work for values of t greater than the tBB corresponding to the Big Bang,” we would have to acknowledge that there’s nothing at all that obstructs our looking at points on the circle for t < tBB. All such points are perfectly well defined.

• "Eternal Inflation" suggest that there is "space" outside what we regard as our (bubble) universe, in which case there is nothing that prevents a perpetual cycle before our big bang. Commented Jul 18 at 10:53
• Yes, @DikranMarsupial, I agree. It’s just that in writing my answer I didn’t have to even address that case. Commented Jul 18 at 10:55
• Without e.g. eternal inflation, in our universe, $t < t_BB$ does not exist, so it is not true that the points are well defined in that case (i.e. if $t \in \mathbb{R}_{>0}$ and $t_{BB} = 0$ then $t < t_{BB}$ is not well defined, so anything derived from it will not be well defined either). Commented Jul 18 at 11:32
• You are ignoring the point that time does not exist prior to t_BB. If you are ignoring that, then your last paragraph is a non-sequitur becuase you are saying that the retort that "But that can only work for values of t greater than the tBB corresponding to the Big Bang,” by ignoring that fact in your response (if t does not represent time then the well definedness of x**t under those conditions is irrelevant). Setting t_BB = 0 is a clarifying transformation that makes t belong to the set of non-negative reals. Commented Jul 18 at 12:46
• Sorry you are evading the issue that time is not defined prior to t_BB. Making things more complicated to derail an argument is one of Schopenhauers strategems - I can't be bothered to look up the number, it is enough for the evasion to be noted and for me to recognise further discussion is unlikely to be productive, so I will leave it there. It is a shame as your answer is a good one (and I upvoted it), apart from the last paragraph, which is a non-sequitur. Commented Jul 18 at 13:35

I mean a loop apparently has a beginning and an end, given that a classical loop is just a spiral with one winding.

If you however abstract the loop to a perfect circle and to a definition of f(x) = f(x + Δx) than you could start that loop at any x. And if you picture you're circle as a sine/cosine wave every arbitrary x that you would choose would have an infinite number of siblings which could also be the origin of the loop.

And while a "classical loop" enters and leaves the ALMOST perfect circle, so if you'd run your finger over the material you'd enter and leave the loop. The same could not be said about a perfect circle. If you'd metaphorically would try the same with a perfect circle you'd never be able to leave the circle (at either end (start or finish) and would always return to a point on the circle.

So in that regard a perfect circle has either no beginning or at least no uniquely defined beginning as you'd be able to pick an infinite number of arbitrary starting points.

So if you're on a perfect loop, you'd not be able to tell how it started.

That being said, from our intuition of cause and effect, we'd assume that any effect has a cause and that a perfect cycle is actually more like a loop or some form of limit cycle (see conifold's comment), that has a beginning that we're just unable to see. Or that it's actually a spiral and it only looks like a perfect circle from our vantage point or that it was constructed/conceived as such a loop and that the construction/conception of the loop is it's "beginning".

Though in either case the circle itself usually isn't going to help us to figure that out because it will only ever show us the same things over and over again and for that we'd likely need to take a different perspective on it.

• An end is not necessary i mean given enough energy a loop could go indefinitely. Commented Jul 18 at 15:49
• I'm not sure whether this answer is YES or NO ! Commented Jul 19 at 7:39

Something could be both endless and bounded depending on point of view.

Endlessness, or non-beginning, could be true for something from the perspective of being on the loop. e.g. As said in other answers, standing on a circle there is no real point at which there is any meaningful beginning or end.

From the outside, there are boundaries. Any specific circle has maximum and minimum values on some set of axes (with whatever rules they have) that define the portion of the surface that the circle is embedded on. These things are scalable for any dimension of loop and embedding that you care to investigate.

To get to my point: from the position of being "on" the loop, it could be parameterised to tell us how far around the loop we are from some predetermined point, but there is no real way of knowing anything about the embedding without being given that information separately. Note too, that it isn't even a loop (from the point of view of being on the circle)! Without being told about the embedding, it may as well be a straight line that never ends... Even if we have a "starting point".

# Maybe.

So far as we know, closed timelike curves -- time loops, in common parlance -- are consistent with/allowed by all the laws of physics we currently know. We have never observed one, nor do we have any ideas about how to cause one to exist where it didn't before; so whether they exist or not is something of an open question at the moment. (The question could be closed in at least two ways: one would be to observe such loop, and another would be to discover some new physical laws that prevent them.)

There's some fascinating results in the theory of algorithmic complexity in the face of CTCs that may interest you, since you say you are a computer person. For example, being able to loop just one bit "back in time" is already enough to recover all the power of looping arbitrary information, which kind of blows my mind. For a somewhat approachable introduction to these ideas, I really enjoyed the lecture notes from Scott Aaronson's class, Quantum Computing since Democritus. Lecture 19 starts in on CTCs. Or, if dense reading is more your style, you might jump straight to the academic literature.

• Great finding, but it seems that it is completely speculative and unfounded for one the whole CTC lies on purely theoretical quantum assumptions that aren't even consistent with current findings, so CTC necessarily needs to imply retro causality which goes against logical foundations, classical laws of physics and even current quantum mechanics which implies quantum causality which arises as a result of non-locality and superpositions i.e., it is a misconception to think that quantum causality is retrocausality even though this is completely wrong. I don't think its proven. Commented Jul 19 at 18:23
• So, I would definitely be interested in any more consistent findings. Also retrocausality defies the theoretical consistency of quantum mechanics, look no-go/no-cloning theorem. CTC is completely fictional and logically inconsistent but I would really appreciate any other quantum or computing theories that have more inherent consistencies. Also, while reading the paper he assumes the validity of CTC and then goes on to formulate the theory that hasn't been experimentally verified. Commented Jul 19 at 18:25
• @Howwhye I will admit to being a bit out of my depth but I will make some responses anyway. Please apply an appropriate amount of salt before swallowing. 1. I freely admit this has not been experimentally verified... even pre-admitting it in the answer before you objected. ^_^ (1/2) Commented Jul 19 at 19:13
• 2. I believe you are mistaken that CTCs go "against logical foundations". You are probably right that quantum causality is not retrocausality -- but that is not connected to whether CTCs are incompatible with quantum mechanics. 3. I believe there is not a problem with no-cloning. The particles going around the loop the "second time" are not clones, they are the same particle as the one going around the "first time". (Indeed, there is just the one loop, there is no "first" or "second" time around it.) (2/2) Commented Jul 19 at 19:14
• I mean CTC base on the idea of causality that is more improbable than quantum causality i.e., retrocausality this is the philosophical basis, at least we can agree on that. Unless either quantum causality can be adjusted to allow for retro causality or it can be shown that retro causality can fit in with quantum mechanics and the rest of physics as well as grandfather's paradox then I can't see how CTC can't go against the basic logical foundations. Commented Jul 19 at 19:20

Consider generators, as per Python.

Here the loop takes a generator. The generator just produces elements. The loop just acts on them. Sure, the generator has some state that lets it decide what to produce first. But the loop has no idea. It just takes what the generator gives it each time.

So the loop itself has no beginning. That's decided elsewhere.

• In this example, the loop very clearly does not exist before the program is started, and certainly not before the computer is switched on! Commented Jul 19 at 7:42
• @MikeB oh. You’re one of those that believe the river can’t exist without the water. Commented Jul 19 at 9:22
• @candiedOrange Not sure what your comment is meant to mean, (no I don't) and possibly not your original answer either? Commented Jul 19 at 13:35
• Generators do clearly have a beginning and to even start generators are not loops they are actually the opposite they halt and pause loops therefore changing the "loop" that is being observed. Commented Jul 19 at 19:51
• @Howwhye right, generators have a beginning. That way the loop doesn't need one. Commented Jul 19 at 19:55

this might belong in Computer Science

I belongs in science fiction. In physical reality, there can be no time loops. I'll leave it at that, but it's not just an opinion. It's not a matter of "if we were real smart we could figure it out." It's not even just Einstein's opinion. It's a necessary consequence of hypergeometry and the nature of mass.

• I actually agree, please tell that to people that suggest a CCC (Cosmic cyclical cosmology) it's completely science fiction Commented Jul 18 at 17:57
• I love Penrose (and hated his comedy sidekick). But I put down his cyclic time book halfway through and attributed it to old age. Commented Jul 18 at 19:15
• @Howwhye: CCC doesn't have time loops. Rather, it has eons between regions which look like ours right now, and regions which look like the early/late universe. The eons do not necessarily have the same models of particle physics; electrons may be specific to our current eon alone. Commented Jul 19 at 16:07
• @Corbin: My interpretation was that there's something rotating In an imaginary direction: time. Time turns into space as the universe expands. Eventually there's another one. If the second one has the same mass as the first, which it should if it's the same object, and if every other cycle, time runs in reverse, then everything would balance to exactly zero mass energy and you could have a series of white hole big bangs. Anyway I only read half the book but that was what I got out of it. Like I say, I put it down after that. It sounded like Penrose caught the "old people crazy." Commented Jul 19 at 16:19
• @Corbin I get that it is a theory but there are no experimental, empirical evidence to support any of it, I know that Stephen Wolfram's hypergraph cosmological theory states a CCC but even though theoretically it is very strong, there seems to be no suggestive or backing evidence. Commented Jul 19 at 17:06