Infinite regression

[NathanWubs]

Lol, this came up when I looked for Star Trek Voyager Infinitive Regress.

[rozeboosje]

@NathanWubs ROFL ...[steeples fingers a la Mr. Burns] Excellent tags, so

[PlanetJeroen]

Could you explain without formula why that ball stops at 8.24 ? I dun get it :/

[rozeboosje]

@PlanetJeroen Every bounce takes a tiny bit of time, and there are an infinite number of them. But even so, if you add all those bits of time together, you get approximately 8.24

Well, if all the ball's bounces fit in 8.24 seconds, there will be no bounce in progress at 8.25 seconds. The ball is still there though. So if it's there and it's not bouncing and it was bouncing earlier, well, then it must have stopped. Intuitive it's not. But it is correct.

[PlanetJeroen]

@rozeboosje You've just hurt my brain, in a good way .. I'm gonna rewatch the previous in the series and try again :p

[JoakimfromAnka]

I understand nothing of this but it's sure interresting if this idea could describe the origin of universe.

[rozeboosje]

The video is not actually intended as a serious contender for a description of the origin of the universe. It's intended as an illustration of how bald assertions about what cannot be true about the origin of the universe aren't as self-evidently obvious as those who make them claim they are.

[thunder151515]

so if you look the world trough the example of bouncing ball we can explain the creation of everything like the ball bouncing "backwards" and therefor we live backwards :D :D XD and the universe will never end.

[rozeboosje]

LOL

[FranzFafner]

It would have been shouting if the whole comment were in caps. But I just put a couple words in caps, for emphasis. I don't know how do italics or boldface in these comments.

Sorry for the misunderstanding.

I promise you, I grasp the math. It isn't all that advanced. But it seems I find the paradoxical results more interesting than you do. De gustibus...

Anyway, keep on truckin. Your posts are very interesting.

[rozeboosje]

The paradox is only due to our intuition not coping with what is mathematically possible. Mathematically you can cram an infinite number of things within a finite space. For example, take a line segment, and take the point exactly in the middle. Look at the new line segment you can create by taking the line segment from one end of the original line segment to that mid point.

Now repeat the procedure, and repeat ad infinitum. Now look at the collection of "mid points" you produced (more)

[rozeboosje]

with this process. There is an infinite number of them. No matter how close you get to the end of the original line segment, in the tiny amount of space between where you are and the actual end there will still be an infinite number of these mid points. You will never reach the "final" mid point, no matter how close you get to that original end point. And yet, it's still mathematically clear that there are no points beyond that end point.

The bounces in the example are exactly the same. (more)

[rozeboosje]

I took an example with a ball that stopped bouncing after 8.24 seconds, and reversed it. When the ball stops bouncing, you can get as close as you like to that point at approximately 8.24 seconds, and you know there will still be an infinite number of bounces to go between that point, and 8.24. You will not be able to find a "last" bounce. There IS no "last" bounce. And yet, by 8.24 seconds, the bouncing is all done. Over. Reverse that, and the mathematical model accurately describes (more)

[rozeboosje]

a ball that starts bouncing even though there is no such thing as a "first bounce". Of course your intuition is going to respond to that finding by baulking at it, but the correct response is not "but ... but ... that's just crazy!!!". The correct response is to recognise that your intuitions will sometimes let you down.

[FranzFafner]

Thanks for your generous response. It's more than I expected.

I hesitate to keep expressing disagreement with you, since it must seem ungrateful and rude. But I still think the Magic Ball construct reveals a paradox.

It would be best at this point if I posted a video response in which I examined your Magic Ball, as well as Thompson's Lamp and other Supertasks.

I couldn't care less about Aquinas and his theology. I'm just interested in the epistemological implications of paradoxes.

[rozeboosje]

But what paradox does it reveal? As it makes perfect mathematical sense (within the context of the example at least) I don't see a paradox.

[rozeboosje]

Hm....

Ok. Here's another example I just thought of. You know the real numbers, right?

Now imagine you're sitting on the X axis, right at 0. Now you know that to your right there are all the positive number, and to your left there are all the negative numbers. You look over to the right, and in the distance you see the number 1/2. A bit closer you see the number 3/13, and closer again you see the number 1 divided by the square root of 80.

(more)

[rozeboosje]

Those are interesting numbers, and you decide to go visiting them. You put on your walking shoes and you start walking to the right from your starting point at 0.

My question to you is: what is the first positive number you will meet?

If you give that a good think you may realise why the question is invalid. There is no first positive number. Maybe one way of understanding why is by reducing this to absurdity. (more)

[rozeboosje]

Let's make the assumption that the question IS valid, and that there IS a positive number that is the first number you're going to meet. Let's call this number P.

But wait. If P is a positive number, for any positive number P, then P/2 is also a positive number. And if you're walking from 0 to P, then you will meet P/2 on your way, and therefore you will meet P/2 before you meet P ... so P cannot be the first number because at the very least P/2 will be met before P.

(more)

[rozeboosje]

And since this is necessarily true for any candidate number P you can think of as possibly being the "first positive number", NO exceptions, there therefore is no first positive number moving to the right from number 0. And yet, there it is: that pesky number 0. The positive numbers start and end there (depending on what direction one's moving in [wink]), without there being a first c.q. last one, and regardless of how much one's intuition does backflips when confronted with it (more)

[rozeboosje]

The fact is: our intuition fails us when it comes to thinking of infinities like that, especially when they are confined within limits. The only way to make any headway in comprehending them and being able to deal with them in a rational manner is mathematically. Check out Cantor.

[FranzFafner]

In theory, it's possible to discuss ideas without taking every question as a personal attack. It is permissible to pass up the chance to insult someone.

I have rather enjoyed watching your mind in action. But too often it is obscured by this dark hostility and narcissistic arrogance. Maybe it's just a phase.

I think this magic ball construct is the most interesting thing you've offered, and I'll continue to examine it. But apparently we can't discuss it in a civil manner. Jammer..

[rozeboosje]

Start showing me that you have a grasp on what I'm telling you without shouting at me (capitals). Shouting does not hide the fact that you cannot see beyond your intuitions. Intuitions are your worst enemy in mathematics. So show me you can move beyond "common sense" and you can start getting a grip on maths, and then come back.

[FranzFafner]

What can it mean to say it STARTED bouncing - unless it started with a bounce?

The math shows with certainty WHEN it started bouncing, but also shows that it never really STARTED at all, because there was no first bounce. Take any bounce - there was always a bounce before that.

It NEVER started - and we can show PRECISELY when !

A stunning paradox - the whole reason for a sense of humor.

My friend doesn't see the humor. But then, she's a schizophrenic. They have no sense of humor.

[rozeboosje]

Sorry dude, I can't help you if mathematics is an impenetrably mystery to you.

[FranzFafner]

It's an interesting paradox you've presented. It reminds me of Zeno's paradoxes, actually. But if the ball was not bouncing at -8.25 seconds, and it was bouncing at -8.23 seconds, then it must have started bouncing at some time between those times. That's not my intuition. That's logic. And just as Zeno's paradoxes could be solved only with a higher mathematics called calculus, perhaps your paradox will lead to the development of a still higher math. Math is only a tool. It's not reality itself.

[rozeboosje]

You missed the finer nuance of what I said. I didn't say it didn't start bouncing. In fact I do say it starts bouncing. I even calculate exactly when it started bouncing. What I say is that there is no "first bounce". This example is not based in our physical reality anyway, but in the mathematical universe in which it was created the conclusions are derived with absolute certainty and no "higher" maths is ever going to change that.

[stjimmy933499399493]

now i see why a lot of quantum physicists are turning to taoism and buddhism for inspiration. not to say either is empirically true there just seem to be some similarities when it comes to dealing with paradox and their implications. great fucking vids, truly outstanding. bravo

[rozeboosje]

:-)

Thanks

[peanarchist]

I may invert this theory to something I like and therefor understand better, but it sounds to me very much like the Taoist model of a self provided universe where life always is was and will be.

[rozeboosje]

Cool

It's not a theory though, please don't take it as such. It's just that so many people dismiss ideas like infinite regression out of hand, and unless they can show that nothing even remotely like what I'm describing here could possibly exist, their dismissal is premature.

[peanarchist]

I try not to dismiss it, but not build a complete dogma out of it either. That's what I mean by theory.

The same applies to the theory win which our borders are not our skin. Everything we do is projected into our environment, projected back to us ext. Basically cause and effect...

[NihilistImp]

Mathematical models are only as valid as the suppositions made on their outcomes, the framing of their context, and the validity of their pretext.

[rozeboosje]

Well, that's pretty much what I am getting at here. An argument like that made by Aquinas is based on stating as "obviously true" the assumption that there cannot be infinite regression. I show that in a context that he didn't envisage there can quite easily be such a thing, casting his whole argument in doubt.

[NihilistImp]

If your pretext is that every bounce is followed by another bounce of half the magnitude of the previous bounce, then define that statement with a model that says differently, the model is incorrect. You have not created a paradox nor indicted reason itself, you have created a mathematical shell game in which the effort is placed upon the critic to unravel an intentionally complicated mathematical riddle or accept your argument.

[rozeboosje]

Nope

[rlpjr77]

owned much?

[JohnHolmes3000]

Aquinas was a theologian, therefore he was, by definition, a bullshit artist.

[rozeboosje]

Exactly

[JohnHolmes3000]

Thank you!

[UntamedBlueLight]

Let me get this straight:

We look at math -we see infinite regression possible.

We look at Aquinus - we see a first mover. And when we look at reality, we see the bouncing ball come still. So how the hell can the big bang occur under infinite regression? Don't you find it a little odd? What could possibly cause energy to become mass? And under causality how does the world stay still? how are we able to empiracly understand anything within our senses? Answer: Everything exists.

[rozeboosje]

We look at math and we see no viable objection to models that incorporate a form of infinite regression. We look at Aquinas and we see somebody rejecting I.R. through a bald assertion that it is "impossible". Given the first observation we can conclude that we must take Aquinas' claims with a large pinch of salt..... But that's all we can conclude legitimately. Maybe he is right. Maybe I.R. really IS impossible in reality. But at the very least he needs to explain why; he can't baldly assert it.

[JohnHolmes3000]

No, some things, as the Flying Spaghetti Monster, do no exist. And the model is an abstract one, not one in reality.

As for energy becoming mass, etc., you need to turn to physics for answers to those questions.

[robheusd]

Nah, don't hurt your head. We have an easy way out there since from the conservation of matter+energy follows eternity of time.

Philosophically speaking, reality was always there, and there can not be a "cause" of reality (the cause would already preclude a reality). Reality/existence exists, rather then not, and there is nothing that ever can explains. It's a brute fact of reality.

[rozeboosje]

Wonderfully said

[rozeboosje]

Ok. I hope I can entice you to start making videos ;-)

[robheusd]

The bouncing ball anology is I guess not directly applicable to physical reality, but it is very well conceivable (and in fact the best conception) to think of time as beginningless and endless.

No need for extra-natural causes whatsoever.

That we can not "think" of reality as such (since in our experience, all things do have a begin) does not make it less real.

Reality created us, not the other way around. Reality does not require us to be able to understand it.

[rozeboosje]

Thank you. You can almost grasp it when you realise that you can "always" speak of reality, and that that does not change one bit even if "always" only spans a finite amount of time. It does make the head hurt though.

[robheusd]

Mathematical reality is indeed not physical reality, since in physical reality there is a limit to divisibility of time,space,energy,matter (planck time/length/mass, etc).

[rozeboosje]

Yes, indeed. Our current physical theories at their most elementary are "discrete" - you mentioned the planck units. But who knows what will eventually underpin all of that? String- and related theories appear to be doomed due to their background dependence. Interesting times :-)

[MarquisMongaga]

I've actually encountered the idea of a finitely old universe without any specific point of beginning, but your bouncing ball example made me actually get how that could be possible. Good job with these videos.

[rozeboosje]

Thanks a million. The best comments on a video are when someone tells you it helped make something "click" for them. You're welcome, and I'm glad I could help.

[LukeFM]

Superb. I didn't really know where you were going with the bouncy ball, but when then penny dropped the comparison was compelling.

Is it really ok to translate the conclusions made from the bouncy ball onto the real world? Wasn't the ball contained within a mathematically constructed world with axioms that don't work in our universe? Otherwise I love the idea.

[rozeboosje]

Absolutely; the ball is nothing but a theoretical example and it has nothing to do with actual physical reality. But it shows that the idea of infinite regression is conceivable and cannot therefore be dismissed out of hand. For example Aquinas' argument at some point says something like "and that would lead to infinite regression" and then he dismisses a premise. And with this example I have to press the buzzer and say "Er.. you can't do that".

[TheReasonWhyGuy]

ontology=WIN

[rozeboosje]

yer wha now?

[LesPaulLiberty]

I'm glad I'm intelligent *or more intelligent than the people in these comments* to understand this. Good job.

[rozeboosje]

:-) Thanks!

[LesPaulLiberty]

no problem, keep it up!

[MarkBH70]

This is conjecture, giving god-like qualities to objects, meaning the "ball" would have to be self-existent to be from infinity. If self-existent it would have had to have "created" itself, for lack of a better word, ex nihilo. If so, if it has this power, it would seem to have the power to create other things, it'd probably be pretty powerful of necessity; if so, then it'd be god, or God. Congratulations, you just defined God.

[rozeboosje]

God is a ball?

[MarkBH70]

No, you're a ball, to listen to.

[dooyeweerd]

This, I think, shows exactly how desperate atheists are to avoid theism. At the end of your video the language is very confusing. How can you have an ACTUAL infinite in a TEMPORAL time span. There can be no actual infinite in such a universe. The ball example may be interesting but it holds no bearing whatsoever on reality. Atheists are arguing AGAINST accepted empirical science. Mind you, you have to hand it to their public relations dept. since society thinks it's the other way around!!

[robertdigregorio]

The reverse bouncing ball premise is silly; it would require a constant application of energy to the ball, implying an outside force, such as a god or gods.

Personally, I believe that nothing can not mathematically exist, so nothing could not have existed at any time in the past. If the past is finite, as many argue, then something, such as matter or energy, existed at the start of time. If the past is infinite, then the universe has always existed.

I really see no need for a god.

[rozeboosje]

> The reverse bouncing ball premise is silly

Only if you read too much into it. It's just an illustration.

[Knowntje]

hmmm sorry to say it rozeboosje, but I completely disagree with you here. I don't like to actually dismiss such a great argument for atheism, but I really think this argument is invalid eventhough very well thought through and well presented. I'm actually think about making a refutation video this

[rozeboosje]

Yes please because I wouldn't like you to leave it as "it's invalid" without an explanation why.

[Tiwaking]

Since mathematics is itself a construct, it doesnt conform to Scientific Method. Also: The main problem with infinite regression is that the biological brain cannot a) Comprehend chaos b) View non-causal events. We have no evolved to the point where we can see what is actually going on as opposed to what we THINK is going on

[DethMachineEngage]

but what's the cause of time?

[rozeboosje]

What makes you think time is caused? The word "cause" in itself has a temporal element. The cause precedes the effect. So how *can* time be caused in that case. Maybe time is logically implied? But I'm afraid I have no easy answers. Not even difficult ones for that matter.

[stmichael71]

That is rather false, primarily because Aquinas does make a distinction between various types of causal sequences, indicating that some fall under infinite causal series. And Aquinas' phrase is not that every effect requires a cause. He is speaking about efficent causality, a definite species. Further, even here, he makes explicit reference to per se series rather than those accidental series than can become infinite.

[rozeboosje]

This is an argument against Aquinas' second "proof". And his unsubstantiated assumptions in that are pretty clear cut.

[stmichael71]

No, in fact, they aren't. His proofs as they appear in ST are merely outlines of arguments he elaborates elsewhere. All of his metaphysics is not in those paragraphs. He substantiates those claims, but elsewhere. My point is that he does understand this difference and answers it.

[rozeboosje]

His proofs are nothing of the sort. They have been debunked so many times that bringing them up alone shows you haven't a clue what you're talking about. Bye now. Please stop comment-bombing me.

[mwilliams0]

great video, and good thinking. I am wondering if you use stickam at all?

[rozeboosje]

I haven't yet, no. What is stickam all about?

[mwilliams0]

live video, voice and text chat, it is much more useful for in depth technical discussion. Plus you can have several participants at once.

[zorio]

You're oversimplifying the idea of God here. Aquinas himself has five different proofs for the existence of God and you've only dismantled the worst one. The problem is that you treat God like the first billiard ball in a series of billiard balls, when the Creator is meant to be totally unlike His Creation. It's better to see God as the one who made and maintains the billiard balls, and not simply the first in the series.

[rozeboosje]

Sorry dude, but the idea to see God as the first in a series is not mine, and if anybody's "oversimplifying" the idea of God, it's the person who came up with this so-called proof: Thomas himself. That he has four *other* "proofs" is irrelevant; I'm not addressing those here.

[zorio]

But you're over simplifying the proof; for Aquinas God is the source of Being itself, and therefor it is from Him that things gain existence. Nowhere does he portray God as the first in the series, He is necessarily outside of the series.

[rozeboosje]

The basis of that proof is Aquinas' rejection of infinite regression. And for that there is no sound basis. Whatever else he might have thought about his precious God is of no interest to me.

[azrienoch]

Nice job, Roze.

[rUTokKIN2ME]

Quite the brain teaser, but I'll have to watch both vids again. an infinite number of events, all of which are caused except the first, because..... must watch again. fun stuff

[rozeboosje]

first? That's the problem. With an infinite number of bounces there is no such thing as a "first" one, just like, in the original example, there is no such thing as a "last" one. Maybe one way to understand is if you approach the end c.q. the start of the bounces. No matter how close you get to that point, there is always an infinite number of bounces between you and it.

[rUTokKIN2ME]

hmm, I understand the first example set up the second. But with the first ball, you dropped it, and I see that as causal. in the second example, the ball is already bouncing, and because you reversed the math used in the first example you came up with an infinite number of events, pre and post our examination.

[rUTokKIN2ME]

I'm seeing magic there in the sense that perhaps I've been misled, by the dazzling hand of mathematics, and taken my off the hand that "dropped the ball". That's where I'm at right now. As you said, it's difficult to discard our intuituion.

[rozeboosje]

Yup.

[rUTokKIN2ME]

I'm guessing you mean yes to the last sentence. My feeling is you do believe you've given reason to believe there is no need for a first cause. But infinite only means not finite, or not countable. So the first example makes sense, you have a first cause, and you hypothesized an infinite number of bounces in your magical newtonian universe.

[rUTokKIN2ME]

I don't see how our ability to reverse the math says anything about whether a first cause is necessary. It only demonstrates that that with the right mixture of mathematics and hypothesis, you can do magic.

[rozeboosje]

The reversing of the maths only shows that infinite regression cannot be dismissed. Infinite regression *itself* removes the need for a first cause.

[rUTokKIN2ME]

ok, that helps a little. I'm still uncomfortable with the idea that a mathematical exercise in a hypothetical world says anything about reality, but at least I understand that you are challenging a simplistic dismissal of the possibility of infinite regression. Thanks RB

[CousinoMacul]

Do I smell Zeno's paradox?

[rozeboosje]

Not really. Maybe it bears a passing resemblance. I guess Zeno, too, just couldn't get his head around infinity, and without the maths to help him out he had nowhere to go but into paradoxysm.... :-)

[CousinoMacul]

Look up "Convergent series" on Wikipedia. It's a prety good article. I you have any questions after studying that, I'd be happy to try to explain it to you further.

[bubonicnate]

*checks his balls*- whew okay - not bouncing.

I have thought about this stuff for a long time... and it was nice to see you investingate the material. What role do you think this has in relation to the concepts consciousness? I wanted to hear more about the conflict of intution! You moved straight on to God!

[rozeboosje]

Maybe I should have used the word "naïve" instead of "intuitive". Our minds simply aren't equipped to deal with infinities innately; we have to use a tool like mathematics to help us.