It's a great puzzle, really counter-intuitive. I've done up to the case where there are 4 islanders (see below), and it works, so I can see it would work for n islanders. It still just feels weird though.

I see I've arrived a bit late to this debate, but it seems it would be helpful for someone to bring it back to the original topic anyway.

So my 2c is that, yes, there need to be restrictions on speech. AFAIK no modern nation has had absolute free speech. For the sake of public safety, crime-fighting, protecting children, commerce, and other reasons crucial to the functioning of a society, there have always been restrictions.

So how do we define the "right kind" of free speech?
I would say it's not straightforward and it should be an ongoing, nuanced goal. But, in general, we should aim towards everyone being free to state an opinion, and/or disseminate information in good faith. Everything else is fair game for a society to decide on.

What do I mean by "good faith"?
I mean with some reason for believing it is true (I am against pundits having a "right to lie") and without the intent of causing harm (e.g. doxing).

Doh! My mistake.
I meant the bit about when all the brown eyed people realize they have brown eyes...but on checking, that wasn't from the OP, that was from someone's solution.

You're right that in the OP as stated, the blue eyed people all leave on day 100 or whatever, and no-one else.

I've got here late and just read the first and last pages, but I'd agree that this version of the puzzle is not logically sound.
If we follow it through, then if I'm an islander with red eyes, I will still erroneously conclude on day 100 that I have blue eyes and get thrown off the ferry.

A perfect replica is still a replica. Is that a bit clearer? If you are not the exact atoms that make up my body, you couldn't be me. You could be a replica. — AmadeusD

How many of your atoms, and why does it matter?
If the transporter worked by just spitting your atoms across space and reassembling them, is that now you? If not, why not?

To be clear: I don't believe that the transported transports a single instance of consciousness, i am just saying that bodily continuity (or identity...I didn't really follow the distinction) is not as straightforward
an answer as might first appear.

You disagree that someone who loses their legs (or other body parts) is still hte same person? — AmadeusD

No, I disagree with the implied analogy to the problem and your suggestion that it is a "silly question".
Losing a limb does not involve splicing the consciousness. It doesn't solve the problem, it avoids it.

I am suggesting that:

1. Bodily continuity is thought about wrongly (i.e without the spatio-temporal aspect here noted); and
2. That all this does is defeat certain claims (bodily continuity ones).

Perhaps you've misunderstood me. — AmadeusD

Yes it seems there is something not being communicated here, because bodily continuity is defined as requiring continued continuity of the spatio-temporal aspects. So I can't make sense of either your point (1) or point (2) here.

There can't be two yous. There can be two Mijins which are not identical. — AmadeusD

Well this is a critical thing in dispute. Right now I am Mijin, and Mijin is me. And it's all very simple because we have no technological means to duplicate, splice or augment my consciousness.
In a hypothetical time where I could be duplicated, and for some period of time (before they diverge) there are identical Mijin agents, how many are me?
Bodily continuity doesn't make a clear claim here, not in its basic form, and also requires we know the history of how we arrived at this configuration of the universe.

Oops typo. Yes I meant Sent

Right, and most of us accept Copied, and you too, but you want to tackle Sent on their own ground (show them it's a quagmire), so it's tiresome if I don't join you on that ground? — bongo fury

Well explaining the context of the transporter problem was important to the OP. And then, I engaged people to the level that they engaged with me. If you consider Copied to already be refuted then great; I guess you don't need the imperfect transporter (although modified versions such as moving, or replacing, someone's atoms present equivalent problems).

What's consciousness got to do with it? Copied doesn't need consciousness. (Nor unconsciousness of course.) It just needs a reliable basis for individuation (same what? different what?). — bongo fury

Because firstly the whole problem is concerned with what happens to the consciousness.
It's much more important to me than what happens to my body. Whatever process I am subjected to, the most important questions are 1. Whether I am still alive, in any form, from my own point of view and 2. What form that consciousness is in (on earth, on mars, with brain damage etc).

And secondly I don't think we have a good model for answering these questions, apart from the proposition that perhaps our consciousness is never persistent.

Bodily continuity seems like the common sense approach, but only because today in 2025 the only way for a consciousness to be created is within a human brain (and probably other animals, though it's hard to know what level of consciousness to what kind of brain). All we can do is snuff consciousness out of existence or modify it with either trauma or drugs.
But if at some future time we can splice / copy / augment the mind, bodily continuity is way too vague, and our model of consciousness too ill-formed, to make concrete predictions.

Yes no problem.
When it comes to the transporter problem (also called the teletransporter problem) there are two major positions*, let's call them Sent (your consciousness is transported) and Copied (the person on Mars or wherever, is a new instance of consciousness).

I summarized one argument against Sent in the OP, but another common argument against the Sent position is what if the person at the source location is not killed? In such a situation it would be absurd to claim the consciousness has both been sent and retained in the original. They clearly aren't a singular instance of consciousness because I can stick a pin in one person and the other is not going to flinch.

Having been in transporter debates many times, I am familiar with the counter-argument that most Sent proponents will say. They will say that the consciousness was branched. Only for the instance of time that the two mental states were identical could the consciousness be said to be in two places. As soon as their experiences differ, they are two people.
I tried to find the formal name for the position that, essentially, being qualitatively identical entails being a singular instance of consciousness (the philosophical underpinnings of the Sent position), but all I could find was https://en.wikipedia.org/wiki/Personal_identity#Locke's_conception.

* And a third position, which I've already alluded and I won't expand on in this post to keep things clear.

Well a new person starts and ends their life at every instance under that hypothesis, there's not even a singular person constantly dying.

Indeed. The question of what happens if the person at source is not deleted is a common objection to the idea that you are teleported. The common answer is that you have now become two people; not that you are linked now, but basically your existence is branched.

If you find this problematic, so do I. The imperfect transporter I think is a pretty good counter against this position.

But I also find bodily continuity problematic when it comes to questions of how much continuity is sufficient and/or how exactly we define continuity.

The best, though most unfortunate, explanation is simply that there's never really continuity. It's an illusion.

The point is, the measure of our understanding of a phenomenon is what predictions and/or inferences we can make about it.

When it comes to your position on personal identity, a position that I think is basically the bodily continuity position, it seems it doesn't enable you to answer questions like the kind that I have posed; about a mixture of continuous and discontinous material, or of being discontinuous on a time frame far quicker than mental events.
And I've asked why we would take the position that bodily continuity matters, because that might give a clue about how we'll go about answering such questions. But you haven't given an answer why, you've tended to just repeat your position.

I don't want any of this to sound like snark, or as if I am accusing you of bad faith. I'm just saying it seems pretty pointless.
If I were to say that what defines an instance of consciousness is the mojo, but not answer any questions on what the mojo is, how I think this might work in practice, or what led me to think it was the mojo in the first place...then all anyone can say is "good for you". End of debate, nothing learned.

I'll answer again: nothing; only my continued corporeal integrity matters. — bongo fury

Your answers are basically just asserting your position again.
What I am trying to get at, is why. And to also tease out the answers to questions that are problematic for bodily continuity, like why it would make a difference if I move your atoms from point A to point B in one piece or separated for a nanosecond. What was lost in that second scenario?

Radical Lastthursdayism says, that's constantly true, all the time - your existence is being renewed every moment and your memories are effectively implanted. — flannel jesus

Indeed. In fact, even talking of "your existence" being "renewed" could be misleading here, as what we're actually positing is that every instance of consciousness is essentially a new entity that just happens to inherit the memories of that body. And then its existence ends in an instant.

It's not a pleasant conception, but as I say, it's immune to the strong counter arguments to the two more obvious positions on the transporter problem. In fact, I've never heard any argument against it (but I've generally not heard this position discussed very much at all -- most people in this debate implicitly assume continuous existence).

I didn't content they did. Not sure where this is coming from. — AmadeusD

Because I am trying to get your meaning. You're alluding to bodily continuity, so I am asking follow up questions of why bodily continuity is critical.

This doesn't have much relevance to my position, or the claim, to be clear. For sake of discussion, there will be no specific amount. You can lose both legs and still be alive, and you. It's a silly question, in context. That's not the belittle it. It just has no reasonable avenue to a response. — AmadeusD

Hard disagree.
Look, in daily life we all implicitly subscribe to some form of bodily continuity. I have Mijin's memories and I assume that I am one and the same entity as Mijin. If I were to suffer an accident and have brain damage, then that is a damaged Mijin.
The problems for bodily continuity come with hypotheticals like the transporter problem and the follow up questions that I have summarized in this thread. It's much easier of course to insist that we keep our focus only on how personal identity works in daily and handwave questions like the imperfect transporter. But if we have a good model of personal identity we shouldn't need to dodge; we should be able to apply our model.

It removes the potential for my first-person to disappear, but someone to still be me. Which seems ridiculous and intuitively hogwash. — AmadeusD

This is why the terminology is important here. Another entity could be qualitatively identical to me, but if he is not numerically identical to me, then he's arguably Mijin but not me. If you stick a pin in him, I don't feel a thing. And when I'm lights out, I have no reason to believe I will suddenly have his conscious experiences.

Mijin If spatial-temporal continuity is required to maintain identity, then your case adds nothing, the subject is killed no matter what. — hypericin

Can we know that? What if the transporter functions by firing your actual atoms across space? If assembling your own atoms back into the configuration that they were in isn't you, then what is missing?

If it is not required, then your case reduces to, "How much damage can someone sustain before becoming a new person?"

From the third person perspective yes that's what it boils down to. The question is what about the first-person perspective of the person that entered the transporter. Is he gone entirely?

It seems more realistic to infer episodes of relative coherence among otherwise fleeting and unconnected moments of consciousness? — bongo fury

This seems to be alluding to different levels of consciousness. Sure, there are different levels of alertness largely corresponding to brainwave states. This seems a different topic though to personal identity.

They deserve identifying with (or as) one person because they arose in that particular (spatiotemporally continuous) brain and body. — bongo fury

This is just asserting the position of bodily continuity. I'll ask again: what makes the particular atoms that you are made of special, and how many of your own atoms need to be incorporated into an entity for you to survive in any form?

It seems crucial to the viability and identity of an organism, at least? Pre-sci-fi, of course. — bongo fury

But that's my question. When I ask why spatio-temporal continuity matters, I mean why is it critical to whether consciousness persists or not? If we believe that there is some persistence of consciousness from moment to moment then it is a valid question of what is required for this persistence. If the key thing is that it's the same atoms, why is that necessary?

Really? I suppose there are edge cases, like that of conjoined twins? But generally we, like the ship of Theseus, maintain our personal identity by losing and replacing a few planks at a time. — bongo fury

Yes that is the case today but I am not talking about only what is biologically or technologically possible today. If that were a requirement for topics here, then 99% of threads on philosophy forums can be shut down right now.
I am talking about hypothetically copying entire brains, swapping out atoms etc to test a given position or model of personal identity.

I think this is the correct answer to the branch-line case. Any "one" who is me, yet occupied different atoms and extracts difference resources from the environment to maintain homeostatis, and occupies a different "moment' in space, cannot be me. — AmadeusD

But why? What is it that your specific atoms contain that hold your "essence"?
And how many such atoms need to be moved across for you to still be alive? Will 95% do it? 99%?

I think this is a really stupid 'paradox' personally. A ship is "that ship" because of what people call it. There isn't, that I can see, a physical boundary to the identity of a utility/object. — AmadeusD

Agreed, I hate the ship of Thesus. It's only a marginally interesting paradox in its own right, and though it is invoked for good faith reasons, I think it actually derails this topic. Because, as I said upthread, the problem of personal identity chiefly concerns the first-person perspective -- what it is, and under what circumstances it is preserved. The ship of thesus gets us immediately thinking of the third person perspective, and making a completely arbitrary judgement that doesn't actually matter.
Whether my first-person perspective still exists or not matters a hell of a lot to me! It's not like ship of thesus.

Independent medical exam? — bongo fury

In my experience

Spatiotemporal continuity (with me). — bongo fury

Why does that matter? And how, precisely, do we define it? Because of course it is vulnerable to the same sort of "imperfect copy" problem that I talked about in the OP. Whether I am alive or not is binary (NB: alive but damaged is still alive), but whether I as an organism have spatiotemporal continuity with an entity at a past state of the universe is something less clear. Does it matter whether it's the same atoms? What proportion of atoms must be in the same state?

Oh ok.
Yes this is just an IME thing, so no worries if you disagree. But often when there are debates on the transporter problem, and you have the people forming into two groups of either "transported" or "killed" (and, as I say, no-one but me seems to occupy the third group of "no continuity even before the transporter"), the rhetoric is often like this:

"What connects the person at source to the person at the destination, instead of them being separate entities? What was actually transported? Is it a soul?"
Vs
"What does the person at the destination lack in order to be you? Is it the soul? If it makes a difference whether we literally move the individual atoms, does that mean you're suggesting that the atoms held the soul?"

But so (by hypothesis) will any number of duplicates be convinced of their continuity with Kirk. So what? I'm convinced I'm Napoleon. — bongo fury

That was the point. I was explaining that duplicates being convinced they are the original, and third-parties believing the duplicate is the original, doesn't solve the philosophical problem of what happened to the original; whether they were in some sense "transported" or simply killed.

Okay, tell me what you think is wrong with this answer just to make sure that we are on the same page: we might be able to introduce some sort of criteria for determining if someone could be considered to have survived based on the survival of brain function as a result of a certain X. If they pass a cognitive test at a certain X after being transported, then we can say that at that particular X, the person that was transported survived. Thus, it is no longer arbitrary (at least in terms of small differences in X not corresponding to meaningful differences in brain functioning) given we can determine how much someone must be the same after being transported to be considered to have survived. — ToothyMaw

I still don't think you're following me, sorry. I am talking 100% about the first-person perspective of the person going into the transporter. You are talking about what is observable or measurable to third-parties.

In the original, vanilla transporter problem, where the transporter makes perfect copies, it's a given that the person at the destination is identical in every way to the person went in, such that Kirk's colleagues see no discontinuity in their interaction with him, and Kirk is convinced he's just been transported.
This premise is not a solution to the philosophical problem though, because that problem concerns the first person perspective of the Kirk entering at the source. From his own point of view, did he survive?

I am inferring from your answers that probably your position is that, no, the source person is dead, and our focus is just on whether we should consider the facsimile close enough to treat it as Kirk. Right?

I am sorry but I hate this problem. Why would anyone assume the Star Trek transporter could ever possibly work? If one assumed it could possibly work, one could assume any number of solutions to any number of assumed problems. — Fire Ologist

Well it's just a thought experiment. We also can't make Laplace's demon.

A difference though is that personal identity is an issue that will eventually be relevant to human technology. Because, even if transporters are impossible, brain augmentations, splicing etc seem pretty feasible within just the next few centuries. And, if strong AI is true, then transporter-like processes will be absolutely trivial as long as we have sufficient storage to make duplicates.

I actually think there's an argument for consciousness NEVER being continuous, period. Like even just you, now, not being transported. There's an argument that the you that is experiencing the middle of this sentence now is a different you than the one experiencing the end of the sentence now. That continuity of experience is equally illusory in a way, all the time. — flannel jesus

Absolutely. Every time I have discussed, or seen discussions of, the transporter problem, it seems both sides assume that continuity of consciousness is real, and the question is just whether it's preserved through this process. But yes, it occurs to me that there's a third option; that there's never continuity of consciousness.

It seems an unpleasant option -- the me that is typing the last word of this sentence is a different entity to the one that typed the first -- but we have to admit, it's the one that fits the known facts right now. It's immune to all of the arguments against the other positions.

It's not that it's a boring answer @ToothyMaw, and I thank you for it, but I still don't think you're quite getting my point.

Today, yes, if someone has brain damage we can talk about the degree to which that person's personality and other attributes have been preserved. It's the same person, it's just arbitrary how much we consider that person to have the same qualities as before.

However, in the transporter scenario, there's a binary that we've introduced: either you've survived the process -- whether or not you have brain damage -- or you simply died on the source plate, lights out. Remember I am talking about your own perspective. So if Picard uses the transporter, I am talking about the perspective of the Picard that entered at the source, not whether the rest of the bridge crew considers it to be the same Picard.

And there seems no basis for the universe to choose where to set such a line, nor for us to ever know where it is. It's not a refutation of the transporter working per se, it's just showing that there are a number of absurd entailments.

In terms of the OP, I think this is one of the few answerable questions regarding sleep and dreaming.

Our brains have different brainwave states, these correspond with levels of alertness. Dreaming takes place in theta or delta brainwave states, which are the lowest alertness. You can experience theta state while awake, and it's a drowsy "brain fog" feeling, although it is also associated with creativity.

So you're not quite as alert in a dream, although people do still sometimes realize that they are dreaming and enjoy lucid dreams. Personally, I don't only have lucid dreams but also in-between states, like finding everything happening quite odd, but never quite working out that I am dreaming.

Now Kant's idea of the Beautiful is judged by the criteria of the form not the object, for example, the art form, say, literature. — Antony Nickles

It sounds a bit like true scotsman. You or I might consider something beautiful, but it's not true beauty, according to the conceptions of Kant. Well, I have no reason to suppose these conceptions are the correct framing; it's just a proposition that I either accept or reject. It can't be used as an argument to convince anyone of anything.

Of course, my point in beginning my remarks only concerned these concepts in contrast to the disinterested, impersonal, intelligible rationality that the judgement of the Beautiful has. — Antony Nickles

I'm still not sure I entirely follow, as you still have not provided a concrete example.
When people talk about a beautiful face, and we can point to features of our neurology that make humans basically hard-wired to like certain aspects of a face, like symmetry, is your view that that is not *true* beauty? That true beauty has to be based on rationality?

And bear in mind that for the question of the OP, I do not need to show that all aesthetics can be shown to be objective. Merely that any can.

I'm not quite sure it's unfair (or even rude) to say you're going to have to try harder. — Antony Nickles

I would say so.

My post gave multiple examples illustrating exactly what I was talking about.

Asking for one example of what you mean by "sensations of the Pleasant, or the value of the Good" is not unreasonable.

What we can say about art through science refers either to the sensations of the Pleasant, or the value of the Good (popularity). What I am discussing is not a standard to judge the object, it is the way in which a type of art has as its means. This is not a standard or "cultural creation" (as opposed to some "thing" created outside of culture?). And the more "specific" the claim gets, usually the better its argument--the more evidence it incorporates, the deeper the insight, etc. — Antony Nickles

I don't understand any of that.
Can you give an example of the distinction(s)?

Speaking from a more neuroscientific point of view, there are of course aesthetic qualities to things for the vast majority of people. And not just "fire hurts", but studies have shown that young infants can be afraid (or at least pay extra attention to) images of snakes or spiders.

And while it's fashionable to try to define standards of human beauty as arbitrary cultural creations, a lot of factors are cross cultural, for example good luck finding a culture that prizes acne over smooth skin.

There are similar fundamental instincts that drive us to like clear water, green grass and even some architectural features. The more specific we get, the more subjective it gets though. And of course most of us value novelty. So even if, let's say, the letter "X" presses our innate hard-wired desires better than any other letter of the alphabet, if we were surrounded by "X", then "S" might become the most desired letter, or whatever.

Factory farming is not not inherently cruel and abusive; cruelty and abuse could take place just as easily on a little farm as a very big one. Cruelty and abuse occur in human workplaces and shelters, too. — Bitter Crank

Actually I was about to say the exact opposite.
Factory farming is inherently cruel and we don't need examples of specific workers intentionally abusing animals.

We're talking about places where animals may never see the light of day; never get to even turn around in the case of chickens and often pigs. Fattened up (extra cruelly in the case of foie gras), with bodies that have been bred to produce e.g. many times more eggs, and much larger eggs than they ever did in nature; they wouldn't survive long if we didn't kill them, who knows what it must feel like.
Oh and calves taken from their mother immediately so we can take the milk.
I've probably missed a bunch of things.

I don't want to anthropomorphize animals too much. But it does appear that these animals possess sufficient instinct and awareness to find all of this very unpleasant. Animals in zoos display anxiety and frustration in conditions far superior.

Sadly, it seems I am something of a hypocrite currently. I buy free range where the option exists but I still eat out at restaurants that likely use factory farmed meat. It's just something I have put to the back of my mind. Also I know "free range" can be defined somewhat generously in some cases to mean near-as-dammit factory farming.

Agree completely.
It's a bit of a bugbear for me. For example, Matt Dillahunty, who I respect as much as any popular speaker on religion and philosophy, will say things like "There's no evidence that nothing can exist" and "Demonstrate me a nothing". These sentences at first glance seem meaningful because they are at least grammatically correct (well...the second is slightly wonky as "nothing" is generally a non-countable noun), but they're actually garbage.
If I were to translate the second sentence into Mandarin, I'd have to say something like "Don't demonstrate anything". Because Mandarin doesn't not have this contraction of "no" and "thing", so the apparent paradox is not there.

This was only an example, but it seems to me that this is the case every time that the word "nothing" is used in english (or in the italian word "nulla"). The quantifier is always on a finite dominion of things. Because how could you formulate a sentence with "Nothing" using a quantifier without boundaties which makes any sense? Nothing comes to my mind (hehe). — L'Unico

Right. As I said though, sometimes that quantifier is ambiguous.
For example, if I say "There's nothing to be afraid of", I am saying the set of things to be afraid of is empty. But this set is very open-ended in terms of what kind of things belong to it; in a particular context we might be implicitly referring to physical objects like spiders or fire say, but also abstract concepts like "heights". Or not implicitly referring to anything.

So, I agree with your point: "nothing" in English does not point to one singular concept. It's a special noun that means different things in different sentences. And it almost never refers to some discrete entity unto itself. This is the fundamental misconception of the OP and similar threads.

We don't know that all physical things must have a cause
We don't know that all transcendental things do not require a cause
We don't know whether infinity can be realized in reality (in this case that cosmic events are eternal. And note a distinction between universe and cosmos, the latter including multiverse(s))

So the argument only works if you just assert a position on several things that we don't actually know.

As I've said previously, the noun "nothing" in English is special, in that it means different things in different sentences, but almost never refers to some discrete thing unto itself. "There's nothing to eat" does not mean there is actually one foodstuff, that we're calling "nothing". It's simply "logical_NOT(something is available to eat)".
This is always worth bearing in mind when discussing the "nothing" topic.

More specifically on quantum explanations, the issue I have is this:
An understanding should mean that we can make useful predictions and inferences. A good understanding on the ultimate ontological question of "Why is there something rather than nothing?" is no exception.

If we understood how a universe can have a beginning, we should be able to answer questions like "Why does another universe not spring into existence right now in my kitchen?". There are infinite "nothings" in the spaces between matter in my kitchen, after all. The common response to this might be that that is not what is meant here by "nothing"; what is meant here is the absolute nothingness where no universe exists yet.
But, in that case, how can we apply quantum physics spontaneous matter generation, because that is a process which happens within an existing spacetime. We have no reason to suppose it can / did happen when there was nothing and it created spacetime...that's a wholly different thing, not part of the model at all.

disclaimer: I'm not religious, I don't think "god" works as a solution to this intractable problem either.

The discussion about human tetrachromacy is irrelevant to the issue of seeing the world as it is.
Whether or not women with two different cones for perceiving reds can see more shades, the simple fact is that the EM spectrum is much wider than the human eyes' gamut, and indeed many animals can see out of our range.
It would be possible to set up a game like in the OP where a trained animal picks a square based on its color despite all the squares appearing black* to a human.

Or echolocation or whatever...it's pretty clear we don't sense everything that's capable of being sensed, let alone every phenomenon "out there".

* What's "black" anyway? Since we see black where there is a comparative dearth of cone cell activation, is black "out there"?

Im a member of a couple in-person philosophy groups, and they're fun from a social point of view, but the discussion tends to stay in first gear.
Whatever the topic, some people are not familiar with the terms and history, so we always end up just giving the pop Philo summary and not much chance to get into a real debate.
I guess some people would consider that better -- the debates here can sometimes seem impenetrable -- but I feel I learn much more from textual discussion online.

If the only reason to use past experience (memories/knowledge) for making decisions as to what to do, is because that experience shows me it worked most of the time — znajd

Well another reason is a pragmatic one: we know of no alternative.
Deductive logic seems necessary to even be able to reason in the abstract and inductive logic, including the assumption that the future will be like the past / our memories are reliable, seems necessary to do any reasoning in practice.

Without starting with these principles, what reason is there to do, or not do, any action?

In reality, our planet contains many chaotic systems, therefore, in a sense, a small domino can topple a larger one but it's not an amplification or increase in energy. It's not one butterfly's wings flapping becoming the energy of a tornado. It's a difference in initial conditions ultimately delivering a different result set.

In the domino metaphor, it's as if there are many intersecting paths of dominos, some with small dominos, some big, and the exact course of the smaller dominos can ultimately influence which of the larger paths topples.

Perhaps this is too much of a stretch for the dominos metaphor?

Perhaps it's better to imagine, say, a pool table with various sizes of balls. If you run a computer simulation of such a setup, you would find that with precisely the same shots played, the effect of having a single extra ball, even one a couple millimetres in size, will ultimately lead to a different configuration of the big balls.