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I've been thinking about the butterfly effect since I asked my first question on this site, which was different because here I ask for showing me the mechanism for the "how". I even gave one (the first) answer as a favorite. Though many answers were given (many of which contained critical phenomena, which aren't the same as chaos: sure, if you change the direction of a little ball, which is aimed at the detonation device of a thermonuclear bomb, and the ball will miss the device because of this, the difference will be enormous: a bomb blast or not! If this ain't a very different response to a small change of initial conditions...But it ain't chaotic behavior). it's still not clear to me how clapping my hands can cause a hurricane far away. The weather system will the same after clapping my hands already at a little distance from my clapping due to the dissipation of my clapping energy into the surrounding air, and maybe a solution can be given in terms of energy.

If I'm standing in a heavy hurricane, I just can't imagine the storm could not have developed if someone far away didn't clap her hands

The best way to explain this is to give the chain of causes and effects that will lead to this hurricane if I clap my hands instead of not clapping at all. The weather system, for sure, contains no criticalities. The answer can also be given in the causes and effects of larger chunks of air (from little vortices to the similar behavior at larger scales, which are different only in their time-scale), rather than on the atomic level.

In a double pendulum, you don't vary the places in phase space by a small (and non-random) way for just a few atoms to show the dp shows chaotic behavior. You vary both arms of the dp by a tiny amount and see what happens, which, contrary to the weather can easily be done in an experiment.

The same reasoning can be given for a weather system.

Is there someone who can show this chain which causes the faraway hurricane by just clapping my hands and leave everything else the same?

Please don't think I ask this for collecting votes because it did in my first question ever here. You can see the contrary is happening, but I just want to see an argument that shows that you can't say the weather system is chaotic by varying a very tiny small part of it.

Deschele Schilder
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    It is just a metaphor, trying to illustrate the dependence of some systems on apparently irrelevant changes of the initial state. – Jasper Jun 18 '19 at 18:44
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    @Jasper Is correct. It is just a way to explain to people how chaos works. A very small change in initial conditions can give rise to huge changes in the system's behavior over time. This is true for the weather since it is a chaotic system. But no one (to my knowledge) has experimentally shown or theoretically modeled an actual scenario of a butterfly or a clap causing a hurricane. – BioPhysicist Jun 18 '19 at 18:54
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    And don't the answers in your first post exactly the same thing as the above two comments?? Yet you still feel the need to ask essentially the same query? – Kyle Kanos Jun 18 '19 at 19:02
  • Yes, because though you can say it's just a metaphor, then at least use a metaphor that's correct. This doesn't explain how chaos works!. – Deschele Schilder Jun 18 '19 at 20:34
  • By the way, I already expected the downvotes! – Deschele Schilder Jun 18 '19 at 21:02
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    The hurricane is not caused by the butterfly, but by the innate instability of the weather system and by the Sun and the wind Earth's rotation and gravity etc. etc. Singling out the butterfly or whatever as 'the cause' is mostly a failure of understanding. – Andrew Steane Jun 18 '19 at 21:03
  • Now that's a useful comment! – Deschele Schilder Jun 18 '19 at 21:06

2 Answers2

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The fact that a clear chain cannot be provided between cause and effect is the whole point of the butterfly effect. There is an extremely complex set of equations that describes weather. The initial conditions get plugged into those equations, and the resulting weather comes out. The butterfly effect says that a small change in the initial conditions can cause an extremely large change in the results. It says that you need to know (among other things) the exact state of every single air molecule, because changing just one can change the effect.

Hence, if you want to follow how clapping your hands causes a hurricane, you need to track how your clapping your hands affects every single molecule of air. Each molecule would have to be tracked with infinite precision. There's no way we could present such a history, and you couldn't read, let alone understand, the history if we could.

Any human-comprehensible explanation is going to be in terms of high-level descriptions. For instance, in Daedalus' answer, they describe someone clapping, and someone spilling wine, and a table being tipped over, etc. Those are all high-level descriptions. A precise, low-level description would have to describe where every molecule of wine goes, and where every point of the table is at every moment of being tipped over, etc. The butterfly effect says that when studying chaotic systems, you can't predict the ultimate effect by looking at high level descriptions. There can be particular events that can be traced back through a chain of high-level descriptions, but events in general have no guarantee of that being possible.

Furthermore, the butterfly effect doesn't say that clapping your hand will cause a hurricane. It just says it can. As in, among all the possible starting conditions, there are two states that differ only by you clapping your hands versus you not, and there being a hurricane in the former and not in the latter. The number of possible states is vast, arguably infinite. Trying to find one that fits particular criteria can be next to impossible, but that doesn't mean it doesn't exist.

Acccumulation
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  • If it says it CAN, then one must also provide a chain of cause and effect to show how. Otherwise, this argument has no power. If no chain of events can show that a hurricane will develop somewhere, I'm not convinced that clapping your hands has this effect (even though it's just a (wrong) metaphor to illustrate what chaos is about. If I put my bare foot a little too far to the side of the street, where a piece of glass lies and step in it, it's clear my whole day develops in an entirely different way. This isn't an example of chaos though. – Deschele Schilder Jun 18 '19 at 20:54
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    @descheleschilder "If it says it CAN, then one must also provide a chain of cause and effect to show how." My entire answer was arguing the opposite. "Otherwise, this argument has no power." It's not clear what "no power" means. If it means you're convinced, well, that's your opinion. "If no chain of events can show that a hurricane will develop somewhere" Now you're switching from whether we can find a chain, to whether one exists. Since a chain involves a vast number of molecules at infinite precision, just because one exists doesn't mean we can explicitly present it. – Acccumulation Jun 18 '19 at 21:06
  • By no power, I mean no explanatory power. The chain, however, DOES exist. What do you mean by high-level descriptions? Ignoring the atomic structure and seeing the matter in big (continuous) chunks? If one can give an explanation of the butterfly causing a hurricane that's fine by me, and as I already said, your close analogy is an example of criticality, not of chaos. – Deschele Schilder Jun 18 '19 at 21:17
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This would require a detailed explanation on the formation of hurricanes - which is complex and honestly I am ignorant about.

However, I can provide a close analogy.

You're at a party and someone's glass of wine is dangerously close to the edge of the table, so much so that it's nearly at the point of tipping. Someone makes a joke and you laugh and clap your hands very strongly. There was also commotion all around the room and it caused enough disturbance in the room to tip the glass of wine over. The contents of the glass fall on the man's expensive suit and he quickly reacts to dodge it - only to push the table violently and tip everyone's drinks over. Chaos ensues, everyone is drenched in wine and in not so great a mood (or perhaps everyone would burst in laughter).

Consider that you had not clapped. Everything else equal, the glass of wine wouldn't have tipped over, and let's suppose the man realised how his glass was dangerously close to the edge of the table and moved it further away from the edge. Party continues as usual. It all ends with everyone saying good bye to each other in an agreeable fashion.

Your clap can, after all, cause a major event to unfold. However, it's extremely unlikely. Even more so in the case of a hurricane.

Daedalus
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  • The problem only gets more complicated when you consider the other party attendees and that they could have also chosen to clap at the same time, which could also change the entire outcome. This points to the complexity of the statement; although you can in one sense blame the clap for making the glass fall, you equally have to blame every other minuscule event that happened and contributed to the action, or did not prevent it. – JMac Jun 18 '19 at 19:32
  • But the point in this example is that criticality is involved (the straw on the camels back). Chaos is not involved here. This is not involved in the weather system. An illustration by another example: suppose a crack forms in a giant dam (behind which there is a big amount of water with a huge amount of potential energy). If everything would be quiet around the dam, the crack won't propagate. But if someone shouts loudly the crack can propagate, destroying the dam and release a huge amount of energy (like the potential energy of the glass). – Deschele Schilder Jun 18 '19 at 20:44