The problem seems to be treating the butterfly effect as if Lorenz was proposing a law of nature, when in fact it was only meant to raise certain questions, not necessarily answer them.
It's more than cumulative error. A car with poorly-tuned steering will drift off course. That's cumulative.As I see it the butterfly effect is in essence similar to or in fact the same as cumulative error in a dynamic system. The thing is that in complex systems such as weather, cumulative error is not happening in only one place at one time, rather, an ongoing continuous process at an infinite number of places in the system.
This then becomes the straw that broke the camel's back problem, in that the cause of any specific event was not caused by an individual straw, but the effect of all the straws together, and so any effect of a butterfly can never be fully the cause of any effect later in time.
I beg to differ.Certainly. A butterfly's wings cannot result in all the atmosphere leaving the planet. But it can result in a tornado.
All the butterfly flaps cause a tornado, they even cause many tornado's.It's a stretch for sure but of the billions of butterfly wing-flaps how many cause a tornado. I would submit that for a given cause there is an inverse relationship between the magnitude of a given outcome and the probability of that outcome so that no outcome is impossible, but some are highly improbable.
Two real world examples, one natural, one man made.are there any other well known systems in nature that have such discontinuities?
You seem to be talking about the butterfly effect in general. If so, that is not what I refer to. I was talking about DH's non-deterministic system.Two real world examples, one natural, one man made.
1) Go to Switzerland in March, walk into the sowfields near the mountain sides. Start shouting and sooner or later you will trigger an avalance.
Does the ratio of the energy in your shout to the energy of the avalance compare with the ratio of the energy of a butterfly flap to the energy of a tornado?
2) Obtain a length of detcord and wire it to 40 kilos of Semtex. Supply an electrical signal from a battery.
Do this in a safe place not near Guantano Bay.
Does the ratio of the electrical energy to your det cord to the energy of the explosion compare with the ratio of the energy of a butterfly flap to the energy of a tornado?
This is wrong. First off, you are conflating sensitivity and causation. Secondly, you are stating this as as if it were fact. The fact is, we do not yet know the answer to the question raised by Lorentz way back in 1972. Meteorologists do not yet have the tools to even begin answering that question.All the butterfly flaps cause a tornado, they even cause many tornado's.
Once again, very nicely put. A lot of the moderation in this thread resulted from people taking Lorentz question far too seriously and being far too adamant in expressing their opinions."Butterfly effect" is a poetic expression. One should not get too carried away with the poetic aspect of the expression to the detriment of the scientific content it is intended to convey. I can't help but think that people debating whether butterflies actually cause tornados (or some other variety of weather phenomenon) are missing the point somewhat.
Robert May did most of his work in the early 1970s and published his seminal paper on the logistic map in 1976. Lorentz, however, preceded May by more than a decade. Modern chaos theory pretty much started with Lorentz.While I do understand that the original post was very specifically about the butterfly effect, which is clearly a point about weather systems, and DH has given us the precise provenance of that term, as others have pointed out, the term does refer to chaos theory, and according to the account that I read, the origins of chaos theory were not in modelling weather systems, but in population modelling.
Well, there's Painlevé conjecture, which has since been answered in the positive. Painlevé proved that the only singularities in the three body problem involve collisions. He raised the question whether non-collision singularities can arise in the n-body problem, with n>3. In response to this question, Von Zeipel quickly proved that singularities in the (Newtonian) n-body problem will arise only in the case of collisions or in the case of objects going off to infinity in finite time.are there any other well known systems in nature that have such discontinuities?
Robert May did most of his work in the early 1970s and published his seminal paper on the logistic map in 1976. Lorentz, however, preceded May by more than a decade. Modern chaos theory pretty much started with Lorentz.