- #1
BernieM
- 281
- 6
Butterfly effect. Much ado about (almost) nothing.
Not a lot has to be said to introduce the subject of course. But once before I addressed whether, in reality, a butterfly flapping its wings could actually create a tornado. My view essentially was that the degree of disturbance of the local air patterns by a butterfly, would actually be absorbed through a hysteresis process, and essentially just increase the overall net energy in the local system rather than causing an organization of the system which would grow to become a tornado. Of course my personal opinion is that Edward Lorenz never truly believed it was a reasonable scenario, simply that he was trying to illustrate that very insignificant forces may come to influence much larger systems in sometimes spectacular ways.
Then I wondered as to whether or not one could prove the probability that a butterfly, could in effect, ever realistically be considered the cause of an organized storm system such as a tornado, and whether one can definitively prove this one way or the other.
To do this, I suppose one would have to figure out how many butterflies there were in the world, as well as moths and other small flying insects of approximate similar size, and how many times they flapped their wings in a day (are the flapping of a moth's wings at night the same value as a butterfly in the day due to a difference in air density when it's cooler during night time?) Then one would have to figure out what the average number of daily tornadoes there are on Earth (including over the ocean where nobody might see them.)
This would give a probability of a butterfly being the cause of a tornado, expressed, for example, as 1 tornado per 1 quadrillion wing flaps!
But obviously if a butterfly could be the cause, other things that disturb air currents would also have to be considered as a potential cause. And herein lies the question.
A 747 jet is flying from L.A. to Hong Kong and it takes 12 hours of flight. How much air was displaced (turbulence produced) and how many butterfly wing flaps would that be equivalent to? But further, and perhaps more important, is whether it is a single molecule that could cause an organization and tilting of an atmospheric condition to favor creation of a tornado, or whether it is the net effect of the whole disturbance.
So does a jet flying from L.A. to Hong Kong have the same probability of creating a tornado as a butterfly flapping its wings, or does it have the flight's total air disturbed, divided by the amount of air disturbed by a butterfly flapping its wings chances of creating a tornado? Is a jet assigned an equal value of probability of a single butterfly wing flap to create a tornado, or is it equal to billions of butterfly wing flaps?
I believe it depends on the model you have for what is the cause of the tornado. Whether it is the act of a single air molecule that can influence an atmospheric condition in the end or not. In a coffee cup, all molecules move randomly so all forces are generally considered to average out to a net zero directional momentum. But there is the one in an incalculable chance that all the molecules will jump in the same direction and the coffee jumps out of the cup! But even in that cup in which everything averages out to a net directional energy of zero, there will be that one molecule moving in one direction that doesn't pair with an opposing force of another molecule moving the opposite direction, giving that cup just 1 molecule of force bias in one particular direction! If it were in the air, would that be a one-molecule case that causes the tornado? Or do we have to wait until all the molecules in a small region per chance just happen to all decide to move the same way?
And finally, is there a requirement for any force to overcome a hysteresis or resistance in the system for it to be considered sufficient to eventually turn into a tornado? That a single molecule of air nor a butterfly could do it, but perhaps a jet could.
I suppose if these questions could be answered (on a theoretical basis anyhow, as I wasn't really figuring anyone would actually go out and count butterflies in the world and count how many times they flap their wings,) one could actually determine if it's possible or not that such a small force actually grows into a large phenomenon. Most of the things I have seen that respond to small fluctuations and create amplifying effects, are inherently unstable systems with some sort of feedback mechanism in them where the feedback amplifies the fluctuation. Easy to do in a computer program or math equation, but I am not convinced it's so easy to do in the physics of the real world.
All seems a lot of work to prove one way or the other, though it might yield some interesting results if solved. Tornado bombs anyone? Or maybe there is some sort of shortcut to solving it. Wave function of the atmosphere or something.
Not a lot has to be said to introduce the subject of course. But once before I addressed whether, in reality, a butterfly flapping its wings could actually create a tornado. My view essentially was that the degree of disturbance of the local air patterns by a butterfly, would actually be absorbed through a hysteresis process, and essentially just increase the overall net energy in the local system rather than causing an organization of the system which would grow to become a tornado. Of course my personal opinion is that Edward Lorenz never truly believed it was a reasonable scenario, simply that he was trying to illustrate that very insignificant forces may come to influence much larger systems in sometimes spectacular ways.
Then I wondered as to whether or not one could prove the probability that a butterfly, could in effect, ever realistically be considered the cause of an organized storm system such as a tornado, and whether one can definitively prove this one way or the other.
To do this, I suppose one would have to figure out how many butterflies there were in the world, as well as moths and other small flying insects of approximate similar size, and how many times they flapped their wings in a day (are the flapping of a moth's wings at night the same value as a butterfly in the day due to a difference in air density when it's cooler during night time?) Then one would have to figure out what the average number of daily tornadoes there are on Earth (including over the ocean where nobody might see them.)
This would give a probability of a butterfly being the cause of a tornado, expressed, for example, as 1 tornado per 1 quadrillion wing flaps!
But obviously if a butterfly could be the cause, other things that disturb air currents would also have to be considered as a potential cause. And herein lies the question.
A 747 jet is flying from L.A. to Hong Kong and it takes 12 hours of flight. How much air was displaced (turbulence produced) and how many butterfly wing flaps would that be equivalent to? But further, and perhaps more important, is whether it is a single molecule that could cause an organization and tilting of an atmospheric condition to favor creation of a tornado, or whether it is the net effect of the whole disturbance.
So does a jet flying from L.A. to Hong Kong have the same probability of creating a tornado as a butterfly flapping its wings, or does it have the flight's total air disturbed, divided by the amount of air disturbed by a butterfly flapping its wings chances of creating a tornado? Is a jet assigned an equal value of probability of a single butterfly wing flap to create a tornado, or is it equal to billions of butterfly wing flaps?
I believe it depends on the model you have for what is the cause of the tornado. Whether it is the act of a single air molecule that can influence an atmospheric condition in the end or not. In a coffee cup, all molecules move randomly so all forces are generally considered to average out to a net zero directional momentum. But there is the one in an incalculable chance that all the molecules will jump in the same direction and the coffee jumps out of the cup! But even in that cup in which everything averages out to a net directional energy of zero, there will be that one molecule moving in one direction that doesn't pair with an opposing force of another molecule moving the opposite direction, giving that cup just 1 molecule of force bias in one particular direction! If it were in the air, would that be a one-molecule case that causes the tornado? Or do we have to wait until all the molecules in a small region per chance just happen to all decide to move the same way?
And finally, is there a requirement for any force to overcome a hysteresis or resistance in the system for it to be considered sufficient to eventually turn into a tornado? That a single molecule of air nor a butterfly could do it, but perhaps a jet could.
I suppose if these questions could be answered (on a theoretical basis anyhow, as I wasn't really figuring anyone would actually go out and count butterflies in the world and count how many times they flap their wings,) one could actually determine if it's possible or not that such a small force actually grows into a large phenomenon. Most of the things I have seen that respond to small fluctuations and create amplifying effects, are inherently unstable systems with some sort of feedback mechanism in them where the feedback amplifies the fluctuation. Easy to do in a computer program or math equation, but I am not convinced it's so easy to do in the physics of the real world.
All seems a lot of work to prove one way or the other, though it might yield some interesting results if solved. Tornado bombs anyone? Or maybe there is some sort of shortcut to solving it. Wave function of the atmosphere or something.