# Is everything affecting everything on Earth?

If a single butterfly can alter the future, then can't every single action keep the future in chaos? According to the question about butterfly effects, this must be so, is it not? If this is an accurate description of the physical world, if so many things act continuously on other things, is there a way to predict anything or action at all? If so, why are we worrying about it?

• @BarryCarter - The universe is not deterministic. Suppose I give you a molecule of tritium. You cannot predict the exact time at which both of the tritium atoms that comprise that molecule will have decayed into helium-3. – David Hammen Oct 15 '14 at 15:51
• I think you are confusing chaos with entropy. Predictions are based on our knowledge of the present (or past) and our ability to numerically represent physical/chemical changes. All actions on Earth can be summarized and averaged... allowing general predictions to be made. A butterfly flaps its wings and changes the wind field... which is not chaos. – farrenthorpe Oct 17 '14 at 18:46
• @farrenthorpe - Whether the flap of a butterfly wing in Brazil can cause a tornado in Texas is the canonical example of chaos. It's the subject of a rather famous invited talk to the AAAS on this very topic. – David Hammen Oct 18 '14 at 11:46
• @DavidHammen I think you are misinterpreting the metaphor. The tornado is the result of many things, not just the butterfly. Yes the downstream variance of a single occurrence is unpredictable, but that is not the same thing as chaos. A chaotic turbulent flow environment would be more like the surface of the sun, not our atmosphere. – farrenthorpe Oct 18 '14 at 20:47
• @farrenthorpe - I think you aren't reading it poetically enough. Most scientists do think our atmosphere is chaotic. Lorenz, the author of that butterfly talk, is also the author of "Deterministic Nonperiodic Flow," Journal of the Atmospheric Sciences 20.2 (1963): 130-141, which arguably marks the start of chaos theory. That paper has been cited over 5,000 times! – David Hammen Oct 18 '14 at 21:31

Do you know what the weather will be in four hours time? You can probably make a very confident guess. How about this time tomorrow? You can probably make a reasonably confident guess. How about this time, in fourteen days exactly? Now, you're much less confident.

That's because weather is a chaotic system, and it's very sensitive to boundary conditions. In such a system, very small disturbances can make very big changes, far enough out.

Now, for Wisconsin (as that's what the OP's profile gives as their location), let's think about the external air temperature at 05.00 on 1 February 2017, and at 14.00 on 1 July 2017. Which do you think will be higher? Will it be a difference of a few Kelvin, or more than ten Kelvin (18°F) difference? How confident are you in your answer? You're probably very very confident that the July temperature will be higher, by more than ten Kelvin. The climate is still reasonably predictable months or years ahead, even though it gets very hard to predict the weather reliably more than ten days ahead. Climate is a long-term system, and is not sensitive to boundary conditions in the same way that weather is.

If you roll a fair six-sided dice once, you can't be very confident about whether a one will come up, however much you know about the air movements in the room when you throw the dice (you can be reasonably sure that the probability is 1/6, however much you know about the air). However, if you roll that dice 6000 times, you can be reasonably confident that one will come up a thousand times, give or take a hundred times, and you don't need to know anything about the air movements in the room.

That's the difference between weather and climate; even though weather is just a manifestation of climate, it's just a sample from the climate distribution.

We've built the global economy, patterns of habitation and movement, food supplies, energy systems, around the climate that we've had for the last few hundred years. And that should be ok, because climate, sea levels and sea pH levels normally take between thousands and millions of years to change radically. But our releases of greenhouse gases are now causing big changes to happen within years to decades: and it will be enormously expensive, disruptive, and cause huge suffering to billions of people, to reorient the global economy, patterns of habitation and movement, food supplies, and energy systems, to newer, unknown, unfamiliar climates, coupled with rising sea levels and ocean acidification.

The media loves the butterfly effect, but they also love to mis-portray what it means. When Lorenz gave his talk "Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?", that made the media pay attention to the emerging field of chaos theory. The media focused on the title of his talk. It sounds so cool! They didn't read the body of the paper to see what it was all about.

The title was chosen to be provoke thought, not chaos. Lorenz did not mean that everything is interconnected. The butterfly effect simply means that chaotic systems are very sensitive to initial conditions.

Lorenz started his talk with

... The question which really interests us is whether they can do even this—whether, for example, two particular weather situations differing by as little as the immediate influence of a single butterfly will generally after sufficient time evolve into two situations differing by as much as the presence of a tornado. In more technical language, is the behavior of the atmosphere unstable with respect to perturbations of small amplitude?

He ends it with

We must therefore leave our original question unanswered for a few more years, even while affirming our faith in the instability of the atmosphere. Meanwhile, today’s errors in weather forecasting cannot be blamed entirely nor even primarily upon the finer structure of weather patterns. They arise mainly from our failure to observe even the coarser structure with near completeness, our somewhat incomplete knowledge of the governing physical principles, and the inevitable approximations which must be introduced in formulating these principles as procedures which the human mind or the computer can carry out.

That extreme sensitivity to initial conditions means that in theory, a scenario in which a butterfly in Brazil does or does not flag its wings just so are enough to create slightly different conditions that eventually result in tornado hitting Texas. Even if this is the case (and Lorenz did leave that as an open question in hist talk), it's not quite fair to say that the butterfly caused the tornado. The Lyapunov time for the disturbances created by a flap of a butterfly wing is very short. Saying that some event caused some later event else when the two events are separated by hundreds of Lyapunov times just doesn't make sense.

What this means is that forty plus years after Lorenz's talk, weather forecasters still can't make an accurate two week forecast, and they may well not ever be able to do so. They can make now a fairly accurate five or seven day forecast, and that was something that was beyond the skills of meteorologists forty years ago.

Caveat: Don't believe the forecast by your local TV station. They are notoriously inaccurate. If the US National Weather Service says there's a 100% chance of rain tomorrow, it's best to cancel your barbecue. If your local TV station weatherman says the same, there's a good chance tomorrow will be sunny.

• +1 Yes, excellent answer. – milancurcic Oct 19 '14 at 2:34
• Can you explain Lyapunov time or add a good link? I don't think it's self-explanatory (I'm still googling). – mart Oct 20 '14 at 8:32
• Errors in chaotic systems tend to grow exponentially, or even faster than exponential. Assuming an exponential error growth and an initial uncertainty $\epsilon_0$, the uncertainty at some later time $t$ will be $\epsilon_0 \exp(t/\tau)$ where $\tau$ is the "Lyapunov time." Suppose your initial estimates are good to six decimal places. After 18 Lyapunov times, those six places of accuracy become zero places of accuracy. Start with a dozen places of accuracy and that's gone in three dozen Lyapunov times. – David Hammen Oct 20 '14 at 10:50

From experience as a cross continent truck owner-operator, the effect of an insect's beating wings on the earth is minimized or even neutralized by the mass of the truck when it hits the radiator. Logical thinking and close observation reveals this minimizing effect. Just like when we hauled 285,000,000 honey bees, their combined flying power was too minimal to offset the mass of 35,000 pounds accelerating down the open road at 60 mph. By inference therefore, the added weight of one bug plastered to our radiator does not alter the weight or speed of the vehicle. If this logic bears out, then the beating of one set of wings of a lovely butterfly, will not be a deal breaker.

• Yes, the bug on your radiator did indeed change the mass and momentum of the truck, but you had no way of observing that change. – milancurcic Oct 13 '14 at 23:23
• and you typing on your keyboard indirectly, intermittently and imperceptibly altered the rotation of the Earth – user889 Oct 14 '14 at 6:25