The concept of Brownian Motion depicts the path of a thing (like a particle in a gas) as a jagged line where every corner represents a collision. As one zooms in on the path, every line resolves to more, finer corners between the original points. The concept is useful for modeling complex systems (e.g., markets), and its indefinite depth shows the extreme difficulty in developing algorithms for deterministic event mapping.
Chaos theory is depicted in the Brownian model. Tiny events precipitate into larger events, a butterfly flaps its wings, shit happens thousands of miles away. But chaos theory relies on drawing straight effect lines between events. Nature tells us that there are no straight lines. In math, a line is called a “straight curve”.
I submit that the effects caused by a given event resist linear plotting. Influences bend outward from an event, blur and lose distinction, beyond even the additional distortions imposed by neighboring events. A given event is described by a sort of amorphous sphere of influence that becomes less distinct and relevant the farther one moves away from it in space and time.
Our knowledge of history is analogous to this. Was Shakespeare the primary author of that material? Did Bush and Cheney conspire to start a war in Iraq? Did Julius Caesar say “Et tu, Brute? Ergo tolle uxorem, obsecro” as he collapsed with 30 stab wounds in his back? Did your cousin really have a flat tire on the way to christmas dinner? The further and farther removed we are from various events, the less certain we can be about them. And physical influence is not fundamentally distinguishable from knowledge.
Which is to say that the idea of a deterministic future requires deterministic past. The past is perceived to be fixed, set in stone – after all, it did happen, right? But, what exactly was it that happened? If we cannot be sure, we are moving forward with vague, imprecise and sometimes wholly inaccurate information. The future cannot be predetermined if the past is not likewise determined. I do not believe that that has been adequately established.
Let’s try this in Great Debates. Thread relocated from IMHO.
Er, who says that the future can be predetermined? Who suggests they have enough information about the finer details of prior events to accurately predict the future? (I’m excluding gods, because I’ve never met one, and they claim to have full knowledge of all prior history anyway.)
(Of course, if one did have full knowledge of all of history, down to the subatomic level, then I believe the future could be predicted with relative certainty. Reality seems pretty nonrandom. But nobody has the data to actually do this.)
Determinists have said that all the events of the fixed past exert their effects upon the present in a definite way such that the future is fully shaped by the past and will be what it has always been destined to be. My argument is that the past is not a fixed thing.
Then I don’t follow your argument. You have given me no reason to believe that the past is nonstatic - it’s rather a large leap from “the numerous factors and causes of events are hard or impossible to determine” to “the numerous factors and causes of events don’t exist in any real fixed sense.”
Does it really matter how detailed our knowledge is of the past, as long as we have a vague understanding of the big things?
For instance, we’ll never know how many people died exactly at the Battle of Cannae, but we know that it was a big Carthaginian victory over the Romans. We might not know exactly when Carthage fell, but we know it got sacked by the Romans.
I will not argue that the past is dynamic. That is another question entirely. But what matter is the present’s perception of the past amounts to. That, I argue is ill-defined and variable. The present’s perception of the past is a primary influence on what happens in the future. Because of that, a clear, deterministic mapping of the future is infeasible.
The path of light. Spiderweb strands. Anything hanging, the center of a half moon. The horizon of a calm sea. Crystals. Wood splinters. Fractures in all sorts of stuff. The path of falling objects. The veins of a leaf. And on and on and on. There are tons of straight lines in nature.
Sure, you can argue that most of these aren’t “perfectly” straight, but if that’s your criteria, there aren’t any artificial ones, either, and you’ve picked a definition of “straight line” so narrow that it’s not really useful for anything.
I will immediately and with full enthusiasm agree that humans are incapable of mapping out the entirely of the future with perfect accuracy. I will also agree that people’s stupid ideas about what’s going to happen effects future events, because people act on the misguided guesses in their squishy brain tissue.
But this doesn’t mean that the universe isn’t deterministic and the future isn’t determined. The universe could easily be deterministic and the future could easily be fixed, even if people are ignorant idiots (which they are). It just means that people will guess wrong about things a lot, that’s all.
Except, I am saying that physical things respond to influences and causes that are presented to them, which may not represent the reality of what happened in the past. Information is the same to things as it is to people. What happened in the past is not fixed with respect to the present, because causality lines are not linear.
The visual image I formed was like a foam of influence bubble domains expanding out toward time/distance diffusion, to the point that past-rooted determinism is unrealistic because causality roots are increasingly imprecise. Which is to say, I consider the idea of determinism untenable.
From these sentences I think you may be laboring under one of the popular misconceptions about chaos theory.
It’s not that the energy of the butterfly flapping its wings becomes a typhoon; energy is conserved in our universe.
And it’s not even that the butterfly caused the typhoon: even if it’s true that taking away the butterfly from that system would mean no typhoon, that’s true of basically everything else in the system: change anything and you’ll ultimately get a radically different result set.
So in fact there are things you could take out of the environment that would result in a more powerful typhoon happening. What caused that super-typhoon? The whole system.
With that understanding, we see that the notion of drawing “event lines” is far from a requirement of chaos theory, it’s actually shows a fundamental misunderstanding.
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Before anyone says it, I’m aware that the original phrasing of the butterfly analogy used the word “cause”. It’s a shame, because it’s led to this misconception that you can draw a line between the butterfly and the typhoon, as if there is a 1 to 1 relationship.
Sorry for the multiple posting, but this is also wrong:
In math, it depends what kind of space you’re working in and what the axioms are.
In most cases the term “line” does have a distinct meaning, and doesn’t need to be defined in relation to the concept of a curve.
I reject the idea that physical things respond to influences and causes that are presented to them, which may not represent the reality of what happened in the past.
I mean, sure, people seem to be reacting wrongly based on the lies they hear. But at a mechanical level the lies they hear are sound waves which are actually motions of molecules in the atmosphere that were triggered by some physical mechanism, a voice or speaker. And the person’s ‘wrong reaction’ is actually a giant cascade of cognitive events that, at the mechanical level, are a giant series/web of electrochemical reactions that were triggered by the way the physical mechanism of the ear reacted to the sound waves and instigated mental processing based on what was heard.
The words a person heard might have been lies, but the mechanics that underlie both them hearing it and reacting to it are based on cold hard mechanical reality. There is no falsehood of presentation here; there is no ambiguity in the physical motion and chemical processes. Things happen, based on what happened immediately prior, which happened due to what happened immediately prior, and this goes all the way back. The physics don’t lie, and they’re not vague.
It is certainly true that causality isn’t linear; many things have multiple causes. You have to have both mentos and diet coke present to make a mess; neither one alone is the sole cause. But no part of the interaction between the mentos and code is vague and not based in physics and chemistry; your inability to predict where the spray will fall is simply due to the fact that you are failing to track the position, movement, and interaction of every molecule present (you slacker).
So yeah. You only see vagueness and uncertainty because you’re looking at the big picture. At the mechanical level causality is very locked down.
(Well, give or take uncaused random submolecular events, which may or may not exist and may or may not impact things at a macro level. But, again, those things are not what we’re talking about here.)
I always thought there was exactly that relationship… It’s a variant of “For want of a nail…the kingdom was lost.” The concept (absurd, in practice!) is to explore a cascade of events that builds upward in complexity and size, almost purely by chance.
It’s like Jengo. If you pull out just the right piece, the whole structure collapses.
We know, in practice, there are a lot of negative feedback loops that keep things from blowing up. But in abstract theory, there could be a tiny event that causes larger and larger and larger events down the road.
(Another really big problem is that no one can possibly identify such keystone actions. Go ahead, remove one nail from one shoe of one horse of one army: the kingdom is not going to be lost…because you removed the wrong nail!)
Yes I believe this to be a misconception. IANA mathematician or physicist, so I’m waiting for a more detailed response, but I’m confident it’s a misunderstanding of the analogy to assume the butterfly is special in any way.
If a weather system is a jenga puzzle, then for the analogy to be accurate we’d have to say that taking any block out at all, will ultimately result in the puzzle rearranging into a completely new puzzle.
There is no significance to any particular block; a change to any will ultimately result in a new puzzle. Alhough how much of a time interval “ultimately” is, will differ a great deal.
Also: we know that this number is no longer changing. That’s a different kind of uncertainty to the uncertainty of watching some wavering current-time variable and trying to pin it down.
Any given butterfly is probably not special, but there might be a really fortuitous “keystone” butterfly.
Well, yes, but that’s trivially true of any changeable system. When it changes, it becomes a “completely new system.” Almost tautologous.
They point to the butterfly metaphor is that there might be (extremely rare!) keystone events, so that the completely new system is catastrophically different from its earlier version.
“The straw that broke the camel’s back.” Such a thing has probably never actually happened, but it is a valid way of looking at things.
(A single sneeze has set off large alpine avalanches!)
And here is where I have to disagree with you: there may be single blocks that, by chance and leverage, support very large portions of the structure, and the removal of that block produces a disproportionately large change in the state of the system.
Think of a riot that starts by a single person shouting something; think of a landslide that starts by the erosion of a small piece of landscape; think of a fifty-car pile-up on the freeway that starts by one motorcycle whipping across lanes.
Most of these analogies depend on a pre-existing condition of large amounts of potential energy, held in check by a very small restraint. But in the real world, that actually does happen sometimes!
There might be, but that’s not a requirement for the hypothetical or for chaos theory in general.
When Lorenz first came across this phenomenon it was in the context of a model where changing any of a number of variables by any minute amount would ultimately lead to a radically different result set. No “keystone”.
Unfortunately he then went on to use the butterfly metaphor to describe it, which, while certainly an evocative image, has proven to be a very misleading one.
No, I mean “catastrophically different” in your words. Any change at all will ultimately result in an entirely different result set, again as seen by Lorenz.
Of course there might be. Humans have essentially always known this. No-one would dispute that.
The interesting thing with chaotic systems in particular is that any change at all will ultimately result in a dramatically different system.
Or let’s put it this way: imagine two leaves fall off a tree.
Leaf A falls into the path of a cat, which makes the cat run left instead of right, which makes it run into the path of a car, which makes the driver swerve and crash into a pedestrian.
This is the kind of “small event causing larger event” that you’re talking about.
But then imagine Leaf B has no apparent effect on anything.
However, even though we can’t see it, there are tiny effects: minute differences in local air pressure and air currents. A different amount of sun is now reaching the ground. Perhaps the path of an ant is changed.
And there is no way for those effects to “disappear”; they’ll have knock-on effects indefinitely. Perhaps these knock-on effects remain tiny and inpercepible for many years.
But at some point a tiny change will cause some bigger change, and we’ll get the same thing as we had with Leaf A: a radically different result set compared to a model where the leaf had not fallen.
How is this in opposition to the butterfly metaphor? It seems to me you’ve just re-stated the butterfly metaphor, almost exactly. Yes, the fall of a leaf causes a traffic fatality: the flap of a butterfly’s wing causes a hurricane. Where is your disagreement, then?
And…yeah, if it’s truly a chaotic system, then changes can “lurk” for a long time, and express themselves later in ways that are difficult (impossible?) to predict.
Have you seen the physical example of chaos where you have a vertical T-shaped piece of metal on a pivot, with pivoting arms at the ends of the T’s arms? You give the thing a good whirl, and the T-rotates, and then the arms rotate, and the thing just wobbles in the most incredibly lack of any discernible pattern. For seconds at a time, the central T-frame can be static, while the arms whirl, and then, with a great lurch, the T rotates at a high rate. That’s a reasonable real-world example of small changes “pending” until they are expressed in a large change.