Consider a Galton board. A simple bead pummels down the cascade of pegs. Can we predict what path it is going to take?

Well, in principle yes – it's after all just mechanics. If it hits the first peg a little bit to the left of its center, it'll go to the left there. Measure the start state very accurately, and you can predict all that comes later.
But it's evidently hopeless to actually predict the whole path – it's way to sensitive, even the tiniest change at the start will mean it scatters off the first peg with a slightly different spin, and then this again changes the behaviour at the second, so already after two iterations prediction is sure to be off. For all intends and purposes, the behaviour is just random then, despite following deterministic microscopic dynamics.

Roughly the same reason is responsible for weather forecasts being little use over more than a week.

Nevertheless, what we can say with very good confidence is that the bead is going to end up somewhere near the middle after 1000 rows of pegs. It's not strictly speaking impossible that it goes to the left twice as often as to the right, but so very unlikely that we might rather worry about the board being destroyed by a plane crashing into the lab.

And if all the pegs are slightly biased to make it 5% more likely for the bead to go to the right at each of them somehow, that's not going to be evident from observing a couple of beads on the first rows – it'll still look totally unpredictable. However, it will show up clearly in the shifted peak of the distibution after 1000 rows.

Consider a Galton board. A simple bead pummels down the cascade of pegs. Can we predict what path it is going to take?

Well, in principle, yes – it's after all just mechanics. If it hits the first peg a little bit to the left of its center, it'll go to the left there. Measure the start state very accurately, and you can predict all that comes later.

But it's evidently hopeless to actually predict the whole path – it's way too sensitive. Even the tiniest change at the start will mean it scatters off the first peg with a slightly different spin, and then this again changes the behaviour at the second, so already after two iterations prediction is sure to be off. For all intents and purposes, the behaviour is just random then, despite following deterministic microscopic dynamics.

Roughly the same reason is responsible for weather forecasts being little use over more than a week.

Nevertheless, what we can say with very good confidence is that the bead is going to end up somewhere near the middle after 1000 rows of pegs. It's not strictly speaking impossible that it goes to the left twice as often as to the right, but so very unlikely that we might rather worry about the board being destroyed by a plane crashing into the lab.

And if all the pegs are slightly biased to make it 5% more likely for the bead to go to the right at each of them somehow, that's not going to be evident from observing a couple of beads on the first rows – it'll still look totally unpredictable. However, it will show up clearly in the shifted peak of the distribution after 1000 rows.

Consider a Galton board. A simple bead pummels down the cascade of pegs. Can we predict what path it is going to take?

Well, in principle yes – it's after all just mechanics. If it hits the first peg a little bit to the left of its center, it'll go to the left there. Measure the start state very accurately, and you can predict all that comes later.
But it's evidently hopeless to actually predict the whole path – it's way to sensitive, even the tiniest change at the start will mean it scatters off the first peg with a slightly different spin, and then this again changes the behaviour at the second, so already after too iterations our prediction is sure to break down. For all intends and purposes, the behaviour is just random then, despite following deterministic dynamics.

Roughly the same reason is responsible for weather forecasts being little use over more than a week.

Nevertheless, what we can say with very good confidence is that the bead is going to end up somewhere near the middle after 1000 rows of pegs. It's not strictly speaking impossible that it goes to the left twice as often as to the right, but so very unlikely that we might rather worry about the board being destroyed by a plane crashing into the lab.

And if all the pegs are slightly biased to make it 5% more likely for the bead to go to the right at each of them somehow, that's not going to be evident from observing a couple of beads on the first rows – it'll still look totally unpredictable. However, it will show up clearly in the shifted peak of the distibution after 1000 rows.

Consider a Galton board. A simple bead pummels down the cascade of pegs. Can we predict what path it is going to take?

Well, in principle yes – it's after all just mechanics. If it hits the first peg a little bit to the left of its center, it'll go to the left there. Measure the start state very accurately, and you can predict all that comes later.
But it's evidently hopeless to actually predict the whole path – it's way to sensitive, even the tiniest change at the start will mean it scatters off the first peg with a slightly different spin, and then this again changes the behaviour at the second, so already after two iterations prediction is sure to be off. For all intends and purposes, the behaviour is just random then, despite following deterministic microscopic dynamics.

Roughly the same reason is responsible for weather forecasts being little use over more than a week.

Nevertheless, what we can say with very good confidence is that the bead is going to end up somewhere near the middle after 1000 rows of pegs. It's not strictly speaking impossible that it goes to the left twice as often as to the right, but so very unlikely that we might rather worry about the board being destroyed by a plane crashing into the lab.

And if all the pegs are slightly biased to make it 5% more likely for the bead to go to the right at each of them somehow, that's not going to be evident from observing a couple of beads on the first rows – it'll still look totally unpredictable. However, it will show up clearly in the shifted peak of the distibution after 1000 rows.