The future doesn't exist yet
At first glance, unpredictability should be pretty simple. There is little to be known about an unpredictable system other than it is unpredictable.
We tend to be most interested in predictable systems.
Here's an example of a very simple predictable system:
First I define a function that chooses a color according to a number given to it.
if number = 1 then color = red
if color = 2 then color = blue
otherwise color = yellow
Then we call it like this:
which shows red
or print (choose_color(2))
which shows blue
if we go choose_color(3) it shows yellow
if we go choose_color(500) it shows yellow too
We can predict the color returned by a number.
But lets change the function a bit
color = choose at random from red, blue or yellow return (color)
Then we call it like this:
which shows an unpredictable color
or print (choose_color_u(2))
which shows an unpredictable color
if we go choose_color_U(3) it shows an unpredictable color
if we go choose_color_U(500) it shows an unpredictable color too
Be still my beating heart :-)
The unpredictable function in this case is constructed to be unpredictable.
But what if the unpredictability isn't constructed?
Science, since Newton and Galileo, has thought of physical reality as a deterministic system: a system of causes having effects that are predictable.
Artillery provides an example. Given a certain charge of powder and weight of projectile the landing point could be determined by calculation from the angle of the barrel and the direction the gun was pointing.
Of course the projectile never hit exactly on the predicted landing point. This was seen to be caused by unseen factors like gusts of wind that couldn't be factored into the calculation. The assumption was that if you could factor in all those unseen factors then the prediction by calculation would be perfect.
The unpredictability was thought to be a limit of calculation. An equation with billions or trillions of terms is thought to be intractable to calculation and so approximations have to be accepted. And the approximations limit the accuracy of the prediction.
An interesting thing about Newtonian gravitation - it's results are perfectly predictable if 2 things are interacting via gravity when they are in free fall.
You can readily predict the positions of the things at any time in the past or future from knowing the present state of affairs.
With 3 bodies you can't. And that's unpredictability in a deterministic system. But that didn't really get much attention until modern computers showed that to be more than intractibility. It was that you calculate the state of one thing without knowing the state of the other things - but the state of the other things depends on the state of the one thing. The logic is circular.
About 100 years ago both General Relativity and Quantum Mechanics shook up our view of prediction in a deterministic reality.
Both were very strange in terms of our normal perception.
QM has probability at it's core. Given a state of affairs you can only state the probability of an event occurring. But QM is completely deterministic at the level of it's math and is fabulously accurate in terms of agreeing with experimental results. Once long ago, I even did a double slit experiment that demonstrated how photons went through two slits at once and interfered with themselves to produce an interference pattern on a screen. And yup - one slit and you get a line on the screen. And 2 slits you get the pattern.
I accept the view of people who know the math of QM that it's unpredictability is not a matter of an intractable calculation nor is it a matter of hidden forces (as with gusts of wind and the artillary shell).
That it's fundamental to reality.
I have to take their word for it. And in a way the math isn't that hard - I've been able to read the proof of unpredictability and been convinced but can't report the details.
In the 1960s a new kind of unpredictable chaotic system was found. This involved the behavior of quite simple deterministic equations that produced unpredictable results.
Chaos theory studies systems like that. (Admits to not knowing where that name came from)
A favorite example is the famous Mandelbrot Set. This is shown on a computer screen as a big image you can zoom in on. The image shows characteristic spiral patterns with areas of color and areas where the pixels all have random colors. You can magnify the image as much as you want. If you magnify a red pixel in a region that is all red then all you see is red - so what you see in that region is predictable if you zoom
If you find a red pixel in the random color area and zoom in on that then what you see shows a new image of spirals with areas of color. You can't predict what you will see until you actually do the zoom. So it's unpredictable. And it's so unpredictable that it's not always unpredictable. But - it's a thing you can learn about. If you zoom a certain amount on a certain location then what you see is always the same - so it's deterministic.
So "unpredictabity" in a deterministic reality turns out to be more interesting than it seemed at first. There is unpredictability that comes from unseen forces like gusts of wind. There is unpredictability that comes from the intractability of the calculation required for the prediction. There is the unpredictability in QM that arise from the fact that it determines probabilities of outcomes if a wave function collapses but not which actual outcome the collapse will produce. And there is the unpredictability found in Newton's 3 Body Problem or in Chaos Theory.
The first two are a result of our limitations as people with limited perceptual and cognitive abilities.
The latter two seem to indicate why there is time in reality.
Let me explain :-)
One of the implications of the old deterministic universe idea is that time is a dimension on a par with spatial dimensions. This implies a spacetime that is a 4d space. That spacetime was thought to be unchanging as a whole. All that changed was a position within the spacetime. In that view you could travel forward or back in time like you can go this way or that in space.
I play with the idea that chaos theory and QM show that that 4d spacetime does not exist.
What exists is physical reality that changes in a deterministic way.
Reality is a big space and physical influence can't move faster than light speed.
Time is a measure of how things change in space.
I think things do change in space due to influences from other things that are never still. But the unpredictability of the future isn't just a cognitive limitation of people.
Its that the future does not actually exist.
What do you think?