Tl/Dr: There's a simpler version of seeing the future which can't see the future, but can see the best path to take towards it. This can be within the realm of a seer's "fast paced" capability. What I find interesting is that it certainly appears that we mere mortals do this, today -- every day.
This is a topic near and dear to my heart because we're all seers in some sense. We all have some ability to predict the (near) future. It's the little voice in our head which says "This is not the bar to have a drink in tonight" 5 minutes before a bar fight breaks out. It's the little voice which says "I should check on my daughter just one more time, to make sure she's asleep." It's the mother's voice which somehow knows how to check on the daughter even when she's hundreds of miles away at college. We're all seers, just perhaps not as well trained as yours.
So how do we do it? You mention there could be thousands of potential futures. I'll raise the stakes on that. There's an infinite myriad of solutions. In fact, it is "uncountably infinite," which is a particularly large variant of infinity, if you follow those concepts. Surely one will get lost!
So what do we do? I find the key concept for untangling this web is symmetries. Symmetric situations are situations which are related in a way which also relates their outcomes. It doesn't really matter whether you drive on the left side of the street or the right side of the street. However, we find a symmetry here: those who drive on the left side also put the speed limit signs on the left. Those who drive on the right put the speed limit signs on the right. It doesn't matter which way you drive, by symmetry we always put the speed limit signs on the side of the road we drive on (this makes them easier to see).
So with this, we can reduce the complexity of the seer's job. If two sets of strings to follow are symmetric, they only really need to follow one. They can then use the symmetry to figure out what would have happened on the other side.
This can reduce the complexity dramatically, but any number of mirrors or rotations by 45 degrees or such won't make a dent in an uncountable infinity number of possibilities. You need a more advanced concept: continuous symmetries. Consider a free rotation. You could rotate an object 90 degrees, or 45, or 22.5, or 3.14151689371 degrees. Any rotation is possible. And, for each of them, the object will still have a symmetry -- Turning an object around doesn't mean it stops being that object. This is what we call a continuous symmetry.
There's many variants of continuous symmetries. Rotation is only one of them. You also have a continuous symmetry of translation. In many cases, it doesn't matter if you're at one spot and, say, a soccer ball is 5 feet in front of you, or if you're in a different point 3 feet away and the soccer ball has also moved 3 feet to the side so as to remain in front of you. Your interaction with the ball is exactly the same. That's a translational continuous symmetry. You can put that soccer ball and player system anywhere in the universe, and its behavior is still the same (barring minor details like picking somewhere with air to breathe).
Mathematicians have a sub-discipline focused on these symmetries called group theory. This is exciting to me (geek alert!), because if anything has the tools to deal with an uncountably infinite number of strings, it's fundamental mathematics! In particular, group theory looks at how symmetries compose. It can ask the question "If I rotate this ball 90 degrees along one axis, and then 90 degrees along another, what rotation do I actually end up with?"
Because symmetries are so fundamental in the mathematical world, a great deal of effort has been spent characterizing them. Mathematicians have notations which capture the fundamental behaviors of different groups. However, if we focus specifically on the continuous symmetries, we have an even better situation: the continuous symmetry groups, called "Lie groups" (pronounced "Lee") are fully categorized. If you have a continuous symmetry, mathematicians can describe it!
Thus your seers could leverage these continuous symmetries to cut down the threads they have to look at. Instead of uncountably infinite, we may be able cut them down to the mere thousands you were thinking of. Now we're back into the realm of, say Men in Black future telling.
Now with all of that, we can have some real fun (geek alert)! Mathematicians noticed that there's some connection between some sorts of groups. For example, consider the "belt trick." This is a neat trick you can do yourself with a belt that's fixed to a wall, which lets you spin around as much as you like without tangling yourself up in the belt. It's the basis of the candle dance, and it's also at the heart of the physics of getting out from a hold where someone has twisted your arm behind your back. It's what lets you rotate your arm enough to get free without requiring your feet to move. For those who haven't done it, the solution, surprisingly, is simply to step forward. Its only when you're tense that you can't realize that you can do this trick. If you walk forward, you stop concentrating so hard, and your body does it right.
The reason for this is that $SU(2)$ is a double cover of $SO(3)$. Remember when I said mathematicians had this categorization of symmetries thing in the bag? Well that's their funny notation to describe that this "spinor" motion of the belt trick is basically the same as a double rotation in 3-d space. This sounds really abstract, but it leads mathematicians to something which is very practical for our seers. It introduces the idea of a "Lie Algebra," which describes how these groups behave at a single point.
Remember when the wise people in your life told you to live in the moment? Well this is where it factors in. As it turns out, the algebras for $SU(2)$ and $SO(3)$ are the same at all points. If all you care about is the moment, you don't actually have to care about whether this is a $SU(2)$ or $SO(3)$ symmetry you're trying to use to simplify your seeing. If all you need is this moment, and the next step forward, you can treat them both as $B_1$. That's the name associated with the root diagram for that algebra.
Wow, that was a lot of mathematical terms to throw into one paragraph, so let's back it up. If you want to truly see the future, you have to worry about an uncountably infinite number of possibilities. You can use continuous symmetries to bring that down to a managable number. However, you have to be concerned with all of the various symmetries, whethere it's $SU(2)$, $SO(3)$, or $U(1)\times SO(2)$. They are all different, mathematically. However, if all you care about is the best direction to go at the moment, you don't need that detail. You just need to know the algebra for that group, and it will tell you everything you need to know (incidentally, if you think that way, it will point out that the last of my examples is actually fundamentally different from the others).
And, despite being called an "algebra," the algebras for Lie groups are really simple. There's 4 infinite series of them, which all have geometric and physical meanings, along with a spattering of "exceptional" algebras that just don't fit in. Once you have those, you merely combine them in natural ways, like how $x=3$ and $y=4$ can be combined to $x+y=7$ The entire list is:
- $A_n$ - describes symmetries that come about from the special linear group in n-dimensions. For one thing, this is what we use when we are all "in sync" with one another. If a dance troupe all seems to move exactly as one, it's because they all have the same "beat", and that's captured by this sort of thing. When dealing with a well trained army, you will deal with a $A_n$ algebra which captures the army's ability to stay in sync in the heat of battle.
- $B_n$ - describes odd dimensional symmetries that are orthogonal. This describes rotations in odd numbers of dimensions, such as rotating a ball.
- $C_n$ - the symplectic algebras. These are horrible to try to define in non mathematical words, but we find them at the heart of Hamiltonian mechanics. The Hamiltonian typically describes "total energy," so we can think of the $C_n$ series as describing the symmetries in how energy flows through systems. If any martial art speaks of manipulating "energy," it is highly likely that their training helps one be comfortable with manipulating symmetries with a $C_n$ algebraic structure.
- $D_n$ - describes even numbered symmetries that are orthogonal. This describes rotations in even numbers of dimensions, such as rotating a circle.
- $E_6$, $E_7$, $E_8$, $F_4$, $G_2$ - These are the exceptional algebras. They are hard to pin down to a specific physical phenomena, but the $E_n$ series is very popular among particle physicists, because if you break those symmetries, you end up with the symmetries we see in the Standard Model of Quantum Physics. It may be that the mere act of learning how to intuitively work with these is what differentiates an average Joe from a seer.
And that's it. That's all of them. There's literally no more. If you can intuit rotations in any number of dimensions, matrix manipulations such as keeping things in phase, energy manipulation, and a hand full of special cases, you can always determine what direction you should be going as long as the world it continuous... and all of physics says it is.
So there's a lot of math there (geek alert!), but in the end, what we see is that a seer could choose to not tackle "the future," but merely tackle "where do I go next," reducing the complexity of managing these threads of time down to 4 series of simple algebras and 5 exceptional ones. And, in the heat of battle, you really only have time to think about where you're going, so this would be a very interesting skill.
And, with all the geek alerts, what fascinates me is that there's nothing to distinguish what these seers would be doing from what we mere mortals do. The only difference is a level of magnitude, and perhaps an awareness of those 5 exceptional cases which are so hard to learn.
