Don't think of cells as disordered bags of water. They're more like highly ordered liquid crystals.
"program" size limited to 500 tiles IIRC, because the design will break when things get larger. Still amazing, happy googling.
So there is this HUGE part of biophysics that we completely isolate all of the undergraduate students from, with these pretty videos where one machine magically swims out to exactly where it's supposed to go and then the next machine magically swims in to do the next thing and then the next machine, and so on, until you've got this perfect assembly line chugging away at this stuff. That is NOT what happens.
The reason that we make those "schematic" videos is that if we drew the real video, you could get overwhelmed by detail and miss the actual mechanism that we're talking about. What's actually happening is that this whole activity is happening in one big churning sea of all of these things knocking into each other bouncing around chaotically. That one machine that went to the right place is symbolic of hundreds of machines that happened to bounce off into the wrong one; that straight line is symbolic of an average of a million possible bouncy trajectories which went in all sorts of different directions before getting there. Everything is at a high enough concentration and pulsating and buzzing so much that in short order the "right stuff" happens to bounce together to do whatever is happening. Sometimes, even, the cell makes the "local concentration" of some machine or part even higher, via either containing some structure within a bag or else by producing proteins which attract "the right sort of thing" to them, so that more nucleotides or whatever happen to be nearby.
Just to give a more concrete example, in the fertilization of an ovum, we showed you a nice picture of one single solitary spermatozoon which shakes hands nicely with one ovum, and they became best friends. We also tried to scare you with "just one sperm is all it takes!" reasoning, which is technically true but misleading. If we were showing you the absolute truth, you'd see that the ovum is getting beaten down by a bunch of spermatozoa pelting it like a pack of wolves, trying to break down a chink in its shell, called the "corona radiata", until one of them burrows into a thin tear. Then the eggs of most mammals have to chemically shift composition of their borders to actively prevent "polyspermy", getting penetrated by multiple spermatozoa, through that tear. What's really fascinating here is that we're not completely sure how this happens because usually this process is happening during meiosis, another of those things where we separate the story for the textbooks ("meiosis happens, then you store the resulting cells, finally some of them bubble up for fertilization" -- no, meiosis actually has these two long pauses in it; long-term storage happens during the first one (the "dictyate") and fertilization happens during the second one before meiosis is complete). So it's hard to say "this prevention of polyspermy is due to meiosis" vs. "it's due to fertilization."
Suddenly it's not so much of a surprise that some of your friends were trying for years to conceive while some teenagers you know of got pregnant too soon -- that "it only takes one" rhetoric makes people very worried very rapidly, "what if I waited too long, what if I'm infertile" and the "there is literally a wall there and it's a matter of luck whether something breaks through it or not" story reveals the real emotional truth: "oh, we have like no real control over this; whatever will be, will be."
It's just that at the lowest levels there's a ton of bouncing chaotic pulsating activity, things smashing into each other routinely, and heck, the only reason that your proteins even keep their characteristic lumpy shapes is that they're designed by evolution to take on this shape when water molecules are bouncing against them chaotically enough that they happen to curl up into it. The machines to replicate DNA similarly are sitting in a sea of nucleotides smacking against them, which is why the helicase can't unzip too far ahead of the polymerase; that polymerase might be able to handle the stray nucleotide that binds prematurely to the DNA, but it might have real trouble if an extended sequence gets accidentally bound that way.