Coming from a more traditional stats/ML background, I try to view "thinking" traces as a way to explore the search space without getting caught in a local maximum.

A better analogy for me is annealing; you can't cool metal down instantly or the result is brittle. You must cool down gradually, which allows the molecules to arrange into more durable structures. Random but controlled.

In the same way, thinking traces are testing out all sorts of novel connections between tokens ("But wait..", "Actually,.."). Like a highly divergent branching mind map that gets pruned over time, rather than settling directly into the initial answer.

Now consider human cognition. We're constantly diverging, daydreaming, playing "what if" scenarios and measuring up those ideas against our internal objective functions (proxy for reality) to see which ideas stick. Not too dissimilar. But it's hard to call what we do "thinking" either - it's the default mode network wandering.