scale of repeat (evol-human-sci)

What does it mean to repeat something at scale 𝜏?
It is an interesting Mathematical concept that is used implicitly in below example usage. The dialogues does not matter, but my point is the meanin of "the scale of a repeat".

From an evolution/neuroscience perspective, if history (evolution) were repeated, would humans come into existence? Or would humans never come into existence at all? Note: I consider persons separate from the thoughts. This question and answer are considered **once purely within the framework of evolution. That is, they are posed under this assumption. They are also considered within the framework of the brain science/neuroscience: by this, I mean properties that are fundamentally brain-based.
Question from N:
According to evolution, if history were repeated, would humans come into existence? Or would humans never come into existence at all?

An evolution/biologist's answer:
This question is, in fact, two questions. It can be posed in two ways, which are distinct questions:
1. Would a being with the cognitive capacity of the human brain come into existence?
2. Would a being with this particular form and appearance (human-like) come into existence?

Even from an evolutionary and brain-centric perspective, if one wants to speculate, then all answers to such questions are thought experiments—guesses, hypotheses, conjectures—and they exist within a specific paradigm. Here, the nature of the question is framed within an evolution-centered and brain-centered paradigm, so the answer is given from within that mode of thinking.
If history were repeated at evolutionary scale, something similar to humans, in the sense of cognitive capacity, would come into existence. Either perhaps later, or perhaps earlier. I observed monkeys in laboratories, they were very similar to humans; they just simply could not speak. That was the only difference one could see.
Birds, in particular, are very close. Dolphins and elephants went in a different direction; not necessarily them, but dolphins, whales, and similar species were also possible candidates. By “human,” do we mean a being that must necessarily have this exact form? If you mean a being with precisely this appearance, then perhaps not—but that is not important. If by humans coming into existence again we mean a being that is intelligent, but that it is acceptable for it to have a different form, then that is the key point. Because if you mean a being with exactly this shape, then perhaps next time it would have a different form—but the form itself is not what matters.
What matters is that a being reaches a level of intelligence at which it can build tools—create the internet, tractors, and similar things. The important question is whether a being with this level of intelligence would come into existence or not. Even an insect is possible, but insects must have small brains. Given my familiarity with insect brain structures, I would even say that insects could be possible if their brains became larger—but not individually, because insects have size constraints. They cannot carry a one-kilogram brain.
If insects were to become intelligent beings, it would have to be in the form of a colony. A beehive is a very intelligent entity; each bee is highly intelligent, but its intelligence is limited relative to the collective organism that emerges. Perhaps something like bee colonies, or insects that became intelligent at the collective level, could emerge.
Overall, as you mentioned, octopuses—especially squid—birds, dolphins, and whales are all candidates. They are also approaching higher intelligence and will likely become intelligent soon (only a few million years to go 😃). However, humans may drive them to extinction before that happens. Humans have already driven other intelligent beings (such as Neanderthals) to extinction because they perceived competition in intelligence. Humans also drove mammoths to extinction. In reality, mammoths were elephants that were becoming more evolutionarily advanced, yet humans wiped them out. Perhaps intelligence was the reason (this is my own hypothesis; I have not read it anywhere).
Birds are particularly important because they possess communication systems more advanced than those of humans. If bird language were to evolve further, it would become far more complete, complex, and faster than human language. Dolphins also have complex languages, and because of the ocean environment, their group communication is easier. In short, the social and communicative dimension is also essential for forming culture.
However, dolphins and birds lack hands, which would make tool construction more difficult for them. If a human competitor were a bird, it would primarily use its beak, but something like hands would still be necessary. Perhaps the reason for the extinction of dinosaurs was their short arms :))) But over the course of evolution, limb size can lengthen or shorten. Just as in humans the tail shortened, the stomach and intestines became smaller to adapt, and fingers and hand shape became more symmetrical and refined to match the higher intelligence that emerged in human-like species. Dolphin fins would need to return more toward a hand-like form, or bird wings would need to transform back into hands (as in their dinosaur ancestors).


Second question:
N: Perhaps it would have been a jellyfish, or an octopus, or a bird?

A possible answer:
If you mean whether a being with this exact form and appearance would come into existence, then perhaps not—and on this point I agree. It is possible that an intelligent being capable of reaching sufficient self-awareness to ask this question would have a different form and appearance: as you said, a bird, an aquatic organism, a different kind of mammal, or even an entirely different life form with a completely different structure, which I think you have already alluded to in the description.
But if the question is whether **any** intelligent being reaching the scale of human intelligence would come into existence at all—that is, whether the capabilities humans developed were dependent solely on this specific historical path—then in my view, no. Overall, evolution was moving toward intelligence, but it could have manifested elsewhere. It could have been a mammal close to primates, or another organism entirely. Many different evolutionary paths lead in the same direction. If the initial human lineage had been wiped out—for example by an asteroid, or even by extraterrestrials—this intelligence would have emerged elsewhere.
However, we are talking on the scale of millions of years. It might not have happened so soon—perhaps millions of years later—or it is even possible that if history were repeated, it could have emerged earlier along a different path.