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Premise

Let me begin by citing the intellectually charged and equally comical banter between physicist Brian Cox and "Doctor Who":

(aliens appear on console)

Dr. Who: "That's a silent; you gotta admire a monster who puts on a tie."

Cox: "An intelligent bi-pedal lifeform, that's a near impossibility!"

That's the premise; in so many words, anyway. Specifically, in the sci-fi community it is not uncommon to see human-like physiology among intelligent aliens. However in the scientific community there is a certain level of skepticism about this portrayal, as is reflected by Cox's remark above.

Of course there could be aliens of any ecological niche, but I'm setting the scope to intelligent life only, in keeping with human's "niche". Moreover, I'm trying to gather information for a counter-argument to the human-like skeptics. I'm not sure if there will be a sufficient basis in the end, but I already have a few promising findings. One of which being that within our biosphere, eyes/proto eyes have evolved independently hundreds of times. The trait of a photo-receptive organ has proved to be a vital adaptation for life as we know it and can be found in many distant species as a form of convergent evolution.

Question

How similar can we expect intelligent aliens to be? Would factors would likely govern the degree of similarity?

Further Clarification

  • Intelligence: near our own, perhaps more advanced than our own. "Simple" life is out of scope
  • Physiological Features Comparison: which do we share, which would likely be different? (i.e. both have eyes, but aliens may lack tongues)
  • Theoretical Distribution: Imagine the number of features shared on the X Axis, and the number of different alien species on the Y Axis. What shape do you see the distribution being? (no math proof is needed, but please explain your logic) In other words, the likelihood of very, very similar aliens vs the likelihood of slightly similar aliens.
  • Environment: no restrictions are imposed here, but knowing how robust the similar physiological features would be to different environments might help answer the question.
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Here are a number of things that led us humans to be as we are:

  1. We are air breathing and land based
  2. We are not the best adapted for our environment so we had to invent clothes.
  3. We are not the top of the food chain so we needed an upright position and sense organs as high as possible to search for predators.
  4. We were omnivores and had to find food where we could.
  5. We were not fast or strong or had claws or fangs for hunting so we needed manipulative hands to make and use weapons.
  6. An upright position frees up a pair of "feet" to become hands.
  7. We need to group together to survive which gives us social skills and language.

Any creature that is better than us at survival is less likely to develop intelligence. Just look at the Shark.

The above list is not exhaustive and, given out limited data set of sentient creatures, some of the above may not be important.

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EDIT: it occurs to me that I might be one of those "human-like skeptics" you mentioned, and quite frankly I'll own that. I'll defend my points as scientifically accurate, but for world building (with a suspension of disbelief and the nature of fiction writing) this may not be the answer you're looking for.

The short answer to your question is, not very similar at all.

See my answer on this question for a related topic: A mechanism for a level interstellar playing field

Generalized things that nearly all earthen species have (eyes, legs, a nervous system, ears, etc) are still incredibly specialized and therefore incredibly unlikely to evolve in another ecosystem. The solutions that earth organisms devised to environmental problems are far from the only solutions.

For example, nearly every complex organism on earth has eyes. And in many of the cases where an animal doesn't have eyes, it evolved from a creature that did. Think of the specialization there: we have an organ that is both a) sensitive enough to detect incredibly small variations in light waves and b) robust enough to survive direct contact with our outside environment. This organ translates these light waves into electrical impulses that our incredibly specialized brain is capable of understanding. Regardless of how good eyes are at allowing an organism to interact with their environment, the odds of another planet developing something that specialized in even a slightly similar way is ludicrously small. This same argument applies to almost any attribute of any complex organism.

But your question asks where we would likely be similar, and there are definitely some similarities we can count on; they just might not be the similarities you were picturing.

  • Chemically, all earth organisms are based on carbon ("carbon-based lifeforms"). This is because, chemically, carbon is a very stable atom with four valence electrons, thus making it ideal for forming the backbone of complex molecules. It is reasonably likely that an alien lifeform would also be carbon based, though it is also possible that silicon based life may exist, as silicon shares carbon's four-valence bonding property. This means that we and the aliens would likely have certain chemical compatibilities with simple molecules.
  • Biologically, we can fairly safely assume that any living organism must consume input (eat food) and must expel waste as a result. From this we can logically conclude that another organism would, at the base biological/instinctual level, seek out sources of sustenance and also release some form of unnaturally occurring byproduct in the form of complex organic molecules. In other words, its likely the aliens would have some form of hunting/farming/gathering system and a waste management system.
  • Physically, aliens would need to be at the top of their planets food chain. Any species constantly under threat from a superior predator doesn't get very far in terms of social/technological development. What defines the top of the food chain will be specific to the ecosystem, but if we assume that the alien is also intelligent (like us) then it is logical to assume that their dominance of the food chain is due to their intelligence (strong creatures have no need to be clever, clever creatures have no need to be strong). Thus, we can assume that (relative to their home planet) they probably are not physically imposing, though they may very well appear as such to us.
  • Evolutionarily, it is well accepted that all organisms on earth share a common ancestor (way, way, waayyy back there). In all likely hood, the same would hold true on an alien planet. This means that the aliens would likely share many traits with other organisms on their planet. On earth, an example would be eyes. Perhaps on an alien planet, most creatures have an array of heat sensing apparatuses.
  • Socially, any species capable of advanced communication or interstellar travel must have a semi-stable social structure. While we can't assume that their society is democratic, or totalitarian, or anything that specific, we can assume that it is complex and organized.

The key point is that any truly alien species will not really appear similar to us in any readily noticeable way. Because of this (and the limitations of studio budgets) most aliens in sci-fi TV shows and movies adhere to the basic assumptions of legs, arms, eyes, ears, mouths, and oxygen breathing. On a related note, (if I remember the episode you're referencing correctly) I believe that line from Dr. Who is intended to poke fun at Dr. Who's tendency to fall into exactly this trap of assuming aliens are humanoid.

For more information on (what I think is a really fascinating and cool topic) check out this article from NASA on the Definition of Life.

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    $\begingroup$ Eyelike organs have independently re-evolved several times on earth. Most animals live in an environment where light is present. It is quite easy to detect light biologically. While they might have a different number of eyes, and compound eyes are an option, they probably will have some organ that detects light. $\endgroup$ – Donald Hobson Aug 12 '17 at 16:53
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Like Humans Are: I'd expect them to be rather weak and inept in the wild, former prey for bigger, stronger, more vicious animals, big brained that gained their dominant status through better insight, building protections, planning (like hunting, farming) and invention.

They don't need opposable thumbs; but they do need ways to grasp natural objects and transform them. Sticks, rocks, dirt, hair, bones and fur, to start.

They would almost certainly require sight and hearing; these are too ubiquitous and useful to imagine they don't evolve independently.

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Assumptions

As carbon and water are very common, and have a complex chemistry, we will assume that the aliens are carbon and water based. The aliens evolved, as opposed to being designed by other aliens. The aliens are intelligent and developing tech. The aliens are not technologically advanced enough to modify their biology.

Deductions

The aliens intelligence requires some organ to store and process data. While the human brain is far from the theoretical limits of computing, it would be hard for a biological system to be much smaller or more efficient. (in the same way that cheetahs are far slower than light the ultimate speed limit, but biology can't go much faster) So the aliens could be a bit smaller than us up to elephant or so. The aliens can't be arbitrarily big because of ... to be continued

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