Lets step back a little bit and look at the question of 'sentience'. So far, just as we only have one example of a planet full of life, we also only have ourselves (I am being inclusive of all life on Earth that has neuronal structures we collectively call a 'brain') to draw our references from.
Whether we look at snails with 12 neurons for a brain, or a human or cetacean that have the most complex brains on earth, the biochemistry behind how they work is all rooted from the same evolutionary source.
We can hypothesize that on a another planet where life arises using the same kinds of naturally occurring elements (hydrogen, oxygen, carbon, nitrogen, etc etc), and that this life lives in a similar environment (a warm, wet, ball of rock) that we might see convergent evolution across many, many worlds that share these properties.
DNA is what life here on Earth eventually settled on, but remember that the latest theories of life's beginnings on our world is that RNA probably came first. So its not 100% proof positive that DNA or its chemical equivalents are the only way to make a living, complex cell. Different replicative mechanisms could create different biochemistry, even on a world that is nearly identical to Earth.
The point of this is that even on a world with a different kind of replicative biochemical system, complex life could evolve similar large-scale structures. Fins for the water, legs for land, wings for air, eyes for seeing, etc, etc.
So, does this hypothetical situation also extend to things like brains? If this alternate biosphere uses a chemical system very different from DNA, how does that affect the chemistry of what makes a brain? Perhaps arsenic is like seratonin or dopamine, for example.
Putting aside the chemistry for a moment, does a similar physical environment that encourages things like legs, eyes, and skin encourage the development of similar brain structures to control those systems? Or, are there vastly different kinds of brain structures that can control the stuff that makes up a body?
IBM has been working on simulating the neuronal columns that make up a cat brain. Mice, cats, and humans all share some variation of these columns. It makes sense because we all share common ancestors and we inherited these basic structures from them. But would we necessarily expect to see these structures in life coming from a different biochemical history?
So pulling this back to the original question, how much of our mathematics and computing models correspond to how our form of intelligence has evolved?
Based on the universe we can see and test, we have developed a very large and thorough mathematical knowledge-base of how the universe fits together. But it does beg the question, if another kind of sentient life discovers the same mathematics do they utilize that knowledge in the same ways that we have?
Binary logic is a very efficient way to do our kind of computing. But its not the only way. Quantum computation is an easy example of a non-binary way to do computation. We've also only been doing this for a little over a century, and if we can take anything from the lessons of history its that we should never assume what or how we do something now is going to be the best way for all time.
I can't and shouldn't offer a definitive answer to the question. No one on Earth can provide anything more than a strong hypothetical argument one way or another. Remember, black swans and all.
What it would take to answer this would be to find that ever so elusive alien tech and stick some probes in it and start studying it. Experimental evidence is the only way to ever really prove something.
I will offer a hypothetical answer though, here at the end. From everything I have learned in my life, its likely that math and physics work everywhere we can see. And we can see a long, long way away. Even if some sentients on another world with a vastly different arrangement of biochemistry and thinking-stuff (aka brain analogues) invent their types of 'computers' that work differently than ours, I think we can understand how they work.
As we are demonstrating that we can simulate the physics of the universe in our Turing-complete machines (biology to nuclear explosions to air flow over a race car body), when we figure out all the nitty-gritty of how our brains work we'll simulate those too. Given the proper amount of knowledge of how a system works, such as for alien brains and alien computers, we'll be able to load them up and run them as well.
So, as long as the aliens we encounter are based on the same physics we are, there shouldn't fundamentally be a problem to figuring out how their systems work. There might be a high likely-hood that we find many, many similarities at the root level of their computing technologies to our own.
Whether we look at snails with 12 neurons for a brain, or a human or cetacean that have the most complex brains on earth, the biochemistry behind how they work is all rooted from the same evolutionary source.
We can hypothesize that on a another planet where life arises using the same kinds of naturally occurring elements (hydrogen, oxygen, carbon, nitrogen, etc etc), and that this life lives in a similar environment (a warm, wet, ball of rock) that we might see convergent evolution across many, many worlds that share these properties.
DNA is what life here on Earth eventually settled on, but remember that the latest theories of life's beginnings on our world is that RNA probably came first. So its not 100% proof positive that DNA or its chemical equivalents are the only way to make a living, complex cell. Different replicative mechanisms could create different biochemistry, even on a world that is nearly identical to Earth.
The point of this is that even on a world with a different kind of replicative biochemical system, complex life could evolve similar large-scale structures. Fins for the water, legs for land, wings for air, eyes for seeing, etc, etc.
So, does this hypothetical situation also extend to things like brains? If this alternate biosphere uses a chemical system very different from DNA, how does that affect the chemistry of what makes a brain? Perhaps arsenic is like seratonin or dopamine, for example.
Putting aside the chemistry for a moment, does a similar physical environment that encourages things like legs, eyes, and skin encourage the development of similar brain structures to control those systems? Or, are there vastly different kinds of brain structures that can control the stuff that makes up a body?
IBM has been working on simulating the neuronal columns that make up a cat brain. Mice, cats, and humans all share some variation of these columns. It makes sense because we all share common ancestors and we inherited these basic structures from them. But would we necessarily expect to see these structures in life coming from a different biochemical history?
So pulling this back to the original question, how much of our mathematics and computing models correspond to how our form of intelligence has evolved?
Based on the universe we can see and test, we have developed a very large and thorough mathematical knowledge-base of how the universe fits together. But it does beg the question, if another kind of sentient life discovers the same mathematics do they utilize that knowledge in the same ways that we have?
Binary logic is a very efficient way to do our kind of computing. But its not the only way. Quantum computation is an easy example of a non-binary way to do computation. We've also only been doing this for a little over a century, and if we can take anything from the lessons of history its that we should never assume what or how we do something now is going to be the best way for all time.
I can't and shouldn't offer a definitive answer to the question. No one on Earth can provide anything more than a strong hypothetical argument one way or another. Remember, black swans and all.
What it would take to answer this would be to find that ever so elusive alien tech and stick some probes in it and start studying it. Experimental evidence is the only way to ever really prove something.
I will offer a hypothetical answer though, here at the end. From everything I have learned in my life, its likely that math and physics work everywhere we can see. And we can see a long, long way away. Even if some sentients on another world with a vastly different arrangement of biochemistry and thinking-stuff (aka brain analogues) invent their types of 'computers' that work differently than ours, I think we can understand how they work.
As we are demonstrating that we can simulate the physics of the universe in our Turing-complete machines (biology to nuclear explosions to air flow over a race car body), when we figure out all the nitty-gritty of how our brains work we'll simulate those too. Given the proper amount of knowledge of how a system works, such as for alien brains and alien computers, we'll be able to load them up and run them as well.
So, as long as the aliens we encounter are based on the same physics we are, there shouldn't fundamentally be a problem to figuring out how their systems work. There might be a high likely-hood that we find many, many similarities at the root level of their computing technologies to our own.