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# Applied Category Theory and Life Detection on Other Planets

Hi all,

I am enjoying the course immensely- thank you so much for putting it together Dr. Baez!

Simultaneous to this course, I've been a part of a program at Ames Research Center to come up with new ideas for the search for life on other planets. A component of this course has been an introduction to the history of exobiology as a discipline, its practice, and the tools used to find evidence of an unknown unknown quality of life.

One thing that struck me is the scarcity of resources when performing an experiment in situ, and the relative lack of rigorous methods for selecting what experiment to fly. The approach usually taken is to select one instrument (such as the metabolic experiment performed on the Viking landers) designed such that a positive result is sufficient to provide clear evidence of life. The problem is it usually produces inconclusive results, either because of contamination or unexpected effects, and also because this community is by its nature cantankerous.

However, we had Dr. Carol Cleland from UC Boulder speak at the program, and she emphasized the idea of a diverse set of smaller experiments that each provide proximate evidence for life. A sort of high-bandwidth, low-sensitivity approach to searching for biological signs. I think we can build on this approach and design a diverse set of experiments where no single result provides clear evidence for life, but the generative effects that come from the combination of the experiments produces compelling evidence for or against life, and I think we can use applied category theory to formalize the selection of the experiments that fly from the set of all possible experiments to maximize for evidence given the expected sample, environment, etc.

I'm the kind of person who needs examples, so I thought I'd provide one. A famous life detection experiment performed on Earth involved analysis of the Allan Hills 84001 meteorite. If you were around in the 90s, it was a big deal- a few scientists said they found (long dead, fossilized) alien life on a meteroite that had come from Mars. It's been pretty thoroughly challenged over the last two decades.

The crux of the argument for life was:

1. SEM images showed small structures that resembled bacteria
2. These structures appeared to form larger assemblages that were reminiscent of biofilms and colonies
3. The meteorite contained magnetite crystals that were of unusual shape, and had similar features to magnetite produced on Earth by biological processes
4. There were Polycyclic aromatic hydrocarbons found in proximity to the carbonate globules that were being touted as the bacteria-like structures.

The crux of the argument against life was:

1. The observed structures could have been an artifact of the process used to coat the sample (gold)
2. See 1. The structures also had the same crystalline alignment between the globules and the outer rock, suggesting that they were not biological in origin
3. The magnetite crystals could have formed as a part of inorganic processes on proto-mars
4. PAHs are common on comets, asteroids, etc. and there is no life there.

My thinking is, this experiment provides a clear example of how a single line of inquiry- in this case morphological analysis of a meteorite- has trouble being conclusive. If I were to approach this example with some hypothetical applied category theory tool, I would attempt to find what set of alternate analyses- chemical, spectral, etc.- could be used to break the deadlock, and what the optimal/minimal set of criteria would be necessary.

In order to populate this list of alternate analyses, I would comb the literature for other experiments performed on this sample (and it has been done. to death.). I would then use something similar to the partition logic that Dr. Baez described in his Chapter 1 lectures to do... something. That's part of the reason I'm posting here I have no idea what I'd do next but I'm hoping I'll pique the interest of someone smarter than me and we can come up with a solution together.

I'm also wondering if any of this makes sense.

Thanks for reading this wall of text.

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1.

Hi Daniel! I can't give a response related to category theory. I hope that you might get one. But meanwhile I would at least share an idea which I'm curious if you've thought about or not. It has to do with the comparability of life, in terms of its ability to impact the galactic environment, and so that partial order of comparability may be at play in a category theory way. And also the identification of relevant probabilities among the many we could think about.

There are two strikingly seminal events in evolution. The first is the evolution of an ecosystem of self-replicating molecules like RNA and DNA. What is the chance of that happening somewhere in the universe? The second is the evolution of the ability and aptitude to leave our planet and colonize others, which we are nearing. That seems like a novelty as far as our planet is concerned. And what is the chance of that happening somewhere else in the universe?

Now let's do a back-of-a-napkin calculation with a few very rough facts. Our galaxy is 100,000 light years across. With the technology we have, we could travel a light year in 10,000 years (or please correct me). That means that we could colonize our galaxy in 1 billion years. But there are stars in our galaxy which date back to 13 billion years, whereas our sun formed about 5 billion years ago. And what's the chance that our solar system is in the optimal part of the galaxy for life to form? The conclusion is that if life (like us) could form on its own in several places in our galaxy, then it seems likely that at least one of them would have already colonized the entire Milky Way galaxy and would be 1 billion years more intelligent and experienced than us. So they would have catalogued the whole galaxy and everything interesting about it.

In that case, it seems likely they would have seeded us, as they could have seeded so many planets. But then they should be interested in us because, from an evolutionary point of view, we certainly represent a dramatic cusp. And they would be even more interested in us if we were an original source of life. They would certainly find that miraculous and intriguing. But, if they exist elsewhere, then the chance that we are original is much much less than the chance that they seeded us.

So the conclusion is that there are two main possibilities: A) We are alone in our galaxy. B) We have been seeded by a super powerful life force which knows about us but we don't know about them.

Note that I haven't calculated any probabilities but simply used an analysis of probabilities to end up with the relevant candidates. Category theory could perhaps formalize such an analysis and apply it to all kinds of problems which depend on analyzing a diagram of critical points.

By "we" I mean a life form with the aptitude and ability to colonize the galaxy. Once you have something like DNA, it seems reasonable enough by evolution to get to us. And what makes humans special is perhaps just Tomasello's "joint intentionality", which biologically meant the ability to tune into a shared vision, to sing in unison, to harmonize our bodies, to improvise an abstract "we" on a task-by-task basis rather than just have a bunch of one-on-one relationships. So the upshot is that if something like DNA exists, then perhaps 1 billion years later something like human life will likely exist. So if we are alone as humans, then that means that we are similarly alone as DNA because that's where the real statistical miracle is in evolution.

But looking ahead, it is unsettling that computers are progressing so much faster than we are. In particular, consider the victory of Alpha Zero against Stockfish. Stockfish is a powerful but traditional chess program which leverages the sum of our civilization's knowedge about chess to pass a judgment on a position, and then makes calculations. So we can understand exactly why it beats us. Now, Alpha Zero is a program which doesn't have any of that knowledge but simply played against itself 45,000,000 times in 4 hours and kept learning that. And Alpha Zero went undefeated against Stockfish in a 100 game match! It obliterated Stockfish. And nobody can have any understanding of how Alpha Zero won because it simply has developed its own "intuition" based on "experience". It's like a muscle for chess. It's like the neural network that governs our retina. There's no global logic to it. It's just tuned to do what it does. And it can win any game. It has no use for our accumulated knowledge about chess or anything else!

So that means we live in an age where a computer can be set up to win any game, which could be to win the stock market, to manage a candidate and win an election, to start a war and win that. We live in an age where we we are completely exposed, we have digitized our lives. We live in an age where people serve the "system" and where corporations are the true "people". We're not able to stand up to ourselves and to our "progress".

So, in the big picture, then humanity may be as relevant to evolution or to God as the orangutang is or the Neanderthal was. Maybe God just wanted to create computers. Have the extraterrestrials and/or God stepped in yet? Maybe?

I suppose whether its God or super powerful extrarrestrials or our own computers or an evolution towards an ever more abstract representations, but we're not a dominant being, in a galactic sense. And also, our science fictions which suppose that extraterrestrials are more or less our equals, they seem very false.

In conclusion, if we encounter extraterrestrial life, then the chances seem overwhelming that it will be vastly superior beings. Daniel, is this kind of thinking relevant for your question?

Comment Source:Hi Daniel! I can't give a response related to category theory. I hope that you might get one. But meanwhile I would at least share an idea which I'm curious if you've thought about or not. It has to do with the comparability of life, in terms of its ability to impact the galactic environment, and so that partial order of comparability may be at play in a category theory way. And also the identification of relevant probabilities among the many we could think about. There are two strikingly seminal events in evolution. The first is the evolution of an ecosystem of self-replicating molecules like RNA and DNA. What is the chance of that happening somewhere in the universe? The second is the evolution of the ability and aptitude to leave our planet and colonize others, which we are nearing. That seems like a novelty as far as our planet is concerned. And what is the chance of that happening somewhere else in the universe? Now let's do a back-of-a-napkin calculation with a few very rough facts. Our galaxy is 100,000 light years across. With the technology we have, we could travel a light year in 10,000 years (or please correct me). That means that we could colonize our galaxy in 1 billion years. But there are stars in our galaxy which date back to 13 billion years, whereas our sun formed about 5 billion years ago. And what's the chance that our solar system is in the optimal part of the galaxy for life to form? The conclusion is that if life (like us) could form on its own in several places in our galaxy, then it seems likely that at least one of them would have already colonized the entire Milky Way galaxy and would be 1 billion years more intelligent and experienced than us. So they would have catalogued the whole galaxy and everything interesting about it. In that case, it seems likely they would have seeded us, as they could have seeded so many planets. But then they should be interested in us because, from an evolutionary point of view, we certainly represent a dramatic cusp. And they would be even more interested in us if we were an original source of life. They would certainly find that miraculous and intriguing. But, if they exist elsewhere, then the chance that we are original is much much less than the chance that they seeded us. So the conclusion is that there are two main possibilities: A) We are alone in our galaxy. B) We have been seeded by a super powerful life force which knows about us but we don't know about them. Note that I haven't calculated any probabilities but simply used an analysis of probabilities to end up with the relevant candidates. Category theory could perhaps formalize such an analysis and apply it to all kinds of problems which depend on analyzing a diagram of critical points. By "we" I mean a life form with the aptitude and ability to colonize the galaxy. Once you have something like DNA, it seems reasonable enough by evolution to get to us. And what makes humans special is perhaps just Tomasello's "joint intentionality", which biologically meant the ability to tune into a shared vision, to sing in unison, to harmonize our bodies, to improvise an abstract "we" on a task-by-task basis rather than just have a bunch of one-on-one relationships. So the upshot is that if something like DNA exists, then perhaps 1 billion years later something like human life will likely exist. So if we are alone as humans, then that means that we are similarly alone as DNA because that's where the real statistical miracle is in evolution. But looking ahead, it is unsettling that computers are progressing so much faster than we are. In particular, consider the victory of Alpha Zero against Stockfish. Stockfish is a powerful but traditional chess program which leverages the sum of our civilization's knowedge about chess to pass a judgment on a position, and then makes calculations. So we can understand exactly why it beats us. Now, Alpha Zero is a program which doesn't have any of that knowledge but simply played against itself 45,000,000 times in 4 hours and kept learning that. And Alpha Zero went undefeated against Stockfish in a 100 game match! It obliterated Stockfish. And nobody can have any understanding of how Alpha Zero won because it simply has developed its own "intuition" based on "experience". It's like a muscle for chess. It's like the neural network that governs our retina. There's no global logic to it. It's just tuned to do what it does. And it can win any game. It has no use for our accumulated knowledge about chess or anything else! So that means we live in an age where a computer can be set up to win any game, which could be to win the stock market, to manage a candidate and win an election, to start a war and win that. We live in an age where we we are completely exposed, we have digitized our lives. We live in an age where people serve the "system" and where corporations are the true "people". We're not able to stand up to ourselves and to our "progress". So, in the big picture, then humanity may be as relevant to evolution or to God as the orangutang is or the Neanderthal was. Maybe God just wanted to create computers. Have the extraterrestrials and/or God stepped in yet? Maybe? I suppose whether its God or super powerful extrarrestrials or our own computers or an evolution towards an ever more abstract representations, but we're not a dominant being, in a galactic sense. And also, our science fictions which suppose that extraterrestrials are more or less our equals, they seem very false. In conclusion, if we encounter extraterrestrial life, then the chances seem overwhelming that it will be vastly superior beings. Daniel, is this kind of thinking relevant for your question?
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2.
edited May 2018

Not really, sorry :/

I was focusing on the more mundane question of:

I have a spacecraft with a suite of instruments $$S$$ that performs a set of observations $$O$$. There is a subset of those observations that map to one of two conclusions: $${\textrm{life}, \textrm{no life}}$$. How do I select that suite $$S$$ such that the interactions between the observations helps reinforce that final conclusion, given that I have an admittedly poor definition of what qualifies as life, probably noisy/incorrect instruments, biased processes, etc.?

Comment Source:Not really, sorry :/ I was focusing on the more mundane question of: I have a spacecraft with a suite of instruments \$$S\$$ that performs a set of observations \$$O\$$. There is a subset of those observations that map to one of two conclusions: \$$\{\textrm{life}, \textrm{no life}\}\$$. How do I select that suite \$$S\$$ such that the interactions between the observations helps reinforce that final conclusion, given that I have an admittedly poor definition of what qualifies as life, probably noisy/incorrect instruments, biased processes, etc.? 
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3.

So you have some Bayesian network. Say one node is a PCAH reading that stores a probability distribution of the amount of some compound. You have such a node for each possible instrument you might want to use. How they are actually connected requires the domain knowledge. But you can do some obvious (but maximally unhelpful) things like throw away the information of one of the instruments.

Comment Source:So you have some Bayesian network. Say one node is a PCAH reading that stores a probability distribution of the amount of some compound. You have such a node for each possible instrument you might want to use. How they are actually connected requires the domain knowledge. But you can do some obvious (but maximally unhelpful) things like throw away the information of one of the instruments.
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4.

Is there any sensible way of quantifying the orthogonality of the experiments?

Comment Source:Is there any sensible way of quantifying the orthogonality of the experiments?
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5.
edited May 2018

Hi Daniel , intriguing ..a guess of a very beginner on applied category.. perhaps you are looking for a functor that maps of life/earth category to life/Xsystem category, then, what structure would be preserved? Possible it is embeeded on your intial definition that allow to define between life, no life on the earth context and it points out to the optimal delimitation of the required subset of observations using the already known examples. ..maybe some redundancy between subsets of observations would be framed by natural transformations ..I'm also wondering if any of this makes sense...just ideas for discussion .. best

Comment Source:Hi Daniel , intriguing ..a guess of a very beginner on applied category.. perhaps you are looking for a functor that maps of life/earth category to life/Xsystem category, then, what structure would be preserved? Possible it is embeeded on your intial definition that allow to define between life, no life on the earth context and it points out to the optimal delimitation of the required subset of observations using the already known examples. ..maybe some redundancy between subsets of observations would be framed by natural transformations ..I'm also wondering if any of this makes sense...just ideas for discussion .. best