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It might be that to some alien intelligent life form, or for that matter dolphins and cetaceans, the idea of a god is almost incomprehensible. Even with extensive explanation on our parts they might find the idea to be utterly bizarre and impossible to understand how such can be believed. So yeah, maybe they can contribute with new perspectives. We likely have a diverse enough flora of MOL to keep almost everyone happy and busy. Few suicides because of lack of MOL, say. But as far as being a standing problem, it is resolved.
Even the huge problem of increasing population looks set to resolve itself. Which is good because if it continues the other resolutions will not mean anything. It appears that even bacteria actively disagree with this statement.
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One need look no further than the adaptive divergence in experimental populations of pseudomonas fluorescens to see that this statement is purely a rhetorical regurgitation that looks good, sounds good, but is inaccurate. And if that is not it then there is no meaning to life. You just are because you are. Sit back drink a beer and enjoy it. We can barely communicate with other species on our own planet and struggle with language barriers within our own. I think it depends upon whether mathematics is universal.
If you talk to most mathematicians they will say that mathematics is some sort of universal objective truth.
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The most universal system of information encryption is the Fischer-Griess group, also known as the monster group. This is a vast algebraic system, but its automorphism group is the Leech lattice or Matheiu group in 24 dimensions. This exists in a Lorentzian structure that acts on the monster group in 26 dimensions, which connects to string theory and so forth. This is a huge information encryption system, which I think is involved with how black holes encrypt quantum information.
So if I were sending information into space with the idea of providing its recipient a key I would use the Leech Lattice. Of course we would not start with this, where a signal with numerical patterns would be sent first, then primes, then … , which might then lead to the Hurwitz quaternions or icosian quaternions in patters of numerical ratios, which then leads to the master code. This information cipher would be used to encrypt other forms of information, such as maybe the spectrum of atoms, the encryption of other mathematics which would give explicit numerical instructions for assigning bit addresses and so forth.
Of course we have to assume that physics is the same as well, which I think is fairly safe. So ETs around the universe are likely to send and receive electromagnetic waves. Neutrino communications are a distant possibility, but given they interact so weakly it is hard to know how they could really be practically used. If the communications are kept largely on the mathematical level the different psychology of some ET relative to us would not be very important. On the other hand it is not likely to result in the sort of diplomatic communications we experience with each other.
We will not likely ever have informal conversations with ETs if we ever make contact. But they may very well be wrong, and I, being a mathematician, have reasons to say, that mathematics is like other sciences completely made by humans — invented and not discovered. By making appropriate experiments etc. Now, another question is, whether and to what amount reality, nature, the universe forces us and any aliens to converge on the same or nearly the same kind of mathematics or any science. But, as far as I can tell, this question is far from being answered, and I tend to say, that there is not much convergence.
Then, a problem you mentioned already: diplomatic communication. I would go farther: what native English speakers call social conversation, small talk, etc. This will be really difficult, I think e. I really hope nobody will be angry about me, but — for me — trying to start a conversation between us and aliens by exchanging facts about prime numbers and the like, is naive and will fail. It needs much, much more than this.
If we restrain communication with aliens to the mathematical level, nearly everthing important will get lost, or will never get recovered, respectively.
I know a number of mathematicians, though they are not involved with these foundational issues, such as mathematical logic. The nature of mathematical truth is not entirely understood.
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There are those who favor the idea that mathematics just involves models. Some such as AN Whitehead argued that mathematical truth was at best relative. So in modern times there have been ideas such as intuitionism that places mathematics in the mind of the practitioner and constructivism. It has been found of late that some animals have a numerical sense. Even some birds, such as parrots and crows, are able to count and even add or subtract.
I think this gives at least elementary mathematics some basis beyond just pure mental gymnastics, say along side writing poetry. Mathematical objects do often refer to physical objects, such as numbers referring to the number of cattle head, or Pythagorean theorem used to make land surveys and architecture.
The MUH proposes a map, or indeed isomorphism, between physical reality and mathematics. I am agnostic on this idea. I think though that mathematics would be the best approach to trying to communicate with some ETI. If they are able to fabricate radio receivers it seems plausible they use some form of symbolic system to understand physics that is isomorphic to or related to our mathematics. This discipline is definitely no sub-branch of psychology, or something similar. And I can show everybody how to construct e. I am able to manipulate them using e. Everybody would be able to see it. When we observe mathematicians doing their work, when we study mathematical proofs, and when we study biographies of mathematicians, there is not a single piece of evidence, that, what the mathematicians handle — their objects or concepts —, are not down-to-earth physical objects, invented and constructed by themselves.
You may not be surprised to here, that for me the relation between the physical world and mathematics is not at all mysterious. Nobody should fall victim to mysteries and unfounded fantasy mathematics.
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Real, good mathematics, including all the mathematics used in physics, works without these things. It does have to be realized that while one does write symbols on paper or look at numerical output, without the brain processing this these things are pure gibberish. The number 5 for instance engraved on a rock would in the future after humanity becomes extinct mean nothing.
Mathematical objects of course have symbol representations, and they can in some cases be manipulated in computers where there is a Shannon-Khinchin information entropy process. However, I would not go so far as to say mathematics involves objects which have the same ontology as a proton or a black hole. Max Tegmark does do more down to business physics and cosmology.
He is not only known for the MUH. I actually read his paper on this some years ago. I would not go so far as to say the idea is complete nonsense. The whole thing ultimately hangs on a set of postulates which one can take or leave. The biggest problem is that the whole idea is to my mind not testable. There are four levels of the so called multiverse, or what I prefer to think of as a universe with multiple spacetime configurations.
The first two are fairly reasonable; the bubble nucleation in inflationary cosmology leading to pocket universes, and the other are Dp-brane processes which generate inflationary physics on a D3-brane.
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MWI is a quantum interpretation which is physically ineffective. There is no testable method for determining whether quantum physics conforms to MWI. The MUH is far more hopeless. It is beyond my understanding how we could detect the physics of some universe or space which is configured in Plucker coordinates or some other odd configuration we may have not even thought of.
I used to support MW theory, recently I have stepped back to reconsider. MWT is realistic and parsimonious, using axioms less than other QM theories. It has survived testing however, as it seems relativistic decoherence is very much part of physics but I am not sure when I am writing this how clearly it has been tested. There is btw, seeing the discussion on the basis of mathematics, a good argument by Deutsch supporting the construction nature of mathematics by MW theory and perhaps other QM theories.
The maximal computational resources of physical systems is contained in the observable universe.