Aliens and UT Encryption

[Joseph Paul]

Originally Posted by whswhs

That is a widespread theory, or philosophical view, but I'm not convinced that it's sound. The purely syntactic treatment of mathematics has its uses as a way of checking that proofs are actually valid; but treating that as "real" mathematics, with the application of mathematics to the physical world through counting and measuring as an unimportant annex, seems to me to get things backward. It's rather as if one were to suppose that finance was about drawing up balance sheets and income statements, and the actual making of business decisions were subsidiary to "pure accounting."

Cognitive research seems to show that human beings are actually not very good at purely syntactic manipulations. On the other hand, we're much better at navigating and manipulating the physical world, which computers have trouble doing. That we nonetheless have syntactic capabilities at all suggests either that syntax reflects something about the real world, or that it reflects functional requirements of processing information about the real world. Of course we can go on to play with syntax for its own sake, and there are people who do; but that isn't why we have it in the first place.

SO what would a species that was good at syntactic manipulation be like?

[whswhs]

Originally Posted by Joseph Paul

SO what would a species that was good at syntactic manipulation be like?

Well, computers are better at syntactic manipulation than humans are, by a long way. If you can imagine a scenario where computers are capable of reproduction, they might be considered as "species."

You could also envision people on the autistic spectrum trying to survive and maintain a functioning society on their own.

[Ulzgoroth]

Originally Posted by whswhs

That is a widespread theory, or philosophical view, but I'm not convinced that it's sound. The purely syntactic treatment of mathematics has its uses as a way of checking that proofs are actually valid; but treating that as "real" mathematics, with the application of mathematics to the physical world through counting and measuring as an unimportant annex, seems to me to get things backward. It's rather as if one were to suppose that finance was about drawing up balance sheets and income statements, and the actual making of business decisions were subsidiary to "pure accounting."

Cognitive research seems to show that human beings are actually not very good at purely syntactic manipulations. On the other hand, we're much better at navigating and manipulating the physical world, which computers have trouble doing. That we nonetheless have syntactic capabilities at all suggests either that syntax reflects something about the real world, or that it reflects functional requirements of processing information about the real world. Of course we can go on to play with syntax for its own sake, and there are people who do; but that isn't why we have it in the first place.

It is demonstrably sound in that the formal logic construction has been done.

It may or may not be an accurate description of how people relate to mathematics, but that's not what it claimed to be.

Trying to read in a value judgement that applied math is inferior is simply wrong.

[Anders]

Interestingly, humans become dramatically better at solving logical problems if the problem involves discovering if someone has cheated* - gotten a benefit without paying the price or meeting the requirements. I don't know whether this applies to computers, but I doubt it. So syntactic manipulation has real-world benefits, and we are better at solving these problems when these consequences are actualized. This suggests strongly that the ability of syntactic manipulation is something which evolved to solve problems, not just a general byproduct of heightened intelligence.

* if you have two problems, A and B, which both are formally identical - you've only switched the labels - but problem A just involves checking requirements, and problem B involves checking requirements so that no one has cheated, people are considerably better at solving problem B than they are at solving problem A.

[whswhs]

Originally Posted by Ulzgoroth

It is demonstrably sound in that the formal logic construction has been done.

That's confusing the issue. Yes, you can do the formal logic, and by doing it you can formally verify mathematical results. But most human beings who do mathematical reasoning do not do so by working through the formal logic; for example, a couple of nights ago I worked out Spearman's rho values for a small data set, mostly in my head, and occasionally by punching calculator buttons to get decimals. And that process is perfectly capable of being correct, and of being applied to the physical world and producing meaningful results. Moreover, nearly all the mathematics that most people do, from counting up through calculus, was invented before that formal syntactic approach was developed, and yet has been validated; so you don't need the formal syntax to do correct mathematics. And while I'm not au courant with contemporary mathematics, I have the impression that "mathematical intuition" still plays a role in the discovery of new theorems and proofs, even if they're subsequently checked by providing formal proofs.

So it appears to me that "mathematics" is not primarily an elaborate game of formal logic on uninterpreted symbol strings, but an elaboration on the basic human activities of counting and measuring. And we have the ability to do so because they're "survival traits" for our species, which is the case because the physical universe is countable and measurable. If we lived in a universe to which those operations could not be applied, we would never have had those traits in the first place, and even if we developed the formal syntax, it would not be to numbers or spatial relations or anything of the sort that we would be applying it.

And since we're talking about aliens and alien understanding of mathematics, the fact that aliens would exist in the physical universe, and that if they had mathematics it would have emerged from their mode of survival, can't be irrelevant.

[Anthony]

Applied mathematics is fundamentally a language you can use to describe a problem, in a way that makes that problem convenient to solve. Any mathematical system that solves a given problem necessarily produces the same results, because you're trying to solve the same problem, so in a certain sense they're going to be equivalent.

Note, however, that the same problem can be expressed in many ways, and some of them make the problem more or less convenient to solve. A high tech level in math generally includes better methods. Aliens could certainly have methods of expressing (and solving) specific problems that we don't have, and vice versa.

[Ulzgoroth]

Originally Posted by whswhs

That's confusing the issue. Yes, you can do the formal logic, and by doing it you can formally verify mathematical results. But most human beings who do mathematical reasoning do not do so by working through the formal logic; for example, a couple of nights ago I worked out Spearman's rho values for a small data set, mostly in my head, and occasionally by punching calculator buttons to get decimals. And that process is perfectly capable of being correct, and of being applied to the physical world and producing meaningful results. Moreover, nearly all the mathematics that most people do, from counting up through calculus, was invented before that formal syntactic approach was developed, and yet has been validated; so you don't need the formal syntax to do correct mathematics. And while I'm not au courant with contemporary mathematics, I have the impression that "mathematical intuition" still plays a role in the discovery of new theorems and proofs, even if they're subsequently checked by providing formal proofs.

So it appears to me that "mathematics" is not primarily an elaborate game of formal logic on uninterpreted symbol strings, but an elaboration on the basic human activities of counting and measuring. And we have the ability to do so because they're "survival traits" for our species, which is the case because the physical universe is countable and measurable. If we lived in a universe to which those operations could not be applied, we would never have had those traits in the first place, and even if we developed the formal syntax, it would not be to numbers or spatial relations or anything of the sort that we would be applying it.

And since we're talking about aliens and alien understanding of mathematics, the fact that aliens would exist in the physical universe, and that if they had mathematics it would have emerged from their mode of survival, can't be irrelevant.

I submit that in certain important respects it can be irrelevant.

Yes, humans probably hardly ever do mathematics purely by semantic manipulation with no thinking outside that. (Although their intuition may be trained into contexts that don't have meaningful contact with observed reality, depending on what math they're doing.) But it can be done and understood that way.

Depending on your position on Starfish Aliens, human mathematicians might or might not have any chance of grasping the way alien mathematical intuition works. Sharing a physical reality may not guarantee very much, according to some. But if they can force xenomath into the uncaring filter of formal logic, they don't need to understand the minds behind it at all.

Of course, the xenolinguistics to extract any sort of usable content from alien messages...that's a whole other thing.