4 ms·

Mathematics: The only true universal language

17 points by muon 18y ago

tokenadult 18y ago
"An interesting possibility, which I think should not be dismissed, is that a "true" fundamental theory exists, but that it may just be too hard for human brains to grasp. A fish may be barely aware of the medium in which it lives and swims; certainly it has no intellectual powers to comprehend that water consists of interlinked atoms of hydrogen and oxygen. The microstructure of empty space could, likewise, be far too complex for unaided human brains to grasp." That's a distinct possibility. Further mathematical research might still allow considerable refinement in describing what a correct fundamental theory does NOT imply.
- jbert 18y ago
  That's the nice thing about the "shoulders of giants" though. By and large, scientific progress is cumulative. The cutting edge of quantum theory a few decades back is now undergraduate-level. Yes, there are probably theoretical limits to human understanding, but the analogy with fish breaks down because fish don't (as far as we know) have cultural accumulation of knowledge.
  - nazgulnarsil 18y ago
    accumulation of knowledge is different from a the possibility of a fundamental difference in the way reality works and the way our evolved brain works. see "wave/particle duality" for the simplest example of something that might be totally obvious to another type of intelligence.
- newt0311 18y ago
  I don't know... I am with Herbert here: "The universe is always one step beyond logic." We may (and in my opinion, definitely will) continue to refine theories of physics in the future but I don't think we will ever achieve perfection. There will always be some minuscule break that will give rise to a new theory. [UPDATE]: Of course, I have no logical means of proving that except inductive reasoning from history (we haven't come up with a perfect theory yet but we have continued to improve what we have) just as there is no deductive means to prove that a fundamental theory (however complex) does exist.
- gcheong 18y ago
  It would be a cruel joke played upon us if we were to come to the end only to find out that we're the ones riding the cosmic short bus.
IsaacSchlueter 18y ago
Interesting article, but lines like this always make me groan: The aliens would, like us, be astonished by the patterns in our shared cosmos and by the effectiveness of mathematics in describing those patterns. Why should we assume that any intelligent life form should have a psychology that is human-like in any way whatsoever? You can make the case for mathematical sophistication; but astonishment? I mean, if there are conceptually sophisticated aliens out there (which is a huge "if" that we have no evidence for or against), who's to say that they even have such a state as "astonished"? Maybe they're sitting on their planet right now, and some uninformed and unimaginative journalist in their species is writing in their language: The aliens would, like us, take the patterns in our shared cosmos completely for granted, and find it utterly unremarkable that mathematics are effective in describing those patterns. Just say NO to humans in funny suits!
jimfl 18y ago
Mathematics is a human language. It reflects the human mind, as well as the human condition, and has already been shown to be less than universal (i.e. that there are true statements which cannot be arrived at via method of proof given axioms). Human mathematical intercourse is generally couched in cliche (since most humans aren't particularly fluent), and is shot through with concepts that other advanced civilizations are likely to find violently stupid (e.g. infinity).
- jimfl 18y ago
  Also, Humans and Chimpanzees are very similar, and yet we can't use the universal language of mathematics to communicate with them. Dolphins and Octopus are akin to us in intelligence; no spikka math. Alien lifeforms are likely to be order of magnitude radically different from us protein self-assembling macromachines, with a different body plan, and different perception mechanisms, to the point where we might not even recognize them as lifeforms. It does not stand to reason that they would be able to make anything of our chirps and whistles.

17 points by muon 18y ago

"An interesting possibility, which I think should not be dismissed, is that a "true" fundamental theory exists, but that it may just be too hard for human brains to grasp. A fish may be barely aware of the medium in which it lives and swims; certainly it has no intellectual powers to comprehend that water consists of interlinked atoms of hydrogen and oxygen. The microstructure of empty space could, likewise, be far too complex for unaided human brains to grasp." That's a distinct possibility. Further mathematical research might still allow considerable refinement in describing what a correct fundamental theory does NOT imply.

jbert 18y ago
That's the nice thing about the "shoulders of giants" though. By and large, scientific progress is cumulative. The cutting edge of quantum theory a few decades back is now undergraduate-level. Yes, there are probably theoretical limits to human understanding, but the analogy with fish breaks down because fish don't (as far as we know) have cultural accumulation of knowledge.
- nazgulnarsil 18y ago
  accumulation of knowledge is different from a the possibility of a fundamental difference in the way reality works and the way our evolved brain works. see "wave/particle duality" for the simplest example of something that might be totally obvious to another type of intelligence.
newt0311 18y ago
I don't know... I am with Herbert here: "The universe is always one step beyond logic." We may (and in my opinion, definitely will) continue to refine theories of physics in the future but I don't think we will ever achieve perfection. There will always be some minuscule break that will give rise to a new theory. [UPDATE]: Of course, I have no logical means of proving that except inductive reasoning from history (we haven't come up with a perfect theory yet but we have continued to improve what we have) just as there is no deductive means to prove that a fundamental theory (however complex) does exist.
gcheong 18y ago
It would be a cruel joke played upon us if we were to come to the end only to find out that we're the ones riding the cosmic short bus.

IsaacSchlueter 18y ago

Interesting article, but lines like this always make me groan: The aliens would, like us, be astonished by the patterns in our shared cosmos and by the effectiveness of mathematics in describing those patterns. Why should we assume that any intelligent life form should have a psychology that is human-like in any way whatsoever? You can make the case for mathematical sophistication; but astonishment? I mean, if there are conceptually sophisticated aliens out there (which is a huge "if" that we have no evidence for or against), who's to say that they even have such a state as "astonished"? Maybe they're sitting on their planet right now, and some uninformed and unimaginative journalist in their species is writing in their language: The aliens would, like us, take the patterns in our shared cosmos completely for granted, and find it utterly unremarkable that mathematics are effective in describing those patterns. Just say NO to humans in funny suits!

jimfl 18y ago

Mathematics is a human language. It reflects the human mind, as well as the human condition, and has already been shown to be less than universal (i.e. that there are true statements which cannot be arrived at via method of proof given axioms). Human mathematical intercourse is generally couched in cliche (since most humans aren't particularly fluent), and is shot through with concepts that other advanced civilizations are likely to find violently stupid (e.g. infinity).

jimfl 18y ago
Also, Humans and Chimpanzees are very similar, and yet we can't use the universal language of mathematics to communicate with them. Dolphins and Octopus are akin to us in intelligence; no spikka math. Alien lifeforms are likely to be order of magnitude radically different from us protein self-assembling macromachines, with a different body plan, and different perception mechanisms, to the point where we might not even recognize them as lifeforms. It does not stand to reason that they would be able to make anything of our chirps and whistles.