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Saturn’s Strange Hexagon
- charonn0 14y agoMakes one wonder whether nature is defined by mathematics, or is mathematics defined by nature?
- JanezStupar 14y agoMathematics is an internally consistent model. Nature is an internally consistent system. We do not understand how nature works (precise factors and their values), but we understand how mathematics works, since we designed it for a sole purpose of mimicking and modeling the laws of nature. But know that mathematics (modeling in the broadest sense) only makes sense within its set of axioms and that there are many possible kinds of mathematics out there.
- charonn0 14y agoMath is the ideal tool for understanding how nature works. We see math everywhere in nature, like this hexagram. In principle, we can describe exactly how the hexagram got to be there, through math. But we don't understand why. Can we know whether math yields to nature, or nature yields to math? Does the question even follow?
- JanezStupar 14y agoEh, no what we see in nature are laws of nature in action. And we cannot explain the hexagram exactly because we do not have the formula that produced that pattern. What our models do is to give us an vague idea of what is happening. There are barely any perfect geometric shapes in the nature, at least at the macro level. Strictly speaking, math has to yield to the laws of nature as it does not exist outside the laws of nature (as mathematics is in our minds). But that is kind of sideways thinking, as of all the concepts and ideas that are achievable through mathematics we are mostly interested in those that fit to the world around us and we discard the others. That is the reason why so many people get this "Oh my god it is all connected!" feeling. It is precisely so, because we are mostly interested in the aspects that fit the world we see around us and we selectively discard the aspects that do not fit. In a sense we are writing a story we want to hear.
- charonn0 14y agoBut if the math we have is accurate because we have distilled it from the inaccurate, the question remains why is it accurate?
- JanezStupar 14y agoAll the math is accurate, we just distilled the parts we like from the parts we don't like. Regarding accuracy let me try again, it is accurate because it is internally consistent. However notion of two apples being 'same' (e.g. completely interchangeable, satisfying the identity) is silly in absolute terms since laws of nature are much more complex.
- charonn0 14y agoit is accurate because it is internally consistent Internal consistency is necessary for accuracy but not sufficient.
- wfn 14y ago> Strictly speaking, math has to yield to the laws of nature as it does not exist outside the laws of nature (as mathematics is in our minds) There are (within academia) alternative views to this one, e.g. Max Tegmark's "Mathematical Universe hypothesis": - http://arxiv.org/abs/gr-qc/9704009 http://arxiv.org/abs/gr-qc/9704009 - http://arxiv.org/abs/0704.0646 http://arxiv.org/abs/0704.0646 - wiki: http://en.wikipedia.org/wiki/Mathematical_universe_hypothesis http://en.wikipedia.org/wiki/Mathematical_universe_hypothesi... The basic idea being, all internally consistent (viz., mathematical) structures exist (whatever the notion pertains to), and those containing 'self-aware substructures' are perceived as physical realities by virtue of those SASes being embedded within a particular given consistent structure (and hence having a from-within vantage point). Sounds fishy, but it's a hypothesis alright, and there have been (AFAIK) some attempts to provide falsifiability conditions (thus making it a testable scientific hypothesis), but one would first have to address the problem of proper operationalization, i.e. defining the damn concepts at hand; it's probably too all-over-the-place for now - but nevertheless interesting and (heh) internally consistent. Also see (for those interested), e.g. http://plato.stanford.edu/entries/computation-physicalsystems/ http://plato.stanford.edu/entries/computation-physicalsystem... (nice overview of related problem spaces)
- hartror 14y agoA wonderful exploration of this idea as it relates to plants by Vi Hart. http://www.youtube.com/watch?v=ahXIMUkSXX0 http://www.youtube.com/watch?v=ahXIMUkSXX0
- ehsanu1 14y agoNeither. Nature is described by mathematics, and conversely, nature is a kind of manifestation of certain mathematical ideas.
- yk 14y agoI have a tendency to think, that here we need a rather precise meaning of math. On one hand, I tend to view mathematics (and logic) as a special facility of our brains, which evolved to make sense of the surrounding world. For example, we essentially call geometries flat, which look like our local geometry. On the other hand, a intelligent entity which evolved in a curved spacetime, would have a brain to make sense of a curved spacetime and therefore would use a curved space as basis for its mathematics (in a similar fashion as we use |R^n as the standard example of a multidimensional space). But we can proof theorems about curved space (and this entity would be able to recognize theorems about Euclidian space as true. [1]) So to answer your question, mathematics [2] the craft, is very much shaped by nature. However there are apparently fundamental rules of the universe, which we would also call mathematics. [1] This sentence needs a qualifier, which should express that I am certain, to the extent that humans are a general intelligence. [2] Greek, something like 'the subject of study'
- JanezStupar 14y agoThinking about this storm reminded me about how Allen wrench holes are drilled: http://www.youtube.com/watch?v=tg0q2kgIVxo http://www.youtube.com/watch?v=tg0q2kgIVxo
- aptwebapps 14y agoThat's pretty neat, although I couldn't figure it out from that video. This one explains it in detail: http://www.youtube.com/watch?v=gUEcagEmmZo http://www.youtube.com/watch?v=gUEcagEmmZo
- mbq 14y agoThis is not very surprising because such patterns do emerge in various fluid dynamics experiments; especially rotating bucket (like http://magazine.concordia.ca/2008/fall/features/homer.shtml http://magazine.concordia.ca/2008/fall/features/homer.shtml) or hydraulic jump (like http://www.evo.ds.mpg.de/erik/?page=research http://www.evo.ds.mpg.de/erik/?page=research).
- stewie2 14y agointeresting!
- andrewflnr 14y agoRe the first link, it said that hexagonal shapes are unstable. Does that mean the rotational speed of Saturn has to be in a small range, or does it stabilize on larger scales?
- INTPenis 14y agoLayman's opinion but on such large scales unstable might be relative. It could be unstable for longer than the roman empire has existed.
- andrewflnr 14y agoIn principle, but that's not really what I meant. I'm wondering how unlikely it is for Saturn to have a rotational speed that makes the hexagon possible.
- dave1 14y agojust a random thought on a spiritual bent of mind http://jayasreesaranathan.blogspot.in/2010/07/saturns-polar-design-resembles-yantra.html http://jayasreesaranathan.blogspot.in/2010/07/saturns-polar-...
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- FoeNyx 14y agoReminded me of this comic : http://www.smbc-comics.com/index.php?db=comics&id=1930#comic http://www.smbc-comics.com/index.php?db=comics&id=1930#c...