Alien Mathematics
troynikov.io
Alien Mathematics
1–10 of 29 posts
Re: Alien Mathematics
#2Nice piece meant for one to pause and think a little bit about limitation of mathematics and our perception of reality. There, however, I would submit that I find the mixture of several limitations too confusing to even allow (in my view) the question the article outlines to be a valid one. First, our perception limitation (that is a multi-level problem, going from personal all the way to entire species). Im not sure at which level the author wants to start and stop. Second, limitations of mathematics explaining physical phenomena as we perceive them and can measure them. Third, mathematical models are not the reality and never have been considered to represent reality as is. They are necessary abstractions for us to have our linear and local time predictability.
I would further submit for a thought that as of right now there is nothing we understand from first principles using mathematical models. This is not a conjecture or speculation, but a fact. See eg. Wheeler's "More is different", ("More is really different" by another author), or R. Laughlin's book Different Universe which with simple logic shows physical laws cannot be build from first principles, because, well, "more is different" (emergent phenomena acquire characteristics not in the original constituents). Lets think about weather, clima, planet formation, galaxy evolution, economics, etc ... It would be foolish to even begin such enterprise...(imho). But, in any case this is issue is not to be closed for discussion and interpretations and learning...that I agree with the author.
Re: Alien Mathematics
#3I think this article was rather weak.
The double pendulum is not "unexplainable" or "inexplicable behavior", in fact is is explained very well in this very article. It just requires an infinite degree of precision if you desire to simulate it numerically with infinitesimal error. It's (an easily explained) limitation of the numerical methods used, not a lack of explanatory power. It does not contradict universality as defined in the article.
In the same way the ratio of a circle's circumference to its diameter is easily explained and understood, even if expressing it in the base-ten numeral system would require infinite digits.
The suggested equivalence between linear/nonlinear phenomena and inside/outside human perception was also tenuous and poorly justified.
Re: Alien Mathematics
#4> there is no equation (that we know of) that would allow us to write down where the pendulum would be at some point in the future, given its current position.
This is a misunderstanding.
The author uses the sine and cosine functions as if they were “functions which give us values” but if you are allowed to assume that (what is sin(1), by the way?), then one might as well define “Pend2(t)” as “the solution to the double pendulum equation”, and be done with it.
Which, by the way, is how one defines the exponential, trigonometric, even n-th roots! Not to say the erf, Bessel, hypergeometric functions etc.
The fact that there is not a “closed solution involving only elementary functions” is irrelevant as long as the equations ones is solving have a unique solution.
Edit: toned down.
Re: Alien Mathematics
#5a bit vague and hand wavey. also I'm baffled how the author didn't use the term "chaos theory" in the text.
Re: Alien Mathematics
#6I think this article was rather weak. The double pendulum is not "unexplainable" or "inexplicable behavior", in fact is is explained very well in this very article. It just requires an infinite degree of precision if you desire to simulate it numerically with infinitesimal error. It's (an easily explained) limitation of the numerical methods used, not a lack of explanatory power. It does not contradict universality a…
I agree, I just skimmed it but the examples they used and their arguments were weak. It reads as if they haven't actually dug deep into the material they are presenting.
When they mentioned not being able to calculate double pendulum, my mind immediately jumped to concepts of computability. For instance, we know that the Halting Problem cannot be solved by a Turing machine. We (or aliens) can introduce an oracle, but that would have it's own equivalent halting problem. These are truths that have been proven.
This follows for any and all theorems. You start with a set of axioms, and then successively arrive at your proof through logical steps. Aliens might come up with new questions, new answers, etc. But that has no bearing on the validity of our mathematics.
Re: Alien Mathematics
#7The article incorrectly describes the equations of kinematics of the double pendulum as describing its dynamics. They do not; describing its dynamics requires taking time into account and considering how its angles and positions change over time.
It also considers the existence of a general theory of nonlinear mathematics. There's a famous quote to the effect that this makes as much sense as the study of non-elephant mammals. And I think the argument that our everyday experience is linear is very weak; our bodies are made of non-Newtonian fluids, fluid friction is nonlinear, everyday physical phenomena like solid bodies coming into contact with one another are wildly nonlinear.
So in a sense I would criticize this article in the same way it criticizes Deutsch's book: it's flawed and weak, but still thought-provoking. Even if we can't predict the double pendulum's position several Lyapunov times in the future with any degree of certainty, are there things we can say about it that haven't yet been said? Is there a way we can look at things (or that some physical system could look at things) that would enable useful cognition?
Re: Alien Mathematics
#8> there is no equation (that we know of) that would allow us to write down where the pendulum would be at some point in the future, given its current position. This is a misunderstanding. The author uses the sine and cosine functions as if they were “functions which give us values” but if you are allowed to assume that (what is sin(1), by the way?), then one might as well define “Pend2(t)” as “the solution to the dou…
You misunderstand sensitive dependence on initial conditions, though admittedly it’s poorly elucidated in the article.
It’s not about closed form solutions. It’s about how neighborhoods on the line are mapped.
Re: Alien Mathematics
#9Part of this feels like nonsense, but it does chime with what I heard Stephen Wolfram talking about the other day: If we take the world to operate as he describes, which I do, then there are many ways to interpret the world, many different basis that could be constructed that paint a coherent picture. In this sense I think that the fire in the sky aspect of this article makes some sense. I just think that looking for these radically different interpretations of reality by postulating different kinds of mathematics, it doesn't work. imho.
Perhaps a better explanation for glowing orbs in the sky is a natural process, self sustaining plasma balls perhaps, or maybe electromagnetic solitons? Maybe even plasma life forms, self sustaining balls of interacting electromagnetic energy feeding off stuff. Crazy thoughts, but even these crazy thoughts are less crazy than things from other interpretations of reality, those things are weirder, think "cosmic horror".
Let's look into weird weather phenomena, then look into alien technology/plasma life forms. Then when all those things are done we might consider beings from another interpretation of reality!
Re: Alien Mathematics
#10Big Brain is told it might not be a universal understander.
Big Brain rejects this idea as shallow and fallacious.