Recent content by Couchyam

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    Does randomness really exist?

    No, but to me it suggests that it wouldn't be unreasonable to act on the basis that those phenomena are fundamentally deterministic at some level of awareness (unless doing so made one miserable.)
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    Does randomness really exist?

    I guess I'm inclined to assume determinism is more fundamental than randomness because almost every fundamental physical experiment to date has been consistent with the postulate of unitarity in quantum mechanics, and I interpret unitarity (i.e. constant, vanishing von Neumann entropy) as...
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    Is there a better name for "citizen science"?

    It just occurred to me that one potentially crucial distinction between Citizen Science and Amateur Science is that the word 'citizen' suggests a kind of civic connection that might not always exist in the amateur setting, and which could be understood in various ways (for example, that the...
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    Is there a better name for "citizen science"?

    The term Citizen Science has, at least according to wikipedia, existed for at least several decades. Is it time to come up with a hip new 21st century moniker? Or are we happy with "Citizen Science" as it is?
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    Does randomness really exist?

    It's been a while since I've posted here, but I like this general topic and so I couldn't resist getting involved. It sounds as though there are two schools of thought expressed in this thread, one of which centers on whether randomness exists in a fundamental sense, and the other on its...
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    B Coriolis problem - Point mass movement upon release from Earth

    This sounds a bit like a homework question, but here are a few hints: (i) What quantity (or quantities) are conserved? (ii) From a corotating reference frame, what fictitious force determines the magnitude of the longitudinal angular acceleration of the particle? (iii) At a more advanced level...
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    I Best models to describe molecules

    Sean Carroll has given several popular talks about the meaning of quantum mechanics that I would recommend. Part of the OP's confusion might be that the wave function is defined empirically to describe quantum statistics, and, strictly speaking, does not describe the empirical behavior of...
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    Misc. Ideas for DIY projects

    A set of balance scales (sometimes called 'scales of justice') would be extremely useful.
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    Challenge Math Experiment: Let's Prove Something!

    Also, not that this should be necessary, but I also acknowledge that the extent of my mathematical ability is quite meager compared to a large number of readers and members of PF.
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    Engineering Entry level Renewable energy engineering positions?

    There are some pretty cool greenhouse design companies out there now, with what seems to be a good variety of size and composition, ranging from smaller innovation-driven startups to larger and more established groups (though the latter are mainly to be found in Nordic countries.)
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    What are the benefits of STEM Learning Education for kids?

    'STEM education' can mean many things. Ensuring that children are provided the option to become scientists or mathematicians or engineers if they so wish is immeasurably valuable, both for the children and for the legitimacy of the whole enterprise of discovery.
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    Challenge Math Experiment: Let's Prove Something!

    36, 37 Apologies for the more-than-somewhat incomplete post. The idea is to construct ##f_{\frac{1}{2}}(x)## from a given ##f(x)## by solving the 'differential equation' ## f_\frac{1}{2}'(f_\frac{1}{2}(x))f_\frac{1}{2}'(x)=f'(x)## on ##[0,1]##, or whatever the existence interval turns out to...
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    Challenge Math Experiment: Let's Prove Something!

    (11, 12, 16, 17, 24, 25) Uniqueness of 'square roots' The functional ##\mathcal{F}[g](x)=g(1-x)## exchanges the spaces of increasing and decreasing bijections and is its own inverse, and so ##G## consists of two topologically equivalent connected components, say ##G=G_+\cup G_-## (a path from...
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    Challenge Math Experiment: Let's Prove Something!

    (11, 12, 16, 21) Prop: The function ##d(f,g) \equiv \frac{1}{2}(\|x-f^{-1}\circ g(x)\|_2+\|x-g^{-1}\circ f(x)\|_2)## is invariant under left multiplication. Proof: ##d(af,ag) = \frac{1}{2}(\|x-f^{-1}\circ (a^{-1}\circ a)\circ g(x)\|_2+\|x-g^{-1}\circ (a^{-1}\circ a)\circ f(x)\|_2)=d(f,g).##...
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    Challenge Math Experiment: Let's Prove Something!

    I might try using the reflection property of inverse functions, and the fact that ##x<1\Rightarrow x^2<x## (so the ##L^2## norm is bounded by the ##L^1## norm in this case.) It could be there exists a more natural metric, however (one that is invariant with respect to the Lie group multiplication.)
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