mdl4: Image of surface acoustic waves on a crystal of tellurium oxide with (001) surface orientation, coated with a thin gold film of thickness 40 nm
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mdl4:

Image of surface acoustic waves on a crystal of tellurium oxide with (001) surface orientation, coated with a thin gold film of thickness 40 nm

Source: zhk

(image via image09.webshots.com) I ran across a tumblr not long ago that made a joking reference to a standard deviation equal to zero.  That’s an interesting concept when you think about it.  One of the key assumptions in statistics is that all measured data follows some form of distribution which has an average value as well as a variance about this average.  In Gaussian distributions (which are probably the most common statistical distribution), the standard deviation is a measurement of the variance around the average value of a measurement.   I asked myself, is a standard deviation ever equal to zero?   In mathematical terms, if there is no variance around the average, your distribution is now the Dirac Delta Function: an infinitesimally thin spike with a finite area underneath, a singularity.  Nature abhors singularities.  Depending on the school of thought, they’re considered outright impossible or maybe only possible at the very moment of our genesis, when “t” was equal to zero.   But why should nature abhor singularities?   To answer that question, we have to turn to one of the more celebrated physicists of the past century.  Werner Heisenberg stated in his uncertainty principle that at the smallest of scales (smaller than an atom, even) there is a fundamental limit to how precisely you can measure a particle’s velocity or position.  So, if you know the particle’s position perfectly, you don’t know anything about how fast it’s moving and vice versa.   At first, this would seem like an esoteric concept, but it’s responsible for everything about how the physical world around us behaves.  Subatomic particles like electrons are never in one place at any given point in time, nor do they have one specific speed.  Instead, they behave like a “cloud”.  They are both everywhere and nowhere at once with some probability. If electrons didn’t have a cloud of uncertainty associated with them, if their standard deviation were equal to zero, they couldn’t be shared between atoms for bonding and every chemical reaction in the universe wouldn’t work.  Electricity as we understood it wouldn’t work either, because the wave nature of the electron is critical in the way metals and semiconductors carry electricity.  No electron cloud means that two solid objects could pass right through one another and atoms themselves would fly apart or collapse in on themselves due to coulombic repulsion. Can a standard deviation be equal to zero?  Maybe in a formless and nonsensical universe, but not in ours.
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(image via image09.webshots.com)

I ran across a tumblr not long ago that made a joking reference to a standard deviation equal to zero.  That’s an interesting concept when you think about it.  One of the key assumptions in statistics is that all measured data follows some form of distribution which has an average value as well as a variance about this average.  In Gaussian distributions (which are probably the most common statistical distribution), the standard deviation is a measurement of the variance around the average value of a measurement.  

I asked myself, is a standard deviation ever equal to zero?  

In mathematical terms, if there is no variance around the average, your distribution is now the Dirac Delta Function: an infinitesimally thin spike with a finite area underneath, a singularity.  Nature abhors singularities.  Depending on the school of thought, they’re considered outright impossible or maybe only possible at the very moment of our genesis, when “t” was equal to zero.  

But why should nature abhor singularities?  

To answer that question, we have to turn to one of the more celebrated physicists of the past century.  Werner Heisenberg stated in his uncertainty principle that at the smallest of scales (smaller than an atom, even) there is a fundamental limit to how precisely you can measure a particle’s velocity or position.  So, if you know the particle’s position perfectly, you don’t know anything about how fast it’s moving and vice versa.  

At first, this would seem like an esoteric concept, but it’s responsible for everything about how the physical world around us behaves.  Subatomic particles like electrons are never in one place at any given point in time, nor do they have one specific speed.  Instead, they behave like a “cloud”.  They are both everywhere and nowhere at once with some probability.

If electrons didn’t have a cloud of uncertainty associated with them, if their standard deviation were equal to zero, they couldn’t be shared between atoms for bonding and every chemical reaction in the universe wouldn’t work.  Electricity as we understood it wouldn’t work either, because the wave nature of the electron is critical in the way metals and semiconductors carry electricity.  No electron cloud means that two solid objects could pass right through one another and atoms themselves would fly apart or collapse in on themselves due to coulombic repulsion.

Can a standard deviation be equal to zero?  Maybe in a formless and nonsensical universe, but not in ours.

Source: image09.webshots.com

smoot: un: proofmathisbeautiful: freshphotons: Comparison of a Lévy flight with a Brownian random walk. Lévy flights are a theoretical construct that has attracted wide interdisciplinary interest. Empirical evidence shows that the principle applies to the foraging of marine predators. Via. What seems to me to be a common thread in the way our world functions is that things tend to scale up and that you see the same or very similar mathematics at different scales.  Some people call this self-assembly or self-scaling, and our universe appears to operate on this principle to some degree.  This is pretty cool.
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smoot:

un:

proofmathisbeautiful:

freshphotons:

Comparison of a Lévy flight with a Brownian random walk. Lévy flights are a theoretical construct that has attracted wide interdisciplinary interest. Empirical evidence shows that the principle applies to the foraging of marine predators. Via.

What seems to me to be a common thread in the way our world functions is that things tend to scale up and that you see the same or very similar mathematics at different scales.  Some people call this self-assembly or self-scaling, and our universe appears to operate on this principle to some degree.  This is pretty cool.

Source: freshphotons