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Awful mispelling

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edited Jun 21, 2021 at 6:10

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I have to admit that power-laws (in general) used to be my stick,shtick so I am happy to shed some light on their general importance in physics which obviously also hold for astronomy.

The main idea of a power law is nicely written in Wikipedia, but the essential part is the I highlighted in the following quote:

[A Powerlaw is] a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities

The (mathematically) nice part is exactly this, that over a really large range of the x-values, the y-values follow the same dependency. Usually, "really large range" means values spreading over 3 to even 10 powers of ten.

When fitting power laws in practice, there are effects on the sides of the scale, meaning for small and large $x$-values, where usually attributed to "finite size effects".

Further reading

There is the research flavor Self-organized criticality (SOC) which "is considered to be one of the mechanisms by which complexity arises in nature". One of the founding fathers (and mothers) was the late Per Bak. His book How Nature Works is accessible for laypersons and IMHO a good read.

I have to admit that power-laws (in general) used to be my stick, so I am happy to shed some light on their general importance in physics which obviously also hold for astronomy.

The main idea of a power law is nicely written in Wikipedia, but the essential part is the I highlighted in the following quote:

[A Powerlaw is] a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities

The (mathematically) nice part is exactly this, that over a really large range of the x-values, the y-values follow the same dependency. Usually, "really large range" means values spreading over 3 to even 10 powers of ten.

When fitting power laws in practice, there are effects on the sides of the scale, meaning for small and large $x$-values, where usually attributed to "finite size effects".

Further reading

There is the research flavor Self-organized criticality (SOC) which "is considered to be one of the mechanisms by which complexity arises in nature". One of the founding fathers (and mothers) was the late Per Bak. His book How Nature Works is accessible for laypersons and IMHO a good read.

I have to admit that power-laws (in general) used to be my shtick so I am happy to shed some light on their general importance in physics which obviously also hold for astronomy.

The main idea of a power law is nicely written in Wikipedia, but the essential part is the I highlighted in the following quote:

[A Powerlaw is] a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities

The (mathematically) nice part is exactly this, that over a really large range of the x-values, the y-values follow the same dependency. Usually, "really large range" means values spreading over 3 to even 10 powers of ten.

When fitting power laws in practice, there are effects on the sides of the scale, meaning for small and large $x$-values, where usually attributed to "finite size effects".

Further reading

There is the research flavor Self-organized criticality (SOC) which "is considered to be one of the mechanisms by which complexity arises in nature". One of the founding fathers (and mothers) was the late Per Bak. His book How Nature Works is accessible for laypersons and IMHO a good read.

Shortening.

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edited Jun 20, 2021 at 16:26

5.7k
2
19
66

I have to admit that power-laws (in general) used to be my stick, so I am happy to shed some light on their general importance in physics which obviously also hold for astronomy.

The main idea of a power law is nicely written in Wikipedia, but the essential part is the I highlighted in the following quote:

[A Powerlaw is] a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities

The (mathematically) nice part is exactly this, that over a really large range of the x-values, the y-values follow the same dependency. Usually, "really large range" means values spreading over 3 to even 10 powers of ten.

When fitting power laws in practice, there are effects on the sides of the scale, meaning for small and large $x$-values, where usually attributed to "finite size effects", but I spare you the details (for now). Looking forward to your comments...

Further reading

There is the research flavor Self-organized criticality (SOC) which "is considered to be one of the mechanisms by which complexity arises in nature". One of the founding fathers (and mothers) was the late Per Bak. His book How Nature Works is accessible for laypersons and IMHO a good read.

I have to admit that power-laws (in general) used to be my stick, so I am happy to shed some light on their general importance in physics which obviously also hold for astronomy.

The main idea of a power law is nicely written in Wikipedia, but the essential part is the I highlighted in the following quote:

[A Powerlaw is] a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities

The (mathematically) nice part is exactly this, that over a really large range of the x-values, the y-values follow the same dependency. Usually, "really large range" means values spreading over 3 to even 10 powers of ten.

When fitting power laws in practice, there are effects on the sides of the scale, meaning for small and large $x$-values, where usually attributed to "finite size effects", but I spare you the details (for now). Looking forward to your comments...

Further reading

There is the research flavor Self-organized criticality (SOC) which "is considered to be one of the mechanisms by which complexity arises in nature". One of the founding fathers (and mothers) was the late Per Bak. His book How Nature Works is accessible for laypersons and IMHO a good read.

I have to admit that power-laws (in general) used to be my stick, so I am happy to shed some light on their general importance in physics which obviously also hold for astronomy.

The main idea of a power law is nicely written in Wikipedia, but the essential part is the I highlighted in the following quote:

[A Powerlaw is] a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities

The (mathematically) nice part is exactly this, that over a really large range of the x-values, the y-values follow the same dependency. Usually, "really large range" means values spreading over 3 to even 10 powers of ten.

When fitting power laws in practice, there are effects on the sides of the scale, meaning for small and large $x$-values, where usually attributed to "finite size effects".

Further reading

There is the research flavor Self-organized criticality (SOC) which "is considered to be one of the mechanisms by which complexity arises in nature". One of the founding fathers (and mothers) was the late Per Bak. His book How Nature Works is accessible for laypersons and IMHO a good read.

Small changes

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edited Jun 18, 2021 at 8:38

5.7k
2
19
66

I have to admit that power-laws (in general) used to be my stick, so I am happy to shed some light on their general importance in physics which obviously also hold for astronomy.

The main idea of a power law is nicely written in Wikipedia, but the importantessential part is the oneI highlighted in the following quote:

[A Powerlaw is] a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities

The (mathematically) nice part is exactly this, that over a really large range of the x-values, the y-values follow the same dependency. Usually, "really large range" means values spreading over 3 to even 10 powers of ten.

When fitting power laws in practice, there are effects on the sides of the scale, meaning for small and large $x$-values, where usually attributed to "finite size effects", but I spare you the details (interestingfor now) details. Looking forward to your comments...

Further reading

There is the research flavor Self-organized criticality (SOC) which "is considered to be one of the mechanisms by which complexity arises in nature". One of the founding fathers (and mothers) was the late Per Bak. His book How Nature Works is accessible for laypersons and IMHO a good read.

I have to admit that power-laws (in general) used to be my stick, so I am happy to shed some light on their general importance which obviously also hold for astronomy.

The main idea of a power law is nicely written in Wikipedia, but the important part is the one highlighted in the following quote:

a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities

The (mathematically) nice part is exactly this, that over a really large range of the x-values, the y-values follow the same dependency. Usually, "really large range" means values spreading over 3 to even 10 powers of ten.

When fitting power laws in practice, there are effects on the sides of the scale, meaning for small and large $x$-values, where usually attributed to "finite size effects", but I spare you the (interesting) details.

Further reading

There is the research flavor Self-organized criticality (SOC) which "is considered to be one of the mechanisms by which complexity arises in nature". One of the founding fathers (and mothers) was the late Per Bak. His book How Nature Works is accessible for laypersons and IMHO a good read.

I have to admit that power-laws (in general) used to be my stick, so I am happy to shed some light on their general importance in physics which obviously also hold for astronomy.

The main idea of a power law is nicely written in Wikipedia, but the essential part is the I highlighted in the following quote:

[A Powerlaw is] a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities

The (mathematically) nice part is exactly this, that over a really large range of the x-values, the y-values follow the same dependency. Usually, "really large range" means values spreading over 3 to even 10 powers of ten.

When fitting power laws in practice, there are effects on the sides of the scale, meaning for small and large $x$-values, where usually attributed to "finite size effects", but I spare you the details (for now). Looking forward to your comments...

Further reading

There is the research flavor Self-organized criticality (SOC) which "is considered to be one of the mechanisms by which complexity arises in nature". One of the founding fathers (and mothers) was the late Per Bak. His book How Nature Works is accessible for laypersons and IMHO a good read.

Typo

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edited Jun 18, 2021 at 7:57

5.7k
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19
66

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created Jun 18, 2021 at 7:38

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