I disagree… the article talks about defining the meter using the pendulum and the second. Other planets would have their own definition of second, but not their own definition of pendulum. Since one meter is prescribed though a pendulum because of the oscillation formula and dependent on the frequency alone (in this case, 2 seconds), no matter what planet you are on, how strong gravity, is or how long a second is, the pendulum describes a relationship between seconds and meters such that if using this method a planet’s scientists would always define their units such that acceleration of gravity was eerily equal to pi^2.
Makes me think of possible lunar scientists unwittingly making their meter 5/6th shorter(edit: english is hard) and then marveling at the same coincidence…
Your comment is much more rage-bait than the article.
Universal isn't a way we describe numbers. You meant to say dimensionless. Pi is dimensionless constant because it describes a relationship between two measurements of a dimensionless unit circle.
Pi is expressed as a pure ratio between two other dependent numbers. Dimensionless values are special because they don't rely on any particular measurement in any particular location, lending to your misconception of "universal" constant.
This article explains how a particular dimensionful constant (g, the strength of gravity on earth's surface) is related to pi.
They are related because the dimensions in question are both derived from dependent properties of our planet. These dependent properties will be found on any other sphere floating in space if they are derived in the same fashion.
It's good to thoroughly or even marginally understand a topic before adopting a dismissive and authoritative argument against it.
> Universal isn't a way we describe numbers. You meant to say dimensionless.
They probably really meant to say “universal”, since dimensionless values are a less interesting category that includes… well, every number. Pi shows up in math without having to parameterize anything, making it universal in a way that even physical constants of our universe aren’t.
On any planet where you want to define a system of units, you can start by defining a fixed time period (maybe use a fraction of the planetary rotation cycle or something), then make a pendulum that swings with that frequency, and derive a unit of distance from its length.
The local value of g will be roughly pi squared pendulum lengths per tick squared, in that system of measurement.
Nope, it's not a coincidence - it's an interesting exploration of the history of the definition of a metre. Read the article.
As it says, at some point there was an attempt to standardise the length of a metre in terms of a pendulum's length; which related it directly to g through Pi.
I disagree… the article talks about defining the meter using the pendulum and the second. Other planets would have their own definition of second, but not their own definition of pendulum. Since one meter is prescribed though a pendulum because of the oscillation formula and dependent on the frequency alone (in this case, 2 seconds), no matter what planet you are on, how strong gravity, is or how long a second is, the pendulum describes a relationship between seconds and meters such that if using this method a planet’s scientists would always define their units such that acceleration of gravity was eerily equal to pi^2.
Makes me think of possible lunar scientists unwittingly making their meter 5/6th shorter(edit: english is hard) and then marveling at the same coincidence…
Your comment is much more rage-bait than the article.
Universal isn't a way we describe numbers. You meant to say dimensionless. Pi is dimensionless constant because it describes a relationship between two measurements of a dimensionless unit circle.
Pi is expressed as a pure ratio between two other dependent numbers. Dimensionless values are special because they don't rely on any particular measurement in any particular location, lending to your misconception of "universal" constant.
This article explains how a particular dimensionful constant (g, the strength of gravity on earth's surface) is related to pi.
They are related because the dimensions in question are both derived from dependent properties of our planet. These dependent properties will be found on any other sphere floating in space if they are derived in the same fashion.
It's good to thoroughly or even marginally understand a topic before adopting a dismissive and authoritative argument against it.
> Universal isn't a way we describe numbers. You meant to say dimensionless.
They probably really meant to say “universal”, since dimensionless values are a less interesting category that includes… well, every number. Pi shows up in math without having to parameterize anything, making it universal in a way that even physical constants of our universe aren’t.
On any planet where you want to define a system of units, you can start by defining a fixed time period (maybe use a fraction of the planetary rotation cycle or something), then make a pendulum that swings with that frequency, and derive a unit of distance from its length.
The local value of g will be roughly pi squared pendulum lengths per tick squared, in that system of measurement.
If you read the article you would see that it’s not a coincidence because the meter was defined such that pi^2 = g at the surface of the earth.
Nope, it's not a coincidence - it's an interesting exploration of the history of the definition of a metre. Read the article.
As it says, at some point there was an attempt to standardise the length of a metre in terms of a pendulum's length; which related it directly to g through Pi.
[flagged]
[flagged]