Makerspace Constants Clock
Like many ideas in math and science, the idea for this clock came from recognizing a simple pattern and exploring if it can be extended. A friend gave me an old clock of hers and asked if I could make something out of it. In the spirit of being more nerdy-than-thou I quipped that if I were creating a clock face I would replace the numbers with math constants, easily rattling off the first three, the Golden Mean for 1, the Natural Log e for 2, and the constant Pi for 3. I told her that I would need to think what I use for 4 but that some of the others were obvious. This led to weeks of poring through tables of constant’s to find the remaining nine constants I would use. A Google search revealed that many such clocks are commercially available, but none followed these rules.
The criteria for number selection in order of importance was:
1) That the clock have each of its twelve numbers replaced by either a mathematics or physics constant.
2) That the first non-zero integers value be the same as the digits on the clock it replaces.
3) That the constant be well known, but not trivial, i.e. not an integer.
4) That the constant be useful in the context of a maker-space.
5) That the constant avoid calculation, i.e. the square-root of 2.
6) That the constant have a cool symbol, ideally Greek.
7) That the constants be arranged be arranged in a pleasing way.
8) That the constants not be too idiosyncratic to me.
My selection is:
φ = 1.61803398875 The Golden Ratio The ratio of two quantities equals the sum of the larger of the two quantities.
e = 2.718281828 The Natural Logarithm The power that e needs to be raised to to equal that number.
π = 3.141592654 Archimedes constant The ratio of a circle's circumference to its diameter.
δ = 4.6692016091 Feigenbaum_constant Used in the calculation of fractals.
σ = 5.670367(13)×10^-8 W⋅m^−2⋅K^−4 Stefan Boltzman constant The relationship of temperature to radiated light.
h = 6.626070150(81)×10^-34 J·s Planck's constant A photon's energy is equal to its frequency multiplied by the Planck constant.
Alternate Na = 6.02214076 × 10^23 1/mol Avogadro's constant Although this is a definition, this constant might be more useful in a makerspace.
α = 0.0072973525664(17) = 7.2973525664(17)x10^-3 Sommerfeld's constant The fine structure constant is used to calculate the electromagnetic interaction between elementary charged particles.
R = 8.3144598(48) J⋅mol−1⋅K−1 Gas constant Relating gas energy to temperature.
ɡ = 9.80665 m/s2 Standard gravity Acceleration due to gravity on earth.
Λ = 10.986858055x10^-1 Lengyel's constant Regarding set partitions.
Alternate R∞ = 10.973731568508 m^-1x10^6 Rydberg constant Relating to atomic spectroscopy.
GF = 11.663787(6)x10^-4 GeV^-2 Fermi coupling constant Used in calculating beta decay.
ζ(3) = 12.0205690315x10^-1 Apéry's constant Used in the analysis of random minimum spanning trees.
Alternate A = 12.824271291x10^1 https://en.wikipedia.org/wiki/Glaisher%E2%80%93Kinkelin_constant Glaisher-Kinkelin constant. Derivative of the zeta functions.
For 1) As an artist and an engineer I had learned about the Golden Ratio when I was a child, even incorporating it into the storyline of my first novel.
For 2) I had learned about the Natural Log e in high school mathematics. At that time we built our own table length slide rule.
For 3) Another constant I learned about early was Pi. I still wonder why there should be any relationship of a circle’s diameter and its circumference.
For 4) I had to look up Feigenbaum's constant and its relation to bifurcation. I had encountered it once before in a graduate level computer graphics course, but I don’t think other people would know this. If I found a better value for 4 I would use it.
For 5) I am not entirely happy with the choice of the Stefan-Boltzmann constant, although I did use this in a physics lab where we measured black body radiation. The problem is that it is a derived constant, not primary, but I do think that it could be useful in a makerspace.
For 6) There were several numbers to choose from, Avogadro's number, the gravitational constant, and a couple of others. I finally settled on Planck’s constant because it is a primary constant and so well known among nerds like myself.
For 7) The fine structure constant is so common in particle physics that I had to include it. I am not happy that I needed to shift the decimal point over three places, but still its value is well known.
For 8) Like the Stefan-Boltzmann I am not entirely happy with the use of the gas constant, because it is derived. Still it is both well known and could be useful in a useful in a makerspace.
For 9) I went back and forth on using the value of Standard Gravity instead of using the gravitational constant. But rather than have makers need to look up the mass of the Earth, I thought that this value would be more well known. It also amuses me that it is across from Pi on the clock face, an even older constant related to a sphere.
For 10) I feel that I was reaching by using Lengyel's constant. Even with a minor in math I am not familiar with using this value to partition sets. I used it because it here because it has a cool symbol. Even so, I did need to move the decimal point.
For 11) I feel that I was reaching even further by using the Fermi Coupling constant. I do have an interest in high energy physics, but still I had not encountered this before and doubt that other makers will know it. If I can find another constant with this value I will remake the clock face.
For 12) I am not happy that I used a calculated value for this final number and that I needed to move the decimal point, however I felt that including the Riemann Zeta function was so important that I relaxed these rules. I encountered this in my own studies while attempting to develop my own analytic function for finding primes building on Goldbach’s conjecture, https://en.wikipedia.org/wiki/Goldbach%27s_conjecture now proved, http://www.math.vt.edu/people/linnell/Ugresearch/farley.pdf. It is worth looking up the Zeta function as it pertains to finding primes as one of the unsolved Millennium problems, https://en.wikipedia.org/wiki/Millennium_Prize_Problems.
I hope that you have enjoyed this research and its associated clock face.