Fine Structure Conjectures
The Wolfram Knowledgebase includes the current best value for the fine-structure constant, as well as its uncertainty. This example gives a list of numeric expressions that have been proposed as possible exact values for the fine structure constant.
Express both together using Around.
For more than a century, scientists have come up with conjectures for closed forms.
Format them in a text grid, displaying the name of the author, proposal year and proposed form.
One can measure the complexity of a conjectured closed form in an entropy-like way through the logarithm of the size of involved integers. Mathematical functions count exponentially.
Conjectured values that are closer to the experimental value are typically more complex, and no closed form is known that is simultaneously precise and short. Examining the relationship between complexity and conjectured values as plotted here suggests the two satisfy an inequality of the form , where the orange curve assumes , , and .