On Wednesday, January 9, 2019 at 4:01:46 PM UTC-6, Bruce wrote:
> On Thu, Jan 10, 2019 at 7:53 AM John Clark <johnk...@gmail.com 
> <javascript:>> wrote:
>> On Wed, Jan 9, 2019 at 1:58 PM Philip Thrift <cloud...@gmail.com 
>> <javascript:>> wrote:
>> >> Is the Fine Structure Constant a rational number? Is it a algebraic 
>>>> number? Is it a transcendental number? Nobody knows.
>>> *> Is it computable at least?*
>> Because the Fine Structure Constant has a physical and not a 
>> mathematical definition my intuition tells me it must be computable; and 
>> indeed we've already computed a very good approximation of it and there is 
>> no reason to think we couldn't do even better if we had faster computers 
>> that could sum up more of those Feynman diagrams.  
> Rubbish. The fine structure constant is not computable by Feynman 
> diagrams. What might be confusing you is that QED calculations of 
> physically measurable  things like the Lamb Shift and g-2 for the electron 
> depend on the value of the FSC. Comparing the calculations with experiment 
> gives an accurate value for the FSC. the fine structure constant itself is 
> an arbitrary constant of nature, and not directly callable.
> Bruce

On computability of "constants" of a theory, a bit unsettled:

*Computability and Physical Theories*
Robert Geroch, James B. Hartle

*The familiar theories of physics have the feature that the application of 
the theory to make predictions in specific circumstances can be done by 
means of an algorithm. We propose a more precise formulation of this 
feature --- one based on the issue of whether or not the physically 
measurable numbers predicted by the theory are computable in the 
mathematical sense. Applying this formulation to one approach to a quantum 
theory of gravity, there are found indications that there may exist no such 
algorithms in this case. Finally, we discuss the issue of whether the 
existence of an algorithm to implement a theory should be adopted as a 
criterion for acceptable physical theories.*

("The fine structure constant is measurable.")

- pt

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