Battle Of The Paradigms
I think the only scientific way to decide whether the new discrete fractal paradigm or the standard paradigm of particle physics/cosmology represents a superior model and understanding of the cosmos is through observational testing of predictions made by the competing paradigms.
Discrete Scale Relativity has made 15 definitive predictions (http://www.academia.edu/2917630/Predictions_of_Discrete_Scale_Relativity), and hundreds more are possible. The list is only limited by our empirical abilities to test them.
If you think the standard paradigm is in a very strong position I can show you 7 very serious problems with the standard model of particle physics that particle physicists also agree are serious problems. Then there is a list of about 15 things the LHC was supposed to find in order to fix for those 7 serious problems. In fact, the LHC only detected one scalar boson that was already expected and it does not solve the 7 serious problems. There are no solutions to these standard model problems in sight.
Regarding the standard cosmological paradigm, here are some serious scientific questions. Where is the definitive evidence for the inflationary scenario? Where are those AWOL dark matter particles: WIMPs, axions, sterile neutrinos,etc? Why are mature galaxies, quasars and globular clusters found with ages much older than predicted? Why are satellite galaxies found in planar orbits around their central galaxies when the LCDM model says they should be distributed randomly? Why does the LCDM model predict cusped dark matter distributions when we observe cored distributions of the dark matter? Why are there only about 50 satellite galaxies around the Milky Way Galaxy when the LCDM model says there should be thousands? How could the observable universe pop out of virtual nothingness? Why are the standard models of particle physics and cosmology so complicated and plastic that definitive predictions are as rare as hen’s teeth, and anomalies can be finessed by tweaking the plastic models? And so on.
It is long past time for new ideas. Discrete Scale Relativity may still be a diamond in the rough, but at least it finally offers something truly different that came from studying nature, that makes 35 fundamental retrodictions, that makes many definitive predictions, and that offers one unified physics for the entire cosmos.
We certainly do not want to put our trust crank theories, of which there are many, nor do we want to rely too heavily on the professional experts (whose funding and status are tied to the old standard paradigm). We should put our trust in our own ability to open-mindedly weigh the observational evidence, to judge the conceptual/theoretical elegance, and to evaluate the retrodictive/predictive successes of the competing paradigms.