IMHO, for the advancement of TOE (physics), this is a critical issue needs to be seriously reckoned with.
Let the following presentations be the basis for starting the dicussion of this issue here. Inevitably I would be assuming a daunting position that is probably against the entirely colony of astronomers, astrophysicists, cosmologists, Earth scientists and etc, but I hope all would understand this is not a personal attack on anyone, any prefession or any establishment.
Although all the content presented here were available from my website on "Overview of UVS", this version is posted here as it was recently compiled, so the content in this original vesion that is being discussed would always be available here, whereas the version from my website might be updated from time to time. Nevertheless, readers can always visit my website for its hyperlinks or explore further. However, I would like to keep the discussion limited to the issues as raised herewith.
Without further ado, here goes:
Critiques of scientific method - The cognitive paradox fallacies
“The first principle is that you must not fool yourself --
and you are the easiest person to fool.” - Richard Feynman
If the basis of a scientific theory was misled by illusions as a result of a cognitive paradox and therefore had developed based on misconceptions, such as had adopted the fallacious concept that world is flat or Earth is the center of the universe, henceforth, regardless of how developed, how profound, how coherent, how accurate the scientific theory could predict quantitatively and how widely the established theory has been accepted by so many elites independently for a very long period of time, the basis is fundamentally incorrect. This is despite the so called proven scientific theory that was misled by its cognitive paradox fallacy could be mathematically validated in its delusion and it has worked in applied science to a great extend.
“As far as the laws of mathematics refer to reality, they are not certain,
and as far as they are certain, they do not refer to reality.” - Albert Einstein
Laws of mathematics though are effective tools in applied science for deductive reasoning, and the propositions of a mathematical model can be indisputably conclusive through deductive reasoning in its evaluation to analytically prove its hypothesis for the natural phenomenon as it has been empirically observed. However, it must not be mistaken that the reality of a natural phenomenon could be absolutely proven by mathematical interpretation with validated and accurate quantitative predictions through the mathematical construct of the hypothesis. A mathematically proven conclusion of its hypothesis solely deduced through quantitative measurement according to its mathematical construct although could have integrated its inference of reality with the empirical observation, in abstractness it was based on a philosophy with varying degree of uncertainties in the interpretation of the numbers obtained from the observation; the assumptions for its philosophical identities are fundamentally based on faith in its belief system.
“Not everything that can be counted counts,
and not everything that counts can be counted.” - Albert Einstein
See external links on "Foundational crisis" that elaborates on the attempts to provide unassailable foundations for mathematics that were found to suffer from various paradoxes, and "Proof theory" that is syntactic in nature and its philosophical logic is based on syntactic entities whose properties may be studied without regard to any meaning they may be given, and, in fact, need not be given any; syntactic entities are merely assumptions that are not needed to be referred to reality.
“One reason why mathematics enjoys special esteem,
above all other sciences, is that its propositions are
absolutely certain and indisputable, ...
How can it be that mathematics, being after all a product of human
thought which is independent of experience,
is so admirably appropriate to the objects of reality.” - Albert Einstein
cont...


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Ptolemaic elements
Apparent retrograde motion of Mars
The orbit of Venus in relationship to the Earth.
Star HL Tau and its protoplanet HL Tau b
The universe's timeline, from inflation to the WMAP. 
Animated raisin pudding model of the BB expansion
Sunrise

