One of the most glaring examples of a bad paradigm is the Copernican world-view foisted on humanity without having been sufficiently tested, let alone proven. Another good example is the evolutionary concept of human origins, which envisages ape-like pre-humans leaving Africa for the Far East, morphing into Homo erectus, then migrating to Europe and becoming Neanderthals or Cro-Magnon in the process, or whatever labels anthropologists have concocted. In my opinion, the Out-of-Africa theory is simply 19th century racial bias dressed up as science. But I will leave that for another post.
Once a paradigm is in place, it is incorporated in the design of all subsequent studies, and collected facts are made to conform to it. If the facts are recalcitrant, they can be twisted, cherry-picked, explained away with bizarre theories or simply swept under the rug. The latter category was referred to as ‘the damned’ by Charles Fort.
A very deeply rooted paradigm is the belief that civilization began around 4,000 BC, roughly coinciding with the Kali-Yuga of the Hindus, and then ‘evolved’ towards modern times in a somewhat linear fashion discernible in increasingly sophisticated systems and tools. The fact that quite similar cultures existed simultaneously on different continents with no documented physical contact and the fact that several cultures are now known to have thrived before the magic ‘time barrier’ of 4,000 BC (Göbekli Tepe and Harappa, for example) does not seem to discourage the advocates of the paradigm.
But there is more. Ancient and well-preserved archeological sites, such as in Peru and Egypt, show a perfectly consistent pattern, not of ‘evolution’, but of loss of technological skill by degrees. Sites which have been occupied on and off by different cultures over the millennia invariably have the most sophisticated structures at the lowest/earliest level. Here is an example showing building techniques from different periods:

1 - remains of ancient and technologically advanced megalithic construction; 2 - authentic Inca work, relatively crude but of good quality; 3 - clumsy repair work probably done by the Spanish; 4 - Spanish colonial-style plastered brick wall; 5 - recent repair work using small stones and plenty of mortar; 6 - modern, low-quality hollow adobe brick wall.
Why do we say megalithic constructions are ‘technologically advanced’?
1 - Generally, the stone blocks are huge and have often been transported over uneven terrain from quarries very far away. For example, the quarry in Aswan, Egypt, is hundreds of kilometers away from the sites where the blocks or objects were installed. We have no clue how single-piece statues and obelisks weighing between 500 and 1,200 tons were moved. The megalithic builders wanted very specific building materials (despite the availability of local sand or limestone) and it apparently didn’t matter how far they had to go to get them, nor did they think it would be better to use standardized blocks of a smaller and more manageable size.
2 - All technologically advanced megalithic constructions are made of granite, diorite, basalt or andesite. At a hardness of 7 on the Mohs scale, these types of stone could not have been cut, let alone shaped, with the tools available to the Incas, dynastic Egyptians or any other ancient people studied by mainstream historians. However, this does not seem to bother the ‘experts’.
3 - The remnants of technologically advanced megalithic constructions display unmistakable signs of machining, such as huge circular saw marks, mirror-perfect cuts at right angles and high-speed tube drill holes. Some of these feats would be difficult to replicate with today’s stone-cutting technology. This also does not seem to bother the ‘experts’.
4 - Building blocks are all of different size and shape (even when disposed in straight horizontal rows) and fit together with eerie perfection, without any mortar. In some locations, huge blocks form incredibly resistant three-dimensional puzzles in an almost playful way. Handling the heavy blocks was obviously not a big deal.
5 - Stone surfaces show signs of having been “softened” for easier extraction or fitting; for example, scoop marks in quarries and on blocks suggest the stone was extracted by scraping, not by impact.

Circular saw marks on large block in Egypt. Based on the curvature of the lines, the saw blade would have measured 6 m.

Clearly machined blocks from Puma Punku in Bolivia.

Roofed box cut out from a single granite block in Egypt.

Detail of clearly machined Egyptian stone box.

Left: one of more than twenty 70-ton stone boxes in an underground complex at Saqqara. The lid weighs 30 tons and was cut from the same block as the box.
Right: hole made with high-speed tube drill advancing 2 mm per rotation. The stone split during the drilling and was discarded.

Example from Peru of uncannily perfect fit, almost marshmallow-like.

The wood and bronze tools we are expected to believe were used to produce the above pieces in granite and basalt.
So, if not within the conventional historical period, when were those technologically advanced pieces produced? Here we move into speculative waters, but I tend to agree with amateur archeologists like Brien Foerster that a transcontinental and technologically advanced megalithic civilization existed which came to an abrupt end sometime around 12,000 years ago. In addition to the five items listed above, the technologically advanced megalithic sites have other things in common:
1 - They bear no inscriptions (I am looking into a possible exception).
2 - They appear to have been made for strictly practical purposes, not ceremonial or religious use. The "temple" and "tomb" designations they are given by archeologists are misnomers.
3 - Those which have not been disinterred recently show signs of extreme weathering.
4 - They appear to have very peculiar magnetic and/or acoustic properties.
5 - Shapes and structures are often radically different from anything in recorded history, making it very difficult to guess what purpose they served.
6 - Sites all over the world were destroyed, apparently around 12,000 years ago, as if by violent explosions or extreme heat; huge blocks were shattered and scattered; yellowish-purplish ‘scorching’ marks are seen on selectively damaged statues and blocks, especially in Egypt.

Scoop marks in a quarry in Egypt and on a wall in Cusco.

Left: characteristic discoloring on megalithic wall in Peru likely caused by extreme heat.
Right: single granite block from Egypt with relatively preserved surface and ‘cooked’ core.
Some have raised suspicion that the machined pieces were created in modern times. We cannot rule out this possibility, considering the countless examples of fakery in the fossil and relics departments, but in the majority of cases of technologically advanced megalithic constructions it would be more difficult to explain the fakery than the existence of advanced stonecutting capabilities in remote times.
In any case, the scenario of cave-dwelling ice-age hominids needs some serious revision!
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Almost all the pictures in this post are screengrabs from videos by Brien Foerster: https://www.youtube.com/user/brienfoerster/videos
edit: date corrected.