I’d have to check papers for the exact ones, but dendrochronology and 14C dating are the most likely options. The former relies on regular seasonal patterns that don’t vary often; the latter on physical constants that if changed would make atoms fall apart or turn the earth into a ball of radioactive plasma.
God does perform miracles, but not for the purpose of deceiving people or altering the world in ways that have no theological point. God could have altered properties of the world in ways which would produce the observed effects within the parameters proposed by modern YEC and flood geopseudology advocates, but such miracles are neither recorded in the text, nor consistent with God’s attributes of faithfulness and truthfulness.
It is asserting that at least part of the reason for people to hold to an old earth is that they fear for their funding or prestige or reputation. That is possibly true for some people. To imply that it is generally true is a slander, as it implies that more of the individuals in question are more concerned with their livelihoods than with honesty than actually are. There certainly are scientists who are more concerned with money or fame than with honesty, but to imply that it is a standard motivation is false and is a slander.
And if the worldview demands honesty, it will not dismiss how measurements work. He’s the math for how a parent/daughter isotope ratio is converted to a date, for situations where the daughter isotope is actively excluded from the parent material (e.g., U-Pb dating of zircons); additional calibration steps are needed for places where the daughter isotope may have been present:
log2(Observed proportion of parent) * (calculated half life based on direct measurements of decay rate of a sample)
Measuring the decay rate generally is using something like energy release from a sample and converting that to decays/time. Decays/time can then be divided by the known number of atoms of the isotope in question in the sample to give the probability of decay of each atom in a given short amount of time, and then that can have its base 2 logarithm taken to give the half-life.
Here’s a paper describing how this was done for 209Bi: chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://arxiv.org/pdf/1110.3138
In other words, it’s just measurements and math, and completely independent of worldview, so long as the worldview demands honesty.
Science is simply a set of procedures and methodologies for figuring out how things work in ways that are systematic, disciplined, rigorous and reproducible. The rules by which it operates have nothing whatsoever to do with “biblical worldviews” versus “materialistic worldviews.” They are the same no matter what worldview you adopt. They are rules such as these:
- You must have accurate and honest measurements.
- You must report the evidence accurately.
- You must interpret the evidence in ways that are mathematically consistent and coherent.
- You must correctly account for sources of error such as contamination.
- You must neither exaggerate nor downplay the extent or significance of sources of error.
- You must avoid logical fallacies.
- You must not quote mine.
- You must make sure that your findings are reproducible by other researchers.
- You must take steps to account for and eliminate cognitive biases.
- You must keep accurate lab notes.

Unfortunately, and not all the time, but there are clearly some instances of when samples are analysed by researchers operating under a ‘deep time’ billions of years paradigm, where the sample, because of the depth or strata that it was found located in, is expected to return a date of around 10 million years, but the sample after the conversion is applied, actually returns an age of say 20,000 years, the sample is considered unreliable or ‘contaminated’ and the result thrown out and further tests are run that confirm the paradigm and those are the dates that are published.
Not publishing results that are driven by contamination as accurate answers is what honesty demands–if I get an answer of 65,000,000 when I do a measurement using 30 independent techniques, and then get 30,000 using a technique that is known to be easily contaminated, which answer should I consider more likely? 14C dating is among the absolute easiest radiometric dating techniques for which to have problems with contamination, because carbon is everywhere–if the sample was in contact with the air, with the researcher, with anything alive after it died, etc., etc., it will be contaminated.
Take for example the claim about carbon-14 in fossils. As @Paraleptopecten has rightly pointed out, we would expect to see trace amounts of carbon-14 in ancient samples because of contamination from modern carbon-14. This is simply one of the most basic, fundamental rules of measurement that applies to every context: you must take into account all possible sources of error, and contamination is one such source of error. Yet young earthists dismiss contamination as some sort of “rescuing device.” By dismissing it as a “rescuing device,” they are demanding that the basic rules and principles of accurate and honest measurement do not apply to them.