The thing about counts in the real world is that it takes time to do counts! Any counting activity shows the passage of time. I just wrote 1, 2, 3 , 4, 5 in about 10 seconds.The thing about radioactivity is that the passage of time reveals itself as counts. This is also how carbon-dating works.
Carbon dating does not work by counting alone. The measurement is the amount of C14 in a sample and applying the half-life of the isotope + the ratio of C14 to C12 to get the age. The amount is measured by several techniques, historlally the number of decay events per unit mass per time period. A modern technique is accelerator mass spectrometry which is an actual count of C14 and C12 (and C13 for calibration) atoms in a sample.
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