The very first thing when trying to explain “magic” of Śrīmad Bhāgavatam “scientifically” should probably be clarification of terms. Direct translation into modern languages is easy but in many cases it’s grossly inadequate because reality of our lives is different from theirs.
Some might object that reality doesn’t change significantly but we often don’t realize how many of our assumptions are influenced by ever changing external conditions. Nowadays, due to introduction of knives, forks, or even chopsticks, not having an overbite would be a medical condition but when people used only hands to eat their food it was the opposite and no one had an overbite at all.
Another example is bodily odor – the sweat gland responsible for it is often completely missing in certain nationalities and so when people of these different cultures meet they can have very surprising and often unpleasant discoveries about each other, most often blaming it on lack of proper hygiene while back at home some wear their odor with pride or maybe fight it with strong cologne or deodorants. In Japan, on the other hand, deodorants are hard to find because no one uses them ever.
I once read that teachers in Ireland were going on a strike because temperature in their classrooms has risen to 26 Celsius while in tropical countries people work outdoor in 40s and then set their air conditioners to 26 to cool off inside. That’s roughly 100 and 80 in Fahrenheit.
Maybe these are not very good examples overall but I just wanted to demonstrate that our perception of what is “normal” can vary greatly even now, what to speak of “normal” in previous yugas. People can grow 10 cm taller in only a couple of hundred years, imagine if they kept growing for a couple of thousand. The only conditions necessary are better food and less diseases, which depend on climate as much as on human practice of medicine. I’m not going to discuss why the skeletons of these giants are missing from our fossil record here, maybe some other time.
When “normal” reality changes so greatly we shouldn’t try to see ancient people through our prism. We just can’t see the same things anymore because they no longer exists and so we use our poor substitutes which seem real to us but would probably not be recognized by the ancients themselves.
We don’t believe in yoga siddhis, for example, because no one has them in our society. Well no one practices celibacy in our society either and that’s the primary condition for developing “supernatural” abilities. Another example is that no one can see God anymore and therefore we assume that it was true in Vedic times, too. When Vedic sages wrote about demigods appearing on certain occasions we can’t believe it either. Conditions for demigods to grace us with their presence are still the same and we use the same words but their meanings are different now.
The place needs to be pure, for example. We can clean it up, get a guy with a mop in and scrub it, and disinfect it, too, but that won’t be “pure” by Vedic standards. They probably won’t consider anything plastic as pure in principle and they would require purity from people being present, too. We can send everyone to take a shower but that won’t be enough because demigods require internal purity, ie freedom from lust, and that we can’t provide. It just doesn’t exist anymore. Anyone who has ever eaten unoffered food, let alone meat, would contaminate the place with his gluttony, too.
We can’t even imagine what a really pure assembly place would look like even though we still use the same words. They mean different things to us from what they meant in Vedic times.
For scientific discussion specifically we should highlight the difference in meaning of fire, water, air, earth etc – gross material elements. We assume that ancients used these words just like we do – because they didn’t know what water or earth was made of. For them these elements were prime building materials – take some earth, meaning clay, shape it, put it into fire, and get a pot. Primitives! We can’t even begin to think that these words meant something completely different in Vedic terminology.
Take “earth”, for example. How do we expect to differentiate it from water? By touch, of course. Earth is more or less solid, just put your hand on the substance and you’d know whether it’s “earth” or liquid. In Vedic times, however, earth was associated with smell. If it smells, it’s earth, while touch was a symptom of air. What what?
We are clearly talking about different things here, not common clay and water. We don’t grant the ancients the ability to analyze the matter differently from us. We think that the only way to understand common water, earth, etc is to find their chemical composition and this again forces us to see the world in a very restricted way without even realizing it.
We can’t imagine ancients to make scientific progress using their weird classification, we think that we have the monopoly on honest scientific inquiry while they were hopelessly corrupt and invoked gods to mask their ignorance all the time. That’s another common stereotype, probably completely without merit. We can’t even think about ancients advancing in their scientific understanding on their terms, our brains are not wired for that, there’s a societal pressure, and no one honestly tried it, even for fun. The fact that people even in India can’t pursue yoga anymore doesn’t help either. Even if there are successful yogis there they won’t be mixing with us, the modern people, and so they can’t be studied in laboratories. They’d avoid our atheistic mentality like a plague, and they should be very good at it, too – due to the same yogic powers.
What I mean is that they’d practice mind control where mind means something different from what it means to us. They would practice control of their senses where senses mean something different from what they mean to us. How can we withdraw the sense of smell, for example? Or the sense of sight? We completely lack the ability and so we don’t believe it’s possible for yogis either. That’s just projection of our own limitations and it’s unscientific but often that is all the modern science can offer on this subject.