Q: According to science, there was a world prior to humans where there were no living, conscious things. If nothing can exist independently of consciousness like Advaita suggests, then how could there have been a world prior to a perceiver? If there was no sentient being to experience the Big Bang, how could it have possibly existed?
A: Your questions relate to the apparent creation. The final teaching of Advaita is that there is no creation – there is only the non-dual Brahman. This means that the entire teaching of Advaita is interim only since it takes place in what is only empirical reality.
Having said this, the traditional teaching says that the creation, maintenance and dissolution of the universe is ‘managed’ by Ishvara, using the ‘power’ of mAyA. This means that He governs all of the laws that relate to creation and the jIva-s who inhabit it. Now you have to realize that science has ‘advanced’ significantly since the time of the Vedas. While they speak of the raw elements being space, earth, water, fire and air, we have a somewhat more complex cosmology! And I don’t think it is particularly fruitful to try to map one onto the other. Science can never explain Consciousness so is of no value in trying to understand the nature of reality.
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