Husserl’s Cartesian Meditations are based upon a series of lectures that he delivered at the Sorbonne in 1929. Husserl describes the aims of transcendental phenomenology as being a version of Neo-Cartesian philosophy even though it rejects almost all of the doctrines of Cartesian philosophy. The Meditations propose first an absolute foundation for philosophy in order to translate it into a science. 

I find this terrifically amusing: Descartes skeptically broke down everything he could in his experience and reduced it to the one undeniable absolute truth of his own existence. Yet, in mindfulness based meditative practices of Eastern cultures, the self is the first illusion and the first myth to overcome and let go. I am not sure what to do with this yet. I think my farthest lead on a resolution is that Descartes misjudged something inherent about the ever-presentness of a moment to be experienced, and assumed that an identity-bearing ego would need to have a role in all experience. However, there are so many varieties of experience which do not involve conscious oversight or ego involvement. I think the most immediate Western-based association is the unconscious, but we can also think of autonomous systems. Your hair grows itself, the digestive processes happen on their own, and the breath for the most part happens without attention.