Some websites show that it is ideal to get 1.5 m distance between the person and the kasina object.
Is there any science behind the recommendation to get that specific distance?
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You're using a word that is troubling me - namely "science". A lot of modern people are drawn to Buddhism because, at least at the beginning, it seems that the Buddha is offering an empirical path to liberation. Let me turn you off that idea now. As you progress, you are going to find that Buddhism will ask of you things that are not rational, require faith, and are not falsifiable. Buddhism requires fundamental trust. Be prepared to offer it.
But to answer your question...eh. Not really. Meditation is an art. What you are looking to do with a kasina is establish it so that it fills your field of consciousness. You want something that you can hold in your mind. Too big and you lose the edges. Too small and it might be hard to hold onto at first. Play around with it. See what works for you. Ultimately, you want something you can hold steadily in your mind. So as long as that can happen, don't worry about how far away it or how much of your inner field of vision it takes up.
Let's say you are an artist who put a small bowl of fruits in front of him (or her) as the object of inspiration and intends to paint it on a canvas.
How far away from you should it be?
I would say 1.5 meters would be a pretty good distance. Not too far and not too near, for you to be able to make it the foreground of your visual focus, covering all parts of the bowl and the fruits, and their details, adequately.
That is the same idea behind the kasina visualization recommendation.
It doesn't matter, contemplation & visualization is sufficient.
The colors can appear just due to contemplating the bodyparts, eg the whiteness of bones or the red hue of blood.
The colors are a good way to start because it's quite simple but if one is skilled at defining the elements one can direct the mind to all the kasina bases by contemplating the 6 constituents of a person; earth element, water element, air element, fire element, consciousness element & space element.
The earth element, water element, air element, fire element & space element can be contemplated as both internal & external elements.
The space-kasina and consciousness-kasina are the formless bases and the others pertain to the heavens of form.
As a side note, all kasina attainments are jhana but not all jhana are associated with a kasina.