Baking soda is weakly alkaline in water. Weakly alkaline materials, and any foreign materials at all, are what you are trying to wash off. Mere drops of detergent in the wash water is all that you need, and in the rinse water, nothing. Look at, say, Wiki for info. about non-polar (non-ionic) detergents.

Mad, conceivably. Scientist by choice. I leave it to you to sort out the implications.

de :-x