To answer your question first you make sure that child has the same education resources available that the professors child does throughout all aspects of their life. You also make the professors available to children from those inner city areas widening the networking effects that the children of the professor gets. they won't be as good but you open them up.
Improving objective outcomes is some Krypton level shit, "Your a black doctor and were trained to be one from birth due to the outcome we wanted." "I wanted to be an artist."
You meant at t0, the movement the baby is born to a parent optimizes education vs a baby that is born to a parent that cares much less. Impossible for government to "make sure" this happens.
That is where the problem lies, yes, the inequality is as they "systemic", rooted in practical reality.
There is no real way to perfect this - but if an effort is made a good result can be achieved nonetheless. The fallacy with the professor example is that they will have the time to teach their child, and that their child must necessarily be receptive to their limited tuition.
Unless they quit their job, and thus are no longer professors, a majority of their time will be spent teaching multiple students, and while one on one coaching has it's merits there is also value in classroom peer experiences. If an effort is made to provide tutoring to all the kids, it may even be in the parents interest not to provide tutoring services, if the quality is good, because that takes away from their own time spent being able to provide the most effective teaching experience they can offer.
We can't build perfect bridges, but we can sure as hell mandate they are good enough, it's some nonsense to say we shouldn't try because we can't get it perfect.
The child of the professors has the parents who are supposedly smart and teach him or her all the time at home, how exactly do you make this available to children from those inner city areas?
It's called a teacher you find them in schools. If you pay them properly and give them adequate resources they can achieve these goals. You also add in libraries and other places where kids can learn independently.
I am not sure how does this answer my question. "Paying properly" a teacher will make one's parents millionaire professors or as interested and capable in their children education how?
Or do you simply deny that parents educate their children? Do you believe that as long as they have the same teachers at school, who are 'paid properly', say, a farmer's son and a son of a musician will have the same knowledge and skills in animal husbandry and musical theory?
Are you saying that your parents are millionaire college professors and they have not told you anything other than to do your homework? That sucks, I imagine most parents are more involved with their children. My parents are just research scientist but I had no problem learning from them, they answered all kinds of questions for me.
Father is a plumber, mother is an accounter. I had a problem with understanding fractions, mom helped me. There was no more help, because I understood everything else myself and they don't know more advanced topics, because they had school program long ago. My brother is decently educated and knows school program, but can't help his kids - they just don't understand (their (modern) school has zero discipline).
I am sorry, I don't understand your point then. How is your case relevant to children of college professors or even mere PhDs? You apparently didn't have the same educational opportunities as them by your own account.
Teachers can only do so much, it is really hard for them to make up for deficiencies at home. Kids have to learn to learn independently, again, an advantage that kids with a better home life have over those that don't.
Improving objective outcomes is some Krypton level shit, "Your a black doctor and were trained to be one from birth due to the outcome we wanted." "I wanted to be an artist."