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It is generally held that below a certain age the student simply cannot "grok" a lot of math. — tim wood

Not in conflict with anything you've written, but it brought to mind some studies done by Karen Wynn and others that show that even infants have a sense of quantity and some very basic "arithmetic" skills.

Welcome to the forum. This general subject is something I've thought a lot about. Some thoughts:

Calling knowledge "holographic" seems a bit highfalutin to me. It gives the concept a veneer of exotic science that I don't think is needed.

This gives me a chance to bring out my favorite quote from Franz Kafka:

You do not need to leave your room. Remain sitting at your table and listen. Do not even listen, simply wait, be quiet, still and solitary. The world will freely offer itself to you to be unmasked, it has no choice, it will roll in ecstasy at your feet. — Franz Kafka

When I've posted this quote before, people respond that obviously you can't know about Newton's laws sitting alone in your room, but that's not the point. What you can learn is how the world works, how we know what we know, how we fit in the world. I think this is the kind of thing we learn "holographically." Not something specific, but an awareness of our own thinking process and how to use it to know things.

The other thing we get from small bits of knowledge is bricks for our wall. In my experience, I have a mass of connected knowledge that builds a model of the world I live in. Each small piece of knowledge is connected to others to make a structure of interconnected pieces. I have a vivid visual image of this model as a cloud, lit from within, which contains everything - dogs, cats, protons, love, poundcake, values, Donald Trump, and oxygen. Areas where I have a lot of knowledge are more in focus than those where my knowledge is lacking. As I understand it and experience it, this model is the source of my intuition. I can make judgments about ideas based on how they fit into my model, even if I have relatively little knowledge. That doesn't mean I don't have to go back and verify things with more formal methods of justification, but it helps tell me where to get started and what is worth worrying about.