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Manipulating Perceptions Inside the Puzzle
It helps to understand the goal

Regarding my recently published story, “Puzzle, Puzzle, on my Screen,” … Yes, that is a tough puzzle! Perhaps a bit advanced, so here are further explanations to help your skill development efforts.
Why is it difficult?
Our binocular vision locks each eye onto a seemingly identical feature. When you read, it helps if both eyes are looking at the same word! We don’t think our way through normal reading, at least not to the task our eyes have been put to. Our thoughts belong more properly with the information conveyed in the letters, numbers, and words on the page.
This puzzle uses a Dot Field with special characteristics. The dots are arranged on perfectly horizontal and parallel lines. This is because our eyes are aligned horizontally and they need to find the intended viewing details along that horizontal axis.
Each dot looks the same, so you can visually merge any two dots and your eyes will be happy! However, once you get into the Cross view mode, and can see just one box with dots arranged like a bumpy field inside the box, it is difficult to stay at the level of the box edge. Your eyes will start converging a bit and suddenly it can firmly lock onto a pair of dots just about anywhere in the field.
As you converge your eyes a bit further they easily find additional dot-pairs to lock onto. At each of those levels of convergence the entire field of dots can be seen without a visual conflict between your eyes. But the dots all seem to be in this bumpy up/down pattern. That’s because they have been placed randomly by small amounts. Differences in the horizontal placement makes them appear at different depths in the image.
When you get to the range where the hidden figure, in this case a number, is resting, those dots are not bumped up/down like the others. This allows you to stay locked at that level and explore the flat surface which you found inside all the dots. It’s easy to go beyond that flat surface and go deeper, but as you do, all the dots get paired up differently, and the bumpy up/down pattern returns, as if that flat area is transparent or has simply gone away. Its only seen when you are converged at close to the right…