the more..., the more...结构中，前面是从句，后面是主句。这种结构有一个 变体：主句在前，从句在后，此时主句中的比较级不用定冠词，也不前置。例如：

The more you eat, the fatter you will get. 从句在前，主句在后。

You will get fatter the more you eat. 主句在前从句在后。

网友的这个句子就是采用的变体，主句在前：

Secrets tend to take up more brain space the more one tries not to think about them.

= The more one tries not to think about secrets, the more brain space they tend to take up.

one在此为不定代词，意为“一个人”。