The Torah says:
הַנִּסְתָּרֹת--לַיהוָה, אֱלֹהֵינוּ; וְהַנִּגְלֹת לָנוּ וּלְבָנֵינוּ, עַד-עוֹלָם--לַעֲשׂוֹת, אֶת-כָּל-דִּבְרֵי הַתּוֹרָה הַזֹּאת.
The secret things belong unto the Lord our God, but the things that are revealed belong unto us and to our children for ever, that we may do all the words of this law. [Deut. 29:28]
What are these secret areas of knowledge we must stay away from? How can we recognize them beforehand so we don't try to inquire into them? We discover things all the time, by studying Torah or secular subjects.
Only hints are provided in the Sources, not enough to fully answer the question. For example:
-You shall not eat of the tree of knowledge of good and evil. [Gen. 2:16-17] That's clear -- it was a physical object to stay away from.
-Job 38 and Ecclesiastes 11:5 tell us there are specific things we CANNOT know. That's also easy to follow. We can inquire all we want, but we will learn nothing.
-Don't study mysticism until after the age of forty. [Shakh on Shulchan Arukh Yoreh Deah 246:6]
The Gemara is a tad more specific:
Everyone who tries to know the following four things, it would have been better for him if he had never come into the world: What is above, what is below, what was before [creation], and what will be after [all is destroyed]. [Hagigah 2.1 -- 11b]
The Gemara in Hagigah quotes the apocryphal book of Ben Sira:
Do not seek out the things that are too hard for you, and do not inquire in the things that are hidden from you. Instruct yourself in what is permitted; you have no business with the secret things. [Hagigah 13a; Ecclesiasticus 3:21-22]
Any other hints on what these "secret things" are? Why they are not explicitly listed in the Sources?