Long before he met the real-life little girl who inspired him to write Alice in Wonderland under the pseudonym Lewis Carroll (January 27, 1832–January 14, 1898), Charles Lutwidge Dodgson was a prominent mathematician and logician. In addition to his scientific bend and his love of language, Carroll also had strong convictions about what it takes to cultivate a healthy mind. He married all three of these passions in the introductory essay to one of his textbooks on Symbolic Logic, included in the fantastic 1973 volume A Random Walk in Science (public library) — the same compendium of scientists’ irreverent ideas and comments that gave us this wonderful 1969 essay on how laughter saves us from the despotism of automation and that goes on to explore such curiosities as the physics of holding up a strapless dress and the math of why any horse actually has an infinite number of legs.

Under the unambiguous title "How to Learn," Carroll offers four pointers on cultivating critical thinking and digesting even the most challenging of passages while reading.

The Learner, who wishes to try the question fairly, whether this little book does, or does not, supply the materials for a most interesting mental recreation, is earnestly advised to adopt the following Rules:

1. Begin at the beginning, and do not allow yourself to gratify a mere idle curiosity by dipping into the book, here and there. This would very likely lead to your throwing it aside, with the remark "This is much too hard for me!, and thus losing the chance of adding a very large item to your stock of mental delights. This Rule (of not dipping) is very desirable with other kinds of books—-such as novels, for instance, where you may easily spoil much of the enjoyment you would otherwise get from the story, by dipping into it further on, so that what the author meant to be a pleasant surprise comes to you as a matter of course. Some people, I know, make a practice of looking into Vol. III first, just to see how the story ends: and perhaps it is as well just to know that all ends happily—that the much-persecuted lovers do marry after all, that he is proved to be quite innocent of the murder, that the wicked cousin is completely foiled in his plot and gets the punishment he deserves, and that the rich uncle in India (Qu. Why in India? Ans. Because, somehow, uncles never can get rich anywhere else) dies at exactly the right moment—-before taking the trouble to read Vol. I.

   This, I say, is just permissible with a novel, where Vol. III has a meaning, even for those who have not read the earlier part of the story; but, with a scientific book, it is sheer insanity: you will find the latter part hopelessly unintelligible, if you read it before reaching it in regular course.

2. Don’t begin any fresh Chapter, or Section, until you are certain that you thoroughly understand the whole book up to that point, and that you have worked, correctly, most if not all of the examples which have been set. So long as you are conscious that all the land you have passed through is absolutely conquered, and that you are leaving no unsolved difficulties behind you, which will be sure to turn up again later on, your triumphal progress will be easy and delightful. Otherwise, you will find your state of puzzlement get worse and worse as you proceed, till you give up the whole thing in utter disgust.
3. When you come to any passage you don’t understand, read it again: if you still don’t understand it, read it again: if you fail, even after three readings, very likely your brain is getting a little tired. In that case, put the book away, and take to other occupations, and next day, when you come to it fresh, you will very likely find that it is quite easy.
4. If possible, find some genial friend, who will read the book along with you, and will talk over the difficulties with you. Talking is a wonderful smoother-over of difficulties. When I come upon anything—in Logic or in any other hard subject—that entirely puzzles me, I find it a capital plan to talk it over, aloud, even when I am all alone. One can explain things so clearly to one’s self! And then, you know, one is so patient with one’s self: one never gets irritated at one’s own stupidity!

If, dear Reader, you will faithfully observe these Rules, and so give my little book a really fair trail, I promise you, most confidently, that you will find Symbolic Logic to be one of the most, if not the most, fascinating of mental recreations!

[…]

Mental recreation is a thing that we all of us need for our mental health; and you may get much healthy enjoyment, no doubt, from Games… But, after all, when you have made yourself a first-rate player at any one of these Games, you have nothing real to show for it, as a result! You enjoyed the Game, and the victory, no doubt, at the time: but you have no result that you can treasure up and get real good out of. And, all the while, you have been leaving unexplored a perfect mine of wealth. Once master the machinery of Symbolic Logic, and you have a mental occupation always at hand, of absorbing interest, and one that will be of real use to you in any subject you may take up. It will give you clearness of thought—the ability to see your way through a puzzle—the habit of arranging your ideas in an orderly and get-at-able form—and, more valuable than all, the power to detect fallacies, and to tear to pieces the flimsy illogical arguments, which you will so continually encounter in books, in newspapers, in speeches, and even in sermons, and which so easily delude those who have never taken the trouble to master this fascinating Art. Try it. That is all I ask of you!

A Random Walk in Science is a gem in its entirety. Complement this particular bit with Carroll on feeding the mind and his tips on dining etiquette, then revisit this 1936 guide to the 14 ways to acquire knowledge.

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