The mathematical and the intuitive mind

I am reading  Pascal’s Thoughts and Minor Works, and asking myself why I did not read this before.

His first thought in the book is about the difference between intuitive thinking and mathematical thinking. Intuitive thinking is also that which I believe it’s called Poetic Knowledge.

I very much believe that many of us may be applying mathematical thinking to some places in life where it doesn’t belong. Mathematical thinking is based on axioms, principles, definitions, and reasoning, and the omission of one principle leads to error. Another book I am reading, Intuitive Eating, confirms that tendency of applying Mathematical thinking to food, thus all the diets and counting calories, making food rules, and numbing that intuition we all have to know what to eat and when to eat it.

Intuitive thinking is based on, quote,

“principles that are scarcely seen; they are felt rather than seen; there is the greatest difficulty in making them felt by those who do not of themselves perceive them. These principles are so fine and so numerous that a very delicate and very clear sense is needed to perceive them, and to judge rightly and justly when they are perceived, without for the most part being able to demonstrate them in order as in mathematics; because the principles are not known in the same way, and because it would be an endless matter to undertake it.”

The world of practices (eating, homeschooling, parenting) doesn’t belong to mathematical principles, which is not the same as saying that it does not have principles. I think we get confused and believe that, if we don’t apply mathematical reasoning to our life, we’ll be left in a jungle, a mad world, or even worse, an immoral one. We fail to see that our world is governed by principles, and reasoning is to be practiced by us, but once that the principle is understood, the practices that will ensue shouldn’t be seen as steps to solve an algebra problem.

This means that, from having an adequate weight, to, say, teaching your children effectively, we need to have a keen eye, and be able to perceive these no so tangible principles, sharpen our senses, and judge them justly and rightly.

But, Pascal tells us,

dull minds are never either intuitive or mathematical.

Mathematicians who are only mathematicians have exact minds, provided all things are explained to them by means of definitions and axioms; otherwise they are inaccurate and insufferable, for they are only right when principles are quite clear.

And men of intuition who are only intuitive cannot have the patience to reach to first principles of things speculative and conceptual, which they have never seen in the world, and which are altogether out of the common.

Practices inform and illustrate those speculative and conceptual principles that make up our philosophy of life. Our life principles spill to all our areas of life (nutrition, education, parenting, etc.), but the practices should never be excised with mathematical rigor, this will lead to legalism (diets, success formulas), yet they require discipline and order (it is not about floating in thin air). As I said in another post, plans (and any formulas),  or practices, do not validate intuitive principles the same way a mathematical theorem can be proofed and thus validated. Intuitive principles, though, should always be attached to practices. It is crucial to remember that the practices of intuitive principles look similar as much as they honor the principles they illustrate, and different as much as those who are acting upon them.

When you look at principles, judge rightly and justly, when you look at practices, judge rightly and justly as well, never doubting your allegiance to the principles because of the difference in the outcome.


One thought on “The mathematical and the intuitive mind

  1. I haven’t read much of Pascal but he’s on my list. I’ll have to look into this one you’ve been reading/read. Thanks for posting this!


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