As a Prelude to idea-making, a poem…

To the Insight,

and all the messy roads to get it right.

During [these] periods of relaxation after concentrated intellectual activity, the intuitive mind seems to take over and can produce the sudden clarifying insights which give so much joy and delight. — Fritjof Capra, physicist

Winkler, Peter. Mathematical Puzzles: A Connoisseur’s Collection (p. 1). Taylor & Francis — A. Kindle Edition

I tinker with, attack a problem in all sorts of ways, hours, weeks, a long time it often takes.

Then I surrender to enough effort for the day, time to rest, give it a break,

Not having left the maze, lost the feeling of play, the fun to engage…

A temporary state! It just did not come out today!

I need some time to ruminate on the question at stake.

And then… a long while has passed,

After a lot of sleep and rest, and it really seems I did forget, that issue that inside lasts.

Out of nowhere there comes the curiosity, out of the blue, an insight perhaps?

Tickling my kid back, a motivation and playfulness, go figure that.

Back to the many sheets of paper, the scribblings and aftermath.

The knowledge bricks I failed to connect, I take them back from the drawer and

Back to see it all on top of my desk.

Fresh new eyes, a now clean mind…

Navigating a maze, hitting dead-end routes, oh, discovery painful steps… Now I want my payback.

A piece of paper, why am I now so upbeat and with a light-weighted head?

Let me get this straight, I won’t rest until it breaks, I retell myself.

There’s no way I will look for help — in friends, classrooms, bookshelves,

Why am I now thinking too much? It feels no issues remain,

A strange feeling, the torment is over, it now belongs to the past.

That reenacting my pattern-hunter had a why, and not a warning it’d come back

It was not to dwell and things complicate, should I erase all that mess?

Should I? Those wrong turns, all that stress, headaches, and all those drafts?

I will leave it as a souvenir, it may come in handy later on, looking back.

A record of the way I used to think, and the process of insight, the mistakes, a good guess here and there.

May it remind my future self, great ideas don’t come out of nowhere.

At least not often here in my head.

I solved it, I solved it! I scream and laugh! Around the house, to anyone I come across!

Yes! I nailed it! How about that!?

Meanwhile, not aware my mind seemingly elsewhere.

The solution came after much pressure, my relaxation, allowing for the dots to self-connect

I found a way, I found a way, to think about it as clear as a sunny day.

Those are moments of joy, and I write about to celebrate.

(Francisco Costa)

After the prelude, here’s a reflection on the value of questioning and entertaining doubt

Doubt is the vestibule which all must pass before they can enter the temple of wisdom. When we are in doubt and puzzle out the truth by our own exertions, we have gained something that will stay by us and will serve us again. But if to avoid the trouble of the search we avail ourselves of the superior information of a friend, such knowledge will not remain with us; we have not bought, but borrowed it. — C. C. Colton

Winkler, Peter. Mathematical Puzzles: A Connoisseur’s Collection . Taylor & Francis — Kindle Edition.

In that very same spirit, I wish to give salience to how questions should be treasured in ways that answers are just by-products of what really matters — The Journey of Discovery, Or The Pleasure of Finding Things Out, as Feynman would say. Would you entertain an answer to a very personal puzzle given to you on a silver plate? I reckon you would not. What’s more, if you understand something, you don’t need to remember about it. (Credits to The Art of Problem Solving team)

And in that same key, there lies the central skill of learning to cope with, seize the most out of, those branching points where we find ourselves vexed with a hard problem.

Those are moments of paradox, conflicts, doubts, insecurity, even crises.

The shift, and it’s most certainly easier said than done, is the art of turning the way we think from seeing problems at those bifurcating moments, to a reframing of them into opportunities for growth, development, self-discovery, reinvention, rebirth.

There’s so much in ruminating on questions that matter to oneself!

When the famous mathematician David Hilbert (I hope it was really him in case) was asked about why he didn’t attack the Fermat’s Last Problem (Now Fermat’s Last Theorem) he is said to have replied as follows:

— Why would I kill the goose that lays the golden egg?

The famous book Fermat’s Enigma, as well as the BBC documentary on the long road, around three hundred years till the solution was finally reached, gives a beautiful perspective on how many great ideas come out of a puzzle,a seemingly insurmountable obstacle.

Fermat claimed to have a proof of what was then a conjecture, but we aren’t really sure to this very day whether or not he actually had a demonstration for the now celebrated theorem.

As a matter of fact, the proof that was crafted after so many contributions and collaborations through centuries involve ideas Fermat could not possibly have had access back then. Well, I won’t bend to either side. The key concept is that good questions can give birth to a multiverse of ideas, new questions, theories, new vistas.

I don’t wish to take the value of answers away. Good answers lead to further insights and questions. The overarching theme is the value of the action that links the birth of a quest and its resolution.

“It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment. When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again.”― Gauss

In addition, you can enjoy competence without comprehension.

By that I simply mean one is allowed for making mistakes, falling and standing up again. Once, at the occasion of my grandfather’s seventieth birthday, a couple of cartoonists were among our guests.

My grandfather Aldu was a writer, humorist, author of a couple of books and more. But I digress.

I mentioned to one of those cartoonists that I enjoyed drawing when I was a kid but then [regretfully] stopped doing so.

He replied, in turn ― But, why don’t you draw any longer?

[since it was something you had fun with and seems to feel nostalgic about]

Then what I said was, well, he got me.

I didn’t, actually, I don’t need to know how to draw in order to do so. I just pick a pencil and paper, and have fun, which is what counts, I think.

So, there was this style around cartoonists, and other artists drawing caricatures and other kinds of art, where one would not really get concerned about the “right way” of doing it. Actually, this is all around, you see artists with their own DNA, doing their thing with a spirit, not working with a middle layer of a technique, which I don’t reckon as being worthless, I do think it matters a lot.

But the point is that, as I do play my guitar, in my humble way of doing so, I like the feeling of doing it even with all the “wrong” fingerings, tempo and whatnot. I draw with lots of correcting traces, sketches of sorts, not really based on geometry. [in the case of drawing] it is not the case I do it based on precise abiding by musical scores, when I start playing an acoustic guitar. I make my mistakes along my drawings and playing, and actually there’s no such a thing to a huge extent while I do those things. I want to learn more and get better at those artful endeavors, but I am able to get a kick out of what I am able to do so far.

In fact, what I may, while engaged in the task, be conscious of as sort of straying away from a desired tone or sketching, is picking up those “errors” of sorts, and develop on them.

Let’s say I drew a line and screw a previous image I had in mind. It is often a thing to do not to erase the traces, and develop on top of them. Most times I screw up my drawings, for instance, but it doesn’t really matter, to me, at those moments, at least.

I am not knowledgeable on either of those skills, I just have fun with them, or used to have, actually.

And my recollection is that of having fun despite not mastering all it takes an artist to improvise.

The playful spirit, the shutting down of pressures of how it should be done, just forget about all those things, in case it makes you, or myself feel good.

I recall once being with a friend who happens to be a mathematician.

One day I expressed concerns on forgetting previous knowledge of many things I reckoned I needed to know.

He told myself the following:

“Do you think that I recall everything or most of what I learned!? You should care for knowing how to learn. Learning to explore, to find things out, to rediscover when necessary, know where to look for or what to do when the desired piece of information-knowledge is called for.” It was something along those lines.

“Your preparation for the real world is not in the answers you’ve learned, but in the questions you’ve learned how to ask yourself.” ― Bill Watterson

Finally, I beg you to entertain a comics entitled A Day at The Park, rather an enlightening one!

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