POEM 3: Spiral of the Uncertain: Embracing the Unseen

Spiral of the Uncertain: Embracing the Unseen

- John Paul 

I. Invocation - Not Cold Mathematics

Not from cold mathematics alone

did the universe loosen into flame

not because mathematics is false,

but because they are lenses, not the same.

a disciplined way of seeing,

not the whole of what is seen.

Equations trace the paths that relate,

yet never exhaust the pulse of the whole;

not from drifting where formulas wait,

nor from frozen calculus void of soul.

Not from blind equation drifting without witness,

nor from frozen calculus turning in vacancy,

but from a depth that thinks

and endures its own thinking;

a source vast enough

to enter fracture,

to enter wound,

so the fragile might learn to stand.

A Logos that breathes through fire and desire,

reason that tenderly loves, not tires.

II. Descent - Layered Fires

We walk through layered fires,

circles of longing, circles of desire,

descending through attachments

we once called love,

we once admired.

Betrayal does not strike like thunder;

it comes as a voice we knew,

speaking differently under the sky,

the hand once trusted slipping through,

the sweetness once shared turning askew.

We are squares in Flatland

arguing about dimensions

we cannot see,

laughing at spheres

until the sky opens

and depth is glimpsed.

Testis interior, Sākṣī;

the silent sky within,

watching anger like shifting weather,

watching ambition rise and fall

like galaxies spinning together.

The invisible confesses itself

through consequence,

revealing the currents

beneath our small certainties.

III. Matter Becoming 

On a silica plate so smooth

it seems almost to deny friction,

a migrating trace separates and resolves.

A single traveling stain confirms completion.

No eye has witnessed

the hidden exchange of electrons,

yet the faint path declares

that bonds have broken,

that new unions hold.

In flasks where carbon rehearses its grammar,

rings open, chains extend,

nucleophiles seek their moment,

electrophiles yield,

intermediates flicker and vanish;

brief, unstable, necessary.

Mechanism is choreography:

arrows drawn to honor

motions we infer but cannot behold.

Some reactions require heat,

some require patience,

some must be quenched

before they shatter the vessel.

Change is not measurement;

it is metamorphosis,

not reduction,

but re-patterning,

true novelty not in smallness

but in transformed response,

a dance of matter,

a pulse of form,

a whisper of becoming,

made manifest.

IV. Fields and Thresholds 

Beyond the flask, the scale expands.

Electrons drift through ordered lattices,

no longer bound to single addresses,

described not as points alone

but as spread, as shimmer, as possibility;

patterns of probability

threaded through structure.

Energy gathers into bands;

permitted regions of motion,

separated by silent intervals

where no state may rest.

When the gap narrows, flow awakens.

When wide, resistance prevails.

Statistical mechanics listens

not to one particle

but to multitudes.

Temperature becomes collective restlessness.

Entropy counts unseen arrangements.

Equilibrium is not stillness;

it is dynamic balance,

a swing, a drift,

a whisper between order and undoing.

Gradual pressure gathers unseen,

until fracture declares itself.

Critical points arrive suddenly,

after seasons of accumulation.

The world is not linear:

a slight perturbation ripples, amplifies,

feedback loops tighten, spiral, coil.

Chaos births pattern;

systems fold into strange attractors.

Predictability survives

only as pattern within unpredictability,

a lattice of possibility

waving across the infinite.

V. The Brain - Repetition and Release

And the brain;

pliant architect of itself;

rewires along repeated pathways.

Fear rehearsed becomes corridor.

Courage practiced becomes bridge.

The depth that thinks

now thinking through neuron,

entering fracture again;

this time in us.

Practice inscribes structure

in living tissue.

Rest, too, obeys law.

In darkness, the mind resets its circuits.

Memory settles into deeper strata.

Without surrender to stillness,

No lasting creation endures.

Act fully and unclench.

VI. Ecologies - Forest and Body

Among trees,

the air is not empty.

Invisible compounds drift from leaves;

molecules that quiet inflammation,

that tune immune vigilance.

The forest does not preach;

it recalibrates.

Our bodies remember green.

Isolation thins resilience.

Love too is ecological.

It is not possession

but mutual flourishing.

A friend who becomes brother without shared blood.

A woman who becomes sister through loyalty.

Standing beside family in crisis

because belonging is chosen.

Like stable molecules sharing electrons

without losing identity,

love balances bond and freedom.

Where chemistry traces pathways

and physics maps fields of possibility,

we ask a further question:

If matter follows patterned relation,

if mind rewires through repetition,

if systems bend toward equilibrium

through cost and release—

might consciousness itself

also admit alignment?

Not imposed from outside,

not interruption of law,

but coherence so complete

that it appears luminous.

The spiral narrows here;

from cosmos

to carbon

to cortex

to character.

And sometimes,

in history,

that alignment takes flesh.

VII. Sacred Embodiments - Alignment in Flesh

Across history, certain lives

embody this pattern vividly.

The Lamb of Logos

born under threat, carried into exile,

trembling in a garden,

yet aligning human will with deeper purpose;

divine in form, yet human in doubt,

facing uncertainty even in whispered prayers,

learning courage in the shadow of fear.

The Blue Child on Peacock

born in captivity, hidden from violence,

speaking clarity amid a battlefield,

playful, human, yet embodying cosmic consciousness;

confused, questioning, testing the path,

yet teaching us that clarity emerges through trial.

The Rose who resists in the green doom

orphaned early, shaken in solitude,

learning to trust the voice that unsettled and summoned him,

divine presence wrestling with human fear,

uncertain from the first breath,

yet showing that steadfastness grows from struggle.

Even gods, clothed in flesh, know the weight of doubt,

and in their hesitation, their trials, their uncertainty,

they show us the way.

Beneath the rituals, beyond the traditions,

lies this deeper meaning;

that courage, like a river, carves its course through shadow,

that alignment is learned in fracture,

and that fragility is not weakness, but passage to transcendence.

Divinity does not erase humanity;

it flows through it.

Not as domination,

but as coherence under strain,

as light emerging through the cracks of doubt,

as faith born in the laboratory of uncertainty.

VIII. Wound and Refinement

Sin is more than surface stain.

It is rupture in alignment,

distortion in relationship.

For distortion left unattended

repatterns the whole field.

And yet;

what can deform

can also be transformed.

It cannot be wiped away by denial;

it must be treated from within.

As infection spreads through tissue,

so concealed fault reshapes the soul

until courage consents to incision

and mercy becomes medicine.

Carbon under pressure becomes diamond.

Consciousness sheds ignorance

through cycles of refinement.

Life is purposeful becoming.

IX. Love (Second Movement)

For love is more than intimacy.

It is understanding before touch,

recognition before embrace.

To know another’s fracture

and guard it, not use it.

To share strength

without creating dependence.

Closeness without suffocation.

Care without control.

As lattices hold structure

without crushing motion,

When the inner gap narrows,

trust conducts again.

When widened by fear,

resistance prevails.

Affection must balance

bond and freedom.

Innocence is not ignorance.

It is knowing one’s capacity for ruin

and choosing restraint.

Wisdom is self-mastery.

X. The Witness

We think,

and then we examine the thinker.

A lantern turned inward

studies the flame that holds it.

Anger passes like weather.

Ambition swells and thins.

Behind them

a wider sky remains.

Witness within the storm.

Sky behind the weather.

We are small;

yet capable of turning awareness upon itself.

Perhaps the real transformation

is not matter shrinking into strangeness,

but consciousness widening

until fear loosens its claim.

The universe expands.

So can we.

XI. Spiral Conclusion

The universe continues outward;

not cold mathematics alone,

but relation widening.

And you;

storm of elements,

maker of models,

witness of your own becoming;

are not asked for certainty,

but for alignment.

Not sterile arithmetic;

but courage entering fracture.

The depth that thinks

now thinks through you.

And in probability and ash,

in exile and awakening,

in fracture and forgiveness,

a deeper order breathes;

unfinished,

yet quietly healing

toward wholeness.

As the spiral of the poem draws to a close, the reader has traversed layers of thought, matter, and feeling through fracture, alignment, and awakening. From the patterns of the cosmos to the inner workings of the mind, and from the bonds of love to the courage of the human spirit, a path has been traced: one that does not seek certainty, but embraces possibility.

It is here, at this threshold between reflection and experience, that the poem offers its final invitation:

The poem invites the reader to move with uncertainty, rather than against it. Fractures, doubts, and challenges are not obstacles, but openings, opportunities for growth, reflection, and courage. By observing the mind and its patterns, we discover the possibility of transformation. Through patience, practice, and careful attention, alignment can emerge, within ourselves, in our relationships, and in the world around us. Life is not a problem to be solved, but a process to be lived. True strength arises when we engage with the unknown, allowing it to shape, guide, and refine us.

Math in Alice in wonderland

 Math in Alice in wonderland 

"Who in the world am I?' Ah, that's the great puzzle!"

In chapter 2: Pool of tears

"Let me see: four times five is twelve, and four times six is thirteen, and four times seven is—oh dear! I shall never get to twenty at that rate! However, the Multiplication Table doesn’t signify.."

In the pool of tears, Alice’s attempts at simple multiplication leave her confounded. In regular math, four times six would never be thirteen. We work in base ten, meaning we have zero-through-nine digits, and then when we get to ten we move over and put a one in the next column. However, if you play around with the base systems, things can change. While Alice was calculating in base ten, in this new, crazy wonderland, her answers slipped into higher base systems. People are at risk of getting lost like Alice when they stay anchored to original standards or beliefs in the face of changing systems.

In chapter 5: Advice from a caterpillar

By this point, Alice has fallen down a rabbit hole and eaten a cake that has shrunk her to a height of just 3 inches. Enter the Caterpillar, smoking a hookah pipe, who shows Alice a mushroom that can restore her to her proper size. The snag, of course, is that one side of the mushroom stretches her neck, while another shrinks her torso. She must eat exactly the right balance to regain her proper size and proportions. While some have argued that this scene, with its hookah and “magic mushroom”, is about drugs, I believe it’s actually about what Dodgson saw as the absurdity of symbolic algebra, which severed the link between algebra, arithmetic, and his beloved geometry.

The first clue may be in the pipe itself: the word “hookah” is, after all, of Arabic origins, like “algebra”, and it is perhaps striking that Augustus De Morgan, the first British mathematician to lay out a consistent set of rules for symbolic algebra, uses the original Arabic translation in Trigonometry and Double Algebra, which was published in 1849. He calls it “al jebr e al mokabala” or “restoration and reduction” – which almost exactly describes Alice’s experience. The restoration was what brought Alice to the mushroom: she was looking for something to eat or drink to “grow to my right size again”, and reduction was what actually happened when she ate some: she shrank so rapidly that her chin hit her foot. De Morgan’s work explained the departure from universal arithmetic – where algebraic symbols stand for specific numbers rooted in a physical quantity – to that of symbolic algebra, where any “absurd” operations involving negative and impossible solutions are allowed, provided they follow an internal logic. Symbolic algebra is essentially what we use today as a finely honed language for communicating the relations between mathematical objects, but Victorians viewed algebra very differently. Even the early attempts at symbolic algebra retained an indirect relation to physical quantities. De Morgan wanted to lose even this loose association with measurement and proposed instead that symbolic algebra should be considered as a system of grammar. “Reduce” algebra from universal arithmetic to a series of logical but purely symbolic operations, he said, and you will eventually be able to “restore” a more profound meaning to the system – though at this point he was unable to say exactly how. 

In chapter 6: Pig and Pepper

"The baby grunted again, and Alice looked very anxiously into its face to see what was the matter with it. There could be no doubt that it had a very turn-up nose, much more like a snout than a real nose; also its eyes were getting extremely small, for a baby: altogether Alice did not like the look of the thing at all, “—but perhaps it was only sobbing,” she thought, and looked into its eyes again, to see if there were any tears. No, there were no tears. “If you’re going to turn into a pig, my dear,” said Alice, seriously, “I’ll have nothing more to do with you. Mind now!” The poor little thing sobbed again, (or grunted, it was impossible to say which,) and they went on for some while in silence. Alice was just beginning to think to herself, “Now, what am I to do with this creature when I get it home?” when it grunted again, so violently, that she looked down into its face in some alarm. This time there could be no mistake about it: it was neither more nor less than a pig...."

Carroll craftily paly down the work of mathematician Jean-Victor Poncelet in this section. Poncelet talked about the transformation of geometric figures and perpetuated the belief that geometric figures undergoing a continuous transformation, without any sudden changes or subtractions, are likely to retain some of their original features. However, this might not necessarily be physically tangible and would be possible only through the use of things like imaginary numbers. The baby transforming into a pig is Carroll’s way of showing how absurd and grotesque he found this idea. You can either be a baby or a pig, but no amount of tiny changes can make you both.

In chapter 7: At the mad tea party

"Alice sighed wearily. “I think you might do something better with the time,” she said, “than waste it in asking riddles that have no answers.” “If you knew Time as well as I do,” said the Hatter, “you wouldn’t talk about wasting it. It’s him.” “I don’t know what you mean,” said Alice. “Of course, you don’t!” the Hatter said, tossing his head contemptuously. “I dare say you never even spoke to Time!” “Perhaps not,” Alice cautiously replied: “but I know I have to beat time when I learn music.” “Ah! that accounts for it,” said the Hatter. “He won’t stand beating. Now, if you only kept on good terms with him, he’d do almost anything you liked with the clock. “Is that the way you manage?” Alice asked. The Hatter shook his head mournfully. “Not I!” he replied. “We quarreled last March—— just before he went mad, you know——” (pointing with his teaspoon at the March Hare,). “And ever since that,” the Hatter went on in a mournful tone, “he won’t do a thing I ask! It’s always six o’clock now.” 

 “Take some more tea,” the March Hare said to Alice, very earnestly. “I’ve had nothing yet,” Alice replied in an offended tone, “so I can’t take more.” “You mean, you can’t take less,” said the Hatter: “it’s very easy to take more than nothing.”"

The tea party floats ambiguously, seemingly around a tree, and is interspersed with butterflies and oversized insects. In Carroll’s tea party, the Doormouse, the Mad Hatter, and the March Hare are all going in a circle around a table in a perpetual tea time as Carroll took away the fourth member of their party, Time. In the mid-1800s, mathematician William Rowan Hamilton had come up with a new number system called quaternions. This was a sort of coordinate system based on four terms, three that designate a place or spatial dimensions, and one that designated, or so Hamilton decided time. With these four terms, Hamilton could describe rotation in a three-dimensional universe. He could only do this, though, if he added that fourth component. Without “time”, they would keep rotating round and round in a plane, like the hands of a clock. Carroll was miffed that someone could simply appropriate time as a fourth dimension. By taking away time, he left the other three to keep going around in circles forever, like an incomplete quaternion.

The logic was another weapon of choice for Carroll, and the text of Alice in Wonderland is widely sprayed with riddles and logical statements. The Mad Hatter is trying to tell Alice that she can have more tea, given that she has not yet had anything to drink, but what she cannot do is “take less.” It seems like a typical maths word problem right. 

If you the book now, with this mathematical viewpoint you will be able to appreciate Lewis Carroll for his hidden math work in a fantasy fiction story. This is how the mind of a person who understands maths looks.

Note on the author Lewis Carrol

Charles Lutwidge Dodgson, better known by his pen name Lewis Carroll, was an English writer of children's fiction, notably Alice's Adventures in Wonderland and its sequel Through the Looking-Glass. He was noted for his facility with wordplay, logic, and fantasy. The poems Jabberwocky and The Hunting of the Snark are classified in the genre of literary nonsense. He was also a mathematician, photographer, inventor, and Anglican deacon.

Carroll developed the earliest modern use of today's 'logic trees', a graphical technique for determining the validity of complex arguments that he called the 'method of trees'. This was a step towards automated approaches to solving multiple connected problems of logic.

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