The Kakeya Conjecture, Memory, and Above The Clouds
One Spring, a Whole World¶
In a few days I'll be at the Calabazas Branch of the San José Public Library, talking with readers about Above The Clouds.
The book covers more than forty years.
It runs from the springs, mud walls, and stones of the Sichuan mountains, through school, cities, and the internet, to Singapore, Wall Street, Silicon Valley, and artificial intelligence.
Sixty-some thousand characters.
Three hundred sixty pages in the Chinese edition.
Several decades of a life, pressed into one book.
But I know that when a ninety-minute book talk ends, no one will walk out remembering all those pages.
Not even after reading the whole thing.
Someone may remember only a spring.
Someone remembers the father.
Someone remembers a childhood punishment.
Someone remembers a classmate, a teacher, an exam.
Someone may remember a single sentence.
And someone else, closing the book, can no longer recount the plot at all, yet is left with a vague feeling:
that they, too, once lived there as a child.
Which raises an interesting question:
How do we actually remember a book?
And, one level deeper:
How do we remember our own lives?
The answer may be stranger than we'd expect.
The brain may never have tried to store a complete world.
What it stores are cues from which a world can unfold again.
1. What Remains of a Book¶
Reading is a strange thing.
A month after you finish a two-hundred-thousand-word novel, most of its sentences are gone.
Ten years later, you may not remember the characters' names.
But one scene is still there.
Years after reading Dream of the Red Chamber, you may not be able to untangle who is related to whom, yet you still remember Daiyu burying the fallen petals.
From Water Margin, you've long lost track of the hundred and eight outlaws and their nicknames, but you still remember Wu Song killing the tiger on Jingyang Ridge.
A song from childhood works the same way.
You can't sing it all the way through.
You have the lyrics wrong.
But the moment the intro plays, an afternoon that vanished twenty years ago comes back.
The sunlight.
The room.
Someone's face.
Even the smell of the air.
Where do these things come back from?
They can't possibly have been sitting in some corner of the brain as high-definition video.
If a life really were recorded by a camera, the visual, auditory, tactile, spatial, linguistic, and emotional input we take in every day would add up to a staggering volume.
The brain has no reason to keep that kind of "raw data."
It seems to take a different approach:
keep a few cues, and regenerate the rest when needed.
Not storing the world,
but storing a way back to it.
2. How Many Directions Can a Needle Hide?¶
In 2025, mathematicians Hong Wang and Joshua Zahl resolved the Kakeya conjecture in three dimensions.
The problem sounds simple.
Take a set in three-dimensional space, with one requirement:
for every direction in space, the set contains a unit line segment pointing in that direction.
The question is:
how "small" can such a set be?
Intuition says: line segments can be arbitrarily thin, so why not squeeze every direction into some tiny region?
That is exactly where the Kakeya problem gets its hold on you.
The set's volume really can shrink to zero.
But Wang and Zahl proved that in three dimensions, as long as the set contains a unit segment in every direction, its Hausdorff and Minkowski dimensions must still be 3.
In other words:
it can be almost nothing in the sense of measure, yet it cannot collapse in the sense of dimension.
That is deeply counterintuitive.
Small
and low-dimensional
are not the same thing.
A set can have no volume and still carry the full complexity of three dimensions.
When I first really understood this result, what came to mind wasn't geometry.
It was memory.
A line has to be drawn here first, of course.
The Kakeya conjecture proves nothing about how the brain stores memories.
A nervous system is not a Kakeya set.
There is no isomorphism here in the mathematical sense.
But the two raise a strikingly similar question:
Can a very small representation retain the structure needed for a vast space to unfold again?
That question runs all the way from mathematics into neuroscience.
3. Memory Is Reconstruction, Not Recording¶
In 2026, Eleanor Spens and Neil Burgess published a compelling model of memory in Nature Communications: Hippocampo-neocortical interaction as compressive retrieval-augmented generation.
They frame the collaboration between the hippocampus and the neocortex as a kind of compressive retrieval-augmented generation — a phrase anyone working in AI today will hear as RAG.
The basic idea:
an experience doesn't need to be stored verbatim in the hippocampus.
The hippocampus can keep a compressed episodic representation,
while the neocortex holds a world model built up slowly from vast amounts of experience.
When you remember,
the compressed representation is retrieved,
and with the structure the neocortex has already learned,
something far richer is generated.
This matters a great deal,
because it means:
compression does not make information disappear.
Much of that information already lives inside the reconstruction system.
Say I give you one word:
classroom.
I haven't told you the color of the walls.
Or how the desks are arranged.
Or where the windows are.
Or how big the blackboard is.
Yet your brain has already unfolded a space.
Because classroom is only an index.
The real bulk of the structure has been sitting in your experience for decades.
So an index can be small
not because the whole world has been crammed into it,
but because:
the index only tells the brain where to look.
The rest
is filled in by a model that already exists.
4. From a Low-Dimensional Pointer to a High-Dimensional World¶
In July 2026, another striking study of the human brain came out.
Casper Kerrén, Sebastian Michelmann, and Christian Doeller analyzed memory activity in twelve patients undergoing intracranial EEG monitoring: Hippocampal ripples initiate cortical dimensionality expansion for memory retrieval.
The picture they propose fits in a single line:
low-dimensional hippocampal representation → high-dimensional cortical representation.
During successful recall, the researchers saw the representational dimensionality of cortical activity increase after hippocampal ripples, and this expansion went along with faster responses and with reinstatement of the target memory. The paper goes so far as to describe the hippocampal representation as a lower-dimensional pointer to a higher-dimensional cortical one.
Twelve patients can't establish that all memory follows one simple law, of course.
But the result opens a beautiful window.
What we call "remembering"
may not be pulling a complete file out of a warehouse.
It's more like this:
a small cue fires first,
and then the brain begins to unfold.
Sound comes back.
Color comes back.
Space comes back.
Relationships come back.
Feelings come back.
Until, for a moment,
a past world stands there again.
Remembering is more a verb
than a noun.
Memory does not store the past.
Memory regenerates it.
5. Above The Clouds Does the Same Thing¶
With all this in mind, I looked back at how Above The Clouds is written, and found that the research happens to bear out choices I made long ago.
It isn't an autobiography in the usual, densely packed sense.
One word makes a chapter.
Two words make a section.
Short sentences make lines.
White space makes paragraphs.
Much goes unexplained.
Many people appear and are soon gone.
Some events are just one gesture.
One sentence.
One look.
One small object.
People have asked me:
Why not explain more of the background?
Why not tell readers what became of this person?
Why not write out everything going on in your head at the time?
I now think the answer may be simple.
Because that isn't how anyone actually keeps a life.
When I remember my childhood,
I'm not pulling up 4K footage from forty years ago.
What comes back first may be nothing more than a spring.
Once the spring is there,
the mountain appears.
Once the mountain is there,
the path appears.
Once the path is there,
primary school, my classmates, my father, my mother, the Sichuan of those years
gradually all come back.
One index,
unfolding a world.
So what Above The Clouds really preserves may never have been forty years of my life.
That can't be preserved.
What it preserves are a few hundred entrances like these.
A spring.
A water vat.
Kneeling as punishment.
A car.
A classroom.
A classmate.
An exam.
A job.
A street.
A night.
A goodbye.
Each of these is small on its own.
Sometimes only a few lines.
But behind each one lies a vast world.
Words are not the world.
Words are coordinates for finding your way back into it.
6. White Space Is Not an Absence of Information¶
Seen this way, white space means something different.
We usually treat restraint in literature as an aesthetic:
say less,
and let the reader feel the rest.
But from the standpoint of memory, it may mean something more.
The reader never needed the author to encode the whole world.
The reader has a world model of their own.
There are two lines in the book:
Food sat on the table until it was cold
and still my father didn't eat.
I didn't say how much money we were short, or what was going through my father's mind.
One reader fills those lines with their own father.
Another thinks of the hardest year their own family went through.
A third may not think of a father at all,
and suddenly remember a silent person from many years ago.
What the author gives is finite.
The space the reader unfolds can be enormous.
So one book,
in a hundred heads,
becomes a hundred different books.
In that sense,
literature's most important skill may not be describing the world as completely as possible,
but finding the indexes that unfold most efficiently.
How much experience
can a few words open?
How many memories
can one gesture wake?
How many lives
can one object connect?
Good writing
is sometimes not the densest in information,
but the one that
opens the largest space of feeling with the fewest words.
7. Why I Want to Explain Above The Clouds Less and Less¶
On the afternoon of September 26, I'll be at the Calabazas Branch of the San José Public Library, talking with readers about Above The Clouds.
The library has set aside ninety minutes for the event, and posted the Chinese edition on the event page so people can read it beforehand.
I've been thinking since
that the least necessary thing I could do there
is stand up front and tell everyone
"what this passage really means."
If a book only works once its author has explained it,
it hasn't really left its author yet.
The interesting question is:
What did you remember?
One reader may remember the mountains.
Another, the exams.
A father remembers the child.
A child remembers the father.
Some see education.
Some see social mobility.
Some see technology.
Some see loss.
Some see a person who never stopped climbing.
And some reach the end and remember only this:
But here there is no wind or rain and no clear sky either.
These readings don't have to agree.
Reading is itself an act of reconstruction.
The author supplies the indexes.
The reader supplies their own world.
Only where the two meet
does that reader's own Above The Clouds take shape.
So what makes a book talk worthwhile isn't the author announcing the answers.
It's dozens of different brains
following the cues one book has left behind
and unfolding dozens of different worlds.
8. What We Really Remember May Never Have Been Knowledge¶
In the age of AI, all this takes on another layer.
We used to think of learning as
packing as much knowledge into our heads as possible.
Memorize the formulas.
Memorize the dates.
Memorize the vocabulary.
Memorize the definitions.
Memorize book after book.
Today, most external knowledge is a search away.
AI can store and process far more text than any one person could read in a lifetime.
And so the human question starts to shift.
What matters is no longer only:
How much do I remember?
but:
What is worth remembering?
What deserves to become an index?
Someone who truly understands mathematics doesn't need to remember every proof.
They know where the key structures are.
A good engineer doesn't need to memorize every API.
They know which direction to look when the system breaks.
Someone who has lived forty years doesn't keep every day either.
What really stays
is usually just a handful of nodes.
But touch one of those nodes
and an entire era comes back.
That is not a flaw in memory.
It may be the most ingenious thing about it.
9. A Life May Be One Long Act of Indexing¶
Once you think this way,
life suddenly becomes interesting.
When we're young, we feel
we can't afford to forget anything,
we should own everything,
we should keep it all.
Only later do we find
that keeping a whole world is impossible.
Houses change.
We leave cities.
Companies disappear.
Friends drift apart.
Parents grow old.
Many voices we swore we'd never forget
eventually slip away.
But some very small things stay.
A table.
A tree.
A bowl of rice.
A sentence.
A backward glance.
Someone's laugh.
They are like coordinates.
Most days they hardly exist.
But one day
some chance stimulus brushes against one,
and a world from decades ago spreads out again in your mind.
So what we really own
may never have been the past.
What we own
are only a few paths back to it.
10. A Small Index Can Reopen a World¶
What the Kakeya conjecture gives us is a rigorous geometric fact:
a set can be vanishingly small in measure
and still keep its full dimension.
Memory science studies something else:
a compressed hippocampal representation
may, during recall, help trigger higher-dimensional, distributed cortical activity.
They are not the same theory.
Neither one proves the other.
But set side by side,
they produce a curious structural echo:
Small is not the same as poor.
Compressed is not the same as gone.
A tiny entrance may open onto a vast space.
A book is the same.
A life is so long,
and what makes it into a book
can only ever be a few fragments.
A book is so thick,
and what stays with a reader
may also be only a few fragments.
That doesn't mean the rest was written for nothing.
Perhaps just the opposite.
Writing that truly matters
doesn't ask the reader to keep it forever.
It only leaves a few coordinates.
Many years later,
when a person reaches some point in their life
and meets a similar rain,
a similar failure,
a similar departure,
a similar mountain,
those coordinates suddenly light up.
And a book closed long ago
opens again.
An era that has passed
unfolds again.
Someone you thought you had forgotten
stands before you again.
That's when I understood:
The brain does not store the world.
It stores the cues to unfold it again.
And what literature can do
may be the very same thing.
What we write down
was never a whole life.
Only, after a life has passed through,
a few entrances left behind,
waiting for the day
someone passes by
and gives one a light touch.
And then
the whole world comes back.