In an interview in the 1970s, Bell summarized his view of the decades long debates:
Einstein was consistent, clear, down-to-earth and wrong.
Bohr was inconsistent, unclear, willfully obscure and right.
arXiv papers
Optimal Bounds for Open Addressing Without Reordering
Martin Farach-Colton, Andrew Krapivin, William Kuszmaul
https://arxiv.org/abs/2501.02305
In this paper, we revisit one of the simplest problems in data structures: the task of inserting elements into an open-addressed hash table so that elements can later be retrieved with as few probes as possible. We show that, even without reordering elements over time, it is possible to construct a hash table that achieves far better expected search complexities (both amortized and worst-case) than were previously thought possible. Along the way, we disprove the central conjecture left by Yao in his seminal paper Uniform Hashing is Optimal. All of our results come with matching lower bounds.
Undergraduate Upends a 40-Year-Old Data Science Conjecture
Tiny Pointers
Michael A. Bender, Alex Conway, Martín Farach-Colton, William Kuszmaul, Guido Tagliavini
https://arxiv.org/abs/2111.12800
This paper introduces a new data-structural object that we call the tiny pointer. In many applications, traditional \( log n \) -bit pointers can be replaced with \( O(log n) \) -bit tiny pointers at the cost of only a constant-factor time overhead. We develop a comprehensive theory of tiny pointers, and give optimal constructions for both fixed-size tiny pointers (i.e., settings in which all of the tiny pointers must be the same size) and variable-size tiny pointers (i.e., settings in which the average tiny-pointer size must be small, but some tiny pointers can be larger). If a tiny pointer references an element in an array filled to load factor , then the optimal tiny-pointer size is bits in the fixed-size case, and expected bits in the variable-size case. Our tiny-pointer constructions also require us to revisit several classic problems having to do with balls and bins; these results may be of independent interest.
Using tiny pointers, we revisit five classic data-structure problems: the data-retrieval problem, succinct dynamic binary search trees, space-efficient stable dictionaries, space-efficient dictionaries with variable-size keys, and the internal-memory stash problem. These are all well-studied problems, and in each case tiny pointers allow for us to take a natural space-inefficient solution that uses pointers and make it space-efficient for free.
Du-Hwang Characteristic Area: Catch-22
A.O.Ivanov, A.A.Tuzhilin
https://arxiv.org/abs/1402.6079
The paper is devoted to description of two interconnected mistakes generated by the gap in the Du and Hwang approach to Gilbert-Pollack Steiner ratio conjecture.
My English Phrases List - Jannuary - 2026
put down
put him down with a sharp retort
put down the gossip
he has the annoying habit of putting down others under the guise of offering constructive criticism
one in a million
Thanks for all the help you’ve given me. You’re one in a million.
a chance in a million
Though Mrs. Busssman fully acquainted with this story, she thought that there was a chance in a million that she might be right. A few days later, she sent a boy to the workman to ask him if his name was Hans Bussman. Needless to say, the man’s name was Hans Bussman and he really was Franz’s long-lost brother. - Lesson 36 A chance in a million, New Concept English Book 3: Developing Skills
as every schoolboy/schoolchild knows
As every schoolboy knows, the earth revolves around the sun.
hammer out
In the year from 1925 to 1927, they were hammering out a mathematically logical physics to describe how the quantum world operated (quantum mechanics) and struggling to come up with a sensible explantion for why the quantum world behaved as it did (quantum theory). They succeeded at one but fumbled the other. - The Quantum Ten, by Sheilla Jones
alma mater
Ehrenfest recalled his first meeting with Schrödinger, back in 1912 at the Boltzmann library in the University of Vienna, his old alma mater. - The Quantum Ten, by Sheilla Jones
at sea
I said we had to do two things. First is to be a bastion. The second is to be a beacon – an example to a world at sea. - Building Canada together: Prime Minister Carney delivers remarks at the Citadelle of Québec
snowed in
The road was snowed in.
How to survive if you’re snowed in during a winter storm
Don’t wait until you’re snowed in to order a shovel — get one now. — Amanda Tarlton, USA TODAY, 23 Dec. 2020
My English Words List - Jannuary - 2026
whatever
pronoun
take whatever you want
whatever he says, they won’t believe him
adjective
There’s no evidence whatever to support your theory.
adverb
go see a movie, watch TV,—whatever
whatsoever
pronoun or adjective
- whatever
matter-of-fact
adjective
All his life Paul Dirac had a simple and matter-of-fact way of talking.
half-truth
noun
Unfortunately this is only a half-truth.
longan
noun
gulp
verb
She told him not to gulp his food.
introverted
adjective
a quiet, introverted child who likes to sit at home and read books
Even Ehrenfest, with his keen interest in people, had been unable to get the introverted Dirac to open up. - The Quantum Ten: A Story of Passion, Tragedy, Ambition and Science, by Sheilla Jones
tacit
adjective
tacit consent
Magic requires tacit cooperation of the audience with the magician—an abandonment of skepticism … the willing suspension of disbelief. — Carl Sagan, The Demon-Haunted World, 1996
crunch
noun
Crunch, crunch, crunch, his feet sank into the snow.
interdisciplinary
adjective
Modern mathematics is a very social, networked experience. The trend is very much towards interdisciplinary, highly collaborative research. - Terence Tao
retell
verb
The movie retells the story of Romeo and Juliet.
paddle
noun
table tennis paddle
pothole
noun
by and large
adverb
But by and large, the American people are good people. — ABC News, 28 Dec. 2025
canola
noun
canola oil
Use canola oil or another neutral cooking oil in place of olive oil. — Kimberly Holland, Southern Living, 13 Dec. 2025
quintessential
adjective
Beethoven is considered the quintessential bridge between the Classical and Romantic eras.
Heisenberg was the quintessential handsome German lad, fair-haired and blue-eyed. - The Quantum Ten, by Sheilla Jones
slop
noun
The rise of AI has raised concerns about low-quality content, aka “AI slop.”
watching the usual slop on TV
cleaned the slops out of the cow barn
verb
She slopped coffee on her sweater.
technocrat
noun
Carney is ideologically characterized as a centrist, technocrat, and a Blue Grit Liberal.
beacon
noun
These countries are beacons of democracy.
frosty
adjective
cordial
adjective
a cordial welcome
flounder
noun
saury
noun
puffer fish
noun
tuna
noun
lemur
noun
meerkat
noun
bald
adjective
He covered his bald head with a baseball cap.
He had gone completely bald by the age of 30.
Bald eagle nests are often very large in order to compensate for size of the birds. The largest recorded nest was found in Florida in 1963, and was measured at 2.9 m (9.5 ft) wide and 6.1 m (20 ft) deep.
Solitude
Laugh, and the world laughs with you;
Weep, and you weep alone;
For the sad old earth must borrow its mirth,
But has trouble enough of its own.
Sing, and the hills will answer;
Sigh, it is lost on the air;
The echoes bound to a joyful sound,
But shrink from voicing care.
Rejoice, and men will seek you;
Grieve, and they turn and go;
They want full measure of all your pleasure,
But they do not need your woe.
Be glad, and your friends are many;
Be sad, and you lose them all,—
There are none to decline your nectared wine,
But alone you must drink life’s gall.
Feast, and your halls are crowded;
Fast, and the world goes by.
Succeed and give, and it helps you live,
But no man can help you die.
There is room in the halls of pleasure
For a large and lordly train,
But one by one we must all file on
Through the narrow aisles of pain.
Winter Walk
She left the hut and bright log fire at noon
And walked outside on crisp white winter snow
To find the iced slopes shadowed like the moon,
The wild wood desolate and bare below;
The red trees wet, adrift with icy flow,
The evergreens with glassy needled leaves;
A bloodstone veined red and white this view weaves.
But lifted off the path like crystal spheres
There lay cut prints of glinting stylised forms
Of birds not seen, large sparkling twig-like spears,
And squirrel pricks where fox’s paw transforms
White single roses out of petal storms;
While keltic scrolls transcribe where birds had been:
Then stamped in ice another track was seen.
A slight right turn of foot. She sensed him there,
Tree like with raincoat shouldered, fine large looks,
A four-armed god. From this sweet honeyed snare
She turned, upspraying, Marsh Tits, Finch and Rooks,
Through brushwood hills, seeing by frosted brooks
His footprints: these she retraced like a bride
With loaves and wood returned to his keen side.
Proverbs
If a job’s worth doing, it’s worth doing well.
No sweet without sweat.
No pains, no gains.
He that is once born, once must die.
No man knows when he shall die, although he knows he must die.
A dead bee makes no honey.
A dead mouse feels no cold.
Dead dogs bark not.
Praise a fair day at night.
Men fear death as children fear to go in the dark.
We must live by the living, not by the dead.
The devil is not black as he is painted.
Sooner begun, sooner done.
No time like the present.
One good turn deserves another.
Good hand, good hire.
Like fault, like punishment.
Such answer as man gives, such will he get.
Every man after his fashion.
Every one to his taste.
So many men, so many options.
All roads lead to Rome.
Diligence makes an expert workman.
Business is the salt of life.
No bees, no honey; no work, no money.
First come, first served.
Early to bed and early to rise, makes a man healthy, wealthy and wise.
Bread is the staff of life.
The belly carries the legs.
Eat to live and not live to eat.
After dinner sit awhile, after supper walk a mile.
An apple a day keeps the doctor away.
There is no royal road to learning.
Never too late to learn.
Everything must have a beginning.
Everything has an end.
Garbage in, garbage out.
Practise what you preach.
Example is better than precept.
Practice makes perfect.
Keep your mouth shut and your eyes open.
Let bygones be bygones.
A friend in need is a friend indeed.
God helps them that help themselves.
A good heart conquers ill fortune.
All happiness is in the mind.
Laughter is the best medicine.
A merry heart goes all the way.
Great hopes make great men.
Hope for the best.
Tomorrow is another day.
Every man has his faults.
To err is human.
Forgive and forget.
Every path has a puddle.
Life is short and time is swift.
Life begins at forty.
It is easy to be wise after the event.
Better be safe than sorry.
Everyman for himself, and God for us all.
Skill is no burden.
A little body often harbours a great soul.
Many small maka a great.
Time and tide wait for no man.
Now is now, and then was then.
Travel broadens the mind.
The language of truth is simple.
It is too late to call back yesterday.
Time flies.
Time will tell.
Times change and we with them.
My English Phrases List - December - 2025
be supposed to
You are supposed to listen to your parents.
slip/escape someone’s mind
His name slips/escapes my mind at the moment.
pay off
I finally paid off the loan.
beat the rush
I suggested that we get there by 11:30 to beat the lunchtime rush.
miss the boat
missed the boat on buying stock in the company early on
kettle of fish
I’m used to paddling, but those rapids are a whole other kettle of fish.
My English Words List - December - 2025
snowsuit
noun
arrogance
noun
Programming is the best antidote to arrogance I’ve come across — I make so many errors that I am continually reminded of my own fallibility.
gut
noun
The guts uphold the heart, and not the heart the guts.
ballpoint pen
noun
curiosity
noun
Curiosity killed the cat.
Curiosity is endless, restless, and useless.
chip
noun
The best carpenter makes the fewest chips.
wood chips were spread over the ground between the plants
caravan
noun
bought a caravan and drove cross-country to California
toadstool
noun
- a fungus that has an umbrella-shaped cap, one that is poisonous or unfit for food
A toadstool generally refers to a poisonous mushroom.
schoolchild
noun
Almost every schoolchild in America learns Lincoln was born in a Kentucky log cabin. — Frank Witsil, Detroit Free Press, 13 July 2023
soggy
adjective
Be sure to keep the soil moist but not soggy. — Sheryl Geerts, Better Homes & Gardens, 15 Dec. 2025
pal
noun
We’ve been pals since we were kids.