by Chelsea Martin

Eating food from McDonald’s is mathematically impossible.
Because before you can eat it, you have to order it.
And before you can order it, you have to decide what you want.
And before you can decide what you want, you have to read the menu.
And before you can read the menu, you have to be in front of the menu.
And before you can be in front of the menu, you have to wait in line.
And before you can wait in line, you have to drive to the restaurant.
And before you can drive to the restaurant, you have to get in your car.
And before you can get in your car, you have to put clothes on.
And before you can put clothes on, you have to get out of bed.
And before you can get out of bed, you have to stop being so depressed.
And before you can stop being so depressed, you have to understand what depression is.
And before you can understand what depression is, you have to think clearly.
And before you can think clearly, you have to turn off the TV.
And before you can turn off the TV, you have to free your hands.
And before you can free your hands, you have to stop masturbating.
And before you can stop masturbating, you have to get off.
And before you can get off, you have to imagine someone you really like with his pants off, encouraging you to explore his enlarged genitalia.
And before you can imagine someone you really like with his pants off encouraging you to explore his enlarged genitalia, you have to imagine that person stroking your neck.
And before you can imagine that person stroking your neck, you have to imagine that person walking up to you looking determined.
And before you can imagine that person walking up to you looking determined, you have to choose who that person is.
And before you can choose who that person is, you have to like someone.
And before you can like someone, you have to interact with someone.
And before you can interact with someone, you have to introduce yourself.
And before you can introduce yourself, you have to be in a social situation.
And before you can be in a social situation, you have to be invited to something somehow.
And before you can be invited to something somehow, you have to receive a telephone call from a friend.
And before you can receive a telephone call from a friend, you have to make a reputation for yourself as being sort of fun.
And before you can make a reputation for yourself as being sort of fun, you have to be noticeably fun on several different occasions.
And before you can be noticeably fun on several different occasions, you have to be fun once in the presence of two or more people.
And before you can be fun once in the presence of two or more people, you have to be drunk.
And before you can be drunk, you have to buy alcohol.
And before you can buy alcohol, you have to want your psychological state to be altered.
And before you can want your psychological state to be altered, you have to recognize that your current psychological state is unsatisfactory.
And before you can recognize that your current psychological state is unsatisfactory, you have to grow tired of your lifestyle.
And before you can grow tired of your lifestyle, you have to repeat the same patterns over and over endlessly.
And before you can repeat the same patterns over and over endlessly, you have to lose a lot of your creativity.
And before you can lose a lot of your creativity, you have to stop reading books.
And before you can stop reading books, you have to think that you would benefit from reading less frequently.
And before you can think that you would benefit from reading less frequently, you have to be discouraged by the written word.
And before you can be discouraged by the written word, you have to read something that reinforces your insecurities.
And before you can read something that reinforces your insecurities, you have to have insecurities.
And before you can have insecurities, you have to be awake for part of the day.
And before you can be awake for part of the day, you have to feel motivation to wake up.
And before you can feel motivation to wake up, you have to dream of perfectly synchronized conversations with people you desire to talk to.
And before you can dream of perfectly synchronized conversations with people you desire to talk to, you have to have a general idea of what a perfectly synchronized conversation is.
And before you can have a general idea of what a perfectly synchronized conversation is, you have to watch a lot of movies in which people successfully talk to each other.
And before you can watch a lot of movies in which people successfully talk to each other, you have to have an interest in other people.
And before you can have an interest in other people, you have to have some way of benefiting from other people.
And before you can have some way of benefiting from other people, you have to have goals.
And before you can have goals, you have to want power.
And before you can want power, you have to feel greed.
And before you can feel greed, you have to feel more deserving than others.
And before you can feel more deserving than others, you have to feel a general disgust with the human population.
And before you can feel a general disgust with the human population, you have to be emotionally wounded.
And before you can be emotionally wounded, you have to be treated badly by someone you think you care about while in a naive, vulnerable state.
And before you can be treated badly by someone you think you care about while in a naive, vulnerable state, you have to feel inferior to that person.
And before you can feel inferior to that person, you have to watch him laughing and walking towards his drum kit with his shirt off and the sun all over him.
And before you can watch him laughing and walking towards his drum kit with his shirt off and the sun all over him, you have to go to one of his outdoor shows.
And before you can go to one of his outdoor shows, you have to pretend to know something about music.
And before you can pretend to know something about music, you have to feel embarrassed about your real interests.
And before you can feel embarrassed about your real interests, you have to realize that your interests are different from other people’s interests.
And before you can realize that your interests are different from other people’s interests, you have to be regularly misunderstood.
And before you can be regularly misunderstood, you have to be almost completely socially debilitated.
And before you can be almost completely socially debilitated, you have to be an outcast.
And before you can be an outcast, you have to be rejected by your entire group of friends.
And before you can be rejected by your entire group of friends, you have to be suffocatingly loyal to your friends.
And before you can be suffocatingly loyal to your friends, you have to be afraid of loss.
And before you can be afraid of loss, you have to lose something of value.
And before you can lose something of value, you have to realize that that thing will never change.
And before you can realize that that thing will never change, you have to have the same conversation with your grandmother forty or fifty times.
And before you can have the same conversation with your grandmother forty or fifty times, you have to have a desire to talk to her and form a meaningful relationship.
And before you can have a desire to talk to her and form a meaningful relationship, you have to love her.
And before you can love her, you have to notice the great tolerance she has for you.
And before you can notice the great tolerance she has for you, you have to break one of her favorite china teacups that her mother gave her and forget to apologize.
And before you can break one of her favorite china teacups that her mother gave her and forget to apologize, you have to insist on using the teacups for your imaginary tea party. And before you can insist on using the teacups for your imaginary tea party, you have to cultivate your imagination.
And before you can cultivate your imagination, you have to spend a lot of time alone.
And before you can spend a lot of time alone, you have to find ways to sneak away from your siblings.
And before you can find ways to sneak away from your siblings, you have to have siblings.
And before you can have siblings, you have to underwhelm your parents.
And before you can underwhelm your parents, you have to be quiet, polite and unnoticeable.
And before you can be quiet, polite and unnoticeable, you have to understand that it is possible to disappoint your parents.
And before you can understand that it is possible to disappoint your parents, you have to be harshly reprimanded.
And before you can be harshly reprimanded, you have to sing loudly at an inappropriate moment.
And before you can sing loudly at an inappropriate moment, you have to be happy.
And before you can be happy, you have to be able to recognize happiness.
And before you can be able to recognize happiness, you have to know distress.
And before you can know distress, you have to be watched by an insufficient babysitter for one week.
And before you can be watched by an insufficient babysitter for one week, you have to vomit on the other, more pleasant babysitter.
And before you can vomit on the other, more pleasant babysitter, you have to be sick.
And before you can be sick, you have to eat something you’re allergic to.
And before you can eat something you’re allergic to, you have to have allergies.
And before you can have allergies, you have to be born.
And before you can be born, you have to be conceived.
And before you can be conceived, your parents have to copulate.
And before your parents can copulate, they have to be attracted to one another.
And before they can be attracted to one another, they have to have common interests.
And before they can have common interests, they have to talk to each other.
And before they can talk to each other, they have to meet.
And before they can meet, they have to have in-school suspension on the same day.
And before they can have in-school suspension on the same day, they have to get caught sneaking off campus separately.
And before they can get caught sneaking off campus separately, they have to think of somewhere to go.
And before they can think of somewhere to go, they have to be familiar with McDonald’s.
And before they can be familiar with McDonald’s, they have to eat food from McDonald’s.
And eating food from McDonald’s is mathematically impossible.

McDonalds Is Impossible

veggie

veggie

noun

• vegetable

In addition to vitamin A, the veggie also provides lutein and zeaxanthin, two nutrients that are critical for eye health. — Emily Laurence, Good Housekeeping, 28 July 2022

carton

carton

noun

• a box or container usually made of cardboard and often of corrugated cardboard

several cartons of books

a carton of orange juice

double

adjective

an egg with a double yolk

triple

adjective

• being three times as great or as many

quadruple

quadruple

adjective

• being four times as great or as many

quintuple

quintuple

adjective

• being five times as great or as many

sextuple

sextuple

adjective

• being six times as great or as many

septuple

septuple

adjective

• being seven times as great or as many

octuple

octuple

adjective

• being eight times as great or as many

tug-of-war

tug-of-war

noun

• a contest in which two teams pull against each other at opposite ends of a rope with the object of pulling the middle of the rope over a mark on the ground

Tug of war

tambourine

tambourine

noun

• a shallow drum with one head and loose metal disks at the sides that is played by shaking or striking with the hand

Tambourine

syringe

syringe

noun

Syringe

sledgehammer

sledgehammer

noun

sit-up

sit-up

noun

Sit-up

sequoia

sequoia

noun

Sequoiadendron giganteum

Redwoods are a type of sequoia.

sedan

sedan

noun

• a 2- or 4-door automobile seating four or more persons and usually having a permanent top

Sedan (automobile)

scorpion

scorpion

noun

Scorpion

scooter

scooter

noun

Kick scooter

receptionist

receptionist

noun

Receptionist

pout

pout

verb

• to show displeasure by thrusting out the lips or wearing a sullen expression
• to show displeasure by pushing out the lips

She pouted her lips and stared at him angrily.

The boy didn’t want to leave—he stomped his feet and pouted.

Facial expression

oak

oak

noun

-

The table is solid oak.

Oak

noose

noose

noun

Noose

nightingale

nightingale

noun

Common nightingale

hydrant

hydrant

noun

Fire hydrant

grill

grill

noun

She put the hamburgers on the grill.

Barbecue grill

gear

gear

noun

Gear

dribble

dribble

verb

dribble a basketball

dribble a puck

He skillfully dribbled the soccer ball towards the goal.

Dribbling

detergent

detergent

noun

We have tried different laundry detergents.

We have tried different laundry detergents.

boomerang

boomerang

noun

Boomerang

selfie

selfie

noun

• n image of oneself taken by oneself using a digital camera especially for posting on social networks

Selfie

limerick

limerick

noun

• a light or humorous verse form of five chiefly anapestic verses of which lines 1, 2, and 5 are of three feet and lines 3 and 4 are of two feet with a rhyme scheme of aabba

Lines 1, 2 and 5 of a limerick rhyme with one another, as do Lines 3 and 4. — Pat Myers, Washington Post, 18 Aug. 2022

Limerick (poetry)

stanza

stanza

noun

• a division of a poem consisting of a series of lines arranged together in a usually recurring pattern of meter and rhyme

Stanza

The stanza in poetry is analogous with the paragraph in prose

prophesize

prophesize

verb

Others say he could prophesize the future

dike

dike

noun

• a bank of earth constructed to control water

Levee

kith

kith

noun

• familiar friends, neighbors, or relatives

kith and kin

kin

kin

noun

• one’s relatives : kindred

our neighbors and their kin

close kin

They are her distant kin.

invited all of his kith and kin to his graduation party

Problem

2129. Capitalize the Title

C++

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class Solution {
public:
    string capitalizeTitle(string title) {
        int len = title.length();
        int start = 0;
        int end = 0;
        for(int i = 0; i < len; i++) {
            if (title.at(i) == ' ') {
                end = i-1;
                if (end - start <= 1) {
                    for(int j=start; j<=end; j++)
                        title.at(j) = tolower(title.at(j));
                }
                else {
                    title.at(start) = toupper(title.at(start));
                    for(int j=start+1; j<=end; j++)
                        title.at(j) = tolower(title.at(j));
                }
                start = i + 1;
            }
            if (i == len-1) {
                end = len -1;
                if (end - start <= 1) {
                    for(int j=start; j<=end; j++)
                        title.at(j) = tolower(title.at(j));
                }
                else {
                    title.at(start) = toupper(title.at(start));
                    for(int j=start+1; j<=end; j++)
                        title.at(j) = tolower(title.at(j));
                }
            }
        }
        return title;
    }
};

Submission Detail

• 200 / 200 test cases passed.
• Runtime: 3 ms, faster than 69.22% of C++ online submissions for Capitalize the Title.
• Memory Usage: 6.3 MB, less than 74.15% of C++ online submissions for Capitalize the Title.

Java

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class Solution {
    public String capitalizeTitle(String title) {
        String[] arr = title.split(" ");
        for(int i=0; i < arr.length; i++) {
            if (arr[i].length() <= 2)
                arr[i] = arr[i].toLowerCase();
            else {
                char[] charArr = arr[i].toCharArray();
                charArr[0] = Character.toUpperCase(charArr[0]);
                for(int j=1; j < charArr.length; j++)
                    charArr[j] = Character.toLowerCase(charArr[j] );
                arr[i] = new String(charArr);
            }
        }
        return String.join(" ", arr);
    }
}

Submission Detail

• 200 / 200 test cases passed.
• Runtime: 10 ms, faster than 47.35% of Java online submissions for Capitalize the Title.
• Memory Usage: 42.8 MB, less than 67.17% of Java online submissions for Capitalize the Title.

A few words about the lives of Euler and Riemann:

Analogies

Both Euler and Riemann received their early education at home, from their fathers, who were protestant ministers, and who both were hoping that their sons will become like them, pastors. At the age of fourteen, Euler attended a Gymnasium in Basel, while his parents lived in Riehen, a village near the city of Basel. At about the same age, Riemann was sent to a Gymnasium in Hanover, away from his parents. During their Gymnasium years, both Euler and Riemann lived with their grandmothers. They both enrolled a theological curriculum (at the Universities of Basel and G¨ottingen respectively), before they obtain their fathers’ approval to shift to mathematics.

Differences

Euler’s productive period lasted 57 years (from the age of 19, when he wrote his first paper, until his death at the age of 76). His written production comprises more than 800 memoirs and 50 books. His Opera Omnia fill over eighty volumes. He worked on all domains of mathematics (pure and applied) and physics(theoretical and practical) that existed at his epoch. He also published on geography, navigation, machine theory, ship building, telescopes, the making of optical instruments, philosophy, theology and music theory. Besides his research books, he wrote elementary schoolbooks, including a well-known book on the art of reckoning. The publication of his collected works was decided in 1907, the year of his bicentenary, the first volumes appeared in 1911, and the edition is still in progress (two volumes appeared in 2015), filling up to now more than 80 large volumes.

Unlike Euler’s, Riemann’s life was short. He published his first work at the age of 25 and he died at the age of 39. Thus, his productive period lasted only 15 years. His collected works stand in a single slim volume. Yet, from the points of view of the originality and the impact of their ideas, it would be unfair to affirm that either of them stands before the other. They both had an intimate and permanent relation to mathematics and to science in general.

• Looking backward: From Euler to Riemann
• If we had to mention a single mathematician of the eighteenth century, Euler would probably be the right choice. For the nineteenth century, it would be Riemann. And Gauss is the main figure astride the two centuries.
• Euler died on 18 September 1783.
• Riemann was born on 17 September 1826.

by Ron Padgett

The morning coffee. I’m not sure why I drink it. Maybe it’s the ritual of the cup, the spoon, the hot water, the milk, and the little heap of brown grit, the way they come together to form a nail I can hang the day on. It’s something to do between being asleep and being awake. Surely there’s something better to do, though, than to drink a cup of instant coffee. Such as meditate? About what? About having a cup of coffee. A cup of coffee whose first drink is too hot and whose last drink is too cool, but whose many in-between drinks are, like Baby Bear’s porridge, just right. Papa Bear looks disgruntled. He removes his spectacles and swivels his eyes onto the cup that sits before Baby Bear, and then, after a discrete cough, reaches over and picks it up. Baby Bear doesn’t understand this disruption of the morning routine. Papa Bear brings the cup close to his face and peers at it intently. The cup shatters in his paw, explodes actually, sending fragments and brown liquid all over the room. In a way it’s good that Mama Bear isn’t there. Better that she rest in her grave beyond the garden, unaware of what has happened to the world.

Prose Poem (“The morning coffee.”)

There are well over 371 Pythagorean Theorem proofs, originally collected and put into a book in 1927, which includes those by a 12-year-old Einstein (who uses the theorem two decades later for something about relativity), Leonardo da Vinci and President of the United States James A. Garfield.

Elisha Scott Loomis, an eccentric mathematics teacher from Ohio, spent a lifetime collecting all known proofs of the Pythagorean Theorem and writing them up in The Pythagorean Proposition, a compendium of 371 proofs. The manuscript was prepared in 1907 and published in 1927. A revised second edition appeared in 1940, and this was reprinted by the National Council of Teachers of Mathematics in 1968 as part of its‘ Classics in Mathematics Education’ series. Loomis received literally hundreds of new proofs from after his book was released up until his death, but he could not keep up with his compendium. As for the exact number of proofs, no one is sure how many there are.

• Pythagoras: Everyone knows his famous theorem, but not who discovered it 1000 years before him
• the sense that it reveals the connection between length and area that is at the heart of the theorem. (Albert Einstein)
• Euclid I 47 is often called the Pythagorean Theorem, called so by Proclus.
• Garfield’s aptitude for mathematics extended to a notable proof of the Pythagorean theorem, which he published in 1876.

cram

cram

verb

He crammed the suitcase with his clothes.

tarmac

tarmac

noun

• a tarmacadam road, apron, or runway

tarmacadam

tarmacadam

noun

• a pavement constructed by spraying or pouring a tar binder over layers of crushed stone and then rolling

Tarmacadam

Tarmacadam is a road surfacing material made by combining crushed stone, tar, and sand.

myopia

myopia

noun

She wears eyeglasses to correct her myopia.

Myopia

glide

glide

verb

The swans glided over the surface of the lake.

We watched the skiers glide down the slope.

glitter

glitter

noun

Glitter

clumsy

clumsy

adjective

I have very clumsy hands and tend to drop things.

a clumsy error

I’m sorry about spilling your wine—that was very clumsy of me.

platypus

platypus

noun

• a small water-dwelling mammal of Australia that lays eggs and has webbed feet, dense fur, and a bill that resembles that of a duck

Platypus

glee

glee

noun

• great joy

They were dancing with glee.

prep

prep

verb

• [short for prepare] : to get ready

She spent all night prepping for the test.

It took me about 20 minutes to prep the vegetables.

cryptocurrency

cryptocurrency

noun

Cryptocurrency

android

android

noun

• a mobile robot usually with a human form

heir

heir

noun

Riemann was an heir of Euler.

tutorial

tutorial

noun

An online tutorial gives basic instructions for using the software.

decent

decent

adjective

it’s very decent of them to help

Do the decent thing and confess.

decent grades

jot

jot

verb

• to write briefly or in a hurry

I jot down their names and requests.

He paused to jot a few notes on a slip of paper.

jot this down

agnostic

agnostic

noun

political agnostics

Agnosticism

comforter

comforter

noun

• a thick bed covering made of two layers of cloth containing a filling (such as down)

Comforter

bleach

bleach

verb

• to make white by removing the color or stains from

bleach clothing

wicker

wicker

noun

Wicker

whirlpool

whirlpool

noun

Whirlpool

webcam

webcam

noun

Webcam

rinse

rinse

verb

rinse out the mouth

I rinsed my face in the sink.

He washed the dishes and then rinsed them thoroughly.

Rinse, a step in washing

Rinse cycle of a washing machine

Rinse cycle of a dishwasher

Rinse

tollbooth

tollbooth

noun

Maybe the most straightforward problem on leetcode. Super simple. Its intention?

Problem

2235. Add Two Integers

C#

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public class Solution {
    public int Sum(int num1, int num2) {
        return num1 + num2;
    }
}

Submission Detail

• 262 / 262 test cases passed.
• Runtime: 25 ms, faster than 86.75% of C# online submissions for Add Two Integers.
• Memory Usage: 26.7 MB, less than 8.86% of C# online submissions for Add Two Integers.

Java

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class Solution {
    public int sum(int num1, int num2) {
        return num1 + num2;
    }
}

Submission Detail

• 262 / 262 test cases passed.
• Runtime: 0 ms, faster than 100.00% of Java online submissions for Add Two Integers.
• Memory Usage: 40.7 MB, less than 78.42% of Java online submissions for Add Two Integers.

JavaScript

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/**
 * @param {number} num1
 * @param {number} num2
 * @return {number}
 */
var sum = function(num1, num2) {
    return num1 + num2;
};

Submission Detail

• 262 / 262 test cases passed.
• Runtime: 136 ms, faster than 5.20% of JavaScript online submissions for Add Two Integers.
• Memory Usage: 41.4 MB, less than 97.69% of JavaScript online submissions for Add Two Integers.

by Will Allen Dromgoole

An old man going a lone highway,
Came, at the evening cold and gray,
To a chasm vast and deep and wide.
Through which was flowing a sullen tide
The old man crossed in the twilight dim,
The sullen stream had no fear for him;
But he turned when safe on the other side
And built a bridge to span the tide.

“Old man,” said a fellow pilgrim near,
“You are wasting your strength with building here;
Your journey will end with the ending day,
You never again will pass this way;
You’ve crossed the chasm, deep and wide,
Why build this bridge at evening tide?”

The builder lifted his old gray head;
“Good friend, in the path I have come,” he said,
“There followed after me to-day
A youth whose feet must pass this way.
This chasm that has been as naught to me
To that fair-haired youth may a pitfall be;
He, too, must cross in the twilight dim;
Good friend, I am building this bridge for him!”

• The Bridge Builder
• The Bridge Builder

In the late 19th century, scientists were trying to solve a mystery. They found that if they had a vacuum tube like this one and applied a high voltage across it, something strange happened. They called them cathode rays. But the question was: What were they made of?

In England, the 19th-century physicist J.J. Thompson conducted experiments using magnets and electricity, like this. And he came to an incredible revelation. These rays were made of negatively charged particles around 2,000 times lighter than the hydrogen atom, the smallest thing they knew. So Thompson had discovered the first subatomic particle, which we now call electrons.

Now, at the time, this seemed to be a completely impractical discovery. I mean, Thompson didn’t think there were any applications of electrons. Around his lab in Cambridge, he used to like to propose a toast: “To the electron. May it never be of use to anybody.”

He was strongly in favor of doing research out of sheer curiosity, to arrive at a deeper understanding of the world. And what he found did cause a revolution in science. But it also caused a second, unexpected revolution in technology. Today, I’d like to make a case for curiosity-driven research, because without it, none of the technologies I’ll talk about today would have been possible.

Now, what Thompson found here has actually changed our view of reality. I mean, I think I’m standing on a stage, and you think you’re sitting in a seat. But that’s just the electrons in your body pushing back against the electrons in the seat, opposing the force of gravity. You’re not even really touching the seat. You’re hovering ever so slightly above it. But in many ways, our modern society was actually built on this discovery. I mean, these tubes were the start of electronics. And then for many years, most of us actually had one of these, if you remember, in your living room, in cathode-ray tube televisions. But – I mean, how impoverished would our lives be if the only invention that had come from here was the television?

Thankfully, this tube was just a start, because something else happens when the electrons here hit the piece of metal inside the tube. Let me show you. Pop this one back on. So as the electrons screech to a halt inside the metal, their energy gets thrown out again in a form of high-energy light, which we call X-rays.

And within 15 years of discovering the electron, these X-rays were being used to make images inside the human body, helping soldiers’ lives being saved by surgeons, who could then find pieces of bullets and shrapnel inside their bodies. But there’s no way we could have come up with that technology by asking scientists to build better surgical probes. Only research done out of sheer curiosity, with no application in mind, could have given us the discovery of the electron and X-rays.

Now, this tube also threw open the gates for our understanding of the universe and the field of particle physics, because it’s also the first, very simple particle accelerator. Now, I’m an accelerator physicist, so I design particle accelerators, and I try and understand how beams behave. And my field’s a bit unusual, because it crosses between curiosity-driven research and technology with real-world applications. But it’s the combination of those two things that gets me really excited about what I do. Now, over the last 100 years, there have been far too many examples for me to list them all. But I want to share with you just a few.

In 1928, a physicist named Paul Dirac found something strange in his equations. And he predicted, based purely on mathematical insight, that there ought to be a second kind of matter, the opposite to normal matter, that literally annihilates when it comes in contact: antimatter. I mean, the idea sounded ridiculous. But within four years, they’d found it. And nowadays, we use it every day in hospitals, in positron emission tomography, or PET scans, used for detecting disease.

Or, take these X-rays. If you can get these electrons up to a higher energy, so about 1,000 times higher than this tube, the X-rays that those produce can actually deliver enough ionizing radiation to kill human cells. And if you can shape and direct those X-rays where you want them to go, that allows us to do an incredible thing: to treat cancer without drugs or surgery, which we call radiotherapy. In countries like Australia and the UK, around half of all cancer patients are treated using radiotherapy. And so, electron accelerators are actually standard equipment in most hospitals.

Or, a little closer to home: if you have a smartphone or a computer – and this is TEDx, so you’ve got both with you right now, right? Well, inside those devices are chips that are made by implanting single ions into silicon, in a process called ion implantation. And that uses a particle accelerator.

Without curiosity-driven research, though, none of these things would exist at all. So, over the years, we really learned to explore inside the atom. And to do that, we had to learn to develop particle accelerators. The first ones we developed let us split the atom. And then we got to higher and higher energies; we created circular accelerators that let us delve into the nucleus and then create new elements, even. And at that point, we were no longer just exploring inside the atom. We’d actually learned how to control these particles. We’d learned how to interact with our world on a scale that’s too small for humans to see or touch or even sense that it’s there.

And then we built larger and larger accelerators, because we were curious about the nature of the universe. As we went deeper and deeper, new particles started popping up. Eventually, we got to huge ring-like machines that take two beams of particles in opposite directions, squeeze them down to less than the width of a hair and smash them together. And then, using Einstein’s \(E = mc^2\), you can take all of that energy and convert it into new matter, new particles which we rip from the very fabric of the universe.

Nowadays, there are about 35,000 accelerators in the world, not including televisions. And inside each one of these incredible machines, there are hundreds of billions of tiny particles, dancing and swirling in systems that are more complex than the formation of galaxies. You guys, I can’t even begin to explain how incredible it is that we can do this.

So I want to encourage you to invest your time and energy in people that do curiosity-driven research. It was Jonathan Swift who once said, “Vision is the art of seeing the invisible.” And over a century ago, J.J. Thompson did just that, when he pulled back the veil on the subatomic world.

And now we need to invest in curiosity-driven research, because we have so many challenges that we face. And we need patience; we need to give scientists the time, the space and the means to continue their quest, because history tells us that if we can remain curious and open-minded about the outcomes of research, the more world-changing our discoveries will be.

Thank you.

• Suzie Sheehy
• Paul Dirac: the purest soul in physics
• A great deal of my work is just playing with equations and seeing what they give. simply examining mathematical quantities that physicists use and trying to fit them together in an interesting way, regardless of any application the work may have.
• God used beautiful mathematics in creating the world. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe.
• Of all physicists, Dirac has the purest soul. (Niels Bohr)
• Another story told of Dirac is that when he first met the young Richard Feynman at a conference, he said after a long silence, “I have an equation. Do you have one too?”
• As a young man I had the privilege of learning my quantum theory at the feet of Paul Dirac, as he gave his celebrated Cambridge lecture course. Not only was Dirac the greatest theoretical physicist known to me personally, his purity of spirit and modesty of demeanour(he never emphasized in the slightest degree his own immense contributions to the fundamentals of the subject) made him an inspiring figure and a kind of scientific saint. (Quantum Theory: A Very Short Introduction, John Polkinghorne)