When imaginary numbers are inevitable

\( x^2 + 1 = 0 \) has no real solutions.

The magic number \( i = \sqrt{-1} \)

Cubic equations \( x^3 = px + q \)

has a solution given by Del Ferro‘s formula

\( x \ = \sqrt[3]{ \frac{q}{2} + \sqrt{\frac {q^2}{4} - \frac {p^3}{27}} } + {\sqrt[3]{ \frac{q}{2} - \sqrt{\frac {q^2}{4} - \frac {p^3}{27}} }} \)

Rafael Bombelli considered the cubic equation given by \( x^3 = 15x + 4 \) and found

\( x = \sqrt[3]{ 2 + \sqrt{-121} } + \sqrt[3]{ 2 - \sqrt{-121} } = \sqrt[3] { 2 + 11i } + \sqrt[3]{ 2 - 11i } \)

\( x = 2 + \sqrt{-1} + 2 - \sqrt{-1} = 2 + i + 2 - i = 4 \)

In fact, \( x^3 - 15x - 4 = 0 \)

\( (x-4)(x^2+4x+1) = 0 \) has three real solutions.

\(
\begin{align*}
\begin{cases}
x_1 = 4 \\
x_2 = \sqrt{3} - 2 \\
x_3 = -2 - \sqrt{3}
\end{cases}
\end{align*}
\)

Bombelli demonstrated how real numbers are engendered from complex ones, He proved how a combination of imaginary roots could lead to a real number.

Bombelli’s discovery is considered the “Birth of Complex Analysis”.

The imaginary unit \( i \) appears in the Schrödinger equation

\(
\displaystyle \huge i\hbar {\frac {d}{dt}}\vert \Psi (t)\rangle ={\hat {H}}\vert \Psi (t)\rangle
\)


  • Week1Lecture1: History of complex numbers by Petra Bonfert-Taylor
  • In Imagining numbers (particularly the square root of \( \sqrt{-15} \) ), Barry Mazur mentioned Bombelli’s work many times.
  • Bombelli, however, was interested in pursuing the opposite, more obstreperous case - that is, when \( \frac {q^2}{4} - \frac {p^3}{27} \) is a negative real number.(Chapter 7 Bombelli’s Puzzle, Imagining numbers)
  • But the equation \( x^3 = 15x + 4 \) clearly did have a solution — indeed, \( x = 4 \) is one — it was just that applying the cubic formula required computing \( \sqrt{-121} \). … It was bombelli, also a mathematician and engineer, who decided to bite the bullet and just see what happened. (The Princeton Companion to Mathematics - Part II The Origins of Modern Mathematics, II.1. From Numbers to Number Systems, 6 Real, False, Imaginary)
  • Galois theory offers deep insight into what is happening with casus irreducibilis.
  • In fact, complex numbers are endemic in the formalism of quantum theory. (Chapter 2 The light dawns - 8 Probalility amplitude, Quantum Theory: A Very Short Introduction, John Polkinghorne)
  • It would, no doubt, have come as a great surprise to all those who had voiced their suspicion of complex numbers to find that, according to the physics of the latter three quarters of the 20th century, the laws governing the behaviour of the world, at its tiniest scales, is fundamentally governed by the complex number system. (Chapter 4 Magical complex numbers, The Road to Reality, Roger Penrose)

How playing sports benefits your body... and your brain - Leah Lagos and Jaspal Ricky Singh

The victory of the underdog over the favored team. The last minute penalty shot that wins the tournament. The high-energy training montages. Many people love to glorify victory on the playing field, cheer for favorite teams, and play sports. But here’s a question: Should we be so obsessed with sports? Is playing sports actually as good for us as we make it out to be, or just a fun and entertaining pastime?

What does science have to say? First of all, it’s well accepted that exercise is good for our bodies and minds, and that’s definitely true. Exercising, especially when we’re young, has all sorts of health benefits, like strengthening our bones, clearing out bad cholesterol from our arteries, and decreasing the risk of stroke, high blood pressure, and diabetes. Our brains also release a number of chemicals when we workout, including endorphins. These natural hormones, which control pain and pleasure responses in the cental nervous system, can lead to feelings of euphoria, or, what’s often called, a runner’s high. Increased endorphins and consistent physical activity in general can sharpen your focus and improve your mood and memory. So does that mean we get just as much benefit going to the gym five days a week as we would joining a team and competing?

Well, here’s where it gets interesting: because it turns out that if you can find a sport and a team you like, studies show that there are all sorts of benefits that go beyond the physical and mental benefits of exercise alone. Some of the most significant are psychological benefits, both in the short and long term. Some of those come from the communal experience of being on a team, for instance, learning to trust and depend on others, to accept help, to give help, and to work together towards a common goal. In addition, commitment to a team and doing something fun can also make it easier to establish a regular habit of exercise. School sport participation has also been shown to reduce the risk of suffering from depression for up to four years. Meanwhile, your self-esteem and confidence can get a big boost. There are a few reasons for that. One is found in training. Just by working and working at skills, especially with a good coach, you reinforce a growth mindset within yourself. That’s when you say, “Even if I can’t do something today, I can improve myself through practice and achieve it eventually.” That mindset is useful in all walks of life. And then there’s learning through failure, one of the most transformative, long-term benefits of playing sports. The experience of coming to terms with defeat can build the resilience and self-awareness necessary to manage academic, social, and physical hurdles. So even if your team isn’t winning all the time, or at all, there’s a real benefit to your experience. Now, not everyone will enjoy every sport. Perhaps one team is too competitive, or not competitive enough. It can also take time to find a sport that plays to your strengths. That’s completely okay. But if you spend some time looking, you’ll be able to find a sport that fits your individual needs, and if you do, there are so many benefits. You’ll be a part of a supportive community, you’ll be building your confidence, you’ll be exercising your body, and you’ll be nurturing your mind, not to mention having fun.

My English Phrases List - August - 2024

play coy

When asked about his next book, he played coy.

chill out

Instead, chill out with a movie or a luxurious hot bath.

shoot hoops

he’d rather play golf or shoot hoops than work

At the weekend, we play video games and shoot hoops.

kick off

I’ll kick off the discussion on ethics with this question.

kick off the campaign

road rage

Road rage

take the credit

I did all the work, and she took the credit.

So many people were involved in this, I can’t take all of the credit.

She tries to get by doing as little as possible, then tries to take credit for other people’s work.

My English Words List - August - 2024

graffiti

graffiti

noun

Graffiti made by school children in Rijeka, Croatia

The walls of the old building are covered with graffiti.

verb

graffitied walls

curling

curling

noun

Men curling in Toronto, Ontario, Canada, in 1909

Curling

acorn

acorn

noun

Illustration of acorn

sumac

sumac

noun

Drupes of a staghorn sumac in Coudersport, Pennsylvania

Sumac

promenade

promenade

noun

a beautifully landscaped park with a wide promenade along the riverside

credit

credit

verb

Marine Studio biologists have pointed out that, however intelligent they may be, it is probably a mistake to credit dolphins with any motive of lifesaving. - Lesson 18 Porpoises, Book 4: Fluency in English, New Concept English, Window in the Sea, by RALPH NADING HILL

eraser

eraser

noun

Pink erasers

Eraser

involuntary

involuntary

adjective

Breathing and circulation are involuntary processes.

intimidate

intimidate

verb

tried to intimidate a witness

He tries to intimidate his opponents.

gecko

gecko

noun

Illustration of gecko

Gecko

time-consuming

adjective

a time-consuming process/task/job

stipulation

stipulation

noun

We agreed to the deal with the stipulation that she pay the expenses herself.

omnipresent

omnipresent

adjective

The problem is omnipresent and unavoidable.

bulky

bulky

adjective

bulky packages might cost more to mail

marshal

marshal

verb

She carefully marshaled her thoughts before answering the question.

quadrant

quadrant

noun

Draw two intersecting lines that divide the page into four quadrants.

roadblock

roadblock

noun

That’s the one roadblock to the plan.

meridian

meridian

noun

Prime meridian at Greenwich

flap

flap

verb

The flag flapped in the breeze.

The bird’s wings were flapping.

flip

flip

verb

flip a coin

flip a pancake

flip me the ball

flip a switch

ripple

ripple

verb

the canoe rippled through the water

A cool breeze rippled the water.

aloft

aloft

adverb

The balloon stayed aloft for days.

rant

rant

verb

“You can rant and rave all you want,” she said, “but it’s not going to change things.”

noun

after complaining about the hotel’s lousy service, the woman went off on another rant about the condition of her room

coy

coy

adjective

He gave a coy answer.

cornstarch

cornstarch

noun

Corn starch powder

Corn starch

tinfoil

tinfoil

noun

Wrap the leftover food in tinfoil.

Tin foil

deceive

deceive

verb

Remember that appearances can deceive—just because something looks good doesn’t mean it is good.

conjugate

conjugate

adjective

conjugate complex number

complex roots occurring in conjugate pairs

climax

climax

noun

the climax of her career

cohort

cohort

noun

the cohort of people born in the 1980s

Depression was a common problem for people in that age cohort.

bravo

bravo

noun

  • a shout of approval

hurdle

hurdle

noun

Illustration of hurdle

underdog

underdog

noun

I always root for the underdog instead of the favorite.

orangutan

orangutan

noun

Illustration of orangutan

Mother orangutan with young

Orangutan

chimpanzee

chimpanzee

noun

Illustration of chimpanzee

gorilla

gorilla

noun

Western gorilla

Gorilla

tentative

tentative

adjective

the baby’s first tentative steps

tentative plans

speck

speck

noun

There was not a speck of dust anywhere.

verb

dirt that had specked the windows of the factory for ages

interim

interim

noun

there was a brief interim in the proceedings while everyone got organized

adjective

putting up some students in local motels is obviously just an interim solution to the college’s housing shortage

skateboard

skateboard

noun

Skateboard

Skateboarder doing a hard-flip

verb

He skateboards to school every day.

fraud

fraud

noun

He was found guilty of bank fraud.

automobile insurance frauds

ecotourism

ecotourism

noun

Ecotourism in Svalbard.

Ecotourism

tease

tease

verb

He and his wife enjoy teasing each other about their different tastes in music.

He was always teased by his brother about being short.

metamorphosis

metamorphosis

noun

the metamorphosis of caterpillars into butterflies

the metamorphosis of tadpoles into frogs

The class learned about how caterpillars undergo metamorphosis to become butterflies.

We have watched her metamorphosis from a shy schoolgirl into a self-confident businesswoman.

The Metamorphosis is a novella by Franz Kafka published in 1915.

My English Words List - July - 2024

sandal

sandal

noun

Hiking Sandals

Sandal

wiggle

wiggle

verb

Can you wiggle ten fingers?

the baby wiggled in her sleep

parabola

parabola

noun

Parabolic trajectories of water in a fountain.

The best-known instance of the parabola in the history of physics is the trajectory of a particle or body in motion under the influence of a uniform gravitational field without air resistance (for instance, a ball flying through the air, neglecting air friction).

The parabolic trajectory of projectiles was discovered experimentally in the early 17th century by Galileo, who performed experiments with balls rolling on inclined planes.

Parabola

bola

bola

noun

Illustration of bola

lingo

lingo

noun

It can be hard to travel in a foreign country if you don’t speak the lingo.

The book has a lot of computer lingo that I don’t understand.

scorch

scorch

verb

scorching sun

arbitrage

arbitrage

noun

Arbitrage

seamless

seamless

adjective

a seamless performance

seam

seam

noun

the seams of a dress

verb

creeks seam the valley

detour

detour

noun

We had to make a detour around the heaviest traffic.

verb

We detoured around the heaviest traffic.

gourmet

gourmet

noun

food critics have to be gourmets in order to write about food in an informed way

Gourmet

adjective

a gourmet meal

gourmet cooking

a gourmet chef/restaurant

courier

courier

noun

A courier just left a package for you on the porch.

eliminate

eliminate

verb

the team was eliminated in the first round of the playoffs

The body naturally eliminates waste products.

equilibrium

equilibrium

noun

Supply and demand were in equilibrium.

augment

augment

verb

She took a second job to augment her income.

Heavy rains augmented the water supply.

cobbler

cobbler

noun

Shoemaking

residual

residual

adjective

Residual volume

residual insecticides

Residual network

taper

taper

verb

I’d like a tapered neckline.

sideburns

sideburns

plural noun

Sideburns

courtesy

courtesy

noun

They treated us with courtesy and kindness.

Everyone knows each other here, so we won’t bother with the usual courtesies.

They shook hands and exchanged courtesies before beginning their discussion.

Canada

by Emily Pauline Johnson

Crown of her, young Vancouver; crest of her, old Quebec;
Atlantic and far Pacific sweeping her, keel to deck.
North of her, ice and arctics; southward a rival’s stealth;
Aloft, her Empire’s pennant; below, her nation’s wealth.
Daughter of men and markets, bearing within her hold,
Appraised at highest value, cargoes of grain and gold.


Could we build a miniature sun on Earth? - George Zaidan

In the time it takes to snap your fingers, the Sun releases enough energy to power our entire civilization for 4,500 years. So naturally, scientists and engineers have been working to build a miniature star here on Earth… to plug into our power grid.

And the thing is, we already kind of have. It just doesn’t look like a tiny star floating in a lab.

The stars are made of an almost incomprehensible number of particles, which gravity compresses into a super dense core. This core is hot and dense enough to force atomic nuclei together, forming larger, heavier nuclei in a process known as fusion. The reverse process, where one atom splits into two, is called fission. In both processes, the mass of the end products is slightly less than the mass of the initial atoms. But that lost mass doesn’t disappear — it’s converted to energy according to Einstein’s famous equation. And since \( c^2 \) is such a massive number, both fission and fusion generate a lot of energy.

Fusion in our Sun mostly produces helium nuclei. In the most common pathway, two protons fuse to form a deuterium nucleus, which then fuses with another proton to form a helium-3 nucleus, which then fuses with another helium-3 nucleus to form a helium-4 nucleus. But there’s a catch — that first step is incredibly rare. Only 1 in 100 septillion collisions between protons results in a deuterium nucleus. In the Sun this isn’t a problem because there are so many protons that even a reaction this rare happens all the time. But on Earth, researchers rely on a more easily reproducible reaction, where a deuterium nucleus fuses with a tritium nucleus to form a helium-4 nucleus and a neutron.

We’ve actually been doing reactions like this one inside particle accelerators since the 1930s. But these accelerators are not designed to harness the energy this reaction releases. Rather, they’re used to generate neutrons for a variety of scientific and military purposes. Whereas if we want to use fusion to produce limitless energy, we’d need a device that can harness the energy released, channel enough of that energy back into the device to keep the reaction going, and then send the rest out to our power grid. And for that job, we need a nuclear fusion reactor.

Like a particle accelerator, a reactor would generate helium nuclei and neutrons. But that reaction would happen in a superhot core and the resulting neutrons would shoot outward to heat up a layer of lithium metal. That heat would then boil water, generating steam to run turbines and produce electricity. Meanwhile, the helium nuclei would stay in the core and slam into other nuclei to keep the reaction going — and the electricity flowing.

This tech has many practical challenges, including how to confine a swirling mass of million-degree matter. But the biggest hurdle is achieving what’s called ignition.

An energy technology is only commercially viable if it puts out more energy than it uses. And a fusion reactor needs a lot of energy to get the core hot enough for fusion to occur. So there’s a tipping point: a moment when the fuel is hot enough to start the reaction and release more energy than is needed to reach and maintain that temperature. This is ignition. Stars reach ignition under the force of huge amounts of gravity, but this approach is impossible on Earth since you’d need thousands of times the mass of, well, the entire Earth. So researchers typically rely on vast arrays of lasers, or methods that combine magnets with high energy particles or electromagnetic waves similar to those in your microwave oven.

In 2022, scientists at the US National Ignition Facility demonstrated ignition for the first time ever, using 192 lasers to heat deuterium and tritium to 100 million degrees. While this was a huge step forward, we’re still a ways off from a self-sustaining, long-running reactor that produces more energy than it uses. But once operational, these relatively small reactors could power a city of a million people for a year with just two pickup trucks of fuel. Today, you’d have to burn roughly 3 million tons of coal to produce that much energy. That is the promise of fusion: limitless, on-demand energy with almost no emissions. True star power, right here on Earth.

Everyday Einstein - GPS & Relativity

From Canada’s Perimeter Institute for Theoretical Physics, welcome to Perimeter Inspirations, classroom videos that investigate the frontiers of science. Join host and physicist Damian Pope of Perimeter’s outreach team, and leading scientists as they take you on an educational journey of wonder and discovery.

It’s a navigational tool used by millions of people every day. With it drivers know where they’re going, pilots fly planes more safely, it helps construction workers build straighter roads, farmers plant fields more efficiently, because of it, golfers choose better clubs, skiers find faster ways down mountains. The uses for this innovative tool are virtually unlimited; it’s called the Global Positioning System, better known as GPS.

So exactly how does this incredible tool work? So image you’re on a field and you wanted to triangulate where you were.Because you know the positions of things in the distance, you can see by measuring the direction to one object to another object, you can figure out where you would have to be in the field.

Well GPS is like that but it’s larger. It’s in all three dimensions, not only where in the field but how high and also it’s measuring time. You have four satellites that are sending you signals and you’re measuring accurately where the satellite appears to be and when the signals were sent and from that you can figure out where you are on the Earth’s surface.

The Global Positioning System is a network of over 30 satellites orbiting 20,000 kilometres above us. They move at a speed of 14,000 kilometres per hour. Each satellite follows one of six orbits arranged so at least four satellites are visible from any point on Earth. The satellites constantly transmit signals easily picked up by anyone with a GPS receiver. Each signal contains information on where the satellite is and what time the signal was sent. Using this information the receiver calculates its distance from the satellite. This is done by multiplying the signal speed, the speed of light by the time the signal traveled. The receiver then repeats this procedure for three more satellites narrowing down its location within a few metres. To achieve this incredible accuracy the timing information from the satellites must be extremely precise.

So inside each GPS satellite is an atomic clock, the most accurate timing device ever created. The GPS is so precise it must take into account a number of subtle effects. Some of these are predicted by Einstein’s theory of relativity, an idea that revolutionized our understanding of the universe. This theory includes special relativity and general relativity. Special relativity is a theory of space, time and motion. Key to it is the fact that motion alters time. We see time running slower for a clock that’s moving relative to us. Satellite based GPS clocks are moving past us at 14,000 kilometres per hour. Because of special relativity they gradually fall behind clocks in Earth based receivers at a rate of seven microseconds per day. After Einstein formulated the theory of special relativity he went further ahead and he proposed his theory of general relativity, which is not only a theory of space time but it’s a gravitational theory. Key to Einstein’s theory of general relativity is the fact that gravity alters time. Clocks further away from Earth where gravity is weaker run faster than clocks closer to Earth where gravity is stronger. The GPS satellites are located 20,000 kilometres above Earth where gravity is much weaker than on the surface. Due to general relativity satellite clocks run 45 microseconds faster daily. When we combine the effects of special and general relativity, satellite clocks run 38 microseconds fast every day. This may not seem like much but if uncorrected all GPS measurements would be off by 11 kilometres daily. The effects of relativity on Earth are normally one part in 10 billion. And so that’s an incredibly small effect and you’re used to thinking you can forget it for most things, but when you’re relying on how far light travels in a particular amount of time, if you’re wrong by even microseconds then the distances that you’re getting wrong are that much larger. To correct this error, engineers adjusted the atomic clocks inside the satellites so on Earth they run slower by 38 microseconds per day. This compensated for the effects of relativity and meant once in orbit the clocks ran accurately giving us the powerful tool we have today.

So as you see what began as an abstract theory over one hundred years ago, is now used in every day technology. Every time you use GPS you are using relativity. Whether you’re heading out to meet friends, trying to find the nearest movie theatre or looking for a restaurant in another country, you’ll always know where to go using GPS. So relativity is not just something to study in school, it actually affects daily events in people’s lives, your life.

It’s very amazing that after they were developed, they became such an important factor in designing GPS’ and navigation systems, and basically we would not be able to do them if we didn’t know much about relativity. On one hand you might think of Einstein’s theory of general relativity, this theory that space and time are warped, you live in a four dimensional space and time, you know you might think that that’s the part of physics that’s furthest away from day to day life and yet it shows up in this fundamental way, in GPS technology which is crucial to everyone’s day to day life at this point. Theoretical physics, closer than you think.


  • General relativity is not just an optional geometric reinterpretation of gravity. Mathematically, Newton’s theory is much easier to handle than general relativity. Newton’s law, while being a useful ‘recipe’ for solving most problems - those involving weak gravity and speeds much less than that of light - offers little insight as to what is really going on. So what Einstein saying is that we do not need to invoke a force - the gravity force. Einstein replaced the notion of gravity forces with a completely new conception - that of a curved space. The crux of general relativity is that matter tells space how to curve, and space tells matter how to move. (Relativity: A Very Short Introduction, by Russell Stannard)
  • Ptolemy made a universe, which lasted 1400 years. Newton, also, made a universe, which lasted 300 years. Einstein has made a universe, and I can’t tell you how long that will last. - George Bernard Shaw

The fascinating physics of everyday life - Helen Czerski - TEDxManchester

As you heard, I’m a physicist. And I think the way we talk about physics needs a little modification. I am from just down the road here; I don’t live here anymore. But coming from round here means that I have a northern nana, my mum’s mom. And Nana is very bright; she hasn’t had much formal education, but she’s sharp. And when I was a second-year undergraduate studying physics at Cambridge, I remember spending an afternoon at Nana’s house in Urmston studying quantum mechanics. And I had these folders open in front of me with this, you know, hieroglyphics – let’s be honest. And Nana came along, and she looked at this folder, and she said, “What’s that?” I said, “It’s quantum mechanics, Nana.”And I tried to explain something about what was on the page. It was to do with the nucleus and Einstein A and B coefficients. And Nana looked very impressed. And then she said, “Oh. What can you do when you know that?

“Don’t know, ma’am.”

I think I said something about computers, because it was all I could think of at the time.

But you can broaden that question out, because it’s a very good question – “What can you do when you know that?” when “that” is physics? And I’ve come to realize that when we talk about physics in society and our sort of image of it,
we don’t include the things that we can do when we know that. Our perception of what physics is needs a bit of a shift. Not only does it need a bit of a shift, but sharing this different perspective matters for our society, and I’m not just saying that because I’m a physicist and I’m biased and I think we’re the most important people in the world. Honest.

So, the image of physics – we’ve got an image problem, let’s be honest – it hasn’t moved on much from this. This is a very famous photograph that’s from the Solvay Conference in 1927. This is when the great minds of physics were grappling with the nature of determinism and what it means only to have a probability that a particle might be somewhere, and whether any of it was real. And it was all very difficult. And you’ll notice they’re all very stern-looking men in suits. Marie Curie – I keep maybe saying, “Marie Antoinette,” which would be a turn-up for the books – Marie Curie, third from the left on the bottom there, she was allowed in, but had to dress like everybody else.

So, this is what physics is like – there’s all these kinds of hieroglyphics, these are to do with waves and particles. That is an artist’s impression of two black holes colliding, which makes it look worth watching, to be honest. I’m glad I didn’t have to write the risk assessment for whatever was going on there. The point is: this is the image of physics, right? It’s weird and difficult, done by slightly strange people dressed in a slightly strange way. It’s inaccessible, it’s somewhere else and fundamentally, why should I care?

And the problem with that is that I’m a physicist, and I study this. This – this is my job, right? I study the interface between the atmosphere and the ocean. The atmosphere is massive, the ocean is massive, and the thin layer that joins them together is really important, because that’s where things go from one huge reservoir to the other. You can see that the sea surface – that was me who took this video – the average height of those waves by the way, was 10 meters. So this is definitely physics happening here – there’s lots of things – this is definitely physics. And yet it’s not included in our cultural perception of physics, and that bothers me.

So what is included in our cultural perception of physics? Because I’m a physicist, there has to be a graph, right? That’s allowed. We’ve got time along the bottom here, from very fast things there, to things that take a long time over here. Small things at the bottom, big things up there. So, our current cultural image of physics looks like this. There’s quantum mechanics down in that corner, it’s very small, it’s very weird, it happens very quickly, and it’s a long way down in the general … on the scale of anything that matters for everyday life. And then there’s cosmology, which is up there; very large, very far away, also very weird. And if you go to some places like black holes in the beginning of the universe, we know that these are frontiers in physics, right? There’s lots of work being done to discover new physics in these places.

But the thing is, you will notice there’s a very large gap in the middle. And in that gap, there are many things. There are planets and toasts and volcanoes and clouds and clarinets and bubbles and dolphins and all sorts of things that make up our everyday life. And these are also run by physics, you’d be surprised – there is physics in the middle, it’s just that nobody talks about it. And the thing about all of these is that they all run on a relatively small number of physical laws, things like Newton’s laws of motion, thermodynamics, some rotational dynamics. The physics in the middle applies over a huge range, from very, very small things to very, very big things. You have to try very hard to get outside of this. And there is also a frontier in research physics here, it’s just that nobody talks about it. This is the world of the complex. When these laws work together, they bring about the beautiful, messy, complex world we live in.

Fundamentally, this is the bit that really matters to me on an everyday basis. And this is the bit that we don’t talk about. There’s plenty of physics research going on here. But because it doesn’t involve pointing at stars,
people for some reason think it’s not that. Now, the cool thing about this is that there are so many things in this middle bit, all following the same physical laws, that we can see those laws at work almost all the time around us.

I’ve got a little video here. So the game is, one of these eggs is raw and one of them has been boiled. I want you to tell me which one is which. Which one’s raw?

The one on the left – yes! And even though you might not have tried that, you all knew. The reason for that is, you set them spinning, and when you stop the cooked egg, the one that’s completely solid, you stop the entire egg. When you stop the other one, you only stop the shell; the liquid inside is still rotating because nothing’s made it stop. And then it pushes the shell round again, so the egg starts to rotate again. This is brilliant, right? It’s a demonstration of something in physics that we call the law of conservation of angular momentum, which basically says that if you set something spinning about a fixed axis, that it will keep spinning unless you do something to stop it. And that’s really fundamental in how the universe works. And it’s not just eggs that it applies to, although it’s really useful if you’re the sort of person – and apparently, these people do exist – who will boil eggs and then put them back in the fridge. Who does that? Don’t admit to it – it’s OK. We won’t judge you. But it’s also got much broader applicabilities.

This is the Hubble Space Telescope. The Hubble Ultra Deep Field, which is a very tiny part of the sky. Hubble has been floating in free space for 25 years, not touching anything. And yet it can point to a tiny region of sky. For 11 and a half days, it did it in sections, accurately enough to take amazing images like this. So the question is: How does something that is not touching anything know where it is? The answer is that right in the middle of it, it has something
that, to my great disappointment, isn’t a raw egg, but basically does the same job. It’s got gyroscopes which are spinning, and because of the law of conservation of angular momentum, they keep spinning with the same axis indefinitely. Hubble kind of rotates around them, and so it can orient itself. So the same little physical law we can play with in the kitchen and use, also explains what makes possible some of the most advanced technology of our time.
So this is the fun bit of physics, that you learn these patterns and then you can apply them again and again and again. And it’s really rewarding when you spot them in new places. This is the fun of physics.

I have shown that egg video to an audience full of businesspeople once and they were all dressed up very smartly and trying to impress their bosses. And I was running out of time, so I showed the egg video and then said, “Well, you can work it out, and ask me afterwards to check.” Then I left the stage. And I had, literally, middle-aged grown men tugging on my sleeve afterwards, saying, “Is it this? Is it this?” And when I said, “Yes.” They went, “Yes!”

The joy that you get from spotting these patterns doesn’t go away when you’re an adult.

And that’s really important, because physics is all about patterns, and a small number of patterns give you access to almost all of the physics in our everyday world. The thing that’s best about this is it involves playing with toys. Things like the egg shouldn’t be dismissed as the mundane little things that we just give the kids to play with on a Saturday afternoon to keep them quiet. This is the stuff that actually really matters, because this is the laws of the universe and it applies to eggs and toast falling butter-side down and all sorts of other things, just as much as it applies to modern technology and anything else that’s going on in the world. So I think we should play with these patterns.

Basically, there are a small number of concepts that you can become familiar with using things in your kitchen, that are really useful for life in the outside world. If you want to learn about thermodynamics, a duck is a good place to start, for example, why their feet don’t get cold. Once you’ve got a bit of thermodynamics with the duck, you can also explain fridges. Magnets that you can play with in your kitchen get you to wind turbines and modern energy generation. Raisins in fizzy lemonade, which is always a good thing to play with. If you’re at a boring party, fish some raisins out of the bar snacks, put them in some lemonade. It’s got three consequences. First thing is, it’s quite good to watch; try it. Secondly, it sends the boring people away. Thirdly, it brings the interesting people to you. You win on all fronts. And then there’s spin and gas laws and viscosity. There’s these little patterns, and they’re right around us everywhere. And it’s fundamentally democratic, right? Everybody has access to the same physics; you don’t need a big, posh lab.

When I wrote the book, I had the chapter on spin. I had written a bit about toast falling butter-side down. I gave the chapter to a friend of mine who’s not a scientist, for him to read and tell me what he thought, and he took the chapter away. He was working overseas. I got this text message back from him a couple of weeks later, and it said, “I’m at breakfast in a posh hotel in Switzerland, and I really want to push toast off the table, because I don’t believe what you wrote.” And that was the good bit – he doesn’t have to. He can push the toast off the table and try it for himself.

And so there’s two important things to know about science: the fundamental laws we’ve learned through experience and experimentation, work. The day we drop an apple and it goes up, then we’ll have a debate about gravity. Up to that point, we basically know how gravity works, and we can learn the framework. Then there’s the process of experimentation: having confidence in things, trying things out, critical thinking – how we move science forward – and you can learn both of those things by playing with toys in the everyday world.

And it’s really important, because there’s all this talk about technology, we’ve heard talks about quantum computing and all these mysterious, far-off things. But fundamentally, we still live in bodies that are about this size, we still walk about, sit on chairs that are about this size, we still live in the physical world. And being familiar with these concepts means we’re not helpless. And I think it’s really important that we’re not helpless, that society feels it can look at things, because this isn’t about knowing all the answers. It’s about having the framework so you can ask the right questions. And by playing with these fundamental little things in everyday life, we gain the confidence to ask the right questions.

So, there’s a bigger thing. In answer to Nana’s question about what can you do when you know that – because there’s lots of stuff in the everyday world that you can do when you know that, especially if you’ve got eggs in the fridge – there’s a much deeper answer. And so there’s all the fun and the curiosity that you could have playing with toys. By the way – why should kids have all the fun, right? All of us can have fun playing with toys, and we shouldn’t be embarrassed about it. You can blame me, it’s fine.

So when it comes to reasons for studying physics, for example, here is the best reason I can think of: I think that each of us has three life-support systems. We’ve got our own body, we’ve got a planet and we’ve got our civilization. Each of those is an independent life-support system, keeping us alive in its own way. And they all run on the fundamental physical laws that you can learn in the kitchen with eggs and teacups and lemonade, and everything else you can play with. This is the reason, for example, why something like climate change is such a serious problem, because It’s two of these life-support systems, our planet and our civilization, kind of butting up against each other; they’re in conflict, and we need to negotiate that boundary.

And the fundamental physical laws that we can learn that are the way the world around us works, are the tools at the basis of everything; they’re the foundation. There’s lots of things to know about in life, but knowing the foundations is going to get you a long way. And I think this, if you’re not interested in having fun with physics or anything like that – strange, but apparently, these people exist – you surely are interested in keeping yourself alive and in how our life-support systems work. The framework for physics is remarkably constant; it’s the same in lots and lots of things that we measure. It’s not going to change anytime soon. They might discover some new quantum mechanics, but apples right here are still going to fall down.

So, the question is – I get asked sometimes: How do you start? What’s the place to start if you’re interested in the physical world, in not being helpless, and in finding some toys to play with? Here is my suggestion to you: the place to start is that moment – and adults do this – you’re drifting along somewhere, and you spot something and your brain goes, “Oh, that’s weird.” And then your consciousness goes, “You’re an adult. Keep going.” And that’s the point – hold that thought – that bit where your brain went, “Oh, that’s a bit odd,” because there’s something there to play with, and it’s worth you playing with it, so that’s the place to start.

But if you don’t have any of those little moments on your way home from this event, here are some things to start with. Put raisins in fizzy lemonade; highly entertaining. Watch a coffee spill dry. I know that sounds a little bit like watching paint dry, but it does do quite weird things; it’s worth watching. I’m an acquired taste at dinner parties if there are teacups around. There are so many things you can do to play with teacups, it’s brilliant. The most obvious one is to get a teacup, get a spoon, tap the teacup around the rim and listen, and you will hear something strange. And the other thing is, push your toast off the table because you can, and you’ll learn stuff from it. And if you’re feeling really ambitious, try and push it off in such a way that it doesn’t fall butter-side down, which is possible.

The point of all of this is that, first of all, we should all play with toys. We shouldn’t be afraid to investigate the physical world for ourselves with the tools around us, because we all have access to them. It matters, because if we want to understand society, if we want to be good citizens, we need to understand the framework on which everything else must be based.

Playing with toys is great. Understanding how to keep our life-support systems going is great. But fundamentally, the thing that we need to change in the way that we talk about physics, is we need to understand that physics isn’t out there with weird people and strange hieroglyphics for somebody else in a posh lab. Physics is right here; it’s for us, and we can all play with it.

Thank you very much.


  • Helen Czerski
  • Science is not a collection of facts, it’s a method of asking questions, of testing ideas, of trying to understand the world around us.
  • To understand the world, you have to see it from different perspectives. That’s what science is all about: looking at the same thing in many different ways to get a fuller picture.
  • Science is too important to be left only to scientists. Everyone needs to understand how science works and why it matters to all of us.
  • Curiosity is the engine of science, and the world is full of questions just waiting to be explored.