2024-09-05

My English Words List - September - 2024

raisin

noun

Raisin

manner

noun

Some people have no manners.

Someone should teach you some manners!

mind your manners

winding

adjective

a long and winding path through the woods

a winding staircase leads to the top of the lighthouse

poutine

noun

Poutine

tarmac

noun

a tarmacadam road, apron, or runway

tarmacadam

noun

Tarmacadam

equilateral

adjective

an equilateral triangle

an equilateral polygon

an equilateral polyhedron

lobby

noun

a hotel lobby

I’ll meet you in the lobby after the show.

insomnia

noun

Insomnia, also known as sleeplessness, is a sleep disorder where people have trouble sleeping.

etiquette

noun

the couple exhibited poor etiquette when they left the party without saying good-bye to the host and hostess

courteous

adjective

their customer service department always gives courteous responses, even to rude people

underpin

verb

a wall underpinned by metal beams

the central beliefs that underpin a free society

pragmatic

adjective

a pragmatic [=practical] approach to health care

His pragmatic view of public education comes from years of working in city schools.

a pragmatic man, not given to grand, visionary schemes

plenum

noun

A quantum vacuum is more like a plennum than like empty space. (Chapter 4 Further developments - Quantum field theory, Quantum Theory: A Very Short Introduction, John Polkinghorne)

fatuous

adjective

a fatuous remark

the fatuous questions that the audience members asked after the lecture suggested to the oceanographer that they had understood little

ringette

noun

Ringette

rash

noun

The baby has a skin rash.

dole

noun

Unemployment benefits

In British English, unemployment benefits are also colloquially referred to as “the dole”; receiving benefits is informally called “being on the dole”. “Dole” here is an archaic expression meaning “one’s allotted portion”, from the synonymous Old English word dāl. In Australia, a “dole bludger” is someone on unemployment benefits who makes no effort to find work.

charter

noun

the Canadian Charter of Rights and Freedoms (the Charter)

bedrock

noun

They dug down for 10 feet before they hit bedrock.

Bedrock

pitaya

noun

ethnic

adjective

an ethnic German

ethnic foods

The U.S. has a wide variety of ethnic groups made up of immigrants or their descendants.

brainstorm

verb

they brainstormed about ways to raise money for their organization

caretaker

noun

served as caretaker to the younger children

literacy

noun

The program is intended to promote adult literacy among people who have had very little schooling.

vantage

noun

the vantage had all been ours for the first half of the contest

uphold

verb

promise to uphold the law

empathy

noun

He felt great empathy with the poor.

cover

verb

cover band

song cover

reconciliation

noun

Canada marks 4th annual National Day for Truth and Reconciliation

totem

noun

Totem pole

statutory

adjective

a statutory age limit

a statutory presumption

Today, September 30, is the National day for Truth and Reconciliation. A National day is a Federal Statutory holiday.

crochet

noun

She learned basic crochet stitches from her mother.

Crochet

Knitting

aquatic

adjective

aquatic sports

a lifelong fascination with sharks and other fearsome aquatic creatures

mockingbird

noun

Mockingbird

glow

verb

The fireplace glowed with the dying coals.

This toy glows in the dark.

noun

We could see the glow of the lamp in the window.

Sunset glow

blunder

verb

We blundered along through the woods until we finally found the trail.

noun

fixed a minor blunder in the advertising flyer

2024-08-23

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 \( \sqrt{-15} \) ), 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)
Physicists Take the Imaginary Numbers Out of Quantum Mechanics

2024-08-22

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.

2024-08-08

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.

2024-08-07

My English Words List - August - 2024

graffiti

noun

The walls of the old building are covered with graffiti.

verb

graffitied walls

curling

noun

Curling

acorn

noun

Illustration of acorn

sumac

noun

Sumac

promenade

noun

a beautifully landscaped park with a wide promenade along the riverside

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

noun

Eraser

involuntary

adjective

Breathing and circulation are involuntary processes.

intimidate

verb

tried to intimidate a witness

He tries to intimidate his opponents.

gecko

noun

Illustration of gecko

Gecko

time-consuming

adjective

a time-consuming process/task/job

stipulation

noun

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

omnipresent

adjective

The problem is omnipresent and unavoidable.

bulky

adjective

bulky packages might cost more to mail

marshal

verb

She carefully marshaled her thoughts before answering the question.

quadrant

noun

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

roadblock

noun

That’s the one roadblock to the plan.

meridian

noun

Prime meridian at Greenwich

flap

verb

The flag flapped in the breeze.

The bird’s wings were flapping.

flip

verb

flip a coin

flip a pancake

flip me the ball

flip a switch

ripple

verb

the canoe rippled through the water

A cool breeze rippled the water.

aloft

adverb

The balloon stayed aloft for days.

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

adjective

He gave a coy answer.

cornstarch

noun

Corn starch

tinfoil

noun

Wrap the leftover food in tinfoil.

Tin foil

deceive

verb

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

conjugate

adjective

conjugate complex number

complex roots occurring in conjugate pairs

climax

noun

the climax of her career

cohort

noun

the cohort of people born in the 1980s

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

bravo

noun

a shout of approval

hurdle

noun

Illustration of hurdle

underdog

noun

I always root for the underdog instead of the favorite.

orangutan

noun

Illustration of orangutan

Orangutan

chimpanzee

noun

Illustration of chimpanzee

gorilla

noun

Gorilla

tentative

adjective

the baby’s first tentative steps

tentative plans

speck

noun

There was not a speck of dust anywhere.

verb

dirt that had specked the windows of the factory for ages

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

noun

Skateboard

verb

He skateboards to school every day.

fraud

noun

He was found guilty of bank fraud.

automobile insurance frauds

ecotourism

noun

Ecotourism

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

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.

2024-07-10

My English Phrases List - July - 2024

at the core of

The two principles are similar at their core.

one and done

This is not a one and done process.

Trying something new shouldn’t be a one and done exercise.

2024-07-03

My English Words List - July - 2024

sandal

noun

Sandal

wiggle

verb

Can you wiggle ten fingers?

the baby wiggled in her sleep

parabola

noun

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

noun

Illustration of bola

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

verb

scorching sun

arbitrage

noun

Arbitrage

seamless

adjective

a seamless performance

seam

noun

the seams of a dress

verb

creeks seam the valley

detour

noun

We had to make a detour around the heaviest traffic.

verb

We detoured around the heaviest traffic.

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

noun

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

eliminate

verb

the team was eliminated in the first round of the playoffs

The body naturally eliminates waste products.

equilibrium

noun

Supply and demand were in equilibrium.

augment

verb

She took a second job to augment her income.

Heavy rains augmented the water supply.

cobbler

noun

Shoemaking

residual

adjective

Residual volume

residual insecticides

Residual network

taper

verb

I’d like a tapered neckline.

sideburns

plural noun

Sideburns

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.

2024-07-01

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.

Canada

2024-06-30

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.

2024-06-28

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