Finding a descent job requires hard work and dedication. In many cases, it involves some luck, too. One method of getting your foot in the door is to accept a lower-paying job. Then you need to do your best at the job at every opportunity. And who knows? The lower-paying job might result in a higher-paying job. (Meaning Matters: Vocabulary, Unit 3: Idioms)

get/start off on the right foot

Job interview provide you with the opportunity to start off on the right foot. Put some thought into how you dress. Stains on your outfit leave a negative impression. Choose clean street shoes over running shoes, sandles, or flip-flops. Wear socks or stockings. Leave cool hats, chunky jewellery, and piercings at home. (Meaning Matters: Vocabulary, Unit 3: Idioms)

break the ice

In many cases, starting a new job means meeting new people. Meeting new people can be stressful. Start by shaking hands firmly, making eye contact, and saying your name confidently. Smiling is always a good start to breaking the ice with strangers. (Meaning Matters: Vocabulary, Unit 3: Idioms)

see eye to eye

The two did not see eye to eye on certain political issues.

work tail off

I know you thought it was just a silly New Year’s resolution, but I’ve been working my tail off at the gym!

“You come here like every other new Canadian. You work your tail off,” Ford said. “If you think you’re coming to collect the dole and sit around, it’s not going to happen. Go somewhere else.”

so far, so good

“How’s the work on your house going?”

“There’s a lot more to do, but so far, so good.”

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 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)

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