Achievement | Jotup

Has a mathematician solved the 'invariant subspace problem'? And what does that even mean?

Retrieved on:

Monday, June 12, 2023

The paper is just 13 pages long and its list of references contains only a single entry.

Key Points:

The paper is just 13 pages long and its list of references contains only a single entry.
The paper purports to contain the final piece of a jigsaw puzzle that mathematicians have been picking away at for more than half a century: the invariant subspace problem.

Per Enflo: mathematics, music, and a live goose

By solving the approximation problem, Enflo cracked an equivalent puzzle called Mazur’s goose problem.
Polish mathematician Stanisław Mazur had in 1936 promised a live goose to anyone who solved his problem – and in 1972 he kept his word, presenting the goose to Enflo.

What’s an invariant subspace?

But what about the invariant subspace problem itself?
Another way to think about this is to say that the matrix transforms the eigenvectors (and any lines parallel to them) back onto themselves: these lines are invariant for this matrix.
Taken together, we call these lines invariant subspaces of the matrix.

What about spaces with an infinite number of dimensions?

The invariant subspace problem is a little more complicated: it is about spaces with an infinite number of dimensions, and it asks whether every linear operator (the equivalent of a matrix) in those spaces must have an invariant subspace.
Mathematicians working on this problem narrowed their focus by restricting the problem to particular classes of spaces and operators.
He answered the problem in the negative, by constructing an operator on a Banach space without a non-trivial invariant subspace.

What’s new about this new proposed solution?

Resolving the invariant subspace problem for operators on Hilbert spaces has been stubbornly difficult, and it is this which Enflo claims to have achieved.
This time Enflo answers in the affirmative: his paper argues that every bounded linear operator on a Hilbert space does have an invariant subspace.

Expert review is still to come

Peer review of Enflo’s earlier proof, for Banach spaces in general, took several years.
However, that paper ran to more than 100 pages, so a review of the 13 pages of the new paper should be much speedier.

Australian students in rural areas are not 'behind' their city peers because of socioeconomic status. There is something else going on

Retrieved on:

Monday, June 5, 2023

Major international and national tests show rural students, on average, do not do as well at school as their city peers.

Key Points:

Major international and national tests show rural students, on average, do not do as well at school as their city peers.
For example, in the 2018 PISA test, Australian students outside cities performed at lower levels in reading literacy, mathematical literacy and scientific literacy.
Most of the studies looking at rural students have focused on primary school students.

Our study

The study included all high schools, government (selective and not selective), Catholic and other independent schools, using data from the NSW Education Standards Authority.
For example Advanced English and Mathematics can potentially add more to a student’s ATAR (final rank) than Standard English and Mathematics General 2.

Our results

We found that when SES is controlled for, rural students still achieve lower results than non-rural students in HSC English and maths.
In Mathematics, the difference in average marks was approximately 6% and approximately 3% for Advanced and Standard English.

Why is this happening?

This includes a lack of access to some subjects in rural areas and teachers teaching out of their fields of expertise and training.
In the past, we had the Country Areas Program to help schools make the curriculum more meaningful to rural students.
This is because familiarity with the examples used in questions clouds a students ability to demonstrate the skill being tested.

What now?

The relationship between student background, their location and end-of-school achievement has not improved much in that time, regardless of more students finishing senior secondary school.
At the moment, the federal government is developing the next National Schools Reform Agreement, to start in January 2025.
Firstly, it needs to focus on achieving equity in access to senior secondary subjects for rural students.

AI makes our journalism even more important

Retrieved on:

Monday, June 5, 2023

But the social media age we are living in today makes that sort of manipulation seem like child’s play.

Key Points:

But the social media age we are living in today makes that sort of manipulation seem like child’s play.
And now we have a new and even more potent reality-shaper to contend with, in the form of artificial intelligence.
Using as an example Google’s C4 Data set, The Post listed some of the top 200 sites that are providing “facts” to teach AI.
That’s why there has never been a more important time to invest in quality, evidence-based journalism that is free to read.

'Good soup is one of the prime ingredients of good living': a (condensed) history of soup, from cave to can

Retrieved on:

Sunday, June 4, 2023

The basic nature of soup has a fundamental appeal that feels primordial – because it is.

Key Points:

The basic nature of soup has a fundamental appeal that feels primordial – because it is.
Archaeologists speculate the first soup might have been made by Neanderthals, boiling animal bones to extract fat essential for their diet and drinking the broth.
The widespread distribution of archaeological finds is a reminder soup not only has a long history, but is also a global food.

From rustic to creamy

New ideas about science and digestion in 17th century France promoted natural flavours and thick, rustic preparations gave way to the creamy and velvety smooth soups we know today.
New versions of the liquid food were developed by early modern European chefs, such as the seafood bisque, extracting flavour from the shells of crustaceans.

Easy and affordable

In 1897, a chemist at the Campbell soup company, John Dorrance, developed a condensed canned soup that dramatically reduced the water content.
The new method halved the cost of shipping and made canned soup an affordable meal anyone could prepare.
Read more:
Polaroids of the everyday and portraits of the rich and famous: you should know the compulsive photography of Andy Warhol

‘One of the prime ingredients of good living’

Deceptively simple, the warmth and comfort of soup provide a temporary refuge from the winter chill, comforting the diner from the inside.
He summed up the appeal of soup in a volume dedicated to the dish with over 700 recipes:
Good soup is one of the prime ingredients of good living.
Good soup is one of the prime ingredients of good living.

70 years after the first ascent of Everest, the impact of mass mountaineering must be confronted

Retrieved on:

Saturday, May 27, 2023

But there is one that holds extra-special meaning for many – Mount Everest, or Chomolungma as the Nepalese Sherpa people call it.

Key Points:

But there is one that holds extra-special meaning for many – Mount Everest, or Chomolungma as the Nepalese Sherpa people call it.
A sacred mountain for some, for others the world’s highest peak represents a challenge and a lifelong dream.
Since then, mountaineering has become massively popular and commercial – with serious implications for the cultures and environments that sustain it.

Scaling the heights

From 1854 to 1899 (known as the classic mountaineering period), advances in climbing technology saw ascending peaks by challenging routes become possible and popular.
Since then, all of the world’s 8,000-metre peaks have been climbed in winter, culminating in the historic winter scaling of the 8,611-metre K2 by a Nepalese expedition in 2021.

Mass mountaineering

Pushing to the summit may put their own lives, and the lives of other climbers and rescue teams, at risk.
And yet the number of people attempting to climb famous peaks such as Kilimanjaro in Tanzania or Aconcagua in Argentina has increased dramatically.
In 1992, for example, when the first commercial mountaineering expeditions on Everest began, 22 Sherpas and 65 paying mountaineers summited – one Sherpa for three clients.
This year, however, some estimate a record of more than 1,000 people could reach the summit.

The next challenge

They want stricter regulations and better training to protect the fragile ecosystems of the Himalayas and other mountain ranges worldwide.
Ultimately, the future of mountaineering depends on preserving these unique mountain environments in the first place.
Paradoxically, while it has become more accessible and popular, it has also become more challenging and complex.

Timor-Leste election offers an extraordinary lesson in how to build a stable democracy

Retrieved on:

Saturday, May 27, 2023

After a spirited election campaign, the people of Timor-Leste voted for a new parliament on May 21.

Key Points:

After a spirited election campaign, the people of Timor-Leste voted for a new parliament on May 21.
With roughly 40% of the vote and 31 out of 65 seats, Xanana Gusmão’s National Congress for Timorese Reconstruction (CNRT) looks set to lead a new coalition government.
The rapid departure of UN peacekeepers in 2005 was quickly followed by a political crisis in 2006.
Indeed, it is now the only country in south-east Asia rated by the US-based political advocacy group as “free”.

Surprising success

How did Timor-Leste achieve this surprising success?
The country was able to establish new institutions capable of turning aspirations of a democratic state into reality.
The decades-long independence struggle brought together diverse interests and groups, from both inside the country and throughout the world.

Parliamentary democracy

Parliamentarians are selected by an electoral system of proportional representation that incentivises compromise and coalition building.
These individuals had long maintained order locally and were crucial in resisting Indonesian rule.
External assistance was generally not compromised by ulterior motives, such as securing mineral resources or concerns about fighting terrorism.
Moreover, the international community generally followed the lead of national leaders, rather than trying to impose unwanted policies or practices.

A pandemic silver lining: how kids in some disadvantaged schools improved their results during COVID

Retrieved on:

Tuesday, May 16, 2023

Students from schools in low-income communities did not suffer significant “learning loss” during the pandemic years of 2020-2021, but instead improved in certain areas of study.

Key Points:

Students from schools in low-income communities did not suffer significant “learning loss” during the pandemic years of 2020-2021, but instead improved in certain areas of study.
Our results reveal one silver lining from the past three challenging years, and underscore what’s possible when programs aimed at helping the most disadvantaged students are well funded.

What we did and what we found

From this data we carried out two studies – one comparing student results in 2020 to 2019, the second comparing 2021 to 2019.
In other words, one analysis compared student results from the first year of the pandemic with pre-pandemic kids.
The other compared academic results of pre-pandemic kids with those who’d lived through consecutive years (which included remote learning).

Concerns about ‘learning loss’

As our research shows, major concerns about widespread diminishing academic achievement did not materialise.
Even where students did not achieve at the same rates as they did in pre-pandemic years, they still learned.
Researchers at Harvard University found remote and hybrid learning during the pandemic contributed to significantly widening achievement gaps for disadvantaged students.

What’s behind these results?

The NSW Department of Education’s tutoring scheme, launched in 2021, may have contributed to the positive academic results we found.
The COVID intensive learning support program funded schools to employ more educators to deliver small group literacy and numeracy tuition to students identified as needing it most.
The program has been extended to June 2023, but has been criticised for not being particularly well targeted.

Where to from here?

In fact, their achievement level at the end of 2021 was still below where students in advantaged schools began their school year.
There are clear lessons to be learned from the pandemic and our research on its effects.
David Gonski, appointed by the Gillard government in 2011 to review Australian school funding models, certainly thought so.
Read more:
What is the National School Reform Agreement and what does it have to do with school funding?

4 factors that contributed to the record low history scores for US eighth graders

Retrieved on:

Thursday, May 11, 2023

While one top U.S. education official described the scores as “alarming,” the official rightly pointed out that the decline actually began nearly a decade ago.

Key Points:

While one top U.S. education official described the scores as “alarming,” the official rightly pointed out that the decline actually began nearly a decade ago.
In my view as a historian of education reform and policy, the latest history and civics test scores were a predictable outcome.
While it is difficult to establish an exact cause of the decline, here are four factors that I believe contributed to it.

1. Pandemic fears of learning loss

When students gradually began to return to their physical school buildings after they were closed when the COVID-19 pandemic began, researchers, politicians and critics of teachers unions began to worry about learning loss in math and reading.
Historically, when there are worries about test scores in core subjects like reading and math, other subjects become less of a priority.

2. The politicization of social studies education

At the same time that many education experts were worried about learning loss in reading and math, conservative politicians were working incessantly to limit what can be taught in social studies.
The tip line has since been quietly shut down.
For some teachers, this political context has led them to self-censor and limit what they teach about American history, potentially depriving students of a richer understanding of the nation’s politics and policy.

3. Education budget cuts

Although research has long shown that funding matters for student achievement, many school districts around the country are currently struggling for adequate resources.
The pandemic has amplified existing racial and economic disparities – and recent national test scores in history and civics are an extension of those disparities.
Not only were the average scores on U.S. history tests lower for Black students than white ones, but the decline from 2018 scores to 2022 was 42% greater for Black students.
Black students collectively lost 4.5 points, or 1.8% of their average scores, from 2018 to 2022, versus 3.5 points, or 1.29%, for white students.

4. Teacher shortages

Mounting job stress and the blaming of teachers have led many educators to leave schools altogether, generating widespread teacher shortages.
With that in mind, low test scores in history and civics begin to make more sense.

Keys to improvement

What American kids know – or don’t – about the nation’s history and civics is a reflection not of the kids, but of the political and economic circumstances that affect their schools.
The factors that support student learning – funding, qualified teachers and high-quality curricula – are well known.

Aneurin Bevan's writings still have lessons for contemporary politics – and far beyond the NHS

Retrieved on:

Tuesday, May 9, 2023

Weapon, Capitalism, Politics, Property, Element, Achievement, Parliament, Collection, Risk, NHS, Memory, Disease, Management, Tribune, People, Labour

But Bevan’s political career encompassed far more than this one achievement.

Key Points:

But Bevan’s political career encompassed far more than this one achievement.
While this was essential to Bevan, there is a tendency to overlook his wider principles.
It provides an opportunity to delve deeper into Bevan’s philosophy and to critically engage with his ideas and their relevance to contemporary politics.
Beyond domestic politics, the collection demonstrates Bevan’s ambition to apply his principles of democratic socialism to the international arena.

Bevan today

Although the world has moved on significantly since Bevan’s time, many of the issues he grappled with remain relevant today.
But it is crucial to return to figures like Bevan in greater detail and to critically engage with their ideas.
By doing so, we might find lessons that are relevant today, and avoid reducing significant political figures to snappy one-liners and quotable lines.

The role of the past

He reminded readers that “communal memories are overlaid by a new situation and their influence grows ever more remote and vague”.
Bevan’s words can be read as a reminder of the enduring legacy of the past.

Alone Australia contestants are grappling with isolation and setbacks. Here's what makes a winner

Retrieved on:

Wednesday, May 3, 2023

People, SBS, Perseverance, Food, Failure, Face, Friends, Social, Politics, Survival, Fear, Season, Reward, Research, Emotion, Goal, Loneliness, Mental, Achievement, Wilson, Thought, Athlete, Human, SBS TV, Animal, Nature, Time, Social isolation, Child, Water, Blame, Personality, Weather, Health, Hunger, Environment, Family, Cast Away, Entertainment, Management, Toy, Nursing, Business travel, Design, Retail

The winner of the reality TV show Alone Australia

Key Points:

The winner of the reality TV show Alone Australia
will need more than “survival skills” to succeed.
They will also need to draw on a host of psychological strengths.
Here’s what happens when you take away those social interactions, and some thoughts on who’s most likely to thrive.

Remind me, what’s Alone Australia?

Over the coming days and weeks, they film themselves building a shelter, making fire, and finding food and water.
Contestants were selected on the basis of having survival skills and a personality likely to be engaging on camera.
Read more:
Woman spends 500 days alone in a cave – how extreme isolation can alter your sense of time

Mental toughness is key

Mental toughness is a group of personality characteristics originally identified in elite and successful athletes.
Athletes higher in mental toughness tend to perform better.
Can mental toughness be cultivated in the moment?
When fatigued, mental toughness no longer predicts perseverance towards a difficult physical goal.

Combating loneliness is crucial

Research highlights the difference between social isolation (lack of opportunity for social interaction) and loneliness (the distressing feeling that one’s social needs aren’t being met).
A person can be socially isolated but not feel lonely or feel lonely even in the presence of others.
Indeed, some people place high value on solitude and generally need less interaction to avoid loneliness.
Even people who don’t prefer solitude can get creative about fulfilling social needs when people aren’t around.

How about awe and pride?

But research also points to the potential benefits of positive emotions in this situation, such as awe and pride.
And nature is a prime trigger of
awe – the positive emotional experience when witnessing extraordinary things that are vast and complex.
Awe is linked to a variety of beneficial outcomes, including higher self-reported wellbeing, physical health, critical thinking and humility.
Specifically, savouring the moment is a documented strategy for intentionally increasing the experience of positive emotions such as awe and pride.

Are you a future Alone Australia winner?

If you’re thinking of applying for future seasons of Alone Australia, you might be wondering if you have what it takes.
You can develop mental toughness, your capacity to combat loneliness while socially isolated, and your ability to savour positive emotions such as awe and pride.