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The Mathematics of Knitting

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For a long time, knitting has been considered an elegant art that has many beneficial outcomes. Though it continued to evolve throughout the years, the origin of knitting still hides many mysteries. Moreover, even though everyone agrees that knitting is based on mathematical patterns, very few tried to understand the science behind them. Thus, physicist Elisabetta Matsumoto is taking the first steps toward understanding the mathematics of knitting.

The origin of knitting

Historians tend to believe that knitting originated from the middle east in the 5th century. It then traveled to Europe through merchants and traders in the 13th century AD. Furthermore, the oldest evidence of knitting is found in Egypt but the pattern wasn’t made out of wool. It was made of cotton fibers. Furthermore, the fabric was knitted in the shape of socks in the  11th century CE. 

Moreover, many of these patterns contained Arabic blessings and symbols. Knitting was also mainly used in creating fishnets. 

The inspiration for this study

Physicist Elisabetta Matsumoto started knitting when she was a child. However, it was only when she noticed an unusual stitch while knitting a Japanese red dragon, did she start wondering about the math behind the patterns. “I have books with thousands of different stitch patterns, but the one in the red dragon wall hanging was one I had never seen,” she says.

Imparting new unique properties

According to Matsumoto, the mere basics of knitting involves almost a hundred kinds of stitches. However, switching between the stitches and different variations gives the knitter the ability to alter the elasticity. It also allows the knitter to mechanically strengthen and 3-D  alter the structure of the final outcome. Normally, yarn is not an elastic material. However, once knitted, the fabric can stretch almost twice its initial length. On the other hand, the yarn’s structure itself doesn’t change. Therefore, knitting ends up imparting the final fabric with unique properties that has nothing to do with the materials.

Matsumoto is now working at the Georgia Institute of Technology in Atlanta to figure out all the mathematical rules related to knitting. Furthermore, she is aiming to create a catalog that includes all the different stitch types, as well as their combinations and the resulting fabric properties. She hopes that this dictionary creates a common ground for Knitters, scientists, and manufacturers to benefit from. 

The knot theory

In her research, Matsumoto is using the knot theory as a foundation. The knot theory has succeeded in setting up the mathematical principles that define the science behind knots formation. Later on, these principles played a significant role in explaining the DNA’s ability to both fold and unfold relatively. The principles also laid the basis for the molecule’s makeup theory, along with an explanation behind the physical and chemical characteristics of distribution in space. 

Thus, Matsumoto is using the established theory to better understand the way each stitch entangles with its neighbors. “The types of stitches, the differences in their geometries as well as the order in which you put those stitches together into a textile may determine [the fabric] properties,” she says.

For example, while knitting, if a knitter only used one type of stitch, the fabric would curl at the edges. On the other hand, if a knitter combines two stitch types together while alternating rows or columns, the fabric will have flat edges. Moreover, despite the visual similarity, each one of the final patterns will have its own level of elasticity. Thus, even the smallest alteration will have a  huge impact on the mechanics of the textile. 

Training computers and creating knitting programs

To achieve better results, the team is now teaching a computer to think like a smart knitter. However, they are also imparting it with the knowledge of said knot dictionary as means of solving other unrelated problems. Therefore, with the aid of the multiple yarn properties, mathematical stitch details, and final knitted structures as inputs, the computer will predict the outcome of the pattern. Furthermore, predicting the mechanical properties of fabrics will tailor materials for specific futuristic applications, such as scaffolds for growing human tissue and wearable smart clothing. The program can also aid in everyday knot related problems.

References:

 Morgan, J. (2020, December 17). The Amazing History Of Knitting. A Look Through The Ages Into Knitting History And Who Invented It. Knit Like Granny. https://knitlikegranny.com/knitting-history/#EarlyOriginsRoberts, S. (2019, May 30). ‘Knitting Is Coding’ and Yarn Is Programmable in This Physics Lab. The New York Times. https://www.nytimes.com/2019/05/17/science/math-physics-knitting-matsumoto.htmlRoss, C. B. (2020, March 30). What Is Knitting? A Brief History of Knitting And Its Uses. The Sustainable Fashion Collective. https://www.the-sustainable-fashion-collective.com/2017/05/04/knitting-brief-history-knitting-uses#:%7E:text=Knitting%20is%20believed%20to%20have,with%20wool%20traders%20soon%20afterwards.&text=By%20the%2016th%20century%2C%20knitting,examples%20of%20a%20knitted%20garment.Thompson, H. (2021, January 26). How one physicist is unraveling the mathematics of knitting. Science News. https://www.sciencenews.org/article/how-one-physicist-unraveling-mathematics-knitting

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The Unbroken Spirit of Gaza

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When the guns finally went quiet in Gaza, people stepped out from basements and tents for the first time after months. On this occasion, some cried, some smiled, and others simply looked at the sky in disbelief. There were small moments of celebration, too, in which children waved torn flags, men distributed bread, and women thanked God. However, behind every cheer stood loss. Nearly every street was filled with rubble, while every family was missing someone.

Even in ruins and a completely obliterated picture, Gaza’s people showed the world that their spirit remains unbroken.

The Scale of Destruction

According to Gaza’s Health Ministry figures verified by UN OCHA and international agencies, more than 67,000 Palestinians have been killed since the war began in October 2023. Over 80 percent of Gaza’s 2.2 million people are displaced, many of them living in damaged schools or makeshift shelters.

A UN assessment shared by The Guardian reports that 92 percent of Gaza’s buildings and infrastructure have been destroyed or severely damaged, including hospitals, water systems, and almost all power stations. Even now, bulldozers and rescue teams continue to pull bodies from the debris. Hospitals that still function do so with little medicine and no electricity. Doctors use phone lights to perform emergency operations.

A Short Celebration of Life

When the ceasefire came into effect, people did what they could to feel alive again. In Rafah, small groups lit candles, sang patriotic songs, and shared dates. Children played football in alleys cleared of debris. Others tied white cloth to sticks and waved them as makeshift flags.

“It’s not victory,” said 28-year-old Ameer from Deir al-Balah.

“It’s a breath. We are just breathing again.”

For most, the joy lasted only a few hours. Soon they returned to what was left of their homes, collecting bricks, mattresses, and family photos. The ceasefire gave them time to count who survived.

Women Leading in Crisis

Across Gaza, women have taken the lead in rebuilding daily life. UN Women estimates that three of every four displaced Gazans are women and children.

In tent camps, mothers organize small cooking groups to share food and keep children occupied. They turn broken classrooms into play corners and burned courtyards into community kitchens.

One mother, Samira, said,

“I lost my husband, my house, and everything else. But if I lose hope too, my children will have nothing left.”

Her words sum up the quiet strength that holds Gaza together.

Children Without Schools

Gaza’s children are the face of both loss and endurance. UNICEF reports that about 17,000 children have been orphaned or separated from their families.

With 90 percent of schools damaged, formal education has stopped. Some volunteers now gather children under tents to read simple lessons or tell stories to distract them from fear. Many draw what they remember of their homes—blue skies, olive trees, and the sea.

Faith and Strength

Faith continues to guide daily life. Mosques may be in ruins, but prayers still take place in open spaces. People gather at sunset to recite verses from the Quran and pray for those who have died.

An imam from Khan Younis said, “We will rebuild because rebuilding is part of worship.” For many, faith provides structure in chaos and the belief that justice will come, even if slowly.

Humanitarian Situation in Gaza

The ceasefire has allowed limited aid to enter Gaza. According to sources, around 350 to 400 trucks of aid are entering daily, less than the promised 600.

Aid agencies warn that Gaza still faces a hunger emergency. The UN’s World Food Programme estimates that 1.8 million people are in critical need of food. Hospitals require fuel, and the water network is still mostly down.

The World and Gaza

Protests in more than 50 cities have demanded accountability and long-term peace. The truce, mediated by Egypt and Qatar, has created cautious optimism, but trust is fragile. International organizations call for independent investigations into alleged war crimes and for an end to the blockade that keeps aid limited.

Rebuilding will take years, maybe decades. Engineers estimate that full reconstruction could cost over $30 billion. However, Gazans have already started small repairs, clearing streets, patching walls, and re-planting gardens where possible.

Local radio stations, once silent, are broadcasting again using generators. Young people are sharing footage of survival on social media, determined to show that life continues. Every small act, a cleaned courtyard, a lit candle, a repaired door, is a declaration that Gaza still belongs to its people.

Key Takeaways

The ceasefire has not brought normal life, but it has brought a chance to begin again. Gaza stands today as a place of unimaginable loss and extraordinary courage. People celebrate the smallest victories: a family reunited, a neighbor found alive, a loaf of bread baked over fire.

The world sees a war zone, but Gazans see home. Their houses may be gone, but their faith, love, and unity remain.

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A Fragile Silence: Understanding the Gaza Ceasefire

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For the first time in months, the skies above Gaza seem quiet. No sirens, no distant thud of bombs, and no children running for shelter. This is a fragile silence – one that carries the weight of grief, exhaustion, and the faintest breath of hope. The newly brokered ceasefire between Israel and Hamas has brought an uneasy calm to a land battered beyond recognition. However, what does this truce really mean for Gaza, for its resilient people, and for the uncertain future that still lies ahead?

The Ceasefire Agreement: What is Promised?

Mediated by Egypt, Qatar, and the United States, the ceasefire agreement demands an immediate halt to military operations from both sides. Israeli troops have begun a phased withdrawal from central Gaza, while Hamas is set to release hostages in exchange for Palestinian detainees. Humanitarian aid, fuel, food, and medicines are promised unrestricted access through UN-coordinated corridors.

Yet, as with every truce before, skepticism lingers. The language of peace often hides the reality of fragility. Many Gazans call it not an end, but a pause, like a window to bury the dead and search for the living.

As the dust settles, Gaza reveals its new geography of loss. Satellite images show entire neighborhoods flattened. Hospitals that once stood as shelters now stand as ruins. Roads are cratered, schools turned into makeshift morgues. However, amid the destruction, thousands of displaced families are returning to what remains of their homes.

“We will rebuild even if it’s only with our hands,” says a father from Khan Younis, sweeping rubble from his doorway.

His words echo the quiet defiance of a people who have learned to survive without certainty.

Life Between the Lines of a Truce

Ceasefires in Gaza are rarely moments of celebration. They are interludes between wars and the days when families breathe, mend, and count who is still alive. Markets reopen with candlelight, children chase kites through streets of dust, and teachers gather students in the shells of classrooms.

Yet, the fear never truly leaves. Every drone hum is a reminder. Every tremor of glass recalls nights when silence meant danger. For many Gazans, peace feels less like a right and more like a borrowed hour.

The ceasefire’s greatest test lies in the flow of aid. The United Nations and the Red Crescent have mobilized convoys to deliver supplies, yet logistical chaos and damaged roads make access painfully slow. Hospitals are desperate for anesthesia, blood bags, and clean water, while fuel shortages have forced surgeons to rely on battery lamps and hand-pumped oxygen.

UN officials warn that Gaza is at risk of famine. Every truck that enters carries not just food, but the hope of survival. However, the question still persists—will aid continue once the world’s attention shifts again?

Aid in the Balance: Lifelines Under Pressure

The true test of this ceasefire lies in how quickly and how fully aid flows. The United Nations plans a 60-day escalation in humanitarian deliveries. The goal is to assist 2.1 million people, provide nutrition support to 500,000, and deliver cash assistance to 200,000 families.

Even so, the UN warns that only 28% of the needed $4 billion appeal for Gaza has been funded. UNICEF, in a recent warning, said child mortality could spike if full food aid crossings were not allowed. Therefore, it is estimated that 50,000 children are at immediate risk of acute malnutrition.

Yet logistical barriers remain with wrecked roads, checkpoints, bureaucratic delays, and fuel shortages.

As one UN relief coordinator cautioned:

“This problem won’t go away in two months.”

Politics Behind the Pause

The ceasefire is not only humanitarian but also deeply political. For Israel, it provides breathing space amid growing international criticism. For Hamas, it offers a chance to claim survival as victory. For mediators like Egypt and Qatar, it is a test of diplomatic endurance.

However, beneath these maneuvers lies a truth that without accountability and justice, every ceasefire is temporary. History has seen these pauses crumble under mistrust, missteps, and the politics of vengeance.

Reconstruction promises are once again flooding global headlines. Nations pledge millions, NGOs draft blueprints, and donors speak of hope. But Gazans remember the promises of 2014 and 2021 when funds vanished, and aid projects never began.

This time, the call from Gaza is clear: let rebuilding belong to those who have lived through the ruins. Let aid be about dignity, not dependency.

The Global Conscience

As the truce holds, protests continue in cities from London to Jakarta. Millions march for justice, waving Palestinian flags, chanting for freedom and accountability. The ceasefire may have paused the bombs, but it has amplified Gaza’s voice.

International pressure is mounting for independent investigations into alleged war crimes. Human rights organizations warn that impunity will only plant the seeds of another conflict. The world is watching, but watching alone is not enough.

The fragility of peace in Gaza lies in its repetition as history is written in ceasefires that failed. Still, there is something different this time that a sense that Gaza’s agony has pierced the world’s conscience in a way that can no longer be ignored.

In the heart of the ruins, Gazans are not asking for sympathy. They are asking for justice, protection, and the right to live without counting the seconds between sirens.

Conclusion: Between Hope and History

The Gaza ceasefire is not an end to war but a fragile silence held together by the will of a broken people. It is a pause between grief and survival, between what was destroyed and what might still be rebuilt. Whether it becomes the beginning of peace or just another chapter of waiting depends not only on leaders or treaties, but on the world’s willingness to remember.

For now, Gaza breathes—quietly, painfully, defiantly.

“They have silenced our skies, but not our spirit.”

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The 20-Point Gaza Plan: A Blueprint for Dispossession?

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As Gaza’s hospitals ran out of oxygen and children continued to die of hunger, a new “Peace Plan” emerged from Washington. The US President Donald Trump’s 20-Point Gaza Plan was announced recently in late September 2025. It has promised to rebuild Gaza and bring “a new era of stability.” However, to many Palestinians and observers across the world, it sounded like something else: a blueprint to erase what remains of Gaza’s sovereignty. What was initially discussed with the Arab states as a cooperative humanitarian initiative was, by the time of its release, cleverly reshaped. It is rewritten to preserve occupation under a new label.

From Arab Consensus to American Control

Early drafts of a postwar Gaza plan were reportedly framed through consultations among Arab and Muslim nations. They emphasized three principles: Palestinian self-rule, unrestricted humanitarian access, and reconstruction without foreign trusteeship. Yet as negotiations evolved, the plan was absorbed by U.S. diplomacy and redrafted in a way that aligned with Israeli conditions rather than Arab consensus. Several diplomats confirmed that Washington’s version quietly removed any reference to Palestinian sovereignty, replacing it with phrases like “transitional governance” and “security oversight.”

Even before it was officially unveiled, Reuters reported growing unease among Arab delegations, who complained that the new text ignored their agreed-upon points and reflected Israel’s security agenda. Pakistan’s foreign minister stated openly that “Trump’s 20-Point Gaza Plan is not our plan.” The shift marked more than a diplomatic re-edit as it exposed the power imbalance shaping Gaza’s future.

The 20 Points: Promises and Omissions

Publicly, Trump’s 20-Point Gaza Plan claims to rest on four pillars: ceasefire, hostage release, reconstruction, and demilitarization, yet its deeper clauses reveal troubling gaps. There is no guarantee of Palestinian sovereignty, no timeline for Israeli withdrawal, and no provision for international accountability. Instead, it envisions Gaza’s future under external trusteeship, with reconstruction funds controlled by a multinational board led by Washington and oversight committees dominated by Israel and allied states.

Several points speak of creating “safe redevelopment corridors” and “security zones,” terms human rights experts warn could mask forced relocations and demographic engineering. The plan further ties aid to behavior clauses, conditions governance on foreign approval, and places border control under “temporary supervision,” a phrase that critics fear means indefinite control. Amnesty International cautioned that “reconstruction must not become a pretext for displacement or collective punishment.”

In essence, while the plan’s language of peace and rebuilding appeals to diplomacy, its structure embeds dependency and control. To rebuild Gaza without granting it freedom is, as one Palestinian analyst put it, “to rebuild the prison walls, just higher and cleaner.”

The Human Cost Hidden Behind Diplomacy

Behind every clause of this plan lies a humanitarian catastrophe. The World Health Organization confirms that more than half a million people in Gaza face famine-level hunger, and over 360 have already died from malnutrition. The UN’s humanitarian office says 80% of Gaza’s population now depends on aid that Israel continues to restrict. In this reality, talk of “redevelopment corridors” rings hollow. Gaza does not need trusteeship—it needs food, medicine, and an end to the siege.

On the streets of Rafah and Deir al-Balah, survivors of months of bombardment heard the plan’s announcement with disbelief. “They speak of building new homes,” one displaced teacher told a reporter, “but they won’t even let cement cross the border.” Another woman asked, “Who gives them the right to plan our lives while we bury our dead?” These voices reveal the heart of Gaza’s objection: no document signed abroad can substitute for the will of its people.

Resistance and Rejection

Hamas’s initial response to the plan was mixed. The group welcomed references to reconstruction and aid delivery but rejected disarmament and external trusteeship. “No peace built on surrender will last,” its spokesman said. Across Palestinian civil society, activists dismissed the plan as “occupation repackaged.” Hashtags like #NoTrusteeship and #GazaIsNotForSale flooded social media, uniting Gazans and diaspora voices in digital defiance.

Former U.S. diplomat Robert Malley, writing for Le Monde, described the plan as “a maze of ambiguities and potential pitfalls.” His analysis noted that the proposal’s vagueness is deliberate—creating space for powerful states to interpret its clauses to their advantage. It is a familiar strategy: promise reconstruction while ensuring dependency.

Reactions among Arab and Muslim nations were cautious and divided. The Arab League issued a restrained statement calling for further review, while countries like Algeria, Iran, and Pakistan warned that any plan lacking Palestinian representation was unacceptable. Meanwhile, Western governments praised the proposal as a “bold step toward stability.” For Gazans, these words offered little comfort. They have seen such language before in the Oslo Accords, the Road Map, and countless other documents that delivered control, not liberation.

International law offers a clear measure. The plan’s idea of trusteeship contradicts the principle of self-determination guaranteed by the UN Charter and multiple General Assembly resolutions. Legal scholars argue that placing Gaza under external administration without consent would constitute a new form of occupation. The International Court of Justice’s 2024 advisory opinion warned that “peace agreements cannot validate the continuation of unlawful control.” Trump’s plan, critics say, does precisely that.

What True Peace Would Look Like

A genuine peace framework would begin not with political engineering but with justice. It would:

  • End the blockade entirely, allowing Gaza to trade and rebuild freely.
  • Place reconstruction under Palestinian-led management, not foreign trusteeship.
  • Hold accountable those responsible for war crimes and the starvation policy.
  • Guarantee the right of return and compensation for the displaced.
  • Empower Gaza’s people to elect their own representatives without external approval.

Anything less is not peace but an administrative occupation.

The Moral and Legal Test for the World

The 20-Point Plan is not a diplomatic breakthrough but a moral test. To accept it as written would mean endorsing a future where Gaza remains controlled by the same forces that destroyed it. It would normalize collective punishment under the banner of reform. And it would bury the core demand that Palestinians have made for decades: the right to decide their destiny.

Human Rights Watch, Amnesty International, and UN experts have all warned that Gaza’s crisis cannot be resolved through imposed governance. The path forward must restore dignity, not dependency. Yet, while the world debates corridors and committees, Gaza’s hospitals run without light, and its children die nameless in the dark.

The Bottom Line

Trump’s 20-Point Gaza Plan may speak the language of peace, but its structure carries the logic of control. For Gaza, peace cannot be built by those who silence its voice. True reconstruction will not come from Washington or Tel Aviv, but it will rise from the streets of Khan Yunis and the refugee camps that still believe in freedom.

The people of Gaza do not reject peace but subjugation disguised as diplomacy. Their message to the world remains clear: “We will rebuild, but on our own terms.” And until that right is honored, no plan, however polished, can claim the name of peace.

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