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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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Washington’s Invisible Hand: How US Power Connects Gaza’s Genocide to the Iran War

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Washington usually describes itself as a peacemaker. Yet behind that language lies a trail of weapons, aircraft, military budgets and political protection. Follow it from Gaza to Iran, and America’s role becomes difficult to hide.

The Pentagon estimates that the Iran war will cost $37.5 billion through 30 September, while the current government has sought almost $90 billion more. Meanwhile, the World Food Programme needs $420 million to prevent deeper aid cuts in Gaza.

Projected US spending on the Iran conflict is nearly 90 times Gaza’s WFP funding gap. Washington mobilises enormous resources for warfare, but Palestinians facing genocidal hunger are told that humanitarian agencies lack money.

The Alliance Behind Gaza’s Ruins

Unfortunately, Israel’s genocide has devastated the entire lifecycle in Gaza. Tens of thousands of Palestinians have been brutally killed, most residents displaced, and hospitals, schools, water networks, homes and farmland destroyed.

Even the October 2025 ceasefire did not make Palestinians safe. Israeli strikes continued, and more than 1,160 Palestinians had reportedly been killed during the ceasefire period.

Although Israel is the principal perpetrator, American support sustains its impunity. Washington supplies weapons, military cooperation and diplomatic cover while refusing to impose consequences strong enough to stop the attacks. Its statements about protecting civilians are contradicted by support for the government inflicting their suffering.

When Support Became Direct Intervention

The connection became clearer when the United States and Israel launched attacks on Iran on 28 February 2026. Iran retaliated, and what was presented as controlled military action developed into months of hostilities.

UN experts reported that unlawful operations between 28 February and early April killed at least 3,375 civilians. After an interim ceasefire collapsed, American forces conducted 13 consecutive nights of strikes.

Gaza created a dangerous precedent: mass suffering could be called self-defence while legal objections were ignored.

The Military Network Behind the Diplomacy

American involvement extends beyond money. By late June, 98 US military aircraft were stationed or operating in Israel. Additional aerial-refuelling planes were later deployed to military bases and commercial airports.

Ultimately, these tankers allow combat aircraft to fly farther and remain airborne longer. Their presence reduced activity at Ben Gurion Airport by about 70 percent.

The US House also passed a $1.15 trillion defence bill, highlighting expanded US–Israel military-technology cooperation. Thus, genocide in Gaza and escalation with Iran were being accompanied by plans to deepen the brutal alliance.

When Civilian Infrastructure Becomes a Target

President Trump threatened to destroy an Iranian bridge or power station whenever Iran was witnessed doing an unusual activity across the Strait of Hormuz. Such threats raise serious questions under international humanitarian law.

As per the international order, civilian infrastructure cannot lawfully be destroyed merely as punishment. Even where an installation has military use, an attack must meet the requirements of distinction, necessity and proportionality.

Gaza has shown what destroying essential systems means. Damaged electricity shuts down hospital equipment. Destroyed water networks spread disease. Blocked fuel stops ambulances, bakeries and sewage treatment. Civilians continue dying long after the aircraft leaves.

How the Conflict Reaches Across the Region

Iranian attacks have targeted US positions and facilities in Bahrain, Kuwait and Jordan. On the other hand, the Yemeni Houthis have attacked Saudi oil infrastructure at Jizan and Yanbu and threatened Saudi-linked shipping in the Red Sea.

Renewed hostilities could end Yemen’s fragile ceasefire and revive a devastating conflict. Insecurity around the Strait of Hormuz and Red Sea also raises shipping, fuel and others costs.

The burden enters ordinary homes through expensive food, lost livelihoods and fear of further attacks. Muslim countries are being drawn into a confrontation shaped heavily by American and Israeli decisions, while the region’s civilians pay the price.

What Washington’s Priorities Look Like in Gaza

The contrast between military and humanitarian spending becomes clearest in Gaza through the following stats:

  • Around 1.4 million Palestinians would face acute hunger by December 2026.
  • Food rations for 220,000 households have already been halved by WFP.
  • Cash assistance for 75,000 people has been reduced by 25 percent only
  • WFP supports about 70 percent of Gaza’s population but requires another $420 million.

Gaza is not starving because food does not exist. Palestinians are hungry because Israel has devastated the enclave, restricted daily life and obstructed meaningful recovery through continued genocide.

Washington finds tens of billions for military operations. When Palestinian children need bread, water and medicine, the language changes to shortages and donor fatigue.

Making the Invisible Hand Visible

The US–Israeli partnership has produced neither justice for Palestinians nor security for the Middle East. It has enabled genocide in Gaza, protected occupation, widened conflict with Iran and increased the danger facing Yemen and the Gulf.

In a nutshell, Washington’s hand may be hidden beneath terms such as alliance and deterrence, but its effects are visible in Gaza’s empty kitchens, Iran’s damaged cities and civilian graves. Israel inflicts the principal violence on Palestinians, America provides vital power and protection, and ordinary families carry the loss.

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Israel’s Election Campaign Is Being Fought on Palestinian Land and Lives

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On 17 July 2026, Israel’s parliament dissolved ahead of national elections scheduled for 27 October. As usual, Israeli politicians turned to alliances, opinion polls and political survival. However, in occupied Palestine, families faced a more urgent question: who would survive the next Israeli genocidal attack?

The election will formally be decided at Israeli ballot boxes, but its campaign is already unfolding across Gaza, the occupied West Bank and Al-Aqsa Mosque. Netanyahu, Ben-Gvir and Smotrich are competing to appear tougher on Palestinians and more committed to permanent Israeli control.

Gaza’s “Ceasefire” Still Produces Graves

Israel continues striking Gaza despite the ceasefire that began in October 2025. The bombing may be less intensive than during earlier stages of the genocide, but Palestinians are still being killed in homes and tents.

For example, on 21 July, an Israeli strike hit the al-Masri family’s home in Gaza City. Firas al-Masri, his wife Salsabeel and their four children were killed while sleeping. Meanwhile, twelve Palestinians were killed across Gaza that day, while more than 1,160 had reportedly been killed since the ceasefire began.

Amnesty International and a UN Commission of Inquiry have concluded that Israel is still committing genocide in Gaza.

Palestinian Suffering as Political Strength

Genocidal mastermind Benjamin Netanyahu enters the campaign under pressure over the October 2023 security failure, corruption proceedings and opposition. On his right, Ben-Gvir and Smotrich demand more settlements, harsher military operations and permanent Israeli control over occupied Palestinian territory.

This competition has created a cruel political test: which leader can punish Palestinians more severely and surrender less land?

The problem is not that every strike is necessarily ordered for electoral advantage. It is that Israel’s political system rewards escalation and genocide. Violence against Palestinians is marketed as strength, while restraint is attacked as weakness. Palestinian suffering becomes evidence that a candidate is “tough on security.”

Gaza Is Not Empty Land for Israeli Settlers

In July, Israeli settlers and politicians marched towards Gaza demanding the restoration of settlements dismantled in 2005. Their language of “returning home” concealed a fundamental reality, while Gaza is already the homeland of more than two million Palestinians.

Re-establishing Israeli settlements would require further land seizures, military control and forced Palestinian displacement.

Additionally, Israel is also constructing an earthen barrier more than 23 kilometres long inside Gaza along the so-called Yellow Line. Its forces control more than half of the enclave, while Palestinians have been compressed into a smaller coastal area.

What is described as a temporary security boundary will become a permanent border imposed without Palestinian consent. Gaza is being divided while Israeli politicians discuss taking land from which Palestinians have been driven.

Al-Aqsa Becomes an Electoral Stage

Unfortunately, on 23 July, more than 4,200 Israelis, including National Security Minister Itamar Ben-Gvir, entered the Al-Aqsa Mosque compound under heavy police protection. Nationalist displays and religious rituals challenged the longstanding arrangements governing the site.

For Muslims, Al-Aqsa is not a campaign backdrop. It is the first qiblah and one of Islam’s holiest places. Ben-Gvir’s repeated incursions demonstrate that Israel’s far right believes it can impose its will even within sacred Muslim space.

Each visit helps him appeal to extremists demanding greater Israeli control. Al-Aqsa is thus turned into a stage where provocation is performed for votes.

Settlers Attack, but Palestinians Receive the Punishment

The occupied West Bank shows how settler aggression and state power reinforce one another. In July, armed settlers entered the area around Tal, a Palestinian village near Nablus in Area A, where Israeli civilians are prohibited from entering. A confrontation followed in which four Palestinians were martyred, harming two Israeli soldiers.

Israel responded by sealing roads, raiding Palestinian homes and questioning approximately 80 villagers. Smotrich went further, calling for Palestinian villages to be cleared and settlements established in their place.

Moreover, recent UN figures show the wider crisis:

  • By 20 July, settler-related Palestinian deaths in 2026 had already exceeded the total recorded throughout 2025.
  • Settler attacks accounted for 55 percent of Palestinian injuries in the West Bank during 2026.
  • More than 2,300 Palestinians had been displaced by settler violence and related restrictions by early July.

The pattern seems familiar. Settlers enter Palestinian land and attack or provoke residents. Israeli genocidal forces arrive, but their overwhelming power falls upon Palestinians through arrests, closures and demolitions.

Buying Annexation Before the Election

Israel is using public money to make the occupation harder to reverse. The security cabinet approved 1.3 billion shekels, approximately $434 million, for 34 West Bank settlements.

These decisions brought the number of settlements initiated during Smotrich’s term to 103. Approximately 700,000 Israeli settlers now live among 2.7 million Palestinians in the occupied West Bank.

Roads, budgets and legal recognition create realities that may survive even if Netanyahu loses. Palestinian land is effectively being distributed as an electoral reward to the settler movement.

In fact, for Palestinians, this campaign is not a televised debate. It is experienced through drones over Gaza, armed settlers entering villages, police surrounding Al-Aqsa, and bulldozers approaching homes.

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Gaza’s Genocide Hits 1,000 Days

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Unfortunately, more than 1000 days have now passed since October 7, 2023, when Israel launched what has become one of the most thoroughly documented genocides of the modern era. Although a so-called “ceasefire” has technically been in place since October 2025, the brutal killings haven’t stopped. Neither has the destruction, the displacement, or the impunity.

The Numbers on Day 1,000

More than 73,000 Palestinians have been killed in the genocide, over 21,000 of them children, an entire generation cut down before it had the chance to grow up. Thousands more remain missing, presumed buried under rubble that has never been cleared. Up to 90 percent of Gaza’s buildings and infrastructure have been damaged or destroyed.

Additionally, more than 200 journalists have been deliberately targeted and killed by Israel. It is the deadliest campaign against reporters anywhere in the world in decades — a body count that exists because Israel has worked to make sure the world sees as little of Gaza’s destruction as possible.

Even now, with a ceasefire nominally in force, Israel still occupies roughly 60 percent of the Gaza Strip. Netanyahu also ordered the Israel Defence Forces to push that to 70 percent or more.

A Ceasefire in Name Only

Officially on paper, the guns went quiet in October 2025 under a US-brokered agreement. Whereas in practice, Gaza’s own police force has been hunted since. The UN human rights office has documented more than a dozen separate Israeli attacks on Gaza’s police since January 2026 alone, killing at least 35 officers, alongside medics, local officials, and community figures.

Analysts studying the pattern describe it plainly as a deliberate strategy. A strategy to prevent any functioning Palestinian civil order from taking root, keeping Gaza too broken to govern itself and too dangerous for anyone else to try.

The “Peace Plan” That Was Never Allowed to Begin

The architecture proposed by the “Board of Peace” that was supposed to follow the ceasefire has collapsed into paperwork and stalled committees. Hamas formally dissolved its administration this month and handed authority to a transitional body of Palestinian technocrats. This body is also known as the National Committee for the Administration of Gaza.

However, Israel has refused to let the committee’s own members enter Gaza; they remain stuck in Cairo. The International Stabilization Force (ISF) promised under the peace framework has never been deployed. The so-called Board of Peace, chaired by Donald Trump and meant to oversee reconstruction, has advanced almost nothing, and its funding mechanism holds no money at all.

Instead, the Board recently announced that UNRWA, the UN agency that has supported Palestinian refugees for 75 years, “has no place in the new Gaza”. This is a heinous move that the Palestinian leadership condemned as an attempt to erase the Palestinian refugees and, with it, the right of return.

Cruelty as Policy: The Crocodile-Moat Prisons

If anyone doubted that dehumanization remains official Israeli policy rather than genocidal excess, this month supplied the proof. Israel’s environmental protection minister has signed an order reclassifying crocodiles as “managed wild animals.” Resultantly, it cleared the last legal obstacle to a proposal from National Security Minister Itamar Ben-Gvir to surround prisons holding Palestinian detainees with crocodile-filled moats.

To practice this, the Israel Prison Service has already begun visiting zoos to study crocodile handling. Israeli officials are defending the plan on cost grounds. For example, they said that a young crocodile runs about $8,000, and an adult up to $20,000. So, the deterrent value of a moat full of predators for human beings is a line item to be budgeted rather than a moral horror to be condemned.

Roughly 9,500 Palestinians are currently held in torturous Israeli prisons, including women and children, most without ever being charged. Palestinian and Israeli rights groups alike have documented conditions of starvation, torture, and medical neglect inside these facilities.

These conditions have already killed dozens of detainees before a single moat has been dug. This same season, Israel’s Knesset passed a law making the death penalty the default sentence for Palestinians convicted in military courts. These are the tribunals that operate with none of the due-process protections a civilian court would be required to provide.

Washington’s Fingerprints Are on All of It

The United States brokered the so-called “ceasefire” and takes credit for the peace framework built on top of it. It has been far quieter about everything that has happened since.

Washington’s statements demand that Hamas disarm, but say surprisingly little about the near-daily Israeli strikes that keep breaking the ceasefire, the blockades on humanitarian aid, or the gradual Israeli withdrawal that was supposed to happen and hasn’t. The US has stayed silent as Israel carried out what amounts to a de facto annexation of the West Bank, conducted deadly military raids, and displaced hundreds of communities, which could be called “ethnic cleansing”.

American weapons, funding, and diplomatic cover have underwritten every phase of this genocide, from the first month to the thousandth day. In fact, it is the support that continued even after the International Court of Justice warned, in early 2024, that Israel’s conduct plausibly amounted to genocide under international law.

In a nutshell, the number will keep climbing for as long as the world continues treating Gaza as a diplomatic inconvenience rather than what a thousand days of evidence have already shown it to be.

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