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Deriving Harmony: A ‘Mathematical’ Reading of Parshat Vayigash and the Story of Yosef
Reading from a Torah scroll in accordance with Sephardi tradition. Photo: Sagie Maoz via Wikimedia Commons.
Parshat Vayigash brings us to one of the most emotionally charged moments in the Torah.
Yosef, now a powerful ruler in Egypt, reveals his identity to his brothers, setting the stage for reconciliation after years of separation, pain, and misunderstanding. The parsha highlights themes of forgiveness, unity, and divine providence, as fractured relationships are mended and a family realigns with its shared destiny.
From a mathematical perspective, the resolution in Parshat Vayigash can be seen as a system of linear equations. Just as a system requires each equation to be satisfied simultaneously at a single solution point, the family’s conflicting perspectives and needs converge into a unified outcome. This metaphor provides a structured lens through which to understand the intricate interplay of values, responsibilities, and emotions in this story.
The Mathematical Framework: Systems of Linear Equations
A system of linear equations consists of two or more equations that must be satisfied simultaneously. For example:
Here, x and y represent variables, while the coefficients
This concept mirrors the narrative arc of Parshat Vayigash. Yosef’s perspective, shaped by his journey and Divine purpose, represents one equation, while Yehdah’s plea, grounded in responsibility and repentance, represents another. Both have their own unique parameters, yet the Torah demands that their paths intersect to achieve harmony.
Yosef’s Equation
Yosef’s trajectory is shaped by years of hardship and Divine intervention. Sold into slavery by his brothers, he rises to become the viceroy of Egypt, using his position to save countless lives during a devastating famine. His equation includes parameters such as forgiveness, hidden identity, and the fulfillment of his prophetic dreams. Yosef operates with a long view of history, understanding that his suffering was part of a Divine plan to ensure the survival of his family.
In mathematical terms, Yosef’s line reflects a higher-level perspective. His decisions are calculated, testing his brothers to see if they have truly changed. He places Benjamin in a position of vulnerability, forcing his brothers to confront their past actions and demonstrate growth.
Yehudah’s Equation
Yehudah’s line, meanwhile, is rooted in loyalty, repentance, and self-sacrifice. Once a key player in the sale of Yosef, Yehudah now steps forward as the family’s moral leader. His heartfelt plea to protect Benjamin, even offering himself as a slave in his brother’s place, demonstrates a profound transformation. Yehudah’s parameters include responsibility for his actions, a commitment to his father Yakov, and a willingness to endure personal suffering for the sake of his family’s unity.
Yehudah’s line represents a grounded, immediate perspective. He is not thinking about grand plans or Divine foresight; he is focused on the here and now, ensuring Benjamin’s safety and preserving his father’s fragile spirit.
Solving the System
The brilliance of Parshat Vayigash lies in how these two “lines” converge. Yosef and Yehudah begin from vastly different places: Yosef with his concealed identity and tests, and Yehudah with his guilt and earnestness. Through their charged interaction, each adjusts their position, mirroring the process of manipulating equations to find a solution.
Yosef’s eventual revelation — “I am Yosef” — is the moment when the system resolves. At this point, all conditions are satisfied: Yosef’s need to confirm his brothers’ repentance, Yehudah’s commitment to his family’s well-being, and the overarching Divine plan to reunite Yakov’s children.
The solution to the system is a point of harmony where all variables align. The family’s unity is restored, not by erasing their differences, but by finding a resolution that respects and incorporates each perspective.
Lessons from the Formula
The system of linear equations in Parshat Vayigash teaches us profound lessons about reconciliation and harmony. Just as mathematical systems require each equation to maintain its integrity while finding common ground, human relationships thrive when differing perspectives are acknowledged and balanced. The Torah shows us that unity is not about uniformity; it’s about creating a space where all voices can contribute to a shared solution.
The process of solving such a system highlights the importance of adjustments and dialogue. Yosef and Yehudah’s interactions involve testing, negotiation, and moments of vulnerability. The result is a meaningful reconciliation that strengthens their family’s bond.
Conclusion
Parshat Vayigash offers a timeless blueprint for resolving conflicts and building unity. Through the lens of a system of linear equations, we see how Yosef and Yehudah’s distinct trajectories intersect to create a harmonious outcome. Each perspective brings its own parameters, yet the solution honors them all. This mathematical metaphor not only deepens our understanding of the parsha, but also inspires us to seek alignment in our own relationships, finding points of connection where harmony can flourish.
Rochie Gottheil is an analyst by day and creates high school and college math curricula in her spare time. She can be reached at Rochel.desk@gmail.com
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Stanley Fischer, Former Fed Vice Chair and Bank of Israel Chief, Dies at 81
FILE PHOTO: Vice Chair of the U.S. Federal Reserve System Stanley Fischer arrives to hear Governor of the Bank of England Mark Carney delivering the Michel Camdessus Central Banking Lecture at the International Monetary Fund in Washington, U.S., September 18, 2017. Photo: REUTERS/Joshua Roberts/File Photo
Stanley Fischer, who helped shape modern economic theory during a career that included heading the Bank of Israel and serving as vice chair of the US Federal Reserve, has died at the age of 81.
The Bank of Israel said he died on Saturday night but did not give a cause of death. Fischer was born in Zambia and had dual US-Israeli citizenship.
As an academic at the Massachusetts Institute of Technology, Fischer trained many of the people who went on to be top central bankers, including former Federal Reserve Chairman Ben Bernanke as well as Mario Draghi, the former European Central Bank president.
Fischer served as chief economist at the World Bank, and first deputy managing director at the International Monetary Fund during the Asian financial crisis and was then vice chairman at Citigroup from 2002 to 2005.
During an eight-year stint as Israel’s central bank chief from 2005-2013, Fischer helped the country weather the 2008 global financial crisis with minimal economic damage, elevating Israel’s economy on the global stage, while creating a monetary policy committee to decide on interest rates like in other advanced economies.
He was vice chair of the Federal Reserve from 2014 to 2017 and served as a director at Bank Hapoalim in 2020 and 2021.
Current Bank of Israel Governor Amir Yaron praised Fischer’s contribution to the Bank of Israel and to advancing Israel’s economy as “truly significant.”
The soft-spoken Fischer – who played a role in Israel’s economic stabilization plan in 1985 during a period of hyperinflation – was chosen by then Finance Minister Benjamin Netanyahu and Prime Minister Ariel Sharon as central bank chief.
Netanyahu, now prime minister, called Fischer a “great Zionist” for leaving the United States and moving to Israel to take on the top job at Israel’s central bank.
“He was an outstanding economist. In the framework of his role as governor, he greatly contributed to the Israeli economy, especially to the return of stability during the global economic crisis,” Netanyahu said, adding that Stanley – as he was known in Israel – proudly represented Israel and its economy worldwide.
Israeli President Isaac Herzog also paid tribute.
“He played a huge role in strengthening Israel’s economy, its remarkable resilience, and its strong reputation around the world,” Herzog said. “He was a world-class professional, a man of integrity, with a heart of gold. A true lover of peace.”
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Saudi Arabia’s Foreign Minister Says Israel Blocking Ramallah Meeting Proof of ‘Extremism’
Saudi Minister of Foreign Affairs Prince Faisal bin Farhan Al-Saud attends a news conference at the Arab Gulf Summit in Riyadh, Saudi Arabia, December 9, 2022. Photo: REUTERS/Ahmed Yosri
Saudi Arabia’s Foreign Minister Prince Faisal bin Farhan Al-Saud said the Israeli government’s refusal to allow a delegation of Arab ministers to the West Bank showed its “extremism and rejection of peace.”
His statement came during a joint press conference in Amman with counterparts from Jordan, Egypt and Bahrain, after they met as part of an Arab contact group that was going to meet Palestinian President Mahmoud Abbas in Ramallah.
“Israel’s refusal of the committee’s visit to the West Bank embodies and confirms its extremism and refusal of any serious attempts for (a) peaceful pathway… It strengthens our will to double our diplomatic efforts within the international community to face this arrogance,” the Saudi minister said.
On Saturday, Israel said it would not allow a planned meeting on Sunday that would have included ministers from Jordan, Egypt, Saudi Arabia, Qatar and the United Arab Emirates, Palestinian Authority officials said.
Bin Farhan’s visit to the West Bank would have marked the first such visit by a top Saudi official in recent memory.
An Israeli official said the ministers intended to take part in a “provocative meeting” to discuss promoting the establishment of a Palestinian state.
Jordan’s Foreign Minister Ayman Safadi said blocking the trip was another example of how Israel was “killing any chance of a just and comprehensive” Arab-Israeli settlement.
An international conference, co-chaired by France and Saudi Arabia, is due to be held in New York on June 17-20 to discuss the issue of Palestinian statehood.
Egyptian Foreign Minister Badr Abdelatty said the conference would cover security arrangements after a ceasefire in Gaza and reconstruction plans to ensure Palestinians would remain on their land and foil any Israeli plans to evict them.
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Nonprofit Ship Sets Sail for Gaza After Drone Attack Setback
Police officers detain Swedish climate campaigner Greta Thunberg, during an Oily Money Out and Fossil Free London protest in London, Britain, October 17, 2023. Photo: Reuters/Toby Melville
International nonprofit organization Freedom Flotilla Coalition (FFC) said one of its vessels left the Italian port of Catania on Sunday, heading for Gaza to deliver humanitarian aid, after a previous attempt failed due to a drone attack on a separate ship in the Mediterranean.
The crew of volunteers, including climate activist Greta Thunberg and Irish actor Liam Cunningham, set sail on the Madleen, carrying barrels of what the group called “limited amounts, though symbolic,” of relief supplies.
Another vessel operated by the group, the Conscience, was hit by two drones just outside Maltese territorial waters in early May. FFC said Israel was to blame for the incident. Israel has not responded to requests for comment.
“We are doing this because no matter what odds we are against, we have to keep trying, because the moment we stop trying is when we lose our humanity,” Thunberg told reporters at a conference before the departure.
She added that “no matter how dangerous this mission is, it is nowhere near as dangerous as the silence of the entire world in the face of the lives being genocised”.
FFC said the trip “is not charity. This is a non-violent, direct action to challenge Israel’s illegal siege and escalating war crimes.”
The situation in Gaza is the worst since the war between Israel and Hamas terrorists began 19 months ago, the United Nations said on Friday, despite a resumption of limited aid deliveries in the Palestinian enclave.
Under growing global pressure, Israel ended an 11-week blockade on Gaza, allowing limited U.N.-led operations to resume.
On Monday, a new avenue for aid distribution was also launched – the Gaza Humanitarian Foundation – backed by the United States and Israel, but with which the U.N. and international aid groups have refused to work, saying it is not neutral and has a distribution model that forces the displacement of Palestinians.
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