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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 define the relationships between them. Each equation represents a straight line on a graph, and the solution to the system is the point where the lines intersect — a place where all conditions of both equations are met.

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 

The post Deriving Harmony: A ‘Mathematical’ Reading of Parshat Vayigash and the Story of Yosef first appeared on Algemeiner.com.

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Doorstep Postings: The unbearable lightness of Justin Trudeau’s final Hanukkah as prime minister

This is a special year-end edition of Doorstep Postings, the periodic political commentary column written by Josh Lieblein for The CJN.

You all know the story that we tell this time of year: a group of Jews decided they were done with Jewish particularism and said, “Let us go an make a covenant with the nations around us” (1 Maccabees 1:11) and decided to gaslight the rest of the community into seeing things their way—and it ended very, very badly for them.

As such, Hannukah is a time for the revealing of secrets, the banishing of shadows, and the airing of grievances. Having recently reached a milestone age associated with acquiring Jewish wisdom, my own personal miracle is that after enduring 40 years of threats/promises of the imminent collapse of society and sweeping revolution, 40 years of lectures about the moral and physical decay of the West, 40 years of the most obnoxiously self-righteous folks walking the planet breathlessly informing us all of the latest irreconcilable contradiction within capitalism, I’ve finally gotten to the point where I can’t muster anything more than an eye roll anymore. 

This is because, just like every year before it, 2024 was a year of unmitigated disaster for our self-appointed reformers. I’m not just talking about Trump’s resurgence, Ukraine’s persistence, the overthrow in Syria, Hamas’s withering away, proclamations that we have reached ‘peak wokeness’, the rise of artificial intelligence and the tech bros, and the failure of centrist electoral projects everywhere but here in Canada. This was the year where the left willingly and gleefully discarded the one thing they had going for them: their tenuously held moral authority.

The success of any left-wing project hinges on successfully convincing a critical mass of undecideds that they are not like the amoral and callous right who wants you to die for their profit motive. They’ve got your best interests at heart. They’re going to sit down and hear you out and govern with joy and hope and kindness, which are alien concepts to those weird, cruel, genocidal and greedy conservatives. 

Now those of us who have been on this merry-go-round for a few turns know that it’s not that simple. Plenty of left-folks want to actively harm the rich and those they deem to be colonizers, bigots, and other associated ruling class bootlickers. The violence perpetrated by those in power justifies violence in return. This is a somewhat difficult platform to get elected on, however, because people have a bad habit of hardening their hearts in response to being threatened. And so we need suitable empty vessels to try and convince the voters that the radicals are just that: loud angry voices on the margins. The political operatives charged with laundering the baser left-wing impulses must carefully use language to make it seem that there is some daylight between them and the ends-justify-the-means crowd. 

This is a difficult task to perform because it involves not only fooling a plurality of people, if not all of the time, then for as long as the particular political project lasts. First, the operatives must trick themselves into believing in their own unimpeachable moral authority. Only once they have convinced themselves that they are the most empathic and equity-minded folks to ever draw breath can they engineer the rise of someone like Justin Trudeau. Anyone who was paying attention a decade ago could see the parallel rise of two movements: lifelong Liberals working on earned media pieces announcing the return of the Trudeau dynasty, and mostly anonymous lunatics on Tumblr who were still licking their wounds from the failure of the Occupy Movement, claiming that it was literally impossible to be racist against white people because ‘racism’ against white people wasn’t systematic. 

And as it happened, a lot of the self-proclaimed radicals bought the hype, because they saw in Trudeau something they know all too well in themselves. The desire to be loved and celebrated and told they are good, kind and moral despite, and in many cases because of, their own desire to commit and justify violence in the name of creating a better and more equal world. The Trudeau of 2015 was no less authoritarian than the figure clinging to power at the end of 2024. All that’s changed is that the radicals can no longer excuse Trudeau’s narcissism while holding out for him to bring about a world that is more equal—which is to say, a world where they have the power to do harm to their enemies. These days, Mr. Grow the Economy From the Heart Outward seems more interested in trying and failing to implement GST holidays while forcing Canada Post workers back to actual work. 

Still even as the Liberals try to envision a future without Trudeau, they remain engaged in other muddled projects, such as trying to sell the idea that Canada is engaged in an ongoing genocide but must somehow endure lest we be absorbed into the sucking Trumpist hellhole directly below us. Clearly, the Liberal Party is no longer a place for voters who are into sexy CEO-murderers, or who think Oct. 7 was an act of righteous resistance to oppression, or take China’s claims of imminent world domination seriously while denouncing Elon Musk’s similarly ridiculous pronouncements. 

But even though both the more and less radical wings of the progressive movement have had an off year and are barely speaking to one another again, we can rest assured that so long as they have to convince themselves of their own goodness they will continue to try and split this atom. Attempts to reject binaries will lead to more black and white thinking. Progressive governments will fall back into the status quo. Tumblrs will give way to Blueskys. Trudeau will fall out of favour for a few years only to be asked back after a few years of Poilievre—or some other Liberal saviour will rescue the brand. They will cast about for a new podcast hero or a leftist version of the Hawk Tuah Girl. They will insist that senile politicians are fit as fiddles, anoint barely literate fan-fiction writers as cultural arbiters, and cast lawbreakers as secular saints while vilifying anyone who’s afraid of being attacked on the street or public transit.

If the past 40 years are anything to go by, they will be as confused as ever as to why capitalism persists, why people don’t accept carbon taxes, why the world fails to condemn Israel to their liking, why poor and rural folks don’t “vote their interests”, why voters fall for Poilievre’s slogans, and why there are attempts to draw an equivalence between CEOs who condemn people to death and the people who kill those CEOs. The answer to all these questions are the same, and it’s that impure oil just burns differently—and trying to pass it off as holy can only come off as gaslighting. 

Josh Lieblein can be reached at joshualieblein@gmail.com for your response to Doorstep Postings.

The post Doorstep Postings: The unbearable lightness of Justin Trudeau’s final Hanukkah as prime minister appeared first on The Canadian Jewish News.

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Doorstep Postings: The unbearable lightness of Justin Trudeau’s final Hanukkah as prime minister

This is a special year-end edition of Doorstep Postings, the periodic political commentary column written by Josh Lieblein for The CJN.

You all know the story that we tell this time of year: a group of Jews decided they were done with Jewish particularism and said, “Let us go an make a covenant with the nations around us” (1 Maccabees 1:11) and decided to gaslight the rest of the community into seeing things their way—and it ended very, very badly for them.

As such, Hannukah is a time for the revealing of secrets, the banishing of shadows, and the airing of grievances. Having recently reached a milestone age associated with acquiring Jewish wisdom, my own personal miracle is that after enduring 40 years of threats/promises of the imminent collapse of society and sweeping revolution, 40 years of lectures about the moral and physical decay of the West, 40 years of the most obnoxiously self-righteous folks walking the planet breathlessly informing us all of the latest irreconcilable contradiction within capitalism, I’ve finally gotten to the point where I can’t muster anything more than an eye roll anymore. 

This is because, just like every year before it, 2024 was a year of unmitigated disaster for our self-appointed reformers. I’m not just talking about Trump’s resurgence, Ukraine’s persistence, the overthrow in Syria, Hamas’s withering away, proclamations that we have reached ‘peak wokeness’, the rise of artificial intelligence and the tech bros, and the failure of centrist electoral projects everywhere but here in Canada. This was the year where the left willingly and gleefully discarded the one thing they had going for them: their tenuously held moral authority.

The success of any left-wing project hinges on successfully convincing a critical mass of undecideds that they are not like the amoral and callous right who wants you to die for their profit motive. They’ve got your best interests at heart. They’re going to sit down and hear you out and govern with joy and hope and kindness, which are alien concepts to those weird, cruel, genocidal and greedy conservatives. 

Now those of us who have been on this merry-go-round for a few turns know that it’s not that simple. Plenty of left-folks want to actively harm the rich and those they deem to be colonizers, bigots, and other associated ruling class bootlickers. The violence perpetrated by those in power justifies violence in return. This is a somewhat difficult platform to get elected on, however, because people have a bad habit of hardening their hearts in response to being threatened. And so we need suitable empty vessels to try and convince the voters that the radicals are just that: loud angry voices on the margins. The political operatives charged with laundering the baser left-wing impulses must carefully use language to make it seem that there is some daylight between them and the ends-justify-the-means crowd. 

This is a difficult task to perform because it involves not only fooling a plurality of people, if not all of the time, then for as long as the particular political project lasts. First, the operatives must trick themselves into believing in their own unimpeachable moral authority. Only once they have convinced themselves that they are the most empathic and equity-minded folks to ever draw breath can they engineer the rise of someone like Justin Trudeau. Anyone who was paying attention a decade ago could see the parallel rise of two movements: lifelong Liberals working on earned media pieces announcing the return of the Trudeau dynasty, and mostly anonymous lunatics on Tumblr who were still licking their wounds from the failure of the Occupy Movement, claiming that it was literally impossible to be racist against white people because ‘racism’ against white people wasn’t systematic. 

And as it happened, a lot of the self-proclaimed radicals bought the hype, because they saw in Trudeau something they know all too well in themselves. The desire to be loved and celebrated and told they are good, kind and moral despite, and in many cases because of, their own desire to commit and justify violence in the name of creating a better and more equal world. The Trudeau of 2015 was no less authoritarian than the figure clinging to power at the end of 2024. All that’s changed is that the radicals can no longer excuse Trudeau’s narcissism while holding out for him to bring about a world that is more equal—which is to say, a world where they have the power to do harm to their enemies. These days, Mr. Grow the Economy From the Heart Outward seems more interested in trying and failing to implement GST holidays while forcing Canada Post workers back to actual work. 

Still even as the Liberals try to envision a future without Trudeau, they remain engaged in other muddled projects, such as trying to sell the idea that Canada is engaged in an ongoing genocide but must somehow endure lest we be absorbed into the sucking Trumpist hellhole directly below us. Clearly, the Liberal Party is no longer a place for voters who are into sexy CEO-murderers, or who think Oct. 7 was an act of righteous resistance to oppression, or take China’s claims of imminent world domination seriously while denouncing Elon Musk’s similarly ridiculous pronouncements. 

But even though both the more and less radical wings of the progressive movement have had an off year and are barely speaking to one another again, we can rest assured that so long as they have to convince themselves of their own goodness they will continue to try and split this atom. Attempts to reject binaries will lead to more black and white thinking. Progressive governments will fall back into the status quo. Tumblrs will give way to Blueskys. Trudeau will fall out of favour for a few years only to be asked back after a few years of Poilievre—or some other Liberal saviour will rescue the brand. They will cast about for a new podcast hero or a leftist version of the Hawk Tuah Girl. They will insist that senile politicians are fit as fiddles, anoint barely literate fan-fiction writers as cultural arbiters, and cast lawbreakers as secular saints while vilifying anyone who’s afraid of being attacked on the street or public transit.

If the past 40 years are anything to go by, they will be as confused as ever as to why capitalism persists, why people don’t accept carbon taxes, why the world fails to condemn Israel to their liking, why poor and rural folks don’t “vote their interests”, why voters fall for Poilievre’s slogans, and why there are attempts to draw an equivalence between CEOs who condemn people to death and the people who kill those CEOs. The answer to all these questions are the same, and it’s that impure oil just burns differently—and trying to pass it off as holy can only come off as gaslighting. 

Josh Lieblein can be reached at joshualieblein@gmail.com for your response to Doorstep Postings.

The post Doorstep Postings: The unbearable lightness of Justin Trudeau’s final Hanukkah as prime minister appeared first on The Canadian Jewish News.

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IDF Releases Investigation into Discovery of 6 Hostages’ Bodies

i24 News – The IDF released on Tuesday the investigation into the murder of six abductees at the end of August: Carmel Gat, Eden Yerushalmi,

Goldberg-Polin, Alexander Lubnov, Almog Sarusi, and Sergeant Ori Danino.

According to the findings of the investigation, when the IDF operation began in the area of the tunnel, Major General Nitzan Alon did not believe abductees would be in the area. As the operation continued, the military assessment said the probability was even lower.

The abductee who was extricated, Qaid Farhan Alkadi, was found alone, as neither he nor additional terrorists taken from the area provided indications to the additional abductees.

In the absence of new information, the operation continued in the area, the investigation said. Only then did the forces locate the bodies of the six abductees. In addition, forensic findings were found indicating that Hamas leader Yahya Sinwar had been there. It remains unclear whether he gave the order to murder the abductees himself. No signs of struggle during the murder were found in autopsies.

IDF Spokesperson Daniel Hagri visited the tunnel and described the harsh conditions in which the six abductees endured. “They were heroes who were cold-bloodedly murdered by terrorists who build tunnels under children’s rooms,” he said. “We will hunt them down and know exactly who they are, we will find the one who murdered them. The teams here collect all the evidence from the scene.”

“We didn’t know the exact location of the hostages in the tunnel. They were killed before we could reach them. We are investigating the incident of their names being leaked prior to their rescue. This is a very serious event that is harmful to the families and the security of the forces on the ground.”

The post IDF Releases Investigation into Discovery of 6 Hostages’ Bodies first appeared on Algemeiner.com.

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