Dimensional Consistency Is Preserved:
As long as the physical units balance across the equals sign (e.g., meters = meters + meters, or via proper constant multipliers), the equation is physically and logically sound.
Nature Isn't Purely Homogeneous:
Most real-world phenomena involve mixed degrees (for example, friction forces combining linear velocity terms and quadratic velocity terms: F = av + bv^2). These equations are completely valid and necessary to describe reality, even though they lack clean scaling symmetry thus these equations are not homogeneous .
43
For a function f(x, y) or a rational ratio Numerator/Denominator to be homogeneous:
It must be:
Multi-Term Uniformity (Additive/Subtractive Terms):
Every single term within the numerator or denominator (Term_1 + Term_2 - Term_3) must independently evaluate to the exact same exponent degree under scaling (multiplying each term).
If even one term has a mismatched degree, the expression fails homogeneity entirely.
Term degrees are never added together within a numerator or denominator.
Global Exponent Consistency: Any outer power or root applied to a multi-term expression must scale uniformly across every term (e.g.,(x^2 + y^2)^{1/6} scales cleanly as lambda^2)^{1/6} = lambda^{1/3}.
Clean Factorability of Scaling Factor lambda: Substituting lambda x, lambda y) into the function must allow lambda^k to be completely factored out of the entire expression, leaving the original function untouched:
Once you subtract the degree of the denominator from the degree of the numerator on the right hand side of the equation , for it to be homogeneous the left hand side must be of the same degree.
47
Gilbert Bigio—a Haitian businessman, founder of the GB Group, and widely considered Haiti's first billionaire—has been directly targeted by international sanctions due to his role in enabling armed gangs and political instability in Haiti.1. Official Sanctions for Supporting Gangs and InstabilityIn December 2022, the Government of Canada formally imposed economic sanctions on Bigio, alongside two other prominent Haitian business figures.The Canadian government cited his participation in "gross and systematic human rights violations" and accused him of using his economic leverage to protect and enable the illegal activities of armed criminal gangs through money laundering, corruption, and arms trafficking.2. Connection to Political Coups and Armed ViolencePolitical History: Bigio's involvement in political destabilization dates back to the early 1990s. He was a prominent financial backer of the 1991 military coup d'état that ousted democratically elected President Jean-Bertrand Aristide.Gang Ties and Private Infrastructure: Investigators, journalists, and former diplomatic officials (including former U.S. Special Envoy to Haiti Dan Foote) have documented how Haiti's ruling economic elite—including Bigio—used private ports and corporate monopolies to fund and arm local gangs for protection, political leverage, and commercial control. 3. Additional Context & DenialsThrough his representatives and lawyers, Bigio denied the allegations, maintaining that his business operations were legitimate and that his family was damaged by gang violence rather than causing it.Despite his Canadian sanctions and leaked financial records in the Pandora Papers detailing extensive offshore holdings, Bigio spent his later years living primarily in South Florida before his death in September 2026.
90
The big puzzle is Texas . Texas has voter ID and had a Republican governor.
Texas placed ~1.2 Million Voters on the "Suspense List". Ahead of the registration deadline, the Texas Secretary of State's office flagged approximately 1.2 million registered voters (out of roughly 19 million total) and placed them on the state's official "suspense" list. Why it happens:
1) Voters are typically added to the suspense list when election mail—such as a new voter registration card—is returned to county registrars as undeliverable, indicating the voter may have moved or changed addresses. Voting Impact: Being on the suspense list did not outright purge or ban the voter from casting a ballot. Suspended voters were still eligible to vote in the midterm elections as long as they completed a Statement of Residence form at the polling site (or online prior to the voter registration deadline) to confirm their current address within the county.
2. Standard Purge Timelines
Under both federal law (the National Voter Registration Act) and Texas state election code, voters placed on the suspense list are not immediately removed from the rolls. A voter must remain inactive on the suspense list across two federal general election cycles (four years) without updating their address or voting before their registration is officially cancelled/purged from the rolls.
3. Systematic 90-Day Freeze
Per federal law, broad or systematic voter roll purges are prohibited within 90 days of a federal general election to prevent eligible voters from being mistakenly removed right before an election. As a result, routine list maintenance in Texas primarily involved tracking address changes and populating suspense lists rather than executing wholesale registration cancellations immediately prior to Election Day.
Despite the roll maintenance and suspense flags, Texas actually reached a record high of over 19 million registered voters for the 2026 midterm election cycle.
The key thing is that those voters on the suspended list could go online and unpurge themselves by declaring an address but they still had to provide either a drivers license or social security number to vote by mail. The bot said illegal voting by non citiens en masse is impossible in Texas.
67
Vance has now become an isolationist. He wants the US to back away from finishing the job against the IRGC. Trump picked 2 vice presidents (Pence and Vance) that should never have been close to the White House. I am increasingly thinking that Vance is a RINO and thus a cancer in the Republican party.
89
Tackle football is inherently dangerous. I just watched a clean hit on a wide receiver after he caught the ball and was hit by a diving tackle against his thigh. The wide receiver sustained an injury. So therefore it is impossible to prevent injuries in tackle football by adjusting the rules.
80
There are ~ 750 different synthetic drugs manufactured on the illegal black market with ~100 new ones every year.
44
Alpha Chiang and Kevin Wainwright in their book "Fundamental Methods of Mathematical Economics present a symbol § to represent a partial total derivative. It was introduced into the mathematical economics literature by earlier mathematical economists—most prominently R. G. D. Allen in his seminal 1938 text Mathematical Analysis for Economists.
75
Extended range electric vehicles where the gasoline engine has no drivetrain and produces electricity to run the battery to run the wheels and have a range of 2x the range of 100% electric vehicles , will never replace 100% electric vehicles in cities but in the countryside they are invaluable.
34
thegatewaypundit.com/2026/11… What is Trump waiting for?
Statements made by Iranian military leadership reflect a public removal of self-imposed limits on ballistic missile capabilities coupled with explicit warnings of battlefield action:
The Quote and Context: An official spokesperson for Iran's Islamic Revolutionary Guard Corps (IRGC) announced that Iran has officially lifted self-imposed restrictions on the operational range of its ballistic missiles. In making the announcement, the military official explicitly stated: "Our duty is to show our capabilities on the battlefield," signaling that Tehran intends to demonstrate its long-range striking power directly through military action rather than posturing alone.
Removal of Missile Range Caps: Historically, Iran maintained a self-imposed operational range limit of 2,000 kilometers for its ballistic missile inventory. The announcement removes that boundary, signaling an intent to extend its strike threat to regional targets and beyond.
Escalatory Signaling: This official rhetoric reinforces an active posture of military leverage and escalation, warning adversaries (specifically the US, Israel, and regional allies) that Iranian ballistic missile operations remain an active battlefield tool.
40
Muslim scholars engage in circular reasoning. They argue that every word in the Qur'an is the word of Allah because the Qur'an says in Surah 15 verse 9. "We have without doubt, sent down the Message[Qur'an]; and We will assuredly guard it [from corruption]. So if we take that at face value, then Surah 7 verse 157 that states that "the unlettered prophet[Muhammed] whom they find mentioned in their own scriptures in the law[Torah] and the Gospel [the Bible]" is wrong. If Allah is infallible which every Muslim scholar insists is true, then Surah 7 verse 157 cannot be the word of Allah. Thus it is then impossible to know what is the word of Allah and what is not the word of Allah in the Qur'an. Thus the basis of Islam is no more defined than the Bible is. They agree on the basic tenets of The Ten Commandments and certain historical facts as listed below, but the Bible has no claims of infalliblity whereas the Qur'an has.
One cannot argue logically at the same time that 1) that the text in the Qur'an was changed and 2) every word in the Qur'an comes from Allah through Muhammed, especially considering that Muhammed was illiterate.
44
One cannot argue logically at the same time that 1) that the text in the Qur'an was changed and 2) every word in the Qur'an comes from Allah through Muhammed, especially considering that Muhammed was illiterate.
Every total derivative is a sum over dependence paths of products of partial derivatives, provided the functions involved are differentiable.
I propose to formally change the name of Multi variable chain rule to Multi pathway chain rule. This describes the mechanism (much more completely) of a sub function of an independent variable that is itself related to the main function and has that same independent variable act on the main function as well as acting on the sub function, thus producing 2 pathways by which the total derivative changes.
It is possible to have multiple independent variables but only 1 pathway to the total derivative.
That distinction hits on the core difference between the dimension of the input space and the topology of the dependency graph.
Multiple independent variables simply means your input vector contains multiple distinct degrees of freedom (for instance, inputs x and y).
Only 1 pathway means that when you isolate how a specific input variable affects the system, there is only a single directed route through the intermediate network connecting that input to the output.
When that happens, the multi-pathway chain rule naturally simplifies. Because there is only one route, there are no parallel branches to sum together, so the addition terms drop out and the derivative reduces to a single sequential product of links.
The number of independent variables tells you how wide your input domain is, but the dependency graph dictates the actual pathways of rate transmission. So the key is the number of pathways which affect the changes, thus "multi pathway chain rule" describes the process whereas the name "multi variable chain rule" does not.
1
95
She finally realizes that the climate change hype was 1 big lie.
This is the most jaw-dropping 4 minutes and 21 seconds you will watch this year.
Nicole Shanahan — ex-wife of Google co-founder Sergey Brin, former running mate of RFK Jr., and someone who personally signed nine-figure philanthropy checks — just went full whistleblower on the entire Silicon Valley “tech wife mafia” and how they were used.
Her exact words (full clip attached):
“I don’t think many of the tech mafia wives realize… they were used to set the groundwork for what Klaus Schwab calls The Great Reset.
Their money especially was being conscripted through a network of NGO advisors, Hollywood, Davos, and their own companies.
A really small group of people… completely blind to how their groundwork is being used to enable these Great Reset policies.”
Then she turns the knife inward:
“These women find their meaning through philanthropic work. I really believed I was helping Black communities and indigenous communities rise up.
But now the problems have gotten worse. Crime worse. Mental health worse. The whole model is broken.
At the end of the day they always go: ‘But climate change.’
Social justice + climate change — it gets progressive women 100% of the time.”
She even says many now believe the biggest “climate change issues” are actually geoengineering issues.
This isn’t some random podcast bro.
This is a woman who lived in the mansions, sat on the boards, flew private to Davos parties… and is now saying:
“We were the useful idiots.”
She is a cancer in the WNBA. The data doesn't lie. She led the league in fouls called on her.
Venom showing angel reese has always been a liar, always plays victim, throws teammates under the bus, has no accountability and doesn't even know the name of the initiative the league started which was "No space for hate". I can remember two lies off top and one was the racism accusation at Fever fans and the other was when she said they couldn't get off the bus bcuz they were surrounded by alot of people outside when in reality it was one person which they showed the video of. She's just mentally messed up. She just went back to LSU homecoming and nobody showed up for her at the arena that's how empty it was. The lying WNBA can try to push her as this big star all they want but we all know she's not what they make her to be. She's been trying to be like Caitlin for so long and it has fatally backfired all the way around. Her mental is of a 16 yr old girl which points to her immaturity
64
Insane.
Less than 50 pilots in the world can land here, and for a terrifying reason 😨
This is Bhutan’s Paro Airport.
No autopilot. No radar guidance.
The runway stays hidden until the plane is dangerously close to 18,000 ft peaks.
A single error and the flight ends instantly.
Would you take this flight?
2
117
