@MathMath901 How do you measure tension? (B) has the greatest "tension" in the rope b/c the length of rope is the shortest. But the question asks about the wooden posts, not the rope. Tension = "force density" ? = force/unit length?
Perspective is everything.
This 1986 ad screened by The Guardian changed how we view things with its shocking visual of a 'skinhead' seemingly taking a man's briefcase.
But it's only when you enlarge your view, that you see the full picture.
The Chinese Physicist Who Turned Force Into Geometry
In 1954, Chinese physicist Chen-Ning Yang, together with Robert Mills, introduced a new idea that changed modern physics:
Maybe a force is not just something that pushes or pulls. Maybe a force can come from geometry.
In Yang-Mills Theory, every point in space carries a hidden internal direction. As you move through space, that direction can twist. If you go around a closed loop and the direction does not return exactly the same, the field has curvature. That curvature is what we see as force.
In this animation, the glowing surface shows where the gauge field is strongest. The changing colours show how the hidden internal direction varies across space. The moving rectangular loops are Wilson loops. They travel through the field and measure how much the internal direction changes after completing a closed path.
The key equation behind the scene is
Fₓᵧ = ∂ₓAᵧ - ∂ᵧAₓ + Aₓ × Aᵧ.
The final term, Aₓ × Aᵧ, is the special part. It means the field can interact with itself. That self-interaction is one reason Yang-Mills theory became one of the foundations of particle physics.
#China #ChinesePhysics #YangMills #GaugeTheory #QuantumFieldTheory #NonAbelianGeometry #WilsonLoops #ModernPhysics #STEM
“Capitalism is not a profit system, it is a profit and loss system, and the losses are more important than the profits.”
—Milton Friedman
But the US education system runs on the exact opposite principle.
No failure allowed. Instead of closing or losing funding, failing schools get more taxpayer money, more administrators, and more programs.
And bad teachers rarely face real consequences thanks to tenure and union protection. The “customers” (parents and kids) have almost no exit.
Real per-pupil spending has nearly tripled since 1970 after inflation. NAEP scores flat or eroding in core skills for decades. PISA rankings middling at best, with math especially weak.
Thomas Sowell diagnosed this in Inside American Education, asserting that the system is morally and intellectually bankrupt.
It has turned into a propaganda operation more than an educator primarily pushing ideology, feelings, and self-esteem over knowledge and competence.
With endless public money and zero market test, there is nothing forcing correction. Unions buy political protection so the failure machine keeps running.
Friedman and Sowell both identified the same disease and the same cure, namely real competition and choice.
Vouchers or education savings accounts let parents take the money and flee failure. Good schools grow, while bad ones finally face losses and must improve or die.
Without the discipline of losses, mediocrity is subsidized forever. And the kids, especially in the worst districts, pay the permanent price.
But that’s just the system working exactly as designed.
If you've ever wanted to quit your thing, watch this.
Before he was a household name, before the memes, before the BILLIONS, this was Elon in the trenches.
Most people would have quit. He looked the interviewer in the eye and said: NEVER.
Brandon Gill is an absolute legend. He goes back and forth with this FRAC's director of SNAP idiot about how sugary sodas are not nutrition, and at the end of the questioning he left her looking like a deer in headlights when he exposed who funds EBT 👏🏼
Jeff Bezos explains the Wandering Rule behind real invention:
"When I sit down to work on a problem, I know I don't know where I'm going."
"To go in a straight line, to be efficient, efficiency and invention are sort of at odds."
"Real invention, not incremental improvement... real lateral thinking... requires wandering."
"You have to give yourself permission to wander."
"A lot of people feel like wandering is inefficient."
"I don't know how long the meeting is going to take if we're trying to solve a problem."
The useful distinction:
Use efficiency when the path is known.
Use wandering when the problem is still being discovered.
Most teams kill invention by demanding a straight line too early.