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Math.

3 random tidbits in about 5 minutes.

1.

A Math FAQ.

Subject: Idea Evaluation.

Is Terrance Howard correct when he says zero does not exist?.

Terrence Howard has claimed that zero does not exist and has proposed alternative mathematical theories through what he calls “Terryology.”

Is he correct? No.

Howard argues that zero represents “nothing,” and because “nothing” does not exist as a physical thing, zero should not exist in mathematics. The problem is a category mistake.

In TST terms, zero is not a physical object. It is a rational construct that represents a real state of affairs: the absence of a quantity relative to a defined set. If you have a bowl and it is removed, you possess zero bowls. That does not mean “nothing exists.” It means the quantity in question is absent.

Zero is not metaphysical nothingness. It is a structural placeholder within arithmetic and algebra that preserves consistency in counting, balance, and measurement.

Mathematics does not require zero to be a physical object. It requires zero to function coherently within a system. And it does.

 


That Math FAQ, 

was first published on TST 2 years ago.

 

2.

A Math Quote.

From History:
Subject: Planck Constant.

“It was an act of despair, to sacrifice physics for the sake of finding an explanation.”.

  • Max Planck.
  • circa 1900.

Planck was famously conservative and struggled with the fact that his math had accidentally upended the foundations of classical physics. His full quote is closer to this: 

“It was an act of despair… I was ready to sacrifice any of my previous convictions about physics… for the sake of finding a theoretical explanation.”

Planck’s “trick” was essentially a move of mathematical desperation: he abandoned the long-held belief that energy flows in a smooth, continuous stream and instead modeled it as being exchanged in tiny, finite “packets” or quanta.

To understand how he did it, you have to look at the “Ultraviolet Catastrophe.” Classical physics predicted that an object absorbing and emitting all light (a blackbody) should emit infinite energy at short wavelengths (ultraviolet). This was clearly impossible—it suggested that simply turning on an oven would blast the room with lethal X-rays. Current math and theories had to change.

By forcing the energy to be divided into these discrete chunks, he was able to statistically weigh the probabilities so that high-frequency (ultraviolet) light wouldn’t drain all the energy from the system, effectively “taming” the math to match nature. It was the physics equivalent of realizing that instead of pouring water (continuous), nature was actually handing out individual ice cubes (discrete).

The same year of his epiphany, he presented his revolutionary formula:

 
E=hv

This formula says that energy equals a constant number times the color of light (the vibration or frequency). This formula established that an energy packet of light is strictly determined by its frequency. By its color. The h in his formula is the Planck Constant: a value he reverse engineered in the months after his epiphany. Essentially, he worked backward from the experimental data like a tailor trying to find the exact “stitch size” needed to keep a fabric from tearing. By treating the vibrating atoms in the blackbody as if they could only exchange energy in specific, fixed amounts, he discovered that a universal constant was required to link a wave’s frequency to its energy. 

At the time, he didn’t even call it “the” formula; he saw it as a “lucky intuition” that happened to fit the experimental data perfectly. He later presented the full theoretical justification (the “how”) to the German Physical Society on December 14, 1900: a date now considered the birthday of quantum physics.

 


That Math Quote, 

was first published on TST 3 months ago.

 

3.

A Math FAQ.

Subject: Metaphysics.

Does infinity exist?.

Infinity exists as a philosophical concept, not physically.

You cannot do, see, or produce infinity.

This perspective dates back to Aristotle, who explored infinity as an idea that can never be physically realized. He distinguished between potential infinity—an endless process—and actual infinity, a completed infinite state. Infinity serves as a useful abstract concept that helps describe the physical world conceptually. For instance, consider calculus, which evolved from the infinitesimal concept developed by Galileo and others, laying the groundwork for Newton and Leibniz. They essentially use the concept of an infinite number of straight lines to define a curve.

When discussing infinity, it’s important to remember it cannot take a physical form. When someone says a river stretches to infinity, we understand this as a poetic expression, as a literary device, not literally. 

Various groups are exploring the notion that infinity might actually exist. For example, religiously oriented people often assert their belief in an infinite universe. Similarly, physicists like Stephen Hawking have developed mathematical formulas that predict physical infinities, such as infinitely dense or infinitely hot objects. Just remember, these ideas are built on speculative frameworks. As these frameworks are tested and potentially validated, we’ll update our Grand Rational Framework of common knowledge. Until then, infinity remains only an abstract idea. 

 


That Math FAQ, 

was first published on TST 2 years ago.

 

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