Ted Gast

Ted Gast is an American artist, scientist and inventor. President at ARCH Paper and CEO cfgastco member Soulard fine arts guild. And how are you Mr Wilson?

[The Math Flow @TheMathFlow]

Johann Bernoulli posed the problem to the mathematicians of Europe in 1696; it remains vital today in quantum mechanics and many other fields.

If a ball is to roll down a ramp which connects two points, what must be the shape of the ramp's curve, such that the descent time is a minimum?
Intuition says that it should be a straight line. That would minimise the distance, but the minimum time happens when the ramp curve is a cycloid.

[FOX2now @FOX2now]

A towering symbol of Anheuser-Busch history that once looked over the Newark skyline has been restored and relit above the Anheuser-Busch brewery in STL.

[St. Louis Cardinals @Cardinals]

The first of many home run balls for Joshua Báez!

[Ted Gast @mrted57]

How about that Go Cards

[St. Louis Cardinals @Cardinals]

The first player in Major League history with three home runs in his first three plate appearances:

Joshua Báez! 💥

[Ted Gast @mrted57]

Cool very cool

[LeoDaVinciWave @LeoDaVinciWave]

The LMS Princess Coronation Class 6229 “Duchess of Hamilton” . Built at Crewe in 1938, this magnificent 4-6-2 steam locomotive was designed by Sir William Stanier as part of the LMS’s legendary Princess Coronation Class. Its streamlined body and sweeping gold stripes turned raw engineering into pure 1930s Art Deco style. Built for high-speed express travel, the Duchess could reach speeds of around 110 mph. In 1939, she even crossed the Atlantic to appear at the New York World’s Fair, showcasing British railway engineering to the world.
After decades of service and a period when her streamlined casing was removed 6229 was restored to her iconic streamlined appearance in 2009.
Today, she is preserved at the National Railway Museum in York: a remarkable survivor from the golden age when steam, speed and Art Deco met.

[Ted Gast @mrted57]

Very cool

[Dailyscienceinfo @NatureScienceA1]

The Devil Horns Solar Eclipse
Is one of the rarest sunrise ever photographed and was stunning.

[Ted Gast @mrted57]

@AMAZlNGNATURE

[Ted Gast @mrted57]

Amazing mam

[Augie Nash @AugieNash]

Extremely rare and amazing photo of Cardinals legend Dizzy Dean outside a church with his wife Pat (Date unknown)

#STLCards

[Ted Gast @mrted57]

The itsy bitsy spider

[The Figen @TheFigen_]

Spider dismantling its rain-damaged web and eating the silk to recycle proteins for a fresh rebuild.
Amazing!

[Ted Gast @mrted57]

@mathemetica Clearly an underatedly genius with a short life

[Ted Gast @mrted57]

Ratisbonna on the Danube-right in the center

[Brilliant Maps @BrilliantMaps]

Map of The Holy Roman Empire At Its Territorial Peak In The 12th Century

https://t.co/t6uzqQnC20

[Ted Gast @mrted57]

Thank you for sharing. Now a good reason to visit Wales.
God is good

[ASSYRIA TODAY ܐܬܼܘܪ ܝܘܡܢܐ @TodayAssyria]

🌹❤️ The magnificent statue of King Ashurbanipal at the Cardiff Castle Library in Wales, UK, is a beautiful tribute to one of history's greatest patrons of knowledge. 📚👑✨

King Ashurbanipal, the mighty ruler of the Neo-Assyrian Empire, understood that true power was not only won on the battlefield—it was also preserved through wisdom. ❤️📜 His greatest legacy was the creation of the Library of Ashurbanipal in the ancient capital of Nineveh, one of the most remarkable libraries the world has ever known. 🌹🏛️

Filled with more than 30,000 cuneiform clay tablets, this extraordinary collection safeguarded the knowledge of countless generations. 📖✨ It preserved laws, religious traditions, scientific observations, medicine, astronomy, literature, royal records, and the rich cultural heritage of Assyria, Babylonia, Sumer, Akkad, and neighboring civilizations. 💖🌍

Because of Ashurbanipal's vision and dedication to preserving knowledge, priceless works such as the Epic of Gilgamesh survived the passage of time. 📜❤️ His library became a beacon of learning, allowing modern historians to uncover the political, social, religious, and intellectual life of ancient Mesopotamia. 🌹📚

Without King Ashurbanipal's remarkable foresight, much of humanity's earliest written history might have disappeared forever. His devotion to learning transformed him into more than a great king—he became one of history's greatest guardians of civilization and knowledge. 👑❤️🌹

Today, his statue stands as a timeless reminder that books preserve empires long after their walls have fallen, and that wisdom is one of humanity's greatest treasures. 📚✨💖🌹

❤️🌹 Long live the legacy of King Ashurbanipal—the scholar king, protector of knowledge, and founder of one of the greatest libraries of the ancient world. 👑📜📚✨

#AshurbanipalLibrary #Ashurbanipal #AssyrianKing #Assyrian #Nineveh #Cuneiform #Mesopotamia #Assyria #Babylon #Sumer #Akkad #Assyrians #EpicOfGilgamesh #Library #AncientHistory #History #Knowledge #AncientCivilization #CardiffCastle #CardiffCastleLibrary #Heritage #Archaeology 📚👑🌹❤️

[Ted Gast @mrted57]

He turned down the prize. Yes I remember. lived with his mother. Never cut his nails. Genius. I read his book

[Mathematica @mathemetica]

Grigori Perelman, born June 13, 1966, in Leningrad (Saint Petersburg), Russia, is a mathematician known for proving major conjectures in topology.

In 2002–2003, he solved the Poincaré conjecture and Thurston's geometrization conjecture for 3-manifolds by developing Ricci flow techniques.
The Poincaré conjecture, posed in 1904, states that any closed simply connected 3-manifold is homeomorphic to the 3-sphere.

This resolved a Millennium Prize Problem. Perelman declined the 2006 Fields Medal and the 2010 $1 million Millennium Prize, citing fairness regarding prior contributions by Richard Hamilton.

[Ted Gast @mrted57]

Of course das ist sicher das ist schwarz Meeriisches Land; sicher. How much do I say it

[Terrible Maps @TerribleMaps]

99% of Americans won’t know this country

[Ted Gast @mrted57]

The Scythian way cont'd
It is believed that the Sakhas descend from the Quriqan (Tokarev 1962: 107; Golden 1992: 143–4, 415), which was a Tiele tribe (see Jiu Tangshu 199b.5343).

[Ted Gast @mrted57]

The Scythian Way
“The Sakhas, formerly known as Yakuts, are the easternmost as well as northernmost Turkic people in the world.
They were originally a horse-riding people from the western Baikal region.

[Ted Gast @mrted57]

Im sure I dont Know

[University of Arizona @uarizona]

U of A President @SVGarimella has released his second annual letter to the university community, detailing how the university advanced its strategic imperatives over the past year while positioning itself for even greater impact in the years ahead. https://t.co/UygRYBh3K5

[University of Arizona @uarizona]

“BUT WHY DO THEY SAY ‘BEAR DOWN’ IF THEY’RE THE WILDCATS?”

Class is in session. Our topic? John Byrd “Button” Salmon. ↓

[Ted Gast @mrted57]

Of course he did

[Tech with Mak @techNmak]

In 1683, a Swiss mathematician named Jacob Bernoulli asked a simple question about money.

If you deposit $1 at 100% annual interest, what happens if you compound it more and more frequently?

Once a year → $2.00
Twice a year → $2.25
Monthly → $2.613...
Daily → $2.714...

The more frequently you compound, the higher it goes, but it never grows without limit. It converges.

Bernoulli proved that limit exists:

e = lim (1 + 1/n)ⁿ as n→∞

He couldn't calculate it exactly, but showed it had to fall between 2 and 3.

That limit is e ≈ 2.71828...

He didn't name it. Fifty years later, Leonhard Euler calculated it to 18 decimal places, and the letter e stuck - appearing first in Euler's letter to Goldbach in 1731.

Why e is special:

e is the only number where the exponential function eˣ is its own derivative.

That one property sounds abstract. In practice it means: when you differentiate eˣ, you get eˣ back. The rate of change equals the value itself.

This makes the calculus clean. No extra constants, no messy chain rule artifacts.

And clean calculus is everything when you're training a neural network through millions of gradient updates.

Where e lives in every AI system you build:

1/ Sigmoid function
the S-shaped function that maps any real number to a value between 0 and 1.

σ(x) = 1 / (1 + e⁻ˣ)

Used in logistic regression and binary classification. e is what makes its derivative expressible in terms of itself - σ'(x) = σ(x) · (1 - σ(x)), which keeps backpropagation computationally clean.

2/ Softmax
the function that converts raw model output scores (logits) into a probability distribution across multiple classes.

softmax(xᵢ) = eˣⁱ / Σeˣʲ

Every token probability your LLM produces passes through this. e is used because it keeps all values positive and makes the gradients during training well-behaved.

3/ Cross-entropy loss
the loss function used to train most classifiers and language models. It uses the natural logarithm (ln), which is the inverse of e.

The full picture:

A banker's question in 1683 → a universal mathematical constant → the backbone of every neural network trained today.

Bernoulli was thinking about interest rates. He had no idea he was laying the foundation for gradient descent.

That's what makes pure mathematics dangerous. It doesn't look useful until suddenly it's everywhere.

[Ted Gast @mrted57]

. . . and the taste has nothing to do with it The best hyperbolic paraboloid on the market (sic) I love your mat

[Mathematica @mathemetica]

Pringles chips form a hyperbolic paraboloid: z = x²/a² − y²/b² where x²/a² + y²/b² < 1.

The surface rises parabolically along one axis and falls along the other, producing a saddle that contains two continuous families of straight lines.
Those linear generators give the thin wafer high resistance to bending forces.

Packaging lines use the identical geometry so successive chips interlock in a rigid stack that survives the axial compression inside a sealed cylindrical can from factory to shelf.