Borbin the 🐱

In 1776, the paperwork started. Two hundred and fifty years later, the celebration was still loud enough to be photographed.

3,0s f/13 ISO 100/21° 50-250mm f/4,5-6,3 VR f=175mm/262mm

1,3s 4s, 4s, 5s f/13 ISO 100/21° 50-250mm f/4,5-6,3 VR f=175mm/262mm

5s 3s 4s 1,6s f/13 ISO 100/21° 50-250mm f/4,5-6,3 VR f=175mm/262m

I have watched over twenty of them. Was only supposed to be here for one.

Actually, it all started with Internet Explorer. That was the reason for the trip. One year, a browser, and then back.

Internet Explorer 4. Internal build. Not available in stores.¹
The reason the one-year plan did not end on schedule.

And remember America Online? 100 free hours. At 28.8k, that was about 1.2 GB of theoretical ambition.

Eventually, there were ship parties.²

Major releases. Major parties.

The world kept changing around me. So did the work. The browser became Windows, the one you are probably running right now.

Windows Millennium Edition, Beta 2. The version before the version. Space Needle included.

Still waiting for first boot.

With the credits booklet. One highlight.

The foundation came first. The thank you came later.

And then AI arrived, and suddenly even the tools had tools. Maybe you asked one something today. That answer has a longer history than it looks.

The sky eventually reclaimed the agenda.

3,0s f/13 ISO 100/21° 50-250mm f/4,5-6,3 VR f=175mm/262mm

Photographing fireworks is practice in letting go of the plan. The light does what it wants. The camera catches what it can.³

The horizon always narrows, keeping your outlook undimmed. Rarely a moment ends entirely still.

Piloti is an ultra-thin, self-supported aluminum rotunda by Marc Fornes / THEVERYMANY, commissioned by the City of Bellevue. It stands at the edge of Downtown Park, close to the towers but clearly not designed to think in straight lines. The trees help. So does the sunshine.

It is one of those places where I stop longer than planned.

1/1000s ISO 100/21° f=7,5mm

The sun was bright enough to make every shadow look like it had been organized in advance.

1/1000s ISO 100/21° f=7,5mm

The theme for The World Wide Panorama was "Exception", and this was the view that made the whole series happen. Bellevue around Piloti is all glass, clean edges, and corporate geometry. Downtown edges met one deliberate anomaly, yet the city kept its face straight. Then this thing stands there, soft and strange, like it grew overnight and nobody wanted to ask too many questions.

That was the exception I wanted: not a spectacle, but something that quietly refuses to behave like the city around it.

Interactive Panorama Piloti-Skulptur 1 360x180

1/1000s f/5,6 ISO 100/21° f=7,5mm

The Panorama Supervision Unit also made a brief appearance.⁴

From this side, Piloti feels less like a landmark and more like something the park quietly kept for itself.

Interactive Panorama Piloti-Skulptur 2 360x180

1/1000s f/5,6 ISO 100/21° f=7,5mm

The little planet version gives the park a suspicious amount of authority.

Inside, it feels less like looking at the sculpture and more like standing under its idea.

Interactive Panorama Piloti-Skulptur 3 360x180

1/640s f/5,6 ISO 100/21° f=7,5mm

These are the original NEF frames; with the hard contrast under the sculpture, the RAW data was useful for recovering highlight and shadow detail and building a more natural HDR-like result.

The last little planet makes a tiny roofed world out of it. No permit required.

Chow Mein aus dem Wok 🍜

Nicht alles muss aus Code, Tools und Builds bestehen. Manchmal ist es ganz gut, zwischendurch etwas zu machen, das genauso viel Struktur hat, aber deutlich besser riecht. Diesmal: Chow Mein, also gebratene asiatische Nudeln mit viel Gemüse, Hitze aus dem Wok und genau diesem kurzen Moment, in dem aus einzelnen Zutaten plötzlich ein richtiges Gericht wird.

Ich mag an solchen Gerichten, dass sie schnell wirken, aber trotzdem präzise sind. Alles wird vorbereitet, liegt bereit, und dann geht es Schlag auf Schlag. Fast ein bisschen wie bei einem Deployment: Wenn das Setup stimmt, läuft der Rest sauber durch. Nur eben mit Knoblauch, Sojasauce und Sesamöl statt Logs und Pipelines.

Am Ende ist Chow Mein genau das, was gute Küche oft ist: unkompliziert, direkt und voller Aroma. Hier ein paar Bilder vom Entstehen.

Alle Zutaten im Überblick

Bevor der Wok heiß wird, kommt erst einmal Ordnung auf die Arbeitsfläche: Nudeln, Gemüse, Sauce und alles, was später in wenigen Minuten zusammenfinden soll. Bei so einem Gericht ist die Vorbereitung fast die halbe Miete.

1/40s f/5,6 ISO 100/21° 16-50mm f/2,8 VR f=32mm/48mm

Im Wok: die ersten Schritte

Jetzt wird es ernst. Das Gemüse kommt in den heißen Wok, alles bleibt in Bewegung, und nach den ersten Sekunden entsteht schon dieser typische Duft, bei dem klar ist: Das wird gut.

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Im Wok: Nudeln und Sauce dazu

Sobald die Nudeln dazukommen, wird aus Vorbereitung ein Gericht. Die Sauce verbindet alles, der Wok gibt Röstaromen dazu, und plötzlich sieht es nicht mehr nach Zutaten aus, sondern nach Abendessen.

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Kurz vor dem Finale

Jetzt passt alles zusammen: Farbe, Struktur und genau die Mischung aus gebraten, saftig und leicht karamellisiert, die Chow Mein ausmacht. Noch ein letzter Schwung im Wok, dann kann angerichtet werden.

1/40s f/5 ISO 500/28° 16-50mm f/2,8 VR f=24mm/36mm

Auf dem Teller

Fertig. Ein Teller Chow Mein, frisch aus dem Wok, heiß, würzig und genau richtig für einen Beitrag, der ausnahmsweise nicht von Technik handelt. Wobei: Ein gutes Ergebnis nach sauberer Vorbereitung ist am Ende doch wieder ziemlich vertraut.

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Mit Garnelen

Eine Variante, die dem Gericht nochmal eine etwas andere Richtung gibt. Die Garnelen passen sehr gut zu den gebratenen Nudeln und bringen noch einmal ihren eigenen Charakter mit.

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Fertig angerichtet

Am Teller sieht man dann, wie gut alles zusammenkommt: Farbe, Struktur und genau die Mischung aus Wok-Aroma und frischen Zutaten, die so ein Gericht ausmacht.

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⁵

More than two thousand years ago, Archimedes⁶ tried to calculate the circumference of a circle. It was already known that larger circles have both a larger diameter and a larger circumference, but it was not clear whether the ratio between them would always remain the same.

By enclosing a circle between polygons with an increasing number of sides, he was able to show that this ratio is the same for every circle, and that its value can be bounded within steadily tightening intervals. Using a polygon of 96 sides, he proved that the value is contained in the interval

$$\frac{223}{71} < \pi < \frac{22}{7}$$

Archimedes narrowing the bounds

After Euler adopted the notation in 1736, the world denoted this value as $\pi$ ⁷

As an irrational number, its decimal expansion never repeats and never ends. And the search for more digits has never stopped.

This raises a simple question.

How many of those digits do we actually need to describe something real?

The circumference of a circle provides exactly that test.

The circumference of a circle is

$$C = \pi D$$

So any inaccuracy in $\pi$ directly affects the result.

Example: The Earth

The diameter of the Earth is approximately

$$D_{Earth} \approx 12742\ km$$

We want the circumference to be correct within

$$1\ mm = 0.001\ m$$

This means the allowed error in the circumference is

$$\Delta C \leq 0.001\ m$$

Since

$$C = \pi D$$

any error in $\pi$ causes

$$\Delta C = D \cdot \Delta \pi$$

So the required accuracy of $\pi$ must satisfy

$$D \cdot \Delta \pi \leq 0.001$$

Solving for $\Delta \pi$ leads to

$$\Delta \pi \leq \frac{0.001}{12742\cdot1000}$$

$$\Delta \pi \leq 7.85 \times 10^{-11}$$

That corresponds to roughly 10 decimal places of $\pi$. Using 10 places results in an error of about $10^{-11}$, which is within the required bound.

So if you use

$$\pi_{10} = 3.1415926536$$

you can calculate the circumference of the entire Earth with an error smaller than one millimeter.

Example: A Pizza

The diameter of a pizza is approximately

$$D_{Pizza} \approx 0.30\ m$$

This time we set the target accuracy to the diameter of an atomic nucleus

$$1\ \text{fm} = 10^{-15}\ m$$

Applying the same formula leads to

$$\Delta \pi \leq \frac{10^{-15}}{0.30}$$

$$\Delta \pi \leq 3.3 \times 10^{-15}$$

That corresponds to roughly 15 decimal places of $\pi$.

So if you use

$$\pi_{15} = 3.141592653589793$$

you can calculate the circumference of a pizza with an error smaller than the diameter of an atomic nucleus.

Example: The Observable Universe

Now let us scale things up.

The diameter of the observable universe is estimated at roughly

$$D_{Universe} \approx 8.8 \times 10^{26}\ m$$

Using the same formula with a target accuracy of 1 mm, as in the Earth example, leads to

$$\Delta \pi \leq \frac{0.001}{8.8 \times 10^{26}}$$

$$\Delta \pi \leq 1.14 \times 10^{-30}$$

That corresponds to roughly 30 decimal places of $\pi$.

So if you use

$$\pi_{30} = 3.141592653589793238462643383279$$

you can calculate the circumference of the entire observable universe with an error smaller than one millimeter.

---

Conclusion

Ten digits of $\pi$ are enough for planetary scale.

Fifteen digits are enough to measure a pizza to the width of an atomic nucleus.

Thirty digits are enough for cosmic scale.

Beyond that, the digits describe no physical quantity we can measure, only the internal consistency of mathematics itself.

Fifteen digits are also exactly what NASA uses to navigate spacecraft across the solar system, the same precision that measures a pizza to the width of an atomic nucleus.
They have not yet missed a planet.

Interplanetary navigation with finite precision

See also Engineering Pi Day

Zwischen Rückblick und Ausblick liegt dieser Augenblick.

1/30s f/5,6 ISO 800/30° 16-50mm f/2,8 VR f=50mm/75mm

1/125s f/2,8 ISO 2800 16-50mm f/2,8 VR f=33mm/49mm

1/30s f/5,6 ISO 3200/36° 16-50mm f/2,8 VR f=33mm/49mm

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