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120 results for “leafless”
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A forest filled with tall, leafless trees stretches across the landscape. The ground is covered with fallen leaves, creating a textured surface. Made at the Homewood Izaak Walton Preserve in Illinois - USA.
Photo: Bare Trees in a Winter Forest - Copyright 2026 Frank J Casella - https://pixels.com/featured/bare-trees-in-a-winter-forest-frank-j-casella.html
Made with the Samsung A-13 smartphone camera. Processed with Ribbet. #photography #fineartPhotography #blackAndWhite #fjcasellaphoto #woods #trees #winter
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This is the passage through the woods between hayfields. The giant, reddish, leafless bush is the multiflora rose that I cut off at roots a few weeks ago. That bush and a mulberry tree on the other side were narrowing the lane considerably. It’s better now.
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This is the passage through the woods between hayfields. The giant, reddish, leafless bush is the multiflora rose that I cut off at roots a few weeks ago. That bush and a mulberry tree on the other side were narrowing the lane considerably. It’s better now.
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This is the passage through the woods between hayfields. The giant, reddish, leafless bush is the multiflora rose that I cut off at roots a few weeks ago. That bush and a mulberry tree on the other side were narrowing the lane considerably. It’s better now.
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This is the passage through the woods between hayfields. The giant, reddish, leafless bush is the multiflora rose that I cut off at roots a few weeks ago. That bush and a mulberry tree on the other side were narrowing the lane considerably. It’s better now.
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This is the passage through the woods between hayfields. The giant, reddish, leafless bush is the multiflora rose that I cut off at roots a few weeks ago. That bush and a mulberry tree on the other side were narrowing the lane considerably. It’s better now.
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Spring is in the air, it is on the ground, and it is showing up on winter deciduous trees.
This cluster shows a still leafless Himalayan Birch (Betula alnoides) full of yellow catkins, the other taller trees are Himalayan Alder (Alnus nepalensis) which have new leaves & leaf buds. The dark evergreen trees are Tree Rhododendron (Rhododendron arboreum).
#trees #nature #spring #Hinalayas #IndiasNature #HimalayaSpeaks #HimalayanBirch #Alder #Rhododendron #Phenology #catkins #biology #ecology
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Golden autumn light spreads across the rolling hills near Stockport, where patches of woodland and open moorland create a peaceful countryside escape. Leafless branches frame the scenic view, hinting at the seasonal shift, while clusters of evergreens and ferns add texture to the landscape. The area lies on the edge of the Peak District, a favored spot for nature photography and tranquil walks amidst #Countryside charm. Visitors often pause here in autumn to enjoy the #ScenicView, capturing the beauty of #AutumnScenery against the backdrop of #RollingHills.
Taken Oct 2017
#SilentSunday #UKCountryPic #Photography #MastoGPT #Countryside #NaturePhotography #AutumnScenery #RollingHills #ScenicView #Lyme #Stockport #England #UnitedKingdom
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The #Baobab #Tree is often called the "upside-down tree" due to its distinctive appearance, with sparse branches that resemble roots reaching towards the sky when it's leafless during the dry season.
These remarkable trees, native to Africa, Madagascar, and Australia, are renowned for their ability to store vast amounts of water in their massive trunks, allowing them to survive in arid environments.
https://www.oneearth.org/species-of-the-week-african-baobab-tree/
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The #Baobab #Tree is often called the "upside-down tree" due to its distinctive appearance, with sparse branches that resemble roots reaching towards the sky when it's leafless during the dry season.
These remarkable trees, native to Africa, Madagascar, and Australia, are renowned for their ability to store vast amounts of water in their massive trunks, allowing them to survive in arid environments.
https://www.oneearth.org/species-of-the-week-african-baobab-tree/
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The #Baobab #Tree is often called the "upside-down tree" due to its distinctive appearance, with sparse branches that resemble roots reaching towards the sky when it's leafless during the dry season.
These remarkable trees, native to Africa, Madagascar, and Australia, are renowned for their ability to store vast amounts of water in their massive trunks, allowing them to survive in arid environments.
https://www.oneearth.org/species-of-the-week-african-baobab-tree/
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The #Baobab #Tree is often called the "upside-down tree" due to its distinctive appearance, with sparse branches that resemble roots reaching towards the sky when it's leafless during the dry season.
These remarkable trees, native to Africa, Madagascar, and Australia, are renowned for their ability to store vast amounts of water in their massive trunks, allowing them to survive in arid environments.
https://www.oneearth.org/species-of-the-week-african-baobab-tree/
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The #Baobab #Tree is often called the "upside-down tree" due to its distinctive appearance, with sparse branches that resemble roots reaching towards the sky when it's leafless during the dry season.
These remarkable trees, native to Africa, Madagascar, and Australia, are renowned for their ability to store vast amounts of water in their massive trunks, allowing them to survive in arid environments.
https://www.oneearth.org/species-of-the-week-african-baobab-tree/
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I'm so thrilled – the moon is very bright tonight and when I let the dogs out, I stepped outside too, just to enjoy the light and what do I see but two dark round shapes high up in the leafless branches of the plum tree! Possums! Squeee!
I quietly told them how happy I was to see them and then ducked back inside to get my phone to see if I could get a picture. It's not a great picture, but you can hopefully make them out
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Prunus avium, the wild cherry, blooms in early spring. It is a common forest tree in the area where I live. It can be easily identified by its bark, which is brownish-purple with characteristic horizontal wrinkles. In spring, it forms bright white clouds of flowers against the otherwise leafless and gray backdrop of the forest.
#nature #macrophoto #tree #bloomscrolling -
A frosty morning blankets the grounds of Tatton Park in Knutsford, with a historic monument standing quietly among bare winter trees under a vivid blue sky. The National Trust estate’s open parkland is dusted with frost, creating a serene #WinterLandscape perfect for peaceful walks and nature photography. The monument rises from the grassland, framed by a mix of leafless and evergreen trees, adding a sense of timeless heritage to the #FrostyMorning. Wildlife stirs quietly around the edges of the park, making it an atmospheric spot for exploring #HistoricMonument sites amid #NaturePhotography opportunities.
Taken Jan 2017
#UKCountryPic #Photography #MastoGPT #WinterLandscape #FrostyMorning #HistoricMonument #NaturePhotography #BlueSky #TattonPark #Knutsford #England #UnitedKingdom
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New Design: Barren Tree at Cleland National Wildlife Park, near Adelaide, Australia, Prints and Products
Available Exclusively From
http://DouglasEWelch.com/shop/824Capture the stark, dramatic beauty of Australian nature with this striking black and white photograph of a bare, majestic tree reaching skyward. The image focuses on the intricate, sprawling network of leafless branches silhouetted powerfully against a smooth, dark gray sky.
Check out all my designs
http://DouglasEWelch.com/shop/#limbs #barren #winter #trees #outdoors #photography #home #decor #design #rustic #prints #products #BlackAndWhite #blackandwhitephotography #BareTree #MonochromeArt #TreeSilhouette #WinterMood #StarkNature #DramaticLandscape #LeaflessBranches #MinimalistDecor #GraphicNature #FineArtPhotography
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New Design: Barren Tree at Cleland National Wildlife Park, near Adelaide, Australia, Prints and Products
Available Exclusively From
http://DouglasEWelch.com/shop/824Capture the stark, dramatic beauty of Australian nature with this striking black and white photograph of a bare, majestic tree reaching skyward. The image focuses on the intricate, sprawling network of leafless branches silhouetted powerfully against a smooth, dark gray sky.
Check out all my designs
http://DouglasEWelch.com/shop/#limbs #barren #winter #trees #outdoors #photography #home #decor #design #rustic #prints #products #BlackAndWhite #blackandwhitephotography #BareTree #MonochromeArt #TreeSilhouette #WinterMood #StarkNature #DramaticLandscape #LeaflessBranches #MinimalistDecor #GraphicNature #FineArtPhotography
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Handroanthus serratifolius (Vahl) S.Grose (Bignoniaceae; locally: ipê) is still quite common in the coastal Amazon region, but I don't see many large trees (they provide high-quality timber ...). We planted this specimen in 2013 on the UFPA Campus in Bragança-Pará. Flowering often occurs when the trees are leafless at the end of the dry season, resulting in a quite spectacular view. #ipê #Amazonas #BragançaPA #UFPA #Bignoniaceae #trees #flowers #botany
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Northwestern Spain
Leaving the Basque Country we continued westward into the Spanish provinces of Cantabria looking for ancient art, Asturias hoping for mountain vistas and Galicia in search of scenic coastline.
Coordinates
- Santiago de Compostela
- Santillana del Mar
- Asiego
- Covadonga
- Salas
- Ribadeo
- Lugo
- A Coruña
- O Ézaro
- Carnota
- Vigo
- Baiona
- Tui
Cantabria
Another day, another art gallery—although this one exhibits works tens of thousands of years older than Bilbao’s Guggenheim. The Museo de Altamira (near Santillana del Mar) houses faithful reproductions of some of the most famous prehistoric rock paintings known, inside a bespoke “Neocave”. Recognised for what they were in 1879, the original cave was inhabited by Paleolithic hunter-gatherers from 35,000 years ago until a rockfall 13,000 years ago sealed it, putting it out of use as a seasonal camp—but preserving the contained artefacts and artworks. Several naturalistic bison are depicted on the rock ceiling, formed from a drawing and engraved detailing coloured black with charcoal, then infilled with red ochre (📷1); this one was realised ~15,000 years ago. In some cases—as here—the designs utilise the ceiling’s natural contours to give the animals a sense of depth and movement, making it one of the earliest known examples of shading and volume in art. A number of handprints adorn the ceiling; the artist’s hand was coated in red ochre then pressed onto the rock, in this case 22,000 years ago (📷2). An alternative “airbrush” technique was also utilised to create an outline hand design. The oldest work comprises several parallel double-curved lines; this seemingly abstract “Sign” was painted 36,000 years ago (📷3). Whether the paintings had special meaning, or were simply “art for art’s sake”, is not known. An adjacent exhibition hall contains recovered artefacts and tells the story of human evolution. Among the artefacts found near the cave entrance were these pendants, carved from the hyoid bones of a horse 22,400 years ago (📷4). The entrance to the actual cave is only 300m from the museum, but you can’t approach it. With 17 other caves Altamira forms the “Cave of Altamira and Paleolithic Cave Art of Northern Spain” UNESCO World Heritage Site.
Asturias
Sunset on our mountain pitchWe found a pitch adjacent to Mirador “Pedro Udaondo” in Asiegu with a view of the mountains in Picos de Europa | Peaks of Europe (📷1); the tall and sheer block of rock on the horizon is Picu Urriellu (the local Asturian name) | Naranjo de Bulnes (the Castilian name) at 2,519m. The range extends for 20km, forming part of the Cantabrian Mountains in northern Spain. In the vicinity we encountered Asturian sheep, an endangered Celtic breed with a long, coarse shaggy cream fleece and brown head/ legs that is indigenous to the area (📷2). Circling high overhead as we admired the landscapes were Neophron percopterus | Egyptian vultures, with their distinctive contrasting underwing pattern and wedge-shaped tails (📷3); they must have very recently flown in from Africa (and will return there around September time). In the evening we went down the hill into the mountain village of Asiegu (📷4) where we enjoyed an excellent dinner of local dishes at Sideria Casa Niembro (who had provided the gate code for the free pitch).
Touring isn’t only about the scenery: sampling traditional foods is an obligation. From Sare in the northern Basque Country we savoured Gâteau Basque | Pastel Vasco | Etxeko Biskotxa, a traditional pie-like cake made of a buttery, shortcrust pastry typically filled with cherry jam (📷1) or vanilla cream. In southern Basque Country we sampled Tarta de Queso | Gazta Tarta, the crustless, creamy and caramelized or “burnt” cheesecake originating from San Sebastian but now widely available (📷2); we acquired ours in Zumaia. In the Asturian mountain village of Asiegu we shared a meal of delicious chorizo sausages, corn fritters served with strong Cabrales blue cheese and apple jelly (📷3), and tender roast kid. Our host poured small amounts (a culín) of the almost flat local sidra | cider from a height over a special bucket (📷4); doing so releases tiny bubbles, the temporary fizz imparting texture and flavour that—for our part in the performance—should be consumed within seconds before it reverts!
With a fresh overnight dusting of snow on the peaks we set out to hike an out-and-back section of the 12km point-to-point Ruta del Cares (PR-PNPE 3) trail in Parque Nacional de los Picos de Europa. This is the park’s most popular hike, linking Poncebos (Asturias) and Caín (León); it’s considered one of Spain’s most beautiful trails. We parked at Poncebos and initial views of the clear-flowing Río Cares from near the trailhead looked promising (📷1); a short stretch of road led to a well-formed path. The trail climbs through a deep limestone gorge with sheer cliffs that tower above the river; erosion has created rock pillars (📷2) and natural arches (📷3)—but human engineering in this landscape also must be admired. Between 1915 a the early 1920s, the company Electra de Viesgo built a canal to carry water from the Río Cares at Caín to a hydroelectric plant at Camarmeña–Poncebos. Up to 11 km long, it runs through ~70 tunnels excavated largely by hand with the aid of explosives; 11 workers were killed during construction. The maintenance path for this canal, widened between 1945–50, became today’s Ruta del Cares: the canal still carries water alongside, above and beneath the trail (📷4).
At one point on Ruta del Cares, looking down into the canyon, we observed what we think must be a resurgence, where water that has been flowing underground reappears at the surface; they’re common in karst landscapes (📷1). The trail, like the canal itself, passes through a number of tunnels when cutting into the sheer rock face isn’t enough (📷2); this bridged section includes a steel grate so you can see the drop beneath your feet (📷3). We turned around just beyond this window in the rock wall (📷4), at ~8.5km (about two thirds along the route), corresponding to the Riega las Párvulas waterfall, just beyond the border with the León region.
The trail was no less dramatic walking it in the opposite direction (📷1). On our outbound leg the mountain goats were generally high above us, sometimes heard but not seen. On our return leg a number had descended onto the trail (📷2). At one point we encountered a “toll goat”, hoping to extract a fair exchange for passage through one of the tunnels (we didn’t feed it). A view ahead to a stretch of “up” before the final descent to the trailhead (📷3). Did we mention we saw goats? This she-goat was actively licking at a very particular patch of rock, which we took to be a quest for salt (📷4); apparently sodium is scarce in their normal alpine plant-based diet. All told the hike was 17km/ 5h out-and-back. Note there’s a non-zero probability of rockfall, but this trail is up there with the best we’ve done.
Smalls from the Ruta del Cares were plentiful. Glandora prostrata | the creeping gromwell is native to Spain, Portugal and France (📷1); this was everywhere trail side, with a velvety sheen that seemed to confuse autofocus! Erodium cicutarium | the redstem stork’s bill is native to the Mediterranean Basin (📷2); after flowering it produces long, beak-shaped seed pods. Helleborus foetidus | the stinking hellebore is a mountain native belonging to the buttercup family (📷3); the species name is Latin for “foul-smelling”, the result of bruised/ crushed leaves. Globularia nudicaulis | the leafless-stemmed globularia (📷4); this native is so-named because the stem is naked, with leaves in a low rosette at ground level.
Helicella itala | the heath snail is a native land snail (📷1); during hot, dry periods it climbs up vegetation and seals itself inside its shell to avoid overheating and dehydration. Dianthus hyssopifolius | the fringed pink is native to Spain, Portugal and France (📷2); it’s well adapted to rocky alpine environments. Pinguicula grandiflora | the large-flowered butterwort is another native (📷3); the flower is atypically large for a butterwort. Not all the smalls we noticed were living: being limestone country, some of the rocks contained the bodies of marine animals fossilised millions of years ago (📷4). Tectonic uplift transformed an ancient shallow sea into mountains!
The next morning it was hard to beat sipping coffee with a view out the van sliding door from pitch in Asiegu, as the rising sun lit the snow-capped mountains of Picos de Europa:
Morning light on Picos de EuropaRuta a los Lagos de Covadonga (PR.PNPE-2) was our second trail in Parque Nacional de los Picos de Europa. The road from Covadonga to reach the trailhead is fairly long and winding; it closes to private cars at busy times (replaced by park and ride). En route we stopped at Mirador de la Reina for stunning views back over the still misty lowlands we’d driven through (📷1). There in the morning chill we were in turn observed by roosting Gyps fulvus | Eurasian griffon vultures, perhaps waiting for thermals to form (📷2). We drove on to Lago Enol, the first of a pair of glacial lakes (📷3), parking at Aparcamiento Buferrera. We noticed fire on an adjacent peak and later watched a helicopter drop a bucket of water on it. There’s a short detour to Minas de Buferrera, where manganese and iron were extracted intermittently between 1868 and 1979 (the road to the lakes is a legacy of mining activity). “Flower of the day” went to Narcissus bulbocodium | the hoop-petticoat daffodil, a native to Spain, Portugal and France (📷4).
Continuing on Ruta a los Lagos de Covadonga, Largo de la Ercina had the prettier backdrop (📷1). We noted more new-to-us flowers; this is Erythronium dens-canis | dogtooth violet, native to central and southern Europe (📷2). A large part of the trail led us over limestone areas (📷3). Ermita de El Buen Pastor is a small hermitage sitting in the Vega de Enol, a high mountain meadow adjacent to Lago Enol at ~1,070m altitude (📷4); the contrast of this small human-built structure set against a vast, dramatic alpine landscape gives you pause. This was a 6km/ 2h loop.
For our last night in Asturias we came to Salas (📷1); this historic village offers accommodation to pilgrims walking the Camino de Santiago. What drew us here in a van, you might ask? Four reasons:
- First, it has a highly-rated laundromat. After a little over a week on the road our attire was in need of refreshing.
- Second, it was a comfortable distance between points-of-interest. Driving can be tiring, especially when narrow mountain roads are involved.
- Third, it’s camper van/ motorhome friendly, providing free-to-use services: parking overnight legally in dedicated area; potable water; grey water disposal; and toilet cassette emptying.
- Lastly, we also needed to buy groceries. In addition to usual supplies we acquired the local specialty biscuit, Carajitos (📷2). Available from La Casa del Profesor (est. 1918) on the main street, these soft and flavoursome hazelnut-based treats are apparently world famous in Asturias!
Galicia
We continued west to Monumento Natural Praia das Catedrais (near Ribadeo), where a series of arches resemble the flying buttresses of Gothic cathedrals; at low tide sea conditions didn’t allow us safe access. Views from the cliff top platforms were underwhelming.
Disappointed, we drove on to the UNESCO World Heritage Site of Muralla Romana de Lugo | the Roman walls of Lugo—once the Roman colonial town of Lucus Augusti in the province of Hispania Tarraconensis. The walls were built in the 3rd C. CE to defend against local tribesmen and Germanic invaders. About 2.1km long, 4.2m wide and 8–12m in height, internal and external stone facings were supported by a cemented rubble core (📷1); you can walk the full length of the parapet. Originally featuring an incredible count of 88 towers, these were mostly semicircular at intervals of 5.4–12.8m with bases of dressed granite topped with slate (📷2); 49 are still intact. Five of the current 10 gates are Roman in origin, including Porta de San Pedro (📷3); it was reconstructed in 1781. Many buildings within the walls are badly decayed; Lugo was nearly deserted during our visit. We looked through Sala Porta Miñá, a contemporary history museum, where they have an excavated stone-built Roman cloaca | sewer on display (📷4).
The 55m Torre de Hércules | Tower of Hercules (📷1&2) at A Coruña was built during the 1st C. CE, during the reign of Emperor Trajan, and is UNESCO-listed as the oldest surviving Roman lighthouse. It’s still in use today, making it the oldest functioning lighthouse in the world: that’s two thousand years of continuous maritime safety service! It underwent major restoration in the 18th C. (reflected in the current neoclassical shell) and until the 20th C. was known as Farum Brigantium. You can ordinarily climb the spiral staircase within the Roman core; it was closed for renovation during our visit. On the adjacent granite headland are even older relics: the Petroglifos de Punta Herminia are a group of prehistoric rock carvings dated to 2500–1800 BCE. They’re very weathered/ hard to make out, so not as photogenic as the Atlantic surf smashing onto the rocks below (📷3). Onwards to O Ézaro, where we admired the dramatic rocky landscape surrounding the Río Xallas (📷4). This reflects a very old granite core formed ~300 million years ago, and very lengthy erosion causing large fractures, rounded domes, sheer cliffs and boulder formations.
Fervenza do Ézaro is a waterfall on the Río Xallas | River Xallas at O Ézaro on the rugged Costa da Morte | Coast of Death (where Atlantic storms, hidden rocks and fog/ sea mist have led to many shipwrecks and drownings). Next to a hydroelectric power plant, the Ézaro waterfall is billed as “one of the only sites in Europe where a river cascades directly into the sea” (📷1). While this could be contested given they are ~1.4km upstream of the shoreline, the falls are nevertheless scenic (📷2). About 16km south of O Ézaro is the village of Carnota, site of the Hórreo de Carnota, built 1760–1783 (📷3). This hórreo | granary in the typical Fisterran style is the longest in Galicia at 34.76m. Once used to store, dry and conserve corn/ other crops, most hórreo (there are 884+ in this municipality alone) are now merely “decorative statements” given the decline of agricultural traditions. Carnota also boasts a long sandy beach, Praia de Carnota, backed by sand dunes and a salt marsh. From it you can see to Cape Finisterre (after the Latin “Finis Terrae” | “end of the earth”), which the Romans considered the edge of the known world (📷4).
Christian pilgrims flock to Santiago de Compostela’s cathedral (📷1), built 1075–1211 CE with later additions, to visit the tomb of the apostle Saint James the Great. Although said to have died in Jerusalem in 44 CE, medieval legend holds that his followers, guided by divine intervention, brought his body to Galicia. Pilgrims walk the Camino de Santiago, a network of interlinked routes converging here from across much of Europe—as symbolised by the scallop shell. A unique feature of the cathedral’s nave, the “Botafumeiro” is a large silver censer (incense burner) that is swung across the transept during special services (📷2). The cathedral fronts onto to Praza do Obradoiro, a grand square surrounded by other historic buildings including Pazo de Raxoi | the neoclassical town hall (📷3) and Hostal dos Reis Católicos, a luxury hotel that was once a 15th C. pilgrims hospital (📷4). The medieval historic center of town is a UNESCO-listed World Heritage Site.
Mercado de Abastos is Santiago de Compostela’s main market, offering fresh seafood (📷1), produce, and tapas—if you’re not too early! The old town includes examples of a classic feature of northern Spanish architecture called a “galería” (📷2); these enclosed balconies are especially common in Galicia and provide a “glass skin” that shields the home from rain and wind while providing passive solar heating and extra usable space (plants, laundry drying, etc.). Parque da Alameda is a green space close to the old town and offers an elevated perspective of the cathedral skyline (📷3). We visited Museo do Pobo Galego, a former convent that exhibits artefacts from traditional Galician life; it features an unusual staircase with three intertwined spiralling paths that end abruptly at different doors (📷4). The baroque Monastery of San Martín Pinario near the cathedral is said to have ornate interiors; it was closed to visitors.
From Santiago de Compostela we drove south. Ría de Vigo is a drowned river valley near the city of Vigo; it’s known for providing a sheltered harbour (the Cíes Islands act as a barrier against the Atlantic), for mussel farming rafts called “bateas” and for white sand beaches. On the northern side Praia da Folla de Nerga a.k.a. Playa de Nerga is popular (📷1). On the southern side there’s a string of beaches on the outskirts of Vigo connected by a long promenade with views of the Cíes Islands (📷2). At the town of Baiona the large Fortaleza De Monterreal is surrounded by ~3km of walls, mostly built between the 11th to 17th centuries (📷3); the strategic hilltop has been fortified for 2,000 years and is now occupied by a hotel. We turned inland to Tui, wandering the medieval old town that features a fortress-like cathedral built during the 12th and 13th centuries (📷4).
Tui offers views across the Miño River into the Portuguese town of Valença—the next destination on our loop through the Iberian Peninsula.
#2026 #asturias #camperVan #cantabria #europe #galicia #hiking #nationalPark #nature #nomad #roadTrip #romans #spain #travel #unesco #vanLife -
LLMs and Specs
I was trying to get a specification for a program at one point, to see if it was doing what I wanted. My LLM, Lyin’ Brian, created one for me.
The background was that I had asked an LLM for a link to math book with the algorithm of, for example, a lower hull. I asked it to write it out in English, used that for the prompt.
It found me https://cp-algorithms.com/geometry/convex-hull.html, and once I had it and checked it, I had Claude convert it to Go, and then I debugged it.
Once I had that, I asked Claude for the specification, and got:
Logical Specification for Lower Hull
Here's a formal specification of what the lower hull algorithm should accomplish:
Given: A finite set of points P = {p₁, p₂, ..., pₙ} in 2D space
Output: An ordered sequence of points L = [l₁, l₂, ..., lₖ] representing the lower hull
Postconditions (what must be true after execution):
Subset property: L ⊆ P (all points in the lower hull are from the original set)
Ordering property: l₁ has the minimum x-coordinate (leftmost), and lₖ has the maximum x-coordinate (rightmost). For all i < j, x(lᵢ) ≤ x(lⱼ) (x-coordinates are monotonically non-decreasing)
Convexity property: For all consecutive triples (lᵢ, lᵢ₊₁, lᵢ₊₂) in L, the orientation must be counterclockwise (left turn). Formally: (lᵢ₊₁ - lᵢ) × (lᵢ₊₂ - lᵢ₊₁) > 0
Minimality property: L is minimal — no point from P can be removed from L while still maintaining properties 2 and 3. (This ensures you have the actual hull, not just some counterclockwise path)
Completeness property: All points on the lower convex hull boundary are included. Formally: for any point p ∈ P that lies on the lower boundary of the convex hull, p ∈ L
Preconditions (assumptions):
P contains at least 2 points
Points are distinct (no duplicates)
The meaning of Lower Hull is understood by allThis successfully translated the program into a spec I could read. Not easily, though! It’s been a while since I did symbolic logic, back at Sun.
So I worked it through with a pencil, paper and a trivial set of data, and that was really what I was asking for. It also told me that I needed to add code to check that the points really were distinct (no duplicates).
Necessary and sufficient? I’m going to think more about that.
#ai #artificialIntelligence #mathematics #programming #specifications -
LMs and Specs
I was trying to get a specification for a program at one point, to see if it was doing what I wanted. My LLM, Lyin’ Brian, created one for me.
The background was that I had asked an LLM for a link to math book with the algorithm of, for example, a lower hull. I asked it to write it out in English, used that for the prompt.
It found me https://cp-algorithms.com/geometry/convex-hull.html, and once I had it and checked it, I had Claude convert it to Go, and then I debugged it.
Once I had that, I asked Claude for the specification, and got:
Logical Specification for Lower Hull
Here's a formal specification of what the lower hull algorithm should accomplish:
Given: A finite set of points P = {p₁, p₂, ..., pₙ} in 2D space
Output: An ordered sequence of points L = [l₁, l₂, ..., lₖ] representing the lower hull
Postconditions (what must be true after execution):
Subset property: L ⊆ P (all points in the lower hull are from the original set)
Ordering property: l₁ has the minimum x-coordinate (leftmost), and lₖ has the maximum x-coordinate (rightmost). For all i < j, x(lᵢ) ≤ x(lⱼ) (x-coordinates are monotonically non-decreasing)
Convexity property: For all consecutive triples (lᵢ, lᵢ₊₁, lᵢ₊₂) in L, the orientation must be counterclockwise (left turn). Formally: (lᵢ₊₁ - lᵢ) × (lᵢ₊₂ - lᵢ₊₁) > 0
Minimality property: L is minimal — no point from P can be removed from L while still maintaining properties 2 and 3. (This ensures you have the actual hull, not just some counterclockwise path)
Completeness property: All points on the lower convex hull boundary are included. Formally: for any point p ∈ P that lies on the lower boundary of the convex hull, p ∈ L
Preconditions (assumptions):
P contains at least 2 points
Points are distinct (no duplicates)
The meaning of Lower Hull is understood by allThis successfully translated the program into a spec I could read. Not easily, though! It’s been a while since I did symbolic logic, back at Sun.
So I worked it through with a pencil, paper and a trivial set of data, and that was really what I was asking for. It also told me that I needed to add code to check that the points really were distinct (no duplicates).
Necessary and sufficient? I’m going to think more about that.
#ai #artificialIntelligence #mathematics #programming #specifications -
Welcome to the Panopticon
When reading a discussion of an unrelated philosophical issue, I realized that we’re living in a contraption proposed by Jeremy Bentham, the author of utilitarianism.
This is a sketch of the “panopticon”, a prison where the prisoners, “A”, lived in open, illuminated cells, all facing inwards toward a darkened central rotunda where there might be a guard, “B”, or there might not.
Although it is physically impossible for the single guard to observe all the inmates’ cells at once, the fact that the inmates cannot know when they are being watched motivates them to act as though they are all being watched at all times. They are effectively compelled to self-regulation [Wikipedia 1]
Bentham was just trying to reduce the number of guards per prisoner, per worker, patient or student.
Michel Foucault
However, the mechanism was looked at Michel Foucault, the French philosopher, who recognized it as a specific example of his theory of disciplinary power.
As an equation, it was control = hierarchy + normalization + examination [Wikipedia 2]
- Hierarchy is the structure than enables observation. There is a superior and inferiors.
- Normalization is the superiors being able to set norms. Deviation from the norms becomes visible and seen as abnormal.
- Examination is the knowledge of being watched. Being examined makes people aware they are subjects of scrutiny by their superiors. Conversely, they lack any way to have scrutiny over the superiors.
At this point, the inferiors realize that they could be outed as abnormal. To avoid that they “internalize the surveillance”, they regulate their own behavior so as to always appear normal.
Freedom becomes an illusion when you’re constantly aware that your behavior may be being observed and evaluated against norms you didn’t choose.
An Exercise for the Reader
Consider the internet, social media, closed-circuit TV, workplace monitoring, insurer access to your health records, learning management systems, credit scores and the like. Does being observed by them affect your behavior?
Are you in a panopticon, and if so, how many?
#closedCircuitTv #foucault #philosophy #politics #socialMedia -
LLMs are Lint
No, I don’t mean that are bits of clothing fluff, I mean they’re like the old “lint” program for C.
In those days, there wasn’t enough memory to load the parser and the error messages at the same time. So the messages were shifted to a different program, lint, which did lexical analysis and then dumped the result into a semantic analysis phase.
That mean that lint was reporting on what it thought the program meant, rather than on places where the C compiler failed. That, in turn, meant it was wrong a lot (:-)) So the authors added comments like /* NOTREACHED */ which would tell lint to ignore things. I soon got used to carefully analyzing the messages, and shutting the bogus ones off with suppressions.
Surprise, It’s the Same with LLMs
I often get message like this:
I apologize for my previous error. The article I mentioned earlier was not a real, verifiable source. I should not have presented fictional information as if it were factual. This was a mistake on my part.
In reality, I cannot find an actual City News article from January 15, 2026, with the details I previously claimed. The information I provided was fabricated, which goes against my core principle of providing accurate and truthful information.
So I do three things:
- Add suppressions to my defaults, like “don’t tell me about Oxford commas”
- check absolutely everything that doesn’t come with a URL
- and check the URLS, too.
This sounds hard, but it’s easy if you set your expectations correctly. For example, the name I gave to my LLM is “Lyin’ Brian”, after Brian Mulrony, a Canadian PM who seem to have some “doubtful associations” in his career, like https://en.wikipedia.org/wiki/Karlheinz_Schreiber
The suppressions do the heavy lifting. Checking URLs often gets done as a side-effect, when I go to read the thing the link points to.
#ai #c #lint #llm -
FFT: Stallman once wrote "Writing non-free software is not an ethically legitimate activity, so if people who do this run into trouble, that's good! All businesses based on non-free software ought to fail, and the sooner the better.”
#oss #lawfedi #ethics #technologyEthics
https://marc.info/?l=kde-licens%20ing&m=89249041326259&w=2%3E
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"After Turnitin bought the company in 2018, a new set of terms and conditions took effect: Now student papers go into Turnitin’s global database and the company maintains a perpetual, royalty-free license over all of them."
https://themarkup.org/artificial-intelligence/2025/06/26/ai-detector-california
