For nearly 150 years, geometers and other academics have been trying to imagine a mysterious fourth direction in space to account for the math of 4D geometry, but that abstract spatial axis has never been observed. Space remains three-dimensional.

However, representations of 4D polytopes can perfectly depict the motion of 3D objects through both space and time. A leading expert in the field has said they have not seen this view presented before.

The idea continues toward 5D geometry to represent what directly affects motion: force, comparing the 5D progression of a cube, a penteract, with events of cosmology and particle physics.

What da hell my eyes are doing but after many years and many different doctors I gave up, nobody ever saw nothing like that and can’t explain to me how my eye doing it…

I wasn’t but one of my closest friends was able to no problem

A Taiwanese man's attempt to catch his cheating wife backfired in a way he likely never saw coming, winning him a payout in one courtroom and a prison sentence in another.

According to a Taoyuan District Court ruling released August 18, the man, whose identity was not disclosed, married his wife in 2021. The couple lived mostly with his parents but occasionally stayed at a vacation home the family owned in Guishan, Taoyuan.

In September 2023, his suspicions were triggered after he found a used toothbrush at the vacation home that wasn't his. After reviewing parking garage footage, he identified an unfamiliar man who had previously driven his wife home.

Three months later, on December 24, 2023, he remotely activated the home's robot vacuum through its app, telling the court he originally meant to use its speaker to talk to his wife. Instead, the live camera showed another man inside the house with her. He switched on the recording function and kept watching, capturing footage of his wife embracing the man, changing clothes, and appearing naked in front of him.

He used that footage to sue his wife and the other man for NT$2 million, about $63,000, for violating his marital rights. A civil court agreed the relationship had exceeded ordinary friendship and ordered the pair to jointly pay him NT$500,000, roughly $16,000.

That victory didn't shield him from what came next. His wife filed a criminal complaint accusing him of recording her without consent. He argued the footage had already been accepted in the civil case and that his actions were legally justified.

The criminal court disagreed. Judges ruled that marital obligations do not override an individual's right to privacy, rejecting his claim that lights or sounds from the vacuum warned her she was being recorded. The court found the recording was deliberate and she never consented, including while naked.

He was sentenced to five months in prison and fined NT$150,000, about $4,700, roughly 30 percent of what he'd just won.

NASA's Perseverance rover has sent back its latest images from the Martian surface, giving us another incredibly detailed look at the rocks, terrain and landscape of a world millions of miles away. The rover continues to explore Mars while sending new images and science back to Earth.

Half of Dali Gimba are born blind due to a dominant genetic defect.

A rare photograph from 1927, Albania, shows a way of feeding that seems unusual today, a baby drinking milk directly from a goat's breast.

At that time, especially in rural areas, infant feeding options were much more limited. If the mother could not breastfeed her child, families were often forced to look for alternatives.

Goat's milk was used more as it was believed to be easy to digest and could help nourish the baby.

Doctors are going to be BUSY there in 9 months unless people are prepared.

https://www.independent.co.uk/news/world/americas/uss-abraham-lincoln-pattaya-prostitution-thailand-b3042016.html

Brazilian scientist, Dr. Mariangela Hungria, spent 40 years perfecting bacteria that help crops access nitrogen while saving farmers billions each year.

Hungria developed biological treatments using beneficial soil bacteria that help crops access nitrogen from the air, reducing reliance on synthetic fertilizer. Her technology is used across tens of millions of hectares in Brazil. The World Food Prize estimates her work saves farmers about $25 billion annually and prevents roughly 230 million metric tons of CO₂-equivalent emissions.