Technologies

Google Doodle honors father of fuzzy logic Lotfi Zadeh

The computer scientist and electrical engineer’s concept used mathematics to mimic how people see the world.

In 1964, while contemplating how to program software for handwriting recognition, a mathematician, computer scientist and electrical engineer named Lotfi Zadeh conceived of a new mathematical technique. His fuzzy logic theory offered an alternative to the rigid yes-no logic, in an attempt to mimic how people see the world.

To honor his controversial innovation, Google on Tuesday dedicated its Doodle to Zadeh on the 57th anniversary of the concept’s creation. The Doodle demonstrates his concept, showing that an alternative to the black-or-white Boolean logic, which determines the membership of a given class based on one (yes) or zero (no). His theory provided a means for calculating intermediate values between yes and no.

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Born on Feb. 4, 1921, in Azerbaijan, Zadeh moved with his family at the age of 10 to Iran, where he graduated with a science degree from the University of Tehran. He earned enough money selling goods to the US Army during World War II to move to continue his education in the US, earning a master’s degree in electrical engineering from the Massachusetts Institute of Technology in 1946 and a Ph.D. from Columbia in 1949.

While serving as an electrical engineer professor at the University of California, Berkeley, Zadeh proposed using imprecise data to solve problems that may have more than one solution. His 1965 paper Fuzzy Sets — Information and Control sought to use mathematics to define human concepts such as «slightly,» «tall» or «beautiful» and other concepts that have ambiguous meanings, thus creating a set theory where elements have a degree of membership.

Zadeh’s theory proved controversial, with many in academic circles ridiculing and attacking it, because it challenged other forms of mathematics and used unusual terminology.

«My paper was an object of indifference, skepticism and derision,» he wrote in 2015. «A prominent school of thought claimed that fuzzy set theory is probability theory in disguise.

«In part, many negative reactions to my papers reflected the fact that the word «fuzzy» has pejorative connotations,» he wrote.

Despite the criticism, fuzzy logic became popular with Japanese manufacturers and played a prominent role in everything from medicine to economic modelling to antilock braking and dishwashers, to name just a few.

In recognition of his achievement, Zadeh received dozens of engineering and academic awards, including 24 honorary doctorates.

Zadeh died in 2017 at the age of 96.

Technologies

Today’s NYT Mini Crossword Answers for Monday, July 21

Here are the answers for The New York Times Mini Crossword for July 21.

Looking for the most recent Mini Crossword answer? Click here for today’s Mini Crossword hints, as well as our daily answers and hints for The New York Times Wordle, Strands, Connections and Connections: Sports Edition puzzles.

My favorite Mini Crosswords are ones that take me on a little journey. Today, I learned something new about Hawaii and also basked in a nostalgic moment while thinking about a childhood board game. Need an assist with today’s Mini Crossword? Read on. And if you could use some hints and guidance for daily solving, check out our Mini Crossword tips.

The Mini Crossword is just one of many games in the Times’ games collection. If you’re looking for today’s Wordle, Connections, Connections: Sports Edition and Strands answers, you can visit CNET’s NYT puzzle hints page.

Read more: Tips and Tricks for Solving The New York Times Mini Crossword

Let’s get to those Mini Crossword clues and answers.

Mini across clues and answers

1A clue: Ceremonial band
Answer: SASH

5A clue: First official state hand gesture, following a 2024 Hawaiian bill
Answer: SHAKA

6A clue: Deck with the Major and Minor Arcana
Answer: TAROT

7A clue: Just love
Answer: ADORE

8A clue: Boardwalk has the highest one on a Monopoly board
Answer: RENT

Mini down clues and answers

1D clue: Cool place to be on a sunny day
Answer: SHADE

2D clue: Name that might come first during an alphabetical roll call
Answer: AARON

3D clue: Hybrid athletic garment
Answer: SKORT

4D clue: Just loathe
Answer: HATE

5D clue: One whose name is in lights
Answer: STAR

Technologies

Today’s NYT Connections Hints, Answers and Help for July 21, #771

Here are some hints and the answers for the NYT Connections puzzle for July 21, #771.

Looking for the most recent Connections answers? Click here for today’s Connections hints, as well as our daily answers and hints for The New York Times Mini Crossword, Wordle, Connections: Sports Edition and Strands puzzles.

Hey, Seinfeld fans, today’s NYT Connections puzzle is right up your alley. That makes the blue category fun, but that purple category got me, as always. Read on for clues and today’s Connections answers.

The Times now has a Connections Bot, like the one for Wordle. Go there after you play to receive a numeric score and to have the program analyze your answers. Players who are registered with the Times Games section can now nerd out by following their progress, including number of puzzles completed, win rate, number of times they nabbed a perfect score and their win streak.

Read more: Hints, Tips and Strategies to Help You Win at NYT Connections Every Time

Hints for today’s Connections groups

Here are four hints for the groupings in today’s Connections puzzle, ranked from the easiest yellow group, to the tough (and sometimes bizarre) purple group.

Yellow group hint: Top it off.

Green group hint: Liquid can change forms.

Blue group hint: Big salad, puffy shirt.

Purple group hint: A certain symbol.

Answers for today’s Connections groups

Yellow group: Additional perk.

Green group: Phase transitions for liquids.

Blue group: Concepts from «Seinfeld.»

Purple group: What ‘ can indicate.

Read more: Wordle Cheat Sheet: Here Are the Most Popular Letters Used in English Words

What are today’s Connections answers?

The yellow words in today’s Connections

The theme is additional perk. The four answers are bonus, extra, gravy and icing.

The green words in today’s Connections

The theme is phase transitions for liquids. The four answers are condensation, freezing, melting and vaporization.

The blue words in today’s Connections

The theme is concepts from «Seinfeld.» The four answers are Festivus, regifting, shrinkage and yada yada.

The purple words in today’s Connections

The theme is what ‘ can indicate. The four answers are contraction, foot, possessive and quote.

Technologies

Today’s NYT Connections: Sports Edition Hints and Answers for July 21, #301

Here are hints and the answers for the NYT Connections: Sports Edition puzzle for July 21, No. 301.

Looking for the most recent regular Connections answers? Click here for today’s Connections hints, as well as our daily answers and hints for The New York Times Mini Crossword, Wordle and Strands puzzles.

Golf knowledge is a weak point for me, so I struggled a little with today’s Connections: Sports Edition. It’s nice to see an appearance from one of the best team names in minor league ball. Hello, Yard Goats fans. Stuck? Check out our hints and get the answers.

Connections: Sports Edition is out of beta now, making its debut on Super Bowl Sunday, Feb. 9. That’s a sign that the game has earned enough loyal players that The Athletic, the subscription-based sports journalism site owned by the Times, will continue to publish it. It doesn’t show up in the NYT Games app but now appears in The Athletic’s own app. Or you can continue to play it free online.

Read more: NYT Connections: Sports Edition Puzzle Comes Out of Beta

Hints for today’s Connections: Sports Edition groups

Here are four hints for the groupings in today’s Connections: Sports Edition puzzle, ranked from the easiest yellow group to the tough (and sometimes bizarre) purple group.

Yellow group hint: Don’t skip this step.

Green group hint: Par for the course.

Blue group hint: Constitution state.

Purple group hint: Not bored.