(5) The Unhurried Odyssey of a Turtle!
We’ve already taken a tour through the Kuber Yantra, visited the legendary Lo Shu Square, met the famous fabled Turtle, and even had a friendly chat with the Magic Squares themselves.
The Turtle and these mysterious grids have slowly and quietly travelled across Continents, crossed Dynasties, impressed Emperors, baffled Sages, and—every now and then—caused a scholar to spill tea on his manuscript out of excitement. Just like an equivalent of Eureka Moment of Archimedes!
Now let us appreciate the contribution of Indians, Arabs and Europeans towards Magic Squares in this short blog post which is a kind of a trailler of a long Web Series to be released in many installment now onwards.
Magic Squares by Indians:
Centuries later after Mysterious appearance of Lo Shu, India advanced the idea and said, “We can do better… how about really big magic squares?”
Indian mathematicians didn’t just stop at 3×3; they created 4×4, 8×8, 16×16, even 32×32 squares—just for fun. The great Mathematician Varāhamihira used magic squares in astrology; perhaps planets also follow tidy arithmetic of Magic Squares!(More about him and his Magic Square in the next blog post.)
Then there is this exotic Khajuraho Magic Square, a perfect Magic Square, calmly floating in the ocean of Khajuraho’s world-famous 'artistic enthusiasm' from the 11th and 12th centuries. While the sculptures around it are busy demonstrating advanced levels of human flexibility, this little square sits at the entrance of the Parshvanath Temple, pretending to be all innocent and intellectual!
And yet—ask any mathematician—and they’ll admit this square is a bigger “turn-on” than all the erotic acrobatics carved on the walls. Forget the sculptures; it’s the perfect symmetry of those numbers that really makes their hearts race! And Imagine we don't even know the name or names of the creator of Khajuraho Magic Square, a perfect Magic Square,!
After Varāhamihira’s square, the spotlight will swing to our next star—the enigmatic Khajuraho Square. From there on, the story will get spicier, so brace yourself!
Finally came Ramanujan, who looked at a normal 4×4 magic square and declared, “Nice. Now watch me break Physics.” He created hyper-efficient pattern-based squares, date-of-birth squares, and pandiagonal hybrids so clever that even Mathematicians raise their eyebrows like baffled Aunties! ( Many more posts to follow on him in due course.)
India essentially turned Magic Squares into spicy Mathematical Samosas—crispy outside, mind-blowing inside! So yummy! Go, grab them!! They never disappoint!
Arab Mathematicians: While Europe was busy trying to figure out why fire burns (fair question!), the medieval Arab world was having a full-fledged love affair with numbers inspired by Chinese and Indian Mathematicians.
Scholars like Al-Biruni and Al-Khwarizmi (the word Algorithm is derived from his name) were fascinated by Magic Squares not because they were magical, but because they were excellent algebra playgrounds. They used them for recreational Maths, Puzzles, and occasionally to impress wealthy Caliphs who perhaps thought Mathematics could predict the next sandstorm!
Magic Squares also became part of talismanic traditions, engraved on rings and amulets. Superstitious folks believed a magic square could cure illness, repel evil, and help them remember where they put their camel!
European Mathematicians: Europe finally discovered magic squares in the Middle Ages—mostly through translations of Arabic texts. The Renaissance Mathematicians became absolutely obsessed. Even great artists joined in:
Enter Albrecht Dürer, the stylish German artist. In 1514, Dürer included a perfect 4×4 magic square in his engraving Melencolia I, right above a depressed-looking angel. It is widely believed he added the square because Renaissance artists loved hiding Easter eggs! Or maybe he wanted to show off his Mathematical prowess too! His magic square’s date-of-creation (1514) cleverly appears in its last row. Subtle flex, Herr Dürer! More on him and his Magic Square soon.
This Dürer Magic Square kicked off a centuries-long craze where European intellectuals collected magic squares like rare Pokémon cards!
The Great Explosion of Giant Squares and Mathematical Mischief.
By the 17th and 18th centuries, mathematicians were going wild. Benjamin Franklin created enormous “semi-magic” squares.
French mathematicians invented Knight’s Move construction methods.
Some Jesuit priests used magic squares to teach arithmetic to schoolchildren—probably the only time kids enjoyed the Math Class!
Magic squares became so popular that people tried using them for predicting the future, deciding lottery numbers, and solving romantic problems like,
“Does he love me? Let me consult this 9×9 magic square…”!
Spoiler: The Square refused to help squarely!
Modern Times: From Ancient Turtle to Supercomputers.
Today magic squares appear in:
Puzzle Books, Mathematical Research, Computer science, Recreational Maths Communities, Art, Architecture, and even in blogs by a proven crazy bloke from 'The Parsi Mohalla, Indore' who instead should continue to write on Tawa Sangeet, Rail Sangeet or Cycle Sangeet in Hindi!
Supercomputers can now generate mind-bogglingly huge magic squares; something the ancient Turtle from the Luo River would probably be proud of. We all know all Magic Squares of the World are resting on its strong back!
Some researchers even explore links between Magic Squares and Quantum Mechanics. Because apparently the universe itself likes neat sums.
Why They Still Charm Us!?
Simply because Magic squares perfectly blend Symmetry, Simplicity, Surprise, Pattern, Elegance and huge insanity!
They are like the Sudoku puzzles but with far more swagger. They make us feel like the Universe has a sense of order—while also teasing us with endless complexity.
Plus, let’s be honest, humans simply love anything that looks neat and hides a secret.
In Conclusion…
From turtles to Kings, from Sages to Scientists, Magic Squares have enjoyed a seriously dramatic, globe-trotting journey. And they’re still not done surprising us!
Whenever you draw a magic square next time, remember:
You’re participating in a 4,000-year-old Cosmic Comedy.
Pankaj Khanna
9424810575
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मेरे कुछ अन्य ब्लॉग:
हिन्दी में:
तवा संगीत : ग्रामोफोन का संगीत और कुछ किस्सागोई।
रेल संगीत: रेल और रेल पर बने हिंदी गानों के बारे में।
साइकल संगीत: साइकल पर आधारित हिंदी गाने।
कुछ भी: विभिन्न विषयों पर लेख।
तवा भाजी: वन्य भाजियों को बनाने की विधियां!
मालवा का ठिलवा बैंड: पिंचिस का आर्केस्टा!
ईक्षक इंदौरी: इंदौर के पर्यटक स्थल। (लेखन जारी है।)
अंग्रेजी में:
Love Thy Numbers : गणित में रुचि रखने वालों के लिए।
Epeolatry: अंग्रेजी भाषा में रुचि रखने वालों के लिए।
CAT-a-LOG: CAT-IIM कोचिंग।छात्र और पालक सभी पढ़ें।
Corruption in Oil Companies: HPCL के बारे में जहां 1984 से 2007 तक काम किया।
