The Taylor expansion was like a godsend to Little Ox. It not only helped him solve the problem of simplifying and expanding m/n when it wasn't an integer, but also opened the door to an entirely new world.
For the next two days, Little Ox barely left the house, constantly working to refine the formulas.
To be sure,
that wasn't enough time for Little Ox to systematically define infinitesimals. After all, according to history, the concept wouldn't be formally put into writing until 1704. Even a head start couldn't get him there overnight.
But Little Ox did refine some other ways of expressing things:
For example, using a^1/2 instead of √a, and a-1 instead of 1/a, among other changes.
These notations were long familiar to people in later generations, but in an era when exponents were still very unfamiliar, changing the way things were expressed was an extremely bold move.
Once Little Ox had extended his general analysis of finite-term equations to infinite expressions, he wouldn't be far from formally deriving the Universal Gravitation Formula.
Meanwhile, Xu Yun had spent the past few days playing delivery boy. Once Little Ox got into the zone, he forgot to eat or sleep. One time, if Xu Yun hadn't been watching, Little Ox really would have drunk ink, thinking it was boiling water.
On the other hand, Xu Yun's efforts hadn't gone to waste:
Although no task-completed notification had appeared, Little Ox was gradually starting to recognize Xu Yun's abilities.
Every so often, he'd chat with Xu Yun, and they even discussed a few mathematical and physical problems.
It was worth noting that Little Ox's full name was Isaac Petty Grudge-Holding Newton.
In his eyes, people basically fell into two categories: idiots and somewhat less idiotic people.
Aside from delivering meals, Xu Yun spent his remaining free time wandering around outside, pondering what to do next.
Not having a phone felt a little strange, but Xu Yun wasn't a stranger to that sort of life. He'd earned his Biology Doctor degree in this life through hard work, after all, and spending time in the library was second nature to him.
What's more, Xu Yun had found a good fishing spot by a small river not far from Little Ox's house. With his decent handiness, he'd put together a spinning rod.
Whenever he got bored, he'd go out and cast a few times, and the hours slowly passed.
Over those two days, Xu Yun caught an old boot and a rotting squirrel carcass, knocked down a sparrow, caught a snake, and stumbled upon a pair of lovers cheating on their partners. The one thing he didn't catch was a fish.
Fishermen, you know how it is.
And just like that, two days passed in a flash.
Early on the third morning, Xu Yun woke up at his usual time and, as always, stepped out of the bedroom.
But as soon as he opened the door, he saw Little Ox sitting by the round table, preening in front of a mirror as he fixed his hair. He was wearing Cambridge College's formal uniform.
Xu Yun blinked at the sight.
"Mr. Newton, what's going on?"
Little Ox first picked up a hair clip from the table and used it to pin his wig in place while looking in the mirror. Then he raised his eyes and glanced at Xu Yun.
"Today is Sunday. Have you forgotten Uncle William's invitation?"
Xu Yun was stunned for a moment, then slapped his forehead as he remembered.
"Oh, right. We're going to church, aren't we?"
Little Ox nodded, adopting a solemn expression.
"Come and tidy yourself up too. Worship calls for neatness. The fear of God is the beginning of wisdom, and knowledge of the Holy One is understanding."
Xu Yun muttered under his breath, Then why don't you take a bath? But outwardly, he obediently did as he was told.
After all, faith was one of Little Ox's fatal weaknesses and the core of his spiritual life. There was no point arguing over matters of belief.
Modern mirrors wouldn't be invented by Liebig until 1835. At this time, mirrors were mainly made by coating the back of glass with tin foil and mercury, and they gave a perfectly clear reflection.
Three days had passed, counting the day Xu Yun had first traveled through time, and his complexion had visibly turned sallow. He wasn't sure whether he'd traveled through time in body or soul. The latter was easier to explain; if it was the former, he'd probably have to think about gaining weight once he returned to reality.
He then gave his hair a quick comb and followed Little Ox out of the house, carrying the Holy Bible.
Woolsthorpe was just an ordinary little village, so to attend church, they had to walk to Grantham, seven miles away.
Grantham in the 21st Century had long since become a city. At this time, though, it was merely a small town of just over three thousand people. In the future, however, it would become a place of great significance:
Besides Little Ox, the Iron Lady, Margaret Thatcher, also hailed from there.
In 1665, Grantham had only one church, located in the southwest of town. It was called St. Titus Didymus.
In 1866, it would be replaced by another church, St. Wulfram's Church, which remained a famous tourist attraction to this day.
Seven miles was a little over eleven kilometers. In later generations, most people would probably take the subway or a bus; those better off would drive or hire a cab.
Unfortunately, the William family and Little Ox were dirt poor, and couldn't afford a carriage. So after meeting up at the village entrance, the group had no choice but to take the number eleven bus and walk.
"Mr. Fat Fish, catch."
After they'd met up and set off, William Askew tossed Xu Yun something wrapped in broad leaves as they walked, explaining:
"This is your lunch and dinner. The gathering starts at one in the afternoon and ends at half past three. The round trip will take about seven hours, so we'll have to eat dinner on the road.
"There's bread and water in the leaves. You can throw the leaves away after you're done, but be sure to bring the waterskin back."
Xu Yun nodded and felt the shape of the Leaf Bag.
Hmm, four pieces of bread and a sturdy waterskin. William really was a good, generous man.
Then the eight of them set off:
William carried Lilani on his back, Mrs. William held Elula and Andrea by the hand, and Little Ox continued chattering away with Lisa.
Xu Yun looked around in bewilderment, feeling that something wasn't quite right.
How come I'm still single, even after switching worlds?
The English winter wasn't especially hot, but the William family members weren't very strong due to their poor nutrition. So after walking for a little over an hour, William and the others were visibly sweating.
When the group reached a large tree, Mrs. William let out a tired breath and pointed to the shade.
"Dear, let's rest over there."
William looked at the sky and estimated the time.
"We've still got a few hours before worship starts. All right, let's rest for a while."
The group stopped there.
"Glug, glug—"
William leaned against the tree and took a long drink of water. Just as he was about to speak, a carriage slowly appeared on the forked road not far away.
It was a four-wheeled carriage pulled by two glossy chestnut horses. Its sides were draped in fine, luxurious fabric, and pale blue gauze covered the windows. The corners were carved with many delicate patterns.
It was obvious that whoever was inside the carriage was rich or noble.
Elula, the most timid of them all, shrank back and edged fearfully behind William.
The two chestnut horses slowly made their way along the road, snorting as they passed the group.
But after only a few steps, a whistle sounded, and the carriage suddenly stopped.
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