Lessonpills

1

Think about these questions before watching. Share your ideas with a partner.

Imagine your phone's GPS suddenly stopped working while you were in an unfamiliar place. What steps would you take to find your way?
What do you think were the greatest challenges or fears for sailors undertaking long sea voyages hundreds of years ago?
Besides navigation, can you think of other areas of life where a tiny error in measurement or calculation could have huge consequences?

2

Watch the video carefully. Pay attention to the main ideas and key details.

Video script49 segments · click a timestamp to jump

Transcriber: tom carter Reviewer: Bedirhan Cinar

As you can imagine, 400 years ago,

navigating the open ocean was difficult.

The winds and currents pushed and pulled ships off course,

and so sailors based their directions on the port they left,

attempting to maintain an accurate record of the ship's direction and the distance sailed.

This process was known as dead reckoning,

because being just half a degree off could result in sailing right past the island that lay several miles just over the horizon.

This was an easy mistake to make.

Thankfully, three inventions made modern navigation possible:

sextants, clocks and the mathematics necessary to perform the required calculations quickly and easily.

All are important. Without the right tools, many sailors would be reluctant to sail too far from the sight of land.

John Bird, an instrument maker in London,

made the first device that could measure the angle between the sun and the horizon during the day,

called a sextant.

Knowing this angle was important, because it could be compared to the angle back in England at the exact same time.

Comparing these two angles was necessary to determine the longitude of the ship.

Clocks came next.

In 1761, John Harrison, an English clockmaker and carpenter,

built a clock that could keep accurate time at sea.

The timepiece that could maintain accurate time while on a pitching, yawing deck in harsh conditions

was necessary in order to know the time back in England.

There was one catch though:

since such a timepiece was handmade, it was very expensive.

So an alternate method using lunar measurements and intense calculations was often used to cut costs.

The calculations to determine a ship's location for each measurement could take hours.

But sextants and clocks weren't useful unless sailors could use these tools to determine their position.

Fortunately, in the 1600s, an amateur mathematician had invented the missing piece.

John Napier toiled for more than 20 years in his castle in Scotland to develop logarithms, a calculation device.

Napier's ideas on logarithms involved the form of one over E and the constant 10 to the seventh power.

Algebra in the early 1600s was not fully developed,

and Napier's logarithm of one did not equal zero.

This made the calculations much less convenient than logarithms with a base of 10.

Henry Briggs, a famous mathematician at Gresham College in London,

read Napier's work in 1614, and the following year made the long journey to Edinburgh to meet Napier.

Briggs showed up unannounced at Napier's castle door

and suggested that John switch the base and form of his logarithms into something much simpler.

They both agreed that a base of 10 with the log of one equal to zero

would greatly simplify everyday calculations.

Today we remember these as Briggs Common Logarithms.

Until the development of electric calculating machines in the 20th century,

any calculations involving multiplication, division, powers, and extraction of roots with large and small numbers

were done using logarithms.

The history of logarithms isn't just a lesson in math.

There were many players responsible for successful navigation.

Instrument makers, astronomers, mathematicians,

and of course sailors.

Creativity isn't only about going deep into one's field of work,

it's about cross-pollination between disciplines too.

3

Answer these questions in your own words. Support your answers with evidence from the video.

01According to the video, what was 'dead reckoning' and why was it so risky for sailors?

Sample answerIt was a navigation method where sailors tried to keep a record of their direction and the distance they had sailed from their starting port. It was very risky because a tiny error, even half a degree, could make a ship sail right past its destination.

02How did the sextant and the marine clock work together to help sailors determine their longitude?

Sample answerThe sextant was used to measure the angle of the sun above the horizon. To calculate longitude, this angle had to be compared to the angle in England at the exact same time. The marine clock was essential because it kept the accurate time from England, which was needed for that comparison.

03In what way did Henry Briggs's contribution improve upon John Napier's original invention?

Sample answerJohn Napier invented logarithms, but his first version was very complicated to use. Henry Briggs suggested changing the base of the logarithms to 10, which made the calculations much simpler and more practical for everyday use. These are now known as common logarithms.

04Why does the narrator conclude by mentioning people from many different professions?

Sample answerThe narrator mentions instrument makers, astronomers, and mathematicians to show that successful navigation wasn't just the achievement of sailors. It was a collaborative effort. The main point is that creativity and innovation often come from this 'cross-pollination' between different fields of work.

4

Vocabulary

These expressions will help you communicate more naturally about this topic.

Examples

To find your bearings — to figure out your exact position or location; also, to become familiar with a new situation.

Usage note: This idiom can be used literally for physical navigation (like the sailors in the video) and figuratively for understanding a new job, city, or complex topic.

To chart a course — to plan a route or direction, especially for a ship or aircraft.

Usage note: This is often used figuratively to mean 'to plan a strategy or future actions'. For example: 'The company needs to chart a course for the next decade.'

A breakthrough in (a field) — an important discovery or development that helps solve a problem or advance a field of study.

Usage note: Use this to talk about major, game-changing inventions like the marine chronometer. Common collocations include 'a scientific breakthrough' or 'a technological breakthrough'.

To pave the way for (something) — to create a situation that makes it possible or easier for something else to happen in the future.

Usage note: This is a great phrase for linking historical events. For example: 'The invention of the sextant paved the way for more accurate global navigation.'

By trial and error — a way of solving a problem by trying different methods and learning from your mistakes until you find one that is successful.

Usage note: This phrase describes the process of experimentation, like the work of inventors mentioned in the video. For example: 'Early clockmakers developed their designs by trial and error.'

5

Decide if each statement is true or false. Correct the false ones.

01Before modern inventions, sailors used a method called 'dead reckoning' to estimate their position.

02John Napier, a professional mathematician, invented the first system of logarithms.

03The purpose of the marine clock was to allow sailors to know the correct time in England while at sea.

04Logarithms were the main tool for performing complex calculations until the 20th century.

05Henry Briggs proposed that the most convenient base for logarithms would be the number one.

6

Complete the sentences with words from the box. One word is extra.

Word bank

01The invention of the marine chronometer was a major in the field of navigation.

02Early astronomical observations the way for more accurate map-making and global exploration.

03Without modern instruments, ancient navigators often found new lands through a process of and error.

04After the storm threw them off course, the sailors used the stars to find their .

05Before setting sail, the captain had to carefully a course through the treacherous waters.

7

Choose the best answer based on what you heard in the video.

01Why was an alternative method to using John Harrison's marine clock often employed?

02What does the video tell us about John Napier, the inventor of logarithms?

03According to the narrator, what was a significant consequence of the difficulties in navigation before modern tools were invented?

04Which of the following challenges for sailors is NOT mentioned in the video as a problem addressed by the inventions discussed?

8

Navigating the Seas: Past and Present

Test your knowledge of historical navigation and related vocabulary.

Match each item on the left with the correct item on the right.

A

B

9

Discuss these questions with a partner. Try to use vocabulary from the lesson.

The video highlights the sextant and the marine clock as key breakthroughs. Which of these two inventions do you think was more revolutionary for its time, and why? Or, do you believe a modern invention like GPS has had a far greater impact on how we chart a course today?
Think about a significant invention or discovery from your country's history. How did it pave the way for future developments, and do you think it was created systematically or more by trial and error?
The video describes the immense difficulty sailors had in finding their bearings without modern tools. In an age of GPS and digital maps, do you think people are losing the basic skills of navigation and orientation? What are the potential downsides of this?