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When Columbus sailed the ocean blue in 1492, he didn’t have access to a very important navigational tool that not even Toscanelli’s grid could supply. It was easy to know where you were going North and South. You could calculate your location based on the angle of the sun or the North Star – reliable objects in the sky whose angles never changed relative to the other information every navigator had. That’s because latitude, the lines that go around the world east to west, are the same distance apart going north to south. The world is about 24,900 miles around. There are 360 degrees in a circle. The one-degree lines of latitude are about 24,900 miles divided by 360 degrees apart. About 66.6 miles. Do you remember Ptolemy’s map? There was not much of the southern hemisphere on the map? That’s because they used the North Star to navigate north and south and the star disappeared behind the curvature of the earth when you got too far south. If you went there, you had no idea where you were. No one was afraid they’d fall off the edge of the earth because no one really believed the world was flat. But they were afraid of getting lost.

Longitude is very different. The lines go from one pole to the other so they are wider at the equator than they are at the poles. So there is no reliable solar body that can be used to calculate your longitude – except the sun. It travels from the east and goes to the west every day. Remember, to the medieval mind, the sun went around the earth and what’s interesting is that all these calculations work even with the erroneous world view in mind. It takes 24 hours to go 24,900 miles. That means, even though the distance between the lines of longitude vary from north to south, the time it takes for the sun to travel across the sky doesn’t. Let’s say the earth is 24,000 miles around (just to make the math easy). Each hour the sun travels a thousand miles around the earth at the equator. Those are the time zones. Go north along a time zone, and it gets narrower, but it still takes an hour.

Greenwich is zero degrees longitude. If you’re on the ocean at high noon (you can tell this by looking at the sun) and you know that it’s 3PM at Greenwich, you know you’re three time zones away. Calculate your latitude by looking at the North Star. And you know exactly where you are.

Once again, this technology is all about relationships, perspective and how different elements work together. Longitude and Latitude are a direct result of the grids used in perspective painting. How do we put a three-dimensional spherical globe on a two-dimensional surface in the form of a map? 

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Maps are a good way to evaluate how a culture understands its place in the world because that’s exactly what a map is for. It tries to answer the question “where am I?” Later on, maps would try and answer questions like “where am I going?” and “how can I get back?” but, initially, maps were an attempt to simply locate one’s self.

This is evidenced by the fact that the earliest maps we can find aren’t maps of the world. They’re maps of the sky. Consider this Sumerian Star Chart from around 3300 BC

It’s not just a map. It’s an astrolabe. Very early on people saw themselves in relation to all the other things they could see. They could see the sky. And so technology developed from the information they could gather.

Interestingly, and perhaps paradoxically, everyone had to start all over when they decided to make maps of the world, much of which they couldn’t see or didn’t even know about. The Greeks saw the world as a disk, not because they believed that it was flat as much as they read about it in Homer’s poems and this was as good a place to start as any. Distances were measured in how many days it took to sail or march from place to place.

By the Middle Ages, Europeans had become very practical about maps. Look at this map used during the Crusades. The map is designed with religious considerations in mind. East is at the top. Jerusalem in the middle. That’s where everyone wanted to go anyway.

And this view of the world, with Jerusalem in the middle and the most obvious reference point of the time, the sun rising, at the top, was very much the way the world looked to people. Take a look at a map from The Enchiridion by Byrhtferth of Ramsey Abbey created around 1000AD. Not mistaking where Jerusalem is on this map:

The Vikings did something similar. They needed to know the coastline of Europe, not the interior. They were planning on robbing and pillaging all week and they needed to get back on the weekends. So you shorelines are detailed. The interior doesn’t matter.

What’s really quite strange about all this is that there are no real grids. The map with the lines on it indicated prevailing winds, not locations. People had no real idea how far away something was. At least they didn’t have any objective measure of distance.

And then the Europeans discovered Ptolemy. He had a keen interest in geography and prepared what might be the first map of the world. Here’s a 16th century interpretation of what his map looked like.

It’s likely to be an inaccurate interpretation but it works for our purposes because it shows two very critical elements. It has a grid superimposed on it and Ptolemy’s original very likely showed something similar. Secondly, it didn’t show much of the southern hemisphere. More on that later.

Now, let’s go back to the Renaissance man we talked about. Toscanelli, who you ran across in Burke’s book, was a classic renaissance man. He was interested in architecture, art, history, mathematics, astronomy and, not surprisingly, cartography. Once again, this didn’t make him a renaissance man. What did that was his ability to put together elements of all these disciplines and create a new idea from the mess using, among other tools, the syllogism. He had a keen understanding of Ptolemy’s mathematics and almost certainly was familiar with Ptolemy’s map. With some clever calculations, he figured out how big China was likely to be, added it to his map of Europe, the Middle East and Africa, applied a grid that people were finding useful for perspective painting, and reasoned that it would be easier to get to the orient going west rather than east.

We don’t have Toscanelli’s map but it would have looked something like this:

Of course there’s no America on the map and, based on the wildly exaggerated size of China he had to work with, the Far East coast of Japan is right about where the Bahamas are – exactly where Columbus landed using Toscanelli’s map.



crusades 1321 east


viking 1440

ptolemy 150


Lost at Sea : The Search for Longitude : David R Axelrod (Screenwriter) (Television producer), Peter Jones (Television director), Paula S Apsell (Television producer), Richard Dreyfuss (Narrator), Patrick Malahide (Voice actor), Brian McDairmant (Director of photography.), Eve Gage (Editor of moving image work), William J H Andrewes (Consultant), Jonathan Betts (Consultant), Dava Sobel, City of Prague Philharmonic Orchestra (Performer), Green Umbrella Ltd. (Production company), WGBH (Television station : Boston, Mass.) (Production company), Sveriges television (Production company), WGBH Video (Firm) (Film distributor) : Free Download, Borrow, and Streaming : Internet Archive

Latitude and Longitude: A Global Address – Video – Films On Demand (mnpals.net)

Please watch these videos

Harrison’s hurdles. John Harrison’s struggles involved in solving the problem of longitude continued long after the problem was actually solved. What were they? Some say that this is part of the process of innovation. Do you agree? Give examples of how innovation works today and how it compares to Harrison’s efforts to solve the problem of longitude.

Instructions on writing discussion post

How to write a good initial discussion post:

1. The purpose of writing a discussion post is to reflect on what you have learned from the assigned material. How does it support what you already thought? How does it challenge conventional wisdom? Where it conflicts with your understanding of the world, does it convince you? Where it agrees, what further understandings does it imply?

2. Your initial discussion post must include at least 300 words of your own material. Repeating the question, titles, quotations, paraphrases and other additions are not counted as your own material. Any discussion that does not meet the 300 word minimum will receive a grade of 0.

3. Refer to at least two of the assigned resources. You need to give some thought to what’s presented in the assigned material. For example, you might write: The Stanford Encylopedia of Philosophy explains Locke’s understanding of the relationship between simple and complex ideas this way: “Once the mind has a store of simple ideas, it can combine them into complex ideas of a variety of kinds” (


. Don’t make the class guess at the reference. We have to be able to find it. So it needs to be relevant and specific. People get busy and time is sometimes short, so it may be tempting at times to excerpt something from readings you haven’t considered carefully and stick it in your post to meet this requirement. Try not to do this. See point 5 on why. There is no need to use an MLA style citation to the end of a post. We need to read the quotation, and we need to know what in the material helped you arrive at the conclusions you arrived at and where we can find it. That means you need to include an author and a page number if it’s a printed resource, or a title reference for audio and video resources. Points will be deducted if the location of the reference isn’t obvious. To earn full points for your discussion, you need to refer to more than one of the assigned resources in the module if more are available. The resources work together.

4. Any discussion that includes sufficiently poor grammar or spelling to suggest that the posting was not proof-read and spell checked will receive a grade of 0.

5. The best way to meet the requirement to reference the readings is to quote them directly. But please do not quote lengthy sections of the readings. I am looking for your ideas concerning the readings and classes. See point 3. for a good example. Quotations are not considered part of the 300 word minimum.

6. Remember that you are reflecting on the material presented in the module and taking an informed position on the topic. It doesn’t help to simply repeat facts from the module. What do they mean? Use your existing opinion wisely. The distinction between research and opinion is an artificial distinction we don’t want to make in this class. Criticism is useful but only if it’s thoughtful and reasonable. If, at the end of every unit, you think exactly the same way you did when you started the unit, something has gone wrong.

8. You will need to post your own initial post before you can read the responses from others. It makes for a much more diverse conversation. After you have posted your initial post, I hope you will consider other ideas as well and comment on them. There is no grade-sensitive requirement to comment on other posts but, needless to say, your ideas on others’ thinking is the best way for all of us to learn. And feel free to respond to my comments on your post.

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