The Dilettante – More On Infinity

One other fascinating discovery about infinity in One Two Three… Infinity that was new to me is that the number of points on two lines of any length is the same. Also, that the number of points on a plane, and even three dimensional space is the same.

First of all, what I mean by “number of points… is the same” is what you would naturally think: They can be put in a 1:1 (one to one) relationship, for example:

Set 1: A, D, A, M, Z
Set 2: J, U, L, I, E

Set 1 has five letters and set 2 has five letters. We are only concerned with how many items there are in each set, and not what the letters are. The fact that the letter ‘A’ is repeated twice in set 1 and that neither set has any letter in common are unimportant. To see if the two sets are the same size, or if one is bigger than the other, we pair off the items in the two sets in any order we choose:

J - Z
U - M
L - A
I - D
E - A

We find that both sets are the same size because they can be put in a 1:1 relationship.

Simple enough. So, here is the mind blowing visual proof that two lines have the same number of points:


mind blown

In this diagram the two lines of different length AB and AC are joined at A. The line CB connects the endpoints, and every line parallel to CB, such as DE, connects a unique point on AB with a unique point on AC and vice versa. So, even though there are an infinity of points on both lines, they can be put in a 1:1 relationship.

In case that’s a little too informal, let me just add that CB and all its parallels are just graphs of a line function. You don’t even need to know exactly what the function looks like, just that the input is a point on one line and the output is a point on the other, and that for every input there’s a unique output. To me, it seems entirely counter intuitive, but the logic is inescapable, two lines of unequal length have the same number of points.

End of part 1. Coming in Part 2 – Use this one weird trick to map all the points on a plane to all the points on a line.

The Dilettante on the History of Slavery and Colonialism in the Modern World

Some musings on slavery and colonialism from The Cartoon History of the Modern World, Part II.

In the late 1700’s, the British empire circled the globe. A couple of hold-outs were China; which would trade goods for silver, but never buy anything; and Japan, which after uniting under a single Shogun in 1600, refused all contact with the Western World. Of course, capital being hard to say ‘no’ to, both countries left single ports open to trade.

Although other European countries participated in the slave trade, the British were the most successful. The slave trade was run in a triangle: African slaves were shipped to sugar plantations in the New World, sugar was shipped to New England to be distilled into rum, the rum was then sent back to Africa to trade for more slaves. While that was going on, the British East India Company was busy mismanaging India, and eventually ran the Indian economy into the ground leading to widespread poverty.

There had always been people in Britain that opposed the slave trade, but they were mostly seen as a wacky fringe group. Then, the Zong massacre renewed the anti-slavery activists’ fight, and an anti-slavery MP, William Wilberforce, took up the cause, introducing an anti-slavery bill to Parliament – it was defeated. Every year Wilberforce introduced the bill, and every year it was voted down.

After the British defeated Napoleon, Wilberforce, hit on the idea of outlawing the slave trade on the high seas as an extension of British naval power. By voting to ban the slave trade for all nations, British ships could to stop and board any ship sailing under any nation’s flag. After 20 years, Wilberforce finally got his anti-slavery bill passed. The British didn’t do a lot to stop the slave trade, but over the yeas they managed to free tens of thousands of slaves. The U.S., seeing the reality of the situation, decided to follow the British by voting to ban the slave trade on the open seas in 1808. The American’s did nothing to enforce the ban, however.

After crashing India’s economy, the British hit on the thing that they could sell to China: opium from Indian poppies. This trade was so lucrative that even after the British voted in 1833 to ban slavery throughout the empire, they were able to make up for the loss of revenue with the trade. The opium trade divided China and lead to the Opium Wars which took 60 million lives.

Also at this time, the British were busy competing with the other European countries colonizing Africa. Colonialism was even better than slavery. Instead of the hassle of shipping slaves across the ocean, they could just enslave the people at home. Ten-million Congolese lost their lives in forced labor, harvesting natural rubber for King Leopold of Belgium. Cecil Rhodes (started De Beers and the Rhodes Scholarship) founded Rhodesia, and wanted to see an all British Africa. The European nations had a meeting in Berlin and decided to divide up the entire continent of Africa amongst themselves.

So, as Larry Gonick points out, the start of the century that saw the end of slavery, saw the beginning of colonialism in Africa.


More Chris Hadfield

One of his most famous accomplishments was recording a music video on the ISS: a version of David Bowie’s Space Oddity (I guess it would have qualified on its own for “Nerd Song of the Week”):

The Canadian Space Agency has all his videos from Expedition 34/35, which he commanded:

He’s all over social media and the web (has a Twitter feed, etc.), so check him out.