A brief history of numerical systems - Alessandra King
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0:11 - 0:18One, two, three, four, five, six,
seven, eight, nine, and zero. -
0:18 - 0:24With just these ten symbols, we can
write any rational number imaginable. -
0:24 - 0:27But why these particular symbols?
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0:27 - 0:28Why ten of them?
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0:28 - 0:32And why do we arrange them the way we do?
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0:32 - 0:35Numbers have been a fact of life
throughout recorded history. -
0:35 - 0:40Early humans likely counted animals
in a flock or members in a tribe -
0:40 - 0:43using body parts or tally marks.
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0:43 - 0:47But as the complexity of life increased,
along with the number of things to count, -
0:47 - 0:51these methods were no longer sufficient.
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0:51 - 0:52So as they developed,
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0:52 - 0:57different civilizations came up
with ways of recording higher numbers. -
0:57 - 0:58Many of these systems,
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0:58 - 0:59like Greek,
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0:59 - 1:00Hebrew,
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1:00 - 1:01and Egyptian numerals,
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1:01 - 1:03were just extensions of tally marks
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1:03 - 1:07with new symbols added to represent
larger magnitudes of value. -
1:07 - 1:13Each symbol was repeated as many times
as necessary and all were added together. -
1:13 - 1:16Roman numerals added another twist.
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1:16 - 1:18If a numeral appeared before one
with a higher value, -
1:18 - 1:22it would be subtracted rather than added.
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1:22 - 1:23But even with this innovation,
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1:23 - 1:29it was still a cumbersome method
for writing large numbers. -
1:29 - 1:31The way to a more useful
and elegant system -
1:31 - 1:35lay in something called
positional notation. -
1:35 - 1:38Previous number systems needed to draw
many symbols repeatedly -
1:38 - 1:43and invent a new symbol
for each larger magnitude. -
1:43 - 1:46But a positional system could reuse
the same symbols, -
1:46 - 1:51assigning them different values
based on their position in the sequence. -
1:51 - 1:55Several civilizations developed positional
notation independently, -
1:55 - 1:57including the Babylonians,
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1:57 - 1:58the Ancient Chinese,
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1:58 - 2:00and the Aztecs.
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2:00 - 2:05By the 8th century, Indian mathematicians
had perfected such a system -
2:05 - 2:07and over the next several centuries,
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2:07 - 2:12Arab merchants, scholars, and conquerors
began to spread it into Europe. -
2:12 - 2:16This was a decimal, or base ten, system,
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2:16 - 2:21which could represent any number
using only ten unique glyphs. -
2:21 - 2:24The positions of these symbols
indicate different powers of ten, -
2:24 - 2:27starting on the right
and increasing as we move left. -
2:27 - 2:30For example, the number 316
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2:30 - 2:34reads as 6x10^0
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2:34 - 2:36plus 1x10^1
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2:36 - 2:40plus 3x10^2.
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2:40 - 2:42A key breakthrough of this system,
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2:42 - 2:45which was also independently
developed by the Mayans, -
2:45 - 2:47was the number zero.
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2:47 - 2:51Older positional notation systems
that lacked this symbol -
2:51 - 2:52would leave a blank in its place,
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2:52 - 2:57making it hard to distinguish
between 63 and 603, -
2:57 - 3:00or 12 and 120.
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3:00 - 3:04The understanding of zero as both
a value and a placeholder -
3:04 - 3:08made for reliable and consistent notation.
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3:08 - 3:10Of course, it's possible
to use any ten symbols -
3:10 - 3:14to represent the numerals
zero through nine. -
3:14 - 3:17For a long time,
the glyphs varied regionally. -
3:17 - 3:19Most scholars agree
that our current digits -
3:19 - 3:23evolved from those used in the
North African Maghreb region -
3:23 - 3:25of the Arab Empire.
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3:25 - 3:30And by the 15th century, what we now know
as the Hindu-Arabic numeral system -
3:30 - 3:33had replaced Roman numerals
in everyday life -
3:33 - 3:37to become the most commonly
used number system in the world. -
3:37 - 3:41So why did the Hindu-Arabic system,
along with so many others, -
3:41 - 3:43use base ten?
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3:43 - 3:47The most likely answer is the simplest.
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3:47 - 3:52That also explains why the Aztecs used
a base 20, or vigesimal system. -
3:52 - 3:55But other bases are possible, too.
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3:55 - 3:59Babylonian numerals were sexigesimal,
or base 60. -
3:59 - 4:02Any many people think that a base 12,
or duodecimal system, -
4:02 - 4:04would be a good idea.
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4:04 - 4:08Like 60, 12 is a highly composite number
that can be divided by two, -
4:08 - 4:09three,
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4:09 - 4:10four,
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4:10 - 4:11and six,
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4:11 - 4:15making it much better for representing
common fractions. -
4:15 - 4:18In fact, both systems appear
in our everyday lives, -
4:18 - 4:20from how we measure degrees and time,
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4:20 - 4:23to common measurements,
like a dozen or a gross. -
4:23 - 4:27And, of course, the base two,
or binary system, -
4:27 - 4:30is used in all of our digital devices,
-
4:30 - 4:36though programmers also use base eight
and base 16 for more compact notation. -
4:36 - 4:38So the next time you use a large number,
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4:38 - 4:42think of the massive quantity captured
in just these few symbols, -
4:42 - 4:46and see if you can come up
with a different way to represent it.
- Title:
- A brief history of numerical systems - Alessandra King
- Description:
-
View full lesson: http://ed.ted.com/lessons/a-brief-history-of-numerical-systems-alessandra-king
1, 2, 3, 4, 5, 6, 7, 8, 9... and 0. With just these ten symbols, we can write any rational number imaginable. But why these particular symbols? Why ten of them? And why do we arrange them the way we do? Alessandra King gives a brief history of numerical systems.
Lesson by Alessandra King, animation by Zedem Media.
- Video Language:
- English
- Team:
- closed TED
- Project:
- TED-Ed
- Duration:
- 05:08
Jessica Ruby approved English subtitles for A brief history of numerical systems - Alessandra King | ||
Jessica Ruby accepted English subtitles for A brief history of numerical systems - Alessandra King | ||
Jessica Ruby edited English subtitles for A brief history of numerical systems - Alessandra King | ||
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