Name: 代數學前1--數字的曙光 (Pre-Algebra 1 - The Dawn of Numbers)
Uploaded: 2021-01-14T07:49:52.000Z
Duration: 10 min 17 s
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Hello. I'm Professor Von Schmohawk
and welcome to Why U.

This series of lectures
is an introduction to Algebra.

we should start by taking a closer look
at the things we call numbers.

understanding and communicating quantities
has been essential to everyday life.

Anthropologists tell us that even
the most primitive stone-age cultures

However, early number systems were much more
limited than today's base-10 number system.

We didn't need names for exact quantities.

If you knew that there was
a herd of gazelles nearby

it didn't matter exactly how many gazelles
were in the herd

or exactly how many miles away they were.

What was important was that there were a lot
of gazelles and they were just over the hill.

Even recently, certain Australian
aboriginal tribes counted only to two

with any number larger than two called
"much" or "many".

South American Indians along the Amazon
had names for numbers up to six

although three was called "two-one",
four was "two-two" and so on.

Bushmen of South Africa had a similar way
of naming quantities

but stopped at ten
because the names became too long.

This tribe would not do "financial" transactions
involving numbers greater than two.

For example, they would not
trade two cows for four pigs.

Instead, they would
trade one cow for two pigs

and then in a second transaction
trade another cow for another two pigs.

If you had never heard of numbers
and you wanted to describe to someone

exactly how many gazelles
you had seen just over the hill

you might use your fingers to represent
how many gazelles there were.

Of course this would become difficult
if there were more than ten gazelles.

or maybe gather a group of pebbles
to represent the number of gazelles

but then, this would also become cumbersome
if there were a lot of gazelles.

Another option would be to invent different
names and symbols for each possible quantity.

This seems like a simple solution
but there is still a problem.

Remember that you know nothing about
our modern base-10 number system

which uses only ten symbols in different combinations

so you will have to invent a new word
and symbol for every possible quantity.

For instance, in my primitive tribe
on Cocoloco island

here are the first thirty numbers we use.

After Zortan we just say "a whole bunch".

There were several problems
with this number system.

First of all, since we had over thirty symbols
to memorize, math was really difficult.

For instance, if you have “walaki” coconuts

The answer is obviously “bimpy” coconuts

but it takes many years of school to memorize
all the combinations.

Also, what happens if you have
“bazooloo” coconuts

and then someone gives you “trom” more?

Well, then you'd have
“a whole bunch of” coconuts.

In the past, some of the mathematicians
on Cocoloco Island

actually invented an "advanced" number system

with several thousand names and symbols
to handle problems like this.

someone always came up with a problem which
they did not have a number for

by adding “zoop” to the biggest number.

Then one especially brilliant
Cocoloconian mathematician

came up with the idea of combining symbols.

After zortan, the next number would be zortan-zoop

This worked well
but numbers could get quite long.

For instance, our number "one-thousand"
in Cocoloconian would be

zortan-zortan-zortan-zortan-zortan-zortan

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代數學前1--數字的曙光 (Pre-Algebra 1 - The Dawn of Numbers)

stick

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