0:00:34.460,0:00:36.247
Can you hear me?

0:00:36.503,0:00:37.345
Yes,

0:00:37.542,0:00:39.189
I think you can hear me now,

0:00:39.300,0:00:40.847
but you don't see me.

0:00:40.900,0:00:42.843
That's because you have ears.

0:00:42.975,0:00:45.920
If you close your eyes and reach for the screen

0:00:45.920,0:00:47.520
you will know it's there.

0:00:47.520,0:00:50.020
You feel it through your skin.

0:00:50.020,0:00:52.670
If you have not been allowed to touch it,

0:00:52.670,0:00:54.678
at least you can smell it,

0:00:54.678,0:00:56.710
and after the hot plastic smell

0:00:56.710,0:01:00.294
you will realize that your monitor has to be there.

0:01:00.500,0:01:02.930
Luckily, you have a nose.

0:01:03.023,0:01:05.743
But, what if you taste it?

0:01:06.262,0:01:07.950
Well, it would be more difficult,

0:01:07.950,0:01:09.653
but eventually you'll taste the plastic,

0:01:09.653,0:01:11.689
because you have a tongue.

0:01:12.404,0:01:14.760
You understand the world around you,

0:01:14.760,0:01:17.210
I mean, everything that is around you,

0:01:17.210,0:01:19.064
through those five senses.

0:01:19.412,0:01:20.625
If you have ears,

0:01:20.625,0:01:21.686
you can hear.

0:01:21.686,0:01:22.954
If you have eyes,

0:01:22.954,0:01:24.306
you can see.

0:01:24.556,0:01:25.474
Through your skin,

0:01:25.474,0:01:26.700
you can feel.

0:01:26.800,0:01:28.500
The tongue will help you taste,

0:01:28.660,0:01:31.609
and if you have a nose, you can smell.

0:01:32.252,0:01:37.453
Eyes, ears, nose, tongue and skin are the "tools"

0:01:37.471,0:01:39.000
with which you were born.

0:01:39.020,0:01:41.568
Tools that help you understand [br]the world around you.

0:01:42.467,0:01:44.953
But, how did you know all this?

0:01:45.609,0:01:47.746
Just because you noticed?

0:01:48.073,0:01:51.523
And how did we divide them into five senses?

0:02:26.000,0:02:28.048
The answer is science.

0:02:28.048,0:02:30.350
Because the world is so complicated

0:02:30.350,0:02:33.214
we use science to discover and define.

0:02:33.554,0:02:35.455
But, what is science?

0:02:35.600,0:02:38.310
"Investigation and study of nature

0:02:38.310,0:02:40.661
by observation and reasoning."

0:02:40.821,0:02:42.380
or "the sum of all knowledge

0:02:42.380,0:02:43.977
obtained through research."

0:02:44.377,0:02:47.938
Basically a sum of tests, numbers and letters,

0:02:47.938,0:02:50.800
which, all together can define.

0:02:51.200,0:02:52.000
But how?

0:02:52.500,0:02:55.445
Most people recognize marks as values,

0:02:55.445,0:02:58.755
and the best known groups are [br]letters and numbers.

0:02:58.975,0:03:00.870
They are inventions which help us

0:03:00.870,0:03:03.016
to understand our environment.

0:03:03.517,0:03:05.550
To better understand how these marks

0:03:05.550,0:03:07.130
came into existence

0:03:07.310,0:03:10.457
let's see a brief history of mathematics.

0:03:13.944,0:03:16.000
Human beings, from our earliest beginnings,

0:03:16.300,0:03:18.700
have searched for solutions to basic problems.

0:03:19.750,0:03:21.155
Building homes, measuring space,

0:03:21.355,0:03:23.900
keeping track of seasons and counting objects.

0:03:25.000,0:03:26.350
Over thirty thousand years ago

0:03:26.500,0:03:27.650
early paleolithic people

0:03:27.800,0:03:29.476
kept track of the passing seasons

0:03:29.476,0:03:31.478
and the changes of weather for planting.

0:03:32.200,0:03:33.750
To represent the passing of time

0:03:33.800,0:03:36.049
they carved tally marks on cave walls

0:03:36.283,0:03:38.986
or slashed tallies on bones, wood or stone.

0:03:38.986,0:03:41.986
Each tally stood for one.

0:03:41.986,0:03:43.100
But this system was awkward

0:03:43.250,0:03:44.558
when it came to large amounts.

0:03:44.558,0:03:46.400
So symbols were eventually created

0:03:46.550,0:03:48.195
that stood for groups of objects.

0:03:48.195,0:03:50.550
Sumerian clay stones have been found

0:03:50.700,0:03:52.700
that date to the fourth millennium BC.

0:03:53.400,0:03:56.303
A small clay column was used for one,

0:03:56.303,0:03:58.205
a clay ball was used for ten,

0:03:58.205,0:04:00.207
and a large cone stood for sixty.

0:04:01.000,0:04:04.300
Written records from around 3300 BC show

0:04:04.350,0:04:06.000
that Babylonians inscribed amounts

0:04:06.150,0:04:07.450
on clay tablets with a reed.

0:04:07.500,0:04:09.983
They used a nail shape for ones,

0:04:09.983,0:04:12.553
and a V on its side for tens,

0:04:12.553,0:04:14.955
combining these symbols to write other numbers.

0:04:14.988,0:04:15.750
For example,

0:04:15.850,0:04:18.358
Babylonians wrote the number 19 as...

0:04:19.826,0:04:21.800
The ancient Egyptians used objects

0:04:21.950,0:04:23.730
from their everyday life as symbols.

0:04:23.730,0:04:26.800
A rod stood for one, a cattle hobble was ten,

0:04:26.950,0:04:28.000
a coiled rope was a hundred,

0:04:28.150,0:04:31.004
a lotus flower was a thousand and so on.

0:04:31.400,0:04:34.700
The number 19 was a cattle hobble and nine rods.

0:04:36.150,0:04:37.850
The early Romans created a number system

0:04:38.000,0:04:39.680
that we still see today.

0:04:39.830,0:04:40.850
Along with other symbols

0:04:41.000,0:04:43.650
they used an X for ten and an I for one.

0:04:44.200,0:04:45.000
By the middle ages

0:04:45.100,0:04:47.100
Romans were putting the I to the right of the X

0:04:47.250,0:04:49.756
for eleven and to the left for nine.

0:04:49.756,0:04:52.259
So they wrote 19 as XIX.

0:04:52.800,0:04:54.450
All these creative number systems

0:04:54.600,0:04:57.500
show groups of objects, as well as individual objects.

0:04:58.600,0:05:00.300
Some of the oldest human counting systems

0:05:00.450,0:05:02.700
rely on fingers and toes.

0:05:02.850,0:05:05.706
So they were based on ones, fivers, tens and twenties.

0:05:06.100,0:05:07.950
The Zulu word for six means

0:05:08.100,0:05:10.750
to take the thumb of the right hand.

0:05:10.900,0:05:12.450
Meaning that all the fingers on the left hand

0:05:12.600,0:05:15.500
had been added up and the other thumb was needed.

0:05:16.149,0:05:18.250
Other systems evolved from commerce.

0:05:18.450,0:05:19.500
The Yoruba, in Nigeria,

0:05:19.650,0:05:21.889
used cowry shells as currency

0:05:21.889,0:05:24.858
and developed an amazingly complex number system.

0:05:24.858,0:05:25.950
It was based on 20s

0:05:26.100,0:05:27.880
and on the operations of multiplication,

0:05:28.030,0:05:29.863
subtraction and addition.

0:05:29.989,0:05:30.600
For example:

0:05:30.750,0:05:36.300
they thought of 45 as (3 x 20) - 10 - 5.

0:05:36.700,0:05:38.720
Knots tied in cords and strings were used

0:05:38.870,0:05:41.050
for recording amounts by many cultures,

0:05:41.200,0:05:42.709
like the Persians.

0:05:42.709,0:05:44.150
The Incas used a more refined version

0:05:44.300,0:05:45.345
called the "quipu":

0:05:45.445,0:05:47.600
A thick cord held horizontally

0:05:47.700,0:05:49.416
from which hung knotted string.

0:05:49.883,0:05:51.500
The kind of knot the Incas used

0:05:51.650,0:05:53.200
along with the length and color of the cord

0:05:53.300,0:05:55.756
represented 1s, 10s, and 100s.

0:05:55.800,0:05:57.800
In today's world almost every industrial culture

0:05:57.950,0:06:00.100
uses the numeral 0 through 9.

0:06:00.600,0:06:01.900
But these symbols weren't invented

0:06:02.050,0:06:04.300
until the third century BC in India

0:06:04.665,0:06:06.300
and it took another 800 years

0:06:06.450,0:06:09.800
for the idea of 0 with place value to be constructed.

0:06:10.150,0:06:10.800
This big idea

0:06:11.050,0:06:13.300
dramatically changed the face of mathematics.

0:06:14.700,0:06:16.510
We humans have always shared with one another.

0:06:16.879,0:06:19.279
When early cultures shared their food and water

0:06:19.279,0:06:20.550
or wanted to divide their land

0:06:20.700,0:06:22.400
in ways that were fair and equal,

0:06:22.649,0:06:24.100
fractions gradually emerged

0:06:24.250,0:06:26.550
as symbols for these fair share situations.

0:06:27.888,0:06:29.957
The ancient Egyptians used unit fractions.

0:06:30.224,0:06:32.100
Fractions where the numerator is 1,

0:06:32.250,0:06:34.650
like 1/2, 1/3 and 1/5,

0:06:34.661,0:06:37.064
and would add and halve these fractions.

0:06:37.064,0:06:39.800
If they wanted to divide three loaves of bread equally

0:06:39.950,0:06:41.600
among five family members,

0:06:41.700,0:06:43.900
they'd first divide the first and second loaves

0:06:44.050,0:06:44.700
into thirds.

0:06:46.039,0:06:48.275
Then, they'd divide the third loaf into fifths.

0:06:49.600,0:06:51.450
Finally, they'd take the remaining one third

0:06:51.600,0:06:54.650
from the second loaf and divide that into five pieces.

0:06:56.000,0:07:00.153
They wrote this as 1/3, 1/5, 1/15.

0:07:00.654,0:07:02.150
Today we would represent this sharing

0:07:02.300,0:07:03.650
with the fraction 3/5.

0:07:04.200,0:07:06.450
3/5 of a loaf for each person,

0:07:06.600,0:07:08.900
or 3 loaves divided by 5 people.

0:07:09.530,0:07:11.550
The Sumerians and early Babylonians

0:07:11.700,0:07:13.250
invented a number system of fractions

0:07:13.400,0:07:17.200
based on 60, that we still use 4000 years later.

0:07:17.489,0:07:19.000
Our days have 60 minute hours

0:07:19.150,0:07:20.400
and 60 second minutes,

0:07:20.550,0:07:23.350
and our circles encompass 360 degrees.

0:07:25.212,0:07:27.000
Chinese societies used an abacus

0:07:27.100,0:07:30.117
with a system based on 10s, although it had no 0.

0:07:30.751,0:07:32.250
An early form of decimal fractions

0:07:32.400,0:07:33.400
came from the abacus.

0:07:33.500,0:07:34.300
For example:

0:07:34.400,0:07:37.850
3/5 would be 6 out of 10 on an abacus

0:07:38.125,0:07:40.994
The Chinese lovingly named the numerator "the son"

0:07:40.994,0:07:42.596
and the denominator "the mother".

0:07:43.700,0:07:45.200
It wasn't until the 12th century

0:07:45.350,0:07:46.350
that common fractions,

0:07:46.450,0:07:48.300
with the bar notation that we use today,

0:07:48.400,0:07:49.350
were invented.

0:07:49.500,0:07:51.600
Even then, these fractions weren't widely used

0:07:51.700,0:07:54.500
until the renaissance period, only 500 years ago.

0:07:55.600,0:07:57.650
Throughout history every culture around the globe

0:07:57.800,0:08:00.200
has created inventive ways to calculate.

0:08:00.848,0:08:03.450
To solve a problem, say... 12 x 15,

0:08:03.750,0:08:05.000
early Russian peasants

0:08:05.150,0:08:07.150
used a system of doubling and halving.

0:08:09.523,0:08:12.192
When an odd number halved resulted in a fraction,

0:08:13.093,0:08:14.461
they rounded down,

0:08:15.900,0:08:16.950
then they added the factors

0:08:17.100,0:08:18.950
associated with the odd multipliers.

0:08:24.100,0:08:26.600
Ancient Egyptians relied on a doubling procedure

0:08:26.750,0:08:28.410
until they produced enough groups.

0:08:32.500,0:08:34.900
Then they added these groups to find the answer.

0:08:40.799,0:08:43.049
Across Europe and Asia, during the middle ages,

0:08:43.150,0:08:46.050
the abacus was the handheld calculator of its day.

0:08:46.150,0:08:48.250
But only very few people knew how to use it,

0:08:48.350,0:08:50.430
usually wealthy merchants and money lenders.

0:08:51.000,0:08:53.400
By simply moving beads that each had place value

0:08:53.500,0:08:55.950
an abacus was a highly efficient way to compute.

0:08:56.700,0:08:59.200
Then, the great Arab mathematician al-KhwÄrizmÄŤ

0:08:59.340,0:09:02.000
introduced the Hindu Arabic numerals 0 through 9,

0:09:02.150,0:09:03.700
into North America and Europe

0:09:03.900,0:09:06.250
and created new procedures for computation.

0:09:06.700,0:09:09.349
These algorithms could be written onto paper.

0:09:10.150,0:09:12.050
Over the centuries learning the algorithms

0:09:12.200,0:09:13.800
became the whole mark of an education

0:09:13.950,0:09:15.150
as students were taught to compute

0:09:15.300,0:09:16.900
long columns of figures,

0:09:17.200,0:09:18.000
borrow and carry,

0:09:18.150,0:09:20.900
and do long division efficiently and reliably.

0:09:21.550,0:09:23.050
They could now keep records of these procedures

0:09:23.200,0:09:25.200
and check results.

0:09:26.100,0:09:27.600
Today complex calculations

0:09:27.750,0:09:29.600
are done with a handheld calculator.

0:09:29.850,0:09:31.100
This means students need the ability

0:09:31.250,0:09:33.300
to check the reasonableness of the answer

0:09:33.450,0:09:34.550
and to have a rich repertoire

0:09:34.700,0:09:36.850
of mental math strategies to do that.

0:09:37.500,0:09:40.450
Most simpler computations like 12 x 15

0:09:40.600,0:09:43.400
can be solved mentally using a variety of strategies.

0:09:54.000,0:09:55.300
As we journey through the rich

0:09:55.400,0:09:57.050
and vibrant history of mathematics

0:09:57.200,0:09:59.100
we can see how ideas and creations

0:09:59.250,0:10:00.850
grew out of our very human need

0:10:01.000,0:10:03.550
to solve the problems in our everyday lives.

0:10:03.700,0:10:05.800
Through time, the mathematical explorations

0:10:05.950,0:10:07.950
of men and women from around the globe,

0:10:08.100,0:10:10.100
have given us fascinating lenses

0:10:10.250,0:10:11.650
that help us to mathematically view

0:10:11.800,0:10:14.050
and make sense of our world.

0:10:15.300,0:10:17.250
Science is the collection of facts

0:10:17.400,0:10:20.500
arrived at by defining what we observe

0:10:20.650,0:10:23.200
and running tests to discover.

0:10:23.500,0:10:28.400
Mathematics, chemistry, and physics represent fixed

0:10:28.550,0:10:31.750
languages which are not subject to interpretation.

0:10:31.900,0:10:35.450
Languages used to describe what we observe and

0:10:35.600,0:10:38.950
to test those observations in order to prove them.

0:10:39.200,0:10:41.074
Think of DNA,

0:10:41.074,0:10:43.710
cells, galaxies,

0:10:44.378,0:10:46.146
fruits,

0:10:46.246,0:10:48.282
laptops,

0:10:48.700,0:10:50.551
air conditioning.

0:10:51.118,0:10:53.551
Think about cars,

0:10:54.221,0:10:56.957
food,

0:10:57.300,0:10:58.892
houses,

0:11:00.027,0:11:02.963
fauna,

0:11:03.096,0:11:05.599
flora.

0:11:06.466,0:11:08.635
Think about atoms,

0:11:08.936,0:11:11.305
body parts,

0:11:11.738,0:11:13.974
climate,

0:11:14.708,0:11:17.845
or the clothes you wear.

0:11:20.200,0:11:22.700
And realize that everything is defined,

0:11:22.850,0:11:24.800
or created

0:11:25.000,0:11:27.200
by science.

0:11:33.894,0:11:36.200
To understand the whole concept of science,

0:11:36.350,0:11:40.400
you should know what a scientific theory is:

0:11:40.550,0:11:42.050
"A scientific theory

0:11:42.200,0:11:44.550
comprises a collection of concepts,

0:11:44.700,0:11:48.000
including abstractions of observable phenomena,

0:11:48.150,0:11:50.750
expressed as quantifiable properties,

0:11:50.900,0:11:54.000
together with rules (called scientific laws)

0:11:54.150,0:11:55.750
that express relationships

0:11:55.900,0:11:58.700
between observations of such concepts."

0:11:58.850,0:12:01.850
A scientific theory is constructed to conform to

0:12:02.000,0:12:05.200
available empirical data about such observations,

0:12:05.350,0:12:08.800
and is put forth as a principle or body of principles

0:12:08.950,0:12:11.200
for explaining a class of phenomena.

0:12:11.732,0:12:14.100
A scientific theory is totally different

0:12:14.250,0:12:15.300
from any other theory,

0:12:15.550,0:12:17.750
it is the most probable variant

0:12:17.900,0:12:21.450
resulting from recent discoveries.

0:12:32.850,0:12:36.100
Science is the best tool ever devised

0:12:36.800,0:12:38.950
for understanding how the world works.

0:12:39.100,0:12:42.000
Science is a very human form of knowledge.

0:12:42.200,0:12:44.800
We are always at the brink of the known.

0:12:45.300,0:12:47.450
Science is a collaborative enterprise

0:12:47.600,0:12:49.600
spanning new generations.

0:12:50.700,0:12:53.250
We remember those who prepared the way,

0:12:54.000,0:12:56.550
seeing through them also.

0:12:56.800,0:12:58.500
If you're scientifically literate

0:12:58.650,0:13:00.300
the world looks very different to you,

0:13:00.500,0:13:03.300
and that understanding empowers you.

0:13:08.850,0:13:11.700
There's real poetry in the real world.

0:13:12.100,0:13:15.250
Science is the poetry of reality.

0:13:15.700,0:13:18.150
We can do science, and with it,

0:13:18.950,0:13:20.900
we can improve our lives.

0:13:21.200,0:13:23.950
There's real poetry in the real world.

0:13:24.200,0:13:27.100
Science is the poetry of reality.

0:13:27.350,0:13:30.100
The story of humans is the story of ideas

0:13:30.350,0:13:33.550
that shine light into dark corners.

0:13:39.900,0:13:44.500
Scientists love mysteries, they love not knowing.

0:13:45.500,0:13:48.350
They don't feel frightened by not knowing things.

0:13:48.700,0:13:51.460
I think it's much more interesting.

0:13:52.050,0:13:54.600
There's a larger universal reality

0:13:54.750,0:13:57.500
of which we are all a part.

0:13:57.650,0:14:00.350
The further we probe into the universe,

0:14:00.423,0:14:03.550
the more remarkable are the discoveries we make.

0:14:03.700,0:14:06.250
The quest for the truth, in and of itself,

0:14:06.350,0:14:09.350
is a story that's filled with insights.

0:14:15.800,0:14:18.500
There's real poetry in the real world.

0:14:18.950,0:14:22.250
Science is the poetry of reality.

0:14:22.600,0:14:25.050
We can do science, and with it,

0:14:25.650,0:14:27.600
we can improve our lives.

0:14:27.950,0:14:30.600
There's real poetry in the real world.

0:14:30.800,0:14:34.000
Science is the poetry of reality.

0:14:34.150,0:14:37.350
The story of humans is the story of ideas

0:14:37.500,0:14:39.950
that shine light into dark corners.

0:14:40.050,0:14:43.000
From our lonely point in the cosmos,

0:14:43.300,0:14:45.850
we have through the power of thought

0:14:46.100,0:14:48.850
been able to peer back to a brief moment

0:14:49.550,0:14:51.700
after the beginning of the universe.

0:14:51.850,0:14:53.200
I think that science

0:14:53.350,0:14:55.300
changes the way your mind works.

0:14:55.450,0:14:58.150
To think a little more deeply about things.

0:14:58.500,0:15:01.550
Science replaces private prejudice

0:15:01.700,0:15:04.150
with publicly verifiable evidence.

0:15:04.350,0:15:07.300
There's real poetry in the real world.

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Science is the poetry of reality.

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We can do science, and with it,

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we can improve our lives.

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Science is a great tool

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for understanding the surrounding world

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think of it as a magnifying glass

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through which you can see

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the reality of the world.