Animation basics: The optical illusion of motion - TED-Ed

231,579 views ใƒป 2013-07-13

TED-Ed


ืื ื ืœื—ืฅ ืคืขืžื™ื™ื ืขืœ ื”ื›ืชื•ื‘ื™ื•ืช ื‘ืื ื’ืœื™ืช ืœืžื˜ื” ื›ื“ื™ ืœื”ืคืขื™ืœ ืืช ื”ืกืจื˜ื•ืŸ.

ืžืชืจื’ื: Ido Dekkers ืžื‘ืงืจ: benyamin zinshtein
ืงื—ื• ืกื“ืจื” ืฉืœ ืชืžื•ื ื•ืช ืจืฆื™ืคื•ืช.
00:15
Take a series of still, sequential images.
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00:18
Let's look at them one by one.
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ื‘ื•ืื• ื ื‘ื™ื˜ ื‘ื”ืŸ ืื—ืช ืื—ืจื™ ื”ืฉื ื™ื”.
00:23
Faster.
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ืžื”ืจ ื™ื•ืชืจ.
00:28
Now, let's remove the gaps,
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ืขื›ืฉื™ื•, ื‘ื•ืื• ื ืกื™ืจ ืืช ื”ืžืจื•ื•ื—ื™ื,
00:30
go faster still.
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ืชืžืฉื™ื›ื• ื™ื•ืชืจ ืžื”ืจ.
00:32
Wait for it ...
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ื—ื›ื• ืจื’ืข...
00:36
Bam!
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...ื‘ืื!
00:37
Motion!
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ืชื ื•ืขื”!
00:39
Why is that?
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ืœืžื” ื–ื”?
00:41
Intellectually, we know we're just looking at a series of still images,
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ื‘ืื•ืคืŸ ืื™ื ื˜ืœืงื˜ื•ืืœื™, ืื ื—ื ื• ื™ื•ื“ืขื™ื ืฉืื ื—ื ื• ืžื‘ื™ื˜ื™ื
ื‘ืกื“ืจื” ืฉืœ ืชืžื•ื ื•ืช ืกื˜ื™ืœืก,
00:44
but when we see them change fast enough,
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ืื‘ืœ ื›ืฉืื ื—ื ื• ืจื•ืื™ื ืื•ืชื ืžืฉืชื ื•ืช ืžื”ืจ ืžืกืคื™ืง,
00:46
they produce the optical illusion of appearing as a single, persistent image
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ื”ืŸ ื™ื•ืฆืจื•ืช ืืฉืœื™ื” ืื•ืคื˜ื™ืช
ืฉืœ ื ืจืื•ืช ื›ืื™ืœื• ืชืžื•ื ื” ืื—ืช ืงื‘ื•ืขื”
ืฉืžืฉื ื” ืœืื˜ ืฆื•ืจื” ื•ืžื™ืงื•ื.
00:50
that's gradually changing form and position.
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ื”ืืคืงื˜ ื”ื–ื” ื”ื•ื ื”ื‘ืกื™ืก ืœื›ืœ ื˜ื›ื ื•ืœื•ื’ื™ื•ืช ื”ืกืจื˜ื™ื,
00:53
This effect is the basis for all motion picture technology,
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00:56
from our LED screens of today
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ืžืžืกื›ื™ ื”LED ืฉืœื ื• ื”ื™ื•ื
00:58
to their 20th-century cathode ray forebearers,
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ืžืงื•ื“ืžื™ื”ื ืขื ื”ืฉืคื•ืคืจืช ื”ืงื˜ื•ื“ื™ืช ืžื”ืžืื” ื” 20,
ืžื”ืงืจื ื” ืงื•ืœื ื•ืขื™ืช
01:01
from cinematic film projection to the novelty toy,
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ืœืฆืขืฆื•ืข ,
ืืคื™ืœื•, ื”ื•ืฆืข,
01:04
even, it's been suggested, all the way back to the Stone Age
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ืฉื”ืจื—ืง ืื—ื•ืจื” ืœืขื™ื“ืŸ ื”ืื‘ืŸ
ื›ืฉืื ืฉื™ื ื”ืชื—ื™ืœื• ืœืฆื™ื™ืจ ืขืœ ืงื™ืจื•ืช ืžืขืจื•ืช.
01:07
when humans began painting on cave walls.
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01:09
This phenomenon of perceiving apparent motion in successive images
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ื”ืชื•ืคืขื” ืฉืœ ืงืœื™ื˜ื” ืฉืœ ืชื ื•ืขื”
ื‘ืจืฆืฃ ืฉืœ ืชืžื•ื ื•ืช
01:13
is due to a characteristic of human perception
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ื”ื™ื ื‘ื’ืœืœ ืชื›ื•ื ื” ืฉืœ ื”ืชืคื™ืกื” ื”ืื ื•ืฉื™ืช
01:15
historically referred to as "persistence of vision."
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ืฉืžื›ื•ื ื” ื”ื™ืกื˜ื•ืจื™ืช "ื”ืžืฉื›ื™ื•ืช ื”ืจืื™ื”."
01:18
The term is attributed
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ื”ืžื•ื ื— ืžืฉื•ื™ื™ืš
01:19
to the English-Swiss physicist Peter Mark Roget,
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ืœืจื•ืคื ืื ื’ืœื™-ืฉื•ื•ืฆืจื™ ืคื™ื˜ืจ ืžืืจืง ืจื•ื’'ื”,
01:22
who, in the early 19th century,
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ืฉื‘ืชื—ื™ืœืช ื”ืžืื” ื” 19,
01:24
used it to describe a particular defect of the eye
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ื”ืฉืชืžืฉ ื‘ื• ืœืชืืจ ืชืงืœื” ืžืกื•ื™ื™ืžืช ื‘ืขื™ืŸ
01:27
that resulted in a moving object
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ืฉื’ืจืžื” ืœืื•ื‘ื™ื™ืงื˜ ื ืข
ืœื”ืจืื•ืช ื›ืื™ืœื• ื”ื•ื ื ื— ื›ืฉื”ื’ื™ืข ืœืžื”ื™ืจื•ืช ืžืกื•ื™ื™ืžืช.
01:29
appearing to be still when it reached a certain speed.
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01:32
Not long after, the term was applied to describe the opposite,
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ืžืขื˜ ืœืื—ืจ ืžื›ืŸ,
ื”ืžื•ื ื— ื”ื™ื” ื‘ืฉื™ืžื•ืฉ ื›ื“ื™ ืœืชืืจ ืืช ื”ื”ืคืš,
01:35
the apparent motion of still images,
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ื”ืชื ื•ืขื” ื”ื ืชืคืฉืช ืฉืœ ืชืžื•ื ื•ืช ืกื˜ื™ืœืก,
01:37
by Belgian physicist Joseph Plateau, inventor of the phenakistoscope.
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ืขืœ ื™ื“ื™ ื”ืคืกื™ื›ื™ืื˜ืจ ื”ื‘ืœื’ื™ ื’'ื•ื–ืฃ ืคืœื˜ืื•,
ืžืžืฆื™ื ื”ืคื ืงื™ืกื˜ื•ืกืงื•ืค.
ื”ื•ื ื”ื’ื“ื™ืจ ืืช ื”ื”ืžืฉื›ื™ื•ืช ืฉืœ ื”ืจืื™ื”
01:42
He defined persistence of vision as the result of successive afterimages,
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ื›ืชื•ืฆืื” ืฉืœ ืชืžื•ื ื•ืช ืฉื™ื•ืจื™ื•ืช ืžื—ื–ื•ืจื™ื•ืช
01:46
which were retained and then combined in the retina,
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ืฉื ืฉืžืจื• ื•ืื– ื—ื•ื‘ืจื• ื‘ืจืฉืชื™ืช,
ืžื” ืฉื’ื•ืจื ืœื ื• ืœื”ืืžื™ืŸ ืฉืžื” ืื ื—ื ื• ืจื•ืื™ื
01:49
making us believe that what we were seeing is a single object in motion.
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ื”ื•ื ืื•ื‘ื™ื™ืงื˜ ืื—ื“ ื‘ืชื ื•ืขื”.
01:52
This explanation was widely accepted in the decades to follow
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ื”ื”ืกื‘ืจ ื”ื–ื” ื”ื™ื” ืžืงื•ื‘ืœ
ื‘ืขืฉื•ืจื™ื ืœืื—ืจ ืžื›ืŸ
01:55
and up through the turn of the 20th century,
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ื•ืขื“ ืชื—ื™ืœืช ื”ืžืื” ื” 20,
ื›ืฉืื—ื“ื™ื ื”ื—ืœื• ืœืคืงืคืง
01:58
when some began to question what was physiologically going on.
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ืžื” ืงืจื” ืคืกื™ื›ื•ืœื•ื’ื™ืช.
02:01
In 1912, German psychologist Max Wertheimer
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ื‘ 1912, ื”ืคืกื™ื›ื•ืœื•ื’ ื”ื’ืจืžื ื™ ืžืงืก ื•ื•ืจืชืจืžื™ื™ืจ
02:04
outlined the basic primary stages of apparent motion
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ื”ื ื™ื— ืืช ื”ืฉืœื‘ื™ื ื”ืขื™ืงืจื™ื™ื ืฉืœ ืชืคื™ืกืช ืชื ื•ืขื”
ืขืœ ื™ื“ ืฉื™ืžื•ืฉ ื‘ืืฉืœื™ื•ืช ืื•ืคื˜ื™ื•ืช.
02:07
using simple optical illusions.
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02:09
These experiments led him to conclude
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ื”ื ื™ืกื•ื™ื™ื ื”ืืœื” ื”ื•ื‘ื™ืœื• ืื•ืชื• ืœืžืกืงื ื”
ืฉื”ืชื•ืคืขื” ื”ื™ืชื” ื‘ืฉืœ ืชื”ืœื™ืš
02:11
the phenomenon was due to processes which lie behind the retina.
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ืฉื ืžืฆื ืžืื—ื•ืจื™ ื”ืจืฉืชื™ืช.
02:15
In 1915, Hugo Mรผnsterberg,
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ื‘ 1915, ื”ื•ื’ื• ืžื•ื ืกื˜ืจื‘ืจื’,
02:17
a German-American pioneer in applied psychology,
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ื—ืœื•ืฅ ื’ืจืžื ื™ ืืžืจื™ืงืื™ ื‘ืคืกื™ื›ื•ืœื•ื’ื™ื” ืฉื™ืžื•ืฉื™ืช,
ื”ืฆื™ืข ื’ื ืฉืจืขื™ื•ืŸ ื”ื ืจืื”
02:20
also suggested that the apparent motion of successive images
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ืฉืœ ืชืžื•ื ื•ืช ืื—ืช ืื—ืจื™ ื”ืฉื ื™ื”
02:22
is not due to their being retained in the eye,
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ื”ื•ื ืœื ื‘ื’ืœืœ ืฉื”ืŸ ื ืฉืžืจื•ืช ื‘ืขื™ืŸ,
02:25
but is superadded by the action of the mind.
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ืืœื ื ืขืจืžื•ืช ื‘ืฉืœ ื”ืคืขื•ืœื” ืฉืœ ื”ืžื•ื—.
02:29
In the century to follow, experiments by physiologists
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ื‘ืžืื” ืฉืขืงื‘ื”,
ื ื™ืกื•ื™ื™ื ืขืœ ื™ื“ื™ ืคื™ืกื™ื•ืœื•ื’ื™ื
ื“ื™ ืื™ืฉืจื• ืืช ื”ืžืกืงื ื” ืฉืœื”ื.
02:32
have pretty much confirmed their conclusions.
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02:34
As it relates to the illusion of motion pictures,
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ื›ืฉื–ื” ืžืชื™ื™ื—ืก ืœืืฉืœื™ื™ื” ืฉืœ ืชืžื•ื ื•ืช ื ืขื•ืช,
02:36
persistence of vision has less to do with vision itself
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ื”ื”ืžืฉื›ื™ื•ืช ืฉืœ ื”ืจืื™ื” ืงืฉื•ืจื” ืคื—ื•ืช ืœืจืื™ื” ืขืฆืžื”
02:39
than how it's interpreted in the brain.
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ืžืื™ืš ืฉื”ื™ื ืžืคื•ืจืฉืช ื‘ืžื•ื—.
02:41
Research has shown that different aspects of what the eye sees,
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ื—ื•ืงืจื™ื ื”ืจืื• ืฉืคื ื™ื ืฉื•ื ื™ื
ืฉืœ ืžื” ืฉื”ืขื™ืŸ ืจื•ืื”,
02:45
like form, color, depth, and motion,
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ื›ืžื• ืฆื•ืจื”,
ืฆื‘ืข,
ืขื•ืžืง,
ื•ืชื ื•ืขื”,
02:48
are transmitted to different areas of the visual cortex
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ืžื•ืขื‘ืจื™ื ืœืื–ื•ืจื™ื ืื—ืจื™ื ื‘ืงืœื™ืคื” ื”ืจืื™ื™ืชื™ืช
02:51
via different pathways from the retina.
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ื“ืจืš ืžืขื‘ืจื™ื ืื—ืจื™ื ืžื”ืจืฉืชื™ืช.
02:53
It's the continuous interaction
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ื–ื” ื”ืชืงืฉื•ืจืช ื”ืžืชืžืฉื›ืช
02:54
of various computations in the visual cortex
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ืฉืœ ื—ื™ืฉื•ื‘ื™ื ืฉื•ื ื™ื ื‘ืงืœื™ืคื” ื”ืจืื™ื™ืชื™ืช
02:56
that stitch those different aspects together
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ืฉืชื•ืคืจื™ื ืืช ื”ืคื ื™ื ื”ืฉื•ื ื•ืช ื”ืืœื” ื™ื—ื“
ื•ืžื’ื™ืขื™ื ืœืฉื™ื ื‘ืชืคื™ืกื”.
02:59
and culminate in the perception.
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03:01
Our brains are constantly working,
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ื”ืžื•ื—ื•ืช ืฉืœื ื• ืขื•ื‘ื“ื™ื ืœืœื ื”ืคืกืงื”,
03:02
synchronizing what we see, hear, smell, and touch
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ืžืกื ื›ืจื ื™ื ืืช ืžื” ืฉืื ื—ื ื• ืจื•ืื™ื,
ืฉื•ืžืขื™ื,
ืžืจื™ื—ื™ื,
03:05
into meaningful experience
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ื•ื ื•ื’ืขื™ื
ืœื—ื•ื•ื™ื” ื‘ืจืช ืžืฉืžืขื•ืช
ื‘ื–ืจื™ืžื” ืžืจื’ืข ืœืจื’ืข ืฉืœ ื”ื”ื•ื•ื”.
03:07
in the moment-to-moment flow of the present.
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03:09
So, in order to create the illusion of motion in successive images,
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ืื–, ื›ื“ื™ ืœื™ืฆื•ืจ ืืช ื”ืืฉืœื™ื”
ืฉืœ ืชื ื•ืขื” ื‘ืชืžื•ื ื•ืช ืขื•ืงื‘ื•ืช,
03:12
we need to get the timing of our intervals
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ืื ื—ื ื• ืฆืจื™ื›ื™ื ืœืชื–ืžืŸ ืืช ื”ืžืจื•ื•ื—ื™ื ืฉืœื ื•
03:14
close to the speed at which our brains process the present.
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ืงืจื•ื‘ ืœืžื”ื™ืจื•ืช ื‘ื” ื”ืžื•ื—ื•ืช ืžืขื‘ื“ื™ื ืืช ื”ื”ื•ื•ื”.
03:18
So, how fast is the present happening according to our brains?
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ืื–, ื›ืžื” ืžื”ืจ ื”ื”ื•ื•ื” ืงื•ืจื” ืœืคื™ ื”ืžื•ื— ืฉืœื ื•?
03:21
Well, we can get an idea
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ื•ื‘ื›ืŸ, ืื ื—ื ื• ื™ื›ื•ืœื™ื ืœืงื‘ืœ ื›ื™ื•ื•ืŸ
ืขืœ ื™ื“ื™ ืžื“ื™ื“ืช ื”ืžื”ื™ืจื•ืช ื‘ื” ืชืžื•ื ื•ืช ืฆืจื™ื›ื•ืช ืœื”ืชื—ืœืฃ
03:23
by measuring how fast the images need to be changing
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ื›ื“ื™ ืฉื”ืืฉืœื™ื” ืชืขื‘ื•ื“.
03:25
for the illusion to work.
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03:26
Let's see if we can figure it out by repeating our experiment.
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ื‘ื•ืื• ื ืจืื” ืื ืื ื—ื ื• ื™ื›ื•ืœื™ื ืœื’ืœื•ืช
ืขืœ ื™ื“ื™ ื—ื–ืจื” ืขืœ ื”ื ื™ืกื•ื™ ืฉืœื ื•.
03:29
Here's the sequence presented at a rate of one frame per two seconds
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ื”ื ื” ื”ืจืฆืฃ ืฉืžื•ืฆื’
ื‘ืงืฆื‘ ืฉืœ ืชืžื•ื ื” ืื—ืช ื‘ืฉืชื™ ืฉื ื™ื•ืช
ืขื ืฉื ื™ื” ืื—ืช ืฉืœ ืฉื—ื•ืจ ื‘ื™ื ื”ืŸ.
03:34
with one second of black in between.
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03:36
At this rate of change,
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ื‘ืงืฆื‘ ื”ื–ื” ืฉืœ ื”ืฉื™ื ื•ื™
03:37
with the blank space separating the images,
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ืขื ื”ืžืจื•ื•ื—ื™ื ื”ืจื™ืงื™ื ืžืคืจื™ื“ื™ื ื‘ื™ืŸ ื”ืชืžื•ื ื•ืช,
03:39
there's no real motion perceptible.
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ืื™ืŸ ืžืžืฉ ืชื ื•ืขื” ื ืชืคืฉืช.
03:41
As we lessen the duration of blank space,
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ื›ืฉืื ื—ื ื• ืžืงื˜ื™ื ื™ื ืืช ืžืฉืš ื”ืžืจื•ื•ื— ื”ืจื™ืง,
03:44
a slight change in position becomes more apparent,
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ืฉื™ื ื•ื™ ืงืœ ืฉืœ ืžื™ืงื•ื ื ืขืฉื” ื™ื•ืชืจ ื‘ืจื•ืจ,
ืื ืชื ืžืชื—ื™ืœื™ื ืœืงื‘ืœ ืชื—ื•ืฉื” ืืช ืชื ื•ืขื”
03:47
and you start to get an inkling of a sense of motion
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ื‘ื™ืŸ ื”ืชืžื•ื ื•ืช ื”ื ืคืจื“ื•ืช.
03:49
between the disparate frames.
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ืชืžื•ื ื” ืื—ืช ืœืฉื ื™ื”,
03:51
One frame per second.
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03:55
Two frames per second.
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ืฉืชื™ ืชืžื•ื ื•ืช ื‘ืฉื ื™ื”,
03:59
Four frames per second.
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ืืจื‘ืข ืชืžื•ื ื•ืช ื‘ืฉื ื™ื”.
04:02
Now we're starting to get a feeling of motion,
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ืขื›ืฉื™ื• ืื ื—ื ื• ืžืชื—ื™ืœื™ื ืœืงื‘ืœ ืชื—ื•ืฉื” ืฉืœ ืชื ื•ืขื”,
04:04
but it's really not very smooth.
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ืื‘ืœ ื–ื” ื‘ืืžืช ืœื ื—ืœืง.
04:06
We're still aware of the fact that we're looking at separate images.
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ืื ื—ื ื• ืขื“ื™ื™ืŸ ืžื•ื“ืขื™ื ืœืขื•ื‘ื“ื”
ืฉืื ื—ื ื• ืžื‘ื™ื˜ื™ื ื‘ืชืžื•ื ื•ืช ื ืคืจื“ื•ืช.
04:09
Let's speed up. Eight frames per second.
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ื‘ื•ืื• ื ืื™ืฅ,
ืฉืžื•ื ื” ืชืžื•ื ื•ืช ื‘ืฉื ื™ื”,
ืฉืชื™ื-ืขืฉืจ ืชืžื•ื ื•ืช ื‘ืฉื ื™ื”.
04:14
12 frames per second.
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04:16
It looks like we're about there.
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ื–ื” ื ืจืื” ื›ืื™ืœื• ืื ื—ื ื• ืžืชืงืจื‘ื™ื.
04:21
At 24 frames per second, the motion looks even smoother.
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ื‘ืขืฉืจื™ื ื•ืืจื‘ืข ืชืžื•ื ื•ืช ืœืฉื ื™ื”,
ื”ืชื ื•ืขื” ื ืจืื™ืช ืืคื™ืœื• ื—ืœืง ื™ื•ืชืจ.
04:24
This is standard full speed.
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ื–ื• ืžื”ื™ืจื•ืช ืกื˜ื ื“ืจื˜ื™ืช.
04:28
So, the point at which we lose awareness of the intervals
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ืื–, ื”ื ืงื•ื“ื” ื‘ื” ืื ื—ื ื• ืžืื‘ื“ื™ื ืืช ื”ื™ื“ื™ืขื” ืฉืœ ืžืจื•ื•ื—ื™ื
04:30
and begin to see apparent motion
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ื•ืžืชื—ื™ืœื™ื ืœืจืื•ืช ืชื ื•ืขื”
ื ืจืื” ืฉืžืชื—ื™ืœื” ื‘ื™ืŸ ืฉืžื•ื ื” ืœืฉืชื™ื-ืขืฉืจ ืชืžื•ื ื•ืช ืœืฉื ื™ื”.
04:32
seems to kick in at around eight to 12 frames per second.
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ื–ื” ื”ืื–ื•ืจ
04:36
This is in the neighborhood of what science has determined
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ืฉืœ ืžื” ืฉื”ืžื“ืขื ื™ื ืงื‘ืขื•
ืฉื”ื•ื ื”ืกืฃ ื”ื›ืœืœื™ ืฉืœ ื”ืžื•ื“ืขื•ืช ืฉืœื ื•
04:38
to be the general threshold of our awareness
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ืฉืœ ืจืื™ื” ืฉืœ ืชืžื•ื ื•ืช ื‘ื•ื“ื“ื•ืช.
04:40
of seeing separate images.
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ื‘ืื•ืคืŸ ื›ืœืœื™, ืื ื—ื ื• ืžืชื—ื™ืœื™ื ืœืื‘ื“ ืืช ื”ืชื—ื•ืฉื” ื”ื–ื•
04:42
Generally speaking, we being to lose that awareness
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ื‘ืžืจื•ื•ื—ื™ื ืฉืœ ื‘ืขืจืš 100 ืžื™ืœื™ืฉื ื™ื•ืช ืœืชืžื•ื ื”,
04:44
at intervals of around 100 milliseconds per image,
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ืฉื–ื” ืฉื•ื•ื” ืœืงืฆื‘ ืชืžื•ื ื•ืช ืฉืœ
04:47
which is equal to a frame rate of around ten frames per second.
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ื‘ืขืจืš ืขืฉืจ ืชืžื•ื ื•ืช ื‘ืฉื ื™ื”.
04:50
As the frame rate increases,
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ื›ืฉืžืกืคืจ ื”ืชืžื•ื ืช ื‘ืฉื ื™ื” ื’ื“ืœ,
04:51
we lose awareness of the intervals completely
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ืื ื—ื ื• ืžืื‘ื“ื™ื ืžื•ื“ืขื•ืช ืœืžืจื•ื•ื—ื™ื ืœื’ืžืจื™
04:53
and are all the more convinced of the reality of the illusion.
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ื•ืžืฉื•ื›ื ืขื™ื ื™ื•ืชืจ
ื‘ืžืฆื™ืื•ืช ืฉืœ ื”ืืฉืœื™ื™ื”.
ืขืœ ืืชืจ ื–ื”

ืืชืจ ื–ื” ื™ืฆื™ื’ ื‘ืคื ื™ื›ื ืกืจื˜ื•ื ื™ YouTube ื”ืžื•ืขื™ืœื™ื ืœืœื™ืžื•ื“ ืื ื’ืœื™ืช. ืชื•ื›ืœื• ืœืจืื•ืช ืฉื™ืขื•ืจื™ ืื ื’ืœื™ืช ื”ืžื•ืขื‘ืจื™ื ืขืœ ื™ื“ื™ ืžื•ืจื™ื ืžื”ืฉื•ืจื” ื”ืจืืฉื•ื ื” ืžืจื—ื‘ื™ ื”ืขื•ืœื. ืœื—ืฅ ืคืขืžื™ื™ื ืขืœ ื”ื›ืชื•ื‘ื™ื•ืช ื‘ืื ื’ืœื™ืช ื”ืžื•ืฆื’ื•ืช ื‘ื›ืœ ื“ืฃ ื•ื™ื“ืื• ื›ื“ื™ ืœื”ืคืขื™ืœ ืืช ื”ืกืจื˜ื•ืŸ ืžืฉื. ื”ื›ืชื•ื‘ื™ื•ืช ื’ื•ืœืœื•ืช ื‘ืกื ื›ืจื•ืŸ ืขื ื”ืคืขืœืช ื”ื•ื•ื™ื“ืื•. ืื ื™ืฉ ืœืš ื”ืขืจื•ืช ืื• ื‘ืงืฉื•ืช, ืื ื ืฆื•ืจ ืื™ืชื ื• ืงืฉืจ ื‘ืืžืฆืขื•ืช ื˜ื•ืคืก ื™ืฆื™ืจืช ืงืฉืจ ื–ื”.

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