La Cuarta Dimension explicada por Carl Sagan
Summary
TLDREl video explora conceptos complejos sobre la estructura del universo y las dimensiones. Utilizando la analogía de Flatland, un mundo bidimensional, se ilustra cómo seres en dimensiones inferiores percibirían seres y objetos de dimensiones superiores. Se discute cómo podríamos estar limitados a tres dimensiones, mientras que el universo podría estar curvado en una cuarta dimensión, algo que no podemos experimentar directamente, pero que podemos deducir. La idea de un universo finito pero sin límites se presenta a través de ejemplos sencillos y visuales, estimulando la imaginación sobre las dimensiones más allá de nuestra percepción cotidiana.
Takeaways
- 🌌 El universo podría ser finito pero sin límites, lo que significa que aunque no tenga un borde, está curvado.
- 📏 Flatland es un concepto donde los habitantes solo entienden dos dimensiones: largo y ancho, pero no altura.
- 🍏 Una criatura tridimensional, como una manzana, sería difícil de entender para los habitantes de Flatland, ya que no pueden percibir la tercera dimensión.
- 🔄 Cuando la criatura tridimensional interactúa con Flatland, los habitantes solo ven una sección transversal, causando confusión.
- 🚶♂️ Un habitante de Flatland que camina en línea recta podría eventualmente regresar al punto de partida, descubriendo que su universo está curvado.
- 🔍 Explorar una dimensión adicional permite ver aspectos ocultos del mundo, como tener una visión de rayos X en Flatland.
- 🌀 Un cubo en tres dimensiones proyectado en dos dimensiones no representa perfectamente todas sus propiedades, como la igualdad de longitudes y ángulos rectos.
- 📐 Un tesseracto es la versión en cuatro dimensiones de un cubo, pero solo podemos ver su sombra en tres dimensiones.
- 🌐 Aunque no podemos experimentar una cuarta dimensión, podemos pensar en su existencia y las implicaciones que tendría para nuestro universo.
- 🌀 Al igual que en Flatland, nuestro universo tridimensional podría estar curvado en una cuarta dimensión, lo que no podemos percibir directamente.
Q & A
¿Qué significa cuando los astrónomos dicen que el universo es 'finito pero sin límites'?
-Se refiere a la idea de que el universo tiene un tamaño limitado pero no tiene bordes o límites en el sentido convencional. Un ejemplo es la superficie de una esfera, que es finita en área pero no tiene un borde donde termine.
¿Cómo se describe la vida en 'Flatland'?
-En 'Flatland', los habitantes son completamente planos y viven en un mundo bidimensional, donde solo conocen las direcciones izquierda-derecha y adelante-atrás, pero no tienen concepto de 'arriba-abajo'.
¿Qué sucede cuando una criatura tridimensional como una manzana interactúa con un habitante de Flatland?
-El habitante de Flatland solo puede ver una sección plana de la criatura tridimensional a medida que esta se desplaza a través de su mundo, lo que causa confusión y hace que el habitante piense que ha perdido la razón.
¿Cómo reacciona el habitante de Flatland al ser elevado fuera de su mundo bidimensional?
-Al principio está completamente desconcertado y confuso, pero eventualmente se da cuenta de que puede ver dentro de los objetos y casas en Flatland, obteniendo una nueva perspectiva que nadie más en su mundo tiene.
¿Qué representa la proyección de un cubo tridimensional en dos dimensiones?
-La proyección de un cubo tridimensional en dos dimensiones se muestra como dos cuadrados con sus vértices conectados, lo que no refleja perfectamente el cubo tridimensional, ya que no todas las líneas parecen iguales ni todos los ángulos son rectos.
¿Qué es un tesseracto y cómo se representa?
-Un tesseracto es un hipercubo de cuatro dimensiones. Aunque no podemos visualizar un tesseracto real en nuestro mundo tridimensional, podemos representar su sombra como dos cubos tridimensionales anidados, con todos los vértices conectados por líneas.
¿Cómo podrían los habitantes de un universo bidimensional descubrir una tercera dimensión?
-Podrían deducir la existencia de una tercera dimensión si notan que al caminar en línea recta, eventualmente regresan a su punto de partida, lo que sugiere que su universo bidimensional está curvado en una tercera dimensión.
¿Cómo se relaciona la idea de Flatland con nuestra comprensión del universo tridimensional?
-Flatland sirve como una analogía para ayudarnos a comprender la posibilidad de que nuestro universo tridimensional esté curvado en una cuarta dimensión, una idea que podemos conceptualizar matemáticamente aunque no podamos experimentar directamente.
¿Por qué es difícil para los habitantes de Flatland comprender la tercera dimensión?
-Es difícil porque solo están familiarizados con dos dimensiones y no tienen ninguna experiencia o marco de referencia para entender la existencia de 'arriba-abajo' o cualquier dirección fuera de su plano.
¿Qué enseña la analogía de Flatland sobre las limitaciones de nuestra percepción?
-La analogía muestra que nuestra percepción está limitada por las dimensiones en las que vivimos, pero con la razón y el pensamiento matemático podemos deducir la existencia de dimensiones adicionales que no podemos experimentar directamente.
Outlines
🌌 Estructura del cosmos y la teoría de la cuarta dimensión
El primer párrafo introduce la idea de la estructura a gran escala del cosmos, donde los astrónomos sugieren que el espacio está 'curvado' y el universo es 'finito pero no acotado'. Se utiliza la metáfora de 'Flatland', una novela escrita por Edwin Abbott, para explicar conceptos de dimensionalidad. Los habitantes de Flatland, que son bidimensionales, no pueden percibir la altura y su experiencia cambia drásticamente cuando interactúan con una entidad tridimensional representada por una manzana. Esta interacción lleva a la comprensión de que pueden existir dimensiones adicionales más allá de las que pueden experimentar los 'flatlanders'. El párrafo concluye con la posibilidad de una dimensión adicional, la cuarta dimensión, que aún no se ha explorado en detalle.
📐 Proyecciones y la teoría de la cuarta dimensión
El segundo párrafo profundiza en la idea de la cuarta dimensión a través de la analogía de un cubo, que es un objeto tridimensional creado al mover una línea en dirección perpendicular a sí misma. Se describe cómo el cubo proyectado en dos dimensiones (su sombra) no muestra todas las líneas con la misma longitud ni todos los ángulos como rectos, lo cual es una representación incompleta de la realidad tridimensional. Luego, se proyecta el concepto de un cubo a través de una cuarta dimensión, resultando en un 'tesseract' o hipércubo, el cual se muestra en tres dimensiones como dos cubos anidados. El párrafo también discute cómo una proyección en una dimensión adicional puede resultar en una representación aún más incompleta. Finalmente, se utiliza la idea de un universo bidimensional curvado en una tercera dimensión para ilustrar cómo nuestra percepción del espacio puede ser diferente de la realidad subyacente, sugiriendo que nuestro propio universo podría estar curvado en una dimensión que no podemos percibir directamente.
Mindmap
Keywords
💡estructura a gran escala
💡espacio curvado
💡universo finito pero no acotado
💡Flatland
💡dimensión
💡proyección
💡hipercubo
💡perspectiva
💡teoría de la relatividad
💡cosmología
Highlights
Astronomers discuss the large-scale structure of the cosmos, mentioning that space may be curved and the universe could be finite but unbounded.
Introduction to 'Flatland' by Edwin Abbott, a Victorian England scholar, as a metaphor for understanding dimensions.
Flatland inhabitants are two-dimensional and lack the concept of height, only knowing left, right, forward, and back.
A three-dimensional creature, resembling an apple, attempts to interact with a square in Flatland, causing confusion due to the square's inability to perceive the third dimension.
The three-dimensional creature partially enters Flatland, with only a cross-section visible to the inhabitants, represented by an ink stamp.
As the apple descends through Flatland, the square witnesses objects appearing and changing shape, leading to a sense of going mad.
The apple makes contact from below, causing the square to experience a new perspective, seeing inside closed rooms and gaining a form of x-ray vision.
The square returns to Flatland with a new understanding, unable to point to the third dimension but having experienced it.
Exploration of a fourth dimension by considering a cube and imagining its projection into a higher dimension, resulting in a tesseract.
A tesseract casts a shadow in three dimensions, represented by two nested cubes, illustrating the challenge of representing higher dimensions in lower ones.
The inability to visualize a four-dimensional world does not prevent us from thinking about it, suggesting the possibility of a universe beyond our perception.
A hypothetical two-dimensional universe, curved into a third dimension, is explored, with inhabitants unaware of this curvature.
A Flatland explorer unknowingly circumnavigates a spherical universe, discovering the concept of a curved space without understanding the third dimension.
The idea that our three-dimensional universe might be curved into a fourth dimension is proposed, paralleling the Flatland scenario.
The challenge of perceiving a fourth physical dimension is highlighted, as it exists at right angles to the familiar three dimensions.
The concept of gravitational warping of space, closing it back on itself into a sphere, is introduced as a possible explanation for the universe's curvature.
Transcripts
in discussing the large-scale structure
of the cosmos
astronomers sometimes say that space is
curved
or that the universe is
finite but unbounded whatever are they
talking about
let's imagine that we are perfectly flat
i mean
absolutely flat and that we live
appropriately enough in a flat land a
land designed and named by edwin abbott
a shakespearean scholar who lived in
victorian england
everybody in flatland is of course
exceptionally
flat we have squares circles triangles
and we all
scurry about and we can go into our
houses and
do our flat business now
we have width
and length but no height at
all now these little cutouts have some
little height but
let's ignore that let's imagine that
these are absolutely flat
that being the case we know us
flatlanders
about left right and we know about
forward back but we have
never heard of up down let us imagine
that into flatland hovering above it
comes a strange three-dimensional
creature which
oddly enough looks like an apple and the
three-dimensional creature
sees an attractive congenial looking
square
watches it enter its house and decides
in a
gesture of inter-dimensional amity
to say hello hello says the
three-dimensional creature
how are you i am a visitor from the
third dimension
well the poor square looks around
his closed house sees no one there
and what's more has witnessed a greeting
coming from his insides
a voice from within he
surely is getting a little worried about
his sanity
the three-dimensional creature is
unhappy about being considered a
psychological aberration and so he
descends
to actually enter flatland now a
three-dimensional creature
exists in flat land only partially
only a plane a cross-section through him
can be seen so when the
three-dimensional creature first reaches
flatland it's only the points of contact
which can be seen
we'll represent that by stamping the
apple
in this ink pad and
placing that image in flatland and
as the apple worded descend through
slither by
flatland we would progressively see
higher and higher slices
which we can represent by
clean the apple
so the square as time goes on
sees a set of objects mysteriously
appear
from nowhere and inside a closed room
and change their shape dramatically
his only conclusion could be that he's
gone bunkers
well the apple might be a little annoyed
at this conclusion and so
not such a friendly gesture from
dimension to dimension
makes a contact with the square from
below
and sends our flat creature fluttering
and
spinning above flatland at first the
square has no idea of what's happening
is
terribly confuses utterly outside his
experience
but after a while he comes to realize
that he is seeing inside closed rooms
in flatland he is looking inside his
fellow flat creatures he has seen
flatland from a perspective no one has
ever seen it before to his knowledge
getting into another dimension provides
as an incidental benefit a kind of
x-ray vision now our flat creature
slowly descends to the surface
and his friends rush up
to see him from their point of view he
has mysteriously appeared from nowhere
he hasn't
walked from somewhere else he's come
from some other place
they say for heaven's sake what's
happened to you and the poor square has
to say well
i was in some other mystic dimension
called up and they will pat him on his
side and
comfort him or else they'll ask well
show us where is that three-dimension
third dimension point to it and the poor
square will be unable to comply
but maybe more interesting is the other
direction
in dimensionality what about the fourth
dimension
now to approach that let's consider a
cube
we can imagine a cube in the following
way you take a line
segment and move it at right angles to
itself an equal length
that makes a square move that square in
equal length at right angles to itself
and you have a cube now
this cube we understand um
casts a shadow and
that shadow we recognize it's
you know ordinarily drawn in third grade
classrooms
as two squares with their vertices
connected
now if we look at the shadow of a
three-dimensional object in two
dimensions we see
that in this case not all the lines
appear equal
not all the angles are right angles the
three-dimensional object has not been
perfectly represented in its projection
in two dimensions
but that's part of the cost of losing a
dimension in the projection
now let's take this three-dimensional
cube
and project it carry it through a
fourth physical dimension not that way
not that way
not that way but at right angles to
those three directions i can't show you
what direction that is but imagine that
there is a fourth physical dimension
in that case we would generate a
four-dimensional hypercube
which is also called a tesseract i
cannot show you a tesseract because
i and you are trapped in three
dimensions
but what i can show you is the shadow
in three dimensions of a
four-dimensional hypercube
or tesseract this is it
and you can see it's two nested cubes
all the vertices connected by lines
and now the real tesseract
in four dimensions would have all the
lines of equal length
and all the angles right angles that's
not what we see here but that's the
penalty
of projection so
you see while we cannot imagine the
world of four dimensions
we can certainly think about it
perfectly well
now imagine a universe just like
flatland
truly two-dimensional and entirely flat
in every direction
but with one exception unbeknownst to
the inhabitants
their two-dimensional universe is curved
into a
third physical dimension maybe into a
sphere
but at any rate into something entirely
outside their experience
locally their universe still looks flat
enough
but if one of them much smaller and
flatter than me takes a very long walk
along what seems to be a straight line
he would uncover a great mystery suppose
he marked his starting point
here and set off to explore
his universe he never turns around
and he never reaches an edge he doesn't
know that his
apparently flat universe is actually
curved into an enormous sphere he
doesn't sense
that he's walking around the globe
why should his space be curved because
there's so much matter in this universe
that it
gravitationally warps space closing it
back on itself
into a sphere but our flatlander doesn't
know this
after a long while you'll find he
somehow returns to his starting point
there must be a third dimension
our flatlander couldn't imagine a third
dimension
but he could sure deduce it now increase
all the dimensions in this story by one
and you have something like the
situation which many cosmologists think
may
actually apply to us we are
three-dimensional creatures trapped in
three dimensions
we imagine our universe to be flat in
three dimensions
but maybe it's curved into a fourth
we can talk about a fourth physical
dimension but we can't experience it no
one can
point to the fourth dimension i mean
there's left right
and there's forward back there's up down
and
there's some other direction
simultaneously at
right angles to those familiar three
dimensions
浏览更多相关视频
Entiende La 4ta Dimensión con hormigas
La cuarta dimensión por Carl Sagan
El TEOREMA DE ROUCHÉ-FROBENIUS | Una cumbre de las matemáticas escolares
Los científicos han descubierto la entidad que crea el Universo
¿Que es el principio antrópico? (Origen del universo)
Aprende a programar desde cero con PseInt! | Dimensiones o Arreglos | Parte 23
5.0 / 5 (0 votes)