4th Dimension Explained By A High-School Student
Summary
TLDRこのスクリプトは、私たちが知る三次元世界から四次元世界への視点を探求しています。三次元世界は深さ、長さ、幅を持つ無限の二次元世界の集合体であり、四次元世界は無限の三次元物体の集合体と考えられます。しかし、私たちは三次元世界を二つ次元的に見ているため、四次元の生物は物体を通じて見ることができ、全てを見ることができるとされています。また、スクリプトでは、時間と空間の違いや、物理学者や数学者が考えるディメンションの曲げについても触れています。最後に、無限のディメンションの考え方とそれに付随する問題についても述べられています。
Takeaways
- 📏 一维世界是线性的,生物只能沿直线前后移动。
- 📐 二维世界增加了宽度,生物可以上下左右移动,由无数一维世界组成。
- 📏 三维世界由长度、宽度和深度组成,由无数二维世界构成。
- 🔮 四维世界难以直观理解,但可以想象为由无数三维对象组成。
- 👁️🗨️ 我们作为三维生物,实际上以二维的方式感知三维世界。
- 📊 四维生物能够看到三维物体的内部,就像我们看二维环境一样。
- 🔗 数学上,维度的增加遵循逻辑递进,如一维的线、二维的正方形、三维的立方体。
- 🛍️ 四维的基本形状被称为超立方体或tesseract。
- ⏳ 时间常被误认为是第四维度,但时间和空间是不同的。
- 🌐 一些理论认为维度可能轻微弯曲,导致无限循环的宇宙结构。
- ∞ 理论上存在无限多的空间维度,但这引发了关于无限性的哲学问题。
- 📚 尽管我们无法完全理解或想象高维空间,数学和物理提供了探索这些概念的工具。
Q & A
一つの次元が何を意味するのか説明してください。
-一つの次元とは、線状の空間を意味し、生物は一方向にのみ前後に移動できます。
2次元の世界で生きる生物はどのように動くことができますか?
-2次元の世界で生きる生物は、上下左右に自由に動くことができます。
3次元の世界はどのように構成されていますか?
-3次元の世界は、奥行き、長さ、幅から成り立っており、無限に続く2次元の世界の積み重ねです。
4次元とは何ですか?
-4次元は、3次元の世界に加えてもう一つの次元を持ち、その具体的な姿は人間の知覚では捉えられませんが、数学的には8つの立方体が相互に垂直かつ平行な状態で構成されるテセラクトと推定されます。
私たちはなぜ現実世界を真に受け止められないのですか?
-私たちは3次元の世界で生きており、しかし2次元的な視点で物事を認識しているため、現実の世界の真実を完全に把握することはできません。
2次元の生物がどのように物事を認識するか説明してください。
-2次元の生物は1次元的に物事を認識しており、例えば輪を見ると1次元的な線分に見えます。光の変化によって輪の端々が明るくなり、中が暗くなるように見えます。
4次元の生物が持つ能力とは何ですか?
-4次元の生物は物体を透かして見たり、全ての物を一度に見渡すことができるとされています。
時間は4次元として扱われることの誤りは何ですか?
-時間は空間とは別であり、また全ての次元に時間的概念が存在するため、4次元が特別であるという考え方は筋が通じません。
物理学者によって提案されている空間の曲がりについて説明してください。
-物理学者によっては、無限に続く空間を持つことは不可能であると主張し、1次元が極めて微細に曲がることで最終的に円、2次元が球、3次元がさらに曲がって4次元の宇宙を形成すると考える人があります。
無限の次元を持つ宇宙の考え方にはどのような問題がありますか?
-無限の次元を持つ宇宙の考え方には、無限という概念自体が理解しきれないという問題があります。また、その中でどのくらいの次元が存在するのか、またその限界はどこにあるのかが明確ではありません。
テセラクトとは何ですか?
-テセラクトは4次元の基本的な形状であり、8つの立方体が相互に垂直かつ平行に接続された状態で構成されますが、人間の知覚で捉えられることはできません。
次元がどのように数学的に進化するのか説明してください。
-数学的には、1次元が直線、2次元が正方形、3次元が立方体と進化し、同様に4次元はテセラクトと推定されます。これは、各次元が前の次元の形状を基にし、さらに一つの次元を加えた形で進化していると考えられます。
Outlines
🌐 次元の世界を想像しよう
第1段落では、三次元世界から一つの次元を減らして、二次元の世界を想像する。二次元の世界では、生物は線状のパスで前後にしか動けない。次に、二次元の世界をさらに広がって三次元の世界を考える。三次元の世界は、奥行き、長さ、幅を持つ。さらに、四次元の世界を想像し、私たちが三次元の世界で物体を二つの次元で見ることと同様に、四次元の世界の生物は物体を三つの次元で見ることができると述べている。また、四次元の基本形はテセラクトであり、これは8つの立方体が互いに接続された状態であると説明している。
🕰️ 四次元と時間の誤解
第2段落では、四次元と時間との関係について述べている。一般的には四次元を時間と混同するが、実際には空間と時間は異なる概念であり、全ての次元に時間があるとするなら、四次元は特別であると主張されている。また、物理学者や数学者が次元が微妙に曲がっていると主張していることも触れており、これは無限の次元を持つ可能性を示唆している。しかし、無限の次元を持つという考えには賛同できないという疑問も述べている。
Mindmap
Keywords
💡一次元
💡二次元
💡三次元
💡四次元
💡テセラクト
💡
💡時間
💡曲げ
💡無限
💡知覚
💡数学的進化
Highlights
Imagine a one-dimensional world where organisms can only move in a straight line.
A two-dimensional world allows for movement in all directions on a flat plane.
A two-dimensional world is an infinite series of one-dimensional lines.
Our three-dimensional world is made up of an infinite series of two-dimensional planes.
A four-dimensional world would allow for movement in ways we cannot perceive.
We perceive three-dimensional objects as two-dimensional due to our limited perspective.
A four-dimensional creature would perceive all aspects of a three-dimensional object at once.
The progression from one dimension to another is based on mathematical logic and geometry.
A tesseract is a four-dimensional shape consisting of eight cubes.
Our inability to visualize a fourth dimension is due to our three-dimensional perspective.
The concept of dimensions being curved is a theory proposed by some physicists and mathematicians.
If dimensions are curved, our three-dimensional world exists within a four-dimensional space.
The idea of an infinite number of dimensions challenges our understanding of infinity.
The common misconception that the fourth dimension is time is flawed due to the nature of time versus space.
Time is not spatial, and all dimensions contain time, making the fourth dimension not special in that regard.
The concept of a fourth dimension is challenging to grasp and visualize for three-dimensional beings.
The video aims to provide a better understanding of the theoretical fourth dimension.
Transcripts
imagine that this folder is a
dimensional plane now assuming that it
is no height and no depth what would
this mean it would mean that it's a
one-dimensional world so if
hypothetically an organism was living
inside of it it would only be able to
move in a linear path forward and
backwards in a straight line now if we
go to the second dimension we have two
dimensions we have width and we have
length so hypothetically if an organism
lived inside of here then it would be
able to move up down left right than
anywhere else in between and a two
dimensional world is comprised of an
infinite series of one-dimensional
worlds stacked upon each other just as
our three-dimensional world which has
depth and length and height is comprised
of an infinite series of two dimensional
worlds so this now that I have stamped
many folders upon each other we have
three dimensions we have depth
we have length and we have width now
what happens if you keep going on from
here on out we would have a four
dimensional world what exactly is a
fourth dimension in order to understand
this we need to understand how two
mentions are perceived we live in the
three-dimensional world but despite that
we actually view things to be two
dimensionally take a perfect sphere for
example if you're looking at sphere it
looks just like a regular
two-dimensional circle the only way you
could tell it's just actual sphere
instead of a circle is because of the
hues of light down so just like in a
two-dimensional world if a organism in
the two-dimensional world was looking
upon a circle but the light would make
it appear to be lighter at one end and
darker and in the middle also if you if
an object is moving farther closer and
farther away from you you don't actually
perceive that it's getting closer and
farther away you see that it's beginning
smaller or larger and then you assume
that's giving either farther away or
closer but let's say that object was to
grow in perfectly equilibrium so that it
was growing at the same speed that it
was shrinking as you move it farther
away
then you would not be able to tell
without any lights or if there were
details on the object that it's moving
or growing at all you may have assumed
that since we perceive things to be in
two dimensions that a two-dimensional
organism would see in one dimension so
as we're watching this rubber band
expand as it moves farther away from
this little organism in the
two-dimensional world it's does not
actually perceive anything is happening
to it because it's growing at the same
speed that is moving farther away but
since we can actually see it from the
three-dimensional world and perceive
things to be in two dimensions we can
see things for how they actually are the
reason that the two-dimensional organism
doesn't see things the way they really
are is because the two-dimensional
organism sees things in one dimension
just how we three-dimensional creatures
see things in two dimensions so in a way
we don't really see our world the way it
truly is a four dimensional creature
I've ever seen our three-dimensional
world in three dimensions would be able
to see through things to be able to see
absolutely everything just as we could
see if there was several organisms
spread along a 2d environment on your
floor you'd be able to see inside houses
you would be able to see inside of
people so if a two-dimensional world the
flat surface has just made of an
infinite amount of lines then the 3d
world is just made out of an infinite
amount of planes
so the 4d world logically is made out of
an infinite amount of 3d objects though
they're not just put together like you
would like building blocks it's that's
not how the 4d world is that just be 3d
again so in order to understand this we
need to understand the logical
progression of mathematics in our world
imagine that this connects piece
represents the first dimension it's
simply a straight line which is
basically what the first dimension looks
like and if you add three more of these
straight lines and connect them to do so
that adjacent sides are perpendicular
and opposite sides are parallel then you
have the basic shape of the second
dimension you have a square now if you
keep going from here and you add full
hand it so that there's a total of four
squares and all adjacent sides are
perpendicular and all opposite sides are
parallel then you end up with obviously
a cube so if you try to keep going from
here and you would have a four
dimensional basic shape you would have
eight what's called a tesseract now I
cannot show you a tesseract but you need
to understand that it's basically four
cubes that are within each other that
have all adjacent sides perpendicular
and all parallel and all opposite sides
parallel yet there are three lines
connect that four lines connect into
each vertex so every tesseract would
look somewhat like this picture now that
that's not exactly what it looks like
because this is a two-dimensional
depiction and obviously not all the
lines are straights so I cannot show you
what assessor act actually looks like
because we cannot perceive things in the
third dimension you cannot even imagine
what the tesseract looks like you cannot
physically it you cannot in your mind
picture the fourth of nitrogen or a
fourth dimensional shape and you can
keep going on from the fourth dimension
even you can go to the fifth dimension
the sixth dimension the 71st dimension
it doesn't matter theoretically there
are an infinite amount of spatial
dimensions a common misconception of the
fourth dimension is that the fourth
dimension is time now while some argue
that goodbye going forward and backwards
in time if you move forward the same
distance and backwards the same then you
would end up in the same place you
started just like in the fourth
dimension and while that may seem
logical if you think about it really
doesn't make sense if you imply that the
fourth dimension is actually time well
first of all time is not spatial there's
a difference between space and time
quite obviously and assuming that all
dimensions are according to a pattern
then
that doesn't really make sense either
because saying the fourth dimension is
time every dimension has time in it so
that would mean that the fourth
dimension is special in some way which
doesn't really make any sense another
reason this doesn't make sense is that
we so very very very slightly travel
through time whenever we move due to the
distance that light takes to get to our
body if a group of astronauts were to
get in a spaceship and they are to go
very very very close to the speed of
light then they would and they they went
around in this
impossible nearly the speed of light
spaceship for a few months and then
afterwards they returned earth they
would find that Earth had actually
progressed a few years so they had moved
forward in time I move in that quickly
another interesting concept involving
the fourth dimension is that many
physicists and even mathematicians may
say that the dimensions are very very
slightly curved because if you really
think about it nothing can be truly
absolutely infinite so imagine that a
the first dimension the line is just
very very slightly curved so that after
a very long time it will end up creating
a circle
so as suggest my many physicists if you
keep going in the same direction then
you will end up where you are where you
started after a very very long amount of
time obviously and the same thing would
happen to the second dimension if it's
just a square and then you extend it
very very slightly and a curve and it
will eventually make a sphere and the
same thing happens in our dimension
except it will form a very very slightly
curved third dimension which will form a
four dimensional universe basically so
what this kind of means is that our
three-dimensional world is within a four
dimensional world and the four
dimensional worlds within the fifth
dimensional world and so on now I did
say that nothing can be truly infinite
but if this is true and I dimension is
really within another dimension within
another dimension within
dimension then I'm implying that there's
an infinite amount of dimensions which
is the only problem I really have with
the Serie I'm not sure if it ever stops
or if infinite infinity is really even
possible we don't know that thanks for
watching my video and I hope this gives
you a better idea of what the fourth
dimension is
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