# Visualizing higher dimensions

The trick of visualizing higher dimension is: not to visualize it.

— Wikipedia

— Me@2011.08.19

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Besides trying to visualize, there are other methods to understand higher dimensions.

— Me@2018-10-28 04:28:01 PM

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What is the meaning of visualization?

— Me@2018-09-02 4:35 pm

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feel ~ receive all the data at once

(This definition is not totally correct, but is useful in the meantime.)

visual ~ feel at once through eyes

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you can visualize a 3D object ~ you can see all of a 3D object at once

you cannot visualize a 4D object ~ you cannot see all of a 4D object at once

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Actually, you can only visualize a 2D object, such as a square.

You cannot visualize a 3D object, such as a cube.

That’s why the screen of any computer monitor is 2 dimensional, not 3.

— Me@2018-10-28 04:32:41 PM

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# Juan Maldacena 2

What is the difference between 10 and 11?

The simplest string theory is ten dimensional. Strings can interact with each other. If the interaction among strings is large, the theory is hard to describe. It turns out that when strings interact very, very strongly, something surprising happens. A new dimension opens up and we have a theory in eleven dimensions, the ten we started with plus an extra circle. In eleven dimensions we do not have strings, we have membranes. Membranes wrapped along the 11th dimension give rise to strings.

— Who’s Counting? Is it 10 or 11? (dimensions, that is — M Theory is making me Manic!)

— Prof. Juan Maldacena

2013.09.01 Sunday ACHK

# Juan Maldacena

We do not know yet whether a description in terms of 10 or 11 dimensions is more appropriate for the universe where we live in. But these two possibilities are continuously connected. They are simply different possibilities for the internal geometry. Since the geometry of the internal space is quantum mechanical, asking what its dimension is might not be the right question.

In summary, in a quantum spacetime the dimension might not be a well defined notion. When the space in question is small, it can interpolate continuously between different dimensions.

— Who’s Counting? Is it 10 or 11? (dimensions, that is — M Theory is making me Manic!)

— Prof. Juan Maldacena

2013.08.29 Thursday ACHK

# Meta-time 6

In a computer simulation, the causal chain is fake or artificial. Therefore, “time”-travel is possible.

In reality, time-travel is logically impossible.

— Me@2012.07.05

— Me@2013-07-09 11:30:15 AM

— Me@2013-07-15 02:33:03 PM

# Meta-time 5

Two dimensional time 5 | 二次元時間 5

You are the main author of your future.

In a special sense, the real-present is the meta-time of the potential future timelines, selecting the future among multiple possible timelines.

— Me@2013-07-11 3:48 PM

# Looper, 5.4

Paradox 5.5 | Meta-time 4.5 | Cumulative concept of time, 13.5 | Two dimensional time 4.4 | 二次元時間 4.4

To be logically consistent WITHIN the movie’s story, Young Joe (in the year 2044) should not be able to influence Old Joe, who had time-travelled to the year 2044 from the year 2074，because that Old Joe is from another timeline. The proof is that Young Joe’s experience in the year 2044 is different from Old Joe’s experience in the year 2044 when he was young.

They are not the same person, nor the same person at different ages within the same timeline. At most, they are different versions of the “same” person from two different timelines (aka “parallel universes” or “histories”).

Young Joe’s changes should affect the same-timeline-Old-Joe, but not any Old Joe’s from any other timelines. So the Old Joe within the movie should not have been affected when Young Joe hurt himself.

Also, the changes of the same-timeline-Old-Joe due to the actions of Young Joe should be seen only by the author (meta-time), but not by Young Joe until he has become that Old Joe 30 years later.

The author unintentionally, or intentionally, has confused two story timelines. Moreover, the author unintentionally, or intentionally, has confused the story-time and its meta-time.

— Me@2013-07-05 10:32 PM

# Looper, 5.3

Paradox 5.4 | Meta-time 4.4 | Cumulative concept of time, 13.4 | Two dimensional time 4.3 | 二次元時間 4.3

In a single-mutable-timeline time travel story, the two dimensional time is not due to the internal causal structure of the story. Instead, it is due to the author’s timeline (aka meta-time). The author’s timeline is the second time dimension (aka independent direction).

The single-mutable-timeline model of time travel is not logically consistent within the story. If it is “mutable”, it is not “single”.

The single-mutable-timeline model of time travel is logically consistent only outside the story, from the perspective of the story’s author.

— Me@2013-07-02 3:47 PM

# Looper, 5.2

Paradox 5.3 | Meta-time 4.3 | Cumulative concept of time, 13.3 | Two dimensional time 4.2 | 二次元時間 4.2

In the movie Looper, Young Joe (in the year 2044) influences Old Joe (in the year 2074) in the sense that Young Joe’s every action affects the state of Old Joe, because Old Joe is Young Joe’s future self.

For example, after Young Joe had hurt his own arm, the corresponding wound also appeared on Old Joe’s arm, even though Old Joe had already time-travelled back to the year 2044.

All of Young Joe’s actions are the causes of Old Joe’s state. Young Joe is in the past of Old Joe.

Old Joe (2074-Joe) = [ …, Young Joe (2044-Joe), … ]

B = [ …, A, … ]

However, Old Joe (2074-Joe) had time-travelled back to the year 2044, meeting the Young Joe.

So, some of Old Joe’s actions would affect Young Joe’s decisions on his own actions. In this sense, Old Joe also influences Young Joe indirectly. Some of Old Joe’s actions are the causes of Young Joe’s state. Part of Old Joe is also in the past of Young Joe.

Young Joe (2044-Joe) = [ …, Old Joe (2074-Joe), … ]

A = [ …, B, … ]

However, it is logically impossible to have both

B is in the past of A

and

A is in the past of B

just as it is logically almost impossible to have both

D is a part of C

and

C is a part of D

If you insist that it is the case, the only possibility is that

C = D

In this analogy, neither C nor D is really a “part” of another. In the time travel case, neither A nor B is really in the past of another. In other words, A (Young Joe) and B (Old Joe) have no time relationship. Neither’s actions are the causes of the state of another.

The real causes of Young Joe or Old Joe’s states are actually not within the movie story’s timeline. The real causes are the decisions of the author of the story.

— Me@2013-07-03 6:19 PM

# Looper, 5

Paradox 5.2 | Meta-time 4.2 | Cumulative concept of time, 13.2 | Two dimensional time 4.1 | 二次元時間 4.1

In a “if and only if” case, there is no time.

If A is a necessary condition of B, we say “A is a cause of B“. In other words, A is in the past of B.

However, in some time travel story, it is “possible” to have both

A is a cause of B

(A is a necessary condition of B)

(B -> A)

and

B is a cause of A

(B is also a necessary condition of A)

(A -> B)

In this case, A and B are just equivalent.

(A B)

Neither is in the past of another. A and B have no causal relationship. In this sense, there is no time.

— Me@2013-07-03 6:19 PM

# Dimension transcender

A new dimension is a transcender for the old dimensions. For example, in order to see all of one dimension at once, you have to go to the second dimension.

Every new event can be a new dimension for you to interpret your whole life so far.

— Me@2013-05-12 2:03 AM

# Factors

factors = independent causes

product = the results of factors multiplying together

multiply

— Me@2013-02-28 8:16 pm

# Over

over ~ finished ~ transcended

— Me@2013-02-01 01:54:02 PM

Finishing is one of the two methods of transcending. For example, once you have earned enough money, you would never have to worry about money anymore.

Finishing is more time-consuming and should be avoided if possible. But sometimes, it is necessary.

— Me@2013-02-03 02:02:07 PM

— Me@2013.01.21

— Me@2007.09.17

# 多重小宇宙

（安：你剛才提到：

（安：那是我將今天討論過的句子，重新組合後的化學作用，奇幻想法：

1. 一個宇宙，有一個「時間次元」，即是有一條「時間線」。「時間線」又可以稱為「因果鏈」。

2. 宇宙的次元數目是「三加一」，即是「『三次元空間』加『一次元時間』」。

3. 我剛才視「多重宇宙標籤」為「第二個時間」次元，是建基於「平行宇宙機」的假設。那個科幻故事的主角，發明了「平行宇宙機」，令到自己可以，由原本的宇宙（甲），走到另一個宇宙（乙）行事。那樣，「宇宙甲」的歷史，就可以透過主角，影響到「宇宙乙」的演化，反之亦然。

… –> （2013 年 1 月 14 日，醫生甲）開藥 –> （導致）（2013 年 1 月 21 日，病人乙）痊癒 –> …

— Me@2013.01.19

# 三次元時間

Looper, 2.2 | 二次元時間 2.4 | Dimension 1.3.4 | Two dimensional time 2.4 | 孖生宇宙 2.4

《Looper》故事版本一 –>（影響）《Looper》故事版本二 –>（影響）《Looper》故事版本三 –> … …

（故事版本二，宇宙三，2017 年 5 月 10 日）

— Me@2013.01.18

# Looper, 2

「平行宇宙」中的每一個，內部都會有自己事件演化的「因果鏈」，簡稱「歷史」。所以，每一個宇宙，即為一條「時間線」。那就是「第一個時間次元」。而「平行宇宙」間的演化，即為「第二個時間次元」：

「宇宙一」 –> （影響）「宇宙二」–> （影響）「宇宙三」–> … …

— Me@2013.01.15

# 二次元時間 2.2

Dimension 1.3.2 | Two dimensional time 2.2 | 孖生宇宙 2.2

（安：我覺得有點奇怪。我覺得「多重宇宙的標籤」，既不可以叫做「空間次元」，因為那個標籤或者數字，並不是用來描述「同一個宇宙」中的空間位置；亦不可以叫做「時間次元」，因為「時間」有「因果鏈」的意思。「多重宇宙」是「平行宇宙」，互不相干，沒有「因果關係」可言。）

（安：依你這個講法，除了在科幻小說外，日常現實生活中 —— 如果用比喻 —— 都會有「二次元時間」的現象。）

— Me@2013.01.14

# 二次元時間 2.1

Dimension 1.3.1 | Two dimensional time 2.1 | 孖生宇宙 2.1

（安：我有一點不明白。你說「dimension」（次元）有兩種，可以是「spatial dimension」（空間次元），或者「temporal dimension」（時間次元）。宇宙的次元數目是「三加一」，即是「『三次元空間』加『一次元時間』」。

「解決」之道是，宣稱在「二十歲的主角」殺害「十歲自己」時，宇宙歷史的發展被改變了，形成一分為二的「歷史分支」。或者說，宇宙的「時間線」，由一條分裂成兩條。

— Me@2013.01.12