# Tree rings, 2

Time-traveling to the past is like “making an outside ring more inside”, which is logically impossible.

— Me@2011.09.18

Me@2010

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# Euler Formula

Exponential, 2

$a^x$

general exponential increase ~ the effects are cumulative

$e^x$

natural exponential increase ~ every step has immediate and cumulative effects

— Me@2014-10-29 04:44:51 PM

exponent growth

$e^x = \lim_{n \to \infty} \left(1 + \frac{x}{n}\right)^n$

~ compound interest effects with infinitesimal time intervals

multiply -1

~ rotate to the opposite direction

(rotate the position vector of a number on the real number line to the opposite direction)

~ rotate 180 degrees

multiply i

~ rotate to the perpendicular direction

~ rotate 90 degrees

For example, the complex number (3, 0) times i equals (0, 3):

$3 \times i = 3 i$
$(3, 0) (0, 1) = (0, 3)$

multiplying i

~ change the direction to the one perpendicular to the current moving direction

(current moving direction ~ the direction of a number’s position vector)

exponential growth with an imaginary amount

$e^{i \theta} = \lim_{n \to \infty} \left( 1 + \frac{i \theta}{n} \right)^n$

~ change the direction to the one perpendicular to the current moving direction continuously

~ rotate $\theta$ radians

— Me@2016-06-05 04:04:13 PM

# Exponential

a^x

general exponential increase ~ the effects are cumulative

e^x

natural exponential increase ~ every step has immediate and cumulative effects

— Me@2014-10-29 04:44:51 PM

# 回到過去 3

Cumulative concept of time 20

（Me：那樣，如果我只是「回到過去」，但不「經歷過去」，我豈不是不會「失去青春」？）

— Me@2014-04-24 01:56:35 AM

# The fifth floor

The fifth floor cannot exist without the first 4 floors.

— Me@2012.10.24

That’s why time travel is logically impossible.

— Me@2014.04.17

If you remove the first 4 floors, the original fifth floor is not the “fifth” floor anymore. Instead, it would become the first floor.

— Me@2014.04.16

# Block spacetime, 8

Cumulative concept of time 18 | 原因 7

In block spacetime, whether time is cumulative or not is not an important label.

— Me@2012.10.19

# The Beginning of Time, 3.2

Cumulative concept of time 1.3.2

The past is part of the future.

The first cause is the smallest part.

cause ~ component

The first cause is not a boundary, because there is no “before”.

The first cause is a physical limit, not a physical boundary.

The first cause is a logical boundary, not a physical one.

— Me@2012.10.17

— Me@2014.02.03

# Consciousness 4

Event Realism 3.2 | 事件實在論 3.2 | Cumulative concept of time, 17.2

being conscious

~ having one’s own past information

~ having memory

~ having self-interaction

~ entanglement between past states and the present state

~ some of the past states keep existing through memories and records

~ past-self-and-present-self entanglement

— Me@2013-11-01 7:02 AM

# Information 2

Event Realism 3 | 事件實在論 3 | Cumulative concept of time, 17 | Recursion 8.3 | I am a Strange Loop, 3.3

memory ~ information of the past

Part of the past still exists, in the sense that some states and events of the past are entangled with those of the present.

— Me@2013-10-09 6:50 PM

# Bank account

For a bank account, the past balances are irrelevant and useless.

What is really relevant is the present balance.

And it has encrypted all the past money that can still be used now.

— Me@2011.04.25

— Me@2013.09.03

# The Beginning of Time, 3

Cumulative concept of time 1.3

The past is part of the future.

the earliest time

= the most remote past

= the smallest possible time circle

= a point where radius equals zero (r = 0)

= the centre of the time circle

The time t is like the radius r. It makes no sense to ask, “What happened before the beginning of the universe?”

Just as it is not meaningful to ask, “What if r < 0 ?"

— Me@2013-08-04

# 時間觀 1.2

Cumulative concept of time | 累積時間觀

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Wrong: past –> present –> future

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Right:

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– Me, Inspired by Richard Koch’s The 80/20 Principle

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# 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

# Conscious time

Cumulative concept of time, 15

In 1895, in his novel, The Time Machine, H.G. Wells wrote, “There is no difference between time and any of the three dimensions of space except that our consciousness moves along it.”

— Wikipedia on Spacetime

Consciousness “moves” from the past to the future because consciousness is a kind of reflection.

To be conscious, one has to access its own states. But only the past states are available. Accessing one’s own now-here state is logically impossible, because that creates a metadox (paradox).

— Me@2013-06-26 02:28:51 PM

We can remember the past but not the future because the past is part of the future; the whole contains its parts, but not vice versa.

— Me@2011.08.21

# Backward compatibility, 6

backward compatible

~ cumulative

~ able to access the past

— Me@2013-05-23 08:35:10 PM

# Cumulative concept of time, 14

cause

~ necessary condition

~ part of

Event A is a cause of event B

= Event A is a necessary condition of event B

= Event A is part of event B

We can remember the past but not the future because the past is part of the future; the whole contains its parts, but not vice versa.

— Me@2011.08.21