Monthly Archives: October 2012

Mass–energy equivalence

Posted on by

Second, Einstein’s E = mc^2 is not an equivalence of energy and matter. It is the equivalence of energy and mass (i.e. the number of kilograms). So a unit volume of the empty space carries some mass equivalent to the energy – it’s a mass of a few protons per cubic meter. But the E = mc^2 equation does not imply, in any sense, that the mass equivalent to the energy has to take the form of localized particles. It may be dispersed, much like the cosmological constant – whose generalized form is also called dark energy. The main reason why the vacuum contains mass is that this mass contributes to the curvature of spacetime – the gravitational field of mass – and be sure that dark energy does. That is why it was introduced.

Dark energy, unlike mass, carries a negative pressure, and it’s the real source of the accelerating expansion it induces. Ordinary matter has attractive gravity.

— answered May 3, 2011 at 4:33

— Lubos Motl

2012.10.09 Tuesday ACHK

Nature

Posted on by

地獄篇 6

Nature is evil. So Nature is not the Light.

— Me@2011.11.14

For example, many animals have to kill each other in order to survive.

Many evil aspects of human nature are designed by Nature. In order to be good, we have to transcend Nature. For example, we can create a society in which we can support each other instead of killing each other.

— Me@2012.10.09

2012.10.09 Tuesday (c) All rights reserved by ACHK

Now or Never

Posted on by

活在當下

這段改編自 2010 年 6 月 9 日的對話。

很多同學也有一種逃避的心態。在家裡溫習時，遇到不懂的東西，一點也不思考，而打算回校才問老師；回到學校時，遇到不懂的東西，一點也不發問，而打算回家才慢慢研究。「家中的自己」和「學校的自己」，不斷互相推卸責任，結果一事無成。

恰當的心態是，學習每一個課題時，凡事可以立刻明白的東西，就要做到立刻明白。你要假想，這是你在公開試之前，最後一次的機會，可以詳細地研習這一課。而你亦要知道，這個「假想」，並不真的是「假想」，而是「實情」。

公開試的課程十分緊迫，是一個「長江後浪推前浪」的結構。一課完成後，就會馬上開始下一課，而且一課比一課艱深，並不會有大量時間給你回頭。如果你的智力高到，可以回頭把之前的課題，百分百重新學習一次的話，你當初就不會落後。

留意，有些東西，是不可以立刻明白的。正確的應對是，你先把那些問題，放於你的「魔法筆記」中，容後再發問或者研究；而不是奢望，之後會有時間，把該課的所有東西，重新研習一次。

— Me@2012.10.08

2012.10.08 Monday (c) All rights reserved by ACHK

Existence

Posted on by

Properties of objects are called first-order properties.

Properties of first-order properties are called second-order properties.

Existence is not an property of an object. It is a property of properties.

For example, when we say “X does not exist”, we do not mean that “there is an X and X has a property of non-existence.” Instead,

X does not exist

= the property of being X is useless

= the set which contains X’s has no members

— Me@2012.10.07

— Me@2012.10.08

2012.10.08 Monday (c) All rights reserved by ACHK

Freedom 4

Posted on by

Man is condemned to be free; because once thrown into the world, he is responsible for everything he does.

— Jean-Paul Sartre

Freedom is a headache. But freedom is better than no-freedom because if you have freedom and do not like it, you can use your freedom to decrease your freedom. However, if you have no freedom and do not like it, you do not have freedom to increase your freedom.

— Me@2011.11.17

2012.10.08 Monday (c) All rights reserved by ACHK

Memory 4.5

Posted on by

Copy Me, 5.4

這段改編自 2010 年 4 月 3 日的對話。

另外，寫自傳時，你要知道，你的回憶未必是實情。記憶，就是把「客觀事件」，化成「主觀紀錄」的過程。要保證自傳的真確，就要人證物證俱在。換句話說，你應該把「主觀記憶」和「客觀記憶」比對，包括 信件、文件 和 他人的記憶 等。　

— Me@2012.10.08

2012.10.08 Monday (c) All rights reserved by ACHK

Many-valued logic

Posted on by

Relation to classical logic

Logics are usually systems intended to codify rules for preserving some semantic property of propositions across transformations. In classical logic, this property is “truth.” In a valid argument, the truth of the derived proposition is guaranteed if the premises are jointly true, because the application of valid steps preserves the property. However, that property doesn’t have to be that of “truth”; instead, it can be some other concept.

Multi-valued logics are intended to preserve the property of designationhood (or being designated). Since there are more than two truth values, rules of inference may be intended to preserve more than just whichever corresponds (in the relevant sense) to truth. For example, in a three-valued logic, sometimes the two greatest truth-values (when they are represented as e.g. positive integers) are designated and the rules of inference preserve these values. Precisely, a valid argument will be such that the value of the premises taken jointly will always be less than or equal to the conclusion.

For example, the preserved property could be justification, the foundational concept of intuitionistic logic. Thus, a proposition is not true or false; instead, it is justified or flawed. A key difference between justification and truth, in this case, is that the law of excluded middle doesn’t hold: a proposition that is not flawed is not necessarily justified; instead, it’s only not proven that it’s flawed. The key difference is the determinacy of the preserved property: One may prove that P is justified, that P is flawed, or be unable to prove either. A valid argument preserves justification across transformations, so a proposition derived from justified propositions is still justified. However, there are proofs in classical logic that depend upon the law of excluded middle; since that law is not usable under this scheme, there are propositions that cannot be proven that way.

— Wikipedia on Many-valued logic

2012.10.07 Sunday ACHK

The One

Posted on by

The difficulty is that the probability is so low. The easiness is that the pool is so large, and you only have to find one.

— Me@2011.11.17

.

.

2012.10.07 Sunday (c) All rights reserved by ACHK

在那一年

Posted on by

Memory 4.4 | Copy Me, 5.3 | Memento 4

這段改編自 2010 年 4 月 3 日的對話。

根據我的經驗，近乎只有一個情況，會令我真正明確回憶起，中學時代的某一件特定事件。那就是當收拾房間，整理一大堆物件的時候，偶然會見到那個時代的一些「紀念品」，例如 成績表、筆記、書籍、相片 和 電影戲票 等。

所以，為免遺失原本的自我，你應定期收集和保存「紀念品」，作為人生的「里程碑」。「紀念品」就好像是「記憶保險箱的鎖匙」，助你隨時喚醒多年前的詳細記憶，令你重遇年輕時的自己。你的信件、文章 和 作品，往往就是最佳的「紀念品」。

— Me@2012.10.06

2012.10.06 Saturday (c) All rights reserved by ACHK

Paradox 3.4

Posted on by

Meta-time 3.4

Time travel is only possible if there is a meta-time. Time travel is only possible if our physical time is fake, in a sense that it is not the real causal chain; and the meta-time is real, in a sense that it is the real causal chain.

For example, if our so-called physical world is actually a computer video game simulation, then the “physical” laws and the “physical” time are fake, in a sense that they are illusions simulated by a computer. The world to which that computer belongs is our meta-time. That meta-world is the real physical world. That meta-time is the real causal chain.

— Me@2012-10-01 12:53:48 PM

— Me@2012-10-03 02:21:45 PM

— Me@2012-10-05 11:24:43 AM

2012.10.06 Saturday (c) All rights reserved by ACHK

Paradox 3.3

Posted on by

Meta-time 3.3

Paradox is due to the mixing of para-level (meta-level) and original level, including the time-travel paradoxes.

The grandpa paradox has the similar structure as

“This sentence is true.”

The ontological paradox has the similar structure as

“This sentence is false.”

— Me@2012-10-06 09:35:11 AM

2012.10.06 Saturday (c) All rights reserved by ACHK

Paradox 3.2

Posted on by

Meta-time 3.2

Paradox is due to the mixing of para-level (meta-level) and original level. For example, consider this sentence:

“This sentence is false. “

There are two problems for this sentence.

First, is this sentence true or false? 

If it is true, according to itself, it is false.

But if it is false, then the assertion that “this sentence is false” is false, so it is true.

Second, what is the level of this sentence?

We don’t know, because it is referring to nothing, except itself. Let us just assume that it is an order-n sentence.

But since it describes itself, it describes an order-n sentence. So it is an order-(n+1) sentence.

But since it describes itself, it describes an order-(n+1) sentence. So it is an order-(n+2) sentence.

Contradiction!

How can the same sentence have more than one order?

That is exactly the problem of mixing levels. The meaning of the sentence and the meaning of the meta-sentence may contradict.

“This sentence is false.” is with level n, (n+1), (n+2), … at the same time.

But if it is true at level n, it is false at level (n+1), and true at level (n+2), etc.

So it is true and false and true …

Paradox is due to the mixing of para-level (meta-level) and original level. As long as we do not allow mixing levels, there are no paradoxes. Every sentence should only be allowed to describe sentences which have lower levels. For example, a sentence, S, is with level n.

Then S is not allowed to describe any other level n (or higher than level n) sentences.

— Me@2012-10-05 02:00:04 PM

2012.10.05 Friday (c) All rights reserved by ACHK

Paradox 3.1

Posted on by

Meta-time 3.1

Objects and events are of level zero.

Sentences about objects and events are of level one. They are called order-one sentences, e.g.

“Here is an apple.”

Sentences about sentences are of level two. They are called order-two sentences or meta-sentences, e.g.

“”Here is an apple.” has 4 words.”

Sentences about order-two sentences are of level three. They are called order-three sentences or meta-meta-sentences, e.g.

“”Here is an apple.” has 5 words.” is false.”

…

— Me@2012-10-05 12:00:04 PM

2012.10.05 Friday (c) All rights reserved by ACHK

Memory

Posted on by

.

I have collected in this book memories extending over fifty years.

I am well aware that memory is unreliable.

It not only selects and rearranges that facts of our lives, but also embroiders and invents.

I have checked my version of facts wherever possible against other people’s memories and against written documents.

.

– Freeman Dyson’s Disturbing the Universe

.

.

.

2009.09.05 Saturday ACHK

Digital physics, 6.2

Posted on by

Many other aspects of quantum geometry or minimal length – such as T-duality, a critical, “maximal” Hagedorn temperature, or some kinds of noncommutativity – do emerge when we approach the smallest distance scales. But the naive discreteness is just one possible way how the usual concepts of a continuous geometry could be realized at short distances. And it is a way that is not chosen in quantum gravity because of many reasons, including its incompatibility with the Lorentz symmetry that we will discuss later in the text.

— Myths about the minimal length

— Lubos Motl

2012.10.04 Thursday ACHK

Paradox 2

Posted on by

Meta-time 2

Paradox is due to the mixing of para-level (meta-level) and original level.

— Me@2012-09-29 02:22:14 PM

… including the time-travel paradoxes.

As long as you put time-travel into a story, you mix the meta-time and the original time within that story. Thus time-travel paradoxes appear.

— Me@2012-10-01 10:33:05 AM

The two typical time-travel paradoxes are the grandfather paradox and the ontological paradox.

The grandfather paradox is that time-travel would create an inconsistent story. For example, if you time-travel back to 10 years ago and kill your younger self, you present-self cannot exist. So you could not have time-travelled back to 10 years ago and kill your younger self, you present-self can exist. But your present-self have time-travelled back to 10 years ago and kill your younger self, then you present-self cannot exist.

The ontological paradox is that information can come from nowhere and events can happen with no cause. For example, your future-self goes back in time to give you the solution of a homework problem. After copying it, you go back in time to give your past-self the solution of that homework problem. The question is, where does that homework solution come from?

The meta-time is the author’s time or the readers’ time, which is the real, in a sense that it is the real causal chain. The original-time is the time within that story, which is fake, in a sense that it is not the real causal chain. As long as we distinguish the meta-time (author’s time) and the original-time (story-time) clearly, the two paradoxes can be transcended.

To avoid the grandfather paradox, only the author should be allowed to go back into an earlier story-time. For example, after finishing the 10 chapters of a story, the author goes back to the first chapter to rewrite and polish it. The characters within that story should not be able to go back into an earlier story-time.

To transcend the ontological paradox, we should realize that the “information from nowhere” is actually from the meta-time; the “event with no cause” is actually caused by the author of that story.

— Me@2012-10-03 02:21:45 PM

2012.10.03 Wednesday (c) All rights reserved by ACHK

Memory 4.3

Posted on by

Copy Me, 5.2

這段改編自 2010 年 4 月 3 日的對話。

「十年前的我」和「現在的我」的記憶不盡相同，而導致不是「同一個人」，有兩重意思。

第一重是，「現在的我」（三十歲）比「十年前的我」（二十歲），多了十年的記憶。那就是我剛才所講的「增加」。

第二重是，即使只比較人生頭二十年的記憶，「三十歲的我」回憶（例如）「十六歲那年」發生了什麼事，已經不及「二十歲的我」回憶「十六歲那年」那麼詳細和準確。那就是我剛才所講的「變形、刪減 和 篡改」。

更震撼的是，如果我真的問你，「十六歲那年」發生了什麼事，你可以答到的，可能不出十件，甚至只有一兩件事。震撼的地方在於，「十六歲那年」共有 365 日，而你竟然只講到不夠十件事情。「十六歲那年」對於一個「三十歲的人」來說，只一堆模糊的印象，記憶的疑團。

根據我的經驗，近乎只有一個情況，會令我真正明確回憶起，中學時代的某一件特定事件。那就是當收拾房間，整理一大堆物件的時候，偶然會見到那個時代的一些「紀念品」，例如 成績表、筆記、書籍、相片 和 電影戲票 等。

— Me@2012.10.03

2012.10.03 Wednesday (c) All rights reserved by ACHK