機會率應試 1.4

這段改編自 2010 年 6 月 8 日的對話。

「基礎類型」就好像是「積木方塊」;而「組合化身」就即是那堆「積木方塊」,所砌成的東西。「砌法」有很多,「積木」有很少。那如何令到自己,清晰看到那些「積木方塊」呢?

最理想是有理想的老師教你,直接給予你那些「積木方塊」。另外,你亦可以透過對比不同題目。例如,這題和那題的外表,雖然大大不同,但是,都同樣要用到「技巧甲」。那樣,「技巧甲」就是其中一塊「重要積木」。

我們之所以要有一雙眼,而不是一隻,是為了在任何時間,都可以在同一時刻,從同一個客觀環境中,接收到兩個稍為不同的主觀影像。從左右影像的差別,腦部可以判斷環境中,各個物件的深度,即是距離自己有多遠。兩隻眼看東西,才會有明顯的立體感。同理,透過對比同一個章節中的不同題目,你可以明確判斷,各個技巧的相對重要程度。亦即是話,哪些是核心?哪些是次要?哪些是技節?哪些是不相干?

你不用太擔心,因為那不算是額外的工作。我提議的「魔法筆記」系統,已經「內置」了「對比題目」的功能。如果你平日會做大量題目,而又習慣了每題收集重點的話,那些機會率題目的「基礎類型」,自然會盡收於你的「魔法筆記」之中。

— Me@2012.10.31

2012.10.31 Wednesday (c) All rights reserved by ACHK

Black hole complementarity 2

Instead, an observer can only detect the information at the horizon itself, or inside, but never both simultaneously. Complementarity is a feature of the quantum mechanics of noncommuting observables, and Susskind proposed that both stories are complementary in the quantum sense.

Interestingly enough, an infalling observer will see the point of entry of the information as being localized on the event horizon, while an external observer will notice the information being spread out uniformly over the entire stretched horizon before being re-radiated. To an infalling observer, information and entropy passes through the horizon with nothing strange happening. To an external observer, the information and entropy is absorbed into the stretched horizon which acts like a dissipative fluid with entropy, viscosity and electrical conductivity.

— Wikipedia on Black hole complementarity

2012.10.30 Tuesday ACHK

Steampunk

DanielBMarkham 2 days ago | link | parent

The time between about 1860 and 1910 seems totally magical to me.

For all of history, people lived, loved, and died. Aside from perhaps a few of them writing their thoughts down, they totally disappeared.

With the invention of still photography, and much more audio and moving-picture recording technology, suddenly you could see and hear people who were long gone.

These folks are not just dead. Their kids are dead, their grandkids are dead, their great-grandkids are probably also gone. Yet we are able to hear them play music, tell stories, and laugh. They might even tell a joke and we can laugh along with it.

It’s as if mankind suddenly came out of a very dark tunnel. We are finally able to really coalesce into a multi-generational conversation about what our humanity means. (A little too poetic. Apologies. I just find it amazing[.])

— Hacker News

2012.10.30 Tuesday ACHK

無常

機會率哲學 1.4

這段改編自 2010 年 4 月 3 日的對話。

「隨機」的意思是,沒有原因,而導致我們,不可直接明確推斷,事件會有哪一個結果。但是,你可以再追問,何謂「沒有原因」呢?

我們可以改用,詳細一點的講法。「隨機」的意思是,對於同一個固定不變的物理系統,即使是同一組的輸入,輸出的結果也不一定每次相同。

— Me@2012.10.30

2012.10.30 Tuesday (c) All rights reserved by ACHK

The Beginning of Time

Existence, 5 | Why does the universe exist? 3

The sentence “there is nothing in the north of the North Pole” is inaccurate, because it assumes that there a place in the north of the North Pole, although that place has nothing in it. Instead, we should say

The North Pole has no “north”. 

or

The word “north” is meaningless at the North Pole.

— Me@2012.10.15

2012.10.29 Monday (c) All rights reserved by ACHK

機會率應試 1.3

這段改編自 2010 年 6 月 8 日的對話。

或者這樣,你試試不斷收集各種類型的機會率題目,於「魔法筆記」中。當你已經收集了四十類時,如果竟然再發現有第四十一類,你就應該退修這一科。

(CYW:退修這一科,豈不是會浪費了一年?)

浪費一年,總好過浪費兩年。

(HYC:Drop o左佢?!那樣,我會不夠科目升讀大學。)

那是最極端悲觀的情況,當然不易會發生。公開試中的機會率題目,大概不會有四十類那麼多吧。實情可能是有二十多類。如果只有二十多類,對年青人的頭腦來說,不會是困難,一定會記得到。

而且,我所講的「機會率題目類型」中的所謂「類型」,是指「基礎類型」。「基礎類型」即使不多,它們的組合可以千變萬化,可以有各式各樣的化身。換句話說,我要你收集的,是「基礎類型」,而不是它們的「組合化身」,除非是特別常見的「組合化身」。如果你發現往年的公開試中,機會率題目的類型,竟然有超過四十種的話,你大概是誤入歧途,不是真的在收集「基礎類型」。

— Me@2012.10.29

2012.10.29 Monday (c) All rights reserved by ACHK

Black hole complementarity

Leonard Susskind proposed a radical resolution to this problem by claiming that the information is both reflected at the event horizon and passes through the event horizon and can’t escape, with the catch being no observer can confirm both stories simultaneously.

— Wikipedia on Black hole complementarity

2012.10.28 Sunday ACHK

見仁見智

談情以外,還要談仁談智,愛情方會長久。

如果在對方身上,見不到仁,或者見不到智,愛情較難維持。

— Me@2012-10-27 10:38:16 AM

2012.10.28 Sunday (c) All rights reserved by ACHK

機會率哲學 1.3

這段改編自 2010 年 4 月 3 日的對話。

換句話說,所謂的「隨機事件」,並不真的是隨機。只是因為我們為了可以,大大簡化運算,而把一些複雜事件當作是「隨機」的,令到我們可以避開「牛頓力學」,而改為使用「機會率定律」來預測。「經典物理學」中的「隨機事件」,都是「偽隨機」的。

「隨機」的意思是,沒有原因,而導致我們,不可直接明確推斷,事件會有哪一個結果。「偽隨機」的意思則是,事件不是沒有原因。只是我們「無知」,沒有足夠的資料,而索性把事件當作是「隨機」的。「偽隨機」不是源於「沒有原因」,而是源於「知得不夠詳細」。

那世間上,有沒有一些真正的「隨機」事件呢?

研究微觀世界時,我們需要使用「量子力學」。「量子力學」中「機會率」,主要來自先天固有的「隨機性」。有些事件的發生,是真的「沒有原因」。亦即是話,即使我們百分百知道,一個量子物理系統的所有資料,有些地方,我們都會被迫使用「機會率」。而那些「機會率」,並不是源於我們的「無知」,而是源於大自然「內置」的「任意性」。

— Me@2012.10.28

2012.10.28 Sunday (c) All rights reserved by ACHK

There 1.3

Existence, 3.6 | Why does the universe exist? 1.6

“There” is “那裡” in Chinese. Literally,

here = 這裡 = this inside

there = 那裡 = that inside

For example,

A dog exists

= There is a dog

= A dog is in there

“There” is a container. That is why both the sentence “the universe exists” and the sentence “the universe does not exist” have no meanings. 

— Me@2012.10.15

2012.10.27 Saturday (c) All rights reserved by ACHK

機會率應試 1.2

這段改編自 2010 年 6 月 8 日的對話。

所以,你在平日溫習時,要盡量儲備多些案例,尤其是 past paper(歷屆試題)的案例。如果你在考試前,已經儲了二十種類型的機會率題目,而在考試時,竟然出現第二十一類的話,你不用太擔心,因為其他考生也會同樣驚慌失措。

然後,你要小心一點,真正的公開試歷屆試題,或者考試範圍,會不會有超多類型的機會率題目?

(CYW:我也不太清楚。)

或者這樣,你試試不斷收集各種類型的機會率題目,於「魔法筆記」中。當你已經收集了四十類時,如果竟然再發現有第四十一類,你就應該退修這一科。

— Me@2012.10.27

2012.10.27 Saturday (c) All rights reserved by ACHK

Perfect Ending

The problem of a perfect result is, there is no future, there is no next step. The story cannot continue.

「完美結果」的壞處是,沒有未來,沒有下一步。故事無法繼續。

— Me@2012.10.25

2012.10.26 Friday (c) All rights reserved by ACHK

機會率哲學 1.2

這段改編自 2010 年 4 月 3 日的對話。

(安:你上次講,「機會率」來自於「無知」。當人們沒有足夠資料,而又要預測結果時,就會運用「機會率」。

例如,當我們擲一粒骰子時,理論上,只要擁有該粒骰子的所有力學資料,包括初始位置、方向 和 速度等,就可以運用牛頓力學,百分百準確地預測到,該次擲骰的結果。但是,實際上,要得到該粒骰子,詳細而準確的力學資料,成本甚高。而且,即使你有齊那些力學資料,要透過牛頓力學的運算,來得到擲骰結果,代價太大。

所以,數學家、物理學家、工程師 和 經濟學家 等,退而求其次,不再要求百分百準確地,預測未來會有哪一個結果,而改為描述每一個可能的結果,發生的機會率有多少。)

— Me@2012.10.26

2012.10.26 Friday (c) All rights reserved by ACHK

There 1.2

Existence, 3.5

Why does the universe exist? 1.5

To specify something exists or not, you need a “there”, range for searching. To prove something exists, you may not need to search all over “there”. But to prove something does not exist, you need to. 

— Me@2012.10.15

2012.10.25 Thursday (c) All rights reserved by ACHK