Commutator product rule

[A,BC] = [A,B]C + B[A,C]

This commutator product rule works just like the differentiation product rule:

assume that A is independent of C, you get the first term;

assume that A is independent of B, you get the second term.

— Me@2012-03-27 7:24:30 PM

2012.03.31 Saturday (c) All rights reserved by ACHK


A hologram can be cut in half, and each part still carries the whole picture. That’s because a hologram is the record of a light wave, and the information in a wave is spread over all of the space it occupies.

— arcnets

— physics forums

When a photograph is cut in half, each piece shows half of the scene. When a hologram is cut in half, the whole scene can still be seen in each piece. This is because, whereas each point in a photograph only represents light scattered from a single point in the scene, each point on a holographic recording includes information about light scattered from every point in the scene. Think of viewing a street outside your house through a 4 ft x 4 ft window, and then through a 2 ft x 2 ft window. You can see all of the same things through the smaller window (by moving your head to change your viewing angle), but you can see more at once through the 4 ft window.

— Wikipedia on Holography

2012.03.30 Friday ACHK



I think one of the things that kills great things so often is compromise — letting people talk you out of what your gut is telling you. Not that I don’t value people’s input, but you have to have the strength to ignore it sometimes, too. If you feel really strongly, there might be something to that, and if you see something that other people don’t see, it could be because it’s that powerful and different. If everyone agrees, it’s probably because you’re not doing anything original.

– Evan Williams, Founders at Work




2010.01.09 Saturday ACHK

軟硬智力 3.3

連繫智力 2.3

這段改編自 2010 年 3 月 20 日的對話。





人的大腦是沒有 CPU(中央處理器)的。







— Me@2008.02.06

— Me@2012.03.30 

2012.03.30 Friday (c) All rights reserved by ACHK

Fear | Hope


Fear cannot be without hope nor hope without fear.

– Spinoza


… because they both are due to uncertainties.

— Me@2012-03-27 12:24:02 PM

2012.03.28 Wednesday (c) All rights reserved by ACHK

Quantum cosmology

… the universe is the sum total of all that is in existence. Physically, a (physical) observer outside of the universe would require the breaking of gauge invariance, and a concomitant alteration in the mathematical structure of the theory. Similarly, RQM conceptually forbids the possibility of an external observer. Since the assignment of a quantum state requires at least two “objects” (system and observer), which must both be physical systems, there is no meaning in speaking of the “state” of the entire universe.

This is because this state would have to be ascribed to a correlation between the universe and some other physical observer, but this observer in turn would have to form part of the universe, and as was discussed above, it is impossible for an object to give a complete specification of itself. Following the idea of relational networks above, an RQM-oriented cosmology would have to account for the universe as a set of partial systems providing descriptions of one another. The exact nature of such a construction remains an open question.

— Wikipedia on Relational quantum mechanics

2012.03.27 Tuesday ACHK



King believes that, generally speaking, good stories cannot be called consciously and should not be plotted out beforehand; they are better served by focusing on a single “seed” of a story and letting the story grow itself.

– Wikipedia




2009.07.01 Wednesday ACHK

無限旅程 3

The mind which has become accustomed to the freedom and impartiality of philosophic contemplation will preserve something of the same freedom and impartiality in the world of action and emotion. It will view its purposes and desires as parts of the whole, with the absence of insistence that results from seeing them as infinitesimal fragments in a world of which all the rest is unaffected by any one man’s deeds. The impartiality which, in contemplation, is the unalloyed desire for truth, is the very same quality of mind which, in action, is justice, and in emotion is that universal love which can be given to all, and not only to those who are judged useful or admirable. Thus contemplation enlarges not only the objects of our thoughts, but also the objects of our actions and our affections: it makes us citizens of the universe, not only of one walled city at war with all the rest. In this citizenship of the universe consists man’s true freedom, and his liberation from the thraldom of narrow hopes and fears.

Thus, to sum up our discussion of the value of philosophy; Philosophy is to be studied, not for the sake of any definite answers to its questions since no definite answers can, as a rule, be known to be true, but rather for the sake of the questions themselves; because these questions enlarge our conception of what is possible, enrich our intellectual imagination and diminish the dogmatic assurance which closes the mind against speculation; but above all because, through the greatness of the universe which philosophy contemplates, the mind also is rendered great, and becomes capable of that union with the universe which constitutes its highest good.

— Bertrand Russell: The Value of Philosophy

— Chapter XV of The Problems of Philosophy



— Me@2012-03-26 10:18:27 AM

2012.03.26 Monday ACHK

連繫智力 2.2

無足夠資料 7.2 | 西瓜 4

無知    (matters of facts)    綜合句


愚蠢    (relations of ideas)    重言句


— Me@2012.03.26 

2012.03.26 Monday (c) All rights reserved by ACHK

Classical logic 2

Quantum logic can be formulated either as a modified version of propositional logic or as a noncommutative and non-associative many-valued (MV) logic.

— Wikipedia on Quantum logic

2012.03.25 Sunday ACHK

Dog 2


Intellect is invisible to the man who has none.

– Arthur Schopenhauer


Kindness is invisible to the man who has none.

– Me@2010.07.22


If you pick up a starving dog and make him prosperous, he will not bite you. This is the principal difference between a dog and a man.

– Mark Twain




2010.07.23 Friday ACHK