注定外傳 1.7

Can it be Otherwise? 1.7

3.1415926

3.1415927

（問：如果 3.1 和 3.1 呢？它們不是完全（絕對）相同嗎？）

（問：怎樣為之「有實際因素考慮，真的要應用」？）

3.1 厘米 和

3.1 厘米。

（問：那如果是數數目（使用整體）的情況呢？

— Me@2015-09-30 04:26:45 AM

Exercise Three

You Could Have Invented Monads! (And Maybe You Already Have.)

Show that lift f * lift g = lift (f.g)

——————————

f' * g' = bind f' . g'lift f = unit . ff' = lift f

(lift f * lift g) (x, xs)= bind (lift f . lift g) (x, xs)= (hx, xs++hs)  where     (hx, hs) = lh x     lh x = (f' . g') x    f' = lift f    g' = lift g

This line does not work, since f' cannot be applied to (g' x), for the data types are not compatible:

f' :: Float -> (Float, String)

 g' :: Float -> (Float, String) 

(g' x) :: (Float, String)

The meaning of f' * g' should be bind f' . (bind g') instead.

— Me@2015-09-27 10:24:54 PM

Problem 14.3a

A First Course in String Theory

14.3 Massive level in the open superstring.

~~~

$b_i^2 = 0$

$b_i b_j = - b_j b_i$

$i_1 \ne i_2$

Since the sign is ignored, the number of possible $b^i b^j$ states is $\frac{1}{2} (8) (7) = 28$.

The number of possible $b^i b^j b^k$ states is $\frac{1}{6} (8) (7) (6) = 56$.

The number of possible $b^i b^j b^k b^l$ states is ${8 \choose 4} = 70$.

— Me@2015-09-27 10:40:30 AM

Programming language

A language that doesn’t affect the way you think about programming, is not worth knowing.

— Alan Perlis

2015.09.26 Saturday ACHK

如何拯救眾生 2

How to improve the world indefinitely?

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.

There is law of conservation of energy.
There is law of conservation of mass.
But, there is no law of conservation of ideas.

— Me

.

.

If you have an apple and I have an apple, and we exchange apples, we both still only have one apple. But if you have an idea and I have an idea, and we exchange ideas, we each now have two ideas.

— George Bernard Shaw

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.

. . . it is the action of the thinking power called an idea, which an individual may exclusively possess as long as he keeps it to himself; but the moment it is divulged, it forces itself into the possession of every one, and the receiver cannot dispossess himself of it. Its peculiar character, too, is that no one possesses the less, because every other possesses the whole of it. He who receives an idea from me, receives instruction himself without lessening mine; as he who lights his taper at mine, receives light without darkening me.

That ideas should freely spread from one to another over the globe, for the moral and mutual instruction of man, and improvement of his condition, seems to have been peculiarly and benevolently designed by nature, …

— Thomas Jefferson

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.

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注定外傳 1.6

Can it be Otherwise? 1.6

… 因為，如果真的是「百份百相同」的情境，又怎可能有不同的結果呢？

（問：不是呀。在量子力學中，即使有兩組百分百一樣的物理系統，即使它們獲得完全相同的輸入，都可能有不同的輸出。）

— Me@2015-09-25 10:40:58 AM

flatMap()

Functors, Applicatives, and Monads

skybrian 70 days ago

If functional languages had called them the Mappable, Applicable, and FlatMappable interfaces, and used map(), apply(), and flatMap() instead of operators, it would have avoided a lot of confusion.

— Hacker News

bind ~ flatMap

— Me@2015-07-22 06:30:25 PM

2015.09.23 Wednesday ACHK

Problem 14.2.2

A First Course in String Theory

14.2 Generating function for the unoriented bosonic open string theory.

~~~

How to add “a term that implements the projection to unoriented states”?

What is the projector? $\Omega$?

$f_{os} (x)$

$= \frac{1}{x} \prod_{n=1}^\infty \frac{1}{(1-x^n)^{24}}$

$= \frac{1}{x} \left( 1 + 24 x + 324 x^2 + 3200 x^3 + ... \right)$

To keep only the odd-power terms, we should construct an odd function:

$f_{uos} (x)$

$= \frac{1}{2} \left( f_{os} (x) - f_{os} (-x) \right)$

$= \frac{1}{x} \prod_{n=1}^\infty \frac{1}{(1-x^n)^{24}} - \left( \frac{-1}{x} \prod_{n=1}^\infty \frac{1}{(1-(-x)^n)^{24}} \right)$

— Me@2015-09-17 02:27:20 PM

Englert–Greenberger duality relation, 2

The most recent work claims that Afshar’s core claim, that the Englert–Greenberger duality relation is violated, is not true. They re-ran the experiment, using a different method for measuring the visibility of the interference pattern than that used by Afshar, and found no violation of complementarity, concluding “This result demonstrates that the experiment can be perfectly explained by the Copenhagen interpretation of quantum mechanics.”

Numerous experiments have shown, however, that any modification of the apparatus that can determine which slit a particle passes through reduces the visibility of interference at the screen, thereby illustrating the complementarity principle: that light (and electrons, etc.) can behave as either particles or waves, but not both at the same time. An experiment performed in 1987 produced results that demonstrated that information could be obtained regarding which path a particle had taken, without destroying the interference altogether. This showed the effect of measurements that disturbed the particles in transit to a lesser degree and thereby influenced the interference pattern only to a comparable extent.

In other words, if one does not insist that the method used to determine which slit each photon passes through be completely reliable, one can still detect a (degraded) interference pattern.

— Wikipedia on Englert–Greenberger duality relation

— Wikipedia on Double-slit experiment

2015.09.22 Tuesday ACHK

如何拯救眾生 1

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The meeting of two personalities is like the contact of two chemical substances: if there is any reaction, both are transformed. — Carl Jung

Generalized Newton’s Third Law: You cannot change others without being changed. — John Wheeler

.

.

You are an A person. You befriend with an F person. The result is that your friend becomes a better person, you become a worse person. In theory, you become a C person. Your friend becomes a C person. In practice, since being a bad person is much easier than being a good person, you two will become both F people. — Me

Be slow in making friends, slower in changing. — Benjamin Franklin

You have to know how to accept rejection and reject acceptance. — Ray Bradbury

If you hire all A people, he said, they’ll also hire A people. But if you hire B people, they’ll hire the C people and then it’s all over. — Joel Spolsky

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So that means you cannot help anyone weaker than you?

NO.

Instead, you should help others. But you have to help others in a smart way. — Me

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How?

.

. . . it is the action of the thinking power called an idea, which an individual may exclusively possess as long as he keeps it to himself; but the moment it is divulged, it forces itself into the possession of every one, and the receiver cannot dispossess himself of it. Its peculiar character, too, is that no one possesses the less, because every other possesses the whole of it. He who receives an idea from me, receives instruction himself without lessening mine; as he who lights his taper at mine, receives light without darkening me.

— Thomas Jefferson

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.

.

Can it be Otherwise?

–　Me@2015-09-22 07:41:07 AM

Monads in Haskell can be thought of as composable computation descriptions. The essence of monad is thus separation of composition timeline from the composed computation’s execution timeline, as well as the ability of computation to implicitly carry extra data, as pertaining to the computation itself, in addition to its one (hence the name) output, that it will produce when run (or queried, or called upon). This lends monads to supplementing pure calculations with features like I/O, common environment or state, etc.

— Haskell Official Wiki

2015.09.21 Monday ACHK

Problem 14.2.1

A First Course in String Theory

14.2 Generating function for the unoriented bosonic open string theory.

~~~

What is the difference between oriented and unoriented bosonic open strings?

p.268: “The theory of unoriented strings is obtained by restricting the oriented string spectrum to the set of states that are invariant under the action of  $\Omega$. Unoriented strings are not strings without orientation: they should be viewed as a quantum superposition of states that as a whole, are invariant under orientation reversal.”

An unoriented state is a superposition of 2 opposite oriented states.

— Me@2015.07.03 12:12 PM

Clue 2: “… adding a term that implements the projection to unoriented states.”

Equation (14.63):

The generating function $f_{os}$ for bosonic open string theory is

$f_{os} (x)$
$= \frac{1}{x} + 24 + 324 x + 3200 x^2 + ...$
$= \frac{1}{x} \left( 1 + 24 x + 324 x^2 + 3200 x^3 + ... \right)$

Clue 3: p.278 Problem 12.12e

$\Omega = (-1)^{N^\perp}$

An unoriented string state is a superposition of two opposite-oriented string states. An unoriented string state has twist invariant.

We can choose to keep all states $|\psi \rangle$ with $\Omega |\psi \rangle = + |\psi \rangle$.

We can also choose the states with $\Omega |\psi \rangle = - |\psi \rangle$. However, they are only valid for the basis states, not for other states, because other states are superpositions of basis states. The relative phase between basis states are physical in a superposition.

Effectively, the states $|\psi \rangle$ with $\Omega |\psi \rangle = + |\psi \rangle$ are the only possible choices. In other words, $N^\perp$ must be even.

— This answer is my guess. —

For the unoriented open strings, we should keep only the even powers of $N^\perp$:

$f_{uos} (x) = \frac{1}{x} \left( 1 + 324 x^2 + 176256 x^4 + ... \right)$

— This answer is my guess. —

— Me@2015-09-17 02:27:20 PM

Quantum Indeterminacy

Quantum indeterminacy is the apparent necessary incompleteness in the description of a physical system, that has become one of the characteristics of the standard description of quantum physics.

Indeterminacy in measurement was not an innovation of quantum mechanics, since it had been established early on by experimentalists that errors in measurement may lead to indeterminate outcomes. However, by the later half of the eighteenth century, measurement errors were well understood and it was known that they could either be reduced by better equipment or accounted for by statistical error models. In quantum mechanics, however, indeterminacy is of a much more fundamental nature, having nothing to do with errors or disturbance.

— Wikipedia on Quantum indeterminacy

Quantum indeterminacy is the inability to predict the behaviour of the system with 100% accuracy, even in principle.

If everything is connected , quantum indeterminacy is due to the logical fact that, by definition, a “part” cannot contain (all the information of) the “whole”.

An observer (A) cannot separate itself from the system (B) that it wants to observe, because an observation is an interaction between the observer and the observed .

In order to get a perfect prediction of a measurement result, observer (A) must have all the information of the present state of the whole system (A+B). However, there are two logical difficulties.

First, observer A cannot have all the information about (A+B).

Second, observer A cannot observe itself to get (all of) its present state information, since an observation is an interaction between two entities. Logically, it is impossible for something to interact with itself directly. Just as logically, it is impossible for your right hand to hold your right hand itself.

So the information observer A can get (to the greatest extent) is all the information about B, which is only part of the system (A+B) it (A) needs to know in order to get a prefect prediction for the evolution of the system B.

— Me@2015-09-14 08:12:32 PM

注定外傳 1.4

（問：你不是說理論的成本較低嗎？）

— Me@2015-09-07 08:59:31 PM