# Self-information

The information entropy of a random event is the expected value of its self-information.

In information theory, self-information or surprisal is a measure of the information content [clarification needed] associated with an event in a probability space or with the value of a discrete random variable.

By definition, the amount of self-information contained in a probabilistic event depends only on the probability of that event: the smaller its probability, the larger the self-information associated with receiving the information that the event indeed occurred.

As a quick illustration, the information content associated with an outcome of 4 heads (or any specific outcome) in 4 consecutive tosses of a coin would be 4 bits (probability 1/16), and the information content associated with getting a result other than the one specified would be 0.09 bits (probability 15/16).

— Wikipedia on Self-information

2015.12.31 Thursday ACHK

# Reality 4

Real” has meanings other more than “lasting“.

For example, “pain is real” means “pain is objective“, instead of “pain is lasting“.

real

~ objective

lasting

~ independent of time (to a certain extent)

real

~ independent of most of the things

~ constant with respect to most of the things

— Me@2015-12-21 12:34 AM

# 注定外傳 2.2

Can it be Otherwise? 2.2

「成績注定」和「主動溫習」，根本沒有矛盾。

— Me@2015-12-29 03:12:39 PM

# Ramond sector zero modes

Problem 14.3b4

A First Course in String Theory

What are $\xi_1, \xi_2, \xi_3, \xi_4$ in Equation (14.44)?

p.315 “Ramond fermions are more complicated than NS fermions because the eight fermionic zero mode $d_0^I$ must be treated with care. It turns out that these eight operators can be organized by simple linear combinations into four creation operators and four annihilation operators. Let us call the four creation operators …”

Since there are 8 possible transverse directions, there are 8 possible $d_0^I$‘s, where $I = 2,3, ..., 9$.

What is the meaning of “… organized by simple linear combinations into four creation operators …”?

— Me@2015.11.01 03:53 AM

The $d_0^I$ operators are similar to but different from other $d_r^I$ operators.

$d_0^I$‘s and $d_r^I$‘s are similar in the sense that they all follow Equation (14.43):

$\{ d_m^I, d_n^J \} = \delta_{m+n, 0} \delta^{IJ}$

p.315 “Again, the negatively moded oscillators $d_{-1}^I, d_{-2}^I, d_{-3}^I, ...$, are creation operators, while the positively moded ones $d_{1}^I, d_{2}^I, d_{3}^I, ...$ are annihilation operators.”

$d_0^I$‘s and $d_r^I$‘s are different in the sense that $d_0^I$‘s are neither creation nor annihilation operators.

(Based on the ideas from “Introduction to String Theory, A.N. Schellekens” and “A First Course in String Theory (Second Edition)” p.315:)

If we define $d_0 | 0 \rangle = 0$,

$\{ d_0^I, d_0^J \} | 0 \rangle$
$= \left( d_0^I d_0^J + d_0^I d_0^J \right) | 0 \rangle$
$= 0$

which does not match the requirement of

$\{ d_0^I, d_0^J \} = \delta^{IJ}$

So the definition $d_0 | 0 \rangle = 0$ does not work.

— Me@2015.11.12 11:30 AM

Instead, they are “organized by simple linear combinations into four creation operators”.

(Based on the idea from “Boundary Conformal Field Theory and the Worldsheet Approach to D-Branes, by Andreas Recknagel，Volker Schomerus” and “A First Course in String Theory (Second Edition)” p.315:)

Let

$c_0^i = d_0^{i+1}$
$e_i = \frac{1}{\sqrt{2}} \left( c_0^{2i} - i c_0^{2i - 1} \right)$
$e_i^\dagger = \frac{1}{\sqrt{2}} \left( c_0^{2i} + i c_0^{2i - 1} \right)$.

Then

$\left\{ e_i, e_j^\dagger \right\}$
$= \frac{1}{2} \left\{ \left( c_0^{2i} - i c_0^{2i - 1} \right), \left( c_0^{2j} + i c_0^{2j - 1} \right) \right\}$
$= \frac{1}{2} \delta^{ij} \left\{ \left( c_0^{2i} - i c_0^{2i - 1} \right), \left( c_0^{2i} + i c_0^{2i - 1} \right) \right\}$

By p.315 Equation (14.43):

$\{ d_0^I, d_0^J \} = \delta^{IJ}$

In other words,

$\{ c_0^{I-1}, c_0^{J-1} \} = \delta^{I-1,J-1}$
$\{ c_0^{I}, c_0^{J} \} = \delta^{IJ}$

$\left\{ e_i, e_j^\dagger \right\}$
$= \frac{1}{2} \left\{ \left( c_0^{2i} - i c_0^{2i - 1} \right), \left( c_0^{2j} + i c_0^{2j - 1} \right) \right\}$
$= \frac{1}{2} \delta^{ij} \left[\left\{ c_0^{2i} , c_0^{2i} \right\} - \left\{ i c_0^{2i - 1}, i c_0^{2i - 1} \right\} \right]$
$= \frac{1}{2} \delta^{ij} \left[\left\{ c_0^{2i} , c_0^{2i} \right\} + \left\{ c_0^{2i - 1}, c_0^{2i - 1} \right\} \right]$
$= \frac{1}{2} \delta^{ij} \left[1 + 1 \right]$
$= \delta^{ij}$

This is compatible with the anti-commutator requirement for fermion creation and annihilation operators:

$\{a^{\,}_i, a^\dagger_j\} = \delta_{i j}$

— Me@2015.11.13 11:14 PM

# Inception 11

.

Inception contains most of the important topics I have thought of in these few months:

1. Multi-mind

2. Layers of consciousness

3. Dream time

4. Lucid dream

5. Idea/software as a way to save Earth people

.

The deeper the consciousness, the more powerful it is.

The deepest layer is the Light.

The Light of everyone is the same.

— Me@2010.08.06

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— Me@2010.08.09

.

.

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2011.01.15 Saturday (c) ACHK