# Eikonal Blog

## “Law of Attraction”/”Secret”

One more over-hyped superstition/quackery. It probably brought financial health to the originator of idea, but otherwise …

• “Secret” (Afif’s blog; 2010.12.12) – http://atabsh.wordpress.com/2010/12/12/the-secret/
But after actually reading the book it definitely seems a bit over rated…the law simply tells you that if you really focus hard on thinking and feeling about what you dream in life…you’ll get it. Yes yes you read right…so if you focus…think and feel…very hard on becoming a multi-billionaire…guess what..you will become one! … if you really focus on being happy and living safely you simply will …don’t bother if an earthquake, a tsunami, a car crash, a war breaks …you’ll just live only if you focus on it.

It got me wondering about all the people in Africa who die out of hunger, illness, fights… were they really not focusing on being happy? Living with money? Being safe? …are only the US and Europeans the ones who have had that “Secret” since ages or does it only apply to them or ?

## 2010.11.24

### Fluid dynamics

Filed under: complexity, fluid dynamics, physics — Tags: — sandokan65 @ 11:49

## 2010.11.23

### X-Ray Vans on US streets

It is time for tin-foil hats … and (tin-foil) whole-body uniforms.

Related here: “Surveillance, wiretapping, tracking, etc.” – https://eikonal.wordpress.com/2010/09/27/surveilance-wiretapping-etc/.

## 2010.11.22

### Windows Steady State

Filed under: windows — Tags: , , — sandokan65 @ 14:13

Related:

### Unending stream of Facebook privacy news

Filed under: FaceBook, privacy, surveillance — Tags: — sandokan65 @ 10:47

## 2010.11.20

### Data Loss Prevention / Data Leak Prevention (DLP)

Filed under: infosec — Tags: , , — sandokan65 @ 22:05

## Government sanctioned groping

Elsewhere:

### Cell phones radiation

Filed under: health, mobile and wireless — Tags: , , — sandokan65 @ 10:30
• “World Health Organization Says Mobile Phones May Cause Cancer” (SlashDot; 2011.06.01) – http://science.slashdot.org/story/11/06/01/1219248/World-Health-Organization-Says-Mobile-Phones-May-Cause-Cancer
A new study by the World Health Organization (WHO) concludes that mobile phone radiation presents a carcinogenic hazard. Are cell phones going to be the new tobacco, then?” This seems to be a new interpretation of a long-tern WHO study of possible cellphone health risks that had “inconclusive results” last May.
• “WHO report: Cell phone radiation can cause cancer” by Rachel King (ZDNet; 2011.03.31) – http://www.zdnet.com/blog/btl/who-report-cell-phone-radiation-can-cause-cancer/49638
• “Cellphone Radiation May Cause Cancer, Advisory Panel Says” by Tara Parker-Pope and Felicity Barringer (The New York Times; 2010.05.31) – http://well.blogs.nytimes.com/2011/05/31/cellphone-radiation-may-cause-cancer-advisory-panel-says/
• “Should You Be Snuggling With Your Cellphone?” by Randall Stross (The New York Times; 2010.11.13) – http://www.nytimes.com/2010/11/14/business/14digi.html
• …. But the legal departments of cellphone manufacturers slip a warning about holding the phone against your head or body into the fine print of the little slip that you toss aside when unpacking your phone. Apple, for example, doesn’t want iPhones to come closer than 5/8 of an inch; Research In Motion, BlackBerry’s manufacturer, is still more cautious: keep a distance of about an inch. …
• <em.Brain cancer is a concern that Ms. Davis takes up. Over all, there has not been a general increase in its incidence since cellphones arrived. But the average masks an increase in brain cancer in the 20-to-29 age group and a drop for the older population.
• … subjects who used a cellphone 10 or more years doubled the risk of developing brain gliomas, a type of tumor. …

Related here: Taxonomy of cancers – https://eikonal.wordpress.com/2011/01/07/taxonomy-of-cancers/

## 2010.11.15

### vi editor

Filed under: unix — Tags: — sandokan65 @ 14:45

### Cyclic numbers

Filed under: mathematics, number theory — Tags: , — sandokan65 @ 14:14

Definition: (source: [3]) A number with n digits, which, when multiplied by 1, 2, 3, …, n produces the same digits in a different order. For example, 142857 is a cyclic number: 142857 × 2 = 285714; 142857 × 3 = 428571; 142857 × 4 = 571428; 142857 × 5 = 714285; 142857 × 6 = 857142, and so on. It has been conjectured, but not yet proven, that an infinite number of cyclic numbers exist.

Properties:

• $142,857 X 1 = 142,857$
• $142,857 X 2 = 285,714$
• $142,857 X 3 = 428,571$
• $142,857 X 4 = 571,428$
• $142,857 X 5 = 714,285$
• $142,857 X 6 = 857,142$
• $142,857 X 7 = 999,999$
• $142 + 857 = 999$
• $14 + 28 + 57 = 99$
• from [2]: … Multiplication by an integer greater than 7: adding the lowest six digits (ones through hundred thousands) to the remaining digits and repeat this process until you have only the six digits left, it will result in a cyclic permutation of 142857. Example:
• $142,857 X 142,857 = 20,408,122,449$
• $20,408 + 122,449 = 142,857$

Sources:

## 2010.11.12

### Bilingualism, Multilingualism

Filed under: languages — Tags: , , , , — sandokan65 @ 13:00

Related here: Linguistics links – https://eikonal.wordpress.com/2010/08/07/linguistics-links/ | Learning languages / Language acquisition – https://eikonal.wordpress.com/2010/11/12/learning-languages-language-acquisition/ | Language acquisition – https://eikonal.wordpress.com/2010/11/12/learning-languages-language-acquisition/ | Body language – https://eikonal.wordpress.com/2010/10/19/it-journals/.

### Learning Korean

Filed under: languages — Tags: , , , — sandokan65 @ 12:37

More at this blog:

### Learning Japanese

Filed under: languages — Tags: , , , — sandokan65 @ 12:36
• PeraPeraPenguin’s – http://www.yomiuri.co.jp/dy/columns/0002/: This column is a conversation class for learners of the Japanese language. It is written by Hitomi Hirayama, a Japanese teacher with more than 15 years of experience, and the founder of Shibuya Ward-based Japanese Lunch, a Japanese language school serving businesspeople in Tokyo. Her column is carried once every eight weeks in Tuesday’s Language Connection of The Daily Yomiuri, and may be downloaded at no cost from this page after each installment appears in the newspaper. …

More at this blog:

At this blog:

## Language acquisition in animals

Related here: Linguistics links – https://eikonal.wordpress.com/2010/08/07/linguistics-links/ | Bilingualism – https://eikonal.wordpress.com/2010/11/12/bilingualism-multilingualism/.

## 2010.11.11

### Number stations

Filed under: fun — Tags: , — sandokan65 @ 22:47

## 2010.11.08

### Innovation and creativity

Filed under: business, innovation and creativity, mind & brain — Tags: , — sandokan65 @ 12:41

## Partition function $p(n)$

Definition: The partition function $p(n):{\Bbb N}\rightarrow{\Bbb N}_0$ is defined by

$p(n) = \hbox{number of partitions of } n$.

Examples: The partitions of 5:

• $5 = 5$,
• $5 = 4+1$,
• $5 = 3+2$,
• $5 = 3+1+1$,
• $5 = 2+2+1$,
• $5 = 2+1+1+1$,
• $5 = 1+1+1+1+1$.

i.e. $p(5)= 7$.

Properties:

• $p(1)=1$, $p(2)=2$, $p(3)=3$, $p(4)=5$, $p(5)=7$, $p(6)=11$, $p(7)=15$, $p(8)=22$, $p(9)=30$, $p(10)=42$, … $p(100)=190,569,292$, … $p(200)=3,972,999,029,388$, … $p(1,000)=24,061,467,864,032,622,473,692,149,727,991$, …
• An asymptotic formula: $p(n) \sim \frac{e^{\pi \sqrt{\frac{2n}3}}}{4n\sqrt{3}}$.
• Generating function: $F(x) :\equiv \prod_{m=1}^\infty \frac1{(1-x^m)} = \sum_{n=0}^\infty p(n) x^n$ (where $|x|<1$).
• $p(n) = \oint_C \frac{dx}{2\pi i} \frac{F(x)}{x^{n+1}}$
• … [the] main contributions [to this integral] come from poles of $F(x)$, [and] these lie at every root of $1$.
• Circle Method: using the function $T_q(n)$ that estimates the contribution [to the above integral] from the poles on the circle ${\cal C}$ that are near the q-th roots of unity. The main formula of the method is: $p(n) = \sum_{q=1}^\infty T_q(n)$. Taking the finite number of terms in that sum gives surprisingly good results, due to the fact that the estimated function has integer values.

Some applications of Circle Method:

• Lagrange’s conjecture: Each natural number can be expressed as the sum of at most four squares.
• Waring’s problem: Every sufficiently large natural number can be expressed as the sum of at most $w(k)$ k-th powers.
• Example: To calculate the exact expression for the number of ways ($R_k(N)$) to write number $N$ as a sum of $k$ squares (i.e. $N = \sum_{i=1}^k n_i^2$) use the $k$-th potency of the function $f(x):\equiv \sum_{n=0}^\infty x^{n^2}$:
• $f(x)^k = \sum_{N=0}^\infty R_k(N) x^N$,
• and, therefore: $R_k(N) = \oint_C \frac{dx}{2\pi i} \frac{f(x)^k}{x^{n+1}}$

Goldbach’s conjecture:

• Every even number greater than two can be represented as a sum of two primes.
• Every odd number greater than five can be represented as a sum of three primes.

## Congruences for $p(n)$

Ramanujan’s congruences:

• $p(5n+4) \equiv 0 (mod \ 5)$,
• $p(7n+5) \equiv 0 (mod \ 7)$,
• $p(11n+6) \equiv 0 (mod \ 11)$.

Congruences found in 1960s:

$p(A n + B) \equiv 0 (mod \ l^k)$

for $l = 13, 17, 19, 23, 29, 31$.

Example: $p(13^2\cdot 97^3 \cdot 103^3 \cdot n - 6,950,975,499,605) \equiv 0 (mod \ 13^2)$.

Theorem (Ono, 2000): For prime $l \ge 5$ there exist infinitely many congruences of the form $p(A n + B) \equiv 0 (mod \ l)$.

Theorem (Ahlgren, 2000): For prime $l \ge 5$ and a positive integer $m$ there exist infinitely many congruences of the form $p(A n + B) \equiv 0 (mod \ l^m)$.

## Modular forms

Definition: Ramanujan’s tau-function:

• $\sum_{n=1}^\infty \tau(n) q^n :\equiv q \prod_{m=1}^\infty (1-q^m)^{24} = q -24 q^2 +252 q^3 - 1,472 q^4 + 4,830 q^5 - - 6,048 q^6 - 16,744 q^7 + 84,480 q^8 - 113,643 q^9 - 115,920 q^{10} + \cdots$

Definition: $\Delta(z) :\equiv \sum_{n=1}^\infty \tau(n) q^n :\equiv q \prod_{m=1}^\infty (1-q^m)^{24}$ for $q :\equiv e^{2\pi i z}$ (with $\Im{z}>0$).

The $\Delta(z)$ has modular symmetries: $\Delta\left(\frac{az+b}{cz+d}\right) = (cz+d)^{12} \Delta(z)$ ($\forall z$) for any integer $M= \begin{pmatrix}a & b \\ c & d\end{pmatrix}$ that is unimodular ($\det M = 1$). In another words, $\Delta(z)$ is a modular form of weight 12.

Definition: The function $f:{\Bbb C}\rightarrow{\Bbb C}$ is a modular form of weight $k$ if it satisfies the modularity equation $f\left(\frac{az+b}{cz+d}\right) = (cz+d)^{k} f(z)$ ($\forall z$, ($\forall M\in{\Bbb Z}^{2\times2}/\{\det M=1\}$)).

The $\Delta(z)$ is a prototype of all modular functions. Some other examples are:

• $\theta(z) :\equiv \sum_{n\in{\Bbb Z}} q^{n^2}$,
• $E(z) :\equiv 1+ 240 \sum_{n=1}^\infty (\sum_{d|n} d^3) q^{n}$.

Some properties of $\tau(n)$:

• $\tau(n) \tau(m) = \tau(nm)$ if $gcd(n,m)=1$.
• Ramanujan’s conjecture: $|\tau(p)| \le 2 p^{11/2}$ for every prime $p$.
• Generalized Ramanujan’s conjecture: if $f(z) = \sum_{n=1}^\infty a(n) q^n$ has weight $k$, then $|a(p)| \le 2 p^{{k-1}/2}$ for all primes $p$.

Congruences for $\tau$ function:

• $\tau(p) \equiv 1+ p^{11} \ (\hbox{mod} \ 691)$ for every prime $p$.
• $\tau(p) \equiv 1+p^{11} \ (\hbox{mod} \ 2^5)$ for $p\ne 2$.
• $\tau(p) \equiv 1+p \ (\hbox{mod} \ 3)$ for $p\ne 3$.
• $\tau(p) \equiv p^{30}+p^{-41} \ (\hbox{mod} \ 5^3)$ for $p\ne 5$.
• $\tau(p) \equiv p+p^4 \ (\hbox{mod} \ 7)$ for $p\ne 7$.
• These are the only congruences of the form $\tau(p) \equiv p^a + p^{11-a} \ (\hbox{mod} \ l^k)$.

## Blogs

Related pages here: Privacy articles – https://eikonal.wordpress.com/2011/03/09/privacy/ | Personal computer security – https://eikonal.wordpress.com/2011/02/28/personal-computer-security/ | Online privacy tools – https://eikonal.wordpress.com/2010/12/25/online-privacy-tools/ | Unending stream of Facebook privacy news – https://eikonal.wordpress.com/2010/11/22/unending-stream-of-facebook-privacy-news/ | TSA folies – https://eikonal.wordpress.com/2010/11/16/tsa-folies/