In the diagram, the circumference of the external large circle is
1) longer, or
2) shorter, or
3) equal to,
the sum of the circumferences of all inner circles centered on the common diameter, tangent to each other.
Sunday, 23 June 2013
Quiz
In the diagram, the circumference of the external large circle is
1) longer, or
2) shorter, or
3) equal to,
the sum of the circumferences of all inner circles centered on the common diameter, tangent to each other.
Saturday, 15 June 2013
Facebook & Ranking Elo Formula
Eduardo Saverin (now a Singaporean billionaire investor) gave the wrong Elo formula to his Facebook co-founder Mark Zuckerburg, both of them became 'accidental' billionaire. Watch the video clip in the movie "Social Network":
http://m.youtube.com/#/watch?v=BzZRr4KV59I
The Elo formula is based on the theory of Normal Distribution with Logarithm function, from base of exponential e to base of 10.
The correct Elo Formula should be :
$Latex \boxed
{
E_a =\frac{1}
{1+ \frac{1}{400}.\Huge 10^{(R_b - R_a)}
}
}$
$Latex \boxed
{
E_b =\frac{1}
{1+ \frac{1}{400}.\Huge 10^{(R_a - R_b)}
}
}$
Eduardo had missed the power ^ below:
http://m.youtube.com/#/watch?v=BzZRr4KV59I
The Elo formula is based on the theory of Normal Distribution with Logarithm function, from base of exponential e to base of 10.
The correct Elo Formula should be :
$Latex \boxed
{
E_a =\frac{1}
{1+ \frac{1}{400}.\Huge 10^{(R_b - R_a)}
}
}$
$Latex \boxed
{
E_b =\frac{1}
{1+ \frac{1}{400}.\Huge 10^{(R_a - R_b)}
}
}$
Eduardo had missed the power ^ below:
白马非马
韓非子是战国法家, 荀子的高徒, 秦始皇宰相李斯的同学。他说"白马非马", 即白马不是马, 可以用集合論(Set Theory) 证明:
Let 马 = H = {w, b, r, y ...}
w : 白马
b : 黑马
r ：红马
y：黄马
Let 白马 = W = {w}
To prove:
H = W
We must prove:
H ⊂ W and H ⊃ W
From definition we know:
$latex w \in H \supset W $
$latex H \nsubseteq W $
$latex \implies H \neq W $
白马≠马
白马非马
[QED]
其他例子:
木魚非鱼
Let 马 = H = {w, b, r, y ...}
w : 白马
b : 黑马
r ：红马
y：黄马
Let 白马 = W = {w}
To prove:
H = W
We must prove:
H ⊂ W and H ⊃ W
From definition we know:
$latex w \in H \supset W $
$latex H \nsubseteq W $
$latex \implies H \neq W $
白马≠马
白马非马
[QED]
其他例子:
木魚非鱼
Thursday, 13 June 2013
Tuesday, 11 June 2013
Sunday, 9 June 2013
Friday, 7 June 2013
More on Linguistic "Half Life"
Proto Indo-European and Chinese in the Late Neolithic Age
后新石器时代的原欧-印语与汉语
Tsung-tung Chang[張聰東] 1988:
“Indo-European vocabulary in Old Chinese: A new thesis on the emergence of Chinese language and civilization in the Late Neolithic Age”, Sino-Platonic Papers 7, Philadelphia.
This Chinese scholar wrote the 1988 paper on the Chinese language origin with the proto-Indo-European (proto IE).
Interestingly very similar 'coincidence' occurs in 1500 words between Chinese and proto IE:
Take -> 得 tek (ancient Chinese sound as in Fujian dialect today)
Mort -> 殁 mo
See -> 视 see
Cow -> 牛 gu
...
http://www.sino-platonic.org/complete/spp007_old_chinese.pdf
After the Tower of Babel, God confused the human into different languages, but by the linguistic 'archaeology' 'Half Life' Theory, we can deduce ~ 4,900 years ago the Chinese and the Germanic (English, Denmark, German ...) shared the same common linguistic root.
The ancient Chinese scholar Xu Shen许慎(东汉 : 58 CE -147 CE) who compiled the first dictionary on Chinese characters and its origins "说文解字", wrote that the character :
白 (White) is "从入合二" : from the origin character 入 together with 2 (二).
For 2,000 years nobody understood what Xu meant or he had made a mistake for the character 白 (white)。
Now from the "Half-Life Theory", we trace to the Germanic common root, Chinese scholars confirm Xu was right.
The character '入' pronounced in ancient sound (still remains in southern dialect like Fujian in Singapore / Taiwan) is *njub, '入' is the ancient character for 乳头( nipple). *njub sounds like 'nipple' in Germanic languages.
白 means use 2 fingers or 2 lips (合二) to squeeze out white milk from nipple (入).
In European languages, 'White' / 'Milk' are also connected in etymology by 'b' 'mb':
English: bleach / milk
Denmark: bleg / maek
Sweden: blek / mjök
German: bleich / milch
Dutch: bleek / melk
Ancient Irish: mlicht/blicht (bleacht)
Polish: biały / mleko
Conclusion :
白 => milk => white (color)
-----------------------------------------
Language 'Half-Life' Formula
$latex \boxed{T = \frac{\log N} {2.\log 85\%}}$
(N= % of vocabulary with common root)
Modern English & German:
N=60%
=> T =1.561 (K-Yrs)
=> 1,561 yrs ago the 2 languages shared the common root @ 449 CE. [confirmed by historians]
Genesis 11:1-9 Tower of Babel
God confused Noah's descendants from their common language root 'Proto-Canaanite' to different languages:
Phoenician
Greek
Aramaic -> Arabic / Jewish
Chinese
...
1. Chinese / 日耳曼語系 Germanic (English) have common root T = 4,951 yrs ago [尧/舜]
2. Chinese / Latin (French)
T= 3,700 yrs ago [夏/商]
3. Chinese / Persian (Iran) T= 3,100 yrs ago [商/周]
Proof: [Chinese / Germanic / Latin Common Roots]
背bei -> Back
爸ba -> papa
鳳feng -> [Phoin] = Phoenix [Greek]
殁mo (=死) -> Mort (English) / Mort (French)
民min -> man (eng) / mann (German)
核he /ker -> Heart / kerd (Kernel)
酸suan -> sour
后新石器时代的原欧-印语与汉语
Tsung-tung Chang[張聰東] 1988:
“Indo-European vocabulary in Old Chinese: A new thesis on the emergence of Chinese language and civilization in the Late Neolithic Age”, Sino-Platonic Papers 7, Philadelphia.
This Chinese scholar wrote the 1988 paper on the Chinese language origin with the proto-Indo-European (proto IE).
Interestingly very similar 'coincidence' occurs in 1500 words between Chinese and proto IE:
Take -> 得 tek (ancient Chinese sound as in Fujian dialect today)
Mort -> 殁 mo
See -> 视 see
Cow -> 牛 gu
...
http://www.sino-platonic.org/complete/spp007_old_chinese.pdf
After the Tower of Babel, God confused the human into different languages, but by the linguistic 'archaeology' 'Half Life' Theory, we can deduce ~ 4,900 years ago the Chinese and the Germanic (English, Denmark, German ...) shared the same common linguistic root.
The ancient Chinese scholar Xu Shen许慎(东汉 : 58 CE -147 CE) who compiled the first dictionary on Chinese characters and its origins "说文解字", wrote that the character :
白 (White) is "从入合二" : from the origin character 入 together with 2 (二).
For 2,000 years nobody understood what Xu meant or he had made a mistake for the character 白 (white)。
Now from the "Half-Life Theory", we trace to the Germanic common root, Chinese scholars confirm Xu was right.
The character '入' pronounced in ancient sound (still remains in southern dialect like Fujian in Singapore / Taiwan) is *njub, '入' is the ancient character for 乳头( nipple). *njub sounds like 'nipple' in Germanic languages.
白 means use 2 fingers or 2 lips (合二) to squeeze out white milk from nipple (入).
In European languages, 'White' / 'Milk' are also connected in etymology by 'b' 'mb':
English: bleach / milk
Denmark: bleg / maek
Sweden: blek / mjök
German: bleich / milch
Dutch: bleek / melk
Ancient Irish: mlicht/blicht (bleacht)
Polish: biały / mleko
Conclusion :
白 => milk => white (color)
-----------------------------------------
Language 'Half-Life' Formula
$latex \boxed{T = \frac{\log N} {2.\log 85\%}}$
(N= % of vocabulary with common root)
Modern English & German:
N=60%
=> T =1.561 (K-Yrs)
=> 1,561 yrs ago the 2 languages shared the common root @ 449 CE. [confirmed by historians]
Genesis 11:1-9 Tower of Babel
God confused Noah's descendants from their common language root 'Proto-Canaanite' to different languages:
Phoenician
Greek
Aramaic -> Arabic / Jewish
Chinese
...
1. Chinese / 日耳曼語系 Germanic (English) have common root T = 4,951 yrs ago [尧/舜]
2. Chinese / Latin (French)
T= 3,700 yrs ago [夏/商]
3. Chinese / Persian (Iran) T= 3,100 yrs ago [商/周]
Proof: [Chinese / Germanic / Latin Common Roots]
背bei -> Back
爸ba -> papa
鳳feng -> [Phoin] = Phoenix [Greek]
殁mo (=死) -> Mort (English) / Mort (French)
民min -> man (eng) / mann (German)
核he /ker -> Heart / kerd (Kernel)
酸suan -> sour
Thursday, 6 June 2013
Wednesday, 5 June 2013
Polymath Project
Polymath Project initiated by Terrence Tao inviting mathematicians worldwide to improve on Yitang Zhang's 70 million bounded gap between primes.
Online Seminar by Terrence Tao on Zhang's paper:
http://terrytao.wordpress.com/2013/06/04/online-reading-seminar-for-zhangs-bounded-gaps-between-primes/
Go to this site to get regular update on progress.
http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes
Online Seminar by Terrence Tao on Zhang's paper:
http://terrytao.wordpress.com/2013/06/04/online-reading-seminar-for-zhangs-bounded-gaps-between-primes/
Go to this site to get regular update on progress.
http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes
Monday, 3 June 2013
Sabbath Number 7
Sabbath Number '7':
1. Sunday: God rested on 7th day, a Holy day.
2. Professors rest on 7th year Sabbatical leave to re-charge: overseas exchange-cum-research paid holidays.
3. All farm lands must rest on 7th year before cultivation again.
4. After 6 years (Grade 1 to 6) and the stressful Primary School Leaving Exams (PSLE), relax on Secondary 1 (Grade 7); then after 4+2 years Cambridge 'O' and 'A' levels high-school pressure, 'honey-moon' in Freshman year (1st year University), or 'switch off' from study in the Army National Service.
5. 哈佛一调查报告说，人生平均只有7次决定人生走向的机会，两次机会间相隔约7年，大概25岁后开始出现，75岁以后就不会有什么机会了。这50年里的7次机会，第一次不易抓到，因为太年轻；最后一次也不用抓，因为太老。这样只剩5次，这里面又有两次会不小心错过(*)，所以实际上只有3次机会了。
人生七年之"痒" (机会)
25: 毕业寻职: 第一痒
32: 结婚成家:第二痒
39: 创业: 第三痒 (*)
46: 名利: 第四痒
53: 中年危机: 第五痒(*)
60: 金盆洗手: 第六痒
67: 夕阳无限: 第七痒
1. Sunday: God rested on 7th day, a Holy day.
2. Professors rest on 7th year Sabbatical leave to re-charge: overseas exchange-cum-research paid holidays.
3. All farm lands must rest on 7th year before cultivation again.
4. After 6 years (Grade 1 to 6) and the stressful Primary School Leaving Exams (PSLE), relax on Secondary 1 (Grade 7); then after 4+2 years Cambridge 'O' and 'A' levels high-school pressure, 'honey-moon' in Freshman year (1st year University), or 'switch off' from study in the Army National Service.
5. 哈佛一调查报告说，人生平均只有7次决定人生走向的机会，两次机会间相隔约7年，大概25岁后开始出现，75岁以后就不会有什么机会了。这50年里的7次机会，第一次不易抓到，因为太年轻；最后一次也不用抓，因为太老。这样只剩5次，这里面又有两次会不小心错过(*)，所以实际上只有3次机会了。
人生七年之"痒" (机会)
25: 毕业寻职: 第一痒
32: 结婚成家:第二痒
39: 创业: 第三痒 (*)
46: 名利: 第四痒
53: 中年危机: 第五痒(*)
60: 金盆洗手: 第六痒
67: 夕阳无限: 第七痒
Sunday, 2 June 2013
Love Math
For those who love Math ...
1x8+1=9
12x8+2=98
123x8+3=987
1234x8+4=9876
12345x8+5=98765
123456x8+6=987654
1234567x8+7=9876543
12345678x8+8=98765432
123456789x8+9=987654321
1x9+2=11
12x9+3=111
123x9+4=1111
1234x9+5=11111
12345x9+6=111111
123456x9+7=1111111
1234567x9+8=11111111
12345678x9+9=111111111
123456789x9+10=1111111111
9x9+7=88
98x9+6=888
987x9+5=8888
9876x9+4=88888
98765x9+3=888888
987654x9+2=8888888
9876543x9+1=88888888
98765432x9+0=888888888
1x1=1
11x11=121
111x111=12321
1111x1111=1234321
11111x11111=123454321
111111x111111=12345654321
1111111x1111111=1234567654321
11111111x11111111=
123456787654321
111111111x111111111=
12345678987654321
1x8+1=9
12x8+2=98
123x8+3=987
1234x8+4=9876
12345x8+5=98765
123456x8+6=987654
1234567x8+7=9876543
12345678x8+8=98765432
123456789x8+9=987654321
1x9+2=11
12x9+3=111
123x9+4=1111
1234x9+5=11111
12345x9+6=111111
123456x9+7=1111111
1234567x9+8=11111111
12345678x9+9=111111111
123456789x9+10=1111111111
9x9+7=88
98x9+6=888
987x9+5=8888
9876x9+4=88888
98765x9+3=888888
987654x9+2=8888888
9876543x9+1=88888888
98765432x9+0=888888888
1x1=1
11x11=121
111x111=12321
1111x1111=1234321
11111x11111=123454321
111111x111111=12345654321
1111111x1111111=1234567654321
11111111x11111111=
123456787654321
111111111x111111111=
12345678987654321
Saturday, 1 June 2013
100-digit Pi
One fine day when we reach above 80 years old, if the doctor accuses us of having dementia, then prove the doctor wrong by shocking him with 100-digit Pi memory :)
With Chinese single-syllable sound for numbers, better still if can sing it as a song, memorizing 100-digit pi is easy!
With Chinese single-syllable sound for numbers, better still if can sing it as a song, memorizing 100-digit pi is easy!
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