imagine the speed of light is just 100km per hour

100 km per hour is equal to 27.8 meter per second. which is a high speed for driving, but really slow speed for molecule.

beside of special relativity effect, there are much more funny things will happen. if any one who like to look for the effect due to special relativity, one can set the speed of walk of normal people ( 4km per hour ) to be 4% of speed light in any simulation in the web. or for cycling ( 10 to 20 km per hour) is 15%, and a normal driving will be 50%, the special relativity effect become obvious at this speed.

never the less, the things become funny is due to special relativity, which set a maximum speed be the speed of light.

the first thing come up in my mind is, boiling a water. according to statistical mechanic, the average speed of particle is given by

v = Sqrt [ (2 R T ) / M ],

where R is a physical constant (=8.314472), T is temperature, and M is a molar mass of a particle.

for water, the mass is 16 +2 = 18 gram = 0.018 kg.

thus, for room temperature, which is 300K, the average speed is 526 meter per second! which is much faster then the speed of light!, thus the physic is not applicable in this case.

the correct physics for relativistic particle, which moving very close to the speed of light, is by the Maxwell-Juttner distribution.

we don't have to go to that mathematics. all we have to know is, there is no more boiling water, even liquid water does not exist!

how about air? air is mainly composited of nitrogen gas, the molar mass is 0.014 kg , thus, the highest temperature is 2K. , which - 272 degree! and nitrogen will be solid in the temperature!

WordPress VS Blogger

i just open a blog in WordPress, more correctly, moved a blog from here to there. coz WordPress support Latex, which i can type equation. hope blogger support Latex soon, then i move back to here.

i like Blogger more.

1. it can import google doc without any problem.
2. it is faster, i mean, load faster, and preview is quick and direct
3. the sitting in here is easy to understand
4. the archive can be expand and use it as a blog entry.
5. better integration on other google product another things, like picture, youtube, just use HTML embed.
6. the format can be changed, even you use some template, but you still can change to font, color, apparent, which WordPress cannot, it only allow you to change the BG. sucks

WordPress has its own advantage

1. no need to say, it support Latex
2. it has blog calendar
3. more secured.
4. more notification?

may be i am new to there, so, just feel odd except can post latex~

Jump!

imagine there are 2 suns

we live in earth, which around the sun. the earth orbits around the sun like a perfect circle. because of this circular orbit, the earth's temperature changes little bit. average is 13 degrees and from -89 degrees, to 58 degrees. see the following graph:

Mean January air temperature for the Earth's surface, 1959-1997. 


This is the temperature distribution of earth. most temperature is around 0 to 40 degrees. compare to other planet, like mercury, its surface temperature is as high as 200 degrees and due to this high temperature, small gravity and strong solar wind, all air of it are gone, evaporated! and compare to mars, the average temperature is -47 degrees.

thus, if the earth is not move like a circle, it will get very hot when close to sun, but very close when far away. this big temperature different makes life hard to exist. this is because no know life form on earth can cope with such big temperature different. and also, the protein, and cell membrane cannot stand for this temperature change. but never the less, there may be some life form can stand with this change but we just not discover it yet.

In additional to temperature, the weather also goes crazy. the weather on earth is mainly coz by the temperature different on earth. the hot air goes up and cold air goes down and it makes the rain and weather! so , fluctuation on temperature will coz large change in weather.

OK. what is it about "if there are 2 suns" ? if there are 2 suns, then the orbit of the earth will but so complicated and a simple circular orbit does not exist. some orbits may just therefore, if there are any planet with 2 suns, their orbit is always irregular. and an irregular orbit will result large temperature different.

moreover, our earth motion creates day and night, for so many year, it just changes a bit. and it help creature build a biological clock. but when there are 2 suns, the day and night will goes crazy. one tricky thing may happen is the cycle of the 2 suns are in prime number. say, 1 sun goes 7 hours for completing a cycle while another sun is goes 13 hours. thus, a complete cycle is 7x13 = 91 hours ( the LCM). with in this 91 hours, the day and night time is like this:


you see there are very short day and night some time, while very long sometime. this again, it very difficult for creature to adopt or to develop a energy spending and storing style, which it what the biological clock for. the clock tell it, it is time to spend energy, and it is time for eat, store some energy. Never the less, there many be some creature in space can stand for this crazy living style.

the day time and night time, positive is day, negative is night. the x-axis is hour.

for comparing, this the the day and night of earth.

(* graph by wolframalpha.com *)

there fore, when scientists are looking for some planet that may have life form. they always looking for a single sun system. because it can have circular orbit. and stable orbit.


**************
there may be a stable orbit for 2 sun system. the 2 suns are orbiting each other close by and the planet just far away of them. when looking at far away, the 2 closed-sun like 1 single sun. the other way is 1 sun is so big and the other is like a planet circulating around. it is similar for a bigger size solar system, while the Jupiter becomes a sun.

but in the case the 2 suns are similar size, and the planet are not far away, there are not stable orbit on it.

a little reminder about critical thinking

as i a half nuclear scientist, i have some degree of critical thinking and i use it almost everywhere in my life. and i hope, ordinary people, especially when reading newspapers and chinese. in the matter of fact, the knowledge level of chinese is high but the critical thinking is low.

the basic is really simple, well, the simple thing is the hardest thing to do, like changing your habit.

questioning on relationship, on the reason for cause and consequences. 


for example, does the background of a politician really that important? is the honestly of a politician is a must? people always demand many criteria on a position. But most of it, only have statistical relation but not a logical relation. people believe horoscope affect their life, they sure there are some relation between the position of star and fate, but they don't know that it is just a statistical relation, not a logical one.

what is logical relation? a physical law is a logical, a math theorem is logical, which is undeniable, inescapable that if A happened, B must follow.

what is statistical relation? the relations are based on statistic, like "Starbucks coffee is tasty" means it is tasty for most people, base on large number of sample. but it does not mean it MUST tasty. that is the different. and by the way, in this special case, "tasty" or not is really personal. another example is "it is 50% that tmr is sunny." that does not mean tmr must sunny, but it is just a chance. when talk about chance, that lead to another blog to explain. since there are at least 2 scientific ways to define what is chance.

暨南大學圖書館失物招領狀

紫色水壺：古有云：「永靈刀，食材回春；紫紋壺，注水不漏。」本以是虛言，今於圖書館一詳，果真不假。初見紫輝攏於此身，化作靈光衝至天廳，轉瞬之間及其靈光盡失，殘損之軀已無鎮八方定四夷之猛，須以其命中之擁者重注其魂；灌其靈。

機車鑰匙/紙/筆：機車鑰匙/紙/筆，三樣物品同時間在圖書館發現，或許是某一種神秘的機緣之下，讓他們在圖書館聚首，流連忘返以至於閉館時他們仍依依不捨至於圖書館之內，請認識或是他們的親屬將他們領回，謝謝合作。

灰色連帽薄型外套：預估持有人為身材嬌小，衣料曾多次洗滌，表面產生出多處不規則分布之毛球，除此之外經由鈕扣上端縫線鬆弛的程度，故可以判定此衣服以多次洗滌，唯一無法推斷的僅剩餘遺失動機與失主為何人，這始終是失物招領版的一大遺憾。

強制汽車責任險保險證：水藍白圖紋底，紅方印落款抬頭，文字端正而樸華，內文謹慎而嚴密，條理清晰且文筆著墨細膩，持寶卡可應事故而不慌亂，攜神物可面災險於無拒抗；但需在遵守行政法律一切安全措施等交通條文的大前提之下方能實用；且此神物已授身於人，且不可二主，請持有人速速前往失物招領中心取回。

moRE

Name of wars

When I look at some Japanese history books, ok, I don't understand at all, I just recognize the Chinese letters or the Kanji. One thing I notices is, the name of wars are so different than what we learn in china. And then, I check the wiki, and I found that it is not the problem of Japanese but Chinese!

For example. The Sino-Japanese war, in Japanese, they call it china-japan war. But Chinese call anti-Japanese war.

This term "anti-Japanese" war, if Chinese is still using it, then it shows that Chinese didnot have a proper view of the history but just keep in mind that they are the victim.

In every battle or war in the history, the name of those never indicate the victor or loser, the attacker or defender. This is because of an unbiased view. Can you imagine we call the 2nd world war as anti-axis war? Or anti-Nazi war? The civil war of north america be the anti-north or anti-south war? No, because those biased name distorted the understanding of the war. And also, we don't know which side is good or bad, since war is inhuman in anyway. As war is not about right or wrong or justice but just victor or loser, tactic and strategy.

Anyway, when the day Chinese can say it is the china-japan war instead of anti-Japan war, that is the time Chinese can walk out the shadow of it.

Never the less, I truly believe that Chinese government means to keep that name and educate to their people, coz they think that can take most advantage against japan in any political issues. It is just like "you are criminal 60 years ago. Although you are clean after that, but you are still criminal, so shut up and listen to me."

If we careful enough , we can see, when Chinese government is losing on the negotiating with japan, she will bring out the war. In fact, that really annoying Japanese and bring untruth, since china already said forgiven the war many many years ago. but till now aday, they keep on bringing it back on the table, that make not just japan but neighbor countries feel china has no honor and loyalty, just like a little girl.

Slide rule

Before electric calculator was born, scientists, engineers, accountants and many people demand a tool for accurate calculation without paper and pencil.

After the discovery/innovation of log function. Slide rule was born.

The significant of log function is, it turns a multiplication/division into simple add/subtract. Because:

Log( m x n ) = log( m ) + log( n )

For example:

100 x 1000 = x

We can directly multiple and give the answer, but we can also take log from both side.

Log( 100 x 1000 ) = log ( 100 ) + log ( 1000 ) = log ( x )

2 + 3 = 5 = log ( x )

then, we inverse the log, which is 10^( ). More detail :

If : Log ( x ) = y

Then : x = 10^( y ) , by 10^( log ( x ) ) = x

Back to the topic,

5 = log ( x ) => 10^5 = x

See? For this simple illustration, the multiplication become intuitive adding!

If we have a ruler, on it, already marked the log of number. I. E., the numbers are not evenly distributed on the ruler, not same distance between 2 to 1 and 3 to 2, but marker of 2 is at length log (2) beyond marker of 1, marker 3 is at length log (3) beyond marker of 1, which is to say, a log scale.

Make 2 of such kind of ruler, then we are having a slide rule!

You can pick 2 ordinary rulers and try to do adding and subtraction, but it is naive and boring.

When you have 2 rulers in log scale, things are wonderful! When you adding length, "adding" number, you are actually doing multiplication!

Now aday, there are many function on a slide rule. And they no longer in ruler form but a circular form.

The simplest way to do calculation on slide rule is remember follow principle.

There are many rows on one slide rules. Basically C and D.

The number(x) in these row is read as C(x) = log (x) and D(x) = log (x), when you adding C row and D row, you are doing:

C(x) + D(y) = log (x) + log (y) = log (x * y) = D (x * y)

or

C(x) + D(y) = D(x*y)

The thing inside the log is the answer you want.

The actually step is for doing is, align D(x) by C(1), then read the D row on C(y). Simple!

There are other rows:

A(x) = B(x) = log(x^0.5)

K(x) = log(x^(1/3))

Cl(x) = log(1/x)

L(x) = log( 10^x ) = x

LL2(x) = log ( ln^(x) ), ln is natural log , x from 1.11 to e

LL3(x) = log ( ln^(x) ) x from e to 20000

S(x) = log ( sin(x) ) , x from 0 to 90 degrees

T1(x) = log ( tan(x) ) , x from 6 to 45 degrees

T2(x) = log ( tan(x) ) , x from 45 to 90 degrees

ST(x) = log ( tan(x) ) = log ( sin(x) ) , x from 40' to 6 degrees. Since sin and tan are almost the same in this small angle.

another way to read is :

A and B row is square of D row.

K row is order 3 of D row.

Cl row is inverse of D row.

L row is log of D row, which has a normal scale.

LL2 is exponential of D row in range of 0.05 to 1.

LL2 is exponential of D row in range of 1 to 10.

S row is arcsin of D row, in range of 0.105 to 1.

T1 row is arctan of D row in range of 0.105 to 1.

T2 row is arctan of D row in range of 1 to 9.5.

ST row is arcsin or arctan of D row in range of 0.0116 to 0.105.

See? The slide rule has every function!

and it has memory if there is a pointer!!

The last thing to keep in mind is, the digit has to keep in mind, for example, 2 x 6 = 1.2 in slide rule, but you knew that the 10 is missing.

or, you can use A row and B row. A(x)+ B(y) = A (x*y), and the range of A is from 1 to 100!

A wonderful thing on slide rule is, it is very good in calculating the form :

u x v / w

You just have to align D(u) with C(w) and read the D row on C(v)! One step, KO!

There are many fancy calculations on slide rule. Buy one now! ( interesting people can contact me and I send you one with price. ;P )

Slide rule 2

We knew that slide rule can do multiplication. This post is focus on the applications.

Ratio:
That is the simplest function I can think of. For example, exchange rate. Say, 1 USD = 7.78 HKD. We simply set the D row be USD, C row be HKD. Align the C(7.78) on D(1), then done! If you want to check 4.5 USD = ? HKD, look at the D(4.5) and find out the number in C row.
10 HKD = ? USD, look at the C(10) and find the number on D row.

Given the c and a, find out the b in a^2+b^2= c^2 :
since b = Sqrt(c^2-a^2) = Sqrt( (c+a) (c-a) ) = Sqrt(c+a) Sqrt(c-a)
Thus, we have to use the A and B row, which is Sqrt root.
First, locate A(c+a) and align B(1) on it, check the B(c-a) and read the D row.

Square of x = x^2 :
using the fact that A(x) = D ( Sqrt(x) ) <-> A(x^2) = D(x), so simple read the A row of D(x).

Division x / y :
Locate D(x) and align C(y) on it, read the D row on the C(1). This is a reverse process of multiplication! We really do thing in backward sequence!
another way to do this is using n / m = n x 1/m, thus, Locate D(n) on Cl(1) and read the D row on Cl(m).

another use of Cl row :
For ruler shape user, you will find out 2x6 will be out range, the ruler is just long enough. So, you are going to use the Cl row. The principle is, n x m = n / (1/m), a multiplication is equal 2 times division. The step is: align D(n) on Cl(m), than read the D row on Cl(1). You will find that the answer is 10 times lesser. This out-range problem can be overcome by a circlur slide rule.

10^x :
we have to use the L row. locate the L(x) and read the corresponding C row or D row, no need to slide.


log(x) :
if x <10 , use D(x) and read L row if 100>x >10, use D(x) and read L row, but add 1.
if 1000>x>100, add 2 on the L row.


e^x :
from the fact that, if LL2(x) = D( ln(x) <-> LL2( e^x) = D(x). so, read the LL2 row on the D(x). and if it is out range, use LL3.
e.g.

a^x :
this times, we have to use the fact that a^x = e ^ ( x ln(a) ). so, we align the C(1) on LL2(a), then the LL3 or LL2 row on C(x), the decision on whether LL2 or LL3 is on the range of the result. The reason for this is, LL2(a) + C(x) = log( ln^(a) ) + log (x) = log ( x ln(a) ) = D( x ln(a) ) = LL2( e^ (x ln(a) ) = LL2 (a^x).
e.g.
2^1.1 : LL2(2) + C(1.1) = LL2(2.14)
2^2 : LL2(2) + C(2) = LL3(4)
3^n : LL3(3) + C(n) = LL3( 3^n)


log(x, base a) :
log(x, base a) = log(x) / log(a). this is quit complicate as there is only 1 L row.


x + y :
L(x) + L(y) = D( 10^x) + D (10^y) = D (10^(x+y)) = L (x + y)
align D(1) with L(x), read the D row of L(y) = D(z), remember, and read the L row on D(z).

by applying the above methods, one can calculate everything. The master of slide rule skill require deep understanding of log function, and inverse function. Thus, this is a very good tool to train mathematical skill.

for example,

Sqrt( x^2 + y^2 ) :
use square method, and apply addition method, then use square root method.