數學(數字)有它的奧秘之處,如聖經中提及魔鬼的數目是 666 (注:啟示錄13章18節),英文是

Here is wisdom. Let him who has understanding calculate the number of the beast, for the number is that of a man; and his number is six hundred and sixty-six.

有人這樣計算出來:

1 x 6 = A

2 x 6 = B

3 x 6 = C

.

.

.

如此類推。那麼 mark of beast 加起來就等如 666。 用同樣的算式推算,Jesus 的數字加起來,就是 444,正好相對稱。奧秘哉!但要留意的是

'If p then q' is not equivalent to 'If q then p'(p → q q → p).

亦即是說,你父親有鬚並不等於有鬚的便是你父親。所以在電話簿中可以找出很多總數是 666 的名字,但他們並非一定是魔鬼。很可惜香港的中學課程,早已把數學邏輯 logic 剔除掉。當年的決定可能是覺得太抽象,不切實際。但如果能把它結合實際生活的例子來施教,那是多好的啊!

~ 寫於2016年1月2日


Big Bang:

It is about the creation of dimensions during the big bang.

I am not sure if it is the reality during God's creation at the very beginning. Yet, it provides a clue or one of the possibilities during creation.。

The ellipsoid at the bottom is the cosmic microwave background radiation detected in 1964. It is the radiation remained at the very beginning during the universe formation. I think it is the result due to the formation of a 3-dimensional environment from a 2-dimensional spread-out plane or disk. The 2-dimensional spread-out plane or disk was formed from a 1-dimensional line, similar to the burst of a bag of paint dropping from a very high altitude. If you view it from the rim of the plane (disk), you will feel how an ellipsoid was formed. When a 2-dimensional spread-out disk rotated a little bit, a 3-dimensional environment was formed. That is an ellipsoid image emerged.

A similar picture, but not quite, is the nuclear explosion, http://www.youtube.com/watch?v=-22tna7KHzI

References:

1) 科學Infinity In Your Pocket Mike Flynn著 王琳琳、凌雲飛譯

萬里機構•萬里書店出版2012年8月第一次印刷

Infinity In Your Pocket by Mike Flynn (Chinese translation version)

2) A series of related Discovery Science TV programs

3) http://en.wikipedia.org/wiki/Big_Bang

4) http://en.wikipedia.org/wiki/Cosmic_microwave_background_radiation

I hope you will like it and think about the creation of God.

~ written on December 4, 2012


Christian Theology:

Trinity – an attempt to understand it

A line represents one dimension while two lines compose a 2-dimensional plane. If we draw two parallel lines on a piece of paper, they will never meet. However, if we draw a straight line on a paper strip and another on the back of it in exact position as the line on front, they represent two parallel lines. Now, we twist the paper strip and stick the end to the head of the strip. Then, the two independent lines meet and a Mobius strip is formed. That is a circular object (line) is drawn on both sides of the paper without broken interval. Because of such a twist and stick process, two independent lines were transformed into one circular object from a 2-dimensional plane to a 3-dimensional environment. If we view it from an opposition direction, i.e. when a 3-dimensional object enters into a 2-dimensional plane, then two flat independent pieces will be formed.

By the same token, if we add one more line on top of the above two parallel lines, then a 3-dimensional environment is formed. Now, make this line also parallel to those two lines. In this way, all three independent lines (A, B and C) could never meet one another. Similar to above, by twisting and sticking the head of line A to the tail of line B, and the head of line B to the tail of line C, and finally the head of line C to the tail of line A, one circular object (line) without broken interval is formed. Although this object is 3-dimensional itself, most likely, it is a 4-dimensional or higher dimensional object. (However, it may not be. Please refer to question 1 below for more in depth discussion.) As discussed in another webpage of this website, we can find that the 4th dimension and other higher dimensions are also 3-dimensional themselves.

Similarly, from an opposition direction of transformation, i.e. when ONE 4-dimensional or higher dimensional object enters into a 3-dimensional environment, then THREE independent objects will be formed. It helps us understand trinity a lot more. More, because of such head to tail connection, it also helps us understand God’s self-proclamation in Revelation 22:13:

“I am the Alpha and the Omega, the First and the Last, the Beginning and the End."

 

~ written on July 10, 2011

~ revised on July 17, 2014

Related Questions:

1) Is
Klein bottle a 4-dimensional or higher dimensional object?

Suggested solution to question no. 1:

It seems not. Perhaps, it seems not a complete one. Because we human beings are confined to our 3-dimensional environment, any 4-dimensional or higher dimensional object cannot be visualized by us, unless we are able to enter those environments. The above discussion is only a conceptual attempt to understand trinity. As such, we cannot fully understand trinity for we cannot enter to 4-dimensional or higher dimensional environments, especially those higher dimensional spaces. Hence, the bible says, "No one has seen the Father except the one who is from God; only he has seen the Father." (John 6:46)

2) Because time is a fourth dimensional thing, so how does it appear in 3 independent identities in our 3-dimensional world?

Suggested solution to question no. 2:

It may be in this way: First, it is time itself. Second, it is light (electromagnetic wave in more precise term) in particle form. Third, it is light (electromagnetic wave in more precise term) in wave form.

Because in Einstein’s theory, time is closely related to light, so perhaps, time appears in light too in our 3-dimensional world.

~ written on July 17, 2014

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Something Interesting:

I) Some interesting verses were found in Bible, which may correlate with the concept of dimensions.

1) Isiah 34:4.

All the stars in the sky will be dissolved and

the heavens rolled up like a scroll;

all the starry host will fall like withered leaves from the vine, like shriveled figs from the fig tree.

2) Revelation 6:14.

The heavens receded like a scroll being rolled up,

and every mountain and island was removed from its place.

It seems that the 3-dimensional universe becomes a 2-dimensional plane and then being rolled up to form a 1-dimentional line.

II) Shroud of Turin

It is a whole piece of cloth covering the body from head to toe at front and then turning to the back from toe to head. Some time ago, I watch a TV program of Discovery Channel. It described the Shroud of Turin. It said (if my memory is correct) the images in the front and at the back were of the same size. The body of Jesus seemed to shrink to a 2-dimensional plane and then disappeared. (At least, it is one of the explanations and under the assumption that the Shroud of Turin is real.) Normally, the size of the image at front should be larger than that at the back due to body curvature and gravity on the cloth which covering the front part of the body. Maybe, during transformation to a 2-dimensional plane, the process is similar to taking a photo at front and another at back. As such, the images are of the same size.

In this way, Jesus can also pass through 3-dimensional barriers like wall or door by shrinking to lower dimensions, not necessarily going to higher dimensions.

~ Written on January 11, 2017.

The transformation from the 3-dimensional body to the 2-dimensional plane will form two independent objects as mentioned above and illustrated with the help of the Mobius strip. Here, the two independent objects may be the photos of the front and the back of the body. These photos are parallel to each other, so they are independent to each other mathematically. When they are pressed down and the distance between them becomes zero, then they are on the same plane and can freely sliding away from each other..

~ written on January 12, 2017

Related videos:

1) https://www.youtube.com/watch?v=XTtDhvk_aw4&feature=youtu.be (Please press Ctrl key and click)

2)
https://youtu.be/_voTiCTqv4Q (Please press Ctrl key and click)

3)
https://www.youtube.com/watch?v=yAEUbGoYzr8 (Please press Ctrl key and click)

4)
https://youtu.be/bbl4EmoH_jg (Please press Ctrl key and click)

~ written on January 28, 2017

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Personal Opinion on "Free Will Vs Predestination"

    For a long time, maybe over a thousand years of controversial argument on this topic, no absolute solution has yet been concluded. I also think that this is part of the concealed matters which belong to God (Deuteronomy 29:29). we will know completely later in heaven. This topic often comes up to my mind, sometimes agitated by someone else. Sometimes, it pops up in my brain and makes me headache.

    Recently, an idea (personal) rose up. As mentioned in another webpage of this website and also by Dr. Hugh Ross, time dimension is 3-dimensional itself covering our world. Based on this, you can imagine predestination is like a cage in which we can freely move, think, etc. like a bird or a ball bouncing freely inside according to our own will. However, no matter how we act, the outcome will be the same, predestinated. The only difference is when we act differently, we will touch different position of the cage. As such, the cage which is suspended weightlessly in empty space, will move at different directions due to our hit at certain points. The cage will move forward only in the time dimension. It will not turn back, because we human beings are confined to move forward only in the time dimension. Sometimes, the cage will be hit hardly, and so, it will move faster. Sometimes, it will move slower by a hit in the opposite direction. Sometimes, it will even spin.

    Each point in the time dimension refers to certain location of our world. Hence, in each generation or so, there is similarity of certain prophesy mentioned in the bible, related to certain locations, matters or cases. This is due to correlated effect of the cage which is moving, not coming to a stop yet. This however aroused Christians' vigilance (Matthew 25:1-13) at that period of time concerning the prophesies. As time goes by or as the cage moves on, explanations or correlations are being revised. The cage keeps on moving until one day, it stops at certain time and place. At that moment, it may be the end of our world. On the other hand, because we can act freely according to our own will, the cage is therefore driven randomly over the time dimension. The end-time and its corresponding location are then not fixed. We do not know when the end-time will happen according to our limited knowledge, limited to our own dimensions. That may be the reason why Jesus told us in Matthew 24:36 :

 “No one knows about that day or hour, not even the angels in heaven, nor the Son,a but only the Father knew when the end time would come."

a Some manuscripts do not have nor the Son.                     - The Holy Bible : New International Version

    The above discussion is based on the concept that both free will and predestination exist. That however brings out the question of justice on predestination. I believe God will take care of it by and for His everlasting kingdom, omnipotent power and glory. We will know it completely later in heaven.

    Let's pray:

        Our Father in heaven, hallowed be your name, your kingdom come, your will be done on earth as it is in heaven. Although still we have been puzzling over this point for a long time, please give us wisdom to understand more, strength in our belief and loving hearts to help others. And lead us not into temptation, but deliver us from the evil one. For Yours is the kingdom and the power and the glory, forever and ever. Amen.

~ written on August 10, 2009


禱告篇:

2008年6月3日

神啊!請您讓我有一個禱告的心,為中國四川地震的死傷者禱告。我是一個不善禱告的人,但總覺得要……。

神啊!請您叫死者的靈得以安息,傷者的心得到安慰,肉體得以痊癒,親友的愛心、中國人民的愛心繼續如甘露般灑下。

主啊!請您癒合各人哀傷的心,團結眾人救災的靈,努力面前,向著拯救的標桿直跑。

在馬太福音24章中,我們得知天國近矣。地震數目的增加,也如實的反影在紀錄上。

這是一個苦杯,如若能行,請把這些痛苦日子減少。

神啊!請您讓我們有一個傳福音的心,好叫福音傳至地極。

以上不完全的禱告,謹奉主耶穌基督聖名而求。

                                                                                 —阿們

參考:

1)  http://earth.webecs.co.uk/index.htm

2)  http://www.dlindquist.com

3)  馬太福音24章7–8節 :  民要攻打民,國要攻打國;多處必有飢荒、地震。這都是災難(災難:原文作生產之難)的起頭。


健康篇:

世界排名
估計死因
死亡人數
病源
1
呼吸道感染 3,871,000 (只於2001年內) -
2
愛滋病 2,800,000 (只於2003年內)

3,100,000 (只於2005年內)

黑猩猩
-
SARS
696 (由2001年11月1日至2003年5月24日) (WHO數字)
果子狸
-
黃熱病
-
猴子
-
伊波拉病毒
-
猴子、猩猩
-
瘋牛症
-
-
雪卡毒
-
深海魚

參考:

1)  http://www.who.int/csr/sars/country/2003_05_24a/en/

2)  AIDS Epidemic Update: December 2005 by Joint United Nations Programme on HIV/AIDS (UNAIDS) and World Health Organization (WHO), http://www.unaids.org/epi/2005/doc/report_pdf.asp

3)  http://www.avert.org/origins.htm

4) Bible (NIV)-Revelation 6:8    I looked, and there before me was a pale horse! Its rider was named Death, and Hades was following close behind him. They were given power over a fourth of the earth to kill by sword, famine and plague, and by the wild beasts of the earth.

5) 聖經(新譯本)—羅馬書1章24—32節

    人類種種的罪惡

    24因此,  神就任憑他們順著心中的私慾去作污穢的事,以致羞辱自己的身體。25他們用虛謊取代了  神的真理,敬拜事奉受造之物,卻不敬拜事奉造物的主。他是永遠可稱頌的,阿們!26 因此,  神就任憑他們放縱可恥的情慾:他們的女人把原來的性的功能,變成違反自然的功能;27 同樣地,男人也捨棄了女人原來的性功能,彼此慾火攻心,男人與男人作出可恥的事,他們這樣妄為,就在自己身上受到應該受的報應。28 他們既然故意不認識  神,  神就任憑他們存著敗壞的心,去作那些不正當的事。29 這些人充滿了各樣的不義、邪惡、貪心、陰險;滿懷嫉妒、兇殺、好鬥、欺詐、幸災樂禍;又是好說讒言的、30 毀謗人的、憎恨  神的、凌辱人的、傲慢的、自誇的、製造惡事的、忤逆父母的、31 冥頑不靈的,不守信用的,冷酷無情的、沒有惻隱之心的。32 他們雖然明明知道行這些事的人,  神判定他們是該死的,然而他們不單自己去行,也喜歡別人去行。
 


Organic Chemistry

I know this carbon C60 has been synthesized in 1985.

Can anyone tell me whether this C32H16,

C32H32 , C32H32

or C32H48 has been synthesized or not? EMAIL

(written on August 22, 2002)


名人雋語

It is fitting that the Church should make this passage with a clear awareness of what has happened to her during the last ten centuries. She cannot cross the threshold of the new millennium without encouraging her children to purify themselves, through repentance, of past errors and instances of infidelity, inconsistency, and slowness to act. Acknowledging the weaknesses of the past is an act of honesty and courage which helps us to strengthen our faith, which alerts us to face today's temptations and challenges and prepares us to meet them.

                                                                                                                                                   — by Pope John Paul II on 10 November, 1994

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「權力令人腐化,絕對的權力令人絕對的腐化。」 —阿克頓爵士(1834-1902)

Power tends to corrupt and absolute power corrupts absolutely.Lord Acton (1834-1902)

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自古至今)善和惡的爭戰依然沒改變,這個是不會變的。人類的職責就是將兩者予以識別。 —亞拉岡(魔戒)

                                                            —魔戒作者托爾金(J.R.R. Tolkein

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《愛的說明—共勉》

「人們不講道理、思想謬誤、自我中心,不管怎樣,總是要愛他們;如果你做善事,人們說自私自利、別有用心,不管怎樣,總要做善事;如果你成功以後,身邊盡是假的朋友和真的敵人,不管怎樣,總是要成功;你所做的善事明天就被遺忘,不管怎樣,總是要做善事;誠實與坦率使你易受攻擊,不管怎樣,總是要誠實與坦率;你耗費數年所建設的可能毀於一旦,不管怎樣,總是要建設;人們確實需要幫助,然而如果你幫助他們,卻可能遭到攻擊,不管怎樣,總是要幫助;將你所擁有最好的東西獻給世界,你可能會被踢掉牙齒,不管怎樣,總是要將你所擁有最好的東西獻給世界。」  —德蘭修女(印度加爾各答兒童之家牆上的名句)

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天才科學家牛頓說:「上帝的存在,若無別的證據,單單大拇指一項便夠說服我相信。」(請試僅用其它四個手指握一個水杯,你覺得方便嗎?)我們雖然沒有牛頓聰明,一個大拇指或不能夠說服我們,但構造複雜而精密的眼睛,或心臟、肝、胃、肺等,當可說服我們相信創造主吧!故此,神的存在,單就創造上,便有排山倒海的證據。正似幾何學上的公理,求證也罷,不求證也罷,有常識的人都可知曉。 何天擇博士(節錄自:http://www.ccmhk.org.hk/ChineseToday/2004/0410_5.htm

熱力學第二定律(Second Law of Thermodynamics): 在獨立的系統內,「能」的自然交換作用,有用的位能或勢能(potential energy)變為動能(kinetic energy)及熱能,而逐漸消耗了。例如扭緊的發條漸漸鬆懈,直至完全停止;任其自然,不會向相反的方向進行。所以這定律是關於「能」的作用方向問題,即由秩序趨於混亂,組織趨於鬆懈,步步向下。到了「熱平衡」時,宇宙便到了靜止死寂狀態。所以也可稱為「亂度增大律」。那麼,原初的秩序與組織,必由於超自然的工作。只有超自然的神才能使「死」的物質組織為「活」的生命。上帝用泥土造人,便是如此。 何天擇博士(節錄自:http://www.ccmhk.org.hk/ChineseToday/2004/0410_5.htm

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沒有想像力的靈魂,就像沒有望遠鏡的天文台。  ─愛因斯坦

提出一個問題往往比解決一個問題更重要,因為解決一個問題也許僅僅是一個教學上或實驗上的技能而已。而提出新的問題、新的可能性,從新的角度去看舊的問題,都需要有創造性的想像力,而且標誌著科學的真正進步。  ─愛因斯坦

想像力比知識更重要,因為知識是有限的,而想像力概括著世界上的一切,推動著進步,並且是知識進化的源泉。嚴肅地說,想像力是科學研究中的實在因素。  ─愛因斯坦

要是沒有能獨立思考和獨立判斷的有創造能力的個人,社會的向上發展就不可想像。  ─愛因斯坦

科學是永無止境的,它是一個永恆之謎。  ─愛因斯坦

只有為別人而活的生命才是值得的。  ─愛因斯坦

Science without religion is lame.

Religion without science is blind. Albert Einstein

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問:「理論物理之盡頭,會否與宗教相會?」

諾貝爾物理學獎得獎人楊振寧教授答:「http://www.hkpl.gov.hk/chi/scholar.htm(提問時間)(如果沒有記錯的話,多年前他當時大約的意思是,科學與宗教就好像兩條平行線一樣,各自用不同的角度來看同一樣事物。但我覺得雖然如此,兩者之間的鴻溝,卻在續漸縮小,就如大爆炸理論把兩者之間的距離縮小了,而可惜的是Stephen Hawking卻站在另一條平行線上來看這一個現象。)」

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數學可以達到中國人所說的「天人合一」境界,而其他學科的知識,較難了解數學的重要性。  

─丘成桐教授(丘教授現任美國哈佛大學數學系講座教授、香港中文大學崇基學院2001-02年度「黃林秀蓮訪問學人」,曾獲費爾茲獎(Fields Medal),此獎乃相當於數學界的諾貝爾獎。)(節錄自丘教授於香港中文大學崇基學院金禧校慶教育研討會演辭-「現代數學與社會」)


Footprints     ~ by someone I don't know 

One night I had a dream --

I dreamed I was walking along the beach with the lord and across the sky flashed scenes from my life.  For each scene I noticed two sets of footprints in the sand, one belonged to me and the other to the lord.

When the last scene of my life flashed before me, I looked back at the footprints in the sand.  I noticed that many times along the path of my life, there was only one set of footprints, I also noticed that it happened at the very lowest and saddest times in my life.

This really bothered me and I questioned the lord about it.

"Lord, you said that once I decided to follow you, you would walk with me all the way, but I have noticed that during the most troublesome times in my life there is only one set of footprints."

"I don't understand why in times when I needed you most, you should leave me."

The Lord replied, "My precious, precious child, I love you and I would never, never leave you during your times of trial and suffering."

"When you saw only one set of footprints, it was then that I carried you."


德蘭修女在對病患者的關懷中,看到自己服侍的正是耶穌,這也是對我們在幫助別人時所持有的心態作出嚴肅的挑戰。

                                                ~ created on 19 October, 2003


I work, I laugh and I sing.

I learn, I serve and I care.

But I feel I'm weak in them all.

I need to learn how to serve and care more,

So I could work in laughter and sing in joy.

                                                ~ created on 6 January, 2002


A poem to all those job seekers:

Seek and you will be found;

Knock and you will be answered;

Strive and don't lose your faith;

Be patient and there will be ways;

                                                ~ created on 12 November, 2001


最近看過一篇好文章,希望能與君共賞。這是有關地球年齡之迷的文章,亦是我期望了很久的中文相關文章,請從以下網址觀賞:

http://www.ccmhk.org.hk/ChineseToday/2001/0111_8.htm

接下來的討論文章也是十分精采:

http://www.ccmhk.org.hk/ChineseToday/2002/0202_8.htm

http://www.ccmhk.org.hk/ChineseToday/2002/0203_11.htm

讀後感:

對於上文徐又生先生的「科學假設與事實」, 讀後起了些聯想。

因為神是全能的神 , 所以他的能力 , 是不會被我們身處的有限空間 (limited dimensions) 所局限。或者 , 甚至如果這個宇宙是由 n 維空間 (n dimensions) 所組成 , 而 n 是趨向無限大 (n → ∞) , 那麼神是身處至少 n + 1 維空間 (n + 1 dimensions) , 從而有效地管理這個宇宙。但如果是這樣的話 , 神豈不是受到 n + 1 維空間 所限制? 就像主耶穌基督在世時 , 由於自限 (自我限制自己的能力) , 在我們身處的4維空間 , 在前往髑髏地被釘十字架的途中 , 困難地背負起沉重的十字架 , 羅馬兵丁便找來一個古利奈人替他背負。這是不是主基督沒有能力輕輕鬆鬆地背負起十字架呢? 又或者及後 , 他沒有能力從十字架上走下來呢? 這是主耶穌基督自限的表現 , 自限於我們身處的4維空間。回到最先的問題 , 神是不受 n + 1 維空間 (n → ∞) 所限制的。如是者 , 神是存在於 n = ∞ 維空間? 這是一個抽象的概念 , 我們可以這樣想 , 神是不受數學上和科學上 n 維空間的概念所束縛 , 他是有能力打破數學上或科學上的邏輯而行事。

一個古老的問題 : 「神是否可以舉起一塊自己舉不起的石頭?」像上文的推理 , 那既然是一塊舉不起的石頭 , 那麼神是自限於那石頭所處的n 維空間 (n dimensions) , 只要透過 n + 1 (或更大) 維空間而行事便可以了。

(以上純屬個人的意見)

2002年3月22日 


倫文敘的一首「嵌字詩」﹕

天生一隻又一隻,三四五六七八隻。

鳳凰何少鳥何多?啄盡人間千萬石。

這首詩是題在一幅名為「百鳥朝鳳」的畫上。詩人將一些數學計算放在詩中,你能猜得出嗎?只能用乘法和加法,將詩中的數字運算一次,即每個數字只能使用一次,便得出一百這個數字。詩人是利用這個數字來配對「百鳥朝鳳」這幅畫的「百鳥」。

請認真地想想才按答案,這是適合中學或以上程度的題目。「答案」


還珠格格觀後感                              熊吉民

在看過還珠格格的最後兩集後,最大的感受莫過於紫薇所說的「人生,最大的美德,是寬恕!」在面對一路上對他們追殺的仇人,也能化干戈為玉帛,這是一種震撼。

我很欣賞瓊瑤的文采與對人性的透徹了解,她把人性美好的一面都在紫薇的身上拼擦出來了。我們所見的,雖是一個子虛烏有的人物、一個無中生有的故事,但我們所獲得的訊息都是那麼真摯,那麼感人。饒恕我們的敵人,可以做得到嗎?這好像是聖經裡耶穌對我們的教導,我們真的可以做得到嗎?連我們自己都不能肯定。嗚呼!我們的正義感是怎的?我們人類的「義」,在神面前相比之下,只不過是一件「污穢的外衣」。我們能寬恕別人七十個七次嗎?當別人摑你左臉一記耳光,你還能把右邊的臉給他再摑一次嗎?耶穌教我們要愛人如己、愛我們的仇敵。誰不知這個寬恕已包含在愛裡面了。蕭劍因愛他的妹妹,希望她有一個快樂的生活,而把不共戴天之仇也化解了,把殺父仇人也寬恕了。紫薇因蕭劍寬恕了他的殺父仇人,而深受感動,也寬恕了皇后和容嬤嬤。那麼愛是甚麼呢?除了寬恕外,我看還有很多、很多,就如爾康對紫薇說﹕「就算為妳廢了這隻手,我也心甘情願!」又如紫薇的反應:「如果我的眼睛要用你的手來換,我寧願瞎?」朦朧中,這又好像神為了拯救世人的生命,甘願被掛在木頭上,飽受人類的痛苦。這究竟是為了甚麼?為了甚麼?是神啊!難怪使徒約翰把「愛」和「神」劃上等號了。 1999年10月7日

 

Love

Love is patient, love is kind.

Love is not jealous, it does not put on airs, it is not snobbish.

Love is never rude, it is not self-seeking, it is not prone to anger;

neither does it brood over injuries.

Love does not rejoice in what is wrong, but rejoices with the truth.

There is no limit to love's forbearance, its truth, its hope, its power to endure.

-------1 Corinthians 13:4-7


Magic Square has been intriguing so many people for hundreds of years, maybe even for thousands of years from the first magic square emerged in ancient China. Benjamin Franklin is also interested in Magic Square and Magic Circle. He created some of them. I have been thinking to post his work here later.

Magic Circle is also famous, though it is not as famous as magic square. The first famous Magic Circle is created around the 13th century.

Magic Polyhedron is a new invention. I created it when I was thinking to make a 3-dimensional magic cube from a 2-dimensional magic square, and when I later found a magic circle which gave me an idea one night. I converted a magic circle to a magic polyhedron. This discovery really made me exciting and happy. I hope you will enjoy it too.

--(Keith) HUNG Kut Man

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