Mysteries in Maths!

Snell’s law describes how light rays bend when they pass from air into water, as they do when the sun shines into a swimming pool. Light moves more slowly in water, much like the hiker in the snow, and it bends accordingly to minimise its travel time. Similarly, light bends when it travels from air into glass or plastic, as when it refracts through your eyeglass lenses. The eerie point is that light behaves as if it were considering all possible paths and then taking the best one. Nature — cue the theme from The Twilight Zone — somehow knows calculus.

STEVEN STROGATZ

One of many anecdotes I picked up from Steven Strogatz's recent book 'The Joy of X: A Guided Tour of Mathematics, from One to Infinity'. It is a "pop-maths" book designed to re-introduce the subject to people who have long forgotten it! Well worth the read!

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Spiritual Leadership

J Oswald Sanders (1917-1992) was a Christian leader for seventy years. He wrote more than forty books on the Christian life including one book I dip into often, The Incomparable Christ. He was the director of the China Inland Mission (Overseas Missionary Fellowship), where he was instrumental in beginning many new missions projects throughout East Asia. Spiritual Leadership encourages the church to pray for and develop Spirit empowered leaders. People who are guided by and devoted to the Lord Jesus Christ. The book presents the key principles of spiritual leadership. He illustrates his points with examples from Scripture and biographies of men who have led the people of God in history. The book has 20 chapters. I have tried to summarise the main conclusions of these chapters under five key questions. Most of the ideas presented in this article are directly from the book. But I have communicated these ideas in my own way, except where direct quotes are given. Towards the end, I off

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Inconsistency of Moral Progress

If morality, if our ideas of right and wrong, are purely subjective, we should have to abandon any idea of moral progress (or regress), not only in the history of nations, but in the lifetime of each individual. The very concept of moral progress implies an external moral standard by which not only to measure that a present moral state is different from an earlier one but also to pronounce that it is "better" than the earlier one. Without such a standard, how could one say that the moral state of a culture in which cannibalism is regarded as an abhorrent crime is any "better" than a society in which it is an acceptable culinary practice? Naturalism denies this. For instance, Yuval Harari asserts: "Hammurabi and the American Founding Fathers alike imagined a reality governed by universal and immutable principles of justice, such as equality or hierarchy. Yet the only place where such universal principles exist is in the fertile imagination of Sapiens, and in th

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I am what I am by Gloria Gaynor

Beverly Knight closed the opening ceremony of the Paralympics with what has been dubbed the signature tune of the Paralympics. I had no idea Ms Knight is still in the singing business. And clearly going by the raving reviews she will continue to be around. One media source says her performance was so electric that "there wasn’t a dry eye to be seen as she sang the lyrics to the song and people even watching at home felt the passion in her words" . The song was Gloria Gaynor's I am what I am . Clearly not written by Gloria Gaynor but certainly musically owned and popularized by her. It opens triumphantly: I am what I am / I am my own special creation / So come take a look / Give me the hook or the ovation / It's my world that I want to have a little pride in / My world and it's not a place I have to hide in / Life's not worth a damn till you can say I am what I am The words “I am what I am” echo over ten times in the song. A bold declaration that she

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