Geeking out is something I yearn to do from time to time. Having seen a documentary on infinity from Netflix last year, I decided to pick up a book on the topic. Beyond Infinity , by Eugenia Cheng , is an excellent guide delving into this mind-boggling notion. In this book, Cheng explores some key aspects of infinity that challenge our intuition and understanding of mathematics: Numbers Numbers Numbers, natural, rational, irrational and real: Cheng explains that these number sets are infinite in nature but some are "more infinite" than others. For instance, the set of natural numbers are smaller than its superset of rational numbers, which in turn are smaller than the set of real numbers. So far so good? But... Infinity is but an abstract notion: It certainly is not a number to which the rules of arithmetics apply: ∞ + 1 = ∞ (addition/subtraction does not apply) 2 ⋅ ∞ = ∞ (neither does multiplication/division) 1/∞ =...
I am not usually a fan of biographies. The narcissist in me says there is no one better to learn from but myself. I have always hold in admiration for Jeff Bezos however, having interned for Amazon.com during my university years. Invent and Wander , written by the man himself, is a great summary of Bezos' philosophies on running his businesses -- namely Amazon, but also The Washington Post and Blue Origin. In particular, a few points caught my eye: Go long: Amazon.com is focused on the long term, and I mean really long term. Bezos even raised the eyebrows of his shareholders on numerous occasions by sacrificing short term profits for what he believed to be worthy long term investments (Marketplace, AWS, Amazon Prime) Focus on customers: F ocus on customers' needs, sometimes even before they know it. If you are obsessed with your customers instead of your competition, you will innovate much more. This was how volunta...
Last year, I took a number of vacations which involved cruising, diving, snorkelling and walking on glaciers. Thinking back on those trips, I could not help but notice that water and ice exhibited different colours in different settings. I decided to dive deeper into the colours of water. Finally, here are my findings. Water’s True Colour The colour of an object mainly depends on the colour of light emitted from it. In the case of water its colour is also affected by factors like light source, absorption, scattering, and suspended materials. Absorption by water is stronger for red light, but weaker for blue light. Water is therefore, intrinsically blue. However, this effect is only apparent when the water is reasonably deep. This is why a glass of water appears colourless whereas a big aquarium looks bluish through the thickness of water. Why is the Sea Blue? I did two cruises last year, one in the Caribbean and the other in the South Pacific. Owing to the depth of the wate...
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