## Projection vectors

I had a very interesting conversation with my colleague about projections of reality. When you take a picture of a scene, what you are doing, is to capture and preserve the light that is reflected off the three-dimensional scene and projected on a flat two-dimensional surface such as a film, or a sensor chip. Using mirrors, lenses, and all the other photonic gizmos, we are able to shrink the pictures, create effects on the projection, or to just make edits after the projection has been made.

What happened however, was that a three-dimensional reality is captured somehow in a two-dimensional world. The picture, is a projection of reality at some point of time. That is what we were referring to as projections.

We were speaking more about how we perceive the world as projections – cast not on a surface but in our minds. Each and everyone of us experiences the world differently but the richness of the world is not fully captured by the experience we have because we are limited in our ability to perceive. It is as though our ability to perceive each represents a dimension. Not just the five senses of sights, sounds, smell, taste and touch but there are psychological lenses, cultural lenses by which we perceive and experience the world, and recognise patterns formed from combinations of those senses, and our logical or irrational interpretation of reality, or even events, how they had been sequenced, how they line up in the dimension of time.

If the richness of reality contains N-dimensions, then our ability to perceive is often limited to (N-x) dimensions, where x is an unknown non-negative number and potentially really large. We don’t get to really experience reality, only what can be captured by that (N-x)-dimensional hyperplane that will never truly encapsulate the contents of the N-dimensional hyperspace that the reality consist of.

I hope to be able to explain this better some day – but for now, this hopefully suffice to help encourage me to develop further my capabilities to grow my hyperplane of perception.

## Insuring Nothing

Tyler Cowen mentioned something about product insurance at one part of his book, Discover Your Inner Economist. He says that one should not argue with his wife when she insist on buying product insurance even when you know that the results are economic analysis are at your favour. Presumably, there are some other cost-benefit analysis taking place, at the level where the cost of winning the argument greatly overwhelms the benefit (which of course is the cash saved on the product insurance). The Economist asked why people continue to buy them even when products are unlikely to fail, which means that these product insurances are immensely profitable for the electronics retail sector. The researchers who examined purchase data from a big electronics retailer for over 600 households from November 2003 to October 2004 concluded that the purchases were linked to the shopper’s mood. Of course, a less-than-rational wife might be the explanation, but even the wife has a sound explanation for that:

[…] the emotional tranquillity that comes with buying a new warranty is not in itself without value, even if “rationally, it doesn’t make sense”.

But I find an ingredient missing in this story; the researchers probably falsely assume that all the shoppers have got the same level of perceptiveness. And I believe perception have all to do with the purchase of product insurance. Think about it, when was the last time you had a product which failed and the warranty period was just over and you blame yourself for not buying additional coverage? But how about the last time when you did buy the product insurance and it didn’t fail at all within the span of its usage, not once? Just like the belief that we’re unlucky enough to always join the slowest queue in the supermarket; our erroneous perception of the frequency we get unlucky can make us more frustrated with a product insurance unextended than a product which didn’t fail after we bought the coverage despite the fact that they probably inflicts the same cost on you. Obviously it actually hurts you more when you think back and regret not extending coverage; you probably won’t even think back on how stupid you were to buy product insurance for a reliable product since you’re using it happily.

This creates a bias for purchasing product insurance. Our faulty perception supplements our faulty memory in suggesting that buying product insurance would be the wise choice, going by the seemingly sound argument of ‘if the product fails, I’m protected; and even if it doesn’t, I get a peace of mind plus the retailers deserve the reward if they recommended me the durable kind of good’. You could very well have realised that if the product was that durable the manufacturer would already have taken a cut for that on the retail price and that if the product ran a high chance of failure the retailer wouldn’t even offer you the product insurance in the first place. And if your wife has anything to say about that, it’ll probably be “Must you be that calculative?”