# A Mathematical “Deception”

### Introduction

People often use visual cues to decide whether or not to buy something. How big are those bananas, so how many should I buy of them? The same question gets asked when buying chocolate for Christmas. I was tidying up after last year’s festivities, and I noticed something about one of the empty boxes. Now seems like a good time to explore it.

### Judging By Its Size

This is a picture the Christmas box, with an ordinary bar of chocolate put on top of it:and here is the same thing seem from the edge:From a visual perspective, you might expect the box to contain more, possibly a lot more, than is in the simple wrapper. You would be mistaken. The simple wrapper contains 350g. The box contained only 320g. I leave it you estimate the ratios of width, height and depth from these pictures.

A look at the internal carrier was also revealing:The individual chocolates are held in the widened “bases” as they appear in this picture. Those things that look like upside-down plastic beakers raise the individual chocolates from the bottom of the box. (The carrier is shown upside-down in this picture.) A comparison of the simply wrapped chocolate with all that empty volume is revealing.

### Next Time You Go Shopping …

Next time I go shopping for Christmas, I will be taking a very hard look at the weights printed on the boxes and wrappers!

## 7 thoughts on “A Mathematical “Deception””

1. Bev Sheard says:

Good post Phil, BUT I do need to ask…… Do you hold the purse strings in your household for food shopping? Those of us who do (and have done so for a very long time!) learnt early that packaging is the budget’s worst enemy!
Do hope you enjoyed those chocolates!

2. Phil says:

I remember hearing about it on the radio, and so I was already aware of it at an intellectual level, but it was not until I went through the above exercise that it really hit home.

And yes, we both did! ðŸ™‚

3. Lina Zampichelli says:

Oversized packaging annoys me. As well as being deceptive, it is a waste of energy and resources. Most of it is non-recyclable so an environmental hazard.
“Why would manufacturers make a package that’s twice as big as the lump of food inside? Simple human behavior is the answer. We have all been guilty of grocery-shopping in exactly the manner food manufacturers want us to: Scanning shelves quickly and making decisions based on simple, caveman-like visual cues. Bright colors: Grunt! Picture of food delicious: Ungh! That one’s big: Slurg! How often have you picked a cereal box or package of potato chips based solely on the size of the bag relative to its price?” From How much for the air?http://www.dailyfinance.com/2009/12/08/how-much-for-the-air-as-much-as-half-of-food-packaging-is-empty/

4. Phil says:

I was tempted to highlight the manufacturer’s motives in my post, but I chickened out.

And thanks for providing that very informative link for other readers. ðŸ™‚

5. Charlotte Ellery says:

Little bite size bizes give me more pleasure, so I would choose the box over the bar even if I get less chocolate. More pleasure – less grams -not a bad deal. Mind you, Lindt chocolate is not Fairtrade, whereas Cadbury Pure Milk chocolate bars are Fairtrade…so in actual fact I would buy the cadbury. Supporting slavery is never glamorous.

6. Phil says:

Hello Charlotte,

Thanks for sharing that.

You are quite right – the variety of flavours and textures that you get in a mix of chocolates is better than the sameness that you get in a bar.

The angle on Fairtrade is new to me – I have learned something this day. ðŸ™‚

7. offpagemaster says:

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