Tuesday, November 12, 2013

Time and Relative Dimensions in Cake: Baking a TARDIS (and a Dalek)

"People assume that time is a strict progression of cause to effect, but *actually* from a non-linear, non-subjective viewpoint - it's more like a big ball of wibbly wobbly... time-y wimey... stuff." The Doctor, Blink
There was an incident fifty years ago this month. Another that happened a tenth of that time ago at almost the same time of year. The two events are not connected by cause and effect, except they were today and by a big ball of squeezy wheezy blue stuff.

On November 23 this year we celebrate fifty years of Doctor Who. I'm not that old (though my Mum shares a name of one of his original companions), but I grew up watching the British series. I've been fortunate enough too my son Alex has similarly developed an enjoyment of the program and asked for a Doctor Who cake to celebrate his birthday this year.

What better way to celebrate five and fifty years with a cake of the Doctor's time machine, a blue policebox called the TARDIS? After all, it's rectangular, which hopefully meant it would be relatively easy to bake and decorate. We may have been "forced" to outsource the party to a play centre this year, but at least can put some effort into a decent cake.

Cake decorating seems to have expanded into more general society, judging by the number of cake decorating shops and shows on the topic on Pay TV. I have a couple of colleagues at work who are obsessed by the subject. Neither my wife B nor I are professional, semi-professional or even vaguely professional cake decorators. However, articles on the Internet and various YouTube videos make it seem a lot easier than it actually is.

Armed with a YouTube video and a few blog posts we set about making the TARDIS. Whilst the TV version may be bigger on the inside than the outside ours was just cake on the inside covered with icing.

Baking the actual cakes was the easy bit. B did the orange cake and I the chocolate mud cake (sans coffee). Both recipes are delicious. That night we also made the chocolate modelling paste to construct the outer shell of the TARDIS cake. We used melted white chocolate, corn derived glucose syrup and blue gel dye. This formed a thick blue dough which we rolled up and left overnight and into the next day.

I printed out a picture of the TARDIS as a template, but it was too large. How large should the template be? This is where relative dimensions come in, along with a bit of math. Yes, mathematics is useful!

Volume (V) = height (H) x width (W) x depth (D)

First find the maximum volume of cake available for use (Vc) by using the above equation (Vc = Hc x Wc x Dc) and the dimensions of the cake. Also we need to calculate the relative scale of the TARDIS (t) by using the dimensions of the template (m) where the dimensions can be written as a ratio with one side = 1. Despite the template being only two dimensional we know the depth = width as the base of the TARDIS is square. We need

Vt = Ht x Wt x Dt = (Hm x Wm x Dm)/Dm . Because of the square base this simplifies to Vt = Hm/Dm (neglecting units here).

For your information, Hm/Dm comes out to be about 1.6. So the TARDIS dimensions are of the ration 1:1:1.6.

If we let H, W, D be the dimensions that we'll use for our cake and taking advantage of the fact that the base is square then we get:

D = (Vc * Dm / Hm) ^ 1/3
W = D
H = Hm/Dm * D

And those are the dimensions that you need to make the cake. This meant carving the cake into blocks and pasting together with butter cream. The whole lot was covered with butter cream. We then cut out the four vertical sides of the TARDIS from the blue chocolate modelling paste with white icing for the windows and black writing icing for details. I printed the signs on ordinary paper and cut them out - they stuck easily enough to the chocolate.

And there you have it!

Alex gets a second birthday party at childcare, where he has a Doctor Who obsessed teacher. So we made a simpler Dalek cake using leftover red fondant from the previous year's birthday cake (briefly microwaved to soften), liquorice strips and chocolate coated marshmallows.

Now I've educated you about some mathematics, maybe you would like to read Andy Connelly's article in the Guardian about the Science of Cake.

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