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Green Mathematics

Going green is a becoming mantra among individuals and the corporate. This has given rise to initiatives such as minimalist living and in the extreme living off the grid.

In of those moments where there are many things to do and yet feel bored, I hit upon this ideas of defining a recyclability index for some day-to-day items. I am sure there would be many who would have done some serious research is this area, but I felt I must attempt to do somethink on my own.

Yes, I have coined that word for thinking something!

somethink – the act of doing some thinking typically on a problem, or an upcoming PowerPoint presentation!

Thus, here I present a formula for calculating the recyclability index:


Where RI is the Recyclability Index, Cr is the count of number of items that are recyclable and N is the number of components in the item for which the RI is being calculated. EV is the economic value of the component that can be recycled, while RC is the recycling cost of the item being recycled. ρ is the factor that is determined by the nature in which the component will be recycled. The lesser the effort required to recycle the component higher will be the value. A suggested value set is as follows:

  • Re-use – perform life-extending activities: ρ = 1.3
  • Re-furbish – perform some touchup to continue using as intended: ρ = 1.2
  • Re-purpose – perform activities so that it gets used as something else: ρ = 1.1
  • Re-form – perform morphological/chemical/physical changes to become something else: ρ = 1.0
  • Re-fuse – Dispose and let nature decides what happens:ρ = 0.9

‘e’ is the ease or amenability to be recycled. Paper for example is easier to be recycled than plastic. Therefore, paper will have a larger ‘e’ then plastic. A value of 1 is ideal for ‘e’ while 0 is the lower extreme.

Let us take a ballpoint pen as an example.

We can carry out the calculation for this ballpoint pen. We have 9 components and they have been numbered in the figure on the right. The table below depicts the details.


If we make the simplistic assumption that economic value is same as recycling cost per component, and assume that the ink is not to be recycled, then we have RI as (8/9)*(1/9)*(7*(1.0*0.2)+(1.0*0.5)+(0.9*0.6)) = (8/9)*(1/9)*(2.44) = 0.241.

Organizations can create relevant indices for the materials they deal in, to come up with a method to focus on the green initiatives they can then take forward.

note: this is a modification to take into account the suggestion by readers..


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