## How reasoning on impossible assumptions can be a powerful rule of thought

*Image: Creative commons. An imaginary number* is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i^{2} = −1. The square of an imaginary number bi is −b^{2}. For example, 5i is an imaginary number, and its square is −25.*

**Highlight: “**Microelectronic devices are currently fabricated by using processes that are intrinsically two-dimensional, and the inter-connectivity required in complex systems is achieved by stacking and connecting planar layers of circuits…on the other hand biological structures arise by constrained self-assembly, and are usually three-dimensional (3D)…a new research demonstrates that biomimetic principles of design and self-organization can be applied to generate multifunctional electronic systems of complex, three-dimensional architecture…”

**Insight:** An important field of mathematics deals with so called imaginary numbers* with practical applications in areas such as microelectronics; as a matter of fact most of our modern devices (e.g. mobile phones) exist because of these algorithms. This field makes outrageous assumptions which defies the fundamental rules of mathematics: assuming that the square root of a number can be a negative entity. Yet, by setting accurate reasoning on this single impossible outcome, an entire field of mathematics was developed and the outcomes of the predictions are undoubtedly correct to the point of being the basis of modern electronics!

What this field of mathematics clearly demonstrates is that it is possible to come up with accurate outcomes even based on inaccurate assumptions. The key is to know (and keep track) that the assumption is incorrect but that the logic surrounding it is correct. It is a very powerful trick to reveal hidden outcomes which would otherwise remain invisible by applying conventional logic.

This mindset can be applied to business: sometimes businesses have to deal with complex happenings that don’t seem to have any apparent solutions. Yet, looking at problems from another perspective and anticipating changes to come based on impossible assumptions can help to forge strong strategies.

For instance lets imagine the following scenario: an insurance & financial advisory company is about to launch their new offering for retirement. Like it is common practice before the launch of a new insurance package, they develop a computer model which simulates various scenarios based on in-house algorithms developed by their analytical mathematicians. One of the tests involves running a range of impossible outcomes and in this particular case one of these assumptions is that everyone in the United States lives up to 100 years hold (obviously impossible). While running this assumption into the model an unusual behavior is noticed in the algorithm and quickly rectified. Once fixed they continue to run the models based on realistic life expectancy assumptions based on real life data and the product is soon after launched. The point here is that without this impossible assumption the error would not have been noticed as the odd outcome remained too small to be seen under normal realistic assumptions…

Are you stuck with a complex problem that does not seem to have any solution? If so, perhaps try the above approach by projecting outcomes based on false assumptions; you may be surprised with the outcomes…

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*What is Biomimetics:** the field of gaining inspiration from nature first to solve some of our most difficult challenges. Instead of coming up with our own solutions to a problematic, the odds are that species or natural systems on the planet already offer an ultimate solution. This simple fact is also another strong case to preserve species at all cost as the intellectual heritage contained within or through the study of species is both irreplaceable and invaluable…*