Thursday, 3 December 2009

Where do you want to be in 5 years time?

Could mathematics ever answer this question?

Unusual mathematical studies have got me wondering. Stranger questions than this now have the benefit of a mathematical formula to explain them.

The probability of a biscuit collapsing after dunking in hot liquid is one example. Another memorable piece of work was the formula that explained why cold pizza still tastes good the next day (apparently it’s down to the cheese).

If you are a mathematician and you have worked on studies like these: first and foremost, I salute you; And second, now the big questions about biscuits and pizza have been answered, I’m interested in your thoughts on the following...

Up to your neck in water? Could a simple formula help you swim?

The question “Where do you want to be in 5 years time?” is linear so if my (very) limited formal maths training is correct, this suggests the possibility of a mathematical equation being drawn up.

This question is linear because you have two points, let's call them Point A and Point B. Point A is where you are now. Point B is where you want to be in 5 years time.

Point A is a known/knowable quantity (I appreciate that ‘knowable’ isn’t a maths term but stay with me a little longer maths geniuses!)

Point B is an unknown quantity but the potential to define it exists between the degree an individual understands their position at Point A and the relative difficulty their path from A-to-B represents (based on the Point B that the individual has defined).

For example: if you are at Point A as a student just leaving college with an arts based degree in humanities, and you decide that in five years time (i.e. at Point B) you’d like to be a celebrated rocket scientist, the relative difficulty of the path you have chosen will be high. Much higher than if you had chosen 'Geography Teacher' as your Point B instead.

An additional relationship exists between Point A and Point B that might also help the formula expand. It lies within the experience of individuals who have already reached Point B and how they compare to the individual attempting to move from Point A (to a Point B others have successfully reached).

The relative similarities/differences between the individual at Point A and the individuals already at their target Point B could also enable greater definition of the quotients that decide the relative difficulty of the individual’s five year progression from A-to-B. (Providing the framework for an individual to define both Point A and Point B is also possible but the extrapolation of this might be best left for a later time).

Mathematicians: this will of course be wrong to your trained eyes and minds but, nonetheless, here is a simple formula to get you started with the proving and disproving that you do so well:


A = where you are now

B = where you want to be in 5 years time

x = relative differences to individuals already at point B

n = relative difficulty of proposed route from A-to-B

With the age old biscuit and pizza questions answered by you for all time, maybe the moment has arrived for mathematics to tackle a new question.

I’m not one for throwing down the gauntlet, especially to mathematicians. But let’s pretend for a moment that a gauntlet has clattered to the floor. Are any of you willing to pick it up?

All the best for now,


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Learn how your answer to this question can evolve over time at


  1. can't wait to share this with my dad! thanks Paul!

  2. Would love to hear your Dad's perspective, but only if he's not too busy with biscuits and pizza ;)

  3. UPDATE:

    Well, we got our first feedback from a bona fide mathematician on the above. It said: " The expression in the box is not clearly defined. The author says the left side of the equal sign is "Where you want to be in 5 years time". But he also says that is what B stands for in the denominator on the right. Confusing."

    This feedback helped enormously and the expression in the box has now been updated to correct this elementary mistake. The new expression will still be flawed and wholly inadequate to answer this question but that's not the point. The question remains: Can a mathematical formula provide a framework to answer this question?

  4. Paul, I love the challenge of trying to do this in math, a very logical approach. Two problems come to mind.

    1 - the comparison is between the self and an individual who is presumed to be where the self wants to be. This may work for most standard goals. But if the self is going to a place where no one has gone before, there is no individual to compare and hence provide part of the equation.

    2 - Taking #1 further, the bottom part of the equation creates an impossible solution. With no one to compare to, there is no delta of difference although it can be something approaching infinity. On the bottom you need to determine the level of difficulty of getting there. If it is undefined, it could approach infinity.

    This actually helps us simplify the equation, the infinity above and below on the right cancel each other out. Leaving the individual B = A. A conundrum, no. All change starts with the individual thought, if thought it can be accomplished.

    Wasn't there a popular quote about after all this education, you ended up back where you once were? I need to go look for that.

  5. Steve, you're a genius! I'm also very encouraged by what you have presented, and here's why...

    Your logic in points 1 & 2 is undeniable. I do think there are important external examples to assist an individual's journey from A-to-B but, thanks to you, I now see that they have no part in a mathematical expression.

    I also think there is a strong argument for B = A in the simplified formula you put forward, although it's an argument that philosophy would probably recognise before mathematics (and I say that with the utmost respect for both disciplines).

    I also agree with you that the critical moment on an individual's journey from A-to-B begins with the thoughts of the individual. The equation must therefore quantify or assist these thoughts for the individual if it is to answer the original question.

    To move these thoughts forward, the equation needs to assist the individual's understanding of where they are at Point A. It should also help the individual make a better choice of Point B and assist their transition from A-to-B in the intervening 5 year period.

    I think a way exists to do this, it will need more thought and more contributions from you (and others) but I can't help thinking it's possible :)