Posts Tagged ‘mathematical functions’

Guest Post: Joseph’s Life as a Mathematical Function

For a change of pace, I have a guest blogger this week. Elijah is 15, homeschooled, and apparently has way too much time on his hands.

Joseph’s Life as a Mathematical Function

by Elijah Van Vlack

So a few weeks ago Matt asked me the question of which mathematical function best fits Joseph’s life (Genesis 37-50). After a short discussion we came to the conclusion it was either the sine function or the cosine function. I was thinking later and I decided a polynomial function might actually fit better. After a little trial and error I came up with this function.

(X/10-1.6)^7 – 5(X/10-1.6)^5 + 7(X/10-1.6)^3 – 2.3(X/10-1.6) = Y

I know most if not all of you cannot imagine that so I made a graph for those of you who want the easy path.


Joseph’s life starts at 0 on the X axis, and the X axis continues to represent his age. (Kinda not really close to scale.)

The Y axis represents his favor among the people he regularly interacts with.

At his birth Joseph already had considerable favor with his father for just being the child of Rachel.  He rose after that to his first peak, but he was cast down by his brothers into a pit and sold into slavery. That is represented by the dip around 18 on the X axis.

His next high around 40 is in Potiphar’s house when he becomes next to Potiphar.  However his amazing good looks cause his next dip when Potiphar’s wife falsely accuses  him and he is thrown in jail. This dip is around 62 on the X axis.

Joseph then attains great favor when he interprets the baker’s and cup bearer’s dreams, along with being promoted to chief prisoner. But when his God-sent gift fails to get him out of prison for so long his faith in God (probably) begins to wane and his fellow prisoners doubt his God will ever save him.

However, in a dramatic turn of events God preserves Joseph and takes him out of prison and sets him as the next best man to Pharaoh. This final high starts around 108 on the X axis. He then goes into an unending high which ends with infinity in the Y axis representing his eternal favor with God when he joins his maker in Heaven.

To prove it really does go to infinity I made a second graph with a much larger scale.


As can be clearly seen from that graph, when Joseph goes to be with God it infinitely out-weighs all the troubles of this life. I haven’t come up with an explanation for why the line comes from negative infinity, so I cropped that part out.

It isn’t a perfect graph of his life, but I believe it proves that a polynomial function fits his life best.  It clearly fits better than our previous ideas of sin X = Y and cos X = Y, both of which are in the below graphs. I even included sin (X+0.5) = Y, which also had the possibility of being a better graph than sine and cosine.


In the graph above (sin X = Y) Joseph’s life starts at (0,0). However, in this graph he never reaches infinity with God. Also, every one of his highs is as tall as all the others.


The cosine curve (above) might fit a little better. It has Joseph’s life start at (0,1)  and he immediately goes down from there. It is probably a better fit than the sine in the fact that he is born with favor with his father, however it fails in the other things sine failed in.


I believe this graph, sin(X+0.5) = Y, fits best of the three trigonometric functions. In this graph Joseph starts with favor, but he gains even more favor before his brothers sell him. However, he still never reaches infinity and he would supposedly live forever. I think I have demonstrated that a polynomial function fits better than any of the trigonometric functions.

Thank you for bearing with me.