## The Laplace Transform

**“Mathematics is the art of giving the same name to different things.”**

** Henri Poincare**

**If you look carefully at the above proofs they demo straight that the compound interest rate function and the Laplace transform are virtually the same function. ****The only difference is the Laplace transform has an integration wrapped around it. ****The difference is the kernel of the compound interest rate function and the Laplace transform use a different letter for the exponent, that is s instead of r.**

**Therefore :**** If s = r and P = 1**

**Therefore : e^st = e^rt**

**Therfore : st = rt**

**Therefore : s = r**

**They are therefore same formula and thus the same thing.**

**If two apparently different observable phenomena are described by the same function, then they are the same thing everywhere including the financial. ****This also indicates that compound interest is by definition a complex number and thus can be translated to the complex plane and spectrographically analysed. **

**Markets are by definition elastic and therefore will have the properties of an elastic medium. ****So any impulse (transaction) will create point source interference that will propagate a wave front through the medium.**

**Young’s slit experiment. **

**If many impulses that is to say trades are applied to the medium (market) they will form interference patterns as each wave front decays over time.**

**Where the interference is generated by the impulse responses from transactions.**

**S****pecifically markets are interference patterns which obscure the underlying wave functions that are at work, in other words the function of trend. **

**Using the laplace transform it is possible to measure the magnitude and direction of the trend which can be converted into a transfer function that can be used as a process control input to manage a market position of an automated portfolio system.**

### The charts below are simple process control functions as a single contract track record for the last twenty years the lower panel is the profit per contract traded.

**Example Output**