operator: smooth

    description:
        smooth[dx] ket
        smooths peaks into Gaussian's
        eg: 
            smooth[dx] a|x: 3>
        returns:
            a/4 |x: 3 - dx> + a/2 |x: 3> + a/4 |x: 3 + dx>
        usually invoked in form: smooth[dx]^power
        also used to enable similarity between nearby integers

    examples:
        smooth[0.5] |age: 30>
            0.25|age: 29.5> + 0.5|age: 30> + 0.25|age: 30.5>
            
        -- show what this looks like:
        bar-chart[40] smooth[0.5] |age: 30> 
            ----------
            age: 29.5 : ||||||||||||||||||||
            age: 30   : ||||||||||||||||||||||||||||||||||||||||
            age: 30.5 : ||||||||||||||||||||
            ----------
        
        smooth[1]^5 |age: 40>
            0.001|age: 35> + 0.01|age: 36> + 0.044|age: 37> + 0.117|age: 38> + 0.205|age: 39> + 0.246|age: 40> + 0.205|age: 41> + 0.117|age: 42> + 0.044|age: 43> + 0.01|age: 44> + 0.001|age: 45>
        
        -- show what this looks like:
        bar-chart[40] smooth[1]^5 |age: 40> 
            ----------
            age: 35 :
            age: 36 : |
            age: 37 : |||||||
            age: 38 : |||||||||||||||||||
            age: 39 : |||||||||||||||||||||||||||||||||
            age: 40 : ||||||||||||||||||||||||||||||||||||||||
            age: 41 : |||||||||||||||||||||||||||||||||
            age: 42 : |||||||||||||||||||
            age: 43 : |||||||
            age: 44 : |
            age: 45 :
            ----------

        rescale[1] smooth[1]^5 |age: 40>
            0.004|age: 35> + 0.04|age: 36> + 0.179|age: 37> + 0.476|age: 38> + 0.833|age: 39> + |age: 40> + 0.833|age: 41> + 0.476|age: 42> + 0.179|age: 43> + 0.04|age: 44> + 0.004|age: 45>

        age-simm (*,*) #=> simm(smooth[1]^5 |_self1>, smooth[1]^5 |_self2>)
        age-simm(|age: 36>, |age: 40>)
            0.227|simm>

    see also:
        rescale, simm, Gaussian