4. Draw four chords $P_{1} Q_{1}, P_{2} Q_{2}, P_{3} Q_{3}, P_{4} Q_{4}$ of the parabola $y^{2}=x$ through the point $M(2,-1)$, and the y-coordinates of points $P_{1}, P_{2}, P_{3}, P_{4}$ form an arithmetic sequence. Try to compare $\frac{P_{1} M}{M Q_{1}}-\frac{P_{2} M}{M Q_{2}}$ with $\frac{P_{3} M}{M Q_{3}}-\frac{P_{4} M}{M Q_{4}}$.
4. Let $P_{i}\left(y_{i}^{2}, y_{i}\right), Q_{i}\left(y_{i}^{\prime 2}, y_{i}^{\prime}\right), \lambda_{i}=\frac{P_{i} M}{M Q_{i}}\left(\lambda_{i} \neq-1, i=1,2,3,4\right)$. From $\left\{\begin{array}{c}2=\frac{y_{i}^{2}+\lambda y_{i}^{\prime 2}}{1+\lambda_{i}} \\ -1=\frac{y_{i}+\lambda y_{i}^{\prime}}{1+\lambda}\end{array}\right.$, eliminating $y_{i}^{\prime}$, we get $\left(\lambda_{i}+1\right) y_{i}^{2}+2 y_{i}\left(\lambda_{i}+1\right)=\lambda_{i}^{2}-1$, so $\lambda_{i}=\left(y_{i}+1\right)^{2}$.

Since $y_{1}, y_{2}, y_{3}, y_{4}$ form an arithmetic sequence with a common difference $d \neq 0$, then $\left(\frac{P_{1} M}{M Q_{1}}-\frac{P_{2} M}{M Q_{2}}\right)-\left(\frac{P_{3} M}{M Q_{3}}-\frac{P_{4} M}{M Q_{4}}\right)=\left(\lambda_{1}-\lambda_{2}\right)-$ $\left(\lambda_{3}-\lambda_{4}\right)=-d\left[\left(y_{1}+y_{2}+2\right)-\left(y_{3}+y_{4}+2\right)\right]=-d(-4 d)=4 d^{2}>0$.