Editing Twin paradox (section)

===The distinction between what they see and what they calculate===
To avoid confusion, note the distinction between what each twin sees and what each would calculate. Each sees an image of his twin which he knows originated at a previous time and which he knows is Doppler shifted. He does not take the elapsed time in the image as the age of his twin now.
*If he wants to calculate when his twin was the age shown in the image (''i.e.'' how old he himself was then), he has to determine how far away his twin was when the signal was emitted—in other words, he has to consider simultaneity for a distant event.
*If he wants to calculate how fast his twin was aging when the image was transmitted, he adjusts for the Doppler shift. For example, when he receives high frequency images (showing his twin aging rapidly) with frequency <math>\scriptstyle{f_\mathrm{rest}\sqrt{\left({1 + v/c}\right)/\left({1 - v/c}\right)}}</math>, he does not conclude that the twin was aging that rapidly when the image was generated, any more than he concludes that the siren of an ambulance is emitting the frequency he hears. He knows that the [[Doppler effect]] has increased the image frequency by the factor 1 / (1 − ''v''/''c''). Therefore, he calculates that his twin was aging at the rate of
:<math>f_\mathrm{rest}\sqrt{\left({1 + v/c}\right)/\left({1 - v/c}\right)}\times \left(1 - v/c\right) = f_\mathrm{rest}\sqrt{1 - v^2/c^2}\equiv\epsilon f_\mathrm{rest}</math>
when the image was emitted. A similar calculation reveals that his twin was aging at the same reduced rate of ''εf''<sub>rest</sub> in all low frequency images.