A few days ago I had an e-mail from a university student who was reading Skeptics and True Believers. He wrote: "On page 27 you discuss that there is an arms length of DNA in every cell and the difficulty in believing that it actually fits. I too found this very unbelievable. You mentioned that you did the equation and it works, yet you left out the equation or any of the calculations. I wish you would have sort of walked your reader through the calculation much like you did for Arcturus. This is not to say that I don't trust your calculations. I do. It is just that as a true skeptic, I would have appreciated the equation."
An arm's length of DNA in a space too small to see with the naked eye! Yeah, that's pretty hard to believe. As I said in the book, it strained my credulity too, although of course I had confidence in the result (that's the beauty of science as a collective, peer-reviewed way of knowing).
Here was my response: "Glad to see your skepticism is intact. I will leave the calculation to you. We know from X-ray diffraction studies that a strand of DNA is 1.5 nanometers (1.5 x 10 to the -9 meters) in radius. Assume a cylinder 1 meter long (the arm's length) with a radius of 1.5 nanometers and work out the volume (length x pi r squared). A typical animal cell is about 8 micrometers (8 x 10 to the -6 meters) in radius. Assume a spherical cell and calculate the volume (4/3 pi r cubed). You will see that the DNA fits easily inside the cell."
A nice little illustration of the power of mathematics as an aid to the imagination.
Science began with mathematical reasoning. Eratosthenes figured out the size of the Earth and Aristarchus deduced the sizes and distances of the Sun and Moon with the same sort of Euclidean geometry I used above. When Aristarchus claimed that the Sun was vastly larger than the Earth and an unimaginable distance away, he was apparently met with almost universal skepticism. The philosopher Cleanthes thought Aristarchus should be indicted on a charge of impiety; to imagine such a commodious universe was an insult to the gods.
Like the human senses, the human imagination is limited as an instrument for knowing. Mathematics allows the imagination to go where the senses have not been. And, yes, I guess there is something impious about the mathematical way of knowing -- for those whose gods are made in the image of man.