What we can imagine as plausible is a narrow band in the middle of a much broader spectrum of what is actually possible. [O]ur eyes are built to cope with a narrow band of electromagnetic frequencies. [W]e can't see the rays outside the narrow light band, but we can do calculations about them, and we can build instruments to detect them. In the same way, we know that the scales of size and time extend in both directions far outside the realm of what we can visualize. Our minds can't cope with the large distances that astronomy deals in or with the small distances that atomic physics deals in, but we can represent those distances in mathematical symbols. Our minds can't imagine a time span as short as a picosecond, but we can do calculations about picoseconds, and we can build computers that can complete calculations within picoseconds. Our minds can't imagine a timespan as long as a million years, let alone the thousands of millions of years that geologists routinely compute. Just as our eyes can see only that narrow band of electromagnetic frequencies that natural selection equipped our ancestors to see, so our brains are built to cope with narrow bands of sizes and times. Presumably there was no need for our ancestors to cope with sizes and times outside the narrow range of everyday practicality, so our brains never evolved the capacity to imagine them. It is probably significant that our own body size of a few feet is roughly in the middle of the range of sizes we can imagine. And our own lifetime of a few decades is roughly in the middle of the range of times we can imagine.
[W]e can calculate our way into regions of miraculous improbability far greater than we can imagine as plausible. Let's look at this matter of what we think is plausible. What we can imagine as plausible is a narrow band in the middle of a much broader spectrum of what is actually possible. Sometimes it is narrower than what is actually there. There is a good analogy with light. Our eyes are built to cope with a narrow band of electromagnetic frequencies (the ones we call light), somewhere in the middle of the spectrum from long radio waves at one end to short X-rays at the other. We can't see the rays outside the narrow light band, but we can do calculations about them, and we can build instruments to detect them. In the same way, we know that the scales of size and time extend in both directions far outside the realm of what we can visualize. Our minds can't cope with the large distances that astronomy deals in or with the small distances that atomic physics deals in, but we can represent those distances in mathematical symbols. Our minds can't imagine a time span as short as a picosecond, but we can do calculations about picoseconds, and we can build computers that can complete calculations within picoseconds. Our minds can't imagine a timespan as long as a million years, let alone the thousands of millions of years that geologists routinely compute. Just as our eyes can see only that narrow band of electromagnetic frequencies that natural selection equipped our ancestors to see, so our brains are built to cope with narrow bands of sizes and times. Presumably there was no need for our ancestors to cope with sizes and times outside the narrow range of everyday practicality, so our brains never evolved the capacity to imagine them. It is probably significant that our own body size of a few feet is roughly in the middle of the range of sizes we can imagine. And our own lifetime of a few decades is roughly in the middle of the range of times we can imagine.
A miracle is a violation of the laws of nature; and because firm and unalterable experience has established these laws, the case against a miracle is—just because it is a miracle—as complete as any argument from experience can possibly be imagined to be. Why is it more than merely probable that all men must die, that lead cannot when not supported remain suspended in the air, that fire consumes wood and is extinguished by water, unless it is that these events are found agreeable to the laws of nature, and for things to go differently there would have to be a violation of those laws, or in other words a miracle? Nothing is counted as amiracle if it ever happens in the common course of nature. When a man who seems to be in good health suddenly dies, this isn't a miracle; because such a kind of death, though more unusual than any other, has yet often been observedto happen. But a dead man’s coming to life would be a miracle, because that has never been observed in any age or country. So there must be a uniform experience against every miraculous event, because otherwise the event wouldn't count as a ‘miracle’. And as a uniform experience amounts to a proof, we have here a direct and full proof against the existence of any miracle, just because it’s a miracle; andsuch a proof can’t be destroyed or the miracle made credible except by an opposite proof that is even stronger.This clearly leads us to a general maxim that deserves ofour attention:No testimony is sufficient to establish a miracle unless it is of such a kind that its falsehood would be more miraculous than the fact that it tries to establish. And even in that case there is a mutual destruction ofarguments, and the stronger one only gives us an assurance suitable to the force that remains to it after the force needed to cancel the other has beensubtracted.