It is possible for the earth to appear old to science without it actually being old and without God being deceitful?

Perhaps “trade-offs” was a poor word choice on my part. Think of the issue this way: Just as we would not expect the Lord to create a square circle, so we would not expect Him to create a convex mirror that behaves as a non-convex mirror.

That would be like asking, “What would you speculate to be the advantages of objects in the mirror appearing farther than they are?” There would be no advantages; the very point of the warning on the mirror is that there is an acknowledged disadvantage. The whole reason for the convex mirror is to focus on the existence of objects - not their distance. Distance is sacrificed for the purpose of maximizing awareness of existence. This is precisely why the manufacturer warns the driver not to assume distance from this mirror, just as we would be, on this view, warned by the Bible not to assume the age of the earth from scientific inquiry. It should not be hard to remind ourselves that science has much more to offer us than the answer to a question which, by my reckoning, would not change my life, from a practical standpoint, one way or the other whether it was thousands of years old or billions of years old. (The age of the earth is only of interest to me because of its possible bearing on the veracity of the Bible and its relevance to the subject of evolution.)

By creating nature such that it displays uniformity and regularity in its ordinary processes, God, in essence, is inviting scientific inquiry. Just as He made the sun and the rains to benefit believers and unbelievers alike, so He made nature to respond to the study of believing scientists and unbelieving scientists alike. As for extraordinary processes - such as miracles and, most of all, the resurrection of Christ - scientific inquiry is neither necessary nor desirable. Believers acknowledge extraordinary processes because they either experienced them directly or accepted the testimony of those who did. Thus embedding evidence of extraordinary (supernatural) processes into nature would be both superfluous and distracting to the purpose of inviting humanity to discover truths resident in the physical dimension of our existence. An unpredictable universe does not invite study. On this view, we misuse scientific data if we project its processes into the past beyond the point that God says supernatural (extraordinary) processes began the universe - just as we would misuse a convex mirror to estimate the distance of a car approaching from the rear.

Note that I am merely explaining a point of view - not arguing with anyone.

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