Quranic Wisdom: The Negative Power of Example

We use examples, and mental models, all the time to aid our understanding of various elements of this world. A wrong example, or an inaccurate model, can be of sever consequences. Physicists, in particular, know that the understanding of a certain phenomenon is only possible if they find an appropriate theoretical model that fits all observable behaviors of the system at hand. Theoretical models may bear no correspondence to any familiar aspect, however (10+ dimensions, anyone?).
We have to be careful of inaccurate analogies. From Quran [17-Al-Isra][48]:

انظُرْ كَيْفَ ضَرَبُواْ لَكَ الأَمْثَالَ فَضَلُّواْ فَلاَ يَسْتَطِيعْونَ سَبِيلاً

It may be translated as (By M. Picktall, via islamicity.com)

See what similitudes they coin for thee, and thus are all astray, and cannot find a road!

Also in [25:Al-Furqan][9].
This verse states that they went astray as a result of them making examples for you, by the means of seeking similarities and resemblance.
I believe this is why the technique of analogy (القياس) has deserved such attention from Fiqh scholars, and why we've been instructed not to make examples for God [16:An-Nahl][74].
We can be consumed in, guided, and betrayed by our mental models. Extreme care, validation, and re-examination of these models are necessary for us to have a chance in understanding and making progress.