I would like to propose the following original answer, Bezrat Hashem: In Genesis 46:23, it states that when Jacob and his sons entered Egypt , Dan had only one son named Chusim. To many it would appear that the Tribe of Dan would be a the smallest tribe. Yet, in Bamidbar 2:26 when the Israelites were being counted in the desert , the tribe of Dan is the second highest in terms of the counting. This is precisely the reason why the "leshem" stone was chosen for the tribe of Dan in order to teach us a very important lesson.

Whatever a person's reality may be presently, is by no means an indication of the future..................................

This is why an upside-down image is a characteristic of Dan's gem. At first glance Dan might seem to be the smallest tribe, yet in the future it emerged as the greatest in numbers. A person might think that he or she is lacking in good deeds and Mitzvoth presently, so how can I ever expect to grow in my service to Hashem. However, we must look at Dan's gem and begin to understand that things can definitely change for the better. Even if a person has only 1 Mitzvah presently, this is by no means an indication of the future. The tribe of Dan teaches us the concept of hope as represented by the "leshem" gem. Let us all try to trust in Hashem , and perhaps change our narrow perceptions of the world. Just like the "leshem" gem has the ability to change images, so to is it possible for our lives to be altered for the better. Perhapes we can begin with 1 Mitzvah, and see how it multiplies to many more. Have a good Shabbos