Will Natural Gas Produce Cobwebs Indoors?

This appears to be another 'old wives tale'. I once heard someone tell a story about how they would always put a brick in the oven when baking pies because ' their mother said that it made the pie turn out better. She traced back and found a picture of her great great grandmother backing and noticed a brick in the oven as well. The only thing was, the brick was placed to level the shelf. She then asked her grandmother about this and they all realized that it may have been tradition but the origination was not really due to anything besides an issue with the oven.

Long story short, most of these tales are just that but his one sounds as if it is a resistance to change (natural gas heat instead of other means of heat) and that is something that is inevitable.

It has nothing to do with natural gas heating. If you have forced air heating you will have more cobwebs, noticeable by the accumulation of dust. Even the most perfect furnace filter will not stop dust settling in spiders' webs (the source of cob webs). In addition, spiders tend to build their webs where they feel air movement, which forced air creates. Even so, convection patterns from rising heated air can also create enough movement for a spider to build a web.

Can't figure out any relationship between the two.
Perhaps your heater is not functioning properly and it produces soot and also the air filters are not trapping those particles which then stick to the cobwebs, making them more obvious to your eyes.

I don't know if there any relation between the two. I kind of doubt it. Spiders cause cobwebs. They build spider webs, mostly fine and unnoticeable. By the time we see them, they are covered with dust and become cob webs.

Webs aren't caused from natural gas. Natural gas tends to dry out the air more and make more dust in the house and the dust seem to highlight the webs more.

. . . And my mom used to say "If you pick a guinea pig up by its tail, its eyes will fall out". Sometimes it can take decades to catch the joke.

Blaming cobwebs on "natural gas heating" rather than on ignoring spiders seems similar.