I am interested in this site's members' opinions on how adding two spoons of sugar and two spoons of honey would affect a sourdough culture. I am wondering if adding sugar and honey to the starter culture will have any desirable effects on the resulting sourdough.
I'm experimenting and curious if this addition would lead to any new types of flavour?
Adding sugar or honey to a sourdough culture will increase the activity of the yeast for a little while, but it is unlikely to create "new types of flavour". Honey and Sucrose (Table sugar) are both just simpler sources of glucose and fructose that the sourdough microbes usually get from breaking down the starches in flour. Unlike flour, honey and sugar do not provide much (if any) protein which the sourdough microbes need in order to grow and reproduce. The effect of sugar or honey on the lactobacilli isn't predictable without knowing which specie are active in your specific starter. Some prefer maltose almost exclusively and would slow down if fed sucrose or honey, while others prefer fructose and would become especially active if fed honey; possibly leading to more sourness in the final product.
The purpose of a starter is to leaven bread composed of mostly flour and water. As such, it has always been my opinion that you should only feed your starter flour and water. Adding other things only serves to contaminate the culture or "teach" it to need additional food sources.
If you just really want to experiment feed you mother culture normally a few times, let it become active then set aside half of it for experimentation and half for safe keeping.
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Just to add a comment to Didgeridrew's great summary, the real danger of adding anything other than flour and water to starters is contamination. A sourdough culture consists of a symbiotic community of yeasts (which make the bread rise) and lactic acid-producing bacteria (which make it sour). Like almost any natural fermentation process, sourdough depends on a selective environment with conditions that will tend to allow certain microorganisms to flourish, while not allowing other ones to grow.
Messing with this balance is asking for trouble. I have heard of people trying to add everything from sugar/honey to milk to fruit juices to various foods or spices to their sourdough cultures. While it's possible it might work long-term, the more likely scenario is either (1) the thing you add has undesirable bacteria/mold/whatever already in it and will eventually spoil your culture and/or (2) the added nutrients from these new additions destroy the balance between the "good" bacteria and yeast and allow other bad things to start growing.
If you want to influence the final bread dough and incorporate some other ingredient into your starter early, I would suggest a multi-stage process of building up your dough. Many people just mix their starter directly into the final dough, but you can also begin with a much smaller amount of starter and gradually add flour and water to build up to the final amount of starter you need for the recipe. Along the way, you can introduce other components into the starter (which now more accurately would be called a "pre-ferment"). If you do this in stages, you might be able to add these ingredients hours or even days before the final dough mix, which will allow plenty of time for those ingredients to influence the final bread. Meanwhile, you save the rest of your (uncorrupted) starter for future batches.
I would add that if you are starting your starter (as opposed to feeding it) then honey (though not sugar) could be a good idea in the first day or two as it honey often has yeast/bacteria that can help establish your colony (raw honey would be best for this). Similarly, fresh pineapple juice and probiotic yogurt attempt to do similar things by "seeding" the initial population (and additionally starting with something sour to keep the non-sour-loving beasties away).
This would indirectly eventually affect the taste of your starter because the yeast/bacteria that get established depend on what was there to begin with, but how exactly the taste will change is rather unpredictable.
