I have looked at my share of small peaches. Research states that peach trees have the potential for 1,200 blossoms per tree - much more than any tree I have seen can support. It stands to reason that removing fruit before it has a chance to mature will increase the size and flavor of fruit remaining on the tree to mature.
There are a few methods of removing small fruit when it is the size of a quarter. One of my favorites is a length of one-inch diameter hose doubled at the ends. Using the ends as a handle, strike the lower side of the branch to be thinned. Strike the limb with enough force to dislodge the fruit. Keep looking at the number of fruit on the limbs. Stop thinning (hitting) this limb when you begin to see one fruit remaining every 4 to 6 inches. Start on next limb adjacent to the thinned limb. This method is not without some drawbacks. That's a nice way of saying you won't be able to dislodge one fruit per 4-6 inches - however, it will remove the fruit. You may have some double fruit at one growing point. Until you become proficient with the hose, these few fruit can be removed by a single blow to the fruit, dislodging one of the doubles and resulting in a single fruit spaced away from other fruit. Until you have obtained that level of proficiency, use your hand to remove the fruit. The hose method is much less discriminate.
This brings up another method of fruit thinning, which is very labor intensive but more precise. That is removing each fruit by hand. However, if the eye doesn't see the fruit spacing, the tree doesn't get thinned.
Still another method of fruit thinning is by bloom removal. Due to the fact too many opportunities for fruit loss can occur early in the season, this is not the best method.
We have a couple of good examples in the Noble Research Institute's Horticulture Demonstration Fruit Orchard that illustrate the point of thinning versus not thinning. The non-thinned tree is broken up and half of the tree is very weak. The thinned tree's fruit is much larger and more marketable. See photos and decide which tree you would harvest.
One more item that doesn't have anything to do with fruit production - it does have to do with growing youngsters, though. In 1960, my dad, George P. Barlow, Jr., poured a patio with the help of his three sons and our little sister. With the leftover concrete, he poured and smoothed a gate entrance pad that was decorated with our foot and handprints. We were so proud that we were allowed to put our feet and hands in the wet concrete. My mother like to have died! I can still hear her voice saying, "George, those kids are not coming in this house like that" as the screen door slammed shut. Our names and the date are etched under our prints. It was our proud duty to sweep the sidewalk as well as that entrance pad that proudly identified the Barlow clan's residence. It's every kid's dream to be identified publicly in a warm family way - each visitor to your home will know that a proud parent or grandparent lives there. Oh, by the way - that concrete pad imprinted in 1960 (three years prior to my dad's accidental death) is still in place.
Even after you have moved, it's nice to be able to take your children and show them where your prints are. Hopefully, when they bring your grandchildren around, those prints will still be there!