Save "Forbidden and permitted mixtures"
Forbidden and permitted mixtures
This source sheet explores Shulchan Aruch, Yoreh Deah Siman 98, which deals with mixtures of kosher and non-kosher foods.

Ratios relative to taste alone

In contrast to the first three subsections where the mixture still consists of physical kosher and non-kosher food, here we are dealing with mixtures where there is no physical non-kosher food actually present. Three examples are given, although, as we shall see, the first example is somewhat different to examples 2 and 3. The common factor is our lack of knowledge as to how much taste was actually absorbed, and the resultant need to apply a stringent 60:1 ratio of permitted food to cancel out that taste.
Note: In all of these examples, the 60:1 ratio is Torah-mandated if the non-kosher and kosher elements of the mixture are min be shelo mino (belonging to food types with different tastes, for example meat and fat), and only rabbinically mandated if the elements are min bemino (the same food with the same taste).
(ד) איסור שנתבשל עם היתר אפי' מכירו והוא שלם וזרקו צריך ששים כנגד כל האיסור מפני שאין אנו יודעים כמה יצא ממנו
(4) When a forbidden food is cooked with a permitted food, or a forbidden food, visible and whole, is thrown out of the pot, the quantity of the permitted food must be sixty times that of the entire forbidden food, as it is impossible to evaluate the degree of flavor imparted to the mixture by the forbidden food.

Example 1

A small piece of non-kosher food, such as forbidden fat, falls into the pot of kosher soup. You spot the fat and promptly remove it (or as much of it as you can see) from the mixture. However, that fat has now imparted taste to the soup, and some small unknown anount is still swimming around inside the soup. Nullifying this non-kosher taste requires a volume of kosher meat 60 times the amount of the non-kosher fat that originally fell into it, even though most of that fat is no longer physically there. Of course, if the kosher soup was already 60 times the volume of the forbidden fat, then the soup is kosher and does not require any permitted food to be added to it.
(ד) לפיכך המבשל בקדירת איסור שהיא בת יומא או תוחב כף של איסור בהיתר צריך ס' כנגד כל הקדירה וכנגד כל מה שתחב מהכף שאין אנו יודעין כמה בלעו בין שהם של חרס או עץ או מתכת:
(4) Consequently, when permitted foods are cooked in a pot that, on the same day, was used to prepare forbidden foods, the quantity of foods being cooked must be sixty times the weight of the pot. The same applies when, by mistake, a spoon that was used to prepare forbidden foods is dropped into a pot containing permitted foods; the quantity of the latter must be sixty times greater than the part of the spoon that came into contact with the forbidden foods. Indeed, it is impossible to evaluate the quantity of forbidden food absorbed by the pot or the spoon.

Examples 2 and 3

A pot was used earlier today to cook forbidden food (i.e. a ben yomo pot) and has therefore absorbed the taste of the forbidden food. This same pot is now being used to cook kosher food. We have no means of measuring the amount of non-kosher taste that was absorbed, so the ratio of 60:1 is once again employed in a maximalist way. This time, the amount of permitted food required to render the food kosher is 60 times the volume of the pot. Wow, that sounds like a lot of extra food.
A spoon or spatula was in a pot earlier today when it was used to cook forbidden food, and hence part or all of the spatula acquired the taste of the forbidden food. This same spatula is now accidentally placed into a pot of kosher food, and as a result the amount of kosher food required to annul the prohibition is 60 times the volume of the part of the spatula that was submerged, Some say that when dealing with a metal spoon, the amount required is 60 times the volume of the entire sppon, presumably because metal has powerful heat conduction properties. This law applies regardless of whether the spatula is made of clay, wood, or metal. Presumably this law does not apply to a glass spatula, which does not absorb taste.
In both of these cases it's not clear why we do not ask a non-Jewish chef to taste the food, as we did in the first subsection.