ω-3 and ω-6 Fatty Acids
We hear a lot about these different types of fatty acids these days. It would be good to know what they are, where they come from, and whether it matters how much we eat of them.
Fatty acids are named and numbered
To speak of the many different types of fatty acids, chemists have established certain world-wide rules for nomenclature. This includes numbering the carbon atoms. There are two conventions, which are used when different aspects of the molecules are being discussed:

Chemists commonly refer to the first carbon in a fatty acid as "the α carbon" or simply carbon #1. In some types of conversations, it is more helpful to refer to distance from the other end of the fatty acid tail. Here, chemists refer to the last carbon as "the ω carbon." It is then conventional to count backwards, using negative numbers.
ω-3 and ω-6 and ω-9
The way that these compounds are produced by plants is first to create a fatty acid that is unsaturated (i.e. has a double bond) at carbon ω-9. Let's first illustrate this so that it looks rather like the diagram above:

Of course, it wouldn't really look like this, because this is in the trans configuration. The natural form, as produced by living things, is in the cis configuration, and would look like this:

The next step is to add a cis double bond at the ω-6 carbon:

And then, add another at the ω-3 carbon:

By the time these different fatty acids are assembled into triglycerides for storage, it's possible to build complex, kinked molecules like this:

Solid Fat and Liquid Oil revisited
Thinking in terms of these various complex molecules, it is possible to envision how well or poorly the saturated triglycerides of animal fat -- say, for example, lard -- pack together into a solid, compared to the variously-unsaturated triglycerides of vegetable oil -- say, olive oil.

The American Diet: decreasing amounts of ω-3 fatty acids
Only recently have the possible health effects of ω-3 fatty acids been investigated. Preliminary evidence is that these are particularly helpful in decreasing chronic inflammation and some of the "western diseases" typically associated with the "western diet" (high fat, high sugar). With the recognition of the potential value of these fatty acids has come the surveying of their availability in foods. We know the following:
- Fresh leafy vegetables are the best source of ω-3 fatty acids
- Fish are good sources of ω-3 fatty acids, because their food chain begins with phytoplankton
- Some seeds contain adequate amounts of ω-3 fatty acids, such as flax seed
- Most seeds contain little ω-3 fatty acids, storing primarily ω-6 fatty acids
- The ω-3 fatty acids are unstable; they oxidize and turn stale or rancid quickly
- This is a general feature of unsaturated fats. The double bonds are easily oxidized. This is why whole-wheat flour has a shorter shelf-life than white flour; it contains more of the oils from the seeds.
- Processed foods are designed to be shelf-stable; ω-3 fatty acids are removed during processing
- There are also crop breeding programs designed to decrease the amount of ω-3 fatty acids in commercially-important seeds (soy, corn, etc) to eliminate this problem. Note that the "problem" pertains to sale-of-product, rather than to public-health effects.
- Grass-fed animals are a good source of ω-3 fatty acids
- Grain-fed animals are a poor source of ω-3 fatty acids
- These last two points make sense in view of the fact that grain seeds store relatively little ω-3 fatty acids, while chloroplast-rich leaves contain significant amounts.
- For many Americans, the primary foods are hamburgers, French fried potatoes, and convenience foods
- Most hamburgers are made from grain-fed beef from feedlots.
- Potatoes are underground starch-storage organs, with no active chloroplasts.
- Convenience foods (aka "snacks") are highly-processed shelf-stable products.
- None of these are good sources of ω-3 fatty acids.