Thinking

Algorithms are "sets of steps that, if followed methodically, will guarantee the correct solution to a problem", whereas heuristics are "rule-of-thumb strategies that do not guarantee the correct solution to a problem but offer likely shortcuts to it." The principle difference is that an algorithm guarantees a solution to the problem, whereas a heuristic may sometimes fail.

For example, if you want to figure out which student in your class is the oldest, you might go around and ask everyone their birth date (an algorithm). Alternately, you could look to see who is the tallest, who acts the most mature, who has the most gray hair, etc., as these all tend to be associated with age (a heuristic).

As another example, if you want to figure out how many jellybeans there are in a jar, you can arrive at exactly the right number by counting every single jellybean (an algorithm). However, that is a long and tedious process. A faster way would be to calculate the volume of the jar (pi times the squared diameter, times height, divided by 4) and divide this by the volume of a single jellybean (a heuristic). You might be surprised to see that a heuristic could be more "mathematical" than the algorithm, but notice that this heuristic is still inexact and will only approximate the solution.

Because they are exact, algorithms are preferable when you need to arrive at exactly the right answer every time. Heuristics, which tend to be faster and less effortful, are appropriate when a solution can be just "good enough", when it needs to be achieved faster than the appropriate algorithm will allow, or when an algorithmic solution is unknown.

Affirming the consequent: "When you assume a specific cause is present because a particular result has occurred." For example, you come outside and notice the sidewalk is all wet. "It must have rained," you think, "because the sidewalk is wet when it rains." However, the sidewalk could also be wet because the sprinklers came on, or because someone was washing their car, etc. Just knowing the sidewalk is wet is not enough to be sure that it rained.

Confirmation bias: The bias to seek information that confirms a rule, rather than to disprove it. This is the logical error that scientists must avoid when testing their hypotheses! For example, let's imagine a scientist who has hypothesized that "Only people with the O+ blood type can catch North American Speckled Fever*." If this scientist only examines people with O+ blood type to see if they have the fever, he is demonstrating confirmation bias. To successfully test the hypothesis (that is, to see evidence that disproves it) he must also examine people with other blood types to see whether they have caught the fever. If someone with A- blood type catches the fever, then his hypothesis is false; but studying people with O+ blood can't disprove the hypothesis.

*(a disease just as imaginary as the rest of the example)

Representativeness heuristic: People tend to "assume that the more similar something is to a prototype stored in our memory, the more likely that thing is to be a member of a category." Let's return to our example of North American Speckled Fever. The symptoms for this imaginary disease include feeling tired in the morning, mild indigestion, and headaches. However, North American Speckled Fever is very rare, and only about 1 in 100,000 people will ever catch it. Several patients heard about the symptoms of this disease on the news and then went to to their doctors insisting they had the Fever because they, too, were tired in the morning and sometimes had indigestion and headaches. However, these patients are biased by the representativeness heuristic – just because they have the symptoms described doesn't necessarily mean they have the Fever. Lots of other things are much more likely to cause being tired in the morning (didn't get enough sleep?), indigestion (ate too much greasy food?) and headaches than this disorder, which you'll remember is very rare.

Availability heuristic: People tend to "judge objects or events as more likely, common, or frequent if they are easier to retrieve from memory." For example, people often have friends who have the same political views they do. When asked how many people are likely to support a new political initiative, you might think of all your friends and whether they would support the initiative. If most of them would support the initiative, then you might believe that people in general are also very likely to support it. However, because the people you know are a biased selection of the population in general, you will likely overstate support for the initiative simply because you aren't friends with the types of people who would be opposed to it (and therefore can't easily bring to mind how many people that might be).