# Confidence Interval

A percentage estimate (i.e. 95%) of how confident we are that the actual value lies within the range (interval) of our estimated value.

Example: Imagine a hypothetical company that provides a super low-cost internet search tool. Let’s call them Froogle. Let’s estimate the average salary of the engineers working at Froogle.

We ask 1o0 Froogle engineers for their salary, and find that the average is \$50k. However, those are only 1o0 engineers in a company of 1,000 engineers. And remember, we’re trying to find the average salary of all Froogle engineers.

Since we only asked 10 engineers, we can’t be too sure the average salary actually is \$50k. Using statistical analysis we come up with ranges and confidence intervals. For example, we may estimate that the actual salary is between \$35k-\$75k with a confidence interval of 95%. I.e. we are 95% sure that the actual average salary falls somewhere between \$35k and \$75k.

Wisdom: “There are three types of lies—lies, damn lies, and statistics.” ― Benjamin Disraeli

# Bayes’ Theorem

Prior knowledge of conditions related to an event can be used to give a more accurate estimation of that event.

Example: Ask yourself, what is my life expectancy? Worldwide, the average life expectancy is 71 years. However, you aren’t average, so your life expectancy isn’t exactly 71. For example, if you’re a woman, have already survived 47 years, have no disease, and live in Australia—then your life expectancy is a lot higher than 71 years.

So we can see that the probability of something, such as life expectancy, is conditional on other factors that are directly related to it.

Wisdom: “The wise man is one who, knows, what he does not know.” ― Lao Tzu, Tao Te Ching

# Wisdom of the Crowd

A large group’s aggregated answers to questions involving quantity estimation, general world knowledge, and spatial reasoning has generally been found to be as good as, and often better than, the answer given by any of the individuals within the group.

Example: In our judicial system, it is not the judge who determines the innocence or guilt of a person. We trust in the wisdom of a crowd; jurors.

Wisdom: “The only true wisdom is in knowing you know nothing.” ― Socrates

# Half-life

The time required for a quantity to reduce to half its initial value.

Example: The half-life of caffeine is approximately 6 hours. So if you have a morning coffee at 9 am, half of the caffeine you ingested will have been metabolised by 3 pm.

Wisdom: “Energy has a way of dissipating, you know; what can be done when you’re eleven can often never be done again.” ― Stephen King.

# Inertia

The resistance of any physical object to any change in its state of motion; this includes changes to its speed, direction or state of rest.

Inertia Example:

When we want to change a habit, such as eating ice-cream before bed, it’s difficult when that pattern of behaviour has been ingrained through repetition.

Being aware of inertia reminds us to ask ourselves the question, “Are we doing something simply because we have always done it? Or because it’s the best thing to be doing?”

Wisdom:

“The less there is to justify a traditional custom, the harder it is to get rid of it.” ― Mark Twain

# Inflection Point

The point on a curve where the direction of the curvature changes.

Example: In business, inflection points are infrequent events that result in a significant change in the current developmental course of a person, company, or even an industry.

Andy Grove, Intel’s cofounder, described a strategic inflection point as an event that changes the way we think and act:

“The competitive marketplace and a person’s place in it are dynamic and constantly evolving. In the midst of dramatic change and upheaval, one cannot always distinguish the actual turning points that delineate the ‘new normal.’”

Wisdom: “In a chronically leaking boat, energy devoted to changing vessels is more productive than energy devoted to patching leaks.” —Warren Buffett

# False Positives and False Negatives

A false positive is a test result which wrongly indicates that a particular state is present. A false negative is a test result which indicates that a particular condition is absent.

Example: An example of a false positive is Rubin ‘Hurricane’ Carter being wrongly convicted of murder. Despite him being innocent, his court trial wrongly indicated that he was guilty.

Example: An example of a false negative is when a pregnancy test comes back negative—despite the woman actually being pregnant.

Wisdom: “False facts are highly injurious to the progress of science, for they often endure long; but false views, if supported by some evidence, do little harm, for everyone takes a salutary pleasure in proving their falseness; and when this is done, one path towards error is closed and the road to truth is often at the same time opened.” ― Charles Darwin

# Divergent vs Convergent Thinking

Divergent thinking is a thought process or method used to generate creative ideas by exploring many possible solutions. It is often used in conjunction with its cognitive opposite, convergent thinking. Convergent thinking follows a particular set of logical steps to arrive at one solution, which in some cases is a ‘correct’ solution.

Example: Divergent thinking is like building a city—you add new roads that build off each other in many different directions. They diverge. Convergent thinking is like navigating the many roads of a city to arrive at the one correct address. They converge.

Divergent thinking is coming up with ideas, while convergent thinking is coming to the one correct conclusion.

Wisdom: “The mind is not a vessel to be filled, but a fire to be kindled.” ― Plutarch

# Observer Effect

The act of observing influences the phenomena being observed.

Example: To observe an electron, a photon must first interact with it—and that photon changes the path of the electronic.

A commonplace example is checking your car’s tire pressure; it is hard to observe it without letting some air out of the tire, thus changing the pressure.

Wisdom: “The eye sees only what the mind is prepared to comprehend.” ― Robertson Davies

# Order of Magnitude

An estimate of a variable whose precise value is unknown and estimated to the nearest power of ten.

Example: “The biggest epiphany I’ve had this year is that what really matters is the machine that builds the machine, the factory,” he said. “And that is at least two orders of magnitude harder than the vehicle itself.” — Elon Musk

Musk uses the term ‘order of magnitude’ to emphasise the difficulty of building the Tesla factory because exactly how difficult it will be cannot be calculated.

Wisdom: “Mathematics would certainly have not come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude.” — Friedrich Nietzsche