Uncertainty facts for kids

Sometimes, you have to make a choice when you don't know what will happen.

Uncertainty is when you don't have perfect or complete information about something. It's like not knowing exactly what will happen in the future. It can also be about things that have already happened but you don't know the full details.

Uncertainty pops up in many areas. This includes insurance, physics, statistics, economics, medicine, and even weather forecasting. It happens when things are partly hidden or when events happen randomly. It can also be because someone doesn't know enough or isn't paying attention.

What is Uncertainty?

Even though people use the words "uncertainty" and "risk" differently, experts in fields like decision theory and statistics have specific meanings for them.

Understanding Uncertainty

Uncertainty means a lack of certainty. It's a situation where you have limited knowledge. This makes it impossible to fully describe what's happening now. It also means you can't exactly predict what will happen next.

When we measure uncertainty, we often list all the possible things that could happen. Then, we assign a probability to each one. A probability is a number that tells you how likely something is to happen. For example, if you flip a coin, there's a 50% probability it will land on heads.

Deeper Uncertainty

Sometimes, there's uncertainty about the probabilities themselves. Imagine you're not sure if a coin is fair. You might think there's a 50% chance it's fair, and a 50% chance it's weighted. This is like a "second-order" uncertainty. It's uncertainty about the uncertainty!

What is Risk?

Risk is a type of uncertainty. It's when some of the possible outcomes are bad or could cause a big loss. Measuring risk means looking at these uncertain situations. You figure out which outcomes are losses and how big those losses might be.

Uncertainty vs. Variability

It's important to know the difference between uncertainty and variability.

• Uncertainty is about not knowing the single, true value of something. We use probabilities to describe how likely different values are.
• Variability is about how much something changes or differs. For example, if you measure the height of many different trees, their heights will vary. This is about observing many different instances.

Knightian Uncertainty

In economics, a person named Frank Knight talked about uncertainty in 1921. He made a big difference between two types:

• Risk: This is when you can measure the chances of different outcomes. For example, you know the probability of rolling a certain number on a dice. You can often get insurance for these kinds of risks.
• Uncertainty: This is when you don't have enough information to measure the probabilities. It's like not knowing what might happen at all. Knight called this "Knightian uncertainty." He believed that in many economic decisions, you can't calculate exact probabilities.

Knight said that a known risk can be managed. For example, an insurance company can calculate the chance of a car accident. But for unknown risks, where you can't even guess the probabilities, decisions can be very risky.

This chart shows different types of uncertainty.

Risk and Uncertainty Example

Let's say you're planning a big outdoor event for tomorrow.

• If you don't know if it will rain, that's uncertainty.
• If you check the weather forecast and it says there's a 90% chance of sunshine, you've now quantified the uncertainty.
• If rain would ruin your event and cost you money, then there's risk. The 10% chance of rain is the risk.
• If the event costs $100,000 and you'd lose it all if it rains, then the risk is quantified even more. It's a 10% chance of losing $100,000.

Some people might calculate the "expected loss." This is the chance of loss multiplied by the amount of loss (10% x $100,000 = $10,000). But most people would pay more than $10,000 to avoid losing $100,000. This is why insurance companies exist!

Other Types of Uncertainty

• Vagueness is when you can't clearly tell the difference between two things. For example, "a tall person" isn't very clear. How tall is tall?
• Ambiguity is when a statement can have more than one meaning. If someone says, "He went to the bank," it's ambiguous. Did he go to a river bank or a money bank?

At the tiny, subatomic level, uncertainty might be a basic part of the universe. The Heisenberg uncertainty principle in quantum mechanics says you can't know both the exact position and the exact speed of a particle at the same time. It's not just that we don't know; it's that there might not be a single exact fact to know!

Radical Uncertainty

The term 'radical uncertainty' was created by John Kay and Mervyn King in 2020. It's different from Knightian uncertainty. Radical uncertainty happens when you can't get the information you need to solve the uncertainty. If you *could* find the information through research, then it's not radical uncertainty. It's only radical when there's no way to get the knowledge that would clear things up.

Uncertainty in Measurements

When we measure things in science or engineering, there's always some uncertainty. This is also called the measurement uncertainty or margin of error.

The most common way to figure out measurement uncertainty is described in a guide called "Guide to the Expression of Uncertainty in Measurement" (GUM).

• Some parts of uncertainty are found using statistical methods (Type A).
• Other parts are found using different methods, like assigning a probability distribution based on what we know (Type B).

When you combine these parts, you get the total measurement uncertainty. The simplest way to think about it is the standard deviation of repeated measurements. This tells you how spread out your measurements are.

How to Write Down Uncertainty

When you state a measurement, you often include its uncertainty. You might see it written in a few ways:

• measured value ± uncertainty (e.g., 10.5 ± 0.1 meters)
• measured value +uncertainty
  −uncertainty (e.g., 3.4 +0.3
  −0.2)
• measured value (uncertainty) (e.g., 10.50(5) meters)

In the last way, the number in parentheses applies to the last digits of the measurement. For example, 10.50(5) meters means the uncertainty is ±0.05 meters. So the true value is likely between 10.45 and 10.55 meters.

If the error isn't the same above and below the value, you use the middle notation. For example, 3.4+0.3
−0.2 means the value is 3.4, but it could be as high as 3.7 or as low as 3.2.

You can find the uncertainty of a measurement by doing it many times. If you average these measurements, the average value will have less uncertainty. This is because the errors tend to cancel each other out. However, this method doesn't account for systematic errors, which are consistent errors in your measurement setup.

When uncertainty is given as the standard error, it means that about 68.3% of the time, the true value is within that range. If you double the range, the chance of the true value being outside is much smaller.

Measurement uncertainty depends on both the accuracy and precision of your measuring tool.

• Precision is how close repeated measurements are to each other.
• Accuracy is how close your measurement is to the true value.

A good measurement needs both precision and accuracy.

Uncertainty in the Media

How science is talked about in the news can be different from how scientists talk about it. This is partly because the public is diverse, and scientists sometimes don't explain things clearly.

Sometimes, the media might make science seem more uncertain than it really is. They might report new research that seems to go against old research without explaining why. Or they might give equal time to scientists with minority views and those with majority views, without explaining which view is widely accepted. They might even give non-scientists the same importance as scientists.

On the other hand, journalists might make science seem more certain than it is. They might remove careful wording from scientists that shows there's still some uncertainty. Or they might only use one source for a story, making it seem more definite. When science is presented as a "triumphant quest," uncertainty is often wrongly shown as something that can always be fixed or solved.

Sometimes, business interests can influence how science is reported. If a scientific finding might hurt a company's business, the media might downplay or remove any claims of uncertainty.

How Uncertainty is Used

Uncertainty is a part of many things in our world:

• In games, especially gambling, uncertainty is key to how you play.
• In scientific modelling, predictions about the future always have a range of possible values, not just one exact answer.
• In weather forecasting, meteorologists now often include how uncertain their predictions are.
• In science and engineering, uncertainty is part of every measurement. The tools you use and how you use them affect how much uncertainty there is.
• In physics, the Heisenberg uncertainty principle is a basic idea in modern quantum mechanics.
• In daily life, we often use uncertainty without thinking. If someone says "He is 6 feet tall," we understand there's a small margin of error.
• In engineering, uncertainty helps check if models of materials are correct.
• In art, uncertainty can be a theme, like a character who can't make up their mind. It can also be a challenge for the artist.
• In economics, uncertainty is very important. Frank Knight showed how it's different from risk.
• Investing in financial markets, like the stock market, involves uncertainty. This is especially true when there's a chance of a rare but very bad event.

Philosophy

In Western philosophy, one of the first thinkers to really explore uncertainty was Pyrrho. His ideas led to schools of thought like Pyrrhonism. These philosophies focused on the idea that we can't always be certain about things.

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