Small Number Visualizer

People are prone to exaggerate very unlikely events, according to Daniel Kahneman’s research (chapter 39, Thinking, Fast and Slow).?Humans, evolved to understand the world in ways that benefitted us, and apparently, we had no use to immediately grasp very small numbers, such as very small probabilities. ?We also evolved to exaggerate unfamiliar risks, while downplaying risks to things with which we have continuous exposure, but have not yet experienced an injury.?

Kahneman’s books are excellent.?Read them and you can start to better understand common biases, and try to fight them by training your thinking mind (System 2) instead of relying on your gut feel (System 1).

To attempt to help train your mind a bit, I have created this visualization tool.??Humans have evolved ways to experience the world around them including understanding distance, area, volume, and time.??And, many people are fluent in games of chance, for example dice, coin toss, and cards.??This tool presents those 7 different methods to help you visualize very small fractions, for example those that come from calculating the odds of rare events.

To get you started, I have included fractions (as of Q3, 2021) for the 6 examples, but you can enter your own fractions whenever you encounter very small numbers.?

If I have made any material errors in the numbers, please correct me in the comments and provide a reference to the correct numbers.

Warning:?In using this app, you may acquire cognitive dissonance, an uncomfortable mental condition.?This app is a lens through which to take another look at your own decisions, and decide if your decisions are correct.???If you become uncomfortable, it may be your mind trying not to change despite new information.??That’s human.

Here are some examples of relatively rare events for your comparison:

Being struck by lightning

“Lightning never strikes (the same place) twice.”?Rare chances are compared to being struck by lightning.?It happens in the US to less than 1 in a million people each year.??Being stuck by lightning in a year is about half as likely as getting dealt a royal flush in poker.?Relative to other risks, it is, in fact, very rare.

Death per mile traveled

Road deaths are often in the news.?Your own risk depends how much you travel on the road (as well as where, and what time, etc.).??The risk can be quantified as chance of dying this year in any one mile traveled.??In 2020, 38,680 people died in on the road.?The amount they drove due to the pandemic was down 13.2% or 430.2 billion miles to 2.828 trillion miles, but the risk per mile was up.

At 0.0137 deaths per million per mile driven, the risk of dying in one specific mile of travel is the definition of infinitesimal.?

Multiply this risk by the number of miles you travel to get an average risk of road death in a year.???For example, driving 10,000 miles per year (the average is 16,000), the number of expected deaths per million people is 137.?Enter 137 into the app for the 'Amount within the whole', and 1,000,000 for the 'Amount of the whole'.?The risk is not insignificant, and much more than some other risk fractions given here.??It’s more than a drop in the bucket—it’s 31 drops in the bucket.??Most people completely accept this risk.?You might ask yourself if you are you comfortable with this level of risk.?Is traveling by road a good decision, or is it a case of downplaying familiar risks??

Under 18, death by Covid, USA

605 children (18 and under) have died from Covid, out of a total population of 74 million children. In other words, Covid has killed 8 out of every million children in the US.

In the US, many were worried enough about children to close schools for months and kept children away from friends, and even forced toddlers to wear masks and get by without seeing smiles.??Many people want to vaccinate them for Covid.??[We vaccinate children for other diseases, but to compare, measles is 188 times as deadly. Diptheria is 25,000 times as deadly.]?Is this a case of exaggerating a new risk, combined with a culture of overprotectiveness?

Compare this the Covid risk to children with something familiar, such as riding in a car.???As I just explained, at 137 deaths per million, riding 10,000 miles in a vehicle is 17 times as deadly-- and yet children are still riding in vehicles.?

Someone will say, “But that’s different.?We are just keeping them home to prevent Covid out of an abundance of caution.”?Or, “If we save one child’s life, it will have been worth it.”?

Well, kids already sit in seats to be safer, sure.?But you could also provide some combination of a 5 point harness, a helmet, a Nomex driving suit, and a roll-cage, and drive only on roads below 25 miles per hour out of an abundance of caution.?Or, you could just never let them ride in vehicles again, or at least try to keep the number of miles they ride to a bare minimum.???If we?save one child’s life, would it be worth it?

I expect that you will not make such changes, because you previously felt car-riding was not that risky. ?Did you know ?the lifetime risk of dying in in a motor-vehicle crash is 1 in 107 (not 1 in 107 million)? ?Now that you know the risk, would you take your children away from the life that they might have based on traveling by car??Or, might that lead to even worse risks?

Consider the known risks to children of the Covid precautions that have been implemented.?Test scores in reading are down 3-6% from where they should be.?Scores in math are down 8-12%, especially for underserved communities which are up to 17% below where they would normally be.?Mental health issues are up 22%.?Child abuse is being under-reported by 20-70%.?These effects on many children will be permanently damaging.??

I could not find suicide numbers for 2020 or 2021 for children, but to compare, about 7,000 persons aged 10-24 commit suicide each year.?It would only take a rise of 9% to exceed the total number of children dying from Covid.? And mental health issues are up 22%.?

Visualize the risk of death to children from Covid as less than 2 drops in the bucket.?Visualize the harms being done to children out of an abundance of caution.?Are the decisions about children and Covid correct?

Over 50, death by Covid, USA

So, then Covid isn’t that risky??Not true.?Keeping to the same comparison, for those over-50 in the US, Covid is 44 times as dangerous as riding in a car for 10,000 miles.??That’s not a drop in the bucket.??No, in fact that is 1362 drops in the bucket.?

Vaccinated vs Unvaccinated

Compare the risks to vaccinated people.?So far, the number of breakthrough deaths is 7178 out of a vaccinated population of 187 million.??

The total deaths from Covid of those over 18 are 724,000 in a population of (over age 18) of 256 million.?Here is a visualization of the risk fractions.?The whole black rectangle represents the population of those over 18.?The white square is for the unvaccinated dead from Covid.? The red square is for the vaccinated dead from Covid.

?Of course, many in the white square died before they could get vaccinated.?Not a fair comparison.??So, I will try to correct for that and make a projection.?After vaccines were widely-available, 100,000 unvaccinated died in the 4 months of June through September 2021, compared to 3980 vaccinated. ???

If that picture holds for 12 months, the picture would look like this:

I estimate 312,000 deaths per year from Covid over the next year, based on the past 4 months. That’s about 2706 deaths per million of the unvaccinated population of 111 million (43% of adults).?And, 82 deaths per million of the vaccinated population of 145 million (57% of adults).?(Compare with a normal flu season and 60 deaths per million for the whole population.)

Right now, the risk to the vaccinated, and those with recent, previous infections, is only 19 drops in the bucket.?Right now, if nothing changes, the risk of Covid to the vaccinated is less than 2/3 of the risk of riding in a vehicle 10,000 miles.?

The numbers above are conservative, and I hope will improve as vaccinations, boosters, and immunity from previous infections in the population rise.?

Changing the subject radically…

Being over 7 feet tall

There were 43 players over 7 feet in the National Basketball Association (NBA) league in the US in 2018.?There are about 500 players in the NBA.?Thus, about 10% of people are over 7 feet.?Wrong.??

It is reported in several places that there are only 2800 people in the world that are over 7 feet tall.?(I have no idea how they came up with this number.)?There are 7.4 billion people in the world, therefore it is extremely rare to be this tall.??About 8% of one drop in the bucket.?About 25% as common as a royal flush.?There is an insignificant chance that you will ever meet a 7 footer.?Unless, you happen to meet NBA players.?

Electric Cars

How common are electric cars in 2021? If I drive around, I see a fair number of Tesla cars in my area.?So, I assumed that electric vehicles are not at all rare.?But, on a global scale, the world has quite a large number of cars.? There is one car for every 5 people.?EVs are not at all common in the world—yet, only 5.6 million out of 1.466 billion.??In our journey to make all cars electric, we are only 11 miles out of 3000 mile from Tampa to Seattle.?If we started in downtown Tampa, we are still on I-275 in the greater Tampa area! ?In the US, there are 1.3 million electric vehicles, out of a total of 287 million.?About 14 miles on our way to 3000.?Still a very long way to go.

Summary

I hope you find this useful in understanding what is common, significant, and rare.?Try putting your own numbers in and let me know if anything surprises you.

Getting the App

Link to html5 version,?click here.?Modern browsers should run it (may have problems on Apple devices).

Download Windows version?here.?Copy the link. Paste it into the browser address bar. Go to the downloaded zip file. Extract all the contents to an empty folder and run the .exe file.

Backup download for the Windows version, click?here?to open Dropbox link.?Use the small download button on the right (next to the Sign-Up button) and choose Direct Download.

Build your own version!

All my numbers are very US data-centric.?You can build your own version!??You can build a MacOS version, if you like! ??Also, you might like to see how a simple app like this can be constructed.?It is very easy.

Here are all the files necessary to build this app.?All you need is a copy of Godot Engine, which is free.?Simply extract the files I’m providing to an empty directory, install the Godot Engine file on your computer, and run it.??Click on the Projects tab in the upper left.?Click Import and point to the directory where you put the extracted files.?Select the ‘project.godot’ file, click ‘Open’ and it should display all the code and parts.?Click the ‘run’ button in the upper right and it should run.?If you want help getting started, contact me.

You can make graphics for your app like I made in a program like GIMP or Inkscape.?I made them in Affinity Designer, and included the files for that software.

Good Luck!

Burney Waring Copyright 2021

Burney Waring is an almost-completely retired global consultant engineer, and Director of Retirement Testing at the Waring Retirement Laboratory.