The single most pernicious threat to liberty today is humanity's natural

tendency to misunderstand the statistics of rare events. We're just not wired to have good intuition about things that happen with extreme infrequency.

I'll prove it. If we were good at understanding statistics, then here's what would happen when you flew to Las Vegas. You'd step out of McCarran airport, stare down the Strip at all those glittering, palatial casinos and say to yourself, "Holy crap – think of all the suckers who must have lost everything to finance this place!" Instead, our foolish minds are filled with thoughts like, "Man, look at all the money in this town – I'm going to win big!" And another casino is built.

The rare – and the lurid – loom large in our imagination, and it's to our great detriment when it comes to our safety and security. As a new father, I'm understandably worried about the idea of my child falling victim to some nefarious predator Out There, waiting to break in and take my child away. There's a part of me who understands the panicked parent who rings 999 when he sees some street photographer aiming a lens at a kids' playground.

But the fact is that attacks by strangers are so rare as to be practically nonexistent. If your child is assaulted, the perpetrator is almost certainly a relative (most likely a parent). If not a relative, then a close family friend. If not a close family friend, then a trusted authority figure.

And yet we continue to focus our attention on the meteor-strike-rare paedophile attack instead of protecting our children from the real, everyday dangers they face from the familiar. This has the twin effects of making our children less safe, and of making adults less free, because we are all subjected to scrutiny on the grounds that we may be hunting children.

This is the same calculus that allows the fear of terrorism to take away our liberty: the statistically super-rare terrorist attacks present, on average, a much lower risk to our health, safety and person than, say, depriving us of our liquid medications, or of requiring us to leave our bags unlocked in flight so that sticky-fingered handlers can make off with our laptops and financial data and valuables.

The everyday threat of having our goods stolen, our ability to travel and earn our livings curtailed, and our personal information harvested by every junior terrorist fighter who wants to see your ID before letting you do anything is overshadowed by the one-in-a-billion confluence of someone with terrorist goals, the means to accomplish them, and the intelligence to bring them off (hint: you can't really blow up an airplane with hair-gel and iPods).

Paradox of the false positive

Our innumeracy means that our fight against these super-rarities is likewise ineffective. Statisticians speak of something called the Paradox of the False Positive. Here's how that works: imagine that you've got a disease that strikes one in a million people, and a test for the disease that's 99% accurate. You administer the test to a million people, and it will be positive for around 10,000 of them – because for every hundred people, it will be wrong once (that's what 99% accurate means). Yet, statistically, we know that there's only one infected person in the entire sample. That means that your "99% accurate" test is wrong 9,999 times out of 10,000!

Terrorism is a lot less common than one in a million and automated "tests" for terrorism – data-mined conclusions drawn from transactions, Oyster cards, bank transfers, travel schedules, etc – are a lot less accurate than 99%. That means practically every person who is branded a terrorist by our data-mining efforts is innocent.

In other words, in the effort to find the terrorist needles in our haystacks, we're just making much bigger haystacks.

You don't get to understand the statistics of rare events by intuition. It's something that has to be learned, through formal and informal instruction. If there's one thing the government and our educational institutions could do to keep us safer, it's this: teach us how statistics works. They should drill it into us with the same vigor with which they approached convincing us that property values would rise forever, make it the subject of reality TV shows and infuse every corner of our news and politics with it. Without an adequate grasp of these concepts, no one can ever tell for sure if he or she is safe.