On the fiftieth day of this year, the numbers started to make our heads explode.

Facebook announced on Feb. 19 that it had agreed to acquire WhatsApp for $16 billion. Reporters and readers alike quickly began parsing that number to make sense or nonsense of it: $16 billion worked out to be $35 per user, or nearly $300 million per employee. It was 16X the amount Facebook initially agreed to pay for Instagram in 2012, which was viewed as a jaw-dropping amount at the time.

In reality, $16 billion was somehow too low. The total price tag was $19 billion if you factored in the restricted stock units Facebook kicked in for employees. By the time the deal closed in October, the price tag had inched up to about $22 billion — you know, give or take some negligible but still very large amount of money — as a result of increases in Facebook's stock price during the months in between.

Not that there really is much of a difference between those numbers: $16 billion is every bit as unfathomable as $19 billion, which is every bit as inconceivable as $22 billion. The only difference between $16 billion and $22 billion, as comedian Dave Chapelle once noted when talking about his own blockbuster contract negotiations, is an "astounding" $6 billion.

This is what a billion dollars looks like, WhatsApp just got 16 of these. Need hand @jankoum? pic.twitter.com/stXoBovo8f — ‮nahtanoJ (@DesignUXUI) February 21, 2014

The WhatsApp acquisition was just one of several moments this year when the numbers in tech — and particularly social media — seemed to lose all meaning.

Reports came out this summer that Snapchat, a startup with no meaningful revenue, was valued at $10 billion — more than five times the market value of The New York Times Company. Uber, a five-year old taxi startup, raised more than $1 billion in funding at an $18.2 billion valuation in June. Now, less than six months later, Uber is said to be raising more money at a $25 billion valuation.

Aswath Damodaran, a valuation expert and finance professor at New York University, has a perfectly reasonable explanation for these figures: It's all relative.

"It really becomes a question of what are you pricing it against," Damodaran told Mashable in an interview. Snapchat may not be worth $10 billion to investors by itself, but if the market already values Twitter at $30 billion-$40 billion, then the Snapchat valuation may make more sense. "Twitter, after all, is not that far ahead of Snapchat," he argues. Likewise, Twitter's market cap, which some have argued is too high, seems more reasonable if you believe it is the next Facebook, which has a $200 billion market cap. (The problem now for Twitter is that many investors don't believe it's the next Facebook.)

What matters to investors looking at each of these businesses — more than revenue and more than profits — is user numbers. With enough users and attention time, you can find a way to make money. That, more than anything, is why Facebook agreed to pay so much for WhatsApp: the messaging app had 450 million users in February and more than 600 million now. "From [Facebook's] perspective," Damodaran says, "they're getting a bargain."

A snapshot of tech valuations this year

Just because there is a reason for the large numbers doesn't mean the numbers are actually reasonable. Anything but.

Each time one of these reports comes out, many readers and, yes, many reporters inevitably scratch their heads, throw up their arms and ask: How did we get to the point where a service that lost $138 million last year can be worth about as much as Netflix? Then, after some period of exasperated remarks, we seem to shrug and accept that this is just how things are now.

Some of this can be chalked up to what economist George Loewenstein calls "coherent arbitrariness." As he and two other economists described it in a paper, coherent arbitrariness is when "the entire pattern of valuations can easily create an illusion of order, as if it is being generated by stable underlying preferences."

There was a time when buying a startup for $1 billion was shocking. Then it became par for the course. Now when Facebook buys a company for a couple billion dollars, it almost seems cute. That doesn't mean the $1 billion price tag is rational; it's just consistent with what we've come to expect. We don't leap out of our seats now for less than $10 billion.

How Facebook calculated WhatsApp's value. The vast majority, more than $15 billion, was for "goodwill."

The problem is that it only gets more difficult for the average person to discern the truth in the numbers as those numbers get more outlandish and more difficult to conceive — perhaps all the more so when the one number that matters to most Americans, average wages, is the one number that isn't getting larger fast.

"Our intuitions start failing us as the numbers get big," Loewenstein tells Mashable.

Facebook revealed that the vast majority of the value it assigned to WhatsApp, about $15.3 billion, was for "goodwill," meaning intangibles like the WhatsApp brand and user relationships. Who is to say whether that number could have been $12 billion or $20 billion. More importantly, would you have reacted any differently if it were?

Apple sells 40 million or so iPhones each quarter and consistently reports tens of billions of dollars in revenue. Twitter announced having nearly 700 million tweets about the World Cup throughout the tournament. Square recently touted hitting one billion payments processed. These figures are so large and seemingly impressive that readers may sometimes be confused by subsequent reports that the companies are struggling.

The effect of large numbers can be felt beyond the tech industry.

General Motors recalled some 29 million vehicles throughout this year. This is what 29 million vehicles looks like. In the face of that, another 500,000 recalled vehicles would barely move the dial, even though that would still represent a tremendous number of recalled vehicles.

The Justice Department announced in August that it had recovered almost $37 billion in settlements with the big banks related to their mortgage lending policies during the financial crisis. It sounds like a tremendous sum, but perhaps not so tremendous when you consider the revenues of the major banks and the potential for some like Bank of America to claim tax deductions on those settlements. Or when you consider the enormity of the financial crisis.

"For the average person, a $1 billion fine and a $10 million fine is about the same," Loewenstein says. "It's hugely different for the companies, but for the average person, they're all the same."

The large numbers didn't start this year, but for those who follow tech and business, they did seem to get even more jaw-dropping. All of us, and particularly reporters, will have to work that much harder to be discerning and skeptical of these numbers next year and beyond.

And on that note: Snapchat is now reportedly seeking funding at a $12 billion valuation. Because why not?