It goes far beyond the familiar warning about objects in our rearview mirrors, by now. I hate to tell you this, but all sorts of objects, everywhere, might not be anything like they appear.

I’ve been reading a book that my friend Ron recommended, called *The Drunkard’s Walk: How Randomness Rules Our Lives*, by Leonard Mlodinow. By a few pages in, I loved it so much, I wanted to weep. Give me a book about geeky-fascinating, blow-your-mind science stuff, and I’m a goner.

The book is about (and do NOT run away here – I’m getting ready to tell you some funky-cool things) probability theory, chance, and how psychological illusions cause us to misjudge the world around us – not because we are stupid or gullible, but because these illusions are so powerful.

I think of it this way: our complex psychological and emotional makeup constantly interferes with our ability to analyze data and use pure reasoning. But also, we exist in both a microscopic world and a macro universe, the scopes of which are virtually impossible for most of us to grasp.

Our elegant brains are simply hard-wired to misinterpret data. Here are a few examples.

**Our perceptions of probability and cause & effect are skewed.**

We tend to think, in our own lives and in the world at large, that an event is either more or less likely to occur because it has (or has not) happened recently. (We think: “Her luck has run out…” “He is due…”) This is the same reasoning behind the hiring and firing of CEO’s or studio heads, when they’ve had a run of several good or bad years/movies.

We – and executive boards, and recruiting agents, and on and on – reason that results are based on performance…isn’t this what we’ve been taught, all our lives? But, as has been mathematically proven (and the book goes into great detail on this), much of what happens in the world is the result of randomness – the result of what is called “Bernoulli’s theorem” (after a 17^{th}-century mathematician) or “the law of large numbers.”

Of course, Kobe Bryant’s talent allows him to perform much better in the NBA than, say, my neighbor Sandra would. But Kobe’s individual performance from game to game, or season to season, or throughout his career, is due almost exclusively to chance, and not to fluctuations in his abilities. This might sound like hooey, but it’s a scientific fact.

Success, as it turns out, really *is* most often a matter of repetition. Bad news for the exceptionally talented of this world. Fantastic news for the exceptionally dogged.

**Our perceptions of relevance, and our interpretation of statistics, are skewed.**

During the O.J. Simpson murder trial, it was an accepted fact that Nicole Brown had been previously battered by O.J. So one of the arguments that the defense team pulled out was this: Of the 4 million women who are domestically battered each year, only about 1 in 2,500 are killed by their partners.

This was a true fact. It was a very convincing argument, to the jury. And on an intuitive level, it appeared to be completely and totally relevant to the O.J. case.

But it wasn’t.

Why not? Well, the previous statistic dealt with women who are NOT killed – and Nicole most definitely *had* been killed. The relevant statistic (and one the prosecution failed to bring up) was this: of all the battered women in the U.S. who *are* killed (and Nicole was part of this category), 90 percent of them are killed by their abuser.

The first (irrelevant) statistic created such a powerful illusion, it helped convince the jury to acquit a double-murder defendant.

**Our perception of logic is skewed.**

Here’s a fun example of the way our brains resist reality, from *The Drunkard’s Walk.*

Let’s say you know that someone has twins, and you wish to determine the likelihood that both children are girls. If you don’t know the gender of either child, then the chance that they are both girls is 1 in 4. Sounds logical, right?

Moving along, let’s say you find out that at least *one* of the children *is *a girl. Now the chance of them both being girls increases to 1 in 3. (Still sounds right.)

However, if you are told that one of the children is a girl named Florida (!), then the chances of them both being girls increases to 1 in 2.

*Whoa, whoa, whoa, back that train up.*

How can this be? How can one girl’s strange-sounding name affect the odds on the gender of the other child?

And yet, as Mlodinow painstakingly proves over a few pages, this outlandish statement is an absolute fact. In this example (and in so many others, throughout the book), my own instincts for mathematical reasoning completely failed me.

Moving away from *The Drunkard’s Walk*…

**Our perceptions of space and time are skewed.**

As we’ve all heard, we (and everything else in the universe) are not moving in a linear way through space and time, from point A to point B; instead we are moving through four dimensional space-time, a concept that even Stephen Hawking calls “impossible to visualize.”

When we look at the sun, we are seeing it in the past, as it existed eight minutes ago – but since everything we perceive comes to us via signals (which require time to travel), even as you read these words, you are looking at your computer screen as it existed in the past (infinitesimally so, of course.)

We’re not just “lost in space,” peeps – we’re lost in time.

**Our perception of reality might even be skewed! **

The more you start thinking about all these problems with perception, the more widespread you realize they are. Indeed, this recent article from Discover Magazine suggests that our entire universe might be – are you ready for this? – a giant hologram.

This theory will never be proved in our lifetime, of course, but it certainly dovetails nicely with the Christian belief that this world is but a pale twin of another dimension, the “real” reality that is our eternal destination.

(And may I humbly submit: if you are someone who rejects the concept of God and/or Christian beliefs because they seem too far-fetched, too “hocus-pocus” for practical people, then you haven’t been paying attention to the world of science in the last decade. From space exploration to theoretical physics and everything in between, the physical laws of this universe are far wackier than anyone ever imagined. You can still have *personal *objections to Faith, if you like – but you really can no longer reject it on *intellectual* grounds.)

*********

I’ve barely scratched the surface here – but it sure would be nice if this information made us think twice, the next time we want to dig in our heels about our points of view on something. Because chances are very good that our perception is flawed – that there are factors we haven’t considered, or aren’t even aware of.

If mankind understood this concept, it would deliver a death sentence to arrogance of every sort – intellectual, spiritual, societal.

And that would be a very, very good thing.

It is early and my brain has not yet caught up with the caffeine, but the part of me that has never had much of an affinity for Science stuff is finding fascination anew. Partly because of your excitement and ferver and ability to communicate it in such a way that we the little people can understand, but also…I just completed a class called ‘Interpersonal Neurobiology’ and I stand in awe and wonder by what I’ve learned. I won’t write a blog post response (maybe I’ll do that on my blog at some point), but what fascinates me above all else is how Science and what it proves and is still finding…is right there in Scripture. 🙂 I love that!

I love this stuff so much…I want other people to love it, too! I’m glad my enthusiasm shows through. 🙂

Thanks for letting me know. And let me know if/when you write that post, too! I’d like to read it.

Good post, Cathy. I’m going to have to pick up the book!

Couple comments…. On the OJ trial, you’d think the opposing lawyer would be smart enough to dig up the competing statistic, but they didn’t do it. I was on a jury in LA not long after OJ, and the prosecution did a similar job of not bringing up questions/evidence that could have clarified what happened (I thought the prosecutor stunk). We ended up with a racially divided hung jury when certain jurors refused to believe the testimony of the cop….. sigh. The justice system….

On the probability with the two girls, it’s not so much that one is a girl and you know the name, the key issue is that one specifically was identified as being a girl — ie, you know which one of the two it is. (Could be the one on the right, the one that is smaller, etc.) Once the gender of one is certain, the question becomes a 50/50 on the gender of the 2nd one.

(Sorry! The math teacher in me always wants to throw in his two cents worth to clarify an illustration!)

Really good post. There is so much that is beyond knowing, and our perceptions can’t be trusted. Did you ever see the video clip about being wrong? I’ll see if I can find it and post it to your FB page….

Actually, Dan…the name of the girl DOES change the odds. That’s what blew my mind! (And yes, you must get the book…to read up on all this mind-bending stuff.) When you know that one of the kids is a girl, the odds of them both being girls goes to 1 in 3 (because the options are boy/girl, girl/boy, and girl/girl.)

But here’s what happens when you know one of them is named Florida. Since the chances of BOTH girls being named Florida is virtually nil (according to the author, and according to common sense), you can throw out the option girl-F/girl-F. So then your options become: boy/girl-F, girl-F/boy, girl-NF/girl-F, and girl-F, girl-NF. Which makes the odds of them both being girls: 1 in 2, instead of 1 in 3.

(girl-NF = a girl NOT named Florida.)

CRAZY, huh?

We’re agreeing vehemently! (a favorite phrase some of my physic major college friends liked to use!)

You’re right, either kid could be “Florida” and the math becomes 1 in 2, Given that a girl is Florida, than the odds of the 2nd kid being a girl is 1 in 2. This is because, if order doesn’t matter, then boy/girl-F is the equivalent of girl-F/boy and girl-NF/girl-F is the equivalent of girl-F/girl-NF.

The key to this working out isn’t just that there was one girl named Florida, but the 2nd kid was NOT named Florida — that’s a 2nd “given” that narrows the possible combinations.

This is going to look really absurd laying this out, but I’ll go ahead! There are actually 16 possible combinations if we’re using two variables with two kids and two possible “names” – F & NF. That’s (2 ^ 2) ^ 2 = 16 (where ^ is the exponent, like in Excel.) If we break down our original b/b , g/g , b/g, g/b possiblities each with the F/NF split, you get four naming possibilities with each set, right?

So theoretically, in our girl/girl combo, you could have girl-F/girl-F, girl-F/girl-NF, girl-NF/girl-F, and girl-NF/girl-NF, right? Similarly, in the boy/girl combo, you have four potential name combos…. same for the girl/boy and the boy/boy (don’t worry, I won’t spell them all out!)

In total then, there are 16 possible name/gender combos. By saying that one of the kids is a girl named Florida (girl-F) and that the other kid is NOT named Florida, he’s eliminated all but 4 of the 16 combos possible, leaving the four you named. And 2 of the 4 combos have 2 girls, so the odds are 1 in 2.

Here’s where it gets a little weird (as if it wasn’t already!): if you allow for the possibility that George Foreman could be the parent (and give all his kids the same name) and therefore we do NOT eliminate the possibility of having the 2nd kid – boy or girl – named Florida, then the odds become 3 in 7 that we end up with 2 girls. (That’s because 7 of the 16 combos have at least one girl-F, and 3 of those 7 have 2 girls.)

So, in case you’re not sure, I’m not disagreeing with you! I just gave more backup for why it works this way….

Obviously, the author doesn’t think like George Foreman — I think he has 5 boys all named George!

Oh, okay. Where you threw me off was this statement: “Once the gender of one is certain, the question becomes a 50/50 on the gender of the 2nd one.” Because in this scenario, according to the author, the chance of the 2nd kid being a girl is 1 in 3 (not 50/50).

Options: boy/girl, girl/boy, and girl/girl.

I knew that’s what you meant, and I’m agreeing with you on the 1 in 3. If you eliminate boy/boy, then there’s a 1 in 3 chance of girl/girl.

The type of probability I was referrring to with the 50/50 is a “conditional” — you’ve already checked the result of the first test, and knowing that result (100% chance first one is a girl) leaves you with a 50% chance on the outcomes of the 2nd test.

I know what you meant and agree with it, and I know what I was thinking and have a hard time explaining it!

WOW AND DOUBLE WOW, CATHY!!!!!!

That’s what I thought, Anna! 🙂

“And may I humbly submit: if you are someone who rejects the concept of God and/or Christian beliefs because they seem too far-fetched, too “hocus-pocus” for practical people, then you haven’t been paying attention to the world of science in the last decade.”

Agreed, 100%. It’d be nice if we could someday get to a reconciled explanation that ties the science and faith parts together. But, to get there, we may need the faith side to drop the insistence on literal interpretations of some portions of the Bible, and the non-believing side would have to acknowledge that maybe there is an external force that played a hand in designing the whole thing.

What was that you said? Probably not in our lifetime….. Yeah, that’s probably the case.

Precisely so.

You really do need to read the book…you’d LOVE it.

Simple math: among all two-child families with a girl, the proportion that have two girls is 1/3. It’s because 75% of two-child families have a girl, and 25% have two. Simple math. Similarly, among all families that have a girl named Florida, the proportion that have two girls is just under 1/2. It goes up from the 1/3 derived above because only one child can be a girl-named-Florida in a one-girl family, but either of the two can be in a two-girl family.

But “proportion” is not the same thing as “probability,” a fact Dr. Mlodinow should know since, if I recall correctly, he used the classic argument for why they are different in his book. That argument is called Bertrand’s Box Paradox, and it differs from the Two Child Problem in only one aspect: the number of original cases. It uses three, while the Two Child Problem uses four. I’ll paraphrase Bertrand’s (circa 1890) argument for Mlodinow’s example:

“Suppose you recall that a family has two children, but you don’t recall the genders. What are the chances both genders are the same? That’s easy: 1/2. But what if you remember that one is a girl? You might be tempted to say the chances change to 1/3. But you would have to make the same change if, instead, you remembered that one was a boy. But if the chances are 1/3 no matter what you recall about one child, the Law of Total Probability says the answer to the original problem has to be 1/3 even if you don’t recall anything about one child.

The resolution to this paradox is that an event where a two-child family HAS one girl, is not the same event as the one where you RECALL THAT such a family has one girl. There can be families of a boy and a girl where you recall the boy and not the girl. And just like in the “Florida” version, assuming you have no biases, you are twice as likely to remember a girl from a two-girl family, as from a one-girl family. That makes teh answer to both questions EXACTLY 1/2.

As I said, this difference has been well documented since about 1890. But it wasn’t a brain-teaser then, it was a cautionary tale about the possibility of careless errors in probability. It was applied to brain teasers as early as 1959, when Martin Gardner retracted his answer of 1/3 for a similar question about boys, saying the answer could be 1/3 or 1/2, depending on how you obtained the information about the one child. Dr. Mlodinow’s book is very good, but he committed a major error in this problem.

I just wrote you a long response and now it’s disappeared.

Anyway, perhaps I made an error in my transcription? You sound way smarter than me, so I will defer to you…but it’s possible the error is mine (unless you’ve read the book and seen and error?)

I don’t understand this stuff unless I’m reading it from the beginning, so since it’s been months since I studied up on this (and I am not a scientist), I am not quite tracking what the discrepancy is.

My “learning” posts are intended to get the average lay-person who dislikes science, to see how cool it is! I do try to be completely accurate, so I appreciate you pointing out if I’ve made an error.

Thanks for taking the time to read and comment. Hope you’ll come back and keep me in line if necessary! 🙂

No, you transcribed everything fine. I’ve read Mlodinow’s book, and he is wrong on this point. If you want a comment from others with a similar level of education to his, google for an article by Professors Marks and Smith at Pomona College. I’m on vacation right now, so I don’t have direct access to my links.

BTW, if you don’t understand what I said about the Law of Total Probability, one form of it says that if you can (1) divide the set of all cases into N non-overlapping events {X1, X2, …XN}, (2) determine the probabilities P(X1), P(X2), …, P(XN), and (3) determine the conditional probabilties for some other event E, P(E|X1), P(E|X2), … P(E|XN); then the unconditional probabilty P(E) is equal to P(E|X1)*P(X1)+P(E|X2)*P(X2)+…+P(E|XN)*P(XN).

For the example I gave, there are only two ways you can recall one child, so N=2, X1=”recalll one is a girl,” X2=”recall one is a boy,” and P(X1)+P(X2)=1. (We could assume more specific values for them, but don’t need to.) Let E=”both share a the same gender.” We know P(E|X1)=P(E|X2), but the question is whether they are 1/3 or 1/2. We also know P(E)=1/2. Plug the values that I’ve listed in, and you get P(E|X1)=P(E|X2)=P(E)=1/2.