You’ve just tossed a perfectly fair coin for the 6th time. The five previous times it came up heads. What are the odds of it coming up heads again?
Think about it. I’ll just gaze at my Avril Lavigne wallpaper for a few minutes.
Ok, my patronising encouragement aside, most people (but not you my intelligent insightful reader) will probably estimate that it’s unlikely that the coin will yield another head on the 6th successive flip. Not 6 times in a row surely? The answer is of course 50/50, each time, every time. Unlike humans, the coin has no memory, but it is human magical thinking that clouds our judgement of probability and suggests likely/unlikely things that are pretty ordinary.
For instance, did you know that 0.999… equals 1.0?
Another puzzle: let’s assume there are three boxes (Derren Brown presents this game with a ring in one of the boxes. We however will use a far more valuable gift: a lunch date with me). In one of these boxes is a free security pass through my many levels of groupies, cling-ons, bodyguards, escorts, and hired friends. The holder of the pass may spend a lovely lunch hour with me.
You don’t know which box the pass is in. I ask you to select one at random which will be your box, box A. I’ll now get rid of another box, let’s say C, leaving two boxes. I then give you a choice, do you want to stick with your box, or swap it for B, the one I’m holding?
What are the odds that the ring is A or B? 50/50?
What do you do?
You should always switch. You double your chances of winning if you switch to the other box, and thereby avoid having to eat out of a dustbin whilst reading Hello magazine.
Here’s why: there are three boxes. You have a one-in-three chance of guessing correctly at your first try (assuming your intent is of course to win the lunch-date with me, but then only a fool wouldn’t want to win). Which means you have two-thirds chance of being wrong. Assuming you don’t guess the correct box on your first try, one of the other boxes must contain the pass. I know which box the ring isn’t in, so I will remove it from play, leaving two boxes: one with the pass and one without. In other words, assuming you don’t pick the right box on your first attempt (1/3 chance), it will always be in the other box (2/3 chance). So the odds of winning if you switch double.
This is more famously known as the Monty Hall Problem, but I’ve phrased it far more eloquently than Wikipedia ever could.
How many dimensions are there? Length, breadth, and height we all know. There are of course four dimensions though; the fourth being time. It boggles the brain to think of space in four directions, in the same way that it’s very hard to conceptualise huge objects of mass, like planets and stars, bending the fabric of space-time itself, the way a heavy object on a 2D elastic surface will stretch the elastic and create a dent – but this is how space is, in 4 dimensions!
Can you image life before you existed? Do you find it difficult to comprehend a world before you were born? How about after your death? Can you imagine a universe before time?? Well really there was nothing before time. But think about going back in time now. 1 billion years. 2 billion. Let’s go back about 14 billion years to the Big Bang when it all began. Where did it come from? What was before time?? Can you wrap your brain around that?
Think of something small compared to you. (Now now, stop that!) How many times bigger than an ant are you? Millions. In fact, you’re larger to an ant, than the sun is to the earth. But even ants are quite considerably large than say a human hair, at least in width. Can you imagine holding a human hair in your hand now (where you got it isn’t important). Do this now: stretch it out in front of you and hold it tight at both ends, preferably against a light background. Notice how incredibly thin it is! Try and imagine splitting that hair, widthways, a million times! Impossible? Incomprehensible?
A human hair is 6 million atoms wide!
Just to reduce our brains to quivering jelly even more: imagine a single human cell, which in itself is far too small to be seen with the naked eye. The average human cell contains about 100 trillion atoms!
If you were the size of an atom, travelling at the fastest speeds humans can achieve (comparable to your size), it would take you millions and millions of years to travel across the human body. And yet look at the human body compared to a house, or a country, or the earth itself! What if I told you that like an atom is to our planet, so our planet is to the universe!
Look at the sun on a clear day. Well don’t really as if you get blinded you won’t be able to read any more of my website. But even if you tried, you wouldn’t be able to. It’s so bright. Our eyes can barely look anywhere near the sun on a bright day. Can you imagine if it were twice as bright? What about ten times as bright? That doesn’t even make sense does it? How can something be ten times brighter than the brightest possible thing? But a star called Canopus is 14,000 more luminous than the sun! Impressed? The stars Betelgeuse and Rigel are both over 60,000 times more luminous!
Returning again to size: remember how infinitesimally small the atom is compared to a human hair? And how many hairs are there on a human head? And how many humans on the earth? Now let’s say that over 1.3 million earths could fit inside our sun, does that tell you how massive the sun is? Imagine how big that burning son-of-a-bitch ball of plasma is out there, 93 million miles away. For arguments sake, let’s say god exists, and it’s you. You’re holding the sun in your hands now. It’s the size of a tennis ball. Picture that for me. Good. Next to the tennis ball is another ball, which has the diameter of a row of houses, let’s say 700 tennis balls across. Try and pick that up. Go on! That’s the equivalent of the star Betelgeuse compared to our sun!
One last exercise: imagine that Betelgeuse itself was now the size of a tennis ball and you’re holding it in your hand. The star VV Cephei is now about the size of a football!
Scientists suggest that Betelgeuse will go supernova perhaps as soon as in the next few thousand years. When this happens it will brighten by another 10,000 times. Fortunately for earth, the star is over 400 light-years away. But here’s something: we will see its death from earth! Despite being millions of times further away than the sun, it will appear as bright in the sky as the moon!
We’ve looked at just two stars. There are over 200 billion stars in our galaxy. The nearest galaxy is 2.5 million light years away. And there are billions of galaxies. Daylight Atheism wrote a fantastic article recently putting things in perspective when certain people believe that the universe was created especially for man.
My point is something far more ‘everyday’-ish:
As Richard Dawkins has said: the human race evolved to survive in Africa hundreds of thousands of years ago. We have evolved to see medium-sized things on a medium-scale with medium-sized senses. Given the ranges we have looked at briefly, from an atom to the universe, what a human being can actually see, hear, and feel, is so small on the spectrum of existence that it’s barely worth mentioning. And yet, it’s the sum of our existence. Our entire life is filtered through this average equipment that nature has given us.
It’s why we think magically. It’s why we don’t always think rationally. It’s why logical thinking has to be taught to us. It’s why we believe in fairy tales so easily when we’re children but take so long to walk, speak, learn, and analyse facts. It’s why our brains are not naturally good at logic puzzles and at understanding probability like in the examples above.
There are things humans can do, like love, and enjoy music, that I wouldn’t swap for all the understanding of the universe itself and so in that way, we haven’t exactly been dealt a rough hand by Mother Nature!
Fortunately, we’ve been given another gift too: sapience; self-awareness! Although the Turing and Mirror tests might not be conclusive, I think it’s safe to say we’re the only conscious life-forms on the planet. This really is the greatest evolutionary invention of all; you only have to look at the dominance of man on the earth to see it. Putting aside arguments that we may eventually kill ourselves, it is undoubtedly our intelligence more than anything else that has aided our species. It’s our intelligence that allows us to learn and develop more than any other life-form. We can overcome our animal instincts and primitive superstitious thinking with logic and education.
There is no better example of this than science. Everything we’ve looked at here from atoms to galaxies, we know because of science. Despite our narrow window to the external world, science gives us extra hands, bigger eyes, better ears, and longer legs, to examine the world around us. It is the technological extension of our own senses allowing us into a grander world we were never “meant” to understand or see! But because of it we can tunnel with microscopes and see individual atoms of gold, or push aside the heavens with telescopes and look back through time, at galaxies almost as old as the universe itself.
We live in exciting times. You can know more about yourself, your planet, and the universe than humans could at any other time in history! In the here and now we’re at the cutting edge of understanding. You can understand the world in a way never previously done; you can look at the world with the brain of a critical-thinker and the eyes of a scientist; you don’t always have to be the latter, but you should always strive to be the former.