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“Every man has a right to utter what he thinks truth, and every other man has a right to knock him down for it.” – Samuel Johnson
I have a six-sided die. I’m going to roll it ten times, and record each roll. And when I’m done, I’m going to have an incredibly rare, bet-you-can’t-reproduce-it result!
Image credit: random.org's dice roller.
Look at that! Ten rolls of a six-sided die, and I got: 3, 2, 3, 5, 5, 5, 4, 1, 4, and 3! What a glorious, odds-defying sequence of events!
In fact, if you took a fair six-sided die and rolled it ten times, you’d have less than a 1-in-60,000,000 chance of getting that same sequence of outcomes! And yet, there’s no surprise there, or at least there shouldn’t be.
Image credit: retrieved from http://dreamstime.com/.
Because every possible outcome of ten dice rolls — all 60,466,176 of them — was equally likely. But you might wonder if there was something special about the outcomes that I rolled. After all:
- There are no 6′s in any of my rolls, something that would only happen 16% of the time if you roll a die ten times.
- I got six prime numbers in a row (the first six rolls), something that only happens 7.8% of the time.
- There are three 5′s in a row in there, something that would only happen 3.7% of the time in ten rolls of a fair die.
- And the odds of rolling a six-sided die ten times and getting three 5′s in a row and six primes in a row and also no 6′s are only 0.046%!
That last figure, 0.046%, means there’s just a one-in-2174 chance of that happening, or about the same odds as you and I entering a room with twenty-one adult gavials and randomly choosing the same tooth.
Image credi: The Prague Zoo, http://www.zoopraha.cz/.
But the thing is, that sequence of ten die rolls was really randomly generated, and there are a whole bunch of equally unlikely things that didn’t happen.
- I never rolled two consecutive dice to give me snake eyes, something that happens 22% of the time in ten consecutive fair rolls.
- I didn’t get six even numbers in a row, which should happen 7.8% of the time.
- I didn’t get three rolls in a row with the sequence “1, 2, 3,” which will happen 3.7% of the time in ten rolls.
In fact, this type of reasoning — where you ascribe an undue cause to an unlikely outcome from a random process — is a special type of logical fallacy known as the Inverse Gambler’s Fallacy.
Image credit: Bioteknika Healthcare Pvt. Ltd.
It’s very unlikely that the particular sperm that fertilized the particular egg that made you would have been the one to do it, but it happened, and you’re here. It’s unlikely that the evolution of life on Earth would have proceeded exactly as it did, that the planet Earth would have formed consisting of each one of the atoms that makes it up, or that the finest details of cosmological evolution would have happened the exact way that they did to give us the Universe, today, exactly as we observe it.
Image credit: Michael Blanton for the Sloan Digital Sky Survey.
Some of the things that happened were relatively mundane and fairly likely, others were somewhat unlikely and wouldn’t occur very often if you started the Universe over with comparable initial conditions.
But it’s a logical fallacy to state:
Because some thing (or combination of things) that was unlikely to occur wound up happening, our picture of how the Universe got to be this way is probably incorrect.
Because unlikely things happen all the time: that’s part of what comes along with living in a chaotic Universe where many seemingly random outcomes occur. And people — many of whom are often reasonable scientists otherwise — use these unlikely outcomes from random events to try and sow doubt about the quality of the underlying scientific theories.
Image credit: NASA / WMAP Science Team.
There are people who look at the quadrupole and octopole moments of the Cosmic Microwave Background — or the first two points on the graph above — and question the entirety of modern cosmology. Why? Because they state that the “odds” of having a Universe that conspired to give those two data points just randomly is relatively low. (But, for what it’s worth, better than my dice-roll odds, atop.) When you hear the terminology “Axis of Evil” applied to cosmology, this is what they’re talking about.
But there’s nothing special at all about it: if we simulated our Universe millions of times, alignments like this in those two data points would occur hundreds of times. We just happen to live in a Universe where it did.
Image credit: X-ray: NASA/CXC/CfA/M.Markevitch et al.; Optical: NASA/STScI; Magellan/U.Arizona/D.Clowe et al.; Lensing Map: NASA/STScI; ESO WFI; Magellan/U.Arizona/D.Clowe et al.
This is the Bullet Cluster, two large galaxy clusters in the process of colliding, with their hot, X-ray emitting gas shocks shown in pink. It would take these two clusters colliding at very fast speeds to produce these shocks, speeds that are relatively unlikely — to varying degrees — according to the best simulations of our Universe.
But unlikely is a far cry from impossible, and velocities this high are in no sense forbidden. Seeing one example of this in our Universe is by no means damning evidence against our view of dark matter and structure formation: on the contrary, having a Universe where at least one giant galaxy cluster would be moving this quickly relative to another is again more common than winning the crocodile-tooth lottery described above.
Image credit: Boylan-Kolchin et al. (2009) for the Millenium-II simulation; MPA Garching.
And finally, there’s a new paper — being promoted today — that’s just discovered the largest known structure in the Universe!
There are (probably) two distant, large groups of Quasars — intense, X-ray emitting black holes found at the centers of interacting or active galaxies — found some 13 billion light years away (at a redshift of 1.3), that are spread so far across the Universe that it would take light four billion years to go from the most distant end of one to the other.
Image credit: Roger Clowes et al., from http://arxiv.org/abs/1211.6256.
That’s the exciting part, and that’s the part worth reporting. However, in their paper, the authors also claim that this violates large-scale homogeneity, which is the assumption that the Universe is roughly — on average — the same at all places in space. While this isn’t true for a galaxy or even a group of galaxies, it should be the case that, if we put an imaginary box around a large enough volume of space, all places in space should look roughly the same.
Image credit: Matthew Hall of NCSA's Advanced Visualization Laboratory.
The largest structures in our Universe should be about 1.2 billion light-years on-a-side, but if this gigantic, newly discovered group of quasars is just one giant structure, then it’s got a volume equivalent to being about 1.6 billion light-years on-a-side!
But first off, that’s a big if: this could easily be two (or more) separate structures that just happen to be located relatively near one another. We’re only seeing the quasars, here, due to the great distance, and follow-up observations are necessary. And second, even if this is just one giant structure, it could just be the case that this is the Universe we have, and there are going to be some unlikely objects in it. After all, it made all of us, didn’t it?
Image credit: Adam Block / NOAO / AURA / NSF.
So be aware of the inverse gambler’s fallacy, and remember to keep in mind all the great successes of modern science.
Don’t let the observation of an unlikely event swindle you out of our great understanding of the natural world, but keep an open mind for even better explanations, because that’s how science always moves forwards. In the meantime, enjoy our latest discoveries and what’s quite possibly the largest structure in the Universe: so large it might even (somewhat) defy our preconceived expectations!
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