The Multiverse is not the answer (Synopsis)

“Physical reality does not require that we be pleased with its mechanism; we must see the implications of a theory for what they are and not for what we would like them to be.” -Kevin Michel

If you've been following along for a while -- particularly in light of the recent BICEP2 results -- you're well aware that not only do we understand the history of the Universe all the way back to a hot, dense expanding state, but we've gotten a window into what happened before that: there was a period of Cosmic Inflation!

Image credit: ESA and the Planck Collaboration, modified by me for correctness. Image credit: ESA and the Planck Collaboration, modified by me for correctness.

And while this was going on, there were places where inflation ended, giving rise to a Universe like our own, but other places where it didn't, either giving rise to a Universe much later, or continuing to inflate exponentially until the present day. The consequences of this inevitably create what we know as a Multiverse.

But is that an explanation for why the fundamental constants of the Universe have the values that they do?

No. Not at all, in fact. The Multiverse is not the answer; go and find out why.

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Thanks Ethan for the food for thought.

Something I've wondered about is the value of the quark electric charge:- -2/3 & +1/3. Do we have a "natural" explanation for this? Everywhere I've looked the quark is described as an elementary particle ~ which I take to mean it can't be split into sub-units. I've read up [at layman's level] regarding magnetic monopoles but I don't know why something smaller would necessitate monopoles [if they do!] & I'm not sure that what I've described above is coherent! Sorry.

Is it possible that quarks are not fundamental & there's some further subdivision of the various quark types that leads to the above two charge values?

Do we have confidence somehow that the quark is as far down as it goes or perhaps we can't achieve the energies yet to determine the answer?

By Michael Fisher (not verified) on 02 Apr 2014 #permalink

Sastra put it best when she said that only finding ourselves somehow surviving in a universe that didn't allow us to exist would be convincing proof of God.

Of course we're going to do our best to find out what dark matter is, where all the antimatter went, why all the different fields have the strength they do, and maybe we'll eventually find that they're deeply linked and that this is the only way they could be. This the only universe we have, and it likely has some yet undiscovered underlying regularities even if it's only one of many.

"And while this was going on, there were places where inflation ended, giving rise to a Universe like our own,.."

Is there any reason to suspect they would be "like" our own? Would what we consider universal constants have to be the same there?

The question we want to answer is how: how did the Universe come to be this way, to have these properties? And saying “the anthropic principle” or (even worse) “the multiverse” simply isn’t going to cut it.

I'm a bit less negative about it. The anthropic principle suggests some types of hypotheses, which we could then try and test (though I admit I don't know how we would do that).

As an example, if someone uses the weak anthropic principle to say that we are nothing but 'lottery winners,' then that suggests that the lottery draw is at least somewhat random or probabilistic. I.e. that whatever caused the physical constants to be what they are, that cause could've resulted in many different values, either equiprobable or at least not heavily weighted towards the current values. Well, that's an hypothesis. Or it can be. Someone smart can maybe take that claim and try and develop it into a mechanism (because we now have a posited property: the mechanism must allow for multiple values) and a set of additional testable claims.

So, invoking the anthroptic priciple is not necessarily a science-stopper. It can be, but it doesn't have to be.


Would what we consider universal constants have to be the same there?

I think the only real answer right now to that is "we don't know." The people who posit "they could've been different" are on just as shaky empirical ground as the people who posit "they could not have been different." In order to reach either conclusion, you must have at least a vague notion of the mechanism of formation for constants. But in fact neither group has a well worked out mechanism or evidence for whatever notion of mechanism they may hold in their mind.

Put simply, I don't think "absent a known mechanism, any value was possible," should be the "default" winner. Its an hypothesis just like "the values could not have been different" is. Neither is well worked out, and neither has evidence for or against it.

Re. the mis-use of the anthropic principle:

Another case of "emotions lead and reason follows," whereby individuals who either have limited curiosity or unlimited discomfort about ambiguity, look for a "reason" to put enquiry to bed and seal up their belief systems as complete and final.

To my mind the anthropic principle suggests a line of enquiry (once we have adequate supercomputer capacity) to build and run mathematical simulations using different values for each variable, and see which ones lead to protein synthesis. Let's see how far we can alter each value before the properties that emerge don't support the rudiments needed for life. In this case the emotion that leads is ferocious curiosity, and the reason that follows is all the justification needed to pursue dynamics as far as possible.

Why not start right now and set up a distributed computing project similar to SETI At Home, where people can donate unused CPU cycles to run small parts of some basic alternative-value simulations? Or pester NSA for a few dozen of their obsolete Crays to string together in a secure facility for the purpose?

That segues into the multiverse:

Assume a multiverse that produces universes including our own (home sweet home!;-). A-priori we can assume that the multiverse is lawful, and that its laws lead to the ones we observe. Thus it's hardly a stretch to infer that all of the universes it produces will have similar or even identical laws. There might be different values for key variables, but only within the overall constraint of the starting laws. Thus there might be an infinity of universes, but they would exhibit similar or the same physics to our own. We might be able to work our way backward from observables in our universe, to understand the laws of the multiverse and thereby infer the range of what is possible in other universes.

In a vague intuitive way, this feels like what we went through when we discovered that our universe wasn't just the Milky Way but something much larger that was infested with galaxies. Today we know that physics is uniform across all of those galaxies even though they vary in certain ways. If nothing else, the assumption of underlying uniformity gives us something to work with, which is better than just throwing our hands up in the air.


I think what you are proposing is very similar to what Ethan is saying. The question of why our universe is the way it is would presumably be answered if we could deduce the laws of the multiverse that govern formation of universes. However, it does seem a bit overly simplistic to me to assume that other universes would have essentially the same physics as ours, unless by that you mean that they would be governed by the same overarching "laws of the multiverse". Saying such a thing is analogous to saying that the behavior of humans and that of rocks are the same. Both are governed by the same overarching laws of physics, but obviously both behave in different ways.

Similarly, even though other unvierses would be governed by the same overarching laws, I don't think it's a stretch to think that it's possible for other universes to have significantly different physics from ours. Of course, it's all speculation until (assuming we do) deduce the overarching laws of the multiverse. Some aspect of those laws could well constrain the physics of individual universes.

It's a condom!

In the beginning-GOD!

Hi Ethan,

Of course, the real purpose of the anthropic principle (yes, often abused, and extremely badly named) is to see how knowledge of our own existence affects inferences we can draw about reality.

A simple example would be to imagine an observer finding itself in a universe, unable to identify any other observers - knowing only that it exists. Is it more probable that this universe contains only 1 observer, or a gazillion observers? Some say this is analogous to saying: X won the lottery, what is your best guess for the number of lottery tickets X bought? (Often, lotteries are won by groups who buy large numbers of tickets - there are obvious reasons why this works!)

Nick Bostrom has written quite a bit on these types of problems ( see here for example).

I have tried to investigate what types of anthropic reasoning are valid, but I confess, the problem is difficult, and I've not found a satisfactory answer.

Do you have some insight on this topic? I would love to hear it.

By tom campbell-r… (not verified) on 03 Apr 2014 #permalink

Here is something that may or may not be a coincidence. It is a pure number relation involving aspects of 'number theory' using Ramanujan's constant and Lucas' cannonball problem of 1^2 +2^2 +3^2......+23^2 +24^2 = 70^2. This square form relation of 70^2 also is used to construct the Leech lattice via a Lorentzian lattice II25 iin 26 dimensions.
Quickly before I lose the audience: exp^2(Pi*sqrt(163))*70^2 = 3.37737368....x 10^38 (dimensionless). This relation is very very nearly equal to hc/2PiGm^2 = 3.37722(40) x 10^38 (dimensionless) where h = Planck constant c = speed of light G = Newton gravitational constant and m = neutron mass all using Codata 2010. So here is a pure math relation that may have an equivalent physics form. NIST Codata will be releasing new values for the constants in 2015 to be called Codata 2014. We will see if these numbers and uncertainties get better for this unusual calculation. For additional information see OEIS A161771

By Mark A. Thomas (not verified) on 03 Apr 2014 #permalink

Why is the multiverse a bad answer?

I mean, if someone wind the lottery we assume it's random and that guy got lucky. That doesn't mean you can't figure out the odds of winning.

If your universe is one of an infinite number then by definition there's a universe somewhere out there that has every possible value of alpha, or the mass of the electron, or the charge or dark matter (or no dark matter).

That would say to me that the question for physicists/ cosmologists is "simply" what process governs the values of those constants. That is, is there some overarching set of rules that determines the range of values constants can have over an infinite number of universes, or is the universe really just randomly put together? The latter is a possibility, it's even in principle testable. So from that perspective I don't see why it's necessarily unscientific. But maybe I read the piece wrongly. Did I?


Saying it's so "by definition" isn't proving your answer, it's refusing to consider that it might be wrong.

I don't see anything in the definition of "infinite" that requires all those universes to have different values of alpha, or of the electron mass, or any other physical constant. You're assuming both that the values of the constants are random, and that the number of universes is at least as great as the number of combinations of constants. Even if the values of the constants are random (and you can prove it), that doesn't mean the number of combinations is no larger, unless you can show that the constants are constrained to be rational numbers. I don't see how you could do that without proving or at least theorizing something other than "the multiverse" for the sources of those constants.

Re. Sean @ 7: Yes, I agree with you and with Ethan on this, and apologies for my comment being unclear about that.

Humans and rocks are both made of chemicals, and the interactions of various chemicals are lawful. Both have mass, and the behavior of mass is lawful. But clearly that doesn't mean that humans and rocks exhibit similar behaviors in the sense of "behavior" as voluntary action;-)

Unless there are empirical results or good theories saying otherwise, I'm inclined to believe that there are overarching laws of physics that govern the multiverse and that are reflected in individual universes. But I'm not attached to beliefs, so this belief will change easily if results/theories indicate it's not correct.

Ordinarily I'm inclined to be skeptical of reliance on computer simulations (that is, they are useful up to a point but are often misused), but this is clearly one area where they will have very substantial value. We may be able to at least get a sense of some outer boundaries this way, such as combinations of values that produce universes that immediately self-destruct.

Jesse @ 12: There may be combinations of values that are not possible, or that immediately self-destruct. Those would demonstrate limits on the possible types of universes. I'm inclined to think that applying the concept of "infinite" to "variation" creates risk of blurring together various concepts in ways that leads to errors. The multiverse may be (and probably is) infinite in its extent in spacetime, and the quantity of _universes_ it produces may be infinite, but the quantity of _types_ of universes it produces may be limited. There may also be room for infinite variation _within_ a limited range of possible types of universes, though some of those variations may be so slight as to be inconsequential.

Right now we're at a very early stage of understanding, where we first need to be on firmer ground about the existence of the multiverse and the potential for variation in the core laws of physics, as well as the potential for limits or lack thereof on the values of relevant variables.

Thanks I was thinking that if you have an infinite number of universes, some last for a picosecond and disappear because their constants are "wrong" for a universe like ours. Others go longer before the Big Rip. Some last infinitely long and have nothing in them and are static. It seems to me obvious that if you have an infinite number of anything, odds are you'll have infinite variations there and that is still not a problem -- it's still possible to say that in that random variation there are X number of possibilities (or a range) that make universes conducive to life, and to discover what controls that. Maybe there is a universe where the value of alpha is one over 10 times the square root of two or one over 30 times pi. Needn't be a rational number.

But either way, we got lucky. Just like we can accept that the arrangement of stars in the sky is basically random. (While there are constraints on where in the galaxy we are and such, the particular configuration we see at the particular time humans got smart enough to look up is basically random -- the ecliptic could have been anywhere from 0 to 360 degrees tilted to the galactic plane, for example, and the pole star could have been Antares -- the arrangement we have is just luck).

That seems to me a more logical explanation, anyway. Lots of things are just random, you know?

As my physics teacher just noted this week, the probability of a radioactive decay at any given instant is precisely zero. The probability over time can be measured. You can't know which atom will decay tho, because it is absolutely random. Same for figuring the probability that an electron is somewhere. Yes it is "really" somewhere, by one measure, but you can't tell exactly where. It could be literally anywhere in the universe if you were to measure it's momentum exactly. (The limits are 0 to infinity). So the idea that some things are just random might be a fundamental fact of the universe we just have to live with.

"God" plays dice all right, and He uses fair, unloaded ones.

I look at it lie this: when you die the universe basically disappears as far as you are concerned. Why didn't you die yesterday? Tomorrow? Last week? Is there some fine-tuning of the universe that kept you alive last Tuesday? That gave you birth? That made you want a ham sandwich? We accept that stuff like that happens without the need for worrying about fine-tuning. Every outcome of every event is by itself pretty unlikely if you string enough of them together. Physical laws place constraints on it, but while we accept that baseballs fly the way they do because of Newtonian mechanics, we don't get into why the universe is so fine tuned that Derek Jeter was born precisely when he was to hit that baseball on that particular day.

I don't know why all the fuss with the Anthropic principle. It's a philosophical statement, not a scientific one. Anthropic principle is just truism. It's not a science method or anything of sorts. Universe must be such to support life because we are here.. and alive. Wow, what a revelation.

When taken out of context and applied to physics as a "scientific" explanation for anything, it's just baloney. And the more press it gets, the more people will talk about it, and the idea with get more credence.

Anthropics can be interesting argument when talking about philosophy of science, but it has no place in hard facts, experiments and math of physics.

By Sinisa Lazarek (not verified) on 03 Apr 2014 #permalink

Note that the fine-structure constant is a running constant, see NIST. The coordinate speed of light varies with gravitational potential. The locally measured speed of light is constant by definition, it's a tautology. Gravity is not a force in the Newtonian sense - when you drop an electron some of its mass-energy is converted into kinetic energy and its mass reduces, hence the mass deficit. So the "fine-tuned constants" is a popscience myth. See what Sinisa said above?

"When taken out of context and applied to physics as a 'scientific' explanation for anything, it’s just baloney. And the more press it gets, the more people will talk about it, and the idea with get more credence".

The same goes for the multiverse.

By John Duffield (not verified) on 03 Apr 2014 #permalink

Sinisa @ 16:

The anthropic principle is basically a tautology, but like good art, it can lead to asking interesting questions. Some of those questions are amenable to scientific treatment, per my point about running simulations to see what results occur from altering the values of variables.

The sense of insight that good art inspires isn't science either, but nobody would argue that people who are committed to scientific thinking should eschew art. Nor does art have any place in facts (measurements), experiments, and the math of physics; but nobody would argue that it does.

As for what appears in the press, anthropic or otherwise, we have no direct control over that. But we can go into public forums and seek to correct the sloppy thinking that the sloppy media engender.

Jesse @ 15:

If you have an infinite number of anything, you may have infinite variation, or you may have an infinity of identical objects, or something in between.

If that infinity is the product of lawful physics, then I would assert that the objects in it are as well, and should comport with the same laws. That's a logically-viable statement, but so far it is not empirically testable. It may be correct, or as you say, it may be incorrect, and infinite variation of types is possible. At this point we have no objective basis in facts (measurements) to decide the matter. Instead what happens is that folks such as you & I discuss and debate these points until we find out that someone who is working full time in the field has come up with an answer that makes sense to his/her peers and meets every reasonable criticism.

Randomness adds spice to life, and the converse is also true (life adds spice to randomness;-)

You mention your physics teacher: what year are you in school?


I tend to agree with you. Hoyle's prediction of a then-unobserved excited state of carbon is generally quoted as the classic example of the valid use of the anthropic principle. Yet, the principle in and of itself was basically meaningless. We would not have given any weight to Hoyle's prediction based solely on the anthropic principle; it was only with the actual observation of Hoyle's excited C-12 state that his prediction was accepted.

The AP might lead us to ask the right question or make the right prediction, but it certainly doesn't change anything about how we actually do science.


Then I think we are in agreement. I would tend to think that there must be overarching laws of the multiverse. Of course, that (like almost everything else we can say about the multiverse) is just speculation. I cannot conceive of a multiverse lacking in lawful behavior, but that is just argument from incredulity, not evidence for such laws. The presence of such laws does not imply, however, that other universes cannot be much different from ours in significant ways. That was the main point of my earlier post.

Indeed, the often cited example of Hoyle's triple-alpha process has literally nothing to do with the anthropic principle. The existence of carbon is enough to postulate Hoyle's mechanism - just as falling apples were enough for Newton to postulate gravity.

But this does not mean that Hoyle's mechanism gained acceptability only through its direct experimental verification. If X happens, and theory Y predicts that X happens, then by Bayes' theorem, Y is vastly more probable than any theory according to which X is forbidden.

The real purpose of the anthropic principle is to see what models of the universe are more likely, conditioned on the fact that we are here looking at it. E.g. am I more likely to exist in an infinite multiverse than in a finite universe? (These likelihoods affect the posterior probabilities for each of these hypotheses through Bayes' theorem.)

The prior probability for any particular human to come into existence does seem extremely small. In science, extremely improbable events are generally considered as demanding explanation - they provide strong evidence for something, the question is, what?

The deeper question is, what counts as improbable? We feel like a string of 100 identical random digits is improbable, though in fact, it can be argued to be as improbable as any other string of 100 random digits. If we pursue this thought, though, suddenly we end up with nothing being improbable, and probability theory, hence science also, becoming utterly useless, which is clearly (probably) wrong. I'm not aware of any definitive statement that allows us to determine what is 'surprising' and what isn't - science desperately needs such a principle, however.

Dismissing anthropic reasoning seems premature to me. It potentially affects the plausibility of different models of reality and it exposes some fundamental issues in probability theory, upon which science depends completely.

By tom campbell-r… (not verified) on 04 Apr 2014 #permalink

While on subject of AP vs Multiverse, IMO they shouldn't be in the same basket in the first place.

Multiverse is not a philosophical concept (like AP). Multiverse shouldn't be confused with Many Worlds QM interpretation which could be classified as philosophical.

While some choose to invoke AP as a "reason" why certain things are the way they are in the Universe, which is an extreme falacy IMO, Multiverse was never "invented". It came out of inflation math. The premise of inflation is the pre-existance of a field which which doesn't terminate. Thus, while exponential inflation ends in certain areas, it lasts in other and so on. Thus Multiverse arose from math, not our desire to create more universes or make placeholders for different constants. It arose from a solution to a different problem. It still doesn't make it true or real. It's still a hypothesis that we might never be able to test. But that's how it came to be.

It was only LATER that other physicists thought.. hey, there's a handy thing about all those bubble universes, we can say that each is different and thus the nature values will be randomly distributed.

So, in all honesty, it's just not right to compare the two. Multiverse might not exist, but AP is not an alternative since it's not even physics.

I could argue that the reason why Universe is like it is, is because it prefavours PVC. Yeah.. polyvynilchloride... plastic.. Not life.. And all the arguments are same... proof:
There is much more PVC in the universe now then it was 13 billion years ago. Since PVC is an extremely complex molecule, the chances of it randomly occuring are highly unlikely. Thus any model of the universe we make, must allow for a production of PVC. Life is not special... we are part of universe... tasked with production of PVC...

Absolutely ridiculus, but just shows why AP is not science. One can argue for anything in the universe as a reason for why universe is such.. life or no life.

By Sinisa Lazarek (not verified) on 04 Apr 2014 #permalink


"some choose to invoke AP as a “reason” why certain things are the way they are in the Universe ..."

what you are talking about is indeed a fallacy, but it is a straw-man version of the anthropic principle.

The point of AP is not to explain anything, other than our own existence - what theories are more plausible, viewed in light of the evidence of our own existence?

Your conclusion that "AP is not science" is premature.

By tom campbell-r… (not verified) on 04 Apr 2014 #permalink

Sorry, if this get long :-)
First, I think Einstein was brilliant in exchanging gravity, which he could not find an explanation for, with the observable effects, which he could well describe.
So, if mass deforms space/time, that leads us to observe "gravitational effects" caused by space/time being deformed. We can count and calculate with that pretty good, despite most of us lacking the imagination to actually capture the concept of space/time either being stretched and/or being compressed.
If mass deforms space/time then a black hole retains its mass, contrary to the (common) believe that it would destroy all matter it accumulated. The matter is still there but it is in a heavily compressed part of space time, whereas the total mass of a black hole would stretch the surrounding space/time towards it. Now, my question is again, if we could calculate the theoretical maximum of mass a black hole could have before it starts to disperse, because the matter it contains within a heavily compressed portion of space time must and will disintegrate. If such disintegration would be possible and would happen, we should observe the immediate loss of mass and subsequently the dispersal of the black hole and in turn also we should be able to observe the formerly compressed space/time within to inflate at drastic speeds and the surrounding formerly stretched space/time to "snap back", which we might observe as inflation as well. The light falling in to such black hole from the outside when it was alive, should by now, 13 bin years after dispersal long have passed us, but the light emitted when it dispersed and that is hitting the outer limits of the "now inflating" space/time could not reach us, as space/time expands at speeds beyond those of the relative speed of light. It might reach us once the space/time curvature originally caused by a giant black hole has vanished and in turn inflation slows down. (No, I do not honestly think that there is "black matter", as there might be evidence for existence, but we might just be wrong in our perception of what causes these effects.)
Yes, call me crazy, but hey, I like to tinker strange ideas.

@G - I have 6 more credits to getting a physics BA in my second round in college. I started a physics BS course 20 years back.

So unlike a lot of other people in the class (a 2nd and 3rd year Atomic & Nuclear course) I actually had philosophy at one point :-)

I also have 20 years as a journalist. And you know what? No other job will convince you faster that much of life is random. I've seen some things that were pretty horrible, and some that were beautiful, and never was there any rhyme or reason. That's why people in this business become cynics or activists, IMO. Little space between, you know?

The multiverse may be real, but it doesn’t hold the answer to the question of why the fundamental constants have the values they do. It can constrain what they must be, but that’s all the anthropic principle can do. To get the rest of the way there — to understand why our Universe has the properties it does — requires that we look for dynamics. They may not exist in an accessible way in our Universe, but we have to try, we have to look, and we have to ask.
Sounds good to start with, but doesn't impress me when used in this analogy:
"The galaxy may be real, but it doesn’t hold the answer to the question of why the fundamental planets around the sun are the shapes and sizes they are. It can constrain what they must be, but that’s all the anthropic principle can do. To get the rest of the way there — to understand why our solar system has the properties it does — requires that we look for dynamics (and the music of the spheres perhaps). They may not exist in an accessible way in our solar system, but we have to try, we have to look, and we have to ask.
It was the ancients that looked for speical reasons/mysticism why the planets were the positions and sizes they were, but we now know that is a waste of time because our solar system is jus t one of billions. If the multiverse is the reason, then looking for special reasons for the constants in our universe to be what they are is certain to be a blind alley to pseudo-science and mysticism.

@ Tom #23
"but it is a straw-man version of the anthropic principle."

Wiki states 2 sets of weak and strong AP, and they are all straw-men statements.

if you know of a different formulation, please post it, as I am interested.

Later you write "The point of AP is not to explain anything, other than our own existence" ... How does it explain anything when it only states the obvious.

By Sinisa Lazarek (not verified) on 04 Apr 2014 #permalink

I fail to see how Mr. Siege's article, which rests entirely on the unexplained axiom:

"all the energy that would become matter, antimatter and radiation was locked up in a form that was inherent to space itself.",

answers any part of his self-posed question "where does all this come from."

The anthropic principle applies only in the current era.


Sure, many of the best known versions are quite badly formulated. It is fairly clear, though, what their authors were mainly trying to do - e.g. Carter's doomsday argument makes it clear what kind of inferences he was trying draw: what are the properties of the universe, based on what we know about ourselves (in this specific case, what will be the final total number of humans to have lived, given that so far there have been about 60 billion humans).

There are many other formulations of the anthropic principle, though. For example, the same section you link to includes Bostrom's, which is an attempt (just like most of the others) to prescribe how to reason from the evidence of our existence:

"Each observer-moment should reason as if it were randomly selected from the class of all observer-moments in its reference class."

AP does not, in fact, state the obvious, as you say. (Bostrom's principle is far from obvious, nor, having seen it, is it obvious that it is correct, nor indeed what it actually means.) But it invites us to reason about the nature of the universe from a particular form of evidence (e.g. infinite multiverse v's finite universe).

If you think it's so obvious, perhaps you can offer a definitive answer to the Sleeping Beauty problem. This is not to try to embarrass you (I don't have a definitive answer, though probability theory is a particular interest of mine), but to illustrate that you might have missed some of the subtlety of the matter.

By tom campbell-r… (not verified) on 05 Apr 2014 #permalink

@ Tom #30

Since my knowledge of logic, philosophy and statistics is not very strong, you will probably be disappointed by my answer, but I will give my honest opinion never the less.

One key observation before the answer. This is not a physics experiment. It asks of the observer to state a BELIEF of a certain thing, not what they actually know. And this is why argue AP has no place in physics.

No for my answer. My answer is that the sleeping beauty has ABSOLUTELY no knowledge of what side the coin has landed on. Everything else is biased and flawed by sleeping beauty herself. In other words, any answer given by sleeping beauty is biased by her herself (her knowledge or lack of it in math, statistics, being psychic or whatever) since she doesn't have any information about the original experiment (coin toss).

This "problem" IMO shows the distinction between social and natural sciences. It's required and needed in social sciences to explore our own beliefs and inner clicks. But those things are not part of physics or chemistry i.e. Data is the only thing relevant in physical experiment. In case of sleeping beauty and coins.. she has no data.

By Sinisa Lazarek (not verified) on 05 Apr 2014 #permalink

Answer: God. (p.s. the simplest answer is usually the right answer; occam's razor, etc.)

By observer3 (not verified) on 06 Apr 2014 #permalink


Your answer might be right, but as you can see from the wikipedia article on the sleeping beauty problem, there are experts who disagree with you. I've not yet been able to determine which is the correct answer.

You are wrong about one thing though, and it is very fundamental to the way science works.

You say, "this is not a physics experiment," but sleeping beauty is being asked to draw inferences about real things that happened in the universe - that is physics. It is exactly the way all physics works. There is some set of raw experiences (e.g. a visual sensation that the display on some instrument shows the number 42) from which one attempts to figure out which statements about reality are more plausible.

Every attempt to draw inferences about physical hypotheses is biased by the observer. There is no way out of this. (Observer bias is actually central to the anthropic principle.) Every kind of inference, scientific or otherwise, is an attempt to estimate a 'rigorous' probability assignment. But any probability calculation requires a probability model that must be defined by the user. There is no guarantee that any probability model is correct. In fact, it is not even meaningful to suppose that a probability model may be correct. I've written a very brief glossary entry on theory ladenness, which might help - in particular, some of the material it links to may be useful.

There is no hard distinction between social and natural sciences, only between valid and invalid inferences. Social phenomena are real physical events occurring in the natural world, and so demand exactly the same paradigm of investigation as stars and atoms.

By tom campbell-r… (not verified) on 06 Apr 2014 #permalink

@ Tom

Am not saying that the thinking process involved in sleeping beauty and rest of sciences is not the same. Am saying that if translated into physics, it would constitute a silly experiment and would not be carried out.

i.e. sleeping beauty is trying to give an answer to question which generates 50-50 odds due to experiment setup. Translated into physics it would be like trying to answer if particle is electron or neutrino just by having spin information. You can't. You need at least one more data set in order get the answer (charge in case of leptons). Just like sleeping beauty needs additional information in order to give an accurate answer.

As for valid and invalid inferances, you are correct, but they needn't be the same across disciplines. Thus one line of reasoning could lead to breakthrough in one field and be of no use in some other field.

By Sinisa Lazarek (not verified) on 06 Apr 2014 #permalink

Answer: God. (p.s. the simplest answer is usually the right answer; occam’s razor, etc.)

There has to be scientific evidence that the proposed answer exists before it can be considered in science. You are sorely lacking in that department.

Hi Dean,

I've no idea whether observer3's comment was serious - to me such statements are absurd in the extreme, so I ignored it - but your counter misses the mark. If God is being invoked as an explanation for something, then whatever is being explained is the evidence - this is how probability theory works. I bring this up only because I so consistently see misunderstanding of the structure of scientific inference (even among scientists).

The reason the God hypothesis fails to gain scientific credibility, however, is exactly the mechanism observer3 cites: Ockham's razor. There is nothing simple about the god hypothesis. Its extreme non-simplicity ensures that most forms of god hypothesis are guaranteed to never achieve non-vanishing credibility.

I've covered this in some technical detail here.

By tom campbell-r… (not verified) on 06 Apr 2014 #permalink

The simplest explanation seems to be to be that anything that can exist - does exist. Tegmark 4 etc. I don't see why you should assume that things need an additional reason to exist. This is a simple explanation not requiring a god.

I don't see what other answer you can give to questions like "why does anything exist at all" You can't have a creator because it cant create itself. Not sure how you can apply bayes to this either, seems like a philosophical question with yes/no answer and not many data points.

The anthropic 'principle' is not scientific because it cannot make any testable predictions. It's a tautology wearing fancy clothes.

By Doug Watts (not verified) on 06 Apr 2014 #permalink

Since the subject of God came up...

Propositions about the existence or non-existence of deities aren't testable. Any entity having the characteristics that define deities, could confound any experiment performed to ascertain its existence: therefore no such experiment can be valid, a-priori. By analogy if you're taking a test, and the answer sheet is visible to you, the teacher can't tell whether your answers came from your own learning or from seeing the answer sheet.

Science can only make use of things that are demonstrated through empirical facts (defined as measurements) and theories that are logically and mathematically consistent with empirical facts.

This is not the same as saying that anything science can't work with has no value. For example science can't measure the aspects of art that are most important to us (e.g. there is not a single objective scale for "beauty"), but we would not deny the importance of art. For that matter science can't make value judgements: it can't tell you what's right and wrong. Science enables us to develop technologies, but we have to make the value judgements as to how to use those technologies.

Some people view the universe as proof-in-itself that a deity must exist. Some people view the universe as proof-in-iteself that a deity can't exist. Some feel uncertain. In the end, it's a matter of each person's own inner nature as to whether they feel or believe in the existence or nonexistence of a deity. Science can't settle that issue objectively, which is why working scientists frequently get frustrated when laypeople such as ourselves try to bring it into scientific discussions as an explanation for natural phenomena.

It would be worthwhile to have a forum for philosophical discussions of that kind, in a manner that remains at a high level of conversation and doesn't fall into the kind of name-calling that often occurs when these things come up in high-traffic sites such as the news media and social sites.

Jesse @ 25: Aha, that makes sense. Good for you going back and getting your degree. Journalists and police officers have something in common: many start out idealistic but end up cynical due to seeing both the worst and best in humans. But interestingly, in both professions, and in the military, those who rise to senior positions are more likely to have avoided the cynicism and instead developed a sense of realism that none the less preserves certain ideals.


You describe a mystery, while discussing whether we should keep calling it a "mystery", or decide it is "dynamics" instead. But when you need a reason to continue the dynamics approach, you can offer only a "mysterious" reason: "The cost of giving up, of not looking for an answer that the Universe might actually reveal if we did, is far too high."

HOW DO YOU KNOW THAT? is the mystery I'd like an answer to, before I consider you to be a person who should continue to expound on universal mysteries!

G, # 39

"Propositions about the existence or non-existence of deities aren’t testable."

This is one of those assumptions about science that is often made, but is quite wrong. Any hypothesis with meaningful consequences can be tested. Hypotheses about e.g. omnipotent deities are not falsifiable, but this is not the same as untestable. We can use the machinery of probability theory to test this hypothesis (exactly as every other scientific test is performed) and the hypothesis fails, for exactly the reasons I demonstrate in the linked article - Bayes' theorem laughs at it and scores it with a nice round posterior. (This is actually an automatic consequence of its non-falsifiability.)

"In the end, it’s a matter of each person’s own inner nature as to whether they feel or believe in the existence or nonexistence of a deity. "

But if they have any aspiring commitment to scientific method, they must go in the direction that logic and evidence points. Any other direction is incoherent. Sorry for the bluntness, but it is what it is!

"Science can't settle that issue objectively,"

It absolutely can, exactly as much as it can 'settle' anything. Possibly, you are concerned that science can't produce a statement on this matter that is guaranteed to be correct. This is so for every matter that science investigates. This so because of (1) limited data, and (2) the unavoidable element of theory ladenness I mentioned above, in comment #33. (The issue of an omnipotent entity is just exotic, in that it scores zero credibility, independently of both the data and the probability model.)

Science answers the question, "what exists?" only indirectly, by directly addressing the question, "what can I reasonably believe in?"

By tom campbell-r… (not verified) on 06 Apr 2014 #permalink

Re. Tom @ 43:

I know the difference between untestable and unfalsifiable, and I used the former term because I felt it would be more accessible to the person I was addressing with that comment.

As for Bayes, prior plausibility can be (and often is) used as a rationalization for subjective bias. Theists have an emotional bias in favor of deities, atheists have an emotional bias against. As for Ockham, theists assert that a deity is the simplest possible explanation, whereas atheists "have no need of that hypothesis." Minus controlled experiments, neither is more supportable than the other, despite protestations from each side of the aisle.

Here I should mention that I'm an unabashed frequentist and empiricist with few exceptions, so this may end up being an instance of "agree to disagree" or "walk away from it."

Belief and disbelief in deities has been linked to activity in specific parts of the brain. Variations in the type and degree of activity are associated with variations in type and degree of belief/disbelief. Hypothetically, blind measurements of this should be predictive. If that's supported, the reasonable inference is that belief/disbelief is an outcome of measurable brain activity, in other words inherently subjective.

What I strongly object to, is the degree to which certain strains of theists, and certain strains of atheists, each seek to _dominate_ civil society. Each has its own peculiar language for doing so: theists with sanctimony, atheists with ridicule. I presume you fall into the latter category with your clever quip about laughing at posteriors (and a subsequent read of your blog supports that conclusion). But if we are truly committed to empirical observation and rational thought, we can do better than to laugh at posteriors.

Nor do ham sandwiches wrapped in tinfoil prove anything other than one's ability to engage in verbal fencing matches (or tennis matches if you prefer).

As for science producing correct statements, I'm well accustomed to living with degrees of uncertainty, and I consider that to reflect the underlying nature of things. A statement can reflect a probability that can change as evidence accumulates. So it goes. Not long ago I made the mistake of confusing a multiverse theory with the many worlds interpretation, which led to an apparent paradox, that resolved as I disentangled the error (no pun intended). In the end, curiosity, awe, and wonder are an axis orthogonal to that of domination.

What anyone can "reasonably" believe in depends in very large measure on the structure and chemistry of their brain. To the extent that brains differ, what individuals can "reasonably" believe also differs. To the extent that beliefs differ from empirical realities, individuals risk removing themselves from the gene pool. But beliefs that don't run afoul of nature in either direction are innocuous, so long as one does not seek to impose them upon others, whether by raw force, force of law, or force of social opprobrium.


Thanks for your reply. I'd like to address a few of your points, in the order that they appeared.

"prior plausibility can be (and often is) used as a rationalization for subjective bias"

If we are talking about irrational subjective bias, then such priors are not derived from any legitimate procedure (by definition) - they are not appropriate priors. One's prior experiences are also subjective, but don't make the mistake that subjective and objective are mutually exclusive. If I like reading 'Starts with a Bang,' this is a subjective judgement, but it is also an objective fact about the physical state of my brain. Use of legitimate prior information is not irrational. Failure to use it is.

Re. different interpretations of what is simple:

"Minus controlled experiments, neither is more supportable than the other,"

I would urge you to look more closely at the logic of the arguments - your statement is not correct. The formal argument of Solomonoff induction is similar, if not equivalent to the formalization of Ockham's razor I have presented elsewhere.

"I presume you fall into the latter category"

I have no desire to dominate society, as you put it, only to see society organized according to principles of efficiency and equality (this latter a special case of the former, in fact). I seek to ridicule only the manifestly ridiculous. I have no interest in whether you, for example, believe in gods, fairies, or leprechauns, but if you are going to publicly state that my methods of inference are flawed, then I'll have to ask you to 'show your work.'

"Nor do ham sandwiches wrapped in tinfoil prove anything other than one’s ability to engage in verbal fencing matches"

My reference to ham sandwiches (borrowed from Dennett) was more than a word game, it was a reference to the extreme invalidity of certain common forms of inference.

What anyone can “reasonably” believe in depends in very large measure on the structure and chemistry of their brain.

By 'reasonably,' I mean in accord with the principles of sound reasoning. Yes, what a person is capable of believing is very much influenced by the physics of their brain. This does not mean that all forms of belief formation are logically valid, or equally reliable.

Call me old fashioned, but I believe that irrationality, neglect of scientific method, and wildly invalid methods of forming beliefs are dangerous for society. I have no desire to enforce any particular beliefs on anybody, except those whose beliefs have a big impact on my life. If, however, a person is capable of appreciating the logical arguments that prescribe sound reasoning, I believe they should have the opportunity to do so. I will not pass silently over any absurd beliefs, just because they are traditional. Indeed, we can reasonably predict traditional absurdity to be the most dangerous kind.


By tom campbell-r… (not verified) on 08 Apr 2014 #permalink

Hi Tom-

If I understand Solomonoff's theory correctly, it basically states that the simplicity of a hypothesis can be operationalized as the length of a program that can run on a Turing machine, such that the shortest program is equivalent to the simplest hypothesis and thus has the highest probability of being correct, with longer programs having measurably decreasing probabilities of being correct. Is that even approximately right?

In which case how does one convert to an algorithm the proposition that a deity exists or does not exist, or for that matter the proposition that free will exists or does not exist?

And how do you differentiate between rational subjective bias and irrational subjective bias?

No, I don't make the mistake that the subjective and objective are mutually exclusive. Objectively there is a quantity of photons; subjectively they have the color blue. The subjective experience represents the objective phenomenon, plus certain characteristics that are purely subjective, and minus certain characteristics that are objectively measurable. For example "color" is not an inherent property of photons, but it is an inherent property of subjective experience.

You can know all that is presently known about the nature and behavior of photons, wavelength and frequency, the eye, optic nerve, and brain, and yet be unable to predict the subjective experience of "seeing blue" (much less the emotional associations to it, such as the moods invoked by looking at the ocean, the sky, the flag, and gazing into someone's blue eyes). Nor would the subjective experience of "seeing blue" provide a basis for predicting various cultural and semantic associations such as "the blues" (music), "feeling blue," (an emotional state), and so on.

This gets to the entire question of "qualia," the inherent characteristics of which can't be operationalized on an interval scale. The very existence of qualia demonstrate limits to the use of algorithmic reasoning.

I didn't think you personally have a desire to dominate society (sorry for the unclarity), only that laughing at posteriors follows the form of language used by some of the New Atheists. To be clear, I heartily approve of New Atheist demands for full equality for atheists, and tactics such as creating a social milieu conducive to "coming out of the closet." Where I part with them strongly, is where some of their members/allies engage in ad-hominem attacks on members of certain denominations that would appear overtly bigoted if directed at members of other denominations. And I also part with them over the "cold dead universe" rhetoric, which IMHO is self-defeating (tactical fail) as well as a subjective bias worthy of a prescription for antidepressants.

Also FYI, I don't subscribe to prevailing beliefs regarding deities, leprechauns, faeries, ghosties, or grays, though I do tend to attribute certain apparent anomalies to squirrels;-)

Extreme invalidity of certain common forms of inference: for example?

I agree with you that "...irrationality, neglect of scientific method, and wildly invalid methods of forming beliefs are dangerous for society," though we differ on the details.

This doesn't mean that there should or will be 100% convergence on every piece of content under each of those headers (insistence on "this and only this" is a hallmark of fundamentalist thinking). And it certainly doesn't mean that dominant cultural paradigms necessarily bear any resemblance to empirical realities.

For example the catechism of economic growthism is IMHO a manifest sign of cultural psychosis. The proposition that infinite economic growth is possible on a finite planet is equivalent to the proposition that one can map an infinite plane onto the surface of a Euclidean solid: a feat that would be worthy of a Field Prize (math equivalent of a Nobel) if it was possible, which it is not. The outcome of that particular catechism can be quantified in degrees Celsius above historic mean average, and the tangible consequences thereof. In the end, that's going to be one heck of a Darwin test for our species' ability to think clearly and act accordingly.


G, hi

That's a fair summary of Solomonoff induction. The point is, try to imagine writing a program to simulate the behaviour of a god - that's going to be one heck of a long piece of code. If this is hard for you to verify, then just go back to my original argument with degrees of freedom. (The point of giving you 2 different arguments was simply so that you could pick which one is more intuitive.)

As for free will, that's an incoherent proposition, so no computer program corresponds to that hypothesis. (I mean the libertarian kind of free will, that postulates extra-physical properties of minds - there are other kinds, used e.g. in legal discourse, which are a matter of definition, so there's not much point debating whether such forms exist.) Again, if this is hard to verify, you could try writing a computer program with free will :)

Regarding qualia, you write: "The very existence of qualia demonstrate limits to the use of algorithmic reasoning." I think you have a very long way to go before any such thing is demonstrated. For one thing, you would need to provide a clear description of some fundamental difference between the subjective experience of e.g. a person, and the subjective experience of a digital computer. Good luck with that, but I am strongly of the opinion that this is not possible.

You asked for examples of extremely invalid common forms of inference: any of the many examples in that piece about ham sandwiches that you objected to. Basically, anyone who says "sure, there is no good evidence, but I choose to believe it anyway." Your own examples from economics might also work, as well as a common paradigm of government policy making.

Squirrels: yes, possibly the most challenging philosophical problem to face mankind.

Thanks for the discussion,

By tom campbell-r… (not verified) on 09 Apr 2014 #permalink

If emotions didn't come first, then reason follows, cosmologcst would have already said the data best point to a Creator.

Humanity is not using is emotions to reason God is the best explanation for the world, they are using Logic, Aristotle showed this. He used no emotions and invented formal Logic 101 in the process of his search for why people involked gods.... and it follows---the overwhelming majority of humans still see God as the best explanation.

You want to see emotion? Tell an atheist he is emotionally biased and a hateful red face will emerge. Emotion is what causes a DC Comic book to be used as a real theory to explain away obvious Design.

Dr Evans:

Two questions:

1. Which data is it specifically that demonstrates that a Creator is the best explanation for the state of the universe? AFAIK, all the data that we have can be readily explained without the need for any supernatural entity, so why invoke one? (Please note: that's not the same as stating that no supernatural entities exist, simply that the best way to proceed scientifically is to do so without reference to any).

2. What logic leads one to the conclusion that a creator must exist? Remember, formal logic in and of itself cannot really give us any new information. It can only tell us what the implication of our premises are. We may well disagree about the validity of the premises.

Inflation presumably occurred before the laws of physics had completely evolved. The assumption that our universe is just one of many bubbles assumes that there was, in some sense, a distance between them. But that makes sense only if you can show it plausible that there was such a thing as distance back then.

Similarly, the assumption that anything happened before inflation makes sense only if there was such a thing as time back then.

By Collin Merenoff (not verified) on 19 Sep 2015 #permalink

"Inflation presumably occurred before the laws of physics had completely evolved. "

Not entirely. It's possible that they fell out during some point in inflation, but inflation theory doesn't posit anything different in the physical laws for it to happen.

The rest of it appears reasonably supportable conjecture and presumption based on what is currently widely known.

"If emotions didn’t come first, then reason follows, cosmologcst would have already said the data best point to a Creator."

The conclusion does not follow from the premise. NOTHING about emotions not coming first (whatever THAT means: more primitive mammals have emotions. Even Spiders have the fear emotion response by their actions) denotes a creator must exist.

"Humanity is not using is emotions to reason God is the best explanation for the world"

God is just your dad when you're a kid scaled up to bigger than you are as an adult. It's a fairy tale, and produced like ALL fairy tales to provide instruction and lessons that are to be passed on by that society.

God is no more real than Winnie the Pooh.

"Tell an atheist he is emotionally biased and a hateful red face will emerge."

Yes, if you insult people to their face, they will tend to get angry. What is this supposed to prove?

"obvious Design"

There is no obvious design.

"If God is being invoked as an explanation for something, then whatever is being explained is the evidence "

However, god is the biggest logical fallacy possible. It is merely an "I dunno" wrapped up in mysticism. If I point to a bruise on my arm and proclaim "THIS is proof god exists!", this is not evidence of god. I have to explain WHY it is evidence of god. And defend that explanation (a positive claim) to any alternative non-god or even different-god claims.

"The anthropic ‘principle’ is not scientific because it cannot make any testable predictions."

It doesn't attempt to. It is just saying "We wouldn't be having this conversation if it wasn't". All you need to do is show that the particular thing is POSSIBLE and then it gets selected based on the fact it is there.

Unlike god, it doesn't claim to be the ANSWER though. And doesn't insist you must stop asking.

Replying to year old post would lead one to believe you are arguing with your own self.

By Ragtag Media (not verified) on 19 Sep 2015 #permalink

Too Funny..

By Ragtag Media (not verified) on 19 Sep 2015 #permalink

Replying to a year old post is posting against an argument not refuted that is easily visible today.

What you pretend to make up about it is really very unimportant.

Moral absolutes are as important in regards to our existence as scientific absolutes are to our ability to comprehend them. "I think therefore I am" Ya know..

By Ragtag Media (not verified) on 20 Sep 2015 #permalink

What are the moral absolutes?

Chew on "Liberty" for starters

By Ragtag Media (not verified) on 20 Sep 2015 #permalink

If liberty is a moral absolute, then why do we have incaceration? Why are there laws against illegal immigration? Why close borders? Why insist you can't have a nuclear arms programme?

Even the phrase "Your freedom to swing your fist ends at the tip of my nose" indicates that liberty is not an absolute, since it can easily be rivalrous.

Liberty is so broken that it cannot be a moral absolute.

Try another one.

Your conflating Natural Liberty With Civil (Moral) Liberty.
Natural Liberty, you are free to full swing and punch the nose as you are free to smash a bottle of nitroglycerin with a hammer.
You may not like the results from either but your still free to go for it.

Why it should end at the nose tip is for the good of all and is a Civil (moral) liberty because though you loose the right to punch the nose, you gain a more fortunate outcome as a society as a whole in which you will be better off.
Liberty is not broken, man is.

By Ragtag Media (not verified) on 20 Sep 2015 #permalink

"Your conflating Natural Liberty With Civil (Moral) Liberty."

How on earth is that going to be different? Is this a "No true scotsman" thing?

"Natural Liberty, you are free to full swing and punch the nose as you are free to smash a bottle of nitroglycerin with a hammer"

Yet this moral right is removed all the time. Therefore it's not a moral absolute: we knowingly and reasonably limit the liberty to do that. So it's 100% not an absolute.

And try flying by flapping your arms. See if you're at liberty to take off from the ground.

"Yet this moral right is removed all the time. Therefore it’s not a moral absolute"

Yes it is an absolute of nature (Creator) Ya know, "all men are endowed with Life, "Liberty" ....
Here think of it in a mathematical way that more suits your line of thought processes:…

The X is Natural Liberty and can move in any direction. Thus it is already a natural absolute. Moral Absolute is born out of the act of the Natural movement thus it is of the same family of absolutes because it exist ABSOLUTELY but in a negative frame reference now.
I don't need to flap my wings to go back a negative space, I can build an aeroplane

By Ragtag Media (not verified) on 21 Sep 2015 #permalink

Damn new Windows 10 upgrade glitched me and posted before I finished what I was saying..

By Ragtag Media (not verified) on 21 Sep 2015 #permalink

"Yes it is an absolute of nature "

No, it's not a moral absolute.


What? Your mythological sky idiot insists that you're not allowed to do shitty thought crimes like "covet your neighbours' wife" or asinine BS like "Don't shave".

"The X is Natural Liberty "

What is the moral absolute, retard.

You big dummy I told you already.
Liberty (freedom of thought, expression ect) is a universal absolute because it is given to men by God but Man takes it away from others.
Here idiot, read Jefferson's Virginia Statute for Religious Freedom:…
Either your to fking stupid to grasp the concept or God really does blind people so they can't see.

By Ragtag Media (not verified) on 22 Sep 2015 #permalink

There's a giveaway - look at the spelling of airplane (north American spelling) and aeroplane (British spelling).
RM@#64 ;)

"Liberty (freedom of thought, expression ect) is a universal absolute"

What is the MORAL absolute. Not an "absolute".

Except you're not actually absolutely at liberty, try scratching your adrenal gland.

Also, since there is no god, he can't have given you anything. You DEFINITELY need to show there there is a giver and not just a fiction.

You DO know that most of the founding fathers who put that "endowed by our creator" were deists and really atheists of that time.

And AGAIN, since your liberty is REMOVED by the actions of the state or society (or, indeed your damn mythical beings), they are ALSO not absolute.

Failing harder and harder each time. What a frigging retard you are, teabag.

Your evading the point fallacy man.. and regardless of deist They were wise enough to realize that Liberty granted by a power higher than man is safer than Liberty granted by the man (state). I suppose you would love to live under that fat assed porky pig dictator Kimmy boy.
Did you flunk Western Civ? Remember Xenophanes?

Think of it this way, before we thought the Earth was flat, now we know better, the Laws of physics had the earth ROUND regardless of what men thought.
Thus wise Liberty IS an absolute regardless a man be put to death speaking otherwise about it or a round earth.

By Ragtag Media (not verified) on 22 Sep 2015 #permalink

Your words my friend, "A statement or admission of our own ignorance, that we do not understand ..."

THE CREATOR GOD, lover and redeemer of our souls

"that gave rise to the constants of our Universe, does not mean that there are none, that all values are taken on somewhere in some Universe, and that ours just happens to have the values it does, which are serendipitous to our existence."

From the reference you have provided it is crystal clear that the multivers is the answer and in fact, it is the most elegant and economic answer; thx ...

By banevstefan (not verified) on 27 Mar 2016 #permalink