It is your mind that bends

Two days ago, I was in my car on the way to a go for a walk with a friend, and I was listening to classical music on the radio.  The announcer came on with some of the usual sort of background information before a piece is played.  In this case, she said, "Next, we're going to hear from one of the masters of the classical guitar."  And immediately, I thought, with absolute assurance, "it's going to be Narciso Yepes."

And she continued, "... here's Narciso Yepes, playing Bach's Lute Suite #1."

Now, it's odd that I thought of Yepes at all.  I don't know much about classical guitarists -- the two I've heard the most often are Andrés Segovia and Christopher Parkening, but even them I only listen to intermittently.  I think I have one CD of Yepes, but I'm not sure where it is and I don't think I've listened to it in years.

[Image is licensed under the Creative Commons Kirkwood123, Matao MC-1 classical guitar 01, CC BY-SA 3.0]

So the certainty of my thought is peculiar from a couple of standpoints, even if you believe that it wasn't a premonition (which, predictably, I don't).  The first is that I came up with the name of a guitarist I barely know at all, as soon as the announcer mentioned "classical guitar;" and the second, of course, is that it turned out to be right.

Interestingly (and you might consider this another synchronicity), just yesterday a loyal reader of Skeptophilia sent me a link to a subreddit called Glitch in the Matrix which is devoted to exactly these sorts of occurrences.  The name, of course, comes from the movie The Matrix, in which odd coincidences and experiences of déjà vu are indicative that the Machines are making minor alterations to the computer simulation inside which we all live. 

The fact that we all have these experiences now and again certainly deserves some consideration. Let's take a look at three excerpts from the subreddit:

For about 5 or 6 years now (I'm 21 as of now), I've noticed that, whether it's the time that I check my phone, or it's a donation on a Twitch stream, or any number of other things, there's a decent chance that it'll be the number 619. It's nothing I'm too worried about, but it pops up every so often naturally that it just doesn't seem like a simple coincidence anymore.  It's something that I noticed happened, and then it continued to happen long after that.

 
I'll notice the time as 6:19 every once in a while, and at first I chalked it up to being stuck in the same routine, but it continued to occur after several changes in sleep schedules and school/work schedule.  Again, it's not only the time of day either, but I'll notice it in a phone number, or any number of places.  It's gotten to be like my own private joke that people or places attached to the number must mean something to me, although I never act on it...

 
So any theories on my special little number?  Does anyone else have a number or idea "follow" them around like this?  Or is this an underlying symptom of a mental disorder that I've been ignorant of for 21 years?

Here's another:

One of the most terrifying experiences I've ever encountered was with my friend Gordie last summer and to this day still makes me feel uncomfortable to talk about because I genuinely can not explain what happened on any logical level.

We were driving to Mission and on the way back I noticed I had forgotten something at the store.  By this time we were in downtown Maple Ridge and considering we had nothing to do so we went back.  It's about a 20 minute drive to Mission from where we were.  The clock read 3:23.

The clock reads 3:37. Gordie and I look at each other.  And he asks me "what happened?"  Neither of us remember the drive between Maple Ridge and Mission.  We lost 15 minutes of lives and we have no idea where it went.  All we know is that in between post A and B nothing or probably something happened.

Not a single word was said.  The last thing we remember talking about was how a video game we both play will never have a follow up.  Then at the snap of a universal finger.  Nothing.  15 minutes gone.

The rest of the ride was very quiet and we were both very much on edge and uncomfortable.  We have both experienced something completely unexplainable but yet at the same time we experienced nothing.

I'm the grand scheme of things, 15 minutes seems inconsequential and minimal to the many minutes in our life.  But nevertheless it remains unknown as to where time went.

 
My only explanation is that I passed though a wormhole and somehow ended up on the other side.

And one last one:

I had a problem with a programming question, so I googled it, and I went to the forum Stackoverflow (in which I had signed up 2 years ago).  I found an excellent answer that solved my problem, and I told myself  "Oh.. So many intelligent people out there... I would have never been able to write something like that." 

And then I realized... the author of the answer is my account.  It's me...

 
I am convinced this is caused by a glitch in the matrix.  Most probably, many answers on the forum are generated by the matrix, and the glitch was to attribute my username to it.  Of course, a couple of seconds after that, I was getting a vague idea that I may have written the answer (false memory), but I am not fooled!

So, given that we are starting from the standpoint of there being a natural explanation for all of this, what is going on here?

I think the key is that all of these rely on two things; the general unreliability of perception and memory, and our capacity for noticing what seems odd and ignoring pretty much everything else.  Starting with our 619-noticer, consider how many times (s)he probably looks at clocks, not to mention other sources of three-digit numbers, and it's not 619.  Once you have a couple of precedents -- most likely caused, as the writer noted, by being in the same routine -- you are much more likely to notice it again.  And each subsequent occurrence reinforces the perception that something odd is going on.

Dart-thrower's bias rears its ugly head once again.

As far as the time-slip friends, I think what happened here is a simple failure of attention.  I've driven on auto-pilot more than once, especially when I'm fatigued, and suddenly sat up straight and thought, "How the hell did I get here?"  I honestly had no memory at all of driving the intervening distance.  But a mysterious time-slip is less likely than my brain being elsewhere (leaving some portion of my attention still focused on my driving, fortunately).

And the last one, the person who answered him/herself on an internet forum, certainly has to be a case of a lost memory.  I have a friend from college who has an excellent memory for details from the past, and periodically reminds me of things that happened to the two of us -- and more than once I've had to admit to him that I have no recollection of the events whatsoever.  (In fact, just a month ago I stumbled upon the obituary of a professor we'd both known, and sent it to him, and he responded, "Um... Gordon... I sent this to you in February."  Even after he told me that, I honestly had no memory of it.)  It's disconcerting, but our memories are far less thorough and accurate than we think they are.

My own premonition-like decision that the radio announcer was going to be playing a piece by Narciso Yepes is clearly an example of dart-thrower's bias, similar to the 619-noticer.   Considering how often I listen to the radio, and hear the announcer give a bit of information about the next selection, it's likely I have thoughts like, "I hope she plays something by Scarlatti next!" several times a day.  Most of them, of course, are wrong, and because that's the norm, such events are immediately forgotten.  It's only the coincidental ones, the outliers, that get noticed.

But even so, I think I'll dig up that Yepes album and put it on.  Whether or not it was a glitch in the matrix, he's a pretty damn good guitarist.

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Reversing the arrow

After a deep philosophical discussion, a friend once said to me, "You're only a skeptic because you don't have the balls to be a mystic."

I bristled (of course) and explained that my skepticism came from a desire to base my understanding on something more concrete than feelings and desires.  She shot back, "So you wouldn't have accepted the truth of atoms before the experiments that proved their existence."

"I would not have known they were real, no," I responded.

"So there could be great swaths of knowledge outside your direct experience, of which you are entirely ignorant."

"There could be, but I have no way of knowing."

She gave me a wicked grin and said, "The mystics do."

Predictably, neither of us convinced the other in the end.  I don't think any amount of mysticism would have arrived at the Bohr model of the atom and the periodic table, for example.  But the reason her arrow went in as deeply as it did is that she wasn't entirely wrong.  I have had a fascination with "other ways of knowing" -- mysticism, psychic phenomena, altered states of consciousness, and the like -- for as long as I can remember.  The lack of evidence for most of it has not dulled my interest -- if anything, it's piqued it further.

Woodcut by Camille Flammarion (1888) [Image is in the Public Domain]

So I have this sort of dual life.  On the one hand, I consider myself of the hard-edged, evidence-demanding skeptical type.  On the other, I'm drawn to all sorts of woo-woo stuff that, despite my scoffing at it by day, has me researching it in the wee hours when I figure everyone's asleep and I won't get caught out.

It's also why all of my novels have a paranormal twist.  Living vicariously through my characters, I suppose.

Understandable, then, that my ears perked up immediately when I saw an article written by Dr. Julia Mossbridge in (of all places) The Daily Mail.  I've written about Mossbridge before -- she's been researching telepathy and precognition for fifteen years -- and my problem with her research, then and now, is that I don't see any possible mechanism by which either of those could work.

But.  That a scientist of her stature would continue to stand by this claim means it's worth consideration.  And I have to be careful of my own biases -- we all are prone to confirmation bias, and if my bent is to look at the world in a mechanistic fashion, it might well blind me to what's really going on.  It's never a good idea to jump from "I don't see how this could be true" to "this isn't true."  It's just a thinly-disguised version of the argument from ignorance, isn't it?  As Neil deGrasse Tyson put it, "Going from an abject statement of ignorance to an abject statement of certainty."

As far as what Mossbridge is actually claiming, it's more than a little fascinating.  She writes:

I led a team at the respected Northwestern University in the U.S. that analysed 26 experiments published over the previous 32 years, all of which examined the claim that human physiology can predict future important or emotional events. 

These studies had asked questions such as: ‘Do our bodies give different unconscious signals when we’re about to see a picture of someone pointing a gun at us, versus when we’re about to see a picture of a flower?’ 

In all of the experiments we analysed, a random number generator was used to select the future image so it was impossible to cheat.  The answer, our research concluded, is ‘yes’.  When you add all these experiments together, it became clear the human body goes through changes in advance of future important events — alerting our non-conscious minds seconds earlier to what is likely to happen. 

On average, participants’ bodies showed changes that were statistically reliable.  For instance, they would sweat more (a behaviour associated with fear) before they were shown an image of a gun, and less before they saw a flower. 

This happened too often to be scientifically considered chance.

All of this, of course, runs counter to the sense most of us have that time flow is one-directional.  How could the future influence the present?  But as Mossbridge correctly points out, the "arrow of time" problem is one of the great unsolved mysteries of physics.  Virtually all of the physicists' equations are time-symmetric -- the math works equally well whether time is flowing forward or backward.   One of the only exceptions is entropy -- which deserves a bit more explanation.

We observe that systems tend to progress toward more chaotic (high entropy) states.  A glass breaks, but the pieces never spontaneously come together and reassemble into a glass.  The sugar you've stirred into your coffee never comes back together into solid crystals sitting at the bottom of the cup.  Why is that?

The simplest explanation of this can be illustrated using a deck of cards.  If you were to shuffle an ordinary deck, what's the likelihood that (by random chance) they'd end up in numerical order by suit?

Nearly zero, of course.  The reason is that there are only 24 different states where they are organized that way (depending on the order of the suits), whereas there is a nearly infinite number of possible other arrangements.  So if you jump from one arrangement to another (by shuffling), the chance of landing on one of the 24 ordered states is very close to zero.  Progression toward disorder is the rule because, in general, there are way more disordered states than ordered ones.

But this still doesn't explain all of the other cases where time is completely symmetric.  Why do we remember the past but know nothing about the future?  The simple answer is that no one knows.  Einstein himself said, "The distinction between past, present, and future is an illusion, although a remarkably stubborn one."

So I'm curious to find out more of what Mossbridge is claiming.  And I'll soon have my chance, as I just ordered her new book The Premonition Code, which details the evidence that has convinced her and others that precognition actually exists.  (If you'd like to order the book as well, click the image below.)

 

Until then, I have to say the jury's still out on this one.  I'm trying to push aside both the disbeliever and the mystic that cohabit in my brain, and stick with the skeptic -- look at the argument as dispassionately as I can, and see where it leads.  Faced with a huge, mysterious, and complex universe, that's about the best we can ever do.

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You can't get on social media without running into those "What Star Trek character are you?" and "Click on the color you like best and find out about your personality!" tests, which purport to give you insight into yourself and your unconscious or subconscious traits.  While few of us look at these as any more than the games they are, there's one personality test -- the Myers-Briggs Type Indicator, which boils you down to where you fall on four scales -- extrovert/introvert, sensing/intuition, thinking/feeling, and judging/perceiving -- that a great many people, including a lot of counselors and psychologists, take seriously.

In The Personality Brokers, author Merve Emre looks not only at the test but how it originated.  It's a fascinating and twisty story of marketing, competing interests, praise, and scathing criticism that led to the mother/daughter team of Katharine Briggs and Isabel Myers developing what is now the most familiar personality inventory in the world.

Emre doesn't shy away from the criticisms, but she is fair and even-handed in her approach.  The Personality Brokers is a fantastic read, especially for anyone interested in psychology, the brain, and the complexity of the human personality.

[If you purchase the book from Amazon using the image/link below, part of the proceeds goes to supporting Skeptophilia!]

Lord Dufferin and the man in the garden

For better or worse, being a skeptic doesn't mean that you don't find stories of the paranormal interesting -- nor that you can't react to them on an emotional level.

I mean, I'm the guy who thinks that television programming went into a nosedive the day The X Files was cancelled.  I am also the guy who would love to spend a night in a haunted house, but would be likely to piss my pants and then have a stroke if anything untoward happened.  So while I'd be a good guy to have on a team of ghost hunters, from a scientific and rational perspective, I'd be a bad choice from the standpoint of practical application and laundromat charges.

I still recall many of the ghost stories of my childhood.  My uncle was a grand storyteller, and had lots of tales (usually told in French) of the scary creatures of the Louisiana bayou, including the Loup-Garou (the Cajun answer to a werewolf) and Feu Follet (the "spirit fire," or will-of-the-wisp, which would steal your soul if you saw it -- unless you could cross running water before it caught you).  Later, I voraciously read Poe and Lovecraft, and dozens of books with names like True Tales of the Supernatural.

It was in one of the latter that I ran into the story of Lord Dufferin, a 19th century British statesman who spent most of his career shuttling all over the world -- from Canada to Syria to Russia to India to Burma.  His actual name was Frederick Hamilton-Temple-Blackwood, 1st Marquess of Dufferin, and his life coincided almost perfectly with Queen Victoria's -- she lived from 1819 to 1901, Dufferin from 1826 to 1902.

Dufferin was, by all accounts, well known in the social circuits of high society.  His biographer calls him "imaginative, sympathetic, warm-hearted, and gloriously versatile."  He also was an excellent storyteller, and there was one story he became famous for -- mostly because to his dying day, he swore that it was true.

One night, Dufferin said, he was visiting a friend who owned an estate in Ireland.  For some reason, he was unable to sleep, and after tossing and turning for a while, he finally got up and went out through a door and onto the balcony overlooking the estate gardens.

He became aware that there was a figure moving down in the garden, and as he watched, the figure got closer.  It was a man, carrying something on his back, but he was in shadow and it was impossible to tell anything about the man or his burden.  But after a moment, the man stepped out into a patch of moonlight, and looked up at Dufferin.

Dufferin recoiled.  The man was the most hideously ugly individual Dufferin had ever seen -- and the object on the man's back could be clearly seen to be a coffin.

Terrified, Dufferin retreated to his room.  The next morning, he told his host about what he'd seen, and Dufferin's friend brushed him off -- there was no one in the garden the previous evening, the friend said.  It must have been a nightmare.

Dufferin more or less forgot about the incident.  But many years later, when he was British Ambassador to France in the early 1890s, he was in Paris for a diplomatic meeting and was about to step onto an elevator when he glanced at the elevator operator, and saw that it was the same memorably ugly face as the man he remembered from his vision in the garden.  Alarmed, he backed away, and the door closed.  He was standing there, trying to make sense of what he had just seen, when there was a tremendous crash -- the elevator cable had broken, sending the elevator compartment hurtling down the shaft.  Everyone inside, including the operator, was killed.

Dufferin sought out hotel officials to ask about the elevator operator -- but the officials said that the man had just been hired that day, and no one knew anything about him.

Dufferin lived for another ten years, and enjoyed many a glass of brandy over the telling of this tale.  And you can see why; it's got all of the elements -- a terrifying vision that turns out to be a warning of danger, a scary-looking guy carrying a coffin across a garden at night, a near brush with death.

Now, don't get me wrong.  I doubt very much if the supernatural aspects of this story are true.  Human memory is a remarkably plastic thing, and I strongly suspect that most stories of precognition rely on imperfect recollection of the original premonition, be it a dream or (as in this case) a vision.  That Dufferin saw something in the garden that night is possible; that he had a nightmare is also possible.  That it was true precognition, I seriously doubt.  It is far more likely that, years later, a shock like seeing an ugly guy in an elevator, and narrowly escaping being killed when the elevator cable broke, would have conflated in his mind the incident with the earlier nightmare (or whatever it was).

But you have to admit that despite all of that, it makes a hell of a good story -- even one that a diehard skeptic might read with a cold shudder twanging up the spine.

And with that, I'll wish you all a very spooky and fun-filled Halloween.

Mechanisms, cognitive bias, premonitions, and telepathy

I have a cognitive bias.  When I come across a new phenomenon, and am trying to wrap my brain around it, I need to understand the mechanism by which it works.  If no mechanism is forthcoming, this raises (considerably) the level of evidence I demand before I'll accept that what I'm seeing is real.

I realize that this is, in many ways, getting the cart before the horse.  Rarely in science do researchers discover something, and understand the mechanism by which it works, simultaneously.  Almost always we start out by making some sort of observation that requires explaining, and describe the what of the phenomenon long before anyone is able to give a good explanation of its how.

The problem is that given this bias, this automatically makes me doubt studies that show results that don't seem to have any reasonable mechanism by which they could have occurred.  I'm aware that this could be potentially preventing me from accepting evidence that would be convincing in any other realm, a position hardly befitting a skeptic -- but in my own defense, at least I'm aware of it.

This brings us to today's bit of possibly scientific weirdness -- two studies, just released in the past week, that allege a factual basis for ESP.

The first one, done by a team led by Julia Mossbridge, a neuroscientist at Northwestern University, apparently gives support to the contention that some people experience premonitions.  Mossbridge and her associates analyzed the results of 26 psychological studies, some dating back as far as 1978, looking for evidence that people were experiencing emotional reactions to information they hadn't seen yet.  Subjects were shown photographs that varied in content -- some neutral, some pleasant, some disturbing, some sexually arousing -- and they experienced physiological changes (alterations in electroconductivity of the skin, blood vessel dilation, pupil dilation, EEG readings, and so on) two to ten seconds prior to being shown the relevant photograph.  Mossbridge claims that she has controlled for factors such as the Clever Hans Effect, and has stated, "These results could not be explained by experimenter bias in the normal sense."  Her statistical analysis has placed the odds of the results being due to chance or coincidence at 400 billion to one.

My problem, predictably, is that I don't see how this could possibly work.  I don't see a mechanism.  If you're asking me to believe Mossbridge's results come from some sort of real phenomenon at work, it seems to reverse the temporal order of causality -- placing the effect before the cause.  Causality seems to me to be one of those rock-solid ideas, about which there can't be any reasonable doubt.  But then, that's just all part of my bias, isn't it?

The second study is even sketchier.  In it, a group of neuroscientists from the National Institute of Mental Health and Neurosciences went to Bangalore, India, to do an fMRI on a gentleman who claimed to be telepathic.  In the study, one of the experimenters drew a picture, and simultaneously a control subject and the alleged telepath tried to reconstruct the drawing while inside the fMRI machine.  The telepath created a drawing that had a "striking similarity to the original drawn by the experimenter;" the non-telepathic control's drawing had no resemblance at all.  More interestingly, the fMRI results showed increased activity in the alleged telepath's right parahippocampal gyrus, and no such increase occurred in the control.

This one activates my skepti-senses not only because of my bias against anything for which I can't see a possible mechanism; I also wonder why such a stunning result wasn't published anywhere but the International Journal of Yoga.  But let's pass over that, and attribute that to the known biases that grant funding agencies and peer-reviewed science journals have against anything that smacks of woo-woo.  So even assuming that the study was valid, how on earth could such a thing as telepathy work?  What you're telling me is that somehow, as I draw a picture, my thoughts are creating a change in the electromagnetic field surrounding my head, and you (ten feet away) experience that through the neural connections in your right parahippocampal gyrus, and this makes your visual cortex fire, making you suddenly realize that I'd just drawn a picture of a kitty cat?

I'm just not seeing how this could possibly work.  You'd think that any changes in the electromagnetic field in my vicinity caused by my brain activity would be so weak as to be undetectable at that distance -- especially given that the test subject was inside the giant electromagnets of an fMRI machine at the time!

Of course, many believers in telepathy don't think it's communicated electromagnetically, that there is some sort of "psi field" by which it is transmitted -- but to me, this doesn't explain anything, it just adds one more item to the list of ESP-related phenomena that no one has ever proven to exist.

In any case, the problem is that Mossbridge et al., and the unnamed scientists who fMRI'd the telepath in Bangalore, may well have stumbled upon something that needs explaining.  (Assuming that neither group are hoaxers; I mean no slight to their reputations, but that possibility can never be discounted without consideration.)  If either or both of these results is real, and not a fluke, a hoax, or a statistical artifact, then despite my objection that there seems to be no possible mechanism by which either one could work, we have some serious explaining to do.

But my bias won't be silenced quite so easily.  Despite Mossbridge's claims of a 400 billion to one likelihood against her results being due to chance, and the hard evidence of the fMRI photographs, I just can't bring myself to overturn everything we currently understand about neuroscience, physics, and causality, and throw myself into the Believers' Camp.  I hope, just for the sake of balance, that some scientist or another takes on the challenge of sifting through these studies -- but if I were a betting man, I'd be wagering that neither one will stand up to any kind of rigorous analysis. 

Premonitions, the lottery, and statistics

An interesting post appeared yesterday over at Occult View.  Entitled, "If Psychic Ability Exists, Why Can't Anyone Predict Winning Lottery Numbers?", the post makes the claim that (1) psychic ability does exist, and (2) there have been people who have won the lottery based upon a premonition.  So, q.e.d., more or less.

As evidence, the author gives us three examples of people who allegedly won the lottery (or could have, in one case) because of precognition: Steve (dreamed of the numbers "2895," didn't play them, and six months later, those were the winning numbers); Frank (a friend of a friend who won a seven million dollar payout "around two decades ago" and "said he dreamed the winning numbers"); and Lillian (bought five Pick-Three tickets with the same three numbers, because she'd heard the numbers told to her by "a voice;" the tickets won, despite the fact that the odds were "one in a thousand").

So.  Where to start?

First, as a scientist, I must with some reluctance point out the quality of the evidence.  All of them are after-the-fact reporting -- the person had already won (well, other than Steve, who didn't even win), and reported afterwards that the numbers had come to them in a precognitive fashion.  So first, we run headlong into the problem with anecdotal reporting, which is the plasticity of the human memory and the unfortunate capacity of humans to make stuff up.

But let's assume, just for fun, that all three of these stories are true as written -- all three people did have some sort of hunch about the numbers ahead of time.  Does this constitute evidence for precognition?

Unfortunately, the answer is no.  I say "unfortunately" because it sure would be cool if it worked, wouldn't it?

Let's just look at the statistics first.

According to Matthew Sweeney, author of The Lottery Wars: Long Odds, Fast Money, and the Battle Over an American Institution, about $60 billion is spent annually on lottery tickets.  The number of tickets sold per year proved to be a hard number to find -- I'm not sure why -- but from a paper I looked at called How to Analyze the Lottery, by John Corbett and Charles Geyer, the number looked to be about 400 million annually.

Now, what about premonitions?  According to a 1987 survey conducted by researchers at the University of Chicago, 67% of adults report having "regular episodes of precognition."  The current population of the US stands at a little more than 311 million people, so if we assume that the rates of precognition haven't changed in the last thirty years, it means that something on the order of 100 million people experience regular, accurate precognitive events.

Now, I'm no statistician, but we're talking about very big numbers here, both of ticket sales and of precognition. And with all of those precognitives walking around, you're telling me that the best evidence you could find were (1) a guy who dreamed of four numbers, didn't buy a ticket, and they came up six months later, (2) a guy who "heard from a friend" that the friend had dreamed his winning numbers "a couple of decades ago," and (3) a woman who won a one-in-a-thousand Pick-Three lottery because she heard the numbers from "a voice?"  Given that 67% of Americans claim that they have been able to predict the future, you would think that guessing the correct numbers would happen so often that the lottery commission would go bankrupt from the number of winning tickets sold.

One possible objection to all of this might be that precognitives can't control what their episodes of precognition are about; i.e., they can't choose what their mysterious skill will predict next.  But doesn't this just make all of this a giant case of dart-thrower's bias -- people only remember the times when their hunches proved correct, and forget about all of the hundreds of times that they didn't?  In order to be fair, we'd have to have some sort of accurate way of estimating the number of people who dreamed numbers, were told them by "a voice," or just had a hunch, and didn't win.  And because no one tends to advertise it when that happens, it's impossible even to venture a guess.  But if I can indulge in a hunch of my own, here, I suspect that it occurs a lot -- far more often than such "precognitive events" actually predict the future.

So, that's our look at psychic abilities for today.  If any Skeptophile in the studio audience is good at statistics, let me know what you thought of my analysis, and whether you think my point stands; and if you know of a quantitative way of approaching these data, do post it in the comments section.  Because, after all, the last thing I want to do is to do the same thing that our friends at Occult View did, which is to throw around a few numbers, tell a few stories, wave their arms around, and state a conclusion as if it were self-evident.