Author and journalist Judy Bachrach started volunteering in a hospice in the late 1980s, and her real motive was to try to overcome her fear of death. About two decades later, when her mother came down with Alzheimer’s, Bachrach decided to look into the subject of near-death experiences.
So she delved into the literature, and journeyed around the United States and the world to interview near-death experiencers (NDErs or, as she calls them, “death travelers”) and leading researchers in the field. The result is her book Glimpsing Heaven. Her conclusion from her inquiries: “there are simply, as some of the doctors and scientists I’ve interviewed point out, too many experiencers and too many experiences to discount.”
How many? Dutch cardiologist and NDE researcher Pim van Lommel says that in the last 50 years over 25 million people worldwide have reported NDEs. A 1982 Gallup poll found eight million Americans reporting them. As Bachrach comments: “Not every self-proclaimed death traveler could be an arrant liar or deeply unbalanced or both.” If you want to hear accounts by “travelers” who are evidently balanced, mature, and intelligent, you can easily find them on YouTube.
But were these people really “dead”? Aren’t these experiences just hallucinations caused by oxygen deprivation? Having looked into the NDE subject myself for a few years, I believe one can only hold that view if one is ill-informed or determined.
I have another science story for you, but I promise this one is much more enjoyable than the one about the peanut butter. Travel with me now past Mars, past the asteroid belt, and straight into the heart of Jupiter’s mysterious Great Red Spot:
Scientists in Pasadena, Calif., came to the conclusion after re-creating the effects at NASA’s Jet Propulsion Laboratory. They were able to get a Spot-like red effect by directing ultraviolet light at ammonia and acetylene, gases that are both found on the planet.
Their new theory: “Most of the Great Red Spot is actually pretty bland in color, beneath the upper cloud layer of reddish material,” says a researcher.
“Under the reddish ‘sunburn’ the clouds are probably whitish or grayish.” So why is it confined to just one spot? “The Great Red Spot … reaches much higher altitudes than clouds elsewhere on Jupiter,” the expert notes.
The Spot is actually a storm with winds of up to hundreds of miles per hour, the Daily Mail reports. Wind in the area brings ammonia particles closer to the sun, and a vortex keeps them there, the researchers say.
We don’t know how many centuries — millennia? — old that storm is, but it has been fading in recent years. While an exact cause has yet to be determined, it probably has to do with evil carbon emissions here on Earth.
On an unrelated note, the asteroid belt needs a better name. I like “Solar Rhinestones.”
When I was a kid and first fell in love with dinosaurs, they were lumbering, cold-blooded beasts who died of stupidity. So much of the past keeps changing:
Carrying around an exoskeleton of bony armor is hard work. But armored ankylosaurs figured out a way to shoulder the load and stay cool. These Cretaceous dinosaurs had “Krazy Straw” nasal passages that helped them air-condition their brains, according to a new study.
“These heads are just covered with bone they just look like rocks with eyes. And yet, when you look inside, they have these noses that go all over the place,” said Jason Bourke, a doctoral student at Ohio University who presented his findings on ankylosaurus noses Nov. 8 at the annual meeting of the Society for Vertebrate Paleontology in Berlin.
It gets better:
The airway discovery is interesting, Bourke said, because most modern mammals and birds have their own method for warming air headed to the lungs and for cooling exhaled air: They have respiratory turbinates, or blood-rich structures in the nasal cavity that warm and humidify the air coming in.
“This is the first time we’ve been able to show that an animal that doesn’t have these turbinates found another way around heating the air up or cooling it down, just by making the airway superlong and then curling it around,” Bourke said.
Duck-billed dinosaurs, or hadrosaurs, have similarly loopy noses, he said, which have been linked with helping the dinos create resonant bellows. It’s very likely that, in both hadrosaurs and ankylosaurs, the structures served a dual purpose: warming and cooling air, and amplifying sounds, Bourke said.
I’d like to see one of these skulls 3-D printed into the world’s biggest, loudest conch shell.
But don’t quit your job and empty your bank account just yet. Such a black hole could take trillions of years to topple the universe, and scientists don’t yet have a particle accelerator large enough to create the conditions necessary for such a doomsday.
“A particle accelerator that reaches 100bn GeV [the required giga-electron-volts] would be larger than Earth, and is unlikely to be funded in the present economic climate,” Hawking added, according to the report.
I admire Hawking as much for his dry sense of humor — and in the face of such personal adversity — as I do for how far he’s advanced (and explained) physics. Something tells me I’m far from alone in that.
There are a lot of things in space, but terrestrial sea plankton was not one of them –at least, so we thought. Yet traces of the microorganisms were found on the windows of the International Space Station, as reported by Russia’s Itar-Tass news agency.
Experiments had previously shown that microorganisms such as bacteria are capable of surviving in space, and, further, propagating endospores — but sea plankton is certainly a new discovery, Vladimir Solovyev, chief of the Russian ISS orbital mission, told the news agency.
“The results of this experiment are absolutely unique,” he said. “We have found traces of sea plankton and microscopic particles on the illuminator [window] surface. This should be studied further.”
Life, as Dr. Ian Malcolm says, finds a way.
In October 2004, excavation of fragmentary skeletal remains from the island of Flores in Indonesia yielded what was called “the most important find in human evolution for 100 years.” Its discoverers dubbed the find Homo floresiensis, a name suggesting a previously unknown species of human.
In the first place, they write, the original figures for cranial volume and stature are underestimates, “markedly lower than any later attempts to confirm them.” Eckhardt, Henneberg and other researchers have consistently found a cranial volume of about 430 milliliters (26.2 cubic inches).
“The difference is significant, and the revised figure falls in the range predicted for a modern human with Down syndrome from the same geographic region,” Eckhardt said.
The original estimate of 3.5 feet for the creature’s height was based on extrapolation combining the short thighbone with a formula derived from an African pygmy population. But humans with Down syndrome also have diagnostically short thighbones, Eckhardt said.
I liked the idea of Hobbits sharing an Indonesian island with King Kong, but apparently he isn’t real either.
A paper published in the July 30 issue of Nature by Ian Garrick-Bethell – an assistant professor of Earth and planetary sciences at University of California Santa Cruz – examines the shape of the Moon as it would be had not millions of meteorite collisions knocked chunks off it, and ponders how it got that way.
“If you imagine spinning a water balloon, it will start to flatten at the poles and bulge at the equator,” Garrick-Bethell said. “On top of that you have tides due to the gravitational pull of the Earth, and that creates sort of a lemon shape with the long axis of the lemon pointing at the Earth.”
The Moon formed about four billion years ago and was initially much closer to Earth, and spinning rather more than it does today. As the Moon cooled and hardened, the effects of tidal forces exerted by Earth froze the surface into a slightly elongated shape with a bulge pointing towards Earth and a corresponding bump on the other side.
I think she’s just as rotational and spherical as she was at two billion.
A fascinating NASA presentation suggests that in July 2012 Earth was one week away from being struck by a massive solar storm that would have had devastating effects.
NASA’s own Science News describes this event as being “perilous.” Indeed, as perilous as “an asteroid big enough to knock modern civilization back to the 18th century.”
There are plenty of people here on Earth who are already machinating to send us back to the 18th century. Clearly, there’s something alluring about olden times.
In this case, however, it’s the coronal mass ejection that’s captivating minds. This solar storm “tore through Earth orbit in 2012,” says Science News. “Fortunately Earth wasn’t there.”
I just got back from three days in the woods, with no gadgets, no electricity, no nothin’. It’s fun to get away from all the glowing screens we spend so much of our modern lives staring into, but it’s also a lot of work. I had myself, my two boys, and my young niece to take care of, which meant that by the time I’d finished cleaning up from breakfast, it was nearly time to start on lunch. The afternoons were wet, the nights were cold. At the end of the day I was too tired to even bother with the Kindle I’d brought along. Last night before bed I liberated one of Melissa’s prescription-strength Ibuprofens, just to make sure my woodland collection of aches and pains wouldn’t keep me up. There were extra batteries for a couple of LED lanterns and various flashlights — but if those wore out, then what? Well, civilization was about 45 minutes away by way of an occasionally questionable gravel road.
And if something turned off the lights in town, too?
“Getting away from it all” presumes having something to get away from — and something to get back to, too.
I’ll take modern life, thanks.
1. J.K. Rowling almost broke the Internet. She published a Harry Potter short story and civilization nearly ended.
2. A Turkish student has come up with a 3D printed cast that supposedly heals bones as much as 80% faster than conventional casts.
It’s pretty cool-looking.
After my post a few weeks ago debunking myths about the South, the idea came to me to look into different inventors from Dixie.
I found that, as with many regions of the country, most Southern inventors came up with products we don’t use anymore or don’t really think about. But some really fascinating inventions and innovations originated in the minds of Southern men and women.
From agricultural advances to technological breakthroughs to revolutionary beverages, the South can claim quite a few innovations. Here are fourteen of them…
As long as men have experimented upon animals to gain knowledge of physiology or pathology there have been others who have decried the practice. Among them was Doctor Johnson, who said of vivisection that “if the knowledge of physiology has been somewhat increased [by it], he surely buys knowledge dear, who learns the use of lacteals at the expense of his humanity.”
Doctor Johnson argued that the cure of not a single medical condition had been discovered by the use of animal experimentation, and even if that is no longer the case there are nevertheless those who maintain that the benefits of animal research are small by comparison with their cost in the suffering of sentient beings that such research entails.
Two authors in a recent edition of the British Medical Journal, one of them an eminent epidemiologist and the other a sociologist, attempt to answer the question of whether or not animal research is a boon to medicine. Their conclusion is that it is much less so than is commonly supposed, and in some cases it is actually harmful. Since the only possible moral defense of vivisection is that it promotes medical advance, it should be stopped if it does not.
The authors point out that, according to a survey of medical scientists who perform animal experimentation, more are motivated by a desire to advance knowledge or careers than by a desire to help suffering humanity, and are actually rather indifferent to the practical use or otherwise of their work.
This is perhaps just as well, at least for their own peace of mind, because the practical value to patients of most animal experimentation is nil. This is for more than one reason.
The senior quote. You only get one chance to encapsulate your high school career in a few words. Do you go with something profound? Or funny? Do you make the Oscar speech you’ll never otherwise get to make? Do you quote a famous movie character or historical figure? Do you go with something clever and awesome, or do you just express your desire to party?
The biggest problem with the senior quote is that it’s forever. If you say something dumb, it’s right there in the yearbook for the school to remember forever. (For some reason, the yearbook staff inadvertently left mine out. I had gone all literary with a quote from Laurel Lee’s Godspeed*.)
Then there’s Paris Gray. The senior at Mundy’s Mill High School in Clayton County, just south of Atlanta, went with a little “nerd humor” for her quote, which wound up getting her in trouble.
Her quote? “When the going gets tough, just remember to Barium Carbon Potassium Thorium Astatine Arsenic Sulfur Uranium Phosphorus.” For those of you who aren’t up on your periodic table, the symbol for those elements translate to:
You don’t normally think “cultural commentary” when you watch a Paul McCartney video. But, with his latest video release for the song Appreciate, the septuagenarian King of Rock continues to pull new tricks from up his sleeve. This time, a catchy song and dance number transcends the usual McCartney fantasyland, providing some smart commentary on human culture in an increasingly technological environment. In McCartney’s museum, the humans doing everyday things are the displays to be studied by a robot known as “Newman”. An artistic interpretation of left and right brain segments is displayed as McCartney walks this New Man (get it?) through the exhibit, counselling him on human behavior and how to groove. By the end of the video, even the humans are getting into the act, dropping their technological fancies in favor of dancing to the beat.
The robot itself shouldn’t come as a surprise to hardcore McCartney fans. Back in October, when he graced the cover of Rolling Stone McCartney commented on visions of a robot, possibly influenced by one of his favorite stories shared with his 10 year old daughter, Beatrice, is The Iron Giant. In press for the video’s release, McCartney commented:
“I woke up one morning with an image in my head of me standing with a large robot. I thought it might be something that could be used for the cover of my album ‘NEW,’ but instead the idea turned out to be for my music video for ‘Appreciate’. Together with the people who had done the puppetry for the worldwide hit ‘War Horse,’ we developed the robot who became Newman.”
Having developed a keen interest in filmmaking when he was still one of the Beatles, McCartney has come a long way with his films from his first directorial foray, 1967′s Magical Mystery Tour. Far from the acid-induced country bus tour, Appreciate provides an up-tempo perspective on the 21st century from the guy who, not long ago, was singing about his Ever Present Past.
Yet it isn’t Microsoft that’s keeping Macca relevant among Generation Hashtag; cultural commentary aside, McCartney still knows how to rock a beat. Dubbed a “remarkable album” by POPMatters, NEW was ranked the 4th best album of 2013 by Rolling Stone. Transcending the pop fluff that perpetuated so many of his hits in the 70′s and 80′s, McCartney has entered a new era as much motivated by experimentation as reflection.
McCartney is set to tour with Newman in Japan. Perhaps a Godzilla mashup is already in the works.
Are you just a physical entity, ultimately reducible to the physical entity known as your brain? Is that organ—a bundle of neurons weighing about three pounds—the source of all your thoughts, feelings, and any illusion you may have of a “soul” or a “spirit”?
I recently finished reading a 600-plus-page book by a group of academic psychiatrists, psychologists, and philosophers, called Irreducible Mind, that argues exactly the opposite. The book presents a huge body of evidence from scientific studies of psychokinesis, split personalities, psychic healing, near-death experiences, and other phenomena that seems to constitute powerful proof that, while the mind and the brain obviously interact, the former is not reducible to the latter and there are circumstances where consciousness clearly exists and functions independently of the brain.
Irreducible Mind is a subversive endeavor, swimming against the tide of about a century of scientific reductionism (though not, it should be stressed, in quantum physics) that says all phenomena, including your most delicate or exalted sentiments, are ultimately physical. The book has definitely had some impact; googling the title gets almost two million results, and though published back in 2007 it keeps selling well on Amazon.
One of the coauthors is Bruce Greyson, a professor of psychiatry at the University of Virginia and leading researcher of near-death experiences. A few months ago a video surfaced of a lecture Greyson gave in India in 2011. It’s about an hour long, fascinating, and seems to point to even more dramatic findings since Irreducible Mind was published seven years ago.
Greyson presents four lines of evidence for the mind as an independent entity, which I’ve taken the trouble to summarize, and they could be an eye-opener. First he gives this caveat:
The evidence that I’m going to discuss…is derived entirely from scientific research. But I do not want to give you the impression that this evidence is…accepted by Western scientists. In fact, most Western scientists are completely unaware that this evidence even exists.
My home state of Colorado is a guinea pig for the pros and cons of marijuana legalization. Other states are observing closely to see if they should move down the path towards legalization.
There’s plenty of bad news to go around. Police in other states are pulling over Colorado drivers with no justification other than the green license plate. (We’re all stoners now, I guess.) A college student named Levy Thamba fell to his death from a high balcony during spring break after eating a marijuana cookie. And last week a Denver man who ate pot-infused candy became incoherent and paranoid and shot his wife to death.
Is there good news? Turns out there is. Colorado Springs is the source of the Charlotte’s Web strain of medical marijuana that has sent parents with gravely ill children flocking to the city for treatment.
The strain was developed by Joel Stanley and his brothers in their Colorado Springs medical marijuana facility. They’d read that marijuana strains that are high in a chemical called CBD can help to shrink tumors and prevent seizures. The chemical in marijuana that gets users high is called THC, and since it has an adverse affect on seizures the Stanley’s bred it out of the plant.
Their first patient, 5 year old Charlotte Figis, was so affected by a genetic seizure condition called Dravet’s Syndrome that she was not expected to live much longer. Today, she’s almost seizure free. The Stanley brothers named the strain after their first little patient, and it’s showing the world what medical uses marijuana can offer.
Today there are nearly a hundred families with gravely ill children who have relocated to Colorado Springs, purchasing a treatment for their children that would have landed them in prison just a few years ago. Medical marijuana is well known to help in the treatment of nausea in cancer and AIDs patients, but the strains now being investigated may uncover new lifesaving medicines such as Charlotte’s Web.
The recreational use of marijuana is proving to be the problem it was predicted to be, but while the stoners fill the headlines the researchers in medical marijuana are quietly making amazing advances in the treatment of illnesses. That’s some very good news indeed.
Image via CNN Health.
Megachurch pastor, televangelist and author John Hagee has warned of a “world-shaking event that will happen between April 2014 and October 2015.” He believes that the series of lunar eclipses that will occur between now and then are predictive of major catastrophic historical events. The first “blood moon” will make its appearance on April 15. “There’s a sense in the world that things are changing and God is trying to communicate with us in a supernatural way,” Hagee told CBN earlier this year. “I believe that in these next two years we’re going to see something dramatic happen in the Middle East involving Israel that will change the course of history in the Middle East and impact the whole world,” he predicted.
That’s a rather unsettling prediction, one that is causing a lot of buzz among Christians and non-Christians alike.
What is a blood moon and should you be worried? Here are some facts:
I’ve got cataracts, and thanks to a combination of bureaucratic CF at the doctor, at my new insurance company, and sure enough thanks to Obamacare, I still haven’t been able to get them fixed. (May. Maybe.)
For those of you who’ve never had them, the effect is more or less like having really dirty glasses all the time. Small print is hard. (Small print in Chinese is really hard, I have to resort of a magnifying glass.) You lose contrast, and glare washes out everything.
Now, here I am, reading web pages. I’m not going to mention who I’m using as an example, because it’s not Pejman Yousefzadeh’s fault, it’s some damn hipster web designer, who probably wears plaid pajamas and drinks hot chocolate while talking to his mommy and daddy about healthcare. But here’s a fragment of text:
Notice anything about it? Like it’s a little washed out looking?
So I apply my mad web skillz, and discover the background is, yes, white, but the text color is (102,102,102), or in hex #666.
This is called, technically “40 percent gray.” In other words, it’s 60 percent white. The text color is more white than not.
I mean, WTF? Are we supposed to read this?
It seems to be a trend too. A little googling and I find that #666 is a very popular text color. It’s supposed to be “easier on the eyes.”
Dear web designers: Go buy a book. You know, those paper things? I realize they’re old fashioned, but buy one. Or borrow one for crying out loud.
Open the book. What color is the text? That’s right, it’s black. Or damn near black. A 90 percent gray maybe. If it’s a recent book, and a textbook, it might even be some color like a dark Williamsburg blue. It’s not 40 percent gray.
Oh, and using like 10 point font is silly too, but that’s a rant for another time.
For those of you who find this nonsense hard to read, there’s actually a handy web site called readability.com. What they do is take a web page, strip it of the hipster cutenesses, and present it in a reasonably-large font, using black text. (Or nearly black — it’s actually a slightly yellow-green close to 90 percent gray. But it’s close to black.) Then it looks like this:
As if it were actually meant to be read.
And now get the hell offa my lawn.
Despair is a sin. It’s bhavatrishna. But sometimes …
Here a story that’s being pushed as a Facebook thing now. It apparently started as a story in Edmonton, Alberta. Here’s the money quote:
“Some of the kelp that I found was higher than what the International Atomic Energy Agency sets as radioactive contamination, which is 1,450 counts over a 10-minute period,” she said. “Some of my samples came up as 1,700 or 1,800.”
Can’t blame the poor little girl, who is probably having glow-in-the-dark nightmares now. But one would hope someone, like say her science teacher, would do a little research. (If you want to do a little research, you can do worse than my piece “Understanding Radation” about 3 years ago. But here’s the tl;dr version.)
So, 1700 counts in 10 minutes. Here is the part in which we divide. 1700 counts in 10 minutes is about 170 counts a minute, which is a little less than 3 counts a second.
The Potassium-40 in a 150g banana? Around 20 counts a second.
Good thing this kid didn’t go to the produce section.
More from PJ Lifestyle: 7 Ways Noah Turns the Bible Upside Down
Tey’re calling it “the chicken from hell” — in the Dakotas:
The 11-foot-long (3-meter-long), 500-pound (225-kilogram) Anzu wyliei is an oviraptorosaur—a family of two-legged, birdlike dinosaurs found in Central Asia and North America. These dinosaurs ranged in size from a few pounds to over a metric ton, according to a study published March 19 in the journal PLOS ONE.
With its toothless beak, long legs, huge feet, and claw-tipped arms, A. wyliei looked like a devilish version of the modern cassowary, a large ground bird found in Australia.
It was “as close as you can get to a bird without being a bird,” said study leader Matt Lamanna, a vertebrate paleontologist at the Carnegie Museum of Natural History in Pittsburgh.
This is why I never order the chicken.
Let’s get metaphysical with Jay Sekulow:
Does “ObamaCare” truly exist? Are we actually living with the law that was passed with so much fanfare four years ago?
Gallup says the number of uninsured dropped very slightly from 17.1% of Americans to 15.9% — a result so insignificant that it’s close to the poll’s 1% margin of error and still 1.5% higher than the number of uninsured when President Obama took office.
Did you catch that? Almost four years after ObamaCare was signed into law – rammed through Congress via procedural trickery and against the will of the majority of Americans – a higher percentage of Americans are uninsured than before the law was passed.
How could this happen?
♡bamaCare!!! neither exists nor doesn’t exist. The law is neither known nor settled, as its strictures blip in and out of reality by the exigencies of the moment. Mandates are taxes, penalties are fees, mandates are suggestions, deadlines contain no discernible dates.
It is Schrödinger’s Law, existing in a permanent state of undeterminable impermanence.
Two winter storms in a three week period blanketed the South in snow and ice. Naturally, the Left couldn’t resist the chance to link these winter storms to “climate change.” Qualified scientists like Bette Midler and Politico‘s Roger Simon - not to be confused with PJ Media’s Roger L. Simon - have tried to tie this winter’s weather to an assault on Mother Earth at the hands of capitalism. (News flash: the only climate change causing these storms was the change from fall to winter.) One climate scientist with his fingers on the pulse of reality is fighting back against the climate change madness, and he’s stepping up his game.
Dr. Roy Spencer is one of the most renowned climatologists in the United States. His work for NASA and the University of Alabama at Huntsville over the past three decades has proven valuable to the scientific community. Most importantly, Spencer has become a leading voice against the fallacy of manmade global warming.
Spencer can barely contain his anger against the vitriolic language of the environmental movement – particularly the use of the word “deniers” to describe those of us who do not subscribe to the dangerous, radical, and altogether false premise that civilization and capitalism cause global warming. And he has declared that it’s time to fight back, using their own metaphor against them:
They indirectly equate (1) the skeptics’ view that global warming is not necessarily all manmade nor a serious problem, with (2) the denial that the Nazi’s extermination of millions of Jews ever happened.
Too many of us for too long have ignored the repulsive, extremist nature of the comparison. It’s time to push back.
I’m now going to start calling these people “global warming Nazis”.
The U.S.A. (the well-established, dominant power in speedskating) has had an abysmal performance at the Olympics this year. Big names like Shani Davis and Heather Richardson haven’t held fists full of medals as predicted. So far, they haven’t even been close. A piece in The New York Times (as well as several other news sources) are reporting that the equipment was possibly to blame. The victim? The U.S. speedskating team’s racing suits. (Of course, it must be the equipment’s fault…)
At the games, the U.S. team debuted state-of-the-art skin suits made by Under Armour and Lockheed Martin. The suit was called the Mach 39 and was crafted in a wind tunnel. It was cutting edge.
Athletes and coaches decided not to unveil the suits prior to the Olympics because they didn’t want anyone to steal the technology. Ah, ze secret veapon!
Suits worn but no medals.
It is whispered that the suits must have been defective…
Nope. Stop blaming the suits–and here’s why…
This morning, I walked out our front door and across the street to take a picture:
It reminded me of something Al Gore said a few years back: “the world is changing in such dramatic ways right in front of our eyes because of global warming.”
Then I thought of something Wallace Stevens said:
The Snow Man
One must have a mind of winter
To regard the frost and the boughs
Of the pine-trees crusted with snow;
And have been cold a long time
To behold the junipers shagged with ice,
The spruces rough in the distant glitter
Of the January sun; and not to think
Of any misery in the sound of the wind,
In the sound of a few leaves,
Which is the sound of the land
Full of the same wind
That is blowing in the same bare place
For the listener, who listens in the snow,
And, nothing himself, beholds
Nothing that is not there and the nothing that is.
I think I’ll stick with Stevens.
Let’s take a road trip. We’re going to visit all the capitals of all the 48 contiguous states, starting from Denver.
Now, since we’re taking vacation days to do this, we don’t want to visit any capital more than once, and we want to do this in the least time, or in the shortest distance traveled, which is pretty much the same thing.
Starting from Denver, if we only want to visit one other state capital, planning the trip is easy. Denver to Cheyenne. Boom. Two capitals is easy — you can either go Denver to Cheyenne to Topeka, or Denver to Topeka to Cheyenne. Add in Santa Fe, well, there are several routes. Ignoring, for the sake of keeping my readers awake, some details, basically as we expand the number of cities, we have to explore every possible ordering of the cities. So if we stay in Denver, visiting exactly one capital, we have exactly one route. Visit one other city, we have two choices of trip plan — Denver Cheyenne Denver, or Cheyenne Denver Cheyenne. Visit two other cities — so three cities total — and there are six choices. (Remember this includes trips where someone wants to start and end in Santa Fe or, Gods forbid, Topeka.) So, no other cities, you have 1 choice. One other city, you still only have 2 choices. Two other cities, you have six route choices.
Three other cities? Well, you can use all the routes for two other cities, and go to the new city from each of them. So you multiply the number of routes you’ve already got by the total number of cities. In other words, if we have n cities, we want n × n-1×n-2 … 1.
Many of you already recognize this as n! — “n factorial” — which is an important idea in a lot of different areas of math.