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The Horses that Defied Science

Posted on 05 August 2019, 8:08

There have been many stories of very intelligent and otherwise gifted animals over the years, but I’ve not heard of any more mind-boggling than that of the Elberfeld horses (below) of Germany (then Central Prussia). As the well-documented story goes, these horses could figure out square roots, cube roots, even fourth-power roots of numbers with six or seven figures. They could also communicate in German and French.  Professor Edouard Claparède, a distinguished Swiss psychologist of the University of Geneva, called the phenomenon “the most sensational event that has happened in the psychological world.”


As the story goes, in 1900, Wilhelm von Osten of Elberfeld taught his horse, Hans, a Russian stallion, mathematics.  He would place skittles, or bowling pins, in front of Hans and count, then ask Hans to strike as many blows with his hoof as there were skittles in front of him.  “The results were astonishing,” Dr. Claparède reported.  “The horse was capable not only of counting, but also of himself making real calculations, of solving little problems.”  But Hans was more than a mathematician.  He was a musician, able to distinguish between harmonious and dissonant chords.  And he had an extraordinary memory, able to tell the date of each day of the current week.

However, following Claparède’s investigation,  Oskar Pfungst, representing a committee of 24 professors appointed to study Hans, reported that the horse merely obeyed visual clues given by von Osten, whether conscious or unconscious. This became known as the “Clever Hans effect,” a term still used by animal trainers today.  It was later revealed that of the 24 professors on the committee, only two of them actually observed Hans.  Science was apparently satisfied with the committee’s conclusion and that pretty much put an end to all the excitement concerning Hans.

After von Osten’s death in 1909, Hans was acquired by Karl Krall, a wealthy merchant, who also brought two Arabian stallions, Muhamed and Zarif, and began to train them in the same manner von Osten had taught Hans.  Within a matter of weeks, Muhamed was doing addition, subtraction, multiplication and division and before four months had passed he was able to figure square and cube roots.  Krall then taught Muhamed spelling and reading. Zarif was a little slower in learning, but was eventually able to do almost everything Muhamed was capable of, as the aging Hans went into retirement. 
Having heard much about them, Maurice Maeterlinck, (below) a world-famous Belgian author, playwright, and Nobel prizewinner for literature, decided to visit Elberfeld and observe the horses for himself. After he was introduced to Muhamed by Krall, the horse was asked to spell Maeterlinck’s name (so many taps of the hoof for each letter of the alphabet).  Muhamed began by lifting his hoof and tapping out an “H,” followed by an “E” and an “R.”  The two men suddenly realized that Muhamed was spelling Herr, the German equivalent of Mister.  But Muhamed then struggled with the surname, first spelling M-A-Z-R-L-K.  When told by Krall that it was incorrect, Muhamed tried again, tapping M-A-R-Z-L-E-G-K.  Krall then repeated Maeterlinck’s last name and after two more attempts the horse spelled the name with one small error.  The two men concluded that it was close enough.


“I assure you that the first shock is rather disturbing, however much one expected it,” Maeterlinck wrote in his 1914 book, The Unknown Guest.  “I am quite aware that, when one describes these things, one is taken for a dupe too readily dazzled by the doubtless childish illusion of an ingeniously-contrived scene.  But what contrivances, what illusions have we here?” 

Concerning the math tests, Maeterlinck wrote that “what strikes one particularly is the facility, the quickness, I was almost saying the joyous carelessness with which the strange mathematician gives the answers.  The last figure is hardly chalked on the board before the right hoof is striking off the units, followed immediately by the left hoof marking the tens.  There is not a sign of attention or reflection; one is not even aware of the exact moment at which the horse looks at the problem, and the answer seems to spring automatically from an invisible intelligence.  Mistakes are rare or frequent according as it happens to be a good or bad day with the horse; but, when he is told of them, he nearly always corrects them.  Not unseldom, the number is reversed: 47, for instance, becomes 74; but he puts it right without demur when asked.”

Maeterlinck carried out experiments of his own in the absence of Krall. Since the horses performed without Krall’s presence and gave some answers to questions that Maeterlinck himself did not know the answers to, he discounted the Clever Hans effect. 
Another theory advanced was that of telepathy; that is, the horse was mind-reading. To test this theory, Maeterlinck took some large cards with Arabic numerals on them, shuffled them and placed them in front of the horse without looking at them himself.  “Without hesitation and unasked, Muhamed rapped out correctly the number formed by the cards,” Maeterlinck wrote.  “The experiment succeeded, as often as I cared to try it, with Hänschen, Muhamed, and Zarif alike.”  Since Maeterlinck was the only person present and did not know the numbers, there was no mind present to be read for the answers.
In one test, Maeterlinck wrote a surd – a number which had no square root – on the blackboard, not realizing that it was a surd.  Maeterlinck looked to Muhamed for a square root.  The horse lifted his hoof, paused, looked back at Maeterlinck and shook his head.  This little test also opposed both the Clever Hans effect and the telepathy theory.

One day, Zarif stopped in the middle of a lesson by Krall.  The horse was asked why and replied, “Because I am tired.”  On another occasion he stopped again and explained, “Pain in my leg.”
Maeterlinck also reported on tests run by a Dr. H. Hamel while Krall was on a trip. Hamel began by giving Muhamed simple math problems and ended with asking Muhamed for the fourth power root of 7,890,481, which Hamel himself did not know until after checking Muhamed’s correct answer of 53, which took about six seconds before he began striking out the answer. 
On another day, Krall and a Dr. Scholler decided to make an attempt to teach Muhamed to express himself in speech. The horse made several feeble efforts before stopping and striking out the message, translated from the German to read, “I have not a good voice.”  They then asked Muhamed what was necessary for him to speak.  He replied, again in German, “Open mouth.”  They asked him why he didn’t attempt to open his mouth, and the reply came, “Because I can’t.”

On another occasion, Zarif was asked how he talks to Muhamed.  “Mit Munt” (with mouth), he replied.  Krall asked Zarif why he didn’t tell him that with his mouth, to which Zarif replied, “Because I have no voice.”

Maeterlinck was clearly flabbergasted:  “You rub your eyes, question yourself, ask yourself in the presence of what humanized phenomenon, of what unknown force, of what new creature you stand,” he wrote.  “…You look around you for some sort of trace, obvious or subtle, of the mystery.  You feel yourself attacked in your innermost citadel, where you held yourself most certain and most impregnable.  You have felt a breath from the abyss upon your face.  You would not be more astonished if you suddenly heard the voice of the dead.”

At least 10 other respected scholars and scientists were reported to have studied the horses, all ruling out fraud and the Clever Hans effect, but not having any answers.  In the absence of a scientific explanation, the Clever Hans effect has gone down in recorded history as the probable explanation. 

If not the Clever Hans effect, if not some other type of fraud, if not telepathy, if not true intelligence on the part of the horses, then what other explanation is there?  Maeterlinck considered the possibility that the horses were mediums, much like human mediums, through which some higher power was working. As to why it was necessary to teach the horses in the first place, he opined that it would be like asking an automatic writing medium to do her thing without knowing how to write.  “Unconscious cerebration, however wonderful, can only take effect upon elements already acquired in some way or another,” he explained. “The subconscious cerebration of a man blind from birth will not make him see colors.”

Maeterlinck had studied the reports of psychical researchers like Frederic W. H. Myers, Richard Hodgson, and Sir Oliver Lodge, and accepted the reality of mediumship.  However, he struggled with the spirit hypothesis as he believed that if spirits actually existed they would be in a much more enlightened state, not “groping and groveling” as so many reports from the psychical researchers suggested.  In concluding, Maeterlinck admitted that he had no answers other than that a “spiritual” or “psychic” epoch was taking place.

While not suggesting there is any precedent for animal overshadowing or control by spirits, Archibald Campbell Holmes, a spiritualistic phenomena historian and author of the day, believed that spirit influence was the most logical explanation for the Elberfeld horses.  He reasoned that if spirits can take control of tables by tilting them and levitating them, and, at the other extreme, take control of human mediums, there was no reason to believe that they couldn’t influence or control a horse.  As to why they would do that is an unanswered question, although spiritualism teaches that there are many low-level and mischievous spirits hanging around the earth plane.  Then again, it could have been a mathematically adept spirit who was experimenting or just having some fun.

My more comprehensive report on the Elberfeld Horses can be found in the book, “Paradigm Busters,” edited by J. Douglas Kenyon, an anthology of 30 mysterious events.

Michael Tymn is the author of The Afterlife Revealed: What Happens After We Die, Resurrecting Leonora Piper: How Science Discovered the Afterlife, and Dead Men Talking: Afterlife Communication from World War I.

Next blog post: August 19


Hello Amos, yes I couldn’t agree more, as you can imagine. But again it is human arrogance and incompetence in dealing with life at play… Thank you for sharing your feelings with me. I very seldom, if ever, find somebody to whom I can talk about non-human beings and be understood. A very sad circumstance and a lonely one… And there is a lot to say about plants, too. J. Chandra Bose and lately Stefano Mancuso put it very well, although I suspect there is still more to say…

But “...figuring out the fourth-power root of 7,890,481 within a matter of seconds” and here I also agree with Mike. Yes, something else must have been at play. Perhaps to teach us, humans, a lesson? Which of course we did not learn. As usual… Thanks to both.

Anabela Cardoso, Sat 17 Aug, 19:37

It often saddens me when I see how humans disrespect other animals.  More times than not I just can’t read stories about animals or see movies about them because they are usually treated as some inferior organism or patronized as some cute but incompetent child.  On some level I think I am part of the etheric fabric that includes all animal spirits. It is unusual to find other people who discern animal spirits the way I do and I am comforted to find that you may be one of those few people.

All of my life I have been very observant of animals and identified with them, getting my first broken tooth as a result of a fight with a neighbor boy who was swinging fledgling birds around with a string around their neck until they were dead.  I have raised many different species of animals, fed them, exercised them and yes, even slept with them.  They all were conscious beings who shared my world even though they may not have fully understood it as I did not fully understand their experience in the world.

From the lowliest insect to the largest baleen whale they all are occupants of this world, this reality, and deserve, as I do, an opportunity live out their life as they choose, to learn and to spiritually grow toward God.  I am created equal with them, each of us a small piece of the god source and we all have a god-given right to live our lives according to that spiritual guidance innate in every living being - AOD.

Amos Oliver Doyle, Fri 16 Aug, 18:19


I agree with you and Amos and that there is likely a much higher degree of intelligence among animal than we realize and, as with humans, there is a wide range in intelligence; however, when it comes to figuring out the fourth-power root of 7,890,481 within a matter of seconds, I’ve got believe something else is at work.  Although I have heard of a few humans capable of such a feat, Einstein not among them, I suspect they had something else beyond intelligence going for them.  I’m content to believe it is beyond my comprehension. I doubt that discarnates have that ability, but perhaps some very advanced spirits do.

Michael Tymn, Fri 16 Aug, 17:51

Thank you Mike for the wonderful Lady’s story. I didn’t know about her and was thrilled to find out. I do not think so much of discarnate intelligence, though, why do we have to always attribute every extraordinary actions to discarnate intelligences? I think it is all the animals’ glory not discarnate influences. If there are very intelligent, perceptive humans there are also very intelligent, perceptive animals. As simple as this. But human arrogance does not allow us to recognize this and dedicate to our horses or dogs or whatever, the same degree of attention we dedicate to our human children. I believe this is the main reason.  And, naturally, I fully agree with Amos Oliver Doyle.

Anabela Cardoso, Thu 15 Aug, 17:50

James, I tend to agree with you, although I am not 100% on anything.

Michael Tymn, Thu 15 Aug, 10:11

As noted above: if discarnate spirits can make physical objects move, and affect the minds of adult human mediums, why couldn’t they overshadow the minds of animals?

I believe that they often overshadow the minds of small children, and of persons in a trance state: and that such is the real source of ‘memories’ of the child or trance state person’s alleged prior lives.

I also believe that all of us are under the continual sway of discarnate spirit influences, both for good and for evil. Swedenborg and Kardec both felt so: and Dr. Carl Wickland’s work with mental patients verified it.

James McArthur, Thu 15 Aug, 04:46

Thanks, Anabela, for the comment.  You and others might also want to check out the story of Lady, the wonder horse, who was studied by Dr. Joseph Rhine and other researchers.  One story about Lady can be found at

Michael Tymn, Sat 10 Aug, 09:17

Thank you Mike for this wonderful piece. I knew about the Elberfeld horses but not in such detail. I am particularly delighted because when I tell people, or write, that some of my deceased dogs have communicated with me via ITC, the majority just ignores it or, very conspicuously, show that I must be a bit crazy. Nevertheless, it is completely true and it is not pareidolia or any acoustic delusion. Some of them have spoken with me via the direct radio voices as I have posted in my books. What a disgrace to think and act as if only humans (the great predator species) are sensitive and intelligent! I believe it is just the opposite. Were it not so why would humans have destroyed the planet while the other species have respected and maintained it? What can be more illuminating?  Thanks again!

Anabela Cardoso, Thu 8 Aug, 18:55

One point that I failed to make in my last comment is that intelligence in animals is not necessarily related to any mediumistic abilities.  To put it another way, spirit influence, if that is what it was with the Elberfeld horses, does not necessarily require intelligent animals.

Michael Tymn, Wed 7 Aug, 07:39

Thanks to all so far for the comments. I suspect that there is a large range of intelligence among animals, just as there is in humans.  I recommend renowned biologist Rupert Sheldrake’s 2011 book “Dogs That Know When Their Owners Are Coming Home.” It is a very enlightening read and one has to wonder how instinct fits into the whole consciousness picture.

I think Eric has summed up what I might have otherwise attempted to say.  And, thanks to Lloyd for sharing those two stories. As I mentioned in the more extensive article I wrote for “Paradigm Busters,” I once interviewed the lead trainer at Calumet Farm, one of the leading horse racing stables in the country, about whether horses really know what winning is all about.  He stated that some are smarter than others in that regard, but that many of them definitely have a will to win.  He could not provide any science to back up his statement; it is all just a matter of observation over many years and opinion.

But while there may be geniuses in horse intelligence, there remains the question of being so intelligent as to provide cube roots and fourth-power roots of six-numbered figures within a matter of six seconds.  If there is spirit influence behind it all, it makes one wonder how spirits have that ability, or if only a few of them have such ability.  I tend to accept what Ziaa said in her comment, but I am only at about 75% in believing that spirits can control horses and use them as mediums. That means I am still a skeptic to some degree.

Michael Tymn, Tue 6 Aug, 20:01

When Einstein died his brain was taken, without permission I believe, for study. Apparently nothing at all was found to explain his thought. This is no surprise. As several of your correspondents, Michael, have said, whether in similar phraseology or different, we live in a sea of consciousness which is itself at least partly “above” our own level. That higher level seems to contain or even consist of thoughts that can be transmitted by various means through and into our own level and hence become all sorts of phenomena in our own world-around, from visible ghosts to trance utterances to clairvoyance, to speech by animals in a language of hoof-beats, and so on and so on and so on. This should cause no surprise. The totality (we have called it God even whilst so benighted we thought it only a bearded man on a raincloud) has the ability to reach into consciousness that cannot fully return its gaze, in other words (being clever enough) the greater can find means of transduction into much lower realms of being which cannot perceive that greater source, such as ours relative to that of what we have called angels, and of theirs to what we have called Godhead and other pretty useless and incense-stinking words. In a Universe that contains a spatial level or two, plus one dimension of duration, then another (higher) consisting of three spatial dimensions and one of time, then another (higher) consisting of four spatial dimensions plus one of time, contained with another consisting of five spatial dimensions plus one of time, and so on, one eventually arrives at a Universe with an infinitude of dimensions existing in a perpetual but bustlingly active NOW. The infinitude of dimensions becomes a SINGLE and timeless wholeness. How would THAT be UNable to use a horse’s mind-body system? We all need to ponder, and open our eyes.

A lot more could be said, but the tv here has gone on and the concentration of this limited mind is impaired . . . and more WORDS would not help the imagination anyway.

Thank you, Michael, for further information about Kluge Hans and others that corrects the arrogant views of mega-sceptics.

Eric Franklin

Eric Franklin, Tue 6 Aug, 14:44

A wonderful story, wonderfully told. I have known about the Elberfeld Horses ever since discovering Maeterlinck’s The Unknown Guest in my mother’s book case 70 years ago. I have read it several times, each time with amazement, and nothing more. My lazy thinking, I must admit, is inclined to take action only when a strange account is accompanied by an explanation which includes a mode of action which fits preconceived ideas of cause and effect. Since I have just written a book of such accounts, for popular attention, I am more receptive than usual. In fact I am going to include the Elberfeld Horses in a chapter on animal events. Thank you Michael Tymn, for a prod in that direction.

Alan Sanderson, Tue 6 Aug, 08:23

Excellent article, Mike.  I was not aware that the clever Hans syndrome was another psuedo-debunk.  I should have known.

I have a couple of data points, however, that I would like to bring up that might affect how we explain what those horses could do.

Point one, A few years back, I was watching an NPR special on Secretariat, the famous racehorse who was leaps and bounds ahead of the pack when it came to speed.  It seems he had a larger heart and lung setup than the usual horse, they concluded after his autopsy (he passed over in old age).

However, Secretariat also seemed to have intelligence, if the sincere sounding remark made by a reporter who was being interviewed for the documentary is any indication.  It seems the reporter was standing off to one side of Secretariat, talking to other humans.  He made some remark about how this horse couldn’t possibly understand what he was saying, he was only a horse.

The very next moment, he found that Secretariat had to turned to look him straight in the eyes, and continued to stare at him, until he got the distinct impression that the horse was saying, non-verbally of course, “Oh, yeah, buddy?  What do you know?”  Then the horse turned away.  This was not a documentary on animal telepathy or anything paranormal, and the reporter, again, came off as quite sincere.

Data point two:  While visiting our veterinarian the other day, the vet told us (in front of our dog), that our dog was training US by not eating until we put peanut butter in her food.  And we should stop putting peanut butter in her food, except as an occasional treat.  We agreed to that (in front of the dog).

The very next feeding, our dog did something totally different than usual.  She immediately started eating the dry food, no peanut butter, without hesitation.  Just the day before, she had refrained from eating all day, then pounced on the food when I put the peanut butter in.  She had been doing this for months.  But ever since seeing the vet, she has been eating the non-buttered food right away with no problem.

Coincidence?  Perhaps.  Or maybe she knew the jig was up.

In any case, why must we come up with convoluted theories that tip toe around the idea that animals just might, maybe, have some intelligence?  Perhaps we are the ones lacking in smarts…

Lloyd, Tue 6 Aug, 05:03

Of couse, spirit mathematician using horses prepared for mediumship, yes.  For humans like myself that have been prepared / trained for mediumship—its easy to understand.  Some will be better than others.  But having trained horses myself, Horses and Elephants must be the most sensitive spiritual animals.  They are so willing to serve in the right conditions.  In fact, its possible because horses have no preconceived ideas and if trained with kindness would make perfect vessels for spirit control.

Ziaa, Mon 5 Aug, 18:50

Having lived intimately with dogs for many years I have come to realize that dogs and perhaps other animals are very sensitive to not only human voices but other behaviors which may go unnoticed by other humans. At times they seem to anticipate things by reading subtle human body movements and facial expressions especially when they have some particular interest, e.g., going for a walk, getting fed or getting a snack (reward) etc.

My dogs have always seemed to be on the alert for things that might interest them especially things that might harm them.  My most recent dogs were able to understand English words.  For example Woody, responded to quiet direction to go get his leash.  He would go in the bathroom, open a bottom drawer, pull out his leash and bring it to me.  When I asked, “Where are my shoes?” he would search the house and bring one to me.  This was all in anticipation to going for a walk.  He responded appropriately when on a walk when before crossing a road, I said “Look right” and then “Look left” making sure there were no cars coming.

Rosie on the other hand is not as smart as Woody.  She is a sensitive spirit, having been abused as a puppy.  She responds best when I whisper to her.  Loud voices frighten her.  She has ‘Post Traumatic Stress Syndrome” I think.  After riding in the car for several years, she now refuses to get in a car and often anticipates my efforts to get her in the car by stopping and standing still when she gets several feet away from the car.  Loud traffic noises and a blaring radio when riding in the car are the cause I think.

Hippocrates is reported to have written that the consciousness of people and animals is the same, only the form is different.  I believe that too.  Maybe their consciousness has not evolved as much as a human consciousness but it is basically the same. Obviously they don’t speak a language humans understand but they do communicate with each other and, if one pays attention they can communicate with humans also.

Each living thing contains a small spark of God.  On their level, non-humans experience the same external reality that humans do but only from their unique perspective making their experience unique to their species.  From the smallest maggot to the most advanced dolphin, all living things have a spirit that survives dissolution of their body and continues to evolve until it completes its spiritual growth and returns to the Source. - AOD

Amos Oliver Doyle, Mon 5 Aug, 17:05

It appears to be a surprising example of the universal connectivity of Consciousness.

Paul J. Hauser, Mon 5 Aug, 16:43

What a wonderful story I had never heard of before. I will not even try to offer any kind of explanation or interpretation. It is just a tale for us all to enjoy and be amazed at. That said, Mike, you have just inspired me immediately to order Kenyon’s book on Amazon UK, used, like new, for just 76 pence! I look forward to reading it. Thanks very much for this well written piece.

Keith P in England., Mon 5 Aug, 09:10

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The Hidden Door – Introduction by Peter and Elizabeth Fenwick – Accounts of dreams are as old as human history. People have always been fascinated by their own dreams, and have always looked for significance· in them. From the most ancient civilisations of Assyrians and Babylonians through to Biblical times it was believed that dreams brought messages from the gods in the form of warnings, omens and portents. In ancient Greece they were seen as prophecies, or instructions from Zeus. Read here
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