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Dreams have been described as dress rehearsals for real life, opportunities to gratify wishes, and a form of nocturnal therapy. A new theory aims to make sense of it all.
Verified by Psychology Today
By Berit Brogaard and Kristian Marlow
For those of us who can barely remember the items on a grocery list, these extraordinary memory skills might seem savant-like. Mark laughs as we make this suggestion. “That’s nonsense. I am not a savant,” he insists. “It’s not something that just comes to me. I use advanced systems and algorithms to accomplish what I do.”
When Mark first began remembering Pi he took the digits and converted them into shapes. He used shapes of objects from the real world: humans, animals, fruits. “The number 13 used to be the shape of an apple and 32 used to be fire,” Mark explains. Once he had memorized the shapes, he planted them in imaginary but familiar landscapes: His childhood home, the university, downtown Aarhus in Mark’s hometown, that vacation spot down at the Reviere at the south coast of France.
Emotions play an important role in recalling numbers, cards and names. Mark actually spots the emotion first and then constructs the shapes from what he is feeling. This technique is extremely powerful, Mark tells us, because the emotion in some sense is intrinsic to the shape. For example, if you see a waterfall of milk in the kitchen, that will trigger a feeling of absurdity. If you see broken glass in the living room, that will give rise to a feeling of discomfort.
In order to imagine Pi Mark has a particular route through the landscape that initiate an emotion in him which then gives rise to a mental image.
Concerned about our inability to remember simple grocery lists Mark quickly adds that his method also can be used to remember lists. Next time you go to the store, leave the iPhone at home, he says. Suppose you want to remember a grocery list that has the following items on it: milk, a bottle of red wine and oranges. Now place the milk in the kitchen, the wine in the living room and oranges outside. Then add the different feelings and associations. In the kitchen you might see a waterfall of milk. This may give rise to a feeling of absurdity or pleasure. In the living room you can imagine that the bottle of red wine cracks on the floor. This will trigger a feeling of instability. As you are walking through the aisles of the store, you start your mental journey in the kitchen. There you are hit with a feeling of absurdity and see a waterfall of milk. As you walk into the living room you suddenly have this uncomfortable feeling of instability. You see the broken glass on the floor and remember to pick up wine. You continue this way until you are done.
When Mark competes in memory sports he uses a headset that blocks out sounds. Some use special glasses to block out peripheral visual input but Mark doesn’t find that necessary. He naturally goes into his own world of emotions, shapes and landscapes.
Regrettably, Mark didn’t succeed. After reaching the 17,108th decimal point, he wrote 48 when it should have been 84. He immediately realized that he had made a mistake and stopped the process. We asked Mark why he thought he made the mistake. “Concentration,” he replied. “After hours and hours of writing down digits of Pi, your brain just stops focusing. It’s a bit like hitting the wall in a marathon.” The wall occurs around 20 miles as a physiological response to carbohydrate deletion. Most new marathon runners have heard of it but don’t expect it. “Marathon wall. Yeah, well. If I see one I will break through it or climb over it,” they will say. Then after 20 miles they start to realize what it really means to hit the wall. The legs start tingling until they become almost numb. Then the pain sets in. Red hot lead inside the legs. For Mark it wasn’t quite that bad. But it only takes a fraction of a second to lose concentration and screw up.
Both Mark and Tammet have some way to go before they reach the superhuman abilities of Chao Lu, who holds the Guinness world record in reciting Pi dating back to 2005. Lu recalled 67,890 digits of pi in 24 hours and 4 minutes with an error at the 67,891st digit, saying it was a 5, when it was actually a 0. Most of us have experienced fatigue after a few hours of standardized testing. It’s a bit difficult to contemplate the mental and physical fatigue Lu must have gone through during this day-long recall exercise.
Though Mark can recite pi to the 20,000th decimal points, his favorite memory discipline is not reciting Pi but counting cards. “I can easily beat BlackJack,” he says, “it mainly requires counting cards and then bidding in the right way. It’s not that hard.” When Mark told us this, we both immediately tried to convince him to join us at some casinos to make some quick cash, but he didn’t go for it. “For me, this is a sport, not a way to make money,” he replied sternly. It seems that this memory superhero will only use his powers for good.
For Mark, however, it wasn’t just practice. Interest also played a crucial role. He has always been obsessed with memorizing things. He found memory sports exciting even as a small child. Most of his peers were interested in soccer and outdoor play. Mark was more of a geek. Though he played soccer (all Danes do), he was intensely focused on his memory games and when he didn’t attend soccer practice he would tend to sit in his room figuring out how to memorize things, such as long strings of numbers or the cards in a deck of cards.
Mark’s second favorite memory game is binary number games. Binary number systems are the systems used in programing language. Put a bunch of zeros and ones next to each other and you get a very large number. These languages may be hard to learn, but they are easy to remember, says Mark. You can remember more using a binary system. When Mark sees three binary numbers, he knows exactly what number it is. So there is a sense in which he can remember three times as many binary numbers as he can remember numbers in the ten-digit system.
Ugh, "genius" again
Despite his extraordinary memory skills Mark hesitates to call himself a savant. He doesn’t really believe that there are all that many true savants, as the word is normally construed. “In most cases it’s a matter of learning the right techniques, not about the surfacing of some inner genius, as the media would have it.” Mark thinks terms like “savant” and “genius” often are misused. “People are fascinated by the apparently mysterious abilities people have. So people decide to make some money off of this fascination.”
Antwerp philosopher Carolyn Dicey Jennings concurs: “To me, there is little worse praise than ‘genius’," she says. “The root of the word, shared with 'genie', signifies a magical, impossible to understand element, brushing aside the hard work under the miraculous rug of some innate talent, some God-given gift.”
Carolyn herself is a humble person. She grants that she hasn’t been called “genius” a whole lot. But that doesn’t make her feel much better “since now I can never reach their stature. How could one climb what is divine? When someone uses the word ‘genius,’ they are asking you to kneel. I find this request revolting. Whatever happened to determined effort? To the strength of the collective? Whatever ‘genius’ is, it has nothing to do with these. And so I not-so-humbly request: look to the hours, attend to what is added, praise the support that has enabled this accomplishment. Do not reduce us all by giving it away.”
But it’s not primarily authors like us that Mark and Carolyn are critical of. Mark thinks self-proclaimed savants practice their uncanny skills more than we think. “Daniel Tammet uses techniques that are very similar to those other people competing in memory sports use,” Mark says. “It’s not magic.”
We reminded Mark that Tammet isn’t just a savant but also a synesthete. There is no algorithm you can follow to become a synesthete. However, Mark thinks Tammet’s synesthesia is self-taught. “He probably intentionally associated color, shape and texture with numbers and after doing this for many years, it became automatic. Memory, too, is responsible for automatization of this connection.”
This also applies to Tammet’s amazing language skills, Mark says. As shown in the famous documentary The Boy with the Incredible Brain, Tammet learned Icelandic in a week. But even language skills require memory, Mark reminds us. Learning a language fast is a matter of memorizing certain grammatical rules and lexical entries. People who are used to competing in memory sports can do this very fast.
Joshua Foer, the author of Moonwalking with Einstein: The Art and Science of Remembering Everything, agrees with Nissen that Tammet uses memory techniques similar to those of other memorists. When Foer asked Tammet to multiply three numbers with three numbers, Foer reports that he could see Tammet’s hands move on the table. “He does something very strange with his hands and that’s normal for people who multiply numbers in their mind,” says Mark.
Mark mentions that Tammet used to compete in disciplines where you have to remember faces. “He remembered a lot of faces in a very short time, which is unusual for a person with autism,” Mark says, “Of course, autism is really a spectrum disorder, so having this ability doesn’t rule out that he has some autism spectrum disorder.” Mark, however, would like to know why Tammet keeps it a secret that he used to compete in face recognition games. “He had a different name back then. About ten years ago he changed his name from Daniel Corney to Daniel Tammet and announced that he was an autistic savant. Joshua Foer later tested him on remembering faces and suddenly he couldn’t remember any faces. That’s just a bit weird."
The Number Sense
The sentiments expressed by Carolyn Dicey Jennings and Mark Nissen are not new. French psychologist and cognitive neuroscientist Stanislas Dehaene, who has conducted influential research on how the brain processes numbers, thinks that the biological basis of mathematical savant skills is obsession with numbers.
According to Dehaene, there are two kinds of number manipulations that we all engage in. In most of our daily tasks we make approximations. When driving down the highway during rush hour and we decide to change lane, we don’t count the cars in each lane and then make a decision. We simply note that there are fewer cars in the other lane and then we make a move, sometimes to the dismay of fellow drivers. Non-human animals can do this almost as proficiently as we can.
We don’t really use much exact mathematics in everyday life. When we learn to do exact calculations and other exact manipulations of numbers in school, we learn it by memorizing certain basic facts and algorithms.
Our brains don’t normally consciously represent this type of exact math. The reason for this, Dehaene says, is that our brain normally converts number words (one, two, three, ...) and Arabic numerals (1, 2, 3,...) into conscious representations of quantities of things. The brain processes 3 as a quantity of three things. Of course, we don’t read the word “three” and then three bananas show up in our heads. It may be very schematic. But the way we understand numbers is similar to the way we visualize quantities of things.
It is easy for us to visualize small quantities. Think of three bananas. Piece of cake. Five. Not too hard. Ten. Now it’s starting to get difficult. 104. Impossible. The larger the number is, the fuzzier the representation. So, there is a clearer representation of 3 in the brain than there is of 104.
This way of representing numbers is a product of evolution, says Dehaene. The best survivors were those who could provide good approximations of numerical difference and sameness. Our ancestors didn’t need exact numbers in order to decide whether to fight or run when faced with danger. Whether they were faced with 103 or 106 dangerous animals would not affect their decision to escape.
Dehaene acknowledges that many people with savant syndrome appear to present a counterexample to this theory of how the brain processes numbers. If savants have the ability to calculate numbers accurately with lightning speed, then his theory does not apply to them.
Dehaene, however, believes the difference in abilities between people with savant syndrome and normal individuals is a function of a difference in training and interest. Savants have more training than most of us. They have learned a few tricks. What differs between them and us is that they are more obsessed with numbers and devote more of their time to study numbers and math than “normal individual”. As Dehaene puts it in his book The Number Sense:
Talented people succeed largely because they devote a considerable time, attention and effort to their topic of predilection. Through training, they develop well-tuned algorithms and clever shortcuts that any of us could learn if we tried, and that are carefully devised to take advantage of our brain’s assets and get around its limits. and get around its limits. What is special about them is their disproportionate and relentless passion for numbers and mathematics – a passion which is occasionally of pathological origin, as clearly seen in retarded autistic children with calculation skills. Training experiments indicate that, with a similar amount of training, normal subjects can also enhance their memory and calculation speed (The Number Sense, 2001: 14)
Dehaene thus agrees with Mark that people like Daniel Tammet, who can calculate as fast as a calculator, appear to be doing magical calculations because they have memorized algorithms and have a strong interest in practicing. If this is true, savants are not all that different from the rest of us.
Why don’t we all walk around as living calculators?
But if the majority of us can learn to speed calculate insanely high numbers, why don’t we all walk around as living calculators? Why can’t we beat Daniel Tammet’s European record in reciting Pi from memory to 22,514 digits in five hours and nine minutes? Why don’t we challenge the computing twins Kay and Flo, who can tell you what their favorite television host was wearing on any date you give them, to a memory game?
Daehene offers part of the answer. Most of us are too busy doing all kinds of other things or we simply lack the interest in excelling in this kind of activity much to casino owners’ fortune. We may have various interests and obsessions but most of us are not obsessed with numbers, complex geometrical patterns or the color of the television host’s shirt over the past 3,000 days.
There is another important difference between normal individuals and savants. While most of us can, and sometimes do, learn to imitate savants by using algorithms to speed calculate, we tend to continue to be aware of the method they are using. While the skill can become more automatic over time, normal individuals do not normally reach a result without knowing how they reached it. They are conscious of the method and the steps required to get to the result.
At least in some cases, the brains of people with special mathematical abilities make calculations that are not themselves consciously accessible, even though the result is. Tammet reports that he is not conscious of how the mathematical calculations he performs are carried out in his brain. He provides the input and receives the output in the form of a colorful three-dimensional figure that he can translate into a number.
There are, of course, physical and biological limitations to our brain’s abilities to calculate. But the main limitations of the human brain appear to be limitations to our conscious abilities and limitations imposed by dominant brain regions. We cannot consciously make hugely complex calculations in our heads or perform calculations that spit out a fractal in our field of vision.
It is unlikely that savants are born with a special mathematical organ that predisposes them to be fast calculators. But even if savant syndrome is not genetically encoded and is not the result of a special math faculty, it is probably something over and above extensive training and good memory. The fact that savant syndrome can be acquired after a hard hit on the head suggests that the right kind of brain organization is needed for savantism to develop. But owing to the plasticity of the brain, it is plausible that brain regions common to all of us can develop into “special math organs”.
Which regions of the brain have this potential? The most likely answer is that its the regions that normally prepare us for action, sometimes called “the vision for action pathway,” or dorsal stream. The brain’s action pathway compute exactly how far we have to move to reach to an object. It calculates the path your arm has to make to reach to the object. It calculates the size of the grip aperture. And so on. But while we usually are aware of the movement taking place, we are not aware of these complex calculations. We cannot answer questions about the size of our grip aperture or the precise path our hand has to take to reach to an object--we can merely demonstrate it.
Even when we are not consciously aware of changes in object size, we still adjust our hand apertures to fit the object. If an object suddenly changes location, corresponding adjustments in hand velocity and trajectory are made in less than 100 ms, which is not enough time for the human brain to consciously represent the adjustment of object location or the corresponding change in hand velocity and trajectory.
Studies have further shown that when study participants are asked to use a minimally demanding vocal response (Tah!) to signal their awareness of a change in object location, modification of movement occurs significantly faster than the vocal response. Adjustments of trajectory and hand aperture occur within 100 ms, whereas the vocal response occurs after 420 ms. This may be why if we think too much about our action in killing a fly we behave more slowly than if we just reacted to the fly.
It seems then that the action pathway is a brain region that can make calculations before we even have a chance to become aware of them. Most of these calculations never reach our conscious awareness. People with special math skills have a way of tapping into the unconscious mathematical calculations. Like most of us, they are not typically aware of the calculations taking place but sometimes the calculations reach conscious awareness in different ways. For example, in Jason Padgett’s case, they reach his consciousness in the form of complex mathematical patterns. In Mark Nissen's case, they reach consciousness by being recallable through emotions and images.
Mark is in some sense right. We all have the superhuman abilities inside us but we cannot always tap into them. Sometimes they remain hidden from sight forever, sometimes they remain hidden until someone beats us up or we bang our head against a corner of a swimming pool. It may not be as glamorous as a radioactive spider bite but even these superhuman abilities have their own origin story.
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I can easily defeat BlackJack,” he says, “it mainly needs keeping track of cards and then putting in a bid in the right way. http://www.onlineblackjackaustralia.com/
I'm not giving my name or my primary email because I need to stay anonymous. I beat blackjack consistently, I don't walk away with a profit every single session, but my winning sessions far exceed my losing sessions. Also my winning sessions are usually huge, unless I have decided to only play until I reach some goal that session and stop. For instance I just moved into a new, fairly expensive place and due to some other bills I found myself short of the rent + deposit I would need the next day, by $1600. So I went to sleep early and got up about 4AM and went to a casino (I moved to Nevada so I could play cards) I know that has an easy game for me to beat, I pulled $400 out of the ATM and when I got over $2,150 I quit. I didn't stop exactlyl at a $1600 profit because that last winning bet was a double down and pushed me over. That's how confident I am of winning - I could have found myself even more in the hole had I lost the $400 but I really don't have to worry too much about that, especially at tables like this particular one. When I don't have any particular goal for the night, I am normally careful not to win too much at any one casino and stay sensitive to "heat" (casino personnel surveillance, targeted distractions, intimidation, etc.) and go to another casino before anyone thinks much about me. Some casinos are used to big action, even bigger than mine, and don't freak out over a $30,000 win, and I can play longer at those. I'm not very afraid of anyone identifying me as a card counter, because I no longer actually count cards, as I'll explain.
I've always had exceptional number sense and recall of numbers. I was in a profession that was very numeric and this gift was very useful there, and I rose to the top of that field. But I always thought gambling was for people who never took math and didn't understand that there was a house advantage that, though small, meant that over time you had nowhere to go but downhill. But THEN, when I was about 44 years old, on a business trip to Vegas, I decided to just play a little blackjack. I remember the first session, I was a little slow seeing the card values and adding them up and the dealer had to help me here and there to keep the game moving along. But I caught on very quickly, then after a few hours I just SAW what was going on like a light went off in my head and I won $1,800 that first session. I saw that the game could be beaten and I bought training materials when I got home, books, training software, blackjack equipment to practice at home - everything to train as a card counter. After I could keep the count and started edging over 51-54% winning sessions, which is all it takes to be profitable, I went back to Vegas, to the same place I stayed before. I was only playing low stakes, $5 or $10 minimum tables. I did a couple of successful trips playing low stakes, but then when I moved up in stakes and started playing $100 to $300 per hand, I screwed up and won $12,000 in a single session at a low roller place and got "backed off" - told I could no longer play that game at that casino. That is the only time anything like that has happened to me at it was well over 10 years ago. Putting in all that effort only to find that being good at the game meant I would get kicked out was disheartening, and I decided to learn poker, which was MUCH more difficult for me. Poker isn't purely mathematical like blackjack and it was very difficult for me at first, but I am now also world class at that game. But that's another story. Let me jump ahead in my card career to talk about the subconscious processing in my subject line.
I learned how to camoflauge my card counting and also learned different counting systems so I could switch between them to confuse casino surveillance. There are some dealers, pit bosses, and special security guys who can count cards using the most popular and simple system, the Hi-Lo. Even among dealers who can't count professionally, the experienced ones can spot exactly what you are doing fairly quickly, because in hard core card counting with the Hi-Lo, you are making precision bets that vary with the count like a machine. In fact your play is just plain robotic, if you are playing exactly as you should to maximize your profit and minimize loss. No tourist or even experienced or local but untrained player plays exactly like that. In fact I can spot a card counter at my table very quickly, and in the past others could spot me as well, and with subtle signals like a direct glance and a smile during table patter we signal each other that we know. There is an etiquette that says when you spot each other, the polite thing to do is leave and let the first guy (they're almost all guys) at the table have it. So learning situational awareness and camoflauge let me play all over without so much fear of getting kicked out or marked in the corporate database, and I played for years that way, and I just kept getting better and better. By then I had a good bankroll and winning was becoming easier, so I started sometimes playing just for fun and to socialize, and I would drink too. But then I started noticing a strange thing. Even completely without counting, and while being drunk, just letting myself bet however "felt right," I was winning, really winning - even more than usual. Of course out of habit I was observing all the cards being dealt, but I wasn't consciously adding and subtracting points and dividing by the remaining cards and playing the exact, mathematically correct strategy variations that a card counter memorizes. And I was making some CRAZY plays, too - way out there stuff, for no particular reason I could tell you, just following whatever urge I felt. And my dealer blackjack detection went from only taking insurance when mathematically correct and being wrong sometimes, to just KNOWING when he had a blackjack and taking insurance whether it was correct or not - and being right!! Same thing with making really big bets. I no longer consciously count, and I no longer move my bets up and down, machine like, in exact step with the hi-lo or other count. I just relax my mind, similar to meditation, and I don't question my urges, I just do whatever I have the urge to do, and if I have the urge to suddenly pop it up to $1,000 per hand for no apparent reason, I just do it - and it's almost always right. Another thing that happens now is that once I get warmed up and quite a few hands into the session, I can start predicting cards coming out. Not all of them, mostly just mine and the dealer's, and not every single card, but mostly the ones about to come out after I"ve been dealt my first two. No conscious effort whatsoever, and no pretty mental pictures as you describe, just the number comes to me from somewhere - "7" or "10" or "he's gonna bust." I mean, it's freakin' SCARY, it's very weird, like I've become "Rainman" from that old Tom Hanks movie.
One downside that I have mostly fixed, but it still bites me sometimes, is that when doing this "still my mind and let the urges come" type playing, I play better with some alcohol in me - SOME alcohol in me. But I have had a problem with alcohol in the past and I really do like the stuff a little too much, so I have to be very careful, and disciplined to limit the length of my sessions or walk away when I feel I'm moving beyond relaxed into intoxicated BAC levels. Of course if it hits me before I catch this, then I lose all inhibition and discipline and don't really care anymore hahahah, and I'm just having a ball - party time! Remember when I said that now I have many more winning than losing sessions? Well the losing sessions the last 3+ years have all happened when I was really and truly drunk. Not relaxed, not happy, talkative and buzzed, but really effed up. Honestly I don't even remember almost any of my losing sessions, which have all followed a big winning session, or a day or few days of big winning sessions. I don't remember why I lost, any plays I made, what we talked about at the table - nothing. I just wake up in my room the next day and however many chips I took the night before plus what I remember winning before I got blasted are gone.
Not caring is a related subject. I've always had a very strange relationship with money. I come from a well-to-do family running our own businesses which are ones you might typically think of as being lucrative. So I've always been around a fair amount of money, and I've never had to worry where my next meal is coming from, and I know that if I am out somewhere and I busted my bankroll I can call and get some money put in my account, not a bajillion bucks but certainly enough to be comfortable, safe and secure until I get home. But on the other hand we are from a family and subculture that is not really very materialistic, and I was raised to reject status symbols and any display of wealth. As an adult, I myself am a strange mixture of loving money for the fun and freedom and nice meals and travel and hotel rooms and dates with attractive women, and being totally non-materialistic in all the "normal" ways that society imagines. For instance, I don't own a car. I dress like a hippie or old school rock musician most of the time. I don't own an expensive watch, I get things like wallets, sunglasses and luggage from walmart. And I know I can go out most any night and start with $1200 and keep another $2000 in reserve if I take some negative variance, and I can come home with anywhere from $12,000 to $35,000 just about every time. So I don't care that much about losing money. Every single time I am about to play, and when I start the night, I do get nervous for some reason, probably because I have experienced some big losses at times and you never know for SURE that you'll win that night. And that is where a little alcohol helps. It REALLY cuts any nerves out, kills my adult ADD and let's me focus, and relaxes me and lets me really feel the cards, bets and urges welling up from my subconscious like magic. I can play totally sober but I play in a more risk-averse way and my conscious mind keeps getting in the way, calculating that I better not bet so big because if I got splits and a double down that would be half my stack in one hand, for instance. Or telling me I'm ahead $2500 and I'm tired of the risk giving me stress so, let's just quit for tonight. The right dose of alcohol erases these self-limitations and also it's great for the casinos to see me drink, because they think that no card counter ever drinks, which is true when you are doing the robotic, computer like play. But I have to really be careful and keep a lid on it, because if I take one shot too many, it's gonna be all downhill from there until I pass out in my hotel room the next morning. I wish I could find a safer substitute for erasing any anxiety and inhibition and letting my subconscious take complete control, but I haven't found one yet. I can meditate before and during the first hands of the session, but I definitely play differently with zero alcohol, more mechanically and risk averse like I used to play, and I have trouble doing the wild plays and insurance bets when I know they feel right, because I have more fear that I'm being surveilled. Therefore, I win less. It's also less fun and social with the dealer and other players. On the upside, I almost never lose when stone cold sober, and NEVER win tens of thousands and lose them back later the same night. But I am very welcome and get full complimentary everything in most casinos, and some of those drunken losses has probably helped convince them that I am just another sucker, even though I am so totally not that.
So that's my story. Number sense, just as you said, that comes from my subconscious and tells me what to do, but I have no idea how it arrived at that decision. And this happened after years of hard training and study and playing experience, again just as your article indicates. Again as you indicate, the plays and bets my subconscious feeds me often seem like they don't have any mathematical reason I can identify, but they are almost always right, especially with a little alcohol. But too much alcohol completely breaks this card playing machine and leaves me insensitive to that fact at the same time. Still, I can live a very plush, high end lifestyle whenever I wish by using this. However I am not particularly greedy or in need of money so I don't do this like a job, playing 40-60 hours a week and trying to maximize my income. I do it whenever I feel like it, which can be every night for a couple of weeks, or not at all for months at a time.
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