20110615
4 Steps to Problem Solving
A FOUR-STEP PROCESS
Billstein, Libeskind and Lott have adopted these problem solving steps in their book "A Problem Solving Approach to Mathematics for Elementary School Teachers (The Benjamin/Cummings Publishing Co.). They are based on the problem-solving steps first outlined by George Polya in 1945.
1. UNDERSTANDING THE PROBLEM
* Can you state the problem in your own words?
* What are you trying to find or do?
* What are the unknowns?
* What information do you obtain from the problem?
* What information, if any, is missing or not needed?
2. DEVISING A PLAN
The following list of strategies, although not exhaustive, is very useful.
* Look for a pattern.
* Examine related problems, and determine if the same technique can be applied.
* Examine a simpler or special case of the problem to gain insight into the solution of the original problem.
* Make a table.
* Make a diagram.
* Write an equation.
* Use guess and check.
* Work backward.
* Identify a subgoal.
3. CARRYING OUT THE PLAN
* Implement the strategy or strategies in step 2, and perform any necessary actions or computations.
* Check each step of the plan as you proceed. This may be intuitive checking or a formal proof of each step.
* Keep an accurate record of your work.
4. LOOKING BACK
* Check the results in the original problem. (In some cases this will require a proof.)
* Interpret the solution in terms of the original problem. Does your answer make sense? Is it reasonable?
* Determine whether there is another method of finding the solution.
* If possible, determine other related or more general problems for which the techniques will work.
Billstein, Libeskind and Lott have adopted these problem solving steps in their book "A Problem Solving Approach to Mathematics for Elementary School Teachers (The Benjamin/Cummings Publishing Co.). They are based on the problem-solving steps first outlined by George Polya in 1945.
1. UNDERSTANDING THE PROBLEM
* Can you state the problem in your own words?
* What are you trying to find or do?
* What are the unknowns?
* What information do you obtain from the problem?
* What information, if any, is missing or not needed?
2. DEVISING A PLAN
The following list of strategies, although not exhaustive, is very useful.
* Look for a pattern.
* Examine related problems, and determine if the same technique can be applied.
* Examine a simpler or special case of the problem to gain insight into the solution of the original problem.
* Make a table.
* Make a diagram.
* Write an equation.
* Use guess and check.
* Work backward.
* Identify a subgoal.
3. CARRYING OUT THE PLAN
* Implement the strategy or strategies in step 2, and perform any necessary actions or computations.
* Check each step of the plan as you proceed. This may be intuitive checking or a formal proof of each step.
* Keep an accurate record of your work.
4. LOOKING BACK
* Check the results in the original problem. (In some cases this will require a proof.)
* Interpret the solution in terms of the original problem. Does your answer make sense? Is it reasonable?
* Determine whether there is another method of finding the solution.
* If possible, determine other related or more general problems for which the techniques will work.
20110610
How to stay cool for next to nothing
Central AC is for suckers. Why are you cooling every inch of your house, even the dust bunnies under the couch, when the only part that actually needs to be cooled is your body?
Having endured, sans air conditioning, countless summers in locations including the deep South and the middle of the gigantic urban heat island known as Brooklyn, I've developed the following ultra-simple method for saving myself hundreds of dollars a year in electricity bills.
For lack of a better term, I'll call it the Personal Swamp Cooler, because it works on more or less the same principle as the energy-efficient evaporative coolers that can be found in dry climates everywhere.
1. Buy a fan. A good one. Not too big.
Why would you pay $40 for a 12-inch fan? Because it moves more air than fans twice its size, and for half the energy, that's why. Which is another way to say that I like the Vornado Compact 530.
2. Secret Sauce: Buy a polymer bead-filled bandana or a synthetic "cooling towel"
This is where the magic happens and the unbelievers become converts. Campers, outdoorsfolk and people who work outside for a living have known about these things forever, but office workers, understandably, do not. There is a whole class of bandanas/towels out there that use a variety of synthetic substances to hold onto water for hours, allowing it to slowly evaporate.
Soak something comparable to a HeatMax EverCool bandana, a Frogg Togg Chilly Pad or a Chill Its Cooling Towel in water for a few minutes, wring it out, and wrap it around your neck like you’re Fred from Scooby Doo.
3. Aim fan at head. Marvel at results.
Once you've got one of your special outdoorsperson cooling things draped about your neck, you will be amazed at the degree to which the power of your conventional fan has been magnified. That's because now you're exploiting the magic of evaporative cooling. Every molecule of water that evaporates off your neck carries with it an amount of heat equivalent to water's latent heat, which is pretty damn high.
It also helps that your super-cool definitely-doesn't-make-you-look-like-a-weirdo evaporative bandana is now immediately adjacent to a pair of gigantic arteries running straight into your head. It's as if you've attached your Personal Swamp Cooler directly to a heat exchanger carrying your blood supply.
As I write this, the mercury is climbing. I'm sequestered in my home office, it's 83 degrees inside, yet I'm perfectly comfortable. I'm not spending a dime on air conditioning. Wouldn't you like to be able to say the same?
Having endured, sans air conditioning, countless summers in locations including the deep South and the middle of the gigantic urban heat island known as Brooklyn, I've developed the following ultra-simple method for saving myself hundreds of dollars a year in electricity bills.
For lack of a better term, I'll call it the Personal Swamp Cooler, because it works on more or less the same principle as the energy-efficient evaporative coolers that can be found in dry climates everywhere.
1. Buy a fan. A good one. Not too big.
Why would you pay $40 for a 12-inch fan? Because it moves more air than fans twice its size, and for half the energy, that's why. Which is another way to say that I like the Vornado Compact 530.
2. Secret Sauce: Buy a polymer bead-filled bandana or a synthetic "cooling towel"
This is where the magic happens and the unbelievers become converts. Campers, outdoorsfolk and people who work outside for a living have known about these things forever, but office workers, understandably, do not. There is a whole class of bandanas/towels out there that use a variety of synthetic substances to hold onto water for hours, allowing it to slowly evaporate.
Soak something comparable to a HeatMax EverCool bandana, a Frogg Togg Chilly Pad or a Chill Its Cooling Towel in water for a few minutes, wring it out, and wrap it around your neck like you’re Fred from Scooby Doo.
3. Aim fan at head. Marvel at results.
Once you've got one of your special outdoorsperson cooling things draped about your neck, you will be amazed at the degree to which the power of your conventional fan has been magnified. That's because now you're exploiting the magic of evaporative cooling. Every molecule of water that evaporates off your neck carries with it an amount of heat equivalent to water's latent heat, which is pretty damn high.
It also helps that your super-cool definitely-doesn't-make-you-look-like-a-weirdo evaporative bandana is now immediately adjacent to a pair of gigantic arteries running straight into your head. It's as if you've attached your Personal Swamp Cooler directly to a heat exchanger carrying your blood supply.
As I write this, the mercury is climbing. I'm sequestered in my home office, it's 83 degrees inside, yet I'm perfectly comfortable. I'm not spending a dime on air conditioning. Wouldn't you like to be able to say the same?
20110608
Ringling College Commencement Address
by J.C. Herz
The following is a transcript of Ringling College of Art and Design's 2011 Commencement Address given May 6, 2011"It is an honor and a privilege to be speaking to you today. Because at most commencements, you can talk about following your dream and keep your passion alive. But most of the people you're talking to are going to build careers sending and receiving e-mail, composing Powerpoint slides, and generating Excel spreadsheets. “Click strong! Thank you very much.”
But you? You have gone to school to pursue a creative vision, and have now acquired the skills to do so. This puts you miles ahead of most recent college graduates, who have yet to realize that skills exist, and that skills matter. Expertise matters. The important work that you build your reputation on – you can’t just Google it. You don’t cut and paste it from Wikipedia. You roll up your sleeves, and bring all your creativity and meaningful skills to bear on the problem of building something.
This is what the world requires – this is what the world rewards. Not just calling yourself creative, but understanding how to exercise your creative powers to some end, to bring your vision and skills together in a meaningful way. This is a powerful thing to be able to do. It gives you tremendous value in a society where attention is currency – being able to capture people’s imaginations is the scarcest kind of power in a fractured culture. Creating work that transports and transcends is one of the few ways to create sustainable value in a disposable society. What you do, if you do it well, is never going to be a commodity. Vision, magic, delight. Heart-rocking spectacle. Pulse-pounding action. These things don’t get outsourced to some cubicle drone in the developing world.
You are an influential group of people, and today is an important moment, as you set forth to become the chief stewards of your gifts. Because, this is what it means to be a creative professional: figuring out how to be the best steward of your gifts, so that your power to create grows and deepens meaningfully over time. So that your edges stay sharp, and your light stays bright. The life you’ve chosen is not one that simply requires clocking in and clocking out. You’ve got to bring your soul to it every day. You’ve got to be on your game.
That takes discipline. And it takes awareness – of how you’re spending your time, and of how what you’re doing affects your capability and your capacity. You are going to have to ask yourself, at every turn: is this project making me smarter, or making me stupider. Is this job stoking my fire, or burning me out? How do I top this? How can I learn from this? How do I produce my best work in this kind of environment? Should my next set of projects build up from what I’ve already done? Or do I need to branch out, go sideways, and push myself to try something new, that I’m less comfortable with.
Of course, people in other fields also have to grapple with these issues. But you have to make stuff that concretizes your decisions. You have artifacts of your choices to invest and grow – or coast and call it in. You will build a body of work that reflects those choices at every turn. Some of it – hopefully a lot of it – will make you proud. Some of it will make you cringe. But this is what you have to show for yourself, at the end of the day. And you need to tackle your work, every day, with this in mind: at the end of the month, at the end of six months, a year, five years, this is what I’m going to have to show for myself. There are only so many hours in the day, and when this day is over I’m not getting it back. So how do I make it count.
Think carefully about how you spend your time, because your work isn’t like other people’s work. There isn’t a hard line between uptime and downtime. Your brain is always working, and what you experience in your downtime influences the quality of what you do when you’re on task. Be mindful of what you’re getting out of the time that you spend. Does your downtime refresh and recharge you? Or does it narcotize you? Does it spark new ideas? Or do you find yourself thinking, “well, there’s three hours of my life I’m never getting back.”
Log the amount of time you spend watching TV shows or videos on YouTube. Log the amount of time you spend on Facebook. Add it up, and figure out whether that’s the best use of an astonishing number of hours. It’s so easy to dribble your time away on time-suck distractions that dull your capabilities. Here’s a good rule of thumb: if the amount of time you spend on something leaves you feeling vaguely embarrassed, think twice about what you’re really getting out of it. And if you can’t think of a good answer, just stop for a while, long enough to get in the habit of spending that time differently.
Habits are powerful – people don’t realize how powerful habits are, and how much of their success or lack of success in life is attributable to sheer habit. Be aware of your habits, and what is turning in from an occasional to a regular thing, and what are the regular things that you don’t even think about any more, because they are so habitual that they have become invisible. Down to the very basics: how much and when do you sleep, what you eat, how you sit, whether you walk or bike or drive. When and where do you get your best ideas? What sorts of activities and conversations leave you feeling happier and smarter? What do you continually do that leaves you feeling demoralized. Be mindful of your habits. Make them intentional.
Speaking of habits: take care of your body. Your physical condition affects your mental and psychological state in profound ways. Wherever you end up, run a Google map search for CrossFit and check it out. CrossFit is a way of organizing compressed, high-intensity workouts that make you incredibly strong in less than 30 minutes a day. More importantly, doing CrossFit makes you psychologically capable of tackling things that are challenging and out of your comfort zone, with a kind of psycho glee. CrossFit gyms tend to attract an interesting assortment of characters, who, in addition to spurring you on to mind-blotting sequences of box-jumps, pull-ups and deadlifts, will be different from the people you work with. And it’s important to socialize with different groups of people, especially if the little girls among them can clean your clock. Also, CrossFitters love to make fun of themselves using XtraNormal animation, and posting those videos online. It’s a good sign when people take their pursuits seriously, but themselves, not so much.
But back to the business of creative work: Getting stuck is a big part of creative work, and it’s really important to be good at getting unstuck. There are two main reasons why creative people get stuck on a piece of work: The first is, you don’t actually have an idea. You may have requirements, and you may have tools. But you don’t actually have an idea that’s going to carry the day, and you’re going to be stuck until you get a solid idea. The second reason creative people get stuck is that, while they have the idea, executing the idea takes a lot of work, and not all of that work is fun, and basically you don’t want to do the work, because having the idea in the first place was the fun part. The problem is, you don’t get to say “check mate in four.” You actually have to finish the project. So you get mystically “stuck” after the brilliant sketch is done.
It is very, very important to accurately understand which of these problems you’re having when you get stuck. If you don’t have an idea, you need to play around a little, take a walk, have a good conversation, open the aperture. As they say in drawing class, explore the negative space. If you’re balking at the work, you need to stop playing around, sit down, shut up, go offline, and focus single-mindedly on executing the work, and make it real. In either case, if you try to solve one problem when you’re really having the other, you’re going to waste a lot of time.
When you do procrastinate, learn how to procrastinate productively. This sounds like an oxymoron, but there are a lot of things you can accomplish in ten to 15 minute increments when you’re supposed to be working on something else, and it makes your life a lot smoother, because by the time you get through with the big thing, the other thing that can be accomplished in little chunks is already done. Sometimes your brain does need a break. But it doesn’t need to be playing Angry Birds or checking Facebook during that break. All it needs is a switch – figure out what you can quickly switch to, that’s going to add up to something, five minutes at a time. You’ll be amazed at how productive you become.
Always have a side project that allows you to learn and express things differently than your main work. Side projects are a way to invest in your own growth, and provide a constructive counterpoint and counterbalance to your primary endeavors. Side projects can be small when your main work is big – giving you the satisfaction of completing a personal piece of work while you spend most of your time eating the proverbial elephant. Conversely, a side project can be complex and long-term while your main work is piece-meal, giving you a satisfying sense of progress and accretion towards a more significant achievement while your main work flies out the door in snack-sized bites. When your main work is stretching your brain until it hurts, a side project can be a comfortable piece of familiar knitting. When your main work is all about focused execution, with little room to explore, your side project can furnish oxygen and white space. When your main work is industry-focused, your side project can draw from areas that your colleagues and co-workers are not familiar with, and can prevent you from getting tunnel vision.
Side projects build options, which allows you to walk away when things aren’t working. Sometimes your side project will become your main project. When that happens, recognize that, by virtue of becoming the main project, it will change. It will gain propulsion, but lose the discretionary charm of being a side project. Find another side project, and don’t blame the old side project, now the main project, for not providing the same kind of break-time relief as it used to.
Other times, your side project will flatline, or fizzle. Don’t be afraid to let it go, put it in mothballs, or put it out of its misery. If it’s not adding fizz to your brain or improving your social life, it’s not doing its job. Ask yourself: if I were starting a personal project now, would it be this one? And if the answer is no, find something else to play with.
As a creative professional, you have to get over the idea that your employer or your client owes you a wide blue sky or a creative romper room. You are the one who’s responsible for your continued growth and development. Sometimes, you have to make your own fun, on your own time. The downside is, you don’t necessarily get paid for that. The upside is, you don’t need sponsorship or buy-in. Realize the leverage you have when no-one’s paying you to do something, and use that leverage to carve out new opportunities. Remember: you have talents and skills that are valuable, and there are a lot of ways to leverage that value. It might be the chance to contribute visually to a non-profit organization or shoe-string arts effort that appeals to you. It might give you a chance to collaborate with writers, musicians, or other artists you respect or admire. When you bring your own talent to the table, there are a lot of social and creative dividends you can earn. It’s not just about the dollars.
But when you are talking dollars, realize one thing: Most people say that time is money. But for a creative professional, it’s exactly the opposite. Money is time. Having some extra money gives you time to say no to things that will put you in a professional holding pattern. Money gives you time to say yes to the right thing, not just to the first thing. It’s hard, but try to live in a way that leaves you with enough of a financial buffer to take enough time to make the right career choices. Incidentally, it helps if you marry someone with a job – a real jobby job where artistic fulfillment is not a core on-the-job pursuit. One artist in the family is enough, for all kinds of reasons.
As an artist, realize that mere artistry is not enough, and realize the limits of what your artistry can bring to a project that demands other kinds of talent. One year I went to Game Developers’ Conference, and 3D animation software had evolved to the point where game artists were crowing about being able to put a tiny upside down image of the outside scene in every raindrop on a car windshield. It was impressive. But at the same time, a popular online game review site was rating game quality by the amount of time it took the player to blow up the first crate full of ammunition or new weaponry. The less time it took to blow up the first crate of ammunition or weapons, the more the game sucked, because the designers couldn’t think of anything better to do in the opening moments of a game than blow up crates of ammunition. The most stunning animation in the world won’t make a bad game (or a bad movie) good – if anything, the artistic quality will highlight the project’s creative failure in other respects. This isn’t your fault, as an artist. But it is an occasion to realize that great artistry is only one element of most creative projects, and heighten your awareness of other talents as you choose your next project. Look out for great writers, game designers, musicians – people who can amplify your best efforts.
Realize that “no’s” are good. Yesses are better, but maybes will kill you. The world is full of “maybe” people who want an infinite amount of research and specifications but won’t actually make a decision until something is inevitable. Push those people to say no – or to tell you exactly what they need to say yes. It’ll sae you time and help you figure out who’s serious and who’s just winding you up.
Lastly, consider your portfolio – and your life – from the perspective of yourself at 80 years of age. When you don’t know what to do, picture your old-guy or old-lady self looking back on this moment and being proud of the work you did, or the decision you made, or how you conducted yourself. Picture yourself looking back, and don’t do something that old guy or old lady would regret, or be embarrassed about. Because someday, you will be that old guy or old lady, and you really do want to be proud of the work that you’ve done, and the decisions that you’ve made, and how you acquitted yourself, and how you were the best steward of your gifts.
Thank you, and good luck."
Risk, probability, and how our brains are easily misled
By John Timmer
The World Science Festival's panel on Probability and Risk started out in an unusual manner: MIT's Josh Tenenbaum strode onto a stage and flipped a coin five times, claiming he was psychically broadcasting each result to the audience. The audience dutifully wrote down the results they thought he had seen on note cards, and handed them in when the experiment was over. Towards the end of the program, he announced there were low odds that even one person in the audience had guessed the right order of results. When he announced them, however, about a dozen people raised their hands, saying that was what they had written down.
Is Tenenbaum psychic? The audience sprinkled with liars?
Neither, according to Tenenbaum. Instead, we're the victims of our own tendency to expect that a series of coin tosses will produce results that look satisfyingly random to us. As a result, we're unlikely to suggest a series of four heads followed by a tails. In the same way, we're likely to end up choosing something like TTHTH. So likely, in fact, that if the coin flips do happen to produce one of these random looking patterns, it'll be overrepresented in whatever crowd we're testing. Instant psychic ability, with built in statistical significance.
The funny thing is that this isn't the product of some mental weakness—Tenenbaum suggested that it's the product of an excellent built-in sense of what makes for a random pattern. If you graph the frequency of various possible results, it's possible to see a pattern of peaks at random-looking series and valleys at the ones that chance would seem to disfavor. Comparing the graph generated from our audience to one produced in the 1930s, and it was obvious that the pattern was nearly identical—what we think of as random appears to be quite stable.
The one exception, he noted, was when he performed the experiment with a math-savvy audience. There, a part of the audience recognizes that any series is equally probable, so they are more likely to put down all heads or all tails.
Subverting wisdom
Although Tenenbaum clearly felt that our intuitive feel for randomness was a positive feature, other speakers on the panel noted that human decision-making could obviously get stuck or be manipulated. Mathematician Amir Aczel mentioned that many trained mathematicians can't wrap their heads around the Monty Hall problem, in which changing probabilities dictate how you should act on a popular game show. It's relatively easy to run through the probabilities that show which action you should take, but the answer remains counterintuitive—even for those with an exceptional grasp of math.
And that's assuming, as co-panelist Gerd Gigerenzer noted, that Monty isn't being malicious. A crowd experiment run by physicist Leonard Mlodinow showed how easy it is to manipulate a people's answers to simple questions without doing anything overt. Mlodinow divided the audience in half, and asked both halves separately to estimate the number of countries in Africa. This is a standard "wisdom of the crowds" sort of question, where the mean should be somewhere close to the actual number. Instead, the two groups had wildly divergent means, with one half of the audience answering well above the actual answer, the second significantly below.
How'd he manage this? Prior to asking the actual number, Mlodinow had asked a question that subtly primed each group. For one half of the audience, he asked if they thought there were more than 180 countries in Africa; this group ended up with a much higher mean. The second half was asked if there were more than five. Their answers were, on average, too low. Although this was a case of conscious manipulation, it's easy to see how a similar effect could be generated accidentally, simply based on (for example) the order of questions in a survey.
How do we fix this?
Does all this mean that humans will perpetually remain stuck when it comes to risk and probability? Possibly not, but we have to be careful. That was the message of Gerd Gigerenzer, who helps train decision makers in how to evaluate probabilities. Gigerenzer consistently noted that language was important when it comes to dealing with probabilities.
The most compelling example he gave was one he used when working in medical education. He described the probabilities associated with a breast cancer test: one percent of women tested have the disease, and the test is 90 percent accurate, with a nine percent false positive rate. With all that information, what do you tell a woman who tests positive about the likelihood they have the disease? For a lot of people in medicine, the question leaves them stumped; a typical survey of doctors (and the World Science Festival audience) reveals that there's no single consensus about the probability that the test indicates a real case of cancer.
Gigerenzer then rephrased the statistics: if we ignore the negative tests, nine times out of ten, a positive test for cancer is a false positive. Put that way, it's easy to see that you can tell the person who got a positive result in the test that there's still only a ten percent chance that she has cancer. The use of language makes all the difference.
In short, we've got a good idea of some of the things that the human brain does when when it comes to probabilities, and an even better idea of all the ways in which it goes wrong. If we really want people to understand a given probability, then we have to play to the human brain's strengths, and adjust how we present the information. But there's not a lot we can do if someone decides to intentionally target the brain's weak spots.
The World Science Festival's panel on Probability and Risk started out in an unusual manner: MIT's Josh Tenenbaum strode onto a stage and flipped a coin five times, claiming he was psychically broadcasting each result to the audience. The audience dutifully wrote down the results they thought he had seen on note cards, and handed them in when the experiment was over. Towards the end of the program, he announced there were low odds that even one person in the audience had guessed the right order of results. When he announced them, however, about a dozen people raised their hands, saying that was what they had written down.
Is Tenenbaum psychic? The audience sprinkled with liars?
Neither, according to Tenenbaum. Instead, we're the victims of our own tendency to expect that a series of coin tosses will produce results that look satisfyingly random to us. As a result, we're unlikely to suggest a series of four heads followed by a tails. In the same way, we're likely to end up choosing something like TTHTH. So likely, in fact, that if the coin flips do happen to produce one of these random looking patterns, it'll be overrepresented in whatever crowd we're testing. Instant psychic ability, with built in statistical significance.
The funny thing is that this isn't the product of some mental weakness—Tenenbaum suggested that it's the product of an excellent built-in sense of what makes for a random pattern. If you graph the frequency of various possible results, it's possible to see a pattern of peaks at random-looking series and valleys at the ones that chance would seem to disfavor. Comparing the graph generated from our audience to one produced in the 1930s, and it was obvious that the pattern was nearly identical—what we think of as random appears to be quite stable.
The one exception, he noted, was when he performed the experiment with a math-savvy audience. There, a part of the audience recognizes that any series is equally probable, so they are more likely to put down all heads or all tails.
Subverting wisdom
Although Tenenbaum clearly felt that our intuitive feel for randomness was a positive feature, other speakers on the panel noted that human decision-making could obviously get stuck or be manipulated. Mathematician Amir Aczel mentioned that many trained mathematicians can't wrap their heads around the Monty Hall problem, in which changing probabilities dictate how you should act on a popular game show. It's relatively easy to run through the probabilities that show which action you should take, but the answer remains counterintuitive—even for those with an exceptional grasp of math.
And that's assuming, as co-panelist Gerd Gigerenzer noted, that Monty isn't being malicious. A crowd experiment run by physicist Leonard Mlodinow showed how easy it is to manipulate a people's answers to simple questions without doing anything overt. Mlodinow divided the audience in half, and asked both halves separately to estimate the number of countries in Africa. This is a standard "wisdom of the crowds" sort of question, where the mean should be somewhere close to the actual number. Instead, the two groups had wildly divergent means, with one half of the audience answering well above the actual answer, the second significantly below.
How'd he manage this? Prior to asking the actual number, Mlodinow had asked a question that subtly primed each group. For one half of the audience, he asked if they thought there were more than 180 countries in Africa; this group ended up with a much higher mean. The second half was asked if there were more than five. Their answers were, on average, too low. Although this was a case of conscious manipulation, it's easy to see how a similar effect could be generated accidentally, simply based on (for example) the order of questions in a survey.
How do we fix this?
Does all this mean that humans will perpetually remain stuck when it comes to risk and probability? Possibly not, but we have to be careful. That was the message of Gerd Gigerenzer, who helps train decision makers in how to evaluate probabilities. Gigerenzer consistently noted that language was important when it comes to dealing with probabilities.
The most compelling example he gave was one he used when working in medical education. He described the probabilities associated with a breast cancer test: one percent of women tested have the disease, and the test is 90 percent accurate, with a nine percent false positive rate. With all that information, what do you tell a woman who tests positive about the likelihood they have the disease? For a lot of people in medicine, the question leaves them stumped; a typical survey of doctors (and the World Science Festival audience) reveals that there's no single consensus about the probability that the test indicates a real case of cancer.
Gigerenzer then rephrased the statistics: if we ignore the negative tests, nine times out of ten, a positive test for cancer is a false positive. Put that way, it's easy to see that you can tell the person who got a positive result in the test that there's still only a ten percent chance that she has cancer. The use of language makes all the difference.
In short, we've got a good idea of some of the things that the human brain does when when it comes to probabilities, and an even better idea of all the ways in which it goes wrong. If we really want people to understand a given probability, then we have to play to the human brain's strengths, and adjust how we present the information. But there's not a lot we can do if someone decides to intentionally target the brain's weak spots.
20110603
Small areas of the brain go to sleep when we're up too late
By John Timmer
Sleep deprivation is one of the most common forms of mental impairment, as it reduces performance in a variety of cognitive and motor tasks. A new paper has identified what might be the cause of this poor performance: small parts of a mammal's brain appear to go into a sleep-like state while they're otherwise apparently awake. And, in rats, the degree to which the brain is experiencing these tiny episodes of sleep correlates with their decline in performance on a simple task.
The study relies on differences in the resolution at which we measure neural activity. On a crude level, rats and humans show a similar pattern of neural activity when non-REM sleep is recorded with an EEG: rhythmic peaks of activity, in between which the brain goes largely silent, with the neurons effectively "offline," as the authors call it.
To get down to the level of individual cells, you have to implant electrodes in the brain. When this is done in rats, it's possible to see that the "offline" periods are the product of nearly every neuron in a given brain region going silent, while the peaks of activity involve the frequent firing of most neurons. So, sleep seems to be the product of the coordinated action of most of the brain's neurons, which drop offline and return to activity on a regular cycle.
For the new work, the researchers had both an external EEG reading and electrodes implanted in the frontal motor cortex. It turns out it's remarkably easy to cause rats to deprive themselves of sleep: simply keep giving them new toys for several hours. Although the rats were, by all appearances, wide awake, their performance on a simple motor task (reaching for a sugar pellet) declined with the sleep deprivation.
The readings of the brains, however, often looked like the rats were experiencing what the authors termed "local sleep." After four hours of deprivation, the EEGs would often show the spikes associated with the rhythmic activity of sleep, and most of the neurons near the implanted electrodes would go silent. This wasn't a global phenomenon, however, as other areas of the brain didn't show the same pattern of activity. And, in some cases, the electrodes recorded standard waking activity from many of the neurons they were near. Thus, instead of being part of a global, coordinated sleep pattern, small clusters of neurons were simply taking themselves offline while the animal itself was awake. As the sleep deprivation continued, these local sleep events became more frequent and coordinated.
The authors also obtained an indication that these local sleep events might be related to the poor mental performance seen during sleep deprivation. They looked at the pattern of brain activity when the animals were performing the motor task, and found that they were more likely to fail if a bit of local sleep occurred just before the rats attempted the task.
The paper concludes that local sleep is a precursor to a more general sleep, and resembles the converse of the waking process. Its authors also make comparisons between this local sleep and the needs of birds and marine mammals, which can apparently take large regions of their brains offline instead of sleeping to meet the needs of their lifestyle. That adaptation, they suggest, may be an elaboration of the local sleep that rats appear to use.
An accompanying perspective makes a separate suggestion: the fundamental unit of sleep may be a single cell. When an animal is sleep deprived, individual cells are more likely to take themselves offline. By chance, that will eventually start producing the clusters that produce local sleep events. Over time, the frequency of local events goes up, and the neurons begin to coordinate their activity, ultimately producing the large-scale rhythms seen in sleep.
Sleep deprivation is one of the most common forms of mental impairment, as it reduces performance in a variety of cognitive and motor tasks. A new paper has identified what might be the cause of this poor performance: small parts of a mammal's brain appear to go into a sleep-like state while they're otherwise apparently awake. And, in rats, the degree to which the brain is experiencing these tiny episodes of sleep correlates with their decline in performance on a simple task.
The study relies on differences in the resolution at which we measure neural activity. On a crude level, rats and humans show a similar pattern of neural activity when non-REM sleep is recorded with an EEG: rhythmic peaks of activity, in between which the brain goes largely silent, with the neurons effectively "offline," as the authors call it.
To get down to the level of individual cells, you have to implant electrodes in the brain. When this is done in rats, it's possible to see that the "offline" periods are the product of nearly every neuron in a given brain region going silent, while the peaks of activity involve the frequent firing of most neurons. So, sleep seems to be the product of the coordinated action of most of the brain's neurons, which drop offline and return to activity on a regular cycle.
For the new work, the researchers had both an external EEG reading and electrodes implanted in the frontal motor cortex. It turns out it's remarkably easy to cause rats to deprive themselves of sleep: simply keep giving them new toys for several hours. Although the rats were, by all appearances, wide awake, their performance on a simple motor task (reaching for a sugar pellet) declined with the sleep deprivation.
The readings of the brains, however, often looked like the rats were experiencing what the authors termed "local sleep." After four hours of deprivation, the EEGs would often show the spikes associated with the rhythmic activity of sleep, and most of the neurons near the implanted electrodes would go silent. This wasn't a global phenomenon, however, as other areas of the brain didn't show the same pattern of activity. And, in some cases, the electrodes recorded standard waking activity from many of the neurons they were near. Thus, instead of being part of a global, coordinated sleep pattern, small clusters of neurons were simply taking themselves offline while the animal itself was awake. As the sleep deprivation continued, these local sleep events became more frequent and coordinated.
The authors also obtained an indication that these local sleep events might be related to the poor mental performance seen during sleep deprivation. They looked at the pattern of brain activity when the animals were performing the motor task, and found that they were more likely to fail if a bit of local sleep occurred just before the rats attempted the task.
The paper concludes that local sleep is a precursor to a more general sleep, and resembles the converse of the waking process. Its authors also make comparisons between this local sleep and the needs of birds and marine mammals, which can apparently take large regions of their brains offline instead of sleeping to meet the needs of their lifestyle. That adaptation, they suggest, may be an elaboration of the local sleep that rats appear to use.
An accompanying perspective makes a separate suggestion: the fundamental unit of sleep may be a single cell. When an animal is sleep deprived, individual cells are more likely to take themselves offline. By chance, that will eventually start producing the clusters that produce local sleep events. Over time, the frequency of local events goes up, and the neurons begin to coordinate their activity, ultimately producing the large-scale rhythms seen in sleep.
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