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You can probably beat ChatGPT in these math puzzles. That’s why



It turns out that if you want to solve a puzzle, it’s good to have a brain.

ChatGPT and other AI systems are to be commended for feats that include diagnosing diseases, passing IQ tests, and summarizing scientific papers. But Scientific American wanted to see what would happen if the bot took on the legacy of the legendary puzzle maker Martin Gardnerlongtime contributor to our Math Games column, who passed away in 2010. I tested ChatGPT on several text puzzles described by Gardner, or a tribute to his work by mathematician Colm Mulcahy and computer scientist Dana Richards in 2014. Scientific American.

The results have ranged from satisfactory to downright discouraging, but they provide valuable insight into how ChatGPT and similar AI systems work.

ChatGPT, created by OpenAI, is built on the so-called big language model. This is a deep learning system that has been loaded with a huge amount of text – any books, websites and other materials that AI creators can get their hands on. Humans then train the system by teaching it what types of responses are best for various questions that users might ask, especially about sensitive topics.

And it’s all.

AI “does not have the ability to reason; he does not understand the context; it has nothing that is independent of what is already built into its system,” says Merve Hickok, a policy researcher at the University of Michigan specializing in artificial intelligence. “It may seem that this is reasoning; however, it is bound by its data set.”

Here’s how some relatively simple puzzles illustrate this important difference between the way silicon and gray matter process information.

puzzle 1

First, let’s look at a real logical problem. As described in a 2014 tribute: “There are three switches on the first floor of the building. Only one has a single light bulb on the third floor. The other two switches are not connected to anything. Set the switches in any on/off order you like. Then go to the third floor to check the light bulb. Can you tell which switch is real without leaving the third floor? You only have one try.”

When I entered this into the AI, he immediately suggested that I turn on the first switch for a while, then turn it off, turn on the second switch and go upstairs. If the light is on, the second switch is working. If the light is off, but warm, the first switch works. If the bulb is off and cold, the third switch works. Exactly the same reasoning we proposed in 2014.

But an easy win for ChatGPT in this case may simply mean that he already knew the answer—not necessarily that he knew how to determine that answer himself, according to Kentaro Toyama, a computer scientist at the University of Michigan.

“When it fails, it looks like a spectacularly weird failure. But I actually think that all the cases in which he gets the logic right is just proof that there was a lot of this logic in the training data, ”says Toyama.

puzzle 2

How about something with more math? According to Gardner from his August 1958 column, “Two missiles are flying straight towards each other, one at 9,000 miles per hour and the other at 21,000 miles per hour. They start at a distance of 1317 miles from each other. Not using pencil and paper calculate how far apart they are a minute before they collide.”

ChatGPT has put a lot of effort into this. He showed two different approaches to a key piece of the puzzle: calculating the total distance traveled by two missiles in one minute. In both cases, the correct answer was 500 miles, which is also the final answer to the puzzle. But the AI ​​couldn’t lose sight of the fact that the rockets launched at a distance of 1317 miles, and kept trying to subtract 500 miles from that distance, giving the wrong answer that the rockets would be 817 miles apart one minute before launch. crash.

I’ve been trying to make sure ChatGPT finds the correct answer. For example, I asked him to answer a question like a math professor and told him straight out that his answer was wrong. These interventions failed to dissuade ChatGPT from coming up with the wrong solution. But when he was told that the initial distance between the missiles was a distraction, he adjusted his reaction accordingly and found the correct answer.

However, I was skeptical about whether the AI ​​actually learned. I asked the same problem, but turned the rockets into boats and changed the numbers – and, alas, ChatGPT was again deceived. This indicates that, according to Toyama, there is now a big debate in the field of AI: whether these systems will be able to calculate logic on their own.

“One of the theories is that if you give it so many examples of logical thinking, eventually the neural network will learn what logical thinking looks like and then be able to apply it in the right cases,” says Toyama. “There are some [other] people who think, “No, logic is fundamentally different from how neural networks are currently trained, so you need to embed it specifically.”

puzzle 3

The third puzzle I tried is from Gardner’s March 1964 column on primes: “Using each of the nine digits once and only once, form a set of three primes that have the smallest possible sum. For example, typing 941, 827, and 653 adds up to 2421, but that’s far from the minimum.”

A prime number is a number that is not evenly divisible by any number other than 1 and itself. It is relatively easy to evaluate small prime numbers such as 3, 5, 7, and 11. But the larger a number gets, the more difficult it becomes to judge whether that number is prime or composite.

The following month, Gardner came up with a particularly elegant solution: “How can nine digits be arranged so that there are three prime numbers with the smallest possible sum? First we try numbers with three digits each. The ending digits must be 1, 3, 7, or 9 (this is true for all prime numbers greater than 5). We select the last three, freeing 1 for the first digit. The smallest possible first digits of each number are 1, 2, and 4, which leaves 5, 6, and 8 for the middle digits. Among the 11 three-digit primes that meet these requirements, it is impossible to find three that do not repeat a digit. We refer to the first digits 1, 2 and 5. This gives a unique answer of 149 + 263 + 587 = 999.”

I was genuinely impressed with the first AI answer: 257, 683, and 941 are all prime numbers representing all nine digits and adding up to 1881. This is a fairly low result, although it is higher than Gardner’s solution. But, unfortunately, when I asked ChatGPT to explain how it works, he offered a detailed path to another solution: the numbers 109, 1031, and 683 are all simple, but otherwise ill-suited to other hint requirements.

Recalling its original answer, ChatGPT offered a silly explanation, including stating that “we can’t use 1, 4, or 6 as the first digit of a 3-digit prime, since the resulting numbers will be divisible by 3.” This is patently false: you can recognize numbers that are divisible by 3 because their digits make up a number that is divisible by 3.

I tried to be encouraging by pointing out there was a better solution and suggested to ChatGPT that it was a math professor, but then he suggested 2, 3, and 749. 1647 is better than his first solution, but still not as elegant as Gardner’s .

Alas, that was the best I could get. Another six replies were riddled with hard numbers and missing or extra digits. And then ChatGPT suggested 257, 683 and 941 again.

All of these failures reflect what Toyama says is a key feature of such AI systems. “ChatGPT is very human,” he says. “He’s mastered the style of linguistic humanity, but he doesn’t have the explicit programming to do exactly what computers have been very good at until now, which is very much like a recipe, deductive logic.” It doesn’t solve the problem or even try to solve it – it just roughly shows what the solution might look like.

It also struck me throughout the attempts that nothing seemed to confuse the AI. But Toyama says it’s also a reflection of the creation of ChatGPT and the materials he provided. “From the vast majority of the data he was trained on, you can imagine the average tone of all this text—probably that average tone is pretty sure,” he says.

puzzle 4

The last salvo of the 2014 tribute: “Each letter corresponds to one digit… Can you figure out what digit each letter represents so that the sum… works?”

Credit: Source: “Let the Games Go On” by Colm Mulcahy and Dana Richards, in Scientific American; October 2014

It seemed elegant and fun! How bad can it be? Alas, ChatGPT’s first response was “11111 + 11111 + 11111 + 11111 + 11111 + 11111 + 11111 = FORTY 9”.

The AI’s next suggestion recognized the premise of the replacement puzzle, but it took several rounds to convince the chatbot not to throw a second E in every SEVE N. ChatGPT seemed to stumble upon a combination involving N=7, which was right, miraculously, and first step in the posted solution.

I confirmed that N was accurate and then ran into the AI ​​for the obvious guessing at random. (If he was going to try out specific numbers, he should have started by testing different solutions for E. The easiest way to get started – spoiler alert – is to test E = 0, which ChatGPT completely left out.) systematic solution, and then randomly guessing again , postulating that S = 1. Although I’d like to share the rest of this attempt, it was so nonsensical that it ended up saying “Update the equation again: 116”, which is actually an illusion of an answer.

Since then, ChatGPT has deteriorated. Then it was assumed that S = 9, and I challenged this choice. He postulated that since N + N + N + N + N + N + N = 9, N = 1. He said that with seven E’s that should sum to 2, E = 2. He even suggested S = 47, although he had the decency to shoot himself because of it. I was already losing hope in his ability to solve the puzzle, so I decided to help more actively. I offered ChatGPT a hint: S = 3. When that didn’t work, I also reminded the bot of N = 7, but that just gave four more and more gibberish responses.

Again, this gibberish speaks volumes because it demonstrates how the AI ​​processes any set of facts it receives. In such a situation, although the chatbot seems to have forgotten that I said N = 7, Toyama says that he actually has problems with logic. “The answers he gives you after that sound reasonable,” he says, “but they may or may not take into account the right mix of facts, or the right mix of facts.”

According to Toyama, you don’t really need to understand such complex puzzles to see how ChatGPT struggles with logic. Just ask him to multiply two big numbers. “This is probably one of the easiest logical questions you can ask; it’s a simple arithmetic question,” he says. “And he’s not only wrong once, he’s wrong several times, and he’s wrong in many ways.” This is because while ChatGPT has probably parsed a lot of math textbooks, no one has given it an infinite multiplication table.

Despite its difficulties, the AI ​​chatbot made one key logical breakthrough during the puzzles. “I don’t seem to be able to exactly solve this puzzle at the moment,” ChatGPT told me when I said he seemed to be running out of steam trying to crack the last problem’s code. “I apologize for the disappointment caused. It’s best to approach the problem from a fresh perspective or look to other resources to find the right solution.”

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Guam prepares for Typhoon Mawar: ‘We are in the crosshairs’



Typhoon Mawar, a monstrous Category 4 storm, was due to hit Guam on Wednesday as forecasters warned the island must be prepared for a “direct strike”.

Authorities urged residents of the US island territory to move to higher ground and seek shelter if there are any concerns about the stability of their homes. Island Governor Lou Leon Guerrero ordered the evacuation of residents of flood-prone coastal areas on Tuesday evening.

“Current forecasts are not favorable for our island,” she said in her address on Tuesday evening. “We are under the gunpoint of Typhoon Mawar.”

By Wednesday noon Mawar maximum sustained wind speed According to the National Weather Service, he had to maintain this speed during the night as he moved towards the island. The typhoon is expected to be the worst storm to hit Guam in two decades, and officials have warned that power or water supplies could be out in some areas for days or weeks.

“If you are in doubt about your safety, please go to the shelter immediately,” the agency said early Wednesday morning, saying the island would take “significant hitfrom fierce winds and storm surges. “Conditions will rapidly deteriorate.”

President Joe Biden has approved a state of emergency that will help mobilize resources for the island. Leon Guerrero wrote to the White House as Mawar approached, saying the emergency would help mitigate the effects of “this imminent disaster,” saying it was “particularly important given our distance from the continental United States,” according to the Associated Press. informed.

Guam has a population of about 170,000, three US military bases and about 6,400 military personnel. As a precaution, the military took all the ships out to sea and the personnel on the island took shelter in place.

The New York Times reported on the territory introduced more stringent building codes and warning systems in recent years to minimize injury and damage.

Typhoons and hurricanes are the same storms: The term typhoon is used for storms over the Pacific Northwest that affect Asia.

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Abortion bans scare away doctors and threaten basic health care



Conservative states push to ban abortion after overthrow Row vs Calf leads to an initial consequence that opponents of abortion may not have considered: fewer health services available to all women living in these states.

Physicians show by their words and actions that they do not want to practice in places where making the best decision for the patient can result in huge fines or even jail time. And when abortion clinics close, all other services offered there also close, including regular checkups, breast cancer screening, and contraception.

Concerns about the consequences for women’s health are not limited to abortion rights advocates. The recent warning comes from Jerome Adams, who served as chief surgeon in the Trump administration.

V tweet thread in April, Adams wrote that “the trade-off of limited access (and criminalization of physicians) to a reduction in the number of abortions could result in you actually making pregnancy less safe for everyone and increasing infant and maternal mortality.”

The first signs of an impending medical brain drain appeared in February, when 76% of respondents survey of more than 2000 current and future doctors said they wouldn’t even apply for jobs or training in states with abortion restrictions. In other words, the study authors wrote in accompanying article“Many qualified candidates will no longer even consider working or studying in more than half of the US states.”

Indeed, states with abortion bans saw a larger decline in the number of medical graduates applying for residency in 2023 compared to states without abortion bans, according to the study. Association of American Medical Colleges study. While OB/GYN filings across the country have declined, the number of states with total abortion bans has more than halved compared to states with no restrictions (10.5% vs. 5.2%).

This means that fewer doctors will perform important preventive measures such as Pap smears and screening for sexually transmitted infections that can lead to infertility.

The care of pregnant women is at particular risk as hospitals in rural areas close maternity wards because they cannot find enough specialists to staff them, a problem that predates the abortion order but has only gotten worse since then.

In March, Bonner General Health, the only hospital in Sandpoint, Idaho, announced the termination of employment and delivery servicesdue in part to “Idaho’s legal and political climate” in which state legislators continue to “introduce and pass bills criminalizing physicians for medical care that is nationally recognized as the standard of care.”

Heartbreaking reports from around the country show that the abortion ban is also endangering the health of some patients who survive a miscarriage another other non-viable pregnancies. Earlier this year, pregnant woman with a non-viable fetus in Oklahoma was told to wait in the parking lot until she got sick after being told the doctors “can’t touch you unless you crash in front of us.”

A study by researchers at the State University of New York at Buffalo, published in the journal Women’s Health Issues, found that doctors practicing in states with restrictive abortion policies less likely than those in states with pro-abortion policies are trained to perform the same early abortion procedures that are used for women who have had an early miscarriage.

But more than a shortage of doctors, it can complicate pregnancy and childbirth. The states with the tightest abortion restrictions are also less likely to offer support services for low-income mothers and children. Even before the coup caviarA Commonwealth Fund reportAn unbiased research team found that the maternal mortality rate in states with restrictions or bans on abortion was 62% higher than in states where abortion was more affordable.

Women who know their pregnancy may be high risk will think twice about getting pregnant or getting pregnant in states with abortion restrictions. Carmen Brosder, an Idaho woman who described her difficulties caring for a sick miscarriage. in a series of viral videos on tik tok, told ABC News she doesn’t plan to try to get pregnant again.

“Why would I want my daughter to almost lose her mom again just to have another baby?” She said. “It seems selfish and wrong.”

Once upon a time, the anti-abortion movement seemed more sensitive to arguments that its policies neglected the needs of women and children. Rep. Barney Frank (Democratic Republic of Massachusetts), who once said: “Conservatives believe that from the point of view of the federal government, life begins at conception and ends at birth.”

In fact, an icon of the anti-abortion movement, Rep. Henry Hyde (D-Illinois), who died in 2007, is put an end to the partnership with Liberal Rep. Henry Waxman (D-CA) on legislation to expand Medicaid coverage and provide additional benefits to address infant mortality in the late 1980s.

Few anti-abortion groups are following suit, promoting policies that make it easier for people to get pregnant, have children, and raise children. Most of these efforts go unnoticed.

This year, Americans United for Life and Democrats for America’s Life released a joint position paper urging politicians to “make birth free”. Among their offerings are automatic insurance coverage without deductibles and copayments for pregnancy and childbirth; removing incentives to pay for caesarean sections and hospital deliveries; and a “monthly maternity stipend” for the first two years of a child’s life.

“Giving free births to American mothers can and should become a national alliance in a particularly divided time,” the document says. Such a policy could not only make it easier for women to start a family, but also solve sad record of maternal mortality.

However, in a year when the same Republican legislators who support the national abortion ban are pushing even more vehemently for massive federal budget cuts, it looks like child ban policy will move very far, or very quickly.

This puts adversaries at a crossroads: will they follow Hyde’s example and champion policies that expand and protect access to health care? Or will women’s health suffer from the victory of the anti-abortion movement?

KN (Kaiser Health News) is a nationwide newsroom dedicated to in-depth health journalism. Together with Policy Analysis and Polling, KHN is one of the three major operational programs in KFF (Kaiser Family Foundation). KFF is a charitable non-profit organization providing health information to the nation.

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Why is talking therapy so effective?



in memoirs, group, the young law student ranked first in her class, but in her personal life she struggled with an eating disorder, suicidal thoughts and problems in her intimate life. An acquaintance introduced her to a psychotherapist who recommended that she sign up for group therapy sessions.

The author had to open up to other group members in her sessions and share parts of herself that she would rather hide. In turn, she listened as the other members of the group told their own stories and asked questions about the parts of their lives that made the least sense. The author has been conducting group therapy sessions for decades and has credited them with saving her life.

Psychotherapy (also known as talking therapy is an approach that some historians believe goes back to ancient times. In recent decades, scientists have learned to measure the benefits of talking therapy. In some cases, researchers believe that talking therapy is the best.

What is Talk Therapy?

Talk therapy it is when a person meets with a licensed mental health professional to address their concerns. There are various reasons a person might seek help with talk therapy, including stress, coping with trauma, or certain symptoms such as irritability.

Psychotherapists use a variety of techniques, including problem-solving strategies, mindfulness, or behavior tracking. A therapist may use cognitive behavioral therapy (CBT) to help a person change their behavior patterns. An example of cognitive behavioral therapy would be confronting fear with exposure therapy.

Does psychotherapy work?

Psychotherapy is effective, and two-thirds of people who took part in talking therapy said their mental health improved. They reported less depression, anxiety and neurotic behavior.

Researchers have also found that psychotherapy benefits people with post-traumatic stress disorder (PTSD). In a 2019 study V JAMA Psychiatry, The authors conducted a meta-analysis of 12 randomized clinical trials involving 922 people treated for post-traumatic stress disorder. Participants were treated with either psychotherapy, pharmaceuticals, or a combination of both strategies.

The authors did not see any evidence that pharmaceuticals are an effective first-line treatment. At follow-up, psychotherapy showed greater benefit than medication. The study confirmed previous research that talking therapy provides the most lasting relief for people with post-traumatic stress disorder.

2016 study V depression and anxiety, for example, came to the conclusion that talking therapy should be the first approach to PTSD. The authors analyzed 55 studies that included 6,313 people who were undergoing a variety of treatments for post-traumatic stress disorder, including medication and talking therapy. People who were treated with talking therapy were less likely to drop out of the treatment program.

The authors found that the effects of talk therapy were stronger than those of pharmaceuticals, leading them to conclude: “… for all measures considered in this study, [trauma-focused psychotherapies] outweighed the drugs.

Read more: Do antidepressants change your personality?

Benefits of Talk Therapy

Versatility is an advantage psychotherapy. While one person may benefit from one-on-one talk therapy, another may benefit from support in a group setting. In memoirs groups the author described how she struggled with overeating and admitted to her therapist that she ate seven apples in one sitting. He called her habit of secrecy problematic and encouraged her to call a member of the group every day to report what she ate. She found accountability useful.

Researchers are looking at other ways in which talking therapy can be effective in a variety of settings. A 2020 study in Overview of Clinical Psychology A review of the literature on studies of the effectiveness of talking therapy in a natural setting was carried out.

Between 1994 and 2019, they found 38 relevant articles that detailed outdoor psychotherapy. One of the common themes was that nature-based talk therapy worked in situations where both client and clinician felt at peace in a natural space. They also found that outdoor settings work for people who are uncomfortable or embarrassed by the idea of ​​conventional therapy.

Outdoor therapy can allow the client or therapist to apply metaphors from the natural world to life. For example, a person may think about how a gardener can plant a seed and grow a growing plant, but external factors mean that the outcome is out of his control.

New types of talking therapy

Metaphors of the nature of middle age about the personal problems of life are one of the many new twists in the approach to talking therapy. Psychotherapy as a term came into use at the end of the nineteenth century, but in the middle of the twentieth century it was overshadowed psychoanalysis.

In psychoanalysis, clients stretched out on a couch facing the therapist and recounted their memories of once-forgotten events. Over time, the analyst offered to understand what was bothering the person’s thinking, which was to reduce anxiety and bring a sense of peace.

This method was most associated with the famous neurologist Sigmund Freud, who often attributed clients’ problems to one of his unproven theories. A woman’s anxiety, for example, can be diagnosed as a symptom of penis envy.

One historian described how Freud’s approach fell out of favor “… because of his frequent refusal to take the morbid reasoning of patients at face value; instead, he forced them to confess to esoteric sexual fantasies.”

How to find a therapist

In contrast to psychoanalysis, advocates of talk therapy during Freud’s time encouraged clinicians to be empathetic to the client and to acknowledge “their real sources of distress”.

Today, clients are encouraged to find a therapist that best suits their needs. Many psychotherapists specialize in treating specific conditions, such as post-traumatic stress disorder or anxiety. Others use special therapies like CBT and some offer different settings like virtual or outdoor.

The National Institute of Mental Health (NIMH) recommends that people conduct preliminary interviews with potential therapists and they offer a list of questions on their website that clients can ask potential therapists during the meet and greet.

If a therapist doesn’t feel like a match, NIMH advises people to keep looking because “mutual understanding and trust are essential” in a client-therapist relationship.

Read more: How effective is Alcoholics Anonymous?

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