Bilmek... Ne işimize yarayacak?

Summary

The script explores the practical applications and implications of mathematical concepts, particularly Bayesian Statistics. It narrates the story of Tommy Gregory Thompson, who utilized Bayesian Search Theorem to locate the SS Central America shipwreck, leading to a fortune but also legal troubles. The transcript further delves into the importance of accurate statistical interpretation in medical diagnoses and the tragic case of Sally Clark, highlighting the dire consequences of statistical misinterpretation. It also addresses the misuse of statistics in media, such as cherry-picking data to manipulate public perception, emphasizing the need for critical understanding and ethical use of statistical knowledge.

Takeaways

• 🔍 Pi and Bayesian Theorem are essential mathematical tools with practical applications in various fields.
• 🏴‍☠️ The SS Central America shipwreck case demonstrates how Bayesian Search Theorem was used to successfully locate a sunken treasure.
• 📊 Bayesian Search Theorem involves creating a probability map to determine the most likely locations for a target, which was key in the shipwreck search.
• 💰 Tommy Gregory Thompson's discovery of the shipwreck led to a fortune but also to legal troubles and a mysterious disappearance of some gold.
• 👨‍⚕️ The importance of Bayesian Theorem in medicine is highlighted through an example of a patient misunderstanding test results due to a lack of understanding of conditional probabilities.
• 🤔 The script emphasizes the need for a correct understanding of statistics, especially in medical diagnosis, to avoid false positives and unnecessary treatment.
• 📉 The story of Sally Clark illustrates the devastating consequences of misapplied statistics, leading to wrongful imprisonment and societal stigma.
• 📈 The power of visual representation in statistics can be misused to deceive or mislead, as seen in the manipulation of charts to exaggerate or minimize trends.
• 🚫 The misuse of statistics can have serious societal impacts, as it did in the case of Sally Clark, where a single authority's opinion was taken over collective scientific consensus.
• 🌐 Disinformation and the deliberate misuse of statistics are prevalent in media, often for political purposes, and it's crucial for the public to be aware of these tactics.
• 📚 The script calls for a moral development alongside the discovery of new knowledge, emphasizing the responsibility that comes with understanding and using statistical methods.

Q & A

What is the significance of pi in the context of the transcript?

The significance of pi in the transcript is not directly about its mathematical value but rather as a metaphor for the importance of seemingly abstract mathematical concepts that have real-world applications, such as Bayesian Search Theorem.

What was the SS Central America, and why was it significant?

The SS Central America, also known as the ship of Gold, was a ship that disappeared with hundreds of passengers and crew in 1857 after a hurricane. It was significant because it was carrying $750 million worth of gold at its current value, which made its recovery a high-stakes endeavor.

Who is Tommy Gregory Thompson, and how did he use Bayesian Search Theorem?

Tommy Gregory Thompson was a treasure hunter who, in 1988, used Bayesian Search Theorem to determine the possible sinking location of the SS Central America. He created a probability map based on historical data and successfully found the wreck, recovering gold worth $100-150 million.

What were the consequences of Thompson's actions after finding the wreck?

After finding the wreck and recovering gold, Thompson faced lawsuits for selling some of the gold without paying his team and investors. He then disappeared and was eventually caught and imprisoned. The whereabouts of the remaining gold are still unknown.

How does Bayesian Theorem relate to medical studies as mentioned in the transcript?

Bayesian Theorem is related to medical studies as it helps in understanding conditional probabilities, which is crucial in interpreting medical test results accurately. It helps in calculating the probability of a patient having a disease based on the test's accuracy and the prevalence of the disease in the community.

Can you explain the hypothetical medical scenario presented in the transcript?

The hypothetical scenario involves a patient who tests positive for a rare disease with a test that has a 99% accuracy rate. The patient calculates that, given the low prevalence of the disease, the actual probability of having the disease despite a positive test is only 1%, illustrating the importance of understanding Bayesian reasoning in medical diagnosis.

Who was Sally Clark, and what happened to her?

Sally Clark was a mother whose first child died from Sudden Infant Death Syndrome (SIDS). When her second child died similarly, she was accused and convicted of killing them based on a flawed statistical calculation by an expert witness. She served over three years in prison before being released when the error was revealed. Sadly, she later died from alcohol poisoning.

What is the role of the Royal Statistical Society in the Sally Clark case?

The Royal Statistical Society played a crucial role in the Sally Clark case by challenging the accuracy of the statistical evidence used in her trial. They helped expose the errors in the calculations and contributed to the reevaluation of her case, leading to her release.

What is the issue with the charts presented in the transcript?

The issue with the charts is that they are examples of cherry-picking data and manipulation through selective presentation. They are designed to mislead by omitting context or starting scales at arbitrary points to exaggerate changes or trends.

Why is it important to be critical of statistical information presented in the media?

It is important to be critical of statistical information in the media because it can be manipulated to deceive or mislead. Being aware of common tricks like cherry-picking and selective presentation can help individuals discern the truth and make informed decisions.

What is the moral of the story regarding the use and abuse of statistics as presented in the transcript?

The moral of the story is that knowledge, including statistical knowledge, is powerful but must be used responsibly. It emphasizes the need for moral development alongside the discovery of new information to ensure that knowledge is used for good and not to deceive or harm.

Outlines

00:00

🔍 The Power and Misuse of Bayesian Theorem

This paragraph discusses the practical applications of the mathematical constant Pi and introduces the Bayesian Search Theorem through the story of Tommy Gregory Thompson. Thompson, a treasure hunter, used Bayesian methods to locate the SS Central America, a ship that sank with $750 million worth of gold. He created a probability map to systematically search for the wreck and successfully found it, recovering $100-150 million in gold. However, Thompson's life took a turn as he faced lawsuits for not paying his team and investors, leading to his disappearance and eventual imprisonment. The story illustrates the power of Bayesian statistics but also the potential for misuse and the importance of ethical considerations.

05:02

📊 The Impact of Misinterpreted Statistics in Medicine and Law

The second paragraph delves into the significance of Bayesian Theorem in medical studies and the legal system, using two examples to highlight the consequences of misinterpretation. The first example involves a patient who challenges a doctor's diagnosis based on the accuracy of a medical test and the prevalence of a rare disease, demonstrating how misunderstanding conditional probabilities can lead to false positives. The second example tells the tragic story of Sally Clark, who was wrongfully convicted of killing her children due to a flawed statistical interpretation by a pediatrician. The Royal Statistical Society later exposed the error, leading to her release, but Clark's life was irreparably damaged, culminating in her death due to alcohol poisoning. These stories underscore the necessity for accurate statistical analysis and the devastating effects of its misuse.

10:02

🚫 The Manipulation of Data in Media and the Importance of Critical Thinking

The final paragraph addresses the manipulation of data and statistics in media, particularly for political purposes, and the importance of critical thinking to discern truth from deception. It critiques the use of misleading charts and graphs, such as one from Fox News that exaggerated the decline in Christian Americans by cherry-picking data ranges. The paragraph also mentions a flawed chart claiming a lack of climate change by starting from an anomalously warm year due to El Niño. The term 'cherry picking' is introduced to describe the deliberate selection of data to support a particular narrative. The need for moral development alongside the discovery of new knowledge is emphasized, as the misuse of statistics can lead to widespread misinformation and harm.

Keywords

💡Pi

Pi is an irrational number, approximately equal to 3.14159, which represents the ratio of a circle's circumference to its diameter. In the video, pi is mentioned as an example of mathematical constants that might seem abstract but have practical applications. It's used to introduce the theme of the video, which is the real-world significance of mathematical concepts.

💡Bayesian Search Theorem

The Bayesian Search Theorem is a probabilistic method used to determine the best places to search for a missing object based on prior knowledge and likelihood. It is central to the video's narrative, as it was used by Tommy Gregory Thompson to locate the SS Central America shipwreck, demonstrating how advanced mathematics can be applied to solve real-world problems.

💡SS Central America

The SS Central America, also known as the 'Ship of Gold,' is a historical ship that sank in 1857 carrying a large cargo of gold. The ship's story is used in the video to illustrate the practical application of Bayesian Search Theorem in treasure hunting and how mathematical knowledge can lead to significant discoveries.

💡Bayesian Statistics

Bayesian Statistics is a branch of statistics that deals with the analysis of data and the determination of probabilities using Bayes' Theorem. The video emphasizes the importance of Bayesian reasoning, especially in medical studies, where it can help in making more accurate diagnoses and treatment decisions.

💡Accuracy Rate

Accuracy rate refers to the proportion of true results (both true positives and true negatives) among the total number of cases examined. In the video, the accuracy rate of a medical test is discussed to highlight the potential for misunderstanding and misuse of statistical data, which can lead to incorrect conclusions.

💡Conditional Probability

Conditional probability is the probability of an event given that another event has occurred. The video uses the concept to explain how the probability of a patient having a rare disease can be misunderstood due to the high accuracy rate of a test, emphasizing the importance of understanding the underlying statistics.

💡Sudden Infant Death Syndrome (SIDS)

Sudden Infant Death Syndrome, or SIDS, is a rare condition where an infant dies unexpectedly and without explanation. The video mentions SIDS in the context of the Sally Clark case, where statistical errors led to a miscarriage of justice, underscoring the video's theme of the misuse and importance of statistical knowledge.

💡Statistical Error

A statistical error occurs when incorrect conclusions are drawn from data due to flawed methodology or misinterpretation. The video discusses how a statistical error in the Sally Clark case led to her wrongful conviction, highlighting the severe consequences that can arise from misapplied statistical analysis.

💡Cherry Picking

Cherry picking is the act of selectively choosing data points that support a particular position while ignoring others that contradict it. The video uses this term to criticize the manipulation of data in charts and graphs to deceive the audience, showing how statistics can be abused to support false narratives.

💡Disinformation

Disinformation refers to the deliberate spreading of false or misleading information to deceive people. The video discusses the role of disinformation in the misuse of statistics, particularly in the context of news media and political manipulation, emphasizing the need for critical thinking and statistical literacy.

💡Moral Development

Moral development refers to the growth of an individual's ethical and moral reasoning. The video concludes with a call for moral development alongside the acquisition of knowledge, suggesting that the responsible use of statistical and mathematical knowledge is crucial for ethical decision-making.

Highlights

Pi and Bayesian Statistics are used in various practical applications.

The SS Central America, carrying $750 million in gold, was lost and never found.

Tommy Gregory Thompson applied Bayesian Search Theorem to locate the shipwreck.

Thompson created a probability map to find the gold, leading to his success.

Thompson's discovery of the wreck and salvage of $100-150 million in gold made history.

Despite his success, Thompson faced lawsuits and prison for not paying his team and investors.

The remaining lost gold's whereabouts remain unknown, and Thompson still claims ignorance.

Bayesian Theorem is emphasized for its importance in medical studies.

A hypothetical medical test scenario demonstrates the power of Bayesian reasoning.

The story of Sally Clark highlights the misuse of statistics leading to a wrongful conviction.

The Royal Statistical Society intervened in Sally Clark's case, leading to her release.

Statistics can be manipulated to deceive, as seen in various examples of data presentation.

Cherry Picking is a technique used to mislead by selecting specific data points.

Disinformation and the deliberate misuse of statistics are prevalent, especially in politics.

The importance of understanding and correctly using statistical knowledge to avoid deception.

The necessity for moral development alongside the discovery of new knowledge.

Transcripts

What is the pi number good for?

What will the Pi number really do for us?

Or these weird trigonometry formulas,

or those weird theorems that, maybe we'll never hear again?

I want to show you a few use for it.

Pi. Bayesian Statistics and Mathematics Formulas What will work for us?

In 1857, the SS Central America, also known as the ship of Gold,

disappeared with hundreds of passengers and crew.

A great search was started to find the whereabouts of this ship, which sank after a hurricane.

Because the ship was carrying 750 million dollars of gold with its current value.

But the wreck of the ship was never found.

Of course, this news is great news for these people.

Why?

Well, because they can do this.

Of course, these efforts are of little value.

Until 1988, when someone named Tommy Gregory Thompson used Bayesian search theorem ...

...to determine the possible sinking location of the ship.

What is this now?

Bayesian Search Theorem!

I mean, how many people have heard of it even today, let some treasure hunter all the way back in 1988.

And even utilize it to find this treasure.

Yes, but Thompson had indeed heard of the theorem

and figured out how to change the course of his life with it.

Knowing and using that knowledge.

He set sail upon the historical information that was based on at the time of the event.

Using this data, he created a probability map of where the gold might be.

This map gave him the probability of finding gold in any location.

He began searching from the most likely places to the least likely.

And guess what?

Thompson found the wreck.

He also did salvage gold worth 100-150 million dollars.

His idea to use Bayesian Search Theorem led to his name being engraved in history in golden letters.

But maybe we should say 'cursed gold'.

Because he really became a millionaire, but his story didn't stop there.

Lawsuits have been filed against him.

Selling some of the gold without paying to his team and investors got him into trouble.

Of course, they weren't going to hand him all that much gold easily.

Then he fled and disappeared.

No one but himself knew what happened to the rest of the gold.

Then he was caught with another fugitive at a hotel in Florida and ended up in jail.

Thompson is 70 today and is still in prison.

The whereabouts of the lost gold is unknown.

He was offered to be released from prison in exchange for a confession,

but he claims he doesn't know where the gold is.

It seems that math alone is not enough for some things.

But this Bayes Theorem is very interesting.

I can tell you this much, this is a subject that we should know very well but that we cannot do justice to.

Experts are constantly emphasizing that

it should have an important place in an unimaginable way, especially in medical studies,

So why?

Let's understand this with an example.

One day, a patient comes to the hospital with various complaints and

the doctor suspects a rare disease and makes some tests.

While the patient enters the room and waits nervously in front of the doctor:

"I'm sorry, unfortunately the results of your test were positive.

You have this rare disease.

But don't worry, modern medicine has come a long way in this regard.

So we'll start treatment right away."

"Wait a second, doctor, what did you say about the accuracy of this test?

"The test has an accuracy rate of 99%.

So if we get a positive result, it means 99% of the time that you are sick."

"And how likely was the disease to be seen in the community?"

"It occurs in about 1 out of 10,000 person."

"Well, so the probability of me having the disease is only 1%."

"No, no. I just said that the accuracy of the test is 99%."

The patient grabs a pen and begins to explain his problem to the doctor with mathematics.

Let's say there are 1 million people and the incidence of the disease is 1 in 10,000".

Well, in this case, there are 100 actual patients.

Considering that we have given this test to everyone,

99% of the 999,900 healthy patients should have a negative result.

But due to the margin of error of the test, 1% of them should get a false result and be positive.

This means 9999 healthy people have positive results.

We have 100 real patients and 9999 people who have positive results but are not sick.

Well, in this case, there are 9999 plus 100, that is 10,099 people, which has a positive result.

So how many of those who get positive results are actually sick?

100/10.099 so only 1%.

What, How? Right?

Well, you saw it.

We explained everything with graphics and stuff.

Don't worry, I'm not fooling you at any point.

It is just, such conditional probability calculations push our intuition quite a bit.

This is exactly why it is very important to explain Bayesian Theorem, especially in the field of medicine.

Nobody wants to see a false explanation as if the probability is 99% when the probability is actually 1%, right?

Of course, let me put your mind at ease now, this was a hypothetical example to explain this issue.

In reality, doctors don't get immediate results with just one test.

But mistakes made in such calculations can be perfect to deceive us.

Because our perception is very much inclined to find the wrong thing to make sense.

And if someone uses this better than you do, you could get in trouble.

Now I will tell you the story of Sally Clark.

Sadly, Sally's first child dies just weeks after birth.

This is thought to be related to a rare syndrome in newborn babies which is called Sudden Infant Death Syndrome.

But when her second baby dies, in the same way, two years later,

she raises suspicion around her and is accused of killing her babies.

Sally insists on her innocence in court, but

a professor of pediatrics, who was sent there as an expert witness,

sees the big game and calculates that the probability of both babies dying from this disease is 1 in 73 million.

Unable to convince anyone of this low probability,

Sally is found guilty of killing her newborn babies and

she gets sentenced to life in prison.

In the news, headlines she gets to be dubbed as baby-killer.

The power of statistics.

Right?

Right!

But what kind of power is this?

Meanwhile, another interesting development takes place, and

the Royal Statistical Society claims that the pediatrician's calculation is not accurate.

After a while, another trial takes place and it turns out that ...

...there was a problem with the results of the pathology tests.

So there was a situation in which the statisticians said;

"Look, this is an erroneous approach. In fact, it may be like this and that.

Even if it is claimed, it should be supported by data".

The cause of death of the two children was actually different and completely natural.

After this was revealed, Sally's charges were dropped and

she was released after serving more than 3 years in prison.

However, Sally can never recover from the psychological depression...

...she went through after these traumatic experiences,

and she died in 2007 due to alcohol poisoning.

A simple statistical error results in a society accusing a grieving mother,

who lost her children, of being the murderer of her babies,

and resulting in the death of this innocent mother.

We must be more rational and tolerant about our methods.

As I always say;

we should listen to the common opinion of scientists collectively,

not to the words of a single authority.

Things could have been different today...

... if the statistics community had been listened to in the first place,

rather than just a single pediatrician.

After learning lessons from this sad story, it is decided that similar cases will be opened again,

and it is revealed that others have been imprisoned innocently.

To know and to utilize the knowledge.

When we learn lessons, we can use the information in good faith for the right purposes.

When we don't know, sometimes we can do wrong things even though the intention is good.

The Royal Statistical Society that exposed Sally's case,

recently released a long panel video on their YouTube channel with the title "Use and Abuse of Statistics".

So they are still actively trying to detect such problems, warn people, and fix them.

Maybe as we learn something, we can get the perception that such mistakes are getting less and less.

But that's not the case.

Because there are also those who knowingly and purposefully work with malicious intent.

Of course, this potential of statistics, which can mislead even the professors of pediatrics,

does not go unnoticed by malicious people. How could it?

Let's take a look at the following chart shown in this news on Fox News in the USA with the headline

“We used to be an enthusiastically Christian nation”.

It shows the proportion of Americans who identify as Christians.

While this rate was 77% in 2009, it seems to have decreased to 65% in 2019.

But take a good look at the chart.

There is a difference of almost two to three times between the two charts.

Because they deliberately started the charts from an irrelevant value like 58% and finished at 78%.

However, if the actual range was changed to show between 0% and 100%; The chart would look like this.

In other words, they tried to make the difference bigger by zooming in on the chart.

Because we see and perceive it visually before the numbers themselves.

However, this difference may be so small that it can be explained by a completely unrelated reason that ...

...changes so much from year to year, perhaps with wrong measurement methods.

Or look at that Pizza chart.

By the way, let me tell you right away that this is an unpopular charting method.

Please pay attention to the total.

Adds up to more than 100%.

"Wait a minute, it makes 150%"

Now let's look at the chart shown to claim that there is no climate change;

It shows the temperature changes between 1998 and 2012.

They even did us a favor and added the red trend line.

Well, the temperatures are dropping here.

Even the source is shown as NASA.

Are they deceiving us that there is a climate change?

Yes.

But we are not deceived by NASA, my friends, we are deceived by those who carefully prepared this chart.

There is a particular reason why 1998 was chosen and the chart started from there.

It's an extremely hot year because of the unusual El Niño that year.

Shall we have a look at a wider range to get a better idea?

I guess there isn't much left to doubt.

The little fluctuations in between lost their meaning in an instant.

There is a special name for

"choosing certain values for this kind of manipulation, and ignoring others that don't suit"

Cherry Picking.

Unfortunately, we can see the effect of such tricks at a considerable level.

For if we were not aware of such a trick, how would we know?

Unfortunately, such abuses of statistics are quite common.

Disinformation has become a very popular topic nowadays.

It is now frequently discussed that news channels deliberately produce such content, especially for political purposes.

In fact, no one is truly objective.

There are malicious people who are actively trying to deceive us with the things we use all the time.

So now we have to know.

Knowing gives you something.

Using that knowledge is another thing.

But what really makes the difference is how we use it.

“This is truly the mistake of our time.

We think it's enough to discover new things,

but we don't realize that knowing more also requires a corresponding moral development."