My Graduate Challenge

[Zosimus]

What a truly spurious argument. Since José's diet implies only that Jose has a higher probability of dying at a younger age than the population mean, yoour argument is cow dung. Maybe you should check out some elementary probability theory in the form of Baye's Theorem.

It's not Baye's Theorem, you (bless and do not curse), it's Bayes' Theorem, and I referenced it myself just 3 days ago in my recent post.

This ought to be good. Why don't you demonstrate how you calculate the probability that José will show up tomorrow using Bayes' Theorem. I'm sure the class will find it instructional. Please show your work.

 

[Paul of Eugene OR]

José has worked for the company for 5 years. José has never been absent. Therefore, induction argues that José is more likely to show up for work tomorrow than ever before. However, José smokes, eats lots of salt, and eats lots of saturated fat. Induction argues that these things lead to heart attacks, therefore, induction argues that José is more likely to be dead tomorrow than he was yesterday.

Accordingly, induction argues that it is both more likely and less likely that José will show up for work tomorrow. What a great tool! Maybe we should plan our whole lives around something that regularly contradicts itself.

Only when misused as you did here is there a problem. Actually, Jose's regularity gives one great confidence he will show up tomorrow; but Jose is also mortal and we all know there is a small probability that something such as ill health will stop him from coming to work tomorrow. So, taking that into account we adjust the probability estimate downward from 100 percent to something like 99 per cent. If we wish to also consider his unhealthy life style, the affect on our estimate of tomorrows arrival at work is lowered a very tiny bit in addition.

This is not contradictory. This is the real way to use inductive reasoning.

 

[Paul of Eugene OR]

Neo-Darwinism is an attempt to reconcile Mendelian genetics, which says that organisms do not change with time, with Darwinism, which claims they do. –Lynn Margulis.


Well, no scientific theory is valid. Validity doesn't apply to inductive arguments–they are all invalid! Certainly neo-Darwinism is the current scientific consensus.


I have no particular thoughts on this matter.


Well, I have observed endless arguments between Darwinists and Christians as to whether so-called "macroevolution" occurs vs. "microevolution." As I understand it, many Christians argue that although genetic changes occur, the initial product is a dog and the end product is still a dog thus neo-Darwinism fails. Darwinists, however, claim that macroevolution has been observed and thus cannot be denied. Darwinists usually define macroevolution as so many changes in an organism that a new species is created.

This leads me back to my previous point: Without a clear, objective, and universally accepted definition of "species," it is impossible to determine whether macro-evolution occurs.

Even the fuzzy way species are so hard to pin down allows for macro-evolution to be shown when we show how species such as chimpanzees and humans have a common ancestor several million years back in history.

 

[Zosimus]

Only when misused as you did here is there a problem. Actually, Jose's regularity gives one great confidence he will show up tomorrow; but Jose is also mortal and we all know there is a small probability that something such as ill health will stop him from coming to work tomorrow. So, taking that into account we adjust the probability estimate downward from 100 percent to something like 99 per cent. If we wish to also consider his unhealthy life style, the affect on our estimate of tomorrows arrival at work is lowered a very tiny bit in addition.

This is not contradictory. This is the real way to use inductive reasoning.

I think that you don't have the slightest idea what you're talking about. However, let's give you a little rope and see whether you hang yourself.

John was born and raised on an island. He has a white raven, but he has never seen another raven in his life. John thinks all ravens are white, but his sister doubts that this is true so they ask a guy who regularly visits the island and brings them stuff to help them determine whether all ravens are white.

One month later the guy returns with pictures of all the birds he has seen on his trip. He has pictures of green parrots, pink flamingoes, red robins, blue bluejays, etc., but no pictures of ravens of any kind. John and his sister sit down and reason as follows:

If all ravens are white, then any bird that is not white is not a raven. Since here we have pictures of lots of non-white birds, and none of them were ravens, we can say that our theory that all ravens are white has been confirmed hundreds of times over. Therefore, using Bayes' Theorem, we can conclude that there is better than a 99 percent chance that all ravens are white.

His sister agrees.

Do you agree?

 

[Zosimus]

Even the fuzzy way species are so hard to pin down allows for macro-evolution to be shown when we show how species such as chimpanzees and humans have a common ancestor several million years back in history.

How do you propose to show that chimpanzees and humans share a common ancestor?

 

[lesliedellow]

It's not Baye's Theorem, you (bless and do not curse), it's Bayes' Theorem, and I referenced it myself just 3 days ago in my recent post.

This ought to be good. Why don't you demonstrate how you calculate the probability that José will show up tomorrow using Bayes' Theorem. I'm sure the class will find it instructional. Please show your work.

If the probability that somebody in the general population, and with his attendance record will turn up for work tomorrow is 0,85, and the probability that somebody with his diet, and of his age, will have a heart attack within the next 24 hours is 0.05, then the chances of him turning up for work tomorrow is 0.85 * (1 - 0.05).

So you don't even need Bayes' Theorem.

 

[Paul of Eugene OR]

I think that you don't have the slightest idea what you're talking about. However, let's give you a little rope and see whether you hang yourself.

John was born and raised on an island. He has a white raven, but he has never seen another raven in his life. John thinks all ravens are white, but his sister doubts that this is true so they ask a guy who regularly visits the island and brings them stuff to help them determine whether all ravens are white.

One month later the guy returns with pictures of all the birds he has seen on his trip. He has pictures of green parrots, pink flamingoes, red robins, blue bluejays, etc., but no pictures of ravens of any kind. John and his sister sit down and reason as follows:

If all ravens are white, then any bird that is not white is not a raven. Since here we have pictures of lots of non-white birds, and none of them were ravens, we can say that our theory that all ravens are white has been confirmed hundreds of times over. Therefore, using Bayes' Theorem, we can conclude that there is better than a 99 percent chance that all ravens are white.

His sister agrees.

Do you agree?

Clearly the right answer is that they were not given enough information to decide, yet.

It is exactly the same question we can ask about life elsewhere in the universe. We only know of life on one planet. So what is the probability that there is life elsewhere? We lack information to calculate the true probability.

 

[Zosimus]

If the probability that somebody in the general population, and with his attendance record will turn up for work tomorrow is 0,85, and the probability that somebody with his diet, and of his age, will have a heart attack within the next 24 hours is 0.05, then the chances of him turning up for work tomorrow is 0.85 * (1 - 0.05).

So you don't even need Bayes' Theorem.

Okay, so you invented some numbers, threw them into a formula that doesn't resemble Bayes' Theorem at all, and claimed that the chance is about 89 percent whereas your kindred spirit above suggests that the probability is somewhat closer to 99-100 percent.

So who's right? Here's the big secret of Bayes' Theorem. You both are!! Yes, that's right, both percentages are correct because Bayesian statistics is a measure of subjective probability.

So you see, it's entirely possible for one person to use Bayesian statistics and be 99 percent sure that evolution is true whereas the same person can use Bayesian statistics and be 99 percent true that evolution is false! That's the beauty of the system!

Not to mention the problem of the priors.

 

[lesliedellow]

Okay, so you invented some numbers, threw them into a formula

Yep, I invented some numbers. Of course, in a real world scenario there would be no need to invent them, because they could be collected through research.

 

[Zosimus]

Yep, I invented some numbers. Of course, in a real world scenario there would be no need to invent them, because they could be collected through research.

All right. Let's try it. Let's assume that you really had looked up an 85 percent chance on the Internet. You decided to assign that number to the numerator. However, in order to do so, you first had to assign a 100% probability to the idea that the number you got from the Internet was correct. How did you arrive at that 100 percent probability? Do you really think that every number you Google off the Internet is 100 percent accurate?

Or assume that your history of other employees informed you that there was an 85 percent chance that he would show up. Would you assign a 100 percent chance that history was an accurate predictor of the future? If not, what percentage chance would you use? How would you arrive at that number?

 

[lesliedellow]

All right. Let's try it. Let's assume that you really had looked up an 85 percent chance on the Internet. You decided to assign that number to the numerator. However, in order to do so, you first had to assign a 100% probability to the idea that the number you got from the Internet was correct. How did you arrive at that 100 percent probability? Do you really think that every number you Google off the Internet is 100 percent accurate?

Or assume that your history of other employees informed you that there was an 85 percent chance that he would show up. Would you assign a 100 percent chance that history was an accurate predictor of the future? If not, what percentage chance would you use? How would you arrive at that number?

If I was really interested, I would do the research myself, or else commission some company to do it for me. As always, the larger the sample, the closer its mean is likely to be to the population mean.

 

[Zosimus]

If I was really interested, I would do the research myself, or else commission some company to do it for me. As always, the larger the sample, the closer its mean is likely to be to the population mean.

You haven't answered the question. What percentage would you assign to the likelihood that the number your research or that of the commission is true? How would you arrive at that number? Basically, there are four possibilities:

1. You have some number that you are taking purely on faith.
2. You have a probability calculation that started with some prior probability that you assigned purely on faith.
3. You have some criteria for setting prior probability numbers, and you set a prior probability number for that criteria using the criteria itself in a form of circular logic.
4. You have a probability calculation that started with some prior probability that you assigned using the criteria, which is justified by the criteria itself in a form of circular logic.

So which is it? Dogmatic faith or circular logic?

 

[lesliedellow]

You haven't answered the question. What percentage would you assign to the likelihood that the number your research or that of the commission is true? How would you arrive at that number? Basically, there are four possibilities:

1. You have some number that you are taking purely on faith.
2. You have a probability calculation that started with some prior probability that you assigned purely on faith.
3. You have some criteria for setting prior probability numbers, and you set a prior probability number for that criteria using the criteria itself in a form of circular logic.
4. You have a probability calculation that started with some prior probability that you assigned using the criteria, which is justified by the criteria itself in a form of circular logic.

So which is it? Dogmatic faith or circular logic?

It is more than thirty years since I did my maths degree, and the gathering of statistics is not my profession, so I would have to rely upon the advice of somebody who was a statistician.

https://www.checkmarket.com/2013/02/how-to-estimate-your-population-and-survey-sample-size/

 

[Zosimus]

Okay. So you like the information provided by Checkmarket. Of course, there's no guarantee that what they tell you is true. You would need to provide an initial probability assessment of Checkmarket. How would you do so? Arbitrary numbers based on faith, or a set probability based on a specific criteria?

 

[lesliedellow]

Okay. So you like the information provided by Checkmarket. Of course, there's no guarantee that what they tell you is true.

Try living in the real world for a change. If the results they, or some similar organisation, returned to their clients were rubbish, they wouldn't stay in business for long.

 

[Zosimus]

Try living in the real world for a change. If the results they, or some similar organisation, returned to their clients were rubbish, they wouldn't stay in business for long.

I will take that as a statement that you plan to assign some arbitrary faith-based number that is greater than 50 percent.

 

[lesliedellow]

I will take that as a statement that you plan to assign some arbitrary faith-based number that is greater than 50 percent.

You can take it how you like, but most people would call it being guided by a company's reputation.

 

[Zosimus]

No, I understand. You surely have great faith in the company, and your emotional feel for the company is what convinces you to assign the arbitrary number that you do.

 

[lesliedellow]

No, I understand. You surely have great faith in the company, and your emotional feel for the company is what convinces you to assign the arbitrary number that you do.

Which company would that be exactly? In case you have forgotten, this is all hypothetical. I have never used the services of a company to compile that sort of statistic, and nor am I ever likely to.

 

[Zosimus]

Which company would that be exactly? In case you have forgotten, this is all hypothetical. I have never used the services of a company to compile that sort of statistic, and nor am I ever likely to.

You have already said: "Try living in the real world for a change. If the results they, or some similar organisation, returned to their clients were rubbish, they wouldn't stay in business for long."

Ignoring the fact that the company in question is not a "they," you have clearly indicated that it is your opinion that companies that stay in business are generally reliable organizations that do not return rubbish to their clients.

This belief would, presumably, be the basis for the arbitrary faith-based number that you would assign to the probability that the information hypothetically supplied by the business will be accurate.

Or am I mistaken?