probability

[The Good Michael]

"invisible things can't be disproved."

Not quite correct. Your dictum applies ONLY to empirical objects. Permit an example. The proposition:

(P) 2 + 2 = 5

is invisible

Once you created a representation, it became visible.

Mike

[Simon Wood]

Hi Colin,

Are you denying the possibility of coincidence?

Regards,

Simon

[lynn cates]

syntax vs semantics

Hello Michael. Thanks.

Depends on the antecedent of the pronoun. If "it" refers to the proposition, no IT is still invisible; however, the declarative sentence which DOES assert the proposition IS clearly visible.

Cheers.
LC

[Colin Roberts]

Thanks for posting Colin!

You are quite welcome, Abby. I may answer your call in the other thread later this weekend, if I am able to set aside the necessary amount of time.

I perceive a 99.99% probability that no one other than yourself has taken the time to carefully read my post and internalize the significance of its use of the term "near impossibility".

I would never consider buying a lottery ticket because I cannot justify a willingness to risk money on a near impossibility.

But let's say that my wife decided to tease my obsessive compulsive type 'A' personality by surprising me on my birthday with … a lottery ticket; one for a particular lottery in which the chance of winning was stated as being 1-in-25,000,000, i.e. odds of 24,999,999-to-1 against. And let's say that she happened to purchase the winning ticket, and I was consequently $10,000,000 the richer.

Now, even though a "near impossibility" had just occurred, I would still never go on to buy a lottery ticket myself, and I would scold my wife in the event that she were to do so again.

Why? Because any subsequent lottery would be independent of the one that I had just had the miraculous fortune of winning, and the chances of winning again would be totally unaffected by my remarkable luck in the first instance.

You once cited an incident in which a symphonic musician was killed by a bale of hay whist driving his car, in order to make the point that extraordinary things do occur. Have you since added 'flying hay bale' coverage to your automobile insurance policy? I doubt you have, because even though the aforementioned tragedy did occur, you have the good sense to realize that a reoccurrence would be a near impossibility.

---

Lynn is correct that just because something is a low probability event doesn't allow one to assert that it couldn't happen.

I don't believe that Harry D (i.e. the original source of Lynn's frustrations, in this particular instance) or anyone else that has ever posted to these forums has actually considered an independent (i.e. multi-perpetrator) 'Double Event' to be anything more than a near impossibility in the vein of my earlier post.

In my case (and I don't believe that this portion of my earlier post could be reiterated too often):

My position on this issue notwithstanding, I perceive a chance of as much as 1-in-3, i.e. a probability of as much as 33.33% that Elizabeth Stride and Catherine Eddowes were felled by different hands. I think I would be foolish not to do so.

---

I hated probability theory. I would never use it to try and determine the number of victims...

I sincerely hope that no one believes that I have ever attempted to "determine" the reality of any aspect of this mystery on the basis of probability. All that I have ever done is attempt to quantify the perceptions of likelihood that I consider to be the most rational.

... probability is irrelevant to the number of hands involved.

In as much as the probability that Elizabeth Stride was murdered by her murderer is 100.00%, whereas the probability that she was murdered by anyone else is 0.00%.

But why shouldn't we use probability theory to quantify our perceptions of likelihood?

Case in point:

I define 'Jack the Ripper' as being the person that murdered Annie Chapman (… and that almost certainly murdered Mary Ann Nichols). Period!

Using the Chapman murder therefore as the 'Gold Standard', I perceive the following probabilities that each respective victim was murdered by 'Jack the Ripper':

- Tabram: 9/16, i.e. 56.25%
- Nichols: 15/16, i.e. 93.75%
- Chapman: 1/1, i.e. 100.00%
- Stride: 11/16, i.e. 68.75%
- Eddowes: 7/8, i.e. 87.50%
- Kelly: 3/4, i.e. 75.00%
- McKenzie: 3/16, i.e. 18.75%
- Coles: 1/8, i.e. 12.50%

I therefore perceive a probability of just 16.91% that each of my preferred six (i.e. Tabram, Nichols, Chapman, Stride, Eddowes and Kelly), and just my preferred six, fell at the hands of 'Jack the Ripper': a chance of about one-in-six.

In other words, the (exclusive) 'Ripper' tally that I perceive as being the single most likely of all possible exclusive tallies, only covers about one sixth of the total range of possibilities that I happen to visualize.

Likewise, I therefore perceive a probability of just 23.79% that each of my preferred six (i.e. Tabram, Nichols, Chapman, Stride, Eddowes and Kelly) fell at the hands of 'Jack the Ripper': a chance of about one-in-four.

In other words, the (inclusive) 'Ripper' tally that I perceive as being the single most likely of all possible inclusive tallies, only covers about one fourth of the total range of possibilities that I happen to visualize.

Similarly, I therefore perceive a probability of just 42.30% that each of the so-called 'Canonic Five' (i.e. Nichols, Chapman, Stride, Eddowes and Kelly) fell at the hands of 'Jack the Ripper': a chance of about four-in-ten.

In other words, the (inclusive) 'Ripper' tally that the field presumably perceives as being the single most likely of all possible inclusive tallies, only covers about four tenths of the total range of possibilities that I happen to visualize.

News flash; stop the press:

When Colin Roberts views the so-called 'Canonic Five' individually, he tends to believe that each of them fell at the hands of 'Jack the Ripper'. But when he views the set collectively, he cannot and does not abide by the same belief.

[Varqm]

There is a 99.9% probability that you'll see a face in the clouds but what does that tell us about clouds?

[The Good Michael]

There is a 99.9% probability that you'll see a face in the clouds but what does that tell us about clouds?

I guess I'm in that .1 %.

Mike

[GUT]

There is a 99.9% probability that you'll see a face in the clouds but what does that tell us about clouds?

I guess I'm in that .1 %.

Mike

Me too so that 0.1% is looking shaky.

[lynn cates]

De Probabilitas

Hello Colin. Thanks.

"But why shouldn't we use probability theory to quantify our perceptions of likelihood?"

Well, if used for THAT, go ahead. As I have said, philosophers call probability a "calculation of our ignorance"--ie, not knowing causes/effects. This, PROVIDED we realise that a VERY low order of probability event (eg, Brown and Eddowes) CAN and DID take place.

"I define 'Jack the Ripper' as being the person that murdered Annie Chapman (… and that almost certainly murdered Mary Ann Nichols). Period!"

Stipulative definitions are the prerogative of the presenter. I approve.

"Using the Chapman murder therefore as the 'Gold Standard', I perceive the following probabilities that each respective victim was murdered by 'Jack the Ripper':

- Tabram: 9/16, i.e. 56.25%
- Nichols: 15/16, i.e. 93.75%
- Chapman: 1/1, i.e. 100.00%
- Stride: 11/16, i.e. 68.75%
- Eddowes: 7/8, i.e. 87.50%
- Kelly: 3/4, i.e. 75.00%
- McKenzie: 3/16, i.e. 18.75%
- Coles: 1/8, i.e. 12.50%'

All well and good.

"I therefore perceive a probability of just 16.91% that each of my preferred six (i.e. Tabram, Nichols, Chapman, Stride, Eddowes and Kelly), and just my preferred six, fell at the hands of 'Jack the Ripper': a chance of about one-in-six."

Still fine. I like your word, "perceive."

"In other words, the (exclusive) 'Ripper' tally that I perceive as being the single most likely of all possible exclusive tallies, only covers about one sixth of the total range of possibilities that I happen to visualize."

Again, so far, so good.

"Likewise, I therefore perceive a probability of just 23.79% that each of my preferred six (i.e. Tabram, Nichols, Chapman, Stride, Eddowes and Kelly) fell at the hands of 'Jack the Ripper': a chance of about one-in-four."

Still, no problem.

"In other words, the (inclusive) 'Ripper' tally that I perceive as being the single most likely of all possible inclusive tallies, only covers about one fourth of the total range of possibilities that I happen to visualize."

Very well.

"Similarly, I therefore perceive a probability of just 42.30% that each of the so-called 'Canonic Five' (i.e. Nichols, Chapman, Stride, Eddowes and Kelly) fell at the hands of 'Jack the Ripper': a chance of about four-in-ten."

Good. Less than 50-50.

"When Colin Roberts views the so-called 'Canonic Five' individually, he tends to believe that each of them fell at the hands of 'Jack the Ripper'. But when he views the set collectively, he cannot and does not abide by the same belief."

Splendid. No confusion of series with any one event.

What you have given is what I would consider a legitimate use of probability/statistical theory. However, that is NOT my concern. What I REALLY want to know is whom killed these lasses. And to ascertain that, I must needs look to forensic evidence and the case histories of some of the London East End blokes of 1888.

Hence, when a poster tries to circumvent a perfectly legitimate line of inquiry by adducing a low order of probability, naturally one blows a whistle.

Cheers.
LC

[Colin Roberts]

There is a 99.9% probability that you'll see a face in the clouds but what does that tell

There is 100.00% probability (i.e. an absolute certainty) that on the Day of Judgement no one will remember your username.

[Colin Roberts]

What you have given is what I would consider a legitimate use of probability/statistical theory.

Thank you, Lynn!

[Observer]

What you have given is what I would consider a legitimate use of probability/statistical theory. However, that is NOT my concern. What I REALLY want to know is whom killed these lasses. And to ascertain that, I must needs look to forensic evidence and the case histories of some of the London East End blokes of 1888.

Hence, when a poster tries to circumvent a perfectly legitimate line of inquiry by adducing a low order of probability, naturally one blows a whistle.

Cheers.
LC

Hurrah. Forensic evidence

Now go and take a good hard look and tell me this. If Liz Stride was murdered in the manner as depicted in your little re-enactment, why was there no evidence of any arterial spray deposited in close proximity to her body?

[The Good Michael]

A question for Colin:

I believe I understand your lesson in probability. You show the probability of each person being a Ripper victim as separate cases at a high level, and then as a whole, as much smaller levels of probability. I understand that. Yet, in order to separate the individuals, you must start out with JTR. How can you do that? Once separated, there is no serial killer in the picture so how can probability be so high. I'm not saying this to be amusing by any means. I don't logically see how that can be. And...this may be partly where Lynn's coming from.

Mike

[Varqm]

"There is 100.00% probability (i.e. an absolute certainty) that on the Day of Judgement no one will remember your username."

Yes and on Judgement Day the proceedings will stop so we can see Colin walk by carrying a percentage sign.

[Michael W Richards]

A question for Colin:

I believe I understand your lesson in probability. You show the probability of each person being a Ripper victim as separate cases at a high level, and then as a whole, as much smaller levels of probability. I understand that. Yet, in order to separate the individuals, you must start out with JTR. How can you do that? Once separated, there is no serial killer in the picture so how can probability be so high. I'm not saying this to be amusing by any means. I don't logically see how that can be. And...this may be partly where Lynn's coming from.

Mike

For once we agree, Im sure its not habit forming.

Cheers