An article about the Law of Large Numbers in Psychology Today

#41
Andy, you quoted my post, but did you answer my question? I really don’t know, but if you did then I didn’t understand.
That was an accident. I intended to answer it but answered someone else instead. If you look, you'll see I spent some time on your question and have now answered it.

AP
 
#42
This is the essence of incremental critical path. What a team would employ in a discovery research lab.

Take inference where it deductively leads, but go no further. Falsifying monism in no way supports theism, it only means that some form of pluralism exists.
Thanks, ES, I think I'm beginning to understand your idea of incremental critical path. Robert Ellis has a related concept that he calls incremental objectivity. I struggle a bit with the concept. For whatever reason, it is hard for me to grapple with the idea that a small incremental step toward greater objectivity can still leave you with a concept that is not ultimately reflective of some abstract "ultimate truth or reality."

I like to think in terms of frames of mind. I have different interpretations of events in different contexts / frames of mind. I like the metaphor that I can never be in all of my frames of mind at the same time. I wonder if that is related to what you mean by "pluralism"?
 
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#43
I disagree to an extent. I agree that the forecasting (you call it ex ante) changes the situation and I'm going to write something about that when I have time to think (it's been a busy day as usual), but I still argue that the rolls are not independent. The forecast was for specific rolls in a specific order. The success of each subsequent roll is dependent on the success of the previous roll.(success = meeting the forecast)
Yes, a forecast is ex ante. But it is a specific type of ex ante. A forecast involves feedback dynamics, arrival confidences and distributions, parameters, constraints, stochastic and non-stochastic generators, and scenario models. Like forecasting the demand for men's athletic compression briefs, 18 months pre-season - as my catalog and retailer does. We have used JDA's Forecasting module in the past for instance.

What Andrew did was an intuitive selection - this is not forecasting. But odds are 26 quadrillion to 1, that he drew this selection from something. But it was not necessarily a forecast just yet.

We may find some day - that the ether is a big simulation and our brains can tap into and conduct such forecasting - but for now it is simply an ex ante intuitive selection. :)
 
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#44
Thanks, ES, I think I'm beginning to understand your idea of incremental critical path. Robert Ellis has a related concept that he calls incremental objectivity. I struggle a bit with the concept. For whatever reason, it is hard for me to grapple with the idea that a small incremental step toward greater objectivity can still leave you with a concept that is not ultimately reflective of some abstract "ultimate truth or reality."

I like to think in terms of frames of mind. I have different interpretations of events in different contexts / frames of mind. I like the metaphor that I can never be in all of my frames of mind at the same time. I wonder if that is related to what you mean by "pluralism"?
Monism - There exists only one domain of concrete objects: physical, energy, information, deterministically-constrained consciousness and their interpretations of purpose therein. (sometimes called nihilism, materialism, material monism, Atheism, secularism, etc.) All reality is based upon blocks from this single domain, regardless of whether or not they are directly observable.


Pluralism - There exists more than simply the domain of monist concrete objects. I have no idea what these objects are - all I know is that monism has been falsified to my satisfaction - and more importantly to the necessity under Ockham's Razor.

Pluralism is a way of holding open the alternative that there is something more, without jumping on to the bandwagons of spirituality, theism, NDE's, ghosts, OBE's, Cartesian Dualism etc. It allows a scientist to research the philosophy without the stigma associated with such 'bucketologies'.

One can be an atheist, and still be a pluralist.
A pantheist can also be monist.

The use of monism and pluralism, removes the charged miasma around the hot button monkers - and provides a better set of Wittgenstein logical objects from which to develop dispassionate philosophy and science.

For instance: I am a pluralist ignostic atheist. This affords me a better stance from which to conduct philosophy and science. No one owns my allegiance (except maybe Scarlett Johansson).
 
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#45
That was an accident. I intended to answer it but answered someone else instead. If you look, you'll see I spent some time on your question and have now answered it.

AP
Thanks Andy.
Very interesting, I read Dreamer some years ago. For me it was and is strong evidence that amazing things do in fact happen. We might expect such a book to sell in the millions, yet I fully suspect that’s far from the case, of course.
Also, the answers in the thread were totally beyond me, so as far as I knew, you might well have been replying sensibly but beyond my understanding. :)
 
#47
ad hoc Gaussian Arrival Distribution
The context of the Law of Large Numbers related in this typical Novella hack job is the ad hoc with intuitive averages (Gaussian) serendipity of "If you consider the math more thoroughly (an ambiguous appeal to authority), you will see that amazing coincidences should happen all the time." Wherein earlier he quips "If we do the math (Novella can't do the math), then it becomes clear that very unlikely events should happen all the time, given enough opportunity." This is the ad hoc context of the LOLN = sufficient opportunity.

(a critical thinker will notice that Novella essentially says the same thing twice in the opening argument and then argument substantiation, a circular appeal crafted to make his fluff piece appear more intimidating and substantial)

ex ante (Other than Gaussian)
ad hoc
is not the same as an ex ante forecast, as happened with Andrew here in his case example. In a forecast, this is not an 'amazing coincidence', it is a predicted amazing coincidence, something completely different, - AND something which is the basis of deductive science (prediction). There is NOT 'enough opportunity' in Novella's pseudo-statistics lingo. It is ex ante. Nor do we understand the concavity nor convexity of this particular ex ante prediction over time or circumstance. In Andrew's case he eliminated concavity/convexity by only trying this once. Therefore it cannot be easily intuited as being subject to the LOLN in this manner, nor does the LOLN apply in Andrew's case.

The only critical path option at the fake skeptic's avail here is to call Andrew a liar. NO other plausible dismissal is sequitur in this case example. But they whip out the LOLN ruse so as to not seem mean. A ruse.

The Law of Large Numbers has validity, but Steven Novella is not qualified to assign that validity to any particular case scenario, because:

1. He bears agency (not just bias)​
2. He perceives all probability arrivals as being Gaussian​
3. He is not trained in the disciplines of probability statistics and hypothesis/scenario modeling - nor does he understand it. He just holds a couple canned principles which he grasps about 70%.​
4. He bungles the match between principle and example scenario regularly​
5. He fails to perceive the difference between ad hoc and ex ante.​
6. He bears a club celebrity conflict of interest - and cannot afford to actually look when he risks being wrong (anti-skepticism).​
Nice try, but no cigar.
 
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#48
ad hoc Gaussian Arrival Distribution
The context of the Law of Large Numbers related in this typical Novella hack job is the ad hoc with intuitive averages (Gaussian) serendipity of "If you consider the math more thoroughly (an ambiguous appeal to authority), you will see that amazing coincidences should happen all the time." "If we do the math (Novella can't do the math), then it becomes clear that very unlikely events should happen all the time, given enough opportunity." This is the ad hoc context of the LOLN.

(notice that Novella essentially said the same thing twice, in order to make his fluff piece appear more intimidating and substantial)

ex ante (Other than Gaussian)
ad hoc
is not the same as an ex ante forecast, as happened with Andrew here in this case. In a forecast, this is not an 'amazing coincidence', it is a predicted amazing coincidence, something completely different, - AND something which is the basis of deductive science (prediction). There is NOT 'enough opportunity' in Novella's pseudo-statistics lingo. It is ex ante. Nor do we understand the concavity nor convexity of this particular ex ante prediction over time or circumstance. Therefore it cannot be easily intuited as being subject to the LOLN in this manner.

The Law of Large Numbers has validity, but Steven Novella is not qualified to assign that validity to any particular case scenario, because:

1. He bears agency (not just bias)​
2. He perceives all probability arrivals as being Gaussian​
3. He is not trained in the disciplines of probability statistics and hypothesis/scenario modeling - nor does he understand it. He just holds a couple canned principles which he grasps about 70%.​
4. He bungles the match between principle and example scenario regularly​
5. He fails to perceive the difference between ad hoc and ex ante.​
6. He bears a club celebrity conflict of interest - and cannot afford to actually look when he risks being wrong (anti-skepticism).​
Nice try, but no cigar.
I guess the numbers are tricky to math out.

What we do know is that when the maths is easier to work out, in more controlled environments, magic (or whatever Rawlette is promoting) doesn't seem to impact on "coincidences". Thus casinos always win.
 
#49
I guess the numbers are tricky to math out.

What we do know is that when the maths is easier to work out, in more controlled environments, magic (or whatever Rawlette is promoting) doesn't seem to impact on "coincidences". Thus casinos always win.
Yule-Simpson effect.

Aggregate numbers are never going to show a bias for miracles. The house always wins. But the idea that randomness is prohibitive, has been falsified.
 
#51
Why not? And what is a "miracle"?
Cmon' Malf, these are rhetorical questions. But I will take a shot.

Why is the Yule-Simpson effect in place? You will have to ask whomever or whatever, set up the rules of the universe. This is above my paygrade. I suspect it has something to do with Heisenberg uncertainty and the coherence of matter, energy and space-time.

Miracle - An observed effect in a single, non-repeated test which surpasses a common p-value threshold of .0001 by a factor of 1000x or more, yet bears no known possible mechanism, prior teachable art nor any form of statistical history. So a p-value of .0000001 and less in tailing; with a thin tail. For a single binomial test = 1 in 10,000,000.
 
#52
Cmon' Malf, these are rhetorical questions. But I will take a shot.

Why is the Yule-Simpson effect in place? You will have to ask whomever or whatever, set up the rules of the universe. This is above my paygrade. I suspect it has something to do with Heisenberg uncertainty and the coherence of matter, energy and space-time.
This seems circular? I can’t see how the Yule-Simpson effect could exist if we lived in a ‘miraculous’ world.

I think you’re making my point for me.
 
#53
This seems circular? I can’t see how the Yule-Simpson effect could exist if we lived in a ‘miraculous’ world.

I think you’re making my point for me.
You do not have a coherent point - if you do, then state it. I believe Andrew and his 1 in a Quadrillion prediction. If we put Andrew into a lab and hook him up to electrodes, this observation will not repeat. If we hook 1,000 Andrews up to electrodes and put on lab coats and run his predictive experiment 50,000 times, an effect from this will not show up.

I did not make the rules of universal paradox.

You are asking me to be accountable for the Double Slit experiment, wave-particle duality problems, Quarks appearing from the M-brane from nothing, Non-Locality or NDEs - every form of universal paradox. There are dozens and dozens of them. I don't have an explanation for the paradoxes that make up our realm, and that is not my fault. You are ascribing to me, the idiosyncrasies of our gilded hell. I am only reporting what I observe, and am trying to frame it in as logical a progression as I can make of it.

But I am not going to lie to myself in order to feel rational. I do not possess that inner disease.
 
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#54
You do not have a coherent point - if you do, then state it. I believe Andrew and his 1 in a Quadrillion prediction. If we put Andrew into a lab and hook him up to electrodes, this observation will not repeat. If we hook 1,000 Andrews up to electrodes and put on lab coats and run his predictive experiment 50,000 times, an effect from this will not show up.

I did not make the rules of universal paradox.

You are asking me to be accountable for the Double Slit experiment, wave-particle duality problems, Quarks appearing from the M-brane from nothing, Non-Locality or NDEs - every form of universal paradox. There are dozens and dozens of them. I don't have an explanation for the paradoxes that make up our realm, and that is not my fault. You are ascribing to me, the idiosyncrasies of our gilded hell. I am only reporting what I observe, and am trying to frame it in as logical a progression as I can make of it.

But I am not going to lie to myself in order to feel rational. I do not possess that inner disease.
Actually, I think if Andrew and I sat down and played backgammon, we just might end up getting a repeat.

But I'm not going to wear any electrodes!

And I still think that everyone's statistics are a little off for the reasons I have already mentioned. Maybe after this week is over my brain will return from its current work induced mush like state and I can write up my theory.
 
#55
Actually, I think if Andrew and I sat down and played backgammon, we just might end up getting a repeat.

But I'm not going to wear any electrodes!

And I still think that everyone's statistics are a little off for the reasons I have already mentioned. Maybe after this week is over my brain will return from its current work induced mush like state and I can write up my theory.
LOL!!

You did see that I corrected my stats based on your inputs... you were correct. ;;/?
 
#56
LOL!!

You did see that I corrected my stats based on your inputs... you were correct. ;;/?
I just saw that, TES.

I used to do a lot of time series and survival analysis at work. There's something on the tip of my mind that just won't come through as I am genuinely burned out from a summer of intense deadlines. Something my team did once that was a melding of those techniques and poisson probability distributions for analyzing the accuracy of forecasting - or predicting - extremely rare events.

To my mind, what Andy presents has two components.
1. The raw probability of the series of rolls
2. The prediction as to exactly when that series of rolls would occur.

I believe that both components must be combined to arrive at the true odds.
 
#57
To my mind, what Andy presents has two components.
1. The raw probability of the series of rolls
2. The prediction as to exactly when that series of rolls would occur.

I believe that both components must be combined to arrive at the true odds.
Yes, this is called the difference between an ad hoc and ex ante condition of probability. ad hoc extremely improbable events happen all the time, even though their likelihood is remote. ex ante events are falsifying in their nature. They don't 'just happen' - but rather, are predicted in context.

ad hoc - random improbable event (Your #1 above - or Law of Large Numbers)​
ex ante - predicted improbable event (Your #1 & 2 combined above)​

The math I ran was for the ex ante condition:
MatLab.png

= 2.585 x 10^-16 or 1:25,900,000,000,000,000

Or one in 26 Quadrillion

It is a good thing that Andrew switched his prediction to 'not-2' at the snake-eyes doubles sets - because if he had been successful on those two rolls, I am not sure but I think the Universe might have imploded.
 
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#58
It is a good thing that Andrew switched his prediction to 'not-2' at the snake-eyes doubles sets - because if he had been successful on those two rolls, I am not sure but I think the Universe might have imploded.
A similar thing happened with another prediction thqat happened within weeks of that backgammon game but it involved Scrabble. We had just started the game when I had the sudden inspiration to make a highly specific prediction. It was that I would blindly reach into the Scrabble bag of letters and pull out all of the remaining "E" tiles. Only one "e" had been played at that point and neither of us had any in our tray. That meant there were 11 remaining in the bag. I proceeded to pull out E after E, one after the other, until I'd picked ten in a row. At that point my confidence failed me, I said I wouldn't get the last one, and didn't. The odds on that were more difficult to calculate because you have to take into account the following: 1) total number of tiles (100), 2) the number of tiles on our trays (7 on Kitty's, less than 7 on mine because it was my turn to draw), 3) the number of tiles on the board (unknown now but at the time we wrote down how many there were and used it to check the probability. I do remember we had each played one word), 4) the number of E's remaining in the bag, and 5) the number of non-E letters remaining in the bag.

At the time I recall calculating the odds as one in about 250 billion, so much less striking than the backgammon rolls but impressive regardless. It happened again in a Scrabble game at about the same time but I don't think odds could be calculated for it because of the nature of the prediction. Again it happened the same way. We were playing when I suddenly had the inspiration to make a prediction. Keep in mind that the "inspiration" did not feel like it was coming from me necessarily. In this case, the prediction was that Kitty would play three seven letter words on each of her next three turns. She did. To this day, she hasn't repeated the feat, despite having played thousands of games since then (we keep the score sheets and for years played every night at dinner). To memorialize her feat, I took a Polaroid photo of the board after her third play. I'll attach it here for fun.
 

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#59
It is a good thing that Andrew switched his prediction to 'not-2' at the snake-eyes doubles sets - because if he had been successful on those two rolls, I am not sure but I think the Universe might have imploded.
Here's another one you might have fun with, since you seem to enjoy crunching numbers (though now that I have a PhD and know more about statistics, I suppose I could do it also). In this case, it is one of a handful of dreams that led me to start my dream journal. Here is the account from my book:
"June 20 1988, New York City
Suddenly, I know that I am dreaming. "This is a dream of the future!" I think, and simultaneously realize that I need only shift my attention from the ten losing lottery tickets in my right hand to the list of winning numbers in my left to use this dream to my advantage. The problem is, I can feel myself waking. I want more time, I keep looking at the wrong hand, I have to look at the list...why is it so hard? I just need to focus... Some of the tickets have winning numbers, but not enough...
-​
Then I woke. I grabbed a pen and wrote down what I remembered: two definite winners: 6 and 44, and five others that I thought might be winners, but I wasn't sure. Kitty wanted me to run out and buy tickets, but I resisted. Not only did I not remember all the numbers, but I didn't believe it was possible to dream of the future. Kitty insisted, and I went.
I bought five games instead of ten. This was the first time I'd ever bought lottery tickets, and didn't want to waste ten dollars. This attitude was vindicated when the results came out and none of my tickets won. Then, Kitty surprised me and pulled out five tickets of her own.
"You had ten tickets in the dream, so I bought five more," she said. Hers were losers also, but my dream hadn’t predicted anything different. My dream predicted I would have ten Lotto tickets (correct, despite my attempt to thwart this by purchasing five), we didn’t win any money (correct), that I would have a ticket with three winning numbers (correct, 6,17, and 44), that 6 and 44 would definitely be winners (true), and that I had four winning numbers in my 'pool' of seven possibilities (also true; 6, 17, 23, and 44). The dream was correct on every point."
I've attached an image of eight of the tickets. The other two were lost, so I don't have them to photograph anymore.

Now that I'm thinking about this, I realize that I have several examples of documentation like this that I couldn't put in my book because they didn't want illustrations. I think I'll post another thread with some of those.
 

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#60
You do not have a coherent point - if you do, then state it. I believe Andrew and his 1 in a Quadrillion prediction. If we put Andrew into a lab and hook him up to electrodes, this observation will not repeat. If we hook 1,000 Andrews up to electrodes and put on lab coats and run his predictive experiment 50,000 times, an effect from this will not show up.
Look at Andrew's abilities here and the lists of his incredible successes. Looks like we'd get lots of hits.

And that's what we need. Otherwise it's too easy for the skeptics to appeal to something they (and you) know exists: The delusional, well intentioned fantasist.

(Note to Mods: I am not saying Andrew fits this descriptor. I am saying that the special pleading over the untestibility of his type of magic is just too easy for some to dismiss, and we could really do with a psi superhero)
 
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