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Why I was wrong about the nuclear option

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Nick Thompson

Why I was wrong about the nuclear option

This reminded of our discussion about a year ago concerning the so-called “fallacy of induction”. Do any of you know about grue and green. Grue is a property of grass that it is green, just until you stop looking at it, at which point it turns blue. The point is that every scrupulous observation of grass confirming that it is still green, is equally a confirmation that it is also grue. “Absurd!”, you say, but only if you take for granted that the world is not the sort of place that changes on a dime. And where else could you have learned that save by induction.

http://www.washingtonpost.com/blogs/the-fix/wp/2013/12/04/why-i-was-wrong-about-the-nuclear-option/

Nick

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Gillian Densmore

Re: Why I was wrong about the nuclear option

Mr. Thompson,

New-Clear options? In what context?

============
Logic trap?
The logic trap that's popular in colleges goes about like: Gill is a human able obliterate concrete and kick ass in MMA, therefore all humans can kick ass in MMA and make short work of concrete.

=========

On Wed, Dec 4, 2013 at 10:46 AM, Nick Thompson <[hidden email]> wrote:

This reminded of our discussion about a year ago concerning the so-called “fallacy of induction”. Do any of you know about grue and green. Grue is a property of grass that it is green, just until you stop looking at it, at which point it turns blue. The point is that every scrupulous observation of grass confirming that it is still green, is equally a confirmation that it is also grue. “Absurd!”, you say, but only if you take for granted that the world is not the sort of place that changes on a dime. And where else could you have learned that save by induction.

http://www.washingtonpost.com/blogs/the-fix/wp/2013/12/04/why-i-was-wrong-about-the-nuclear-option/

Nick

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glen ep ropella

Re: Why I was wrong about the nuclear option

In reply to this post by Nick Thompson

On 12/04/2013 09:46 AM, Nick Thompson wrote:
> if you take for granted that the world is not the sort of place that changes
> on a dime. And where else could you have learned that save by induction.

Perhaps the fallacy doesn't lie in the general concept of reinforcement
learning, but in the formulation of what "induction" means?

I found it interesting that this guy was invited to give a talk at a
local CFI meeting:

Matt Thornton on Aliveness in Martial Arts
http://youtu.be/WojPLwqYpzA

the point, of course, being the difference between [un]predictability
and the tightness of the coupling between your innards and your environment.

--
glen ep ropella -- 971-255-2847

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Nick Thompson

Re: Why I was wrong about the nuclear option

In reply to this post by Gillian Densmore

Mr. Densmore,

Not sure why I have been elevated to “Mr. Thompson”. Makes me nervous. The only people who call me Mr. anymore are nurses who are preparing me for colonscopies.

Your question seems a fair one, and I would like to answer it, but I don’t know what MMA means.

Nick

Nicholas S. Thompson

Emeritus Professor of Psychology and Biology

Clark University

http://home.earthlink.net/~nickthompson/naturaldesigns/

From: Friam [mailto:[hidden email]] On Behalf Of Gillian Densmore
Sent: Wednesday, December 04, 2013 12:56 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Why I was wrong about the nuclear option

Mr. Thompson,

New-Clear options? In what context?

On Wed, Dec 4, 2013 at 10:46 AM, Nick Thompson <[hidden email]> wrote:

This reminded of our discussion about a year ago concerning the so-called “fallacy of induction”. Do any of you know about grue and green. Grue is a property of grass that it is green, just until you stop looking at it, at which point it turns blue. The point is that every scrupulous observation of grass confirming that it is still green, is equally a confirmation that it is also grue. “Absurd!”, you say, but only if you take for granted that the world is not the sort of place that changes on a dime. And where else could you have learned that save by induction.
http://www.washingtonpost.com/blogs/the-fix/wp/2013/12/04/why-i-was-wrong-about-the-nuclear-option/
Nick

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Gillian Densmore

Re: Why I was wrong about the nuclear option

Mixed Martial Arts.

and your welcome nick :P

On Wed, Dec 4, 2013 at 6:02 PM, Nick Thompson <[hidden email]> wrote:

Mr. Densmore,

Not sure why I have been elevated to “Mr. Thompson”. Makes me nervous. The only people who call me Mr. anymore are nurses who are preparing me for colonscopies.

Your question seems a fair one, and I would like to answer it, but I don’t know what MMA means.

Nick

Nicholas S. Thompson

Emeritus Professor of Psychology and Biology
Clark University

http://home.earthlink.net/~nickthompson/naturaldesigns/

From: Friam [mailto:[hidden email]] On Behalf Of Gillian Densmore
Sent: Wednesday, December 04, 2013 12:56 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Why I was wrong about the nuclear option

Mr. Thompson,
New-Clear options? In what context?
============
Logic trap?
The logic trap that's popular in colleges goes about like: Gill is a human able obliterate concrete and kick ass in MMA, therefore all humans can kick ass in MMA and make short work of concrete.

=========

On Wed, Dec 4, 2013 at 10:46 AM, Nick Thompson <[hidden email]> wrote:

This reminded of our discussion about a year ago concerning the so-called “fallacy of induction”. Do any of you know about grue and green. Grue is a property of grass that it is green, just until you stop looking at it, at which point it turns blue. The point is that every scrupulous observation of grass confirming that it is still green, is equally a confirmation that it is also grue. “Absurd!”, you say, but only if you take for granted that the world is not the sort of place that changes on a dime. And where else could you have learned that save by induction.

http://www.washingtonpost.com/blogs/the-fix/wp/2013/12/04/why-i-was-wrong-about-the-nuclear-option/

Nick

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Meets Fridays 9a-11:30 at cafe at St. John's College
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============================================================
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Nick Thompson

Re: Why I was wrong about the nuclear option

In reply to this post by Gillian Densmore

Gill,

Ok. Ready to take a whack at this. I am reading Peirce these days (as you all know, ad nauseam). And Peirce is widely regarded as a premier logician and one of the (if not the) greatest American philosopher. So, I will try to give Peirce’s answer.

Yes (he would say), assuming that you were chosen at random from the population of humans, it is a VALID inference from the fact that you can break concrete that humans can break concrete. It is valid because we would, if we continued to pick random individuals indefinitely come ultimately to the correct conclusion, say, that less than .01 percent of humans can break concrete. Unfortunately, though valid, this inference is extraordinarily “weak”. The adjective “weak” seems to relate to how much money you should be willing to bet on it. In this case, with the sample size at one, and the population at billions, Peirce would advise you to bet very little if anything, until you had a much larger sample.

I agree with you that there are traps for the young lurking in the enthusiasm and nostalgia with which the elderly often approach guiding the young. Even worse than “you can do anything you can put your mind to” is “all I want is for you to be happy.” Both set one up for blaming the victim when life screws one over, which it inevitably will. I do believe that “being happy” is a behavior and a skill that comes only to those who work at it, but alas, I see no evidence that it comes to everybody who works at it. And I also believe that whatever sins of guidance may have been inflicted on a child before that child is 21, all those sins are washed clean by the child being emancipated. Whatever the child is at 21, and from whatever causes, s/he is what s/he is from that point on and must make do with that. No value comes to a child from blaming his or her parents.

Does this help?

Nick

Nicholas S. Thompson

Emeritus Professor of Psychology and Biology

Clark University

http://home.earthlink.net/~nickthompson/naturaldesigns/

Mr. Thompson,

New-Clear options? In what context?

On Wed, Dec 4, 2013 at 10:46 AM, Nick Thompson <[hidden email]> wrote:

This reminded of our discussion about a year ago concerning the so-called “fallacy of induction”. Do any of you know about grue and green. Grue is a property of grass that it is green, just until you stop looking at it, at which point it turns blue. The point is that every scrupulous observation of grass confirming that it is still green, is equally a confirmation that it is also grue. “Absurd!”, you say, but only if you take for granted that the world is not the sort of place that changes on a dime. And where else could you have learned that save by induction.
http://www.washingtonpost.com/blogs/the-fix/wp/2013/12/04/why-i-was-wrong-about-the-nuclear-option/
Nick

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Arlo Barnes

Re: Why I was wrong about the nuclear option

The adjective “weak” seems to relate to how much money you should be willing to bet on it. In this case, with the sample size at one, and the population at billions, Peirce would advise you to bet very little if anything, until you had a much larger sample.

So is strength of an inference something we can only determine a posteriori? Or can we infer it based off previous inferences?

I agree with you that there are traps for the young lurking in the enthusiasm and nostalgia with which the elderly often approach guiding the young. Even worse than “you can do anything you can put your mind to” is “all I want is for you to be happy.” Both set one up for blaming the victim when life screws one over, which it inevitably will. I do believe that “being happy” is a behavior and a skill that comes only to those who work at it, but alas, I see no evidence that it comes to everybody who works at it.

I think probably the only advice which does not make irresponsible assumptions is "do stuff; try it, you will like it", which is not very helpful. So any more complex advice is valuable but only if treated skeptically, in the positive sense of that word, rather than merely taken to heart.

No value comes to a child from blaming his or her parents.

I would furthermore posit that blame is a valueless activity much akin to making decisions based on what is moral. It leads to misunderstanding a system much more often than it aids the thinker, and understanding a [social, physical, economic] system to some critical degree is vital in avoiding bad experiences in the future.

New-Clear options? In what context?

Somebody pointed out that society had moved forward because in the recent debate not just a few but many politicians succeeded in not pronouncing it "new-queue-lur".

Do any of you know about grue and green.

I know that when it is light out one is liable to be eaten by a bleen.

-Arlo

Nick Thompson

Re: Why I was wrong about the nuclear option

Arlo,

You are bit by bit dragging me out on thin ice here (statistics and probability) which is fine, so long as you are prepared to rescue me.

I think, as a matter of practice, that the strength of an inference is determined a priori when you define your population and select your sample size.

Does that sound right?

Nick

Nicholas S. Thompson

Emeritus Professor of Psychology and Biology

Clark University

http://home.earthlink.net/~nickthompson/naturaldesigns/

From: Friam [mailto:[hidden email]] On Behalf Of Arlo Barnes
Sent: Wednesday, December 04, 2013 10:18 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Why I was wrong about the nuclear option

The adjective “weak” seems to relate to how much money you should be willing to bet on it. In this case, with the sample size at one, and the population at billions, Peirce would advise you to bet very little if anything, until you had a much larger sample.

So is strength of an inference something we can only determine a posteriori? Or can we infer it based off previous inferences?

I agree with you that there are traps for the young lurking in the enthusiasm and nostalgia with which the elderly often approach guiding the young. Even worse than “you can do anything you can put your mind to” is “all I want is for you to be happy.” Both set one up for blaming the victim when life screws one over, which it inevitably will. I do believe that “being happy” is a behavior and a skill that comes only to those who work at it, but alas, I see no evidence that it comes to everybody who works at it.

No value comes to a child from blaming his or her parents.

New-Clear options? In what context?

Somebody pointed out that society had moved forward because in the recent debate not just a few but many politicians succeeded in not pronouncing it "new-queue-lur".

Do any of you know about grue and green.

I know that when it is light out one is liable to be eaten by a bleen.

-Arlo

Steve Smith

Re: Why I was wrong about the nuclear option

Nick -

Arlo,

You are bit by bit dragging me out on thin ice here (statistics and probability) which is fine, so long as you are prepared to rescue me.

Grin... this is what we keep youth around for... first we pretend to teach them how to stay only on thick ice whilst trusting that at some point they will lure us onto the thin, trusting that they will, in turn, be able to rescue us when it begins to crack under the weight of our ponderous wisdom.

As for your suggestions to Gil regarding what traps the elders can set (and bait) for the yungers, there are many... I appreciate that someone (you) with better "elderly" credentials than mine own can be so direct (and honest?) about those traps.

I think, as a matter of practice, that the strength of an inference is determined a priori when you define your population and select your sample size.

I liked the parts about grue, green and bleen better... but from my remembrances of the works of Brothers Grimm, I thought that grue (as in gruesome) was a somewhat greasy and rancid stew made of human body parts, usually by ogres or trolls or some similarly untrustworthy sort. I can find no objective evidence that this is the case for anyone else. Strictly (yet another) a phenomena of my own private universe I suspect.

- Steve

Does that sound right?

Nick

Nicholas S. Thompson

Emeritus Professor of Psychology and Biology

Clark University

http://home.earthlink.net/~nickthompson/naturaldesigns/

From: Friam [[hidden email]] On Behalf Of Arlo Barnes
Sent: Wednesday, December 04, 2013 10:18 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Why I was wrong about the nuclear option

The adjective “weak” seems to relate to how much money you should be willing to bet on it. In this case, with the sample size at one, and the population at billions, Peirce would advise you to bet very little if anything, until you had a much larger sample.

So is strength of an inference something we can only determine a posteriori? Or can we infer it based off previous inferences?

I agree with you that there are traps for the young lurking in the enthusiasm and nostalgia with which the elderly often approach guiding the young. Even worse than “you can do anything you can put your mind to” is “all I want is for you to be happy.” Both set one up for blaming the victim when life screws one over, which it inevitably will. I do believe that “being happy” is a behavior and a skill that comes only to those who work at it, but alas, I see no evidence that it comes to everybody who works at it.

I think probably the only advice which does not make irresponsible assumptions is "do stuff; try it, you will like it", which is not very helpful. So any more complex advice is valuable but only if treated skeptically, in the positive sense of that word, rather than merely taken to heart.

No value comes to a child from blaming his or her parents.

I would furthermore posit that blame is a valueless activity much akin to making decisions based on what is moral. It leads to misunderstanding a system much more often than it aids the thinker, and understanding a [social, physical, economic] system to some critical degree is vital in avoiding bad experiences in the future.

New-Clear options? In what context?

Somebody pointed out that society had moved forward because in the recent debate not just a few but many politicians succeeded in not pronouncing it "new-queue-lur".

Do any of you know about grue and green.

I know that when it is light out one is liable to be eaten by a bleen.

-Arlo
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Meets Fridays 9a-11:30 at cafe at St. John's College
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glen ep ropella

Re: Why I was wrong about the nuclear option

In reply to this post by Nick Thompson

On 12/04/2013 07:39 PM, Nick Thompson wrote:

> Yes (he would say), assuming that you were chosen at random from the
> population of humans, it is a VALID inference from the fact that you can
> break concrete that humans can break concrete. It is valid because we
> would, if we continued to pick random individuals indefinitely come
> ultimately to the correct conclusion, say, that less than .01 percent of
> humans can break concrete. Unfortunately, though valid, this inference is
> extraordinarily "weak". The adjective "weak" seems to relate to how much
> money you should be willing to bet on it. In this case, with the sample
> size at one, and the population at billions, Peirce would advise you to bet
> very little if anything, until you had a much larger sample.

This effectively demonstrates the fragility of logic (or any purely
delusional/mental construct). In practice, were you to go around
actually testing people against concrete, the success rate would
_increase_ over time for 2 reasons: 1) people would game the test and 2)
your test would evolve.

In the end, inference relies, in a rather circular way, on ever more
inference.

--
glen ep ropella -- 971-255-2847

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Arlo Barnes

Re: Why I was wrong about the nuclear option

In reply to this post by Nick Thompson

You are bit by bit dragging me out on thin ice here (statistics and probability) which is fine, so long as you are prepared to rescue me.

I think, as a matter of practice, that the strength of an inference is determined a priori when you define your population and select your sample size.

Does that sound right?

The ice is as thin for me as for you but I would think that the probable maximum strength of an inference is determined by the nature of the sample (that can be measured within just the sample). So we can only make very weak inferences concerning life on other planets, because we have a sample size of one. But if the first exoplanet we find with life on it has only hominids, then an inference that 'dominant' lifeforms can only be hominids would appear to double in strength but might not actually be stronger than before at all if it turns out just to be luck.

I may revise this opinion upon further rumination, though, as I feel like my analytical skills are not at their strongest currently.

-Arlo

David Eric Smith

Re: Why I was wrong about the nuclear option

Hi Nick (who started the thread, regarding induction, but teasing with current events), and Arlo who has kept it alive,

For days I have been trying not to respond, but …

This is about the nuclear option, not about induction.

Malcolm Gladwell had a piece in the New Yorker about David and Goliath a few years ago:

http://www.newyorker.com/reporting/2009/05/11/090511fa_fact_gladwell

A team of under-skilled basketball players makes it to the semifinals by pushing the full court press on every play, every game.

One story gets most of the time here, and it is Gladwell's message. Pure determination and the self-discipline to be more fit and stronger than your opponents can overcome large differentials in gifts. Maybe gifts aren't so much earned as bestowed by luck of the draw, whereas conditioning is earned with suffering, and so is more noble, etc. Okay.

Let me acknowledge that there is a lot in this half of the story that I admire and agree with, and Gladwell tells good stories.

There is another part of the story that does get mentioned, but not in more than a sentence or two. Many of the girls in the other teams, who were hoping to win by skill, were not only frustrated but somewhat embittered at being beaten through sheer unrelenting obstruction. Gladwell does not demean this, but he doesn't give it a lot of space either, as it is different from the story he is here to tell.

A different take on the same story, however, might be that the purpose of sport isn't (or shouldn't be) principally to provide a chance to declare winners; it should be to use competition to bring out a certain form of excellence, or skill, or beauty, or momentarily attaining a state of grace, or whatever you want to call it. David Rudisha's 800 or McKayla Maroney's Amanar. Not everybody who feels entitled to win and gets beaten by a more determined opponent is mourning the loss of these things, but some do, and if enough didn't, what would be left of anything, except a kind of uniform grey siege?

I can't stand the republican obstructionism, because if there is any good faith behind any of it, in any rare individual, it is so far buried beneath the pure meanness that all I can see left is doing a dance around the "bonfire" as Rome burns. We have much to lose, and I can't see any difference of moral worth between people who are gleeful at its loss, and the most degraded Taliban mentality, in which nothing is left but the saboteur.

But it's just the full court press, on every play, in every game.

So why doesn't -- why shouldn't (unless you believe it should) -- everything degenerate to a simple siege? What had ever maintained anything of enough worth that there could be a "nuclear option" to threaten to take it away? I think I mean this as a science question.

I guess, said another way, by the time you are down to being limited by the rules, most hope is lost. The role of rules must be, it seems, to function as catalysts within a system that is much more complicated than the rules themselves, and what they catalyze is the preservation of honor (or other value) by the system. The preservation of things that can only be preserved by more complicated systems than rules. But without well-designed rules as catalysts, the larger system could not be counted on to maintain these things on its own. What is the larger system? What is its natural language? How do we worry about it in the right way (meaning, a productive way) when we should worry?

There is a kind of meanness or cynicism that likes to see hope dashed and beauty destroyed, and this meanness answers me by saying that if it isn't in the rules enforced with a gun, it isn't real, and only patsies fail to know that.

I think that is an error, but it would be nice to have satisfying ways to get at the thought, at some level closer to the precision we can bring to bear when thinking about rules.

For a group of girls to win a season of basketball through a lot of guts and planning is okay, and basketball will survive. To lose a norm of honor in the senate (already as wondrous as a snowball in hell) is not okay.

Eric

On Dec 6, 2013, at 2:50 PM, Arlo Barnes wrote:

You are bit by bit dragging me out on thin ice here (statistics and probability) which is fine, so long as you are prepared to rescue me.
I think, as a matter of practice, that the strength of an inference is determined a priori when you define your population and select your sample size.
Does that sound right?
The ice is as thin for me as for you but I would think that the probable maximum strength of an inference is determined by the nature of the sample (that can be measured within just the sample). So we can only make very weak inferences concerning life on other planets, because we have a sample size of one. But if the first exoplanet we find with life on it has only hominids, then an inference that 'dominant' lifeforms can only be hominids would appear to double in strength but might not actually be stronger than before at all if it turns out just to be luck.

I may revise this opinion upon further rumination, though, as I feel like my analytical skills are not at their strongest currently.
-Arlo

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Marcus G. Daniels

Re: Why I was wrong about the nuclear option

In reply to this post by Nick Thompson

Eric writes:

"There is a kind of meanness or cynicism that likes to see hope dashed and
beauty destroyed, and this
meanness answers me by saying that if it isn't in the rules enforced with a
gun, it isn't real, and only
patsies fail to know that."

What a fantastic post.

I would answer this way, but it isn't because I want to see hope dashed and
beauty destroyed. It's because
I want to destroy the destroyers.

Marcus

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David Eric Smith

Re: Why I was wrong about the nuclear option

> I would answer this way, but it isn't because I want to see hope dashed and
> beauty destroyed. It's because
> I want to destroy the destroyers.
>
> Marcus

Yes. I understand.

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Jim Dunn

Re: Why I was wrong about the nuclear option

In reply to this post by David Eric Smith

Thanks Joyce! I did receive the message you forwarded to me. I think I’m set.

Jim

On Dec 6, 2013, at 1:50 PM, Eric Smith <[hidden email]> wrote:

Hi Nick (who started the thread, regarding induction, but teasing with current events), and Arlo who has kept it alive,

For days I have been trying not to respond, but …

This is about the nuclear option, not about induction.

Malcolm Gladwell had a piece in the New Yorker about David and Goliath a few years ago:
http://www.newyorker.com/reporting/2009/05/11/090511fa_fact_gladwell
A team of under-skilled basketball players makes it to the semifinals by pushing the full court press on every play, every game.

One story gets most of the time here, and it is Gladwell's message. Pure determination and the self-discipline to be more fit and stronger than your opponents can overcome large differentials in gifts. Maybe gifts aren't so much earned as bestowed by luck of the draw, whereas conditioning is earned with suffering, and so is more noble, etc. Okay.

Let me acknowledge that there is a lot in this half of the story that I admire and agree with, and Gladwell tells good stories.

There is another part of the story that does get mentioned, but not in more than a sentence or two. Many of the girls in the other teams, who were hoping to win by skill, were not only frustrated but somewhat embittered at being beaten through sheer unrelenting obstruction. Gladwell does not demean this, but he doesn't give it a lot of space either, as it is different from the story he is here to tell.

A different take on the same story, however, might be that the purpose of sport isn't (or shouldn't be) principally to provide a chance to declare winners; it should be to use competition to bring out a certain form of excellence, or skill, or beauty, or momentarily attaining a state of grace, or whatever you want to call it. David Rudisha's 800 or McKayla Maroney's Amanar. Not everybody who feels entitled to win and gets beaten by a more determined opponent is mourning the loss of these things, but some do, and if enough didn't, what would be left of anything, except a kind of uniform grey siege?

I can't stand the republican obstructionism, because if there is any good faith behind any of it, in any rare individual, it is so far buried beneath the pure meanness that all I can see left is doing a dance around the "bonfire" as Rome burns. We have much to lose, and I can't see any difference of moral worth between people who are gleeful at its loss, and the most degraded Taliban mentality, in which nothing is left but the saboteur.

But it's just the full court press, on every play, in every game.

So why doesn't -- why shouldn't (unless you believe it should) -- everything degenerate to a simple siege? What had ever maintained anything of enough worth that there could be a "nuclear option" to threaten to take it away? I think I mean this as a science question.

I guess, said another way, by the time you are down to being limited by the rules, most hope is lost. The role of rules must be, it seems, to function as catalysts within a system that is much more complicated than the rules themselves, and what they catalyze is the preservation of honor (or other value) by the system. The preservation of things that can only be preserved by more complicated systems than rules. But without well-designed rules as catalysts, the larger system could not be counted on to maintain these things on its own. What is the larger system? What is its natural language? How do we worry about it in the right way (meaning, a productive way) when we should worry?

There is a kind of meanness or cynicism that likes to see hope dashed and beauty destroyed, and this meanness answers me by saying that if it isn't in the rules enforced with a gun, it isn't real, and only patsies fail to know that.

I think that is an error, but it would be nice to have satisfying ways to get at the thought, at some level closer to the precision we can bring to bear when thinking about rules.

For a group of girls to win a season of basketball through a lot of guts and planning is okay, and basketball will survive. To lose a norm of honor in the senate (already as wondrous as a snowball in hell) is not okay.

Eric

On Dec 6, 2013, at 2:50 PM, Arlo Barnes wrote:

You are bit by bit dragging me out on thin ice here (statistics and probability) which is fine, so long as you are prepared to rescue me.
I think, as a matter of practice, that the strength of an inference is determined a priori when you define your population and select your sample size.
Does that sound right?
The ice is as thin for me as for you but I would think that the probable maximum strength of an inference is determined by the nature of the sample (that can be measured within just the sample). So we can only make very weak inferences concerning life on other planets, because we have a sample size of one. But if the first exoplanet we find with life on it has only hominids, then an inference that 'dominant' lifeforms can only be hominids would appear to double in strength but might not actually be stronger than before at all if it turns out just to be luck.

I may revise this opinion upon further rumination, though, as I feel like my analytical skills are not at their strongest currently.
-Arlo

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