New way of diagramming certain rules

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Clearly
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New way of diagramming certain rules

Postby Clearly » Sat Jun 09, 2012 1:07 am

So I'm considering changing the way I diagram conditional rules in matching games in which the positions are fixed (not teams that could be in any order).

I realize it's late in the game, and I'm truly not advocating anyone even think of changing things now (myself included). But after realizing that my diagrams for these specific (but fairly common rules) were just plain not easy to read despite being correct, I started thinking of a different way of illustrating the data. This may cause controversy because it goes against one of the commonly taught LSAT methods of keeping all arrows pointing the same way in conditional logic.

I'm posting this because I'd like your valuable feedback on using this myself, not to put any ideas in anyone else head.

I'll illustrate my idea using a real game
If you'd like to follow along open up PT52 to section 2(lg), and game 2 (q 8-12)
Standard stuff, putting people into groups. For the method I've been toying with, the order of the groups need either be irrelevant (as in this game) or fixed.

We're given a bunch of conditional rules (and the contras naturally). I would diagram them in a manner that makes sense, but with several rules gets cumbersome and confusing, and doesn't intuitively reinforce the implications of each rule as I work through the game.

The conditional rules for this game previously looked like this.
Image

The top of each statement being the team, and the bottom being the player. This follows the order they would show up in my diagram later with the people naturally appearing under the teams as I work down the list. It's all sound logic, but it's a mess of rules that I would constantly have to check (time consuming) because it never got internalized, and wasn't quick to reference.


The new plan involves placing the teams in fixed positions (matching the diagram) and illustrating the conditional logic within the diagram. The downside to those who find "ALL ARROWS RIGHT" to be a rule is that obviously if the teams are fixed, the contrapositive would involve rotating the arrow and negating. To reinforce the sufficient/neccesary conditions, I CIRCLE the sufficient condition on top of clearly drawing the arrow (implying the necessary is to follow). What this means is, I have a pretty diagram of my rules that (to me) is MUCH easier to scan and understand the implications of. Rather then knowing the trigger, or sufficient, is always on the left, I know the sufficient/trigger is always circled. When testing an answer choice, I simply look to see if the circled things are in place, and if so, that the condition attached to it is also in place.

This is what my diagram now looks like for this game.
Image

There's nothing revolutionary going on here. Same rules, same order, just a different way of illustrating them. There's several items at play in a rule like this that need to reference each other in a prescribed manner, we have the team, the player and the conditional relationship which we symbolize with the arrow.

These three elements have to keep their relationship uniform and so some element must be fixed, and the other elements tailored around it to reflect the rule.
By the old method of diagramming contrapositives, we fixed the arrow pointing right to ensure the sufficient/necessary (cause->effect) formula was uniform, and to make it work we negated and moved around both the players AND the teams, causing that funky fraction looking illustration.

My new line of thinking is that the relationship between cause and effect could be clearly represented even if it wasn't left to right (circle, arrow). By freeing the arrow to be the mobile element, we can fix the teams and players where they belong and can be clearly referenced in a diagram that happens to look just like my main diagram.


This might seem crazy to others, but to me I can know I'm within all of the implications of those rules in about a second, instead of matching things up like I was having to do with the diagram above.

Please let me know what you think of this new idea I'm toying with.
Last edited by Clearly on Sat Jun 09, 2012 2:00 am, edited 2 times in total.

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StarLightSpectre
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Re: New way of diagramming certain rules

Postby StarLightSpectre » Sat Jun 09, 2012 1:19 am

Clearlynotstefan wrote:So I'm considering changing the way I diagram conditional rules in matching games in which the positions are fixed (not teams that could be in any order).

I realize it's late in the game, and I'm truly not advocating anyone even think of changing things now (myself included). But after realizing that my diagrams for these specific (but fairly common rules) were just plain not easy to read despite being correct, I started thinking of a different way of illustrating the data. This may cause controversy because it goes against one of the commonly taught LSAT methods of keeping all arrows pointing the same way in conditional logic.

I'm posting this because I'd like your valuable feedback on using this myself, not to put any ideas in anyone else head.

I'll illustrate my idea using a real game
If you'd like to follow along open up PT52 to section 2(lg), and game 2 (q 8-12)
Standard stuff, putting people into groups. For the method I've been toying with, the order of the groups need either be irrelevant (as in this game) or fixed.

We're given a bunch of conditional rules (and the contras naturally). I would diagram them in a manner that makes sense, but with several rules gets cumbersome and confusing, and doesn't intuitively reinforce the implications of each rule as I work through the game.

The conditional rules for this game previously looked like this.
Image

The top of each statement being the team, and the bottom being the player. This follows the order they would show up in my diagram later with the people naturally appearing under the teams as I work down the list. It's all sound logic, but it's a mess of rules that I would constantly have to check (time consuming) because it never got internalized, and wasn't quick to reference.


The new plan involves placing the teams in fixed positions (matching the diagram) and illustrating the conditional logic within the diagram. The downside to those who find "ALL ARROWS RIGHT" to be a rule is that obviously if the teams are fixed, the contrapositive would involve rotating the arrow and negating. To reinforce the sufficient/neccesary conditions, I CIRCLE the sufficient condition on top of clearly drawing the arrow (implying the necessary is to follow). What this means is, I have a pretty diagram of my rules that (to me) is MUCH easier to scan and understand the implications of. Rather then knowing the trigger, or sufficient, is always on the left, I know the sufficient/trigger is always circled. When testing an answer choice, I simply look to see if the circled things are in place, and if so, that the condition attached to it is also in place.

This is what my diagram now looks like for this game.
Image

This might seem crazy to others, but to me I can know I'm within all of the implications of those rules in about a second, instead of matching things up like I was having to do with the diagram above.

Please let me know what you think of this new idea I'm toying with.



Wow it's definitely a lot easier to read and understand. Almost wish I could have learned it this in time to work the kinks out and apply it.

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CardozoLaw09
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Re: New way of diagramming certain rules

Postby CardozoLaw09 » Sat Jun 09, 2012 1:19 am

Nice. Have you applied this new way to other games?

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Clearly
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Re: New way of diagramming certain rules

Postby Clearly » Sat Jun 09, 2012 1:27 am

I have. Like I said, it applies only to very specific games in which the order is fixed or doesn't matter, but those come up fairly often, so I've used it on about 7 games without a hitch. Those games were nightmares based off of my old way of diagramming, having to reference that mess so often destroyed time like crazy.

keyanaut
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Re: New way of diagramming certain rules

Postby keyanaut » Sat Jun 09, 2012 2:08 am

Nice

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PDaddy
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Re: New way of diagramming certain rules

Postby PDaddy » Sat Jun 09, 2012 2:14 am

CardozoLaw09 wrote:Nice. Have you applied this new way to other games?


This is really just a variation on the Manhattan in-and-out method (simultaneous horizontal and vertical representation). Appears to be good.

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Clearly
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Joined: Sat Feb 11, 2012 4:09 pm

Re: New way of diagramming certain rules

Postby Clearly » Sat Jun 09, 2012 2:29 am

PDaddy wrote:
CardozoLaw09 wrote:Nice. Have you applied this new way to other games?


This is really just a variation on the Manhattan in-and-out method (simultaneous horizontal and vertical representation). Appears to be good.

Never read any of the Manhattan stuff, but I'm sure it's not a new way of thinking of things, and I'm sure I'm not the first to do it. It just occurred to me today that this rule looks like shit because I've be programmed to leave the arrow fixed to the right, and that by doing so I'm forced into moving ALL of the other elements around it creating these little fractions that aren't as helpful to me as something that matches my main diagram.

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cc.celina
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Re: New way of diagramming certain rules

Postby cc.celina » Sat Jun 09, 2012 10:16 am

Right on! Games got a lot easier for me about a week ago when I stopped trying to represent everything like a textbook, including no longer caring which way the arrows go. Circling the sufficient is a good idea that I hadn't thought of. I do this for any sort of linear or grouping game where there's a rule along the lines of "if J is 4th, L isn't 1st"

__ __ __ __ __ __
1 2 3 4 5 6
L <-- J

If it works for you go for it.




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