[subego]

My dad threw this interesting bit past me.

The logical statement:

A implies B.

Is equivalent to:

Not A, or B.

This is a ridiculous bitch to get my head around. Even my dad, who deals a lot with logic problems, says it's one of those things that you learn to be true rather than really understand to be true.

But phrase those statements in terms of being cheated (as in not getting what you want or expect):

Sleep with my wife, I'll try to kill you.

Don't sleep with my wife or I'll try to kill you.

Everybody gets this.

The gist here is that we have evolved "modules" that deal with things that would be important to us, like getting cheated. They allow an instinctual understanding of the situation that would otherwise be very difficult to understand through straight reasoning.

Even if this isn't true, one can't help but be startled with how easy the second example is to understand versus the first.

He gave me a different example (with a set of three questions) of how your brain is (may be) doing a similar thing with morality. I'm trying to cook up what would be the best way to present that in post form.

[::maroma::]

My brain hurts now.

I'm gonna go watch some T.V.

[subego]

Make my brain hurt, I'll leave you and go watch T.V.

Don't make my brain hurt, or I'll leave you and go watch T.V.

[::maroma::]

Originally Posted by subego 

Make my brain hurt, I'll leave you and go watch T.V.

Don't make my brain hurt, or I'll leave you and go watch T.V.

Hehe, damn you!

[nonhuman]

It makes a lot more sense when you realized that the or is exclusive.

A -> B is equivalent to !A xor B

[mindwaves]

Originally Posted by subego 

My dad threw this interesting bit past me.

The logical statement:

A implies B.

Is equivalent to:

Not A or B.

Simple logic math will show you that is true if you put the parenthesis in the right places.

[Eynstyn]

I will subdue my ego in the pursuit of understanding, subego. I want to believe I'd have a fair shot at understanding the concept if you would explain the problem differently.

[subego]

Originally Posted by nonhuman 

A -> B is equivalent to !A xor B

Oh yeah, that really makes more sense.

[subego]

Originally Posted by mindwaves 

Simple logic math will show you that is true if you put the parenthesis in the right places.

But the idea is that you can understand this instinctually when it is framed in a way your brain is designed to perceive it.

A three year old can understand the second example, simple logic math is probably beyond them.

[subego]

Originally Posted by Eynstyn 

I will subdue my ego in the pursuit of understanding, subego. I want to believe I'd have a fair shot at understanding the concept if you would explain the problem differently.

I'll try doing it in reverse.

Your brain is designed to perform logical evaluation almost instantly in the right context. Taken out of that context, and left to our "general purpose" smarts, this evaluation is much harder.

With the "sleep with my wife" example. It should be obvious that:

Sleep with my wife, I'll try to kill you.

Means the exact same thing as:

Don't sleep with my wife or I'll try to kill you.


With the "A implies B" example, it's not anywhere near as obvious that:

A (sleep with my wife) implies B (I'll try to kill you).

Means the exact same thing as:

Not A (don't sleep with my wife), or B (or I'll try to kill you).

Except to people who have had some training in logic.

[edit 3: removed first two edits]

[Eynstyn]

Originally Posted by subego 

I'll try doing it in reverse.

Your brain is designed to perform logical evaluation almost instantly in the right context. Taken out of that context, and left to our "general purpose" smarts, this evaluation is much harder.

With the "sleep with my wife" example. It should be obvious that:

Sleep with my wife, I'll try to kill you.

Means the exact same thing as:

Don't sleep with my wife or I'll try to kill you.


With the "A implies B" example, it's not anywhere near as obvious that:

A (sleep with my wife) implies B (I'll try to kill you).

Means the exact same thing as:

Not A (don't sleep with my wife), or B (or I'll try to kill you).

Except to people who have had some training in logic.

[edit 3: removed first two edits]

In the hypothetical fantasy election for MacNN president, I cast my vote for you and Doofy as co-presidents.

By the way, I now feel I'm no longer worthy of this nickname. If you'd like to have it, PM me.

I'll be Kakoo (Kaku).

[TheoCryst]

Yeah, thanks a lot for reminding me that I have homework due on Monday for my logic class. Thanks a freaking lot.

Here's one that boggles my mind, even now:

¬(∃x∃y P(x,y)) ≡ ∀x∀y ¬P(x,y) (Generalized De Morgan's law).

Dunno why, but this one rule hurts my head.

[zro]

Sounds more like a byproduct of language if you axe me, I'll try to kill you.

[Eynstyn]

Originally Posted by zro 

Sounds more like a byproduct of language if you axe me, I'll try to kill you.

Could that have been the genesis of "don't axe, don't tell?"

[Mithras]

Originally Posted by nonhuman 

It makes a lot more sense when you realized that the or is exclusive.

A -> B is equivalent to !A xor B

No, that would be A iff B (A <-> B). I might kill you anyway, even if you didn't sleep with my wife.

[OreoCookie]

It's easy, just make a table:

A B A implies B not A or B
t t t t (If A is true, B has to be true as well.)
t f f f (If A is true, B cannot be false.)
f t t t (Even if A is false, B can still be true.)
f f t t (If B is false, A has to be false, too.)

Edit: somehow the code tag doesn't work anymore … 

[Lord Kronos]

It's relatively easy to consider that:

not (A -> B) <-> A and not B

therefore

A -> B <-> not (A and not B) <-> not A or B.

[subego]

Do people really think the arrow stuff is easy?

I mean, easy relative to the plain english version?

The point is you can get the plain english without even thinking about it or understanding logic math. That's easy.

[zro]

Because that's what language was designed to do. We've been using it for no one knows how long. It's what we do and we do it better than every other animal out there. Writing linguistically simple expressions of complex ideas as obscure variables in equations totally out of context is not.

Besides, I say as an equation it should have been "B requires A" which would have been the end of it.

[Kevin]

[OreoCookie]

Originally Posted by subego 

Do people really think the arrow stuff is easy?

Yes.

Originally Posted by subego 

I mean, easy relative to the plain english version?

Yes.

Originally Posted by subego 

The point is you can get the plain english without even thinking about it or understanding logic math. That's easy.

It's a language like any other. Since it's a specialized language, you need to know both vocabulary and grammar. What you are describing is a result of a lack of vocabulary -- which can't be remedied if you translate it into plain English. You will still have trouble understanding it.

To understand a problem means to have an intuition. But my intuition of math and -- say -- quantum mechanics is way different from that of a non-specialist. That's because knowledge and intuition are inseparably linked. A few hundred years ago, the idea of forces or a heliocentrical solar system were ridiculous, but now it's intuitive.

[subego]

Originally Posted by zro 

Because that's what language was designed to do. We've been using it for no one knows how long. It's what we do and we do it better than every other animal out there. Writing linguistically simple expressions of complex ideas as obscure variables in equations totally out of context is not.

Which I believe is more or less what I said.

Originally Posted by zro 

Besides, I say as an equation it should have been "B requires A" which would have been the end of it.

Except B doesn't require A... I think.

[subego]

Originally Posted by Kevin 

Sorry, I switched to decaf today.

[Kevin]

It was just a joke. I loved that movie.

[subego]

Originally Posted by Kevin 

It was just a joke. I loved that movie.

Me too. You don't remember Mr. Vaughn's "decaf" line?

Expect a visit at home from...

[Kevin]

Yeah

[Eynstyn]

Originally Posted by Kevin 

Vincent Andrew Schiavelli (November 10, 1948 – December 26, 2005)



Ray Walston (December 2, 1914 – January 1, 2001)

[subego]

Originally Posted by OreoCookie 

Yes.

Yes.

I may be confused here (wouldn't be the first time) but I think we are assessing this comparison differently because I'm including the difficulty of learning a new language and vocabulary in the comparison.

[OreoCookie]

Originally Posted by subego 

I may be confused here (wouldn't be the first time) but I think we are assessing this comparison differently because I'm including the difficulty of learning a new language and vocabulary in the comparison.

No, I think we're saying the same thing: my point is that in addition to the problem itself, you have to be versed in the language of mathematics (i. e. its vocabulary and its grammar) as well.

There are ways to see this with `plain English' as well, but it's nowhere near as succinct as in the language of mathematics.

[subego]

Originally Posted by OreoCookie 

There are ways to see this with `plain English' as well, but it's nowhere near as succinct as in the language of mathematics.

That's what I was startled by. How clear the connection is in plain english if put in the context of being cheated, while it's close to unfathomable when put into plain english without that context.

Let me toss out the example for the moral module. This works at it backwards in that the test is designed to short circuit your moral module by forcing you to use your more general purpose analytical skills. Think about and answer each question before you move on to the next one.

First question:

A train is coming at 5 people standing on a track. They are oblivious, and you cannot warn them. There is no way they can leave the track. You are next to a switch that will divert the train to another track where there is one oblivious person who cannot leave the track. Do you let the train kill the 5 people, or pull the switch and let the train kill one person?

Second question:

Same deal with 5 people on the track. No switch this time. The only way the train can be stopped is if some obstacle is placed in its path. You are standing on a bridge next to a fat person. Pushing that person off will stop the train. Do you push that person off the bridge to save the 5?

Third question:

You are a doctor with 5 patients who need different organ transplants. A patient comes into your office who you could put to sleep and harvest their organs to save 5 people. Do you do it?

The first question is obvious, and the response should be immediate. You pull the switch. When I took the test, I hesitated on the second question. When taken in the context of the first, I had trouble making an immediate conclusion. Of course, since the third question removes the initial context, you immediately realize the second question and the third question are equivalent, and should have no doubt over the answer to the second.

With me, at least, I can also see that I would likely be able to answer the second question immediately and correctly when taken out of context of the first. Of course, you may not react to the test the same way I did.