Math Fun

For discussing anything related to physics, biology, chemistry, mathematics, and their practical applications.

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Re: Math Fun

Postby James S Saint » Wed Sep 09, 2015 9:21 pm

phyllo wrote:
phyllo wrote: He gave you a bum steer. All his equations are wrong.


Yeah, that is all that I was trying to say. 8)
Then why do you keep using those equations??? :shock:

Silly question. I had to use them in order to ask if that is what he meant. He is saying something that others are not hearing to mean what he really means to say.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
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Re: Math Fun

Postby phyllo » Wed Sep 09, 2015 9:36 pm

If the change due was 34.56, the cashier gave back 56.34 instead. That's it in a nutshell. 8)
"Who loves not wine, woman and song, remains a fool his whole life long."

"Only the educated are free" - Epictetus
"Music is a higher revelation than all wisdom and philosophy" -Beethoven
"Everyday life is the way" -Wumen
"Do not permit the events of your daily life to bind you, but never withdraw yourself from them" - Wumen
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Re: Math Fun

Postby Carleas » Wed Sep 09, 2015 9:52 pm

James S Saint wrote:Blued puzzled:
"If everyone is thinking this ..."
But what IF they weren't?

Master Logician Puzzle:
"If we assume that only the colors we see apply, then..."
But what if something else is assumed?

You'll note that none of my syllogisms contain either of these antecedents:

Blue Eye Syllogism 1
1) If there is 1 Blue, they leave on day 1, i.e. C(1)=L(1)
2) If it's true that N Blues will leave on day N, then it is true that N+1 Blues will leave on day N+1, i.e. C(N) = L(N) -> C(N+1) = L(N+1)

Given those two statement, we know that C(N) = L(N) for all N >= 1


Blue Eye Syllogism 2
1) Without the oracle's statement, no one can learn their eye color. (given)
2) The oracle speaks on day 1. (given)
3) 1 Blue could not leave before day 1 (from 1 and 2)
4) N blues could not leave before day N (assumed for proof by induction)
5) N+1 blues cannot distinguish their situation from the N blues situation without more information (given)
6) The only way N+1 blues can get information from others is by others leaving or staying (given)
7) Staying only conveys information when the blues who stay could leave (given)
8) N blue staying or leaving doesn't convey information until the end of day N (from 4 and 7)
9) The N+1 blues cannot get information until the end of day N (6 and 8)
10) The N+1 blues cannot leave before day N+1 (5 and 9)
11) IF N blues could not leave before day N, THEN N+1 blues could not leave before day N+1 (4 and 10)
Therefore
12) N blues could not leave before day N for any natural number N >=1 (from 3 and 11, by induction)


Master Logician Syllogism 2
1) The colors each logician can see are part of the set C of known correct answers to the question, "what color is my headband?" (given)
2) A color cannot be deduced from a set of colors (given)
3) Therefore, a color cannot be added to C based on the other members of C (from 2, general to specific)
4) For the problem to be possible, a logician's headband color must be a member of C (given)
5) Therefore, if the color of a logician's headband is not in C, then the problem would be impossible (from 3, 4)
6) The problem is not impossible (given)
7) Therefore, the color of every logician's headband must be a member of C (from 5,6)
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Re: Math Fun

Postby James S Saint » Wed Sep 09, 2015 10:05 pm

phyllo wrote:If the change due was 34.56, the cashier gave back 56.34 instead. That's it in a nutshell. 8)

I think we all agree with that.

If e = 34, the received euros, and
c = 56, the received cents then

the proper change ("entitlement") was said to be
x = c.e => 56.34 => 100c + e, in cents (5634 cents)
x = (100c + e) / 100, in euros
x = c + e/100, in euros

Premise: 2 times the proper change was received plus 5 cents more:
2x + 5, in cents was received.

The received euros is "e" and the received cents is "c", so:
2x + 5 = e + c, wherein each e = 100 cents and each c = 1 cent

So:
2x + 5 = 100e + c, in cents, or
2x + .05 = e + c/100, in euros

and
x = 100c + e, in cents
x = c + e/100, in euros

thus using merely cents,
2(100c + e) + 5 = 100e + c, in cents
100c + e + 2.5 = 50e + c/2
100c - c/2 = 50e - e - 2.5
c(100 -1/2) = e(50-1) - 2.5
99.5c = 49e - 2.5
c = 49e/99.5 - 2.5/99.5, in cents (thus e must be at least 6)

And then another equation is required to finish it and find x.

..edited my booboo.
Last edited by James S Saint on Wed Sep 09, 2015 11:11 pm, edited 3 times in total.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend
 
Posts: 25781
Joined: Sun Apr 18, 2010 8:05 pm

Re: Math Fun

Postby James S Saint » Wed Sep 09, 2015 10:14 pm

Carleas wrote:
James S Saint wrote:Blued puzzled:
"If everyone is thinking this ..."
But what IF they weren't?

Master Logician Puzzle:
"If we assume that only the colors we see apply, then..."
But what if something else is assumed?

You'll note that none of my syllogisms contain either of these antecedents

Yes. Your syllogisms do not because you SKIP OVER the assumptions that you are making. That is why your syllogisms are irrelevant.

Carleas wrote:Blue Eye Syllogism 2
1) Without the oracle's statement, no one can learn their eye color. (given) <= FALSE assumption
2) The oracle speaks on day 1. (given)
3) 1 Blue could not leave before day 1 (from 1 and 2)
4) N blues could not leave before day N (assumed for proof by induction)
5) N+1 blues cannot distinguish their situation from the N blues situation without more information (given)
6) The only way N+1 blues can get information from others is by others leaving or staying (given)
7) Staying only conveys information when the blues who stay could leave (given)
8) N blue staying or leaving doesn't convey information until the end of day N (from 4 and 7)
9) The N+1 blues cannot get information until the end of day N (6 and 8)
10) The N+1 blues cannot leave before day N+1 (5 and 9)
11) IF N blues could not leave before day N, THEN N+1 blues could not leave before day N+1 (4 and 10)
Therefore
12) N blues could not leave before day N for any natural number N >=1 (from 3 and 11, by induction)


Master Logician Syllogism 2
1) The colors each logician can see are part of the set C of known correct answers to the question, "what color is my headband?" (given) <= FALSE assumption
2) A color cannot be deduced from a set of colors (given)
3) Therefore, a color cannot be added to C based on the other members of C (from 2, general to specific)
4) For the problem to be possible, a logician's headband color must be a member of C (given)
5) Therefore, if the color of a logician's headband is not in C, then the problem would be impossible (from 3, 4)
6) The problem is not impossible (given)
7) Therefore, the color of every logician's headband must be a member of C (from 5,6)

You are misstating YOUR presumption as a given premise. Your presumptions are wrong thus your following syllogisms are meaningless.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend
 
Posts: 25781
Joined: Sun Apr 18, 2010 8:05 pm

Re: Math Fun

Postby phyllo » Wed Sep 09, 2015 10:28 pm

x = c + e/100
I gave the correct equation and you turned it around. #-o

This is the answer:
Let P be the price of book in cents
Let A be the amount of change due from 100 euros in cents
A= 10000 - P

Let R be the returned change in cents

R= 2A + 5

The amount of change due can be represented as E.C
Therefore A and R can be written as:

A= 100E + C
and
R= 100C + E

Substitute these into the previous equation (R=2A+5) and you get :

100C + E = 2(100E + C) + 5
which rearranges to give :
C= (199E + 5)/98

The only value of E which results in an integer value for C is 31
E=31 and C=63

Calculate A and P :
A=3163
P=6837

Price of book was 68.37 in euros.
"Who loves not wine, woman and song, remains a fool his whole life long."

"Only the educated are free" - Epictetus
"Music is a higher revelation than all wisdom and philosophy" -Beethoven
"Everyday life is the way" -Wumen
"Do not permit the events of your daily life to bind you, but never withdraw yourself from them" - Wumen
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Re: Math Fun

Postby James S Saint » Wed Sep 09, 2015 10:56 pm

phyllo wrote:
x = c + e/100
I gave the correct equation and you turned it around. #-o

This is the answer:
Let P be the price of book in cents
Let A be the amount of change due [ = x ]from 100 euros in cents
A= 10000 - P

Let R be the returned change in cents

R= 2A + 5

The amount of change due can be represented as E.C
Therefore A and R can be written as:

A= 100E + C
and
R= 100C + E

Substitute these into the previous equation (R=2A+5) and you get :

100C + E = 2(100E + C) + 5
which rearranges to give :
C= (199E + 5)/98

The only value of E which results in an integer value for C is 31
E=31 and C=63

Calculate A and P :
A=3163
P=6837

Price of book was 68.37 in euros.

Actually you turned it around in your answer (marked in red). I had defined the e and c in terms of received, not owed (and underlined it several times).
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend
 
Posts: 25781
Joined: Sun Apr 18, 2010 8:05 pm

Re: Math Fun

Postby phyllo » Wed Sep 09, 2015 11:07 pm

Actually you turned it around in your answer (marked in red). I had defined the e and c in terms of received, not owed (and underlined it several times).
You turned it around by multiplying by 100 in one equation and dividing by 100 in the other. If you define it in terms of cents then both equations would have multiplications by 100.
"Who loves not wine, woman and song, remains a fool his whole life long."

"Only the educated are free" - Epictetus
"Music is a higher revelation than all wisdom and philosophy" -Beethoven
"Everyday life is the way" -Wumen
"Do not permit the events of your daily life to bind you, but never withdraw yourself from them" - Wumen
phyllo
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Re: Math Fun

Postby James S Saint » Wed Sep 09, 2015 11:13 pm

phyllo wrote:
Actually you turned it around in your answer (marked in red). I had defined the e and c in terms of received, not owed (and underlined it several times).
You turned it around by multiplying by 100 in one equation and dividing by 100 in the other. If you define it in terms of cents then both equations would have multiplications by 100.

It was only a matter of defining "e" as what was received versus what was owed.
I defined it as what was received.
You ignored that and redefined as what was due.

That is the only difference (other than me leaving out a later division operation).
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend
 
Posts: 25781
Joined: Sun Apr 18, 2010 8:05 pm

Re: Math Fun

Postby phyllo » Wed Sep 09, 2015 11:17 pm

It was only a matter of defining "e" as what was received versus what was owed.
I defined it as what was received.
You ignored that and redefined as what was due.

That is the only difference (other than me leaving out a later division operation).
You just can't admit that you make mistakes. :-"
"Who loves not wine, woman and song, remains a fool his whole life long."

"Only the educated are free" - Epictetus
"Music is a higher revelation than all wisdom and philosophy" -Beethoven
"Everyday life is the way" -Wumen
"Do not permit the events of your daily life to bind you, but never withdraw yourself from them" - Wumen
phyllo
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Re: Math Fun

Postby James S Saint » Wed Sep 09, 2015 11:29 pm

phyllo wrote:You just can't admit that you make mistakes. :-"

I just did, DS. But my mistakes do not translate into the lack of yours. You screwed up and now can't admit it.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend
 
Posts: 25781
Joined: Sun Apr 18, 2010 8:05 pm

Re: Math Fun

Postby phyllo » Wed Sep 09, 2015 11:49 pm

I have made mistakes in the past and I will make mistakes in the future. 8)
"Who loves not wine, woman and song, remains a fool his whole life long."

"Only the educated are free" - Epictetus
"Music is a higher revelation than all wisdom and philosophy" -Beethoven
"Everyday life is the way" -Wumen
"Do not permit the events of your daily life to bind you, but never withdraw yourself from them" - Wumen
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Re: Math Fun

Postby Arminius » Thu Sep 10, 2015 12:58 am

James, please! Note: Phyllo is right. You have to admit that you made mistakes in the said case.
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Re: Math Fun

Postby James S Saint » Thu Sep 10, 2015 2:10 am

Arminius wrote:James, please! Note: Phyllo is right. You have to admit that you made mistakes in the said case.

Okay wake up!

I mentioned the exact mistakes that I made. He denied the ones that he made (possibly still unaware).

Neither of us are claiming to be perfect.

Get your shit straight if you are going to get into the middle.

NOTE!: Phyllo made a mistake in his original complaint because he didn't realize the definition of "e" that was being discussed. He intruded, unaware of the details. End of that story. He later provided the answer .. fine. I have no disagreement with his answer. I provided just short of that answer (trying to not give it all away). In doing that, I made one division error that I pointed out and corrected.

This is NOT an issue of either one of us being egotistical. It is an issue of phyllo not seeing that he had overstepped into an already established discussion (thus redefining the terms). After that point, there was no right and wrong, merely two rights that were different in their nature (due to differently defined terms; specifically "e" and "c"). And then you stepping in, completely blind and making an ... of yourself.
Last edited by James S Saint on Thu Sep 10, 2015 7:27 pm, edited 1 time in total.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend
 
Posts: 25781
Joined: Sun Apr 18, 2010 8:05 pm

Re: Math Fun

Postby Arminius » Thu Sep 10, 2015 2:42 am

James S Saint wrote:
Arminius wrote:James, please! Note: Phyllo is right. You have to admit that you made mistakes in the said case.

Okay ....

I mentioned the exact mistakes that I made.

Yes. It is okay.
Last edited by Arminius on Thu Sep 10, 2015 3:06 am, edited 2 times in total.
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Re: Math Fun

Postby phyllo » Thu Sep 10, 2015 2:45 am

I shall be magnanimous and let James have the pleasure of demonstrating the last part of the solution - calculating E or C from his final equation. O:)
"Who loves not wine, woman and song, remains a fool his whole life long."

"Only the educated are free" - Epictetus
"Music is a higher revelation than all wisdom and philosophy" -Beethoven
"Everyday life is the way" -Wumen
"Do not permit the events of your daily life to bind you, but never withdraw yourself from them" - Wumen
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Re: Math Fun

Postby James S Saint » Thu Sep 10, 2015 2:50 am

phyllo wrote:I shall be magnanimous and let James have the pleasure of demonstrating the last part of the solution - calculating E or C from his final equation. O:)

Just put your answers in reverse, into the equation that I provided. You will get the same result. I merely had e and c defined (before you intruded) to be the opposite of what you chose ... no big deal. It works either way.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend
 
Posts: 25781
Joined: Sun Apr 18, 2010 8:05 pm

Re: Math Fun

Postby phyllo » Thu Sep 10, 2015 3:19 am

Cool. =D>

By the way, I'm not sure how you defined DS. Does it stand for dipstick, dip shit, dumb shit or something else? I would like to know in case you use it again in the future. :D
"Who loves not wine, woman and song, remains a fool his whole life long."

"Only the educated are free" - Epictetus
"Music is a higher revelation than all wisdom and philosophy" -Beethoven
"Everyday life is the way" -Wumen
"Do not permit the events of your daily life to bind you, but never withdraw yourself from them" - Wumen
phyllo
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Posts: 10110
Joined: Thu Dec 16, 2010 1:41 am
Location: ->.

Re: Math Fun

Postby James S Saint » Thu Sep 10, 2015 3:29 am

phyllo wrote:I would like to know in case you use it again in the future. :D

Yeah, I know...

.. Dear Saint. :-"
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend
 
Posts: 25781
Joined: Sun Apr 18, 2010 8:05 pm

Re: Math Fun

Postby Carleas » Thu Sep 10, 2015 3:42 am

James S Saint wrote:1) Without the oracle's statement, no one can learn their eye color. (given) <= FALSE assumption

First, it's important to note that this premise is not that same as "If everyone is thinking this ..." It's not logically equivalent, and the former does not implicitly assume the latter.

Second, this is a given. We know this because 1) they must deduce anything deducible, and 2) they have been on the island for an infinite number of days prior to the Guru speaking. If there were a way for them to deduce their eye color prior to the Guru speaking, they would have. The problem goes to length to rule out other means of learning their eye color: there are no mirrors, they can't otherwise communicate, they don't already know it. In infinite time before the Guru speaks, nothing has let them learn their eye color, and nothing else happens on the island that could communicate their eye color to them.

James S Saint wrote:1) The colors each logician can see are part of the set C of known correct answers to the question, "what color is my headband?" (given) <= FALSE assumption

Similarly to the above, this is not logically equivalent to "If we assume that only the colors we see apply, then..."

But to address the objection, I think it must be a failure of communication. Each color of headband that any logician can see is the correct answer for at least one logician in the circle to the question "what color is my headband?" That's tautologically true. Each color of headband that any logician can see is worn by at least one logician: the logician that is wearing it. Sorry if I was unclear in expressing this premise, but properly stated, it cannot be false.
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Re: Math Fun

Postby James S Saint » Thu Sep 10, 2015 9:43 am

Carleas wrote:
James S Saint wrote:1) Without the oracle's statement, no one can learn their eye color. (given) <= FALSE assumption

First, it's important to note that this premise is not that same as "If everyone is thinking this ..." It's not logically equivalent, and the former does not implicitly assume the latter.

Never said that it was. It is a new presumption. Your next presumption was "if he is thinking blue, then...".

Carleas wrote:Second, this is a given. We know this because

Ummm... no. The only way something is a "given" is if it is GIVEN. If there is a "because we know that....", then it was obviously not a given, but rather a deduction/assumption.

Carleas wrote:1) they must deduce anything deducible,

That is why you failed to solve it. They had many deducible things other than the one you presumed them to start with (ref: "If he is thinking blue, then..."). They MUST immediately deduce anything deducible and there really are many things deducible (I showed some at the time).

Carleas wrote:and 2) they have been on the island for an infinite number of days prior to the Guru speaking. If there were a way for them to deduce their eye color prior to the Guru speaking, they would have.

And that was merely a fallacy of the puzzle. The intent was that they could not deduce until the guru spoke, but that was not the reality of how it was setup (similar to the master saying "it is solvable" when it actually is not).

Carleas wrote:The problem goes to length to rule out other means of learning their eye color: there are no mirrors, they can't otherwise communicate, they don't already know it.

But they did not rule everything out. They merely attempted to. They didn't rule out that the "perfect logicians" already knew that puzzle and thus already knew how to deduce far ahead of the timing. Obviously if you were there today as that scenario began, you would know when most of the people would be leaving long before your proposed turn. And so would they. The only thing that the guru provided was a moment to begin, and I am not sure that they necessarily needed that.

Carleas wrote: In infinite time before the Guru speaks, nothing has let them learn their eye color, and nothing else happens on the island that could communicate their eye color to them.

I don't think it said anything about an "infinite time", but like I said, there was a solution already there. Perfect logicians would have already figured it out before the guru spoke. The puzzle wasn't stated properly for what they wanted. And I don't know that it could have been.

Carleas wrote:
James S Saint wrote:1) The colors each logician can see are part of the set C of known correct answers to the question, "what color is my headband?" (given) <= FALSE assumption

Similarly to the above, this is not logically equivalent to "If we assume that only the colors we see apply, then..."

And similar to above, I never said that it was. The way that is worded is begging the question of whether you meant "known by everyone" or merely "known by the others". The word "known" infers an erroneous premise.

Carleas wrote:But to address the objection, I think it must be a failure of communication. Each color of headband that any logician can see is the correct answer for at least one logician in the circle to the question "what color is my headband?" That's tautologically true. Each color of headband that any logician can see is worn by at least one logician: the logician that is wearing it. Sorry if I was unclear in expressing this premise, but properly stated, it cannot be false.

Yes, but that is kind of irrelevant unless you were intended to use it in an erroneous way. As you said, it is tautologically true if you meant it that way, so why even bring it up.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
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Re: Math Fun

Postby Carleas » Thu Sep 10, 2015 2:43 pm

James S Saint wrote:They didn't rule out that the "perfect logicians" already knew that puzzle and thus already knew how to deduce far ahead of the timing. Obviously if you were there today as that scenario began, you would know when most of the people would be leaving long before your proposed turn. And so would they. The only thing that the guru provided was a moment to begin, and I am not sure that they necessarily needed that.

This tells me that you don't understand the logic of the problem. The Guru's statement does not "only [...] provide[] a moment to begin", it provides crucial information that makes a logical deduction possible that was impossible before (in the proof by mathematical induction, her statement provides the base case).

Again, take the situation of 2 islanders who don't know their eye color, but are familiar with this problem. Without the guru telling them that she sees at least one islander with some eye color, neither islander can deduce his eye color. Unless when you say they "already knew the puzzle" you really mean they "already possessed the information that the Guru provides".

EDIT: alternatively, replace the Guru's statement with, "Begin deducing your eye color now!" If the Guru had said that, no one could deduce their eye color.
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Re: Math Fun

Postby James S Saint » Thu Sep 10, 2015 2:48 pm

Carleas wrote:
James S Saint wrote:They didn't rule out that the "perfect logicians" already knew that puzzle and thus already knew how to deduce far ahead of the timing. Obviously if you were there today as that scenario began, you would know when most of the people would be leaving long before your proposed turn. And so would they. The only thing that the guru provided was a moment to begin, and I am not sure that they necessarily needed that.

This tells me that you don't understand the logic of the problem. The Guru's statement does not "only [...] provide[] a moment to begin", it provides crucial information that makes a logical deduction possible that was impossible before (in the proof by mathematical induction, her statement provides the base case).

Again, take the situation of 2 islanders who don't know their eye color, but are familiar with this problem. Without the guru telling them that she sees at least one islander with some eye color, neither islander can deduce his eye color. Unless when you say they "already knew the puzzle" you really mean they "already possessed the information that the Guru provides".

Don't reintroduce your blindness on that one too. Again, it is irrelevant that the syllogism part of your proposal works. Other syllogisms work even better.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
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Posts: 25781
Joined: Sun Apr 18, 2010 8:05 pm

Re: Math Fun

Postby Carleas » Thu Sep 10, 2015 2:50 pm

James, it looks like your position is based on the possibility that someone can logically deduce the color of their eyes based solely on the color of the eyes of the people around them. Is that right?
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Re: Math Fun

Postby James S Saint » Thu Sep 10, 2015 2:55 pm

Carleas wrote:James, it looks like your position is based on the possibility that someone can logically deduce the color of their eyes based solely on the color of the eyes of the people around them. Is that right?

I don't remember all of the detailed stipulations of that one. I'm not interested in starting it up again.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend
 
Posts: 25781
Joined: Sun Apr 18, 2010 8:05 pm

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