Math Fun

They certainly know how to take the fun out of math. :evilfun:

I tried to get James to discuss the Blue Eye problem privately way back, but he stopped replying. Which is just to say, I’m to blame for this disruption.

I’m having fun. Maybe if you developed a strong opinion about the Blue Eye problem or the Master Logician problem, you’d have fun too!

Two egos trying to wrestle each other to the ground.

Nobody else thinks that it’s fun.

Get over yourselves.

Shove it up your ass, wuss. You hide then try to jump in to make big of yourself. Then jump away again, never facing reality. Get over your insecurity and get off your pretentious high horse. Be man enough to just be part of the fun and you won’t trigger so much lack of it.

LOL

It’s too easy.

Take your own advice chump. You were the one who came onto this thread with demeaning rhetoric … that you are still spewing.

LOL

gone south

Carleas,

It dawned on me that you are making the same mistake as Newton and a great many science philosophers ever since. Newton heard about the idea of a “gravity force”, from Hooke I think it was. If the force called gravity was real, a certain reasoning would follow, a syllogism of logic. He then made measurements to verify the reasoning. Because his measurements turned out to substantiate the reasoning that stemmed from the idea of a gravity force, it became scientific LAW that gravity was due to the “force of gravity”. Most people today still believe in that force of gravity because “it is proven”.

But then later Einstein comes along and proposes the idea of Relativity. Einstein explains that the “force of gravity” supposedly reaching out to affect things at a distance doesn’t really make much sense and what makes better sense is the idea that time and distance are merely relative to an observer. From that, the effect of gravity can be logically explained as a “warping of spacetime” rather than a “force of gravity”. Again working out the logic, the syllogism, based upon the assumption of warping rather than forcing, a proposed “theory” (rather than “law”) is formed. Measurements are made that verify that the warping is even more accurate than the forcing. Einstein takes the forefront being the genius and “Father of Modern Physics”, putting Newton down.

In both cases, an assumption was made, logic was constructed, and measurements were made to confirm that the priori assumption was true. And in both cases, their assumptions turned out to actually be false. There is no gravity force, nether is spacetime warped.

You are doing that exact same thing with those puzzles. You begin with “if we assume that … then make this syllogism … then we get a result that solves the puzzle. Therefore the assumption must have been true.”

That video that I showed spoke of the same issue, just because your theory (assumptions and following logic) matches the “puzzle constrictions” doesn’t mean that your theory is correct. This is something that science has encountered enough to be very aware of at this time. Thus they demand “falsifiability”, requiring that nothing counter could possibly be true. And that is what I am requiring of you in those puzzles, because I can already see possible counter true theories to the ones you propose.

If P → Q
Q
therefore P
petitio principii

All I am really doing is demanding that you be modern-day scientific in your method.

…and I think that I’ll make a separate thread for this.

No, I’m not. First, I’m dealing with a completely abstract problem whose entire set of parameters is known and laid out explicitly. This isn’t a scientific inquiry, it’s a logical inquiry.

And the thing that I’m assuming is not a theory of the problem, it’s a fundamental aspect of the given logical structure. That the islanders don’t have enough information to deduce their eye color prior to the guru speaking is the whole point of the problem. It’s solution is counter-intuitive because they don’t have enough information before the guru speaks, and it looks like the guru isn’t providing any new information.

To be clear, and to state again the assumption you’re complaining about in the Blue Eyes problem: an islander cannot learn his eye color solely from observing the eye color of another islander. I maintain that it is a given of the problem, in the same way that the normal strictures of logic are a part of the set of givens of this problem.

That is why those two puzzles are not legitimate puzzles. And realize that every “logic/math structure” must be independently proven before accepted by logicians/mathematicians.

Having a given in a math puzzle that 2+2=3 disallows the puzzle from being properly resolved regardless of it being a “given”.

And there is no actual distinction between good science and good logic other than one ends by saying “see!” in the physical sense rather than merely the mental sense.

Petitio Principii, If P → Q

That’s false. The most basic aspects of logic are simply defined, they are not and cannot be proven using logic. A system cannot prove itself.

It just isn’t provable that Y doesn’t follow from X alone.

Right, but “2+2=3” and “my eye color does not follow as a logical consequence of your eye color” are not comparably flawed starting premises.

[EDIT: typo]

A declared definition IS irrefutable LOGIC. There is no true or false determination. It is a given, thus “proven independently of all else”; “Logically true by definition.”

But take it up in the other thread.

You seem to be rejecting the statement “my eye color does not follow as a logical consequence of your eye color” as a given of the form you describe. Hopefully you agree that the statement “X does not follow from Y alone” is such a statement, something inherent in the structure of logic that doesn’t need to be independently proven?

The other thread does not address the issue we’re discussing here. The premise of that thread (that my argument is of the form P → Q , Q |- P) is a misunderstanding of my argument. The idea that the methods used in this purely logical problem are the same as the methods used in experimental physics is a misunderstanding of the difference between formal logic and observation, between mathematical induction and scientific induction.

Here you can see a large rectangle, consisting of 10 squares:

rechteck_mit_zehn_quadraten.gif
How big are the sides of each square at least, if they are all different in size and integer (thus: in whole numbers)?

I believe that YOU are misunderstanding your argument (by not seeing that you are skipping a relevant beginning of it). But discuss it on the proper thread.

To rephrase:
What is the least size of each square if they are all different integer sizes?

You are allowed to choose the least size of the sides of each square, but the size should be integer, thus a whole number.

[tab]Choosing the least size is actually part of the task. Knowing you, I am sure that you are going to find the right number for the least size.[/tab]

James, your thread is not about our conversation around the Blue Eye problem. You started a thread at best tangentially related to the discussion, and I’m not interested in that tangent (not least because it misrepresents my positions and our disagreement).

But, to repeat, and ask pointedly: do you agree that the following two propositions are true:

  1. X does not follow from Y alone
  2. my eye color does not follow as a logical consequence of your eye color alone

I’m pretty sure this isn’t what you mean, but it’s true:
[tab]1, because that’s the smallest (positive) integer.

Perhaps the question is better posed like this: ]
Suppose the smallest square is 1x1. How big is the largest square?

Is that the same problem?[/tab]

Be careful, because the following tab contains parts of the solution process:
[tab]Choosing the most qualified integer is alraedy part of the task. At first you have to derive equations from the diagram, then you must pay attention to some subtleties, then you have to solve the equations, and after that you should choose the most qualified integer … and so on.

For reasons of simplification you should choose “1” as the most qualified integer for one variable.[/tab]