Jon Letendre

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1 hour ago, BaalChatzaf said:

Forget drawings.  The proof is abstract and mathematical.  Drawings are crutches for the logically feeble.

Heh.

Why is it always "crutches"?

Also sometimes "cartoons."

When it's a drawing that they understand, it's a serious "diagram," but when they don't get it, it's a stupid crutch cartoon.

And they also misunderstand its function. They act as if WE need and are relying on the drawings and are deriving our opinions from them. The reality is that we are presenting them as visual aids so that people with low visualizing skills can grasp what we can visualize without the drawings. So, there is some truth that the images are crutches, not for us, but for Bob, who, despite our offering, has nevertheless managed to remain mentally incapacitated due to rejecting our devices of assistance. Even with the drawings, he doesn't get it!

Like Tony and Merlin, is he so visuospatially/mechanically incompetent that he treats visual information as not being a valid means of cognition? It seems so.

J

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1 hour ago, BaalChatzaf said:

Case 2.  The starting point  is   (x-lat, x-long)  where x-lat is greater than 0 and less than 90.   Assume  x-long = 0 without loss of generality.   Now leg 1: (x-lat, 0)  to (x1, 0)  where x1 < x-lat  and greater or  equal to 0.   Leg  2  (x1,0)   (x1, y1)  where  y1 > 0  but < 360.   That means leg2 moved us to a different point with the same latitude.  Now leg 3  northward by the same distance.  This gets is to (x2, y1) because going north means following a meridian of longitude.   Notice that x2 not = x1.   The final destination is (x2, y1)  which is different from (x-lat, 0).  So we do not end up at the same place if we started out from a point that was not the pole. 

Q.E.D.

 

Bob, you silly, stubborn doofus, do the math.

Dont do the math starting from a wrong location out of stupid stubbornness. And don't impose the wrong math on the problem.

Do the math starting from one of the right locations near the South Pole.

Jon Letendre provided the ring of latitude of the right starting points. Read my reposting of his post below, and check the math yourself.

 

 

19 hours ago, Jon Letendre said:

The green circle of latitude is located X miles north of the South Pole.

The radius of the green circle is X miles, the diameter, 2*X miles.

The circumference of the green circle is 2*X*pi miles.

“Walk west 1 Mile is the circumference of the green circle” stated mathematically,

1 mile = 2*X*pi

From that we can solve for X:

divide each side of equal sign by 2.

1/2 = X*pi

divide each side by pi, and switch sides.

X = 1 / (2pi)

pi is 3.14159265 ... estimate of X:

X = 1 / 6.2831853

calculator

X = 0.1591549

So Jonathan’s yellow circle of latitude is located 1+ 1 / (2pi) miles, or 1.1591549 miles, north of the South Pole.

 

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3 hours ago, BaalChatzaf said:

That last leg is NOT on the same line of longitude as the first leg.  Why? Because the second leg  is a traverse along a line of latitude  which changes the longitude.  

 

Bob, you like Elon Musk, right? In fact, you kind of have a bit of a crush on him, if I recall correctly.

Anyhoo, did you know that this puzzle is one his favorites, and that he is alleged to have used it in job interviews?

You won't listen to us because we're common trash dunces, but what about listening to your genius hero Musk?

It's even in his authorized biography.

No? Still too stubborn?

J

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2 hours ago, BaalChatzaf said:

The original problem was walk a mile south walk a mile west (was it east -- no matter)  walk a mile north.  The east-west walk  is less than the length of line of latitude  reached by the southword leg so that the return trip is along a  different line of longitude. 

Nowhere in the puzzle is stated that the east-west walk must be less than the lenght of line of latitude, that is a condition you yourself arbitrarily impose. In fact, valid solutions to the original puzzle include versions in which the walk is many times the length of line of latitude. This becomes then a relatively very small circle, but why shouldn't that be allowed?

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2 hours ago, Max said:

 

Nowhere in the puzzle is stated that the east-west walk must be less than the lenght of line of latitude, that is a condition you yourself arbitrarily impose. In fact, valid solutions to the original puzzle include versions in which the walk is many times the length of line of latitude. This becomes then a relatively very small circle, but why shouldn't that be allowed?

Yeah, like Michael Palin circling the pole 264 times in the example I took the time to type out for Bob's benefit (along with an embedded video I took the time to cue up to the exact relevant moment), which he dismissed by saying he doesn't watch videos.  Then he insults everyone by calling them "logically feeble".  Imagine getting stuck with an idiot like Bob as a teacher.  Personally, I don't have to imagine, I went through it. 

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5 hours ago, 9thdoctor said:

Bob, you're a knucklehead.

I'm reading consecutively from where I last posted yesterday.  Ninth's post ends a page, so I've had no glimpse of what, if anything, Bob responded.

If he's responded in true-to-form fashion, he'll have said something along the lines of his having a high IQ, therefore not being a "knucklehead."

However, Mr. Brilliant - especially at math - doesn't seem to be able to grasp that about .159... miles north of the South Pole, one could circumambulate the globe walking one mile west. (Also on smaller circles the circumference of which is a whole-number fraction of one mile.)

Ellen

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3 hours ago, Jonathan said:

 

Bob, you like Elon Musk, right? In fact, you kind of have a bit of a crush on him, if I recall correctly.

Anyhoo, did you know that this puzzle is one his favorites, and that he is alleged to have used it in job interviews?

You won't listen to us because we're common trash dunces, but what about listening to your genius hero Musk?

It's even in his authorized biography.

No? Still too stubborn?

J

It was a brief infatuation. I have come see that E.M.  is a Crony Capitalist and his management of Tesla Motors is an abomination.  It is true that his is brighter than most old line corporate capitalists,  but his intellectual glitz cannot hide two things   1. He lusts and longs for government funded projects  and 2.  His intellectual reach  exceeds his intellectual grasp.   

I regard  Captain Bullshit  as an entertainment, not the second coming of John Galt. 

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34 minutes ago, Ellen Stuttle said:

I'm reading consecutively from where I last posted yesterday.  Ninth's post ends a page, so I've had no glimpse of what, if anything, Bob responded.

If he's responded in true-to-form fashion, he'll have said something along the lines of his having a high IQ, therefore not being a "knucklehead."

However, Mr. Brilliant - especially at math - doesn't seem to be able to grasp that about .159... miles north of the South Pole, one could circumambulate the globe walking one mile west. (Also on smaller circles the circumference of which is a whole-number fraction of one mile.)

Ellen

if he starts out from a pole he will end up back at the same place. Look at case 2 where he starts at at a non polar point.  Unless step 2 of his journey ends at exactly the same point step  1 ended he does not get back because terminates step 2 and a different meridian of longitude  form the meridian he was on at step 1. 

 

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1 hour ago, BaalChatzaf said:

Unless step 2 of his journey ends at exactly the same point step  1 ended he does not get back

 

Bob, news flash: that's exactly the way it works!  Step 2 ends where step 1 ended.  From longitude 0 and .159 miles from the south pole (in an earlier post I used feet), travel west for one mile and you will land on...brace yourself...longitude 0 and .159 miles from the south pole. 

Now give your forehead a gigantic slap, then type out an apology to all the people on this thread who you insulted. 

h431B1E55

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26 minutes ago, BaalChatzaf said:

if he starts out from a pole he will end up back at the same place. Look at case 2 where he starts at at a non polar point.  Unless step 2 of his journey ends at exactly the same point step  1 ended he does not get back because terminates step 2 and a different meridian of longitude  form the meridian he was on at step 1. 

And why shouldn't step 2 end exactly at the same point step 1 ended, if that gives a valid solution to the puzzle? It may be a surprising move, but it satisfies all the conditions of the original question.

 

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8 hours ago, 9thdoctor said:

 

Bob, new flash: that's exactly the way it works!  Step 2 ends where step 1 ended.  From longitude 0 and .159 miles from the south pole (in an earlier post I used feet), travel west for one mile and you will land you on...brace yourself...longitude 0 and .159 miles from the south pole. 

As I'd said in the post Bob replied to.   How many repetitions will be needed before he pays attention?

Ellen

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I just managed to understand the infinite part. My brain is telling me there's even more to understand.

--Brant

boy genius

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20 hours ago, BaalChatzaf said:

It was a brief infatuation. I have come see that E.M.  is a Crony Capitalist and his management of Tesla Motors is an abomination.  It is true that his is brighter than most old line corporate capitalists,  but his intellectual glitz cannot hide two things   1. He lusts and longs for government funded projects  and 2.  His intellectual reach  exceeds his intellectual grasp.   

I regard  Captain Bullshit  as an entertainment, not the second coming of John Galt. 

The point of my post wasn't to get you to open up about your feelings for your ex-boyfriend, but to get you to recognize that he and others, who are infinitely more intelligent than you, long ago grasped the solutions to the puzzle that you, so far, have been too stupid to grasp.

J

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I‘ ve made some calculations for the general case with arbitrary distance Z for the 3 legs of the trip, instead of 1 mile. The calculations are made for an idealized Earth as a perfect sphere, with radius R = 6400 km. See the first figure for the meaning of the different symbols, the drawing is not to scale!

earth.thumb.jpg.ca24aad10d0896548d6460d2408491fb.jpg

The trip starts anywhere on the upper circle with radius r2, goes southwards along a meridian over a distance Z km, then westwards along a circle with circumference Z and radius r1 = Z / 2π, and then back northwards.

 

2π * r1 = Z r1 = Z / 2π

a2 + r12 = R2 a = (R2 – r12)

sin (β) = r1 / R

sin (β + γ) = r2 / R = sin (β) * cos (γ) + cos (β) * sin (γ)

= (r1 / R) * cos (Z / R) + (a / R) * sin (Z / R)

r2 = r1 * cos (Z / R) + ( (R2 – r12)) * sin (Z / R)

 

With these expressions we can now draw a graph of the different variables r1, r2, M and M + Z as a function of Z, see the second figure.*) At the left, for relatively low values of Z, these variables have a linear dependence on Z, but for larger values of Z especially r2 is going to deviate, reaches a maximum and than decreases again to zero, meaning that the radius of the upper circle can increase to the radius of the Earth and then diminishes as the circle becomes smaller when it moves to the North. Finally it shrinks to a point, the North Pole, larger values of Z therefore have no physical meaning.

 

In the next figure *) the first 20 kilometers for Z are given. Here all the variables are quite linear and M r1, and M + Z ≈ r2. For small Z/R the expression for r2 becomes

 

r2 r1 – r1* Z2/(2!*R2) + R (1 – r12/R2) * (Z/R – Z3/(3!*R3)) =

= r1 + Z + O(Z2/R2)

 

as you’d expect when the curvature of the Earth may be neglected. In the graph the value of 1 mile = 1.609344 kilometers is indicated, with the corresponding values for r1 and r2. The large number of decimals seems to be overdone, but this is just to show how small the difference between the exact values and the approximated values in this case is.

 

*) Uh oh, too big to upload here, I'll try it in a separate message

 

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On 1/6/2019 at 2:05 PM, Jonathan said:

The point of my post wasn't to get you to open up about your feelings for your ex-boyfriend, but to get you to recognize that he and others, who are infinitely more intelligent than you, long ago grasped the solutions to the puzzle that you, so far, have been too stupid to grasp.

J

which puzzle is that?

 

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Hm, uploading the third graph doesn't work... In the second one some lines have disappeared when I made it smaller to allow it to upload. Do I have an  upload limit for today or so?

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1 hour ago, BaalChatzaf said:

which puzzle is that?

 

Are you getting even dumber? Perhaps Merlin and Tony have rubbed off on you, infected you with their idiocy.

J

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3 hours ago, Jonathan said:

Are you getting even dumber? Perhaps Merlin and Tony have rubbed off on you, infected you with their idiocy.

J

Bob's not dumb. It's just as a literalist and physicalist he doesn't do abstract reasoning except, I'd suppose, with mathematics. As a compensation he denigrates philosophy and extols science. Science, however, rests on philosophy even into the ethics, aka integrity.

--Brant

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2 hours ago, Brant Gaede said:

Bob's not dumb. It's just as a literalist and physicalist he doesn't do abstract reasoning except, I'd suppose, with mathematics. As a compensation he denigrates philosophy and extols science. Science, however, rests on philosophy even into the ethics, aka integrity.

--Brant

Science parted company with metaphysics  over 100 years go.  The only philosopher  that  physicists mention without spitting is Carl Popper. 

 

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9 hours ago, BaalChatzaf said:

Science parted company with metaphysics  over 100 years go.  The only philosopher  that  physicists mention without spitting is Carl Popper. 

 

Like I said.

Mention Ayn Rand and Bob spits.

In the context of an Objectivist forum metaphysics is reality. Bob has never explained what he means by it.

Reality, reason and integrity. Or, metaphysics, epistemology and ethics (respecting scientific inquiry).

--Brant

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10 hours ago, BaalChatzaf said:

Science parted company with metaphysics  over 100 years go.  The only philosopher  that  physicists mention without spitting is Carl Popper. 

 

Bob, are you blind?  I don't mean the question as an insult, it's a genuine question.  You won't watch videos, you misspell Karl Popper's name (suggesting you use voice to text), and you say you're involved in making recorded books for the blind. 

In any event, below is my first post on this thread.  I hadn't yet figured out how the South Pole solution works.  Notice that I didn't insult anyone, and if you go back you'll find that no one suggested I was a dummy for not getting it right away. 

On 12/30/2018 at 8:21 PM, 9thdoctor said:

I'm a bit confused.  It seems to me that since the lengths are equal, the three points must describe an equilateral triangle, so 60 degrees per side.  If you walk south then turn west, isn't the angle of that turn 90 degrees?  You won't end up at the same starting point.  I can see how it works at the north pole, but since you're not actually touching the south pole, and if you were to touch the south pole there would be no way to travel west to satisfy step two (once there you can only go north)...am I missing something?

Compare this to the way you behaved, and the reaction you got. 

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3 hours ago, Brant Gaede said:

 

Mention Ayn Rand and Bob spits.

 

not true.  She provided a good expression of what I  was thinking about (ugh!)  government, politics and the state.  On scientific and mathematical issues  she was a great Hollywood script writer.

 

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1 minute ago, BaalChatzaf said:

not true.  She provided a good expression of what I  was thinking about (ugh!)  government, politics and the state.  On scientific and mathematical issues  she was a great Hollywood script writer.

 

Who interviewed Robert Oppenheimer apropos a script on the invention of the atomic bomb. He was used to develop the Dr. Stadler character's good parts. She thought Oppenheimer was a fascinating man.

My uncle's wife did a lot of secretarial work in the late 1940s for the nuclear physicists at Livermore who had previously worked on the Manhattan Project.

--Brant  

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11 minutes ago, BaalChatzaf said:

not true.  She provided a good expression of what I  was thinking about (ugh!)  government, politics and the state.  On scientific and mathematical issues  she was a great Hollywood script writer.

 

There was no effective "moral revolution" in AS, though she tried like hell. What she did do was get rid of a lot of reader guilt for natural human selfishness, but it was more of a masculine than feminine orientation. She didn't put enough flesh on the bones. It was a great start, however. Rational self interest is the ethical and moral bedrock. The social and family aspects need more work. You can't take care of whom you love if you don't take care of yourself.

--Brant

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