< Earlier Kibitzing · PAGE 234 OF 234 ·
|Jul-11-14|| ||Sneaky: <If you look inside the computer at the way it works, you find that it keeps track of those nests by counting *all* the steps. So nesting doesn't eliminate the difficulty.> You understand my point, al wazir. |
Had I picked a minuscule number, like 10 to the power of a trillion, then there would be no problem whatsoever. But I picked the most famous of the meaninglessly large numbers, a googolplex.
A number so big, that nests inside nests inside nests never seem to even get into the right ballpark. A googolplex is so ridiculously huge that the entire universe is not even big enough to construct a computer that would theoretically count up to it, given indefinite time. At least, that's my thesis. If somebody could explain how it could be done, I'm all ears.
|Jul-11-14|| ||PinnedPiece: <googolplex>: Well, it seems we are discussing 64-bit integer counters and stack depth limitations, which is what I referred to above.|
Anyway, back to messages from the Cosmos:
Arecibo confirms Australia's Parkes Observatory detection of milisecond bursts in the "D" band -- 1.3Ghz to be exact. The nature of these signals is TOTALLY STUMPING the astrophysics community.
So of course any speculation we want to make may be of interest!
<The split-second burst of radio waves discovered through the Arecibo radio telescope has given scientists new evidence of the rare, mysterious pulses emanating from deep outer space ¨C well beyond the ends of the galaxy. Published July 10 in The Astrophysical Journal, the ˇ°fast radio burstˇ± is the first of similar sounds to be detected by an installation other than the Parkes radio telescope in Australia.
ˇ°Our result is important because it eliminates any doubt that these radio bursts are truly of cosmic origin,ˇ± said Victoria Kaspi, an astrophysics professor at McGill University in Montreal and principal investigator for the pulsar-survey project that detected this fast radio burst. ˇ°The radio waves show every sign of having come from far outside our galaxy ¨C a really exciting prospect.ˇ±
Although <<>exact origins for the radio wave bursts are still an enigma for astrophysicists>, proposed possibilities include evaporating black holes, merging neutron stars, or flares from extremely powerful deep-space magnetic fields.
ˇ°It was a single pulse ¨C additional observations of the same direction on the sky have shown nothing,ˇ± said James Cordes,
Indeed, a true scientific stumper.
If from an intelligent entity, such a signal doesn't HAVE TO be an attempt at communication...
My speculation is this: It's a type of narrow-beam radar signal that happened to cross earth's path:
<D- Band (L-Band Radar)
This frequency band (1 to 2 GHz) is preferred for the operation of long-range air-surveillance radars out to 250 NM (ˇÖ400 km). They transmit pulses with high power, broad bandwidth and an intrapulse modulation often. Due to the curvature of the earth the achievable maximum range is limited for targets flying with low altitude. These objects disappear very fast behind the radar horizon.
In Air Traffic Management (ATM) long-range surveillance radars like the Air Route Surveillance Radar (ARSR) works in this frequency band. Coupled with a Monopulse Secondary Surveillance Radar (MSSR) they use a relatively large, but slower rotating antenna. The designator L-Band is good as mnemonic rhyme as large antenna or long range.>
The properties of electromagnetic pulses are going to be the same everywhere...and if we have found an effective radar signal range, others can too.
|Jul-12-14|| ||al wazir: <PinnedPiece>: I think the "intelligent entity" theory is a long shot. Those bursts have been seen coming from different directions, i.e., from different galaxies. It would be a one-in-a-googol coincidence if *two* different extra-terrestrial species decided to send out signals reaching us at essentially the same time.|
|Jul-12-14|| ||Sneaky: <Indeed, a true scientific stumper. If from an intelligent entity, such a signal doesn't HAVE TO be an attempt at communication... My speculation is this: It's a type of narrow-beam radar signal that happened to cross earth's path> This is all so reminiscent of the pulsar mystery from 1967, when the signal was discovered and nicknamed LGM-1 for "little green men". The conclusion by some was that it was some sort of extraterrestrial beacon used for navigation, or something like that. Then later we learned about the pulsar phenomenon.|
So it's a great and very apropos piece of science news that's bound to teach us something new, but I'm going to curb my hopes for first contact.
|Jul-12-14|| ||Sneaky: <Al Wazir>
I located the exact cause of a misunderstanding between us. When I wrote <write a computer program that runs on any computer in the world> I meant to say, write a computer program that will run on any single computer you can name. (The giant IBM mainframe SAGE, the computer that Cern uses for the Large Hadron Collider, whatever you choose.) I believe you misinterpreted that statement to imply that the program should be universally compatible with all hardware.
And of course <PinnedPiece> is right when he wrote <If [64-bit counters and stack depth] weren't a problem, C++ could easily handle the challenge.> That's sort of the point: the type of stack depth that you would require would be so ridiculously enormous, that there isn't enough mass in the universe to construct such a device. Not even close.
Of course you can easily write a Turing Machine program that can count to a googolplex, because Turing Machines are just mathematical constructs said to have "infinite strips of tape" and so they have infinite stack depth. That's why I went out of my way to specify "any computer in the world". I should have worded that better, reading it again I see why it was confusing.
|Jul-12-14|| ||heuristic: <If you look inside the computer at the way it works, you find that it keeps track of those nests by counting *all* the steps. So nesting doesn't eliminate the difficulty>|
not to be pedantic, but your description does not match actual implementation.
the "way it works" is that two "registers" will be the loop counters.
MOV A, #00
MOV R1, #100 ; outer loop
MOV R2, #100 ; inner loop
CPL A, #01 ;do something
DJNZ R2, loop0 ; repeat until R2=0
DJNZ R1, loop1 ; repeat until R1=0
(simplified ISA for pedagogical purposes!)
note that no one register has the "total".
sneaky and aw are thinking of digital hardware.
pp and I are thinking of stored program computers.
the comments for both perspectives are correct.
|Jul-18-14|| ||johnlspouge: An evil king decides that he will put all his subjects in a long line, so that each subject can only see all subjects in front of them. The king has red or blue hats placed at random on his subjects' heads, and demands that starting at the back of the line and working forward, each subject must say (in an even tone, so that no other information is conveyed) either "red" or "blue". Each subject not calling the color of his own hat is executed.|
The kings' subjects confer on their best strategy.
What is the minimum number of subjects that must die, and what strategy or strategies achieve the minimum number of deaths?
|Jul-18-14|| ||al wazir: <johnlspouge>: "*Must* die"? Zero. But with the optimum strategy there is a 50% chance that one will.|
|Jul-18-14|| ||kellmano: The conferring would likely involve a lot of people arguing why they should not be last in the line.|
|Jul-18-14|| ||johnlspouge: < <al wazir> wrote: <johnlspouge>: "*Must* die"? Zero. But with the optimum strategy there is a 50% chance that one will. >|
|Jul-18-14|| ||diceman: <johnlspouge: An evil king>|
Wow, an Obama riddle.
<The king has red or blue hats placed at random on his subjects' heads, and demands that starting at the back of the line and working forward, each subject must say (in an even tone, so that no other information is conveyed) either "red" or "blue". Each subject not calling the color of his own hat is executed.>
You'd think he'd put the "proper" hats on, and kill the red ones.
< <al wazir> wrote: <johnlspouge>:
"*Must* die"? Zero. But with the optimum strategy there is a 50% chance that one will. >
"Kill the king" is the optimum strategy.
...I guess "religion" doesn't allow them to see it?
|Jul-18-14|| ||Marmot PFL: <diceman> Obsess much?|
|Jul-18-14|| ||johnlspouge: < <kellmano> wrote: The conferring would likely involve a lot of people arguing why they should not be last in the line. >|
Partial credit :)
|Jul-19-14|| ||Sneaky: That's a good stumper.
My first thought was this: "Simple! The guy at the end of the line (call him subject #1) just announces the color of the hat of the person in front of them. Then subject #2 says whatever the guy behind them picked, and he's guaranteed to live."
But I didn't think that through very far. What on earth is subject #3 supposed to do?
If only they could inflect their voices, the problem would be trivial, but johnlspouge specifically said that is forbidden.
On the face of it, this seems absolutely impossible, unless there is some thinking-outside-the-box trick. Like a body motion (not a vocal inflection). But I don't think that's in the spirit of the stumper.
|Jul-19-14|| ||Sneaky: Oh my goodness, I've got it. It's beautiful. It doesn't require any tricks at all, no secret knee-jerks, nothing. Just a well formed strategy.|
The one thing that I believe needs to be added for clarity (correct me if I'm wrong) — the subjects are executed on the spot (not when the whole affair is over) and the prisoners before them know it (they hear the wails of pain, the gunshot, etc.)
|Jul-20-14|| ||Sneaky: I can't contain myself, here is the solution to the evil-king stumper:|
Call the subjects 1 through N, with N being the very last subject.
Subject N counts all of the red hats he sees in front of him. If it's an even number, he calls out "red". If it's an odd number, he calls out "blue".
Then his fate is determined. The other subject either hear him die, or they don't. Now all of the other subject know if he was wearing a red hat.
For each subject in turn, they add up all of the red hats behind them (including the red hat of the unfortunate deceased subject #N, should he not be lucky) as well as all of the red hats in front of them. Just like with subject N, if it's even they call out "red" and if it's odd they call out "blue".
Now why does this work?
When it's your turn to "guess", you know that parity ("evenness/oddness") of the red-hat-count can only change when it's you who is wearing a red hat.
Example: Let's say that you were the second to the last subject, and you are wearing a blue hat, but you don't know it. The guy behind you looks forward as sees 18 red hats and, so he says 'red' telling you that the number of red hats he can see is even. Let's say his life is spared, now you know that his hat was red.
Now it's your turn. You look forward and see the same 18 red hats. If you were wearing a red hat, you'd only see 17 of them... but you see 18. So that means you know you've got a blue hat on, right? So you call out "blue" (because 18+1 = 19, an odd number).
This logic can be extrapolated onward all the way to the guy at the very start. Assuming nobody is mathematically incompetent, the only subject in danger is the guy at the end of the line.
|Jul-20-14|| ||al wazir: <Sneaky: Assuming nobody is mathematically incompetent, the only subject in danger is the guy at the end of the line.> Well, not quite.|
<In individuals with Northern European ancestry, as many as 8 percent of men and 0.5 percent of women experience the common form of red-green color blindness.> http://en.wikipedia.org/wiki/Color_...
|Jul-20-14|| ||Sneaky: Al, OK you got me there. I guess none of them can be blind either. Nor can they be deaf.|
Now that I think about it, I rescind what I said about subjects needing to know the fate of the other subjects. It seemed to me to be important at first, but upon reflection, it really doesn't matter.
Example: Suppose once more you are second-to-last. The guy behind you says "red", so you know he sees an even number of reds. Then something happens to him (you hope for the best, but you don't know) and it's your turn. You count an even number of red hats, so you know yours is blue, and you say "blue" and you're right. His fate is immaterial. Now it's turn for subject #3. Let's say he counts an odd number of red hats, now he knows that he must have a red hat on, so he says "red".
They just need to be able to *see* all the way to the front of the line, and to *hear* what was said behind them.
Very neat riddle. It vaguely reminds me of a genre of puzzle that usually involves people wearing colored hats and coming to conclusions about the color of their own hat based on other people's conclusions (or lack of conclusions).
|Jul-20-14|| ||ughaibu: Infinite numbers of hats? Axiom of choice to the rescue. . . . http://qcpages.qc.cuny.edu/~rmiller...|
|Jul-20-14|| ||johnlspouge: @<Sneaky>: Nicely done. I did intend that everyone is audible to everyone else, but forgot to state it explicitly. I also went through the same faulty logic ending with the unnecessary demise of poor #3.|
< That's a good stumper. >
Hence, I posted it :)
@<al wazir>: My statement of the problem was a clumsy attempt to conceal that obvious lower bound of death can be achieved, whatever metric you use.
@<diceman>: If it makes you feel better, the subjects killed their evil king and lived happily ever after.
When my daughter was 4, I told her stories about the evil witch Dontlafflaiker [ https://www.youtube.com/watch?v=QOu... ]. At the end, my daughter would always insist that the witch and her intended victims have a tea-party and make up.
To each, his or her own.
|Jul-21-14|| ||Sneaky: <ughaibu> linked to what seems to be a master's thesis on what I described as "a genre of puzzle that usually involves people wearing colored hats." I didn't know it had carved a niche in game theory, but apparently it has.|
I first came across the genre in a newsletter by James Randi (who I assume needs no introduction) ... but his answer was hotly contested and in the end I wasn't sure if he had it right himself.
Here is the stumper as originally posed by Randi:
<Curly, Larry, and Moe, having nothing much better to do one evening, agree to play a strange game. There are two red and three white caps in a drawer. They turn out the lights, each reaches into the drawer in the dark, removes one cap, and places it on his head. Then the drawer is closed, the lights are switched on, and the players sit down, each to try to guess which color of cap he himself is wearing. Fifteen minutes goes by.
Perhaps unlike others with the same names we might know about, these three chaps are pretty smart. Each knows that there might be ways, by observing, listening, and reasoning, of knowing what color of cap he's wearing.
Curly is the first to speak. "This is a stupid game! Whose idea was this, anyway? And whose caps are these? I don't know what color I'm wearing, and I don't care! I want a cold beer!" And he calls the delicatessen downstairs to order a cold six-pack. Moe smiles, but stays silent.
Larry is next to break the silence. "I don't know what color I'm wearing, either! I agree this is a dumb game! I might have a green cap, but I'd never know it! Let's order in some pizza and play poker!" Moe smiles even more broadly. Then he speaks up.
"Well, I'm wearing a white cap! I'm absolutely certain, and I knew it before the beer was on its way! So pass me over a cold brew! And I'll buy the pizza!"
And he's right. He is wearing a white cap. He didn't cheat. He figured it out.
Assume that all three guys are astute and clever, and that they speak the truth. Two questions: How did Moe know? And what was the distribution of caps?">
Here is a discussion about it at the excellent Straight Dope website:
|Jul-21-14|| ||PinnedPiece: RRW.
No question about it. Moe saw two reds...how is this a puzzle again? I don't buy the guy's complaints that Moe would have spoke up immediately. He had an additional quality: patience.
Though not mentioned in the puzzle, as soon as Moe did speak up, Curly and Larry would have known their hat colors as well.
|Jul-21-14|| ||al wazir: The usual solution to the hat puzzle is faulty. The one who is smartest has to know *how long to wait* before concluding that the others have failed. How is it possible for anyone to know this?|
In the beer/pizza/poker variant, what if Curly and Larry wait an hour before giving up? Or two hours? Or three?
|Jul-21-14|| ||Sneaky: That's very good, but believe me, there are definitely other interpretations.|
(Keep in mind, that Randi received a lot of criticism for stating the puzzle in such as way that Moe is portrayed on sitting on information. The nature of the game, some say, demands that the players speak up once they know the truth.)
Anyhow, consider this: Larry has a red cap, Curly has a white cap, Moe has a white cap.
In general, if the game starts and you see two red caps, you speak up and win. If you see two white caps, or one of each color, you are confused. But as the game progresses you can glean more information...
At first, nobody speaks up. That tells everybody that the distribution cannot be WRR, because if it was WRR, the person with the white hat would speak up.
Now from Moe's perspective, he knows that Larry has a red cap (because he can see it!) and he knows that Curly is confused. According to the above logic, Curly is either looking at white-white or red-white. But it can't be white-white since Curly can clearly see Larry's red cap.
So at that point Moe instantly knows that he has a white cap on. According to the narrative, that's when he begins to smile.
Larry, seeing two white caps, has no way of knowing if his own is red or white, so he decides to quit the game. So everything fits fine with that arrangement, even though Moe apparently cheated a little bit by not speaking up when he solved it.
I think the problem as stated by Randi is somewhat flawed as others have asserted. He was being a little too smart for his own good, and over-embellished.
|Jul-24-14|| ||PinnedPiece: <Sneaky: So at that point Moe instantly knows that he has a white cap on. According to the narrative, that's when he begins to smile.> |
Truly, this solution seems more in line with the intended storyline.
But since both solutions are possible, I now side with <al wazir> that it is a faulty puzzle, but for different reasons than his!
--- -- --- --- --- ---
(Caution, trickery involved)
A Texas cattle rancher brings an engineer, a physicist, and a mathematician from Texas A&M out to his property for a little challenge. He was curious how to fence off the largest amount of area using the least amount of fence.
The mathematician made his fence in a 100-yd radius circle. "This design is the most efficient" he said.
The physicist took the fence and built it in a long line. "Consider the length infinite...it fences off half the earth, and is the best."
The engineer laughed at the others. In a short time he built his design, which clearly beat the others.
What did the engineer do?
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