466
Rants and Stuff / Re: Shameless plug for my book signing
« on: September 18, 2005, 12:30:15 PM »
It went relatively well. I'd like to thank MsFish, CtrlZed and Oldie Locks for showing up.
News:
"Magic is what makes fantasy fantastic," someone says, "you can't apply rules to them or else it loses wonder!" I respond, "Sure, but if you want to write them you will certainly want to know how they work." Writing is all about execution, and I find applying some basic laws of physics to magic systems make them more understandable and realistic. Here, I'm going to outline my basic method for developing a magic system.
Column by Chaos2651
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467
Everything Else / Re: Riddles Round 2
« on: September 17, 2005, 11:29:06 PM »
Same as last time, only this time you can only ask yes-or-no questions. Update: realized that wouldn't work.
New version: This time, the answers will be no more than one word or identifying via pointing only one person or direction.
New version: This time, the answers will be no more than one word or identifying via pointing only one person or direction.
Quote
OK, back to the Island of Truthtellers, Lietellers, and Outcasts.
The rules this time:
Truthtellers always tell the truth.
Lietellers always lie by telling the exact opposite of the truth, when possible.
Outcasts alternate between telling the truth like Truthtellers and and lying like Lietellers. Natives of the island know instinctively whether an outcast will next tell a lie or tell the truth, but an outsider like you lacks the necessary instinct.
You come upon a fork in the road. A sign indicates that one path leads to the Fountain of Youth and that the other leads to the Pit of Despair. Unfortunately, the sign doesn't have any arrows designating which is which. But it does say that there will always be exactly one Truthteller and one Lieteller standing at the fork. You may ask a total of two questions of any natives you find standing there -- either two questions to the same person, or one question to one person and one question to another.
Unfortunately, there aren't just two natives standing at the fork: there are ten. One is a Truthteller and one is a Lieteller, and the rest are outcasts. Unfortunately, there is no way for you to determine which group any of them belong to, other than by asking questions.
So, explain what two questions you would ask, of whom, in order to determine the way to the Fountain of Youth.
468
Everything Else / Re: Riddles Round 2
« on: September 17, 2005, 10:10:16 AM »
Or you could just leave the herrings out of this and try the following:
The poles of a magnet have much more attractive force toward ferrous materials than the middle.
Place the blue rod on the table. This is the "target" rod. Put the red rod (the "puller") a few inches away, perpendicular to the blue rod and aligned with the middle of the blue rod. Keep moving the red rod closer until the two rods touch. Then do the same, reversing the colors of the rods. In one of the two cases, the "target" rod will start rolling toward the "puller" much sooner.
Whichever rod is the magnet will pull the other rod toward it much more strongly when it is the one with the pole facing the middle of the other rod. Therefore, the "puller" when that happens is the magnet.
The poles of a magnet have much more attractive force toward ferrous materials than the middle.
Place the blue rod on the table. This is the "target" rod. Put the red rod (the "puller") a few inches away, perpendicular to the blue rod and aligned with the middle of the blue rod. Keep moving the red rod closer until the two rods touch. Then do the same, reversing the colors of the rods. In one of the two cases, the "target" rod will start rolling toward the "puller" much sooner.
Whichever rod is the magnet will pull the other rod toward it much more strongly when it is the one with the pole facing the middle of the other rod. Therefore, the "puller" when that happens is the magnet.
469
Everything Else / Re: Riddles Round 2
« on: September 17, 2005, 10:02:49 AM »
Aha! Then why didn't you list them among our assets in the first place?
The red color in the herrings obviously comes from hemoglobin, and hemoglobin contains iron, and iron is attracted to magnets. So you just put each rod close to a herring, and whichever one attracts the fish must be a magnet.
Q.E.D.
The red color in the herrings obviously comes from hemoglobin, and hemoglobin contains iron, and iron is attracted to magnets. So you just put each rod close to a herring, and whichever one attracts the fish must be a magnet.
Q.E.D.
470
Everything Else / Re: Riddles Round 2
« on: September 16, 2005, 05:28:44 PM »
I'm pretty sure mine would work, but if there's a simpler way, then it's not the correct solution.
How about this: Stroke the blue rod lengthwise multiple times in the same direction using one end of red rode. Then do the same to the red rod with the blue rod. Presto: now they're both magnets!
How about this: Stroke the blue rod lengthwise multiple times in the same direction using one end of red rode. Then do the same to the red rod with the blue rod. Presto: now they're both magnets!
471
Everything Else / Re: Riddles Round 2
« on: September 16, 2005, 10:22:44 AM »
I'd tie a piece of thread around the middle of each of the bars, and hold each bar up by the thread to see if it swung to point north-south like a magnetic compass. The one that did so would be the magnet.
472
Everything Else / Re: Riddles Round 2
« on: September 16, 2005, 02:21:49 AM »
How big are the rods?
473
Everything Else / Re: Riddles Round 2
« on: September 16, 2005, 12:36:35 AM »
> Do they alternate strictly or randomly?
Strictly.
Firemeboy, your explanation works.
Strictly.
Firemeboy, your explanation works.
474
Everything Else / Re: Riddles Round 2
« on: September 15, 2005, 05:59:14 PM »
Also, you must use the verbal answers to the questions to make your determination. So you can't ask something like, "Did you hear they're giving away free hot dogs and ice cream at the Fountain of Youth?" and then watch to see which way the natives go.
475
Everything Else / Re: Riddles Round 2
« on: September 15, 2005, 05:56:52 PM »
Not this time. You can ask any question you want.
476
Everything Else / Re: Riddles Round 2
« on: September 15, 2005, 04:51:15 PM »
e, I'm glad to see someone who looks at it the same way I do. I've been arguing for years that .9 repeating is not quite equal to 1 -- it's just the largest number less than one.
Anyway, I guess it's my turn to post a riddle.
OK, back to the Island of Truthtellers, Lietellers, and Outcasts.
The rules this time:
Truthtellers always tell the truth.
Lietellers always lie by telling the exact opposite of the truth, when possible.
Outcasts alternate between telling the truth like Truthtellers and and lying like Lietellers. Natives of the island know instinctively whether an outcast will next tell a lie or tell the truth, but an outsider like you lacks the necessary instinct.
You come upon a fork in the road. A sign indicates that one path leads to the Fountain of Youth and that the other leads to the Pit of Despair. Unfortunately, the sign doesn't have any arrows designating which is which. But it does say that there will always be exactly one Truthteller and one Lieteller standing at the fork. You may ask a total of two questions of any natives you find standing there -- either two questions to the same person, or one question to one person and one question to another.
Unfortunately, there aren't just two natives standing at the fork: there are ten. One is a Truthteller and one is a Lieteller, and the rest are outcasts. Unfortunately, there is no way for you to determine which group any of them belong to, other than by asking questions.
So, explain what two questions you would ask, of whom, in order to determine the way to the Fountain of Youth.
Anyway, I guess it's my turn to post a riddle.
OK, back to the Island of Truthtellers, Lietellers, and Outcasts.
The rules this time:
Truthtellers always tell the truth.
Lietellers always lie by telling the exact opposite of the truth, when possible.
Outcasts alternate between telling the truth like Truthtellers and and lying like Lietellers. Natives of the island know instinctively whether an outcast will next tell a lie or tell the truth, but an outsider like you lacks the necessary instinct.
You come upon a fork in the road. A sign indicates that one path leads to the Fountain of Youth and that the other leads to the Pit of Despair. Unfortunately, the sign doesn't have any arrows designating which is which. But it does say that there will always be exactly one Truthteller and one Lieteller standing at the fork. You may ask a total of two questions of any natives you find standing there -- either two questions to the same person, or one question to one person and one question to another.
Unfortunately, there aren't just two natives standing at the fork: there are ten. One is a Truthteller and one is a Lieteller, and the rest are outcasts. Unfortunately, there is no way for you to determine which group any of them belong to, other than by asking questions.
So, explain what two questions you would ask, of whom, in order to determine the way to the Fountain of Youth.
477
Everything Else / Re: Riddles Round 2
« on: September 15, 2005, 03:54:06 PM »Quote
You cetainly can't prove it, but you could argue it.
Oh, yes. I could argue just about anything.
478
Everything Else / Re: Riddles Round 2
« on: September 15, 2005, 03:24:46 PM »Quote
In fact the highest I think you could go would be 10% if that.
No, it's quite easy to go over 10%. Just consider the numbers from 0 to 99:
0 1 2 4 5 6 7 8 9
10 11 12 14 15 16 17 18 19
20 21 22 24 25 26 27 28 29
40 41 42 44 45 46 47 48 49
50 51 52 54 55 56 57 58 59
60 61 62 64 65 66 67 68 69
70 71 72 74 75 76 77 78 79
80 81 82 84 85 86 87 88 89
90 91 92 94 95 96 97 98 99
3 13 23 30 31 32 33 34 34
36 37 38 39 43 53 63 73 83
93
19 out of 100 numbers have a 3 in them, which is 19%. And the percentage keeps getting higher as you add more digits.
479
Everything Else / Re: Riddles Round 2
« on: September 15, 2005, 03:14:14 PM »Quote
If we don't deal with technicalities, the answer is "All of them". 100% of real number contain the number three...
... But technically you can prove that all numbers contain a three, and you can also prove that all numbers contain an 8.
I'm afraid I don't quite get this. It is not possible to prove something is true for all (100%) members of a group if it is possible to find even one counter-example. Even if the percentage of real numbers that do not contain a 3 is infinitely small, the set of real numbers that do not contain a 3 is not null, and therefore it cannot be said that all real numbers contain a 3.
Unless I'm missing something, of course, and there's some sort of wordplay involved that's just going over my head.
480
Everything Else / Re: Riddles Round 2
« on: September 15, 2005, 02:10:13 PM »
Well, since it involves dividing one infinite (number of real numbers contain 3 as a digit) by another (number of real numbers), and the infinites are of the same order, the answer is technically undefined.
But, in a less rigorously mathematical way of looking at things, you could say that almost all real numbers contain 3 as at least one of their digits.
As an approximation to show this, we can look at percentages of real numbers that do not have 3 at a particular spot.
In the 1's column, 90% of real numbers do not have a 3.
Of that 90%, 90% do not have a 3 in the 10s column.
Of that 90% of 90%, 90% do not have a 3 in the 100s column.
So for each additional column that you examine (whether in front of the decimal point or after) the pool of real numbers without a 3 in them is reduced to 90% of what it was.
It takes only 8 digits to get below 50%. At 23 digits, you're under 10%. At 45 digits, you're under 1%. And as the number of digits goes out to infinity, the percentage of numbers that do not have a 3 in them becomes ever smaller.
But, in a less rigorously mathematical way of looking at things, you could say that almost all real numbers contain 3 as at least one of their digits.
As an approximation to show this, we can look at percentages of real numbers that do not have 3 at a particular spot.
In the 1's column, 90% of real numbers do not have a 3.
Of that 90%, 90% do not have a 3 in the 10s column.
Of that 90% of 90%, 90% do not have a 3 in the 100s column.
So for each additional column that you examine (whether in front of the decimal point or after) the pool of real numbers without a 3 in them is reduced to 90% of what it was.
It takes only 8 digits to get below 50%. At 23 digits, you're under 10%. At 45 digits, you're under 1%. And as the number of digits goes out to infinity, the percentage of numbers that do not have a 3 in them becomes ever smaller.