Score
Title
9418
Megathread: 2017 Hurricane Season
24
Earthquake Megathread
6172
If a nuclear bomb went off in Boston harbor could scientists tell after the fact who had manufactured it, do they leave distinct radioactive signatures?
5747
Why aren't there any orbitals after s, p, d and f?
16
What do sexes in fungus mean?
135
Do black holes have electromagnetic field?
4
Where does the "blast" portion of a nuclear explosion come from?
6
Do atmospheric CO2 measurements include a significant diurnal cycle?
8
How do bionic arms work?
4
Historically, when large numbers of sailboats/ships had to travel in formation as a fleet, are there different dynamics governing the movement of ships in the front, middle and rear of the group?
6
Why are non-differentiable continuous functions integrable?
9
Are Toucans (Americas) and Hornbills (Asia/Africa) an example of convergent evolution?
4
What are the estimated thicknesses for northern sea-ice at the height of the Pleistocene glaciation, and how are those thicknesses estimated?
7
Ask Anything Wednesday - Physics, Astronomy, Earth and Planetary Science
2
Why are rainbows in an arc shape and does the radius change?
4
Why do nuclei release energy when they fuse?
24
How many layers are there in a modern integrated circuit?
8
Why does the Earth's rotation effect Rockets and not Planes?
2
Are there plant/animal somatic hybrids?
2
Would the opposite of codependency issues be considered as unhealthy as codependency? Wherein any form of dependency is abhorrent to the person in question? Does this have a clinical classification?
60
Do people that have degenerative diseases such as Alzheimer's lose their muscle memory as well?
20
How is it possible that something as large as a possible Planet 9 has completely evaded visual observation?
8154
There is a video on the Front Page about the Navy's Railgun being developed. What kind of energy, damage would these sort of rounds do?
8
Would global cooling create more land? If so, how much more land would be available before the whole earth freezes?
11
How did they measure hurricane wind speeds in the 1800's?
4125
In 1972 a woman fell 33,332 feet without dying. How is that possible?
12
How is it that scissors can curl ribbons?
12
What is happening at a molecular level when a knife cuts through nylon rope?
154
Could we railgun the Moon?
15
Why is caesium the largest atom? Shouldn't element 118 be the largest?
1
Why does your metabolism slow down with age?
7
Do snakes that can 'see' heat, such as ball pythons, compare their 'heat vision' with their normal vision?
17
[CHEMISTRY] How do chemical companies determine if one ingredient in a solution can be replaced by another?
2
In emergencies like on CDMX will using cellphone data on a very far state affect the capacity on CDMX cell towers to make calls and/or use cell phone data?
12
Can a human be allergic to any substance? As in, does every material have the potential to elicit an allergic response?
2
What defines an equation of state?
46
How is online gaming possible if there must be some delay?
5
Does my peripheral vision have a different latency than objects I look directly at?
15
Why is gold found in seams?
16
On an alien planet, would a regular compass still point true north?
11
Can someone with reading Aphasia "read" in Braille?
4
Would negative kelvin body always transfer heat to positive kelvin body?
11 mfb- A great problem, and probably something you can write a master thesis on. Some assumptions: * Edge and corner pieces are recognizable as such * If two pieces fit together, we always know this. * We cannot use any sort of pattern on the pieces. Apart from the previous two bullet points we have no idea where a piece belongs to. Some initial thoughts: You can make estimates based on the relative number of center (M) and edge (E) pieces, but different length to height ratios will lead to different E to M ratios. All you get that way is a lower limit on the size (corresponding to square puzzles, asymmetric puzzles will have the same ratio at a larger overall size). Corner pieces (C) help: There are just 4 of them, if you draw the first one it doesn't tell you much, but with the second one you can be reasonably confident that the puzzle is not too much larger than what you have already. The third and fourth will refine these estimates even more. You know the length or height once you have a continuous connection between the corresponding edges (you don't need to have them in a straight line). This is a problem in [percolation theory](https://en.wikipedia.org/wiki/Percolation_theory). In the limit of infinite puzzle size, you need on average half the puzzle pieces for this if I remember correctly. There is another heuristic estimate, and one that will lead to a reliable (but not exact) estimate the fastest: Count the number of connections you found. I don't have an exact formula, but in a puzzle of N pieces (N>>1), the probability that two random pieces are next to each other is approximately 4/N. With sqrt(N) pieces drawn your expected number of connections is 2, while your expected number of corner pieces is 4. With 2sqrt(N) pieces drawn you expect 8 connections and 8 corner pieces. With 4sqrt(N) pieces drawn you expect 32 connections and 16 corner pieces. The number of connections grows much faster, with its inevitable sqrt(observed) scaling it gives a more reliable estimate than the corner pieces. In addition, its dependence on the overall puzzle shape is much smaller.
2 Sell200AprilAt142 Is the Jigsaw being put together as the pieces emerge? If so then the first time a row or column is completed then you know a dimension (ie it has edge pieces on each end). In this case you don't need the corners to know size If not then I suppose you could observe ratios of edge to non edge pieces and make some rough guess of size from that. (the number of non edge pieces increases in proportion to the square of half the number of edge pieces... That means the ratio should point to a specific size)
2 jaggededge13 The absolute minimum number of pieces is the length and width minus 1 (L+W-1) which has to include at least 4 edge/corner pieces. In addition, there has to be a direct path from edge to edge connecting all 4 sides. There are (2L-4)+(2W-4) or 2(L+W)-8 edge pieces (from here called E) and 4 corner pieces and N total pieces where N=L*W. On the other hand the maximum number needed is (L-1)*(W-1)+4 pieces. Or N-E. From this you can basically make a map of the probability the minimum requirement has been solved given a specified number of pieces drawn between the min and max. This will likely be something of a normal distribution. You are then in an N choose x scenario of possible draw combinations with y combinations that spell success. So Y/(N choose x) is the probability you have the answer. After (L+W-1) picks, the probability of success is LW/(N choose (L+W-1)) and so on. This will give you a plot that should exponentially level off and reach 1 at N-E. you can then do an expected value problem with this set of discreet points and get the expected number of selections before the size is known. This method doesn't really take into account the need for edge pieces, as its based on possible solutions as opposed to probability if picking adjacent pieces.
11 0 mfb- A great problem, and probably something you can write a master thesis on. Some assumptions: * Edge and corner pieces are recognizable as such * If two pieces fit together, we always know this. * We cannot use any sort of pattern on the pieces. Apart from the previous two bullet points we have no idea where a piece belongs to. Some initial thoughts: You can make estimates based on the relative number of center (M) and edge (E) pieces, but different length to height ratios will lead to different E to M ratios. All you get that way is a lower limit on the size (corresponding to square puzzles, asymmetric puzzles will have the same ratio at a larger overall size). Corner pieces (C) help: There are just 4 of them, if you draw the first one it doesn't tell you much, but with the second one you can be reasonably confident that the puzzle is not too much larger than what you have already. The third and fourth will refine these estimates even more. You know the length or height once you have a continuous connection between the corresponding edges (you don't need to have them in a straight line). This is a problem in [percolation theory](https://en.wikipedia.org/wiki/Percolation_theory). In the limit of infinite puzzle size, you need on average half the puzzle pieces for this if I remember correctly. There is another heuristic estimate, and one that will lead to a reliable (but not exact) estimate the fastest: Count the number of connections you found. I don't have an exact formula, but in a puzzle of N pieces (N>>1), the probability that two random pieces are next to each other is approximately 4/N. With sqrt(N) pieces drawn your expected number of connections is 2, while your expected number of corner pieces is 4. With 2sqrt(N) pieces drawn you expect 8 connections and 8 corner pieces. With 4sqrt(N) pieces drawn you expect 32 connections and 16 corner pieces. The number of connections grows much faster, with its inevitable sqrt(observed) scaling it gives a more reliable estimate than the corner pieces. In addition, its dependence on the overall puzzle shape is much smaller.
2 0 Sell200AprilAt142 Is the Jigsaw being put together as the pieces emerge? If so then the first time a row or column is completed then you know a dimension (ie it has edge pieces on each end). In this case you don't need the corners to know size If not then I suppose you could observe ratios of edge to non edge pieces and make some rough guess of size from that. (the number of non edge pieces increases in proportion to the square of half the number of edge pieces... That means the ratio should point to a specific size)
2 0 jaggededge13 The absolute minimum number of pieces is the length and width minus 1 (L+W-1) which has to include at least 4 edge/corner pieces. In addition, there has to be a direct path from edge to edge connecting all 4 sides. There are (2L-4)+(2W-4) or 2(L+W)-8 edge pieces (from here called E) and 4 corner pieces and N total pieces where N=L*W. On the other hand the maximum number needed is (L-1)*(W-1)+4 pieces. Or N-E. From this you can basically make a map of the probability the minimum requirement has been solved given a specified number of pieces drawn between the min and max. This will likely be something of a normal distribution. You are then in an N choose x scenario of possible draw combinations with y combinations that spell success. So Y/(N choose x) is the probability you have the answer. After (L+W-1) picks, the probability of success is LW/(N choose (L+W-1)) and so on. This will give you a plot that should exponentially level off and reach 1 at N-E. you can then do an expected value problem with this set of discreet points and get the expected number of selections before the size is known. This method doesn't really take into account the need for edge pieces, as its based on possible solutions as opposed to probability if picking adjacent pieces.