Score
Title
378
AskScience Panel of Scientists XVII
78237
Help us fight for net neutrality!
11142
From my kid: Can you put a marshmallow on a stick out into space and roast it with the sun?
16
What would our world look like if the collision which ejected the material from which formed the Moon had not occurred? Would there be liquid water? What kind of atmosphere if any? Active geological processes? Life?
4
[physics] When I turn off my oven but leave the door closed how does the temperature cool?
3
How accurate is the usual picture of the atomic nucleus of a ball/mass of protons and neutrons? What's really happening in the centre of atoms?
42
On my bike: is it more efficient to pedal fast in a low gear or slower in a high gear?
3
How would the government broadcast an emergency message in today's world where a majority of people watch tv through a streaming service?
1
If the Earth is closer to the sun for a part of the year, why isn't that summer MUCH hotter?
1
How do you define the number of conduction electrons?
10
What makes it "impossible" as of now to detect the hypothetical Graviton particle?
9
How are Muscle Knots / Trigger Points Created at the Cellular Level?
2
Can Dark Matter be explained by scale Invariance of empty space?
17
Is deep-earth nuclear fission heating the Earth's interior?
4
How in the world could a particle have a 1/2 spin value?
3371
Hein et al (2017) have explored scenarios for sending a spacecraft to the recently confirmed interstellar asteroid "Oumuamua". What payloads and capabilities would we wish to prioritize on the exploration of this strange and peculiar object?
11
How are doctors able to determine genetic abnormality in a fetus, by testing the mother’s blood?
11
Are all prime numbers smaller than the biggest prime number discovered?
10
What exactly is the Van Allen radiation belt?
6
Why children with adenoditis fall behind in their neurophychiatric development and do they recover in that aspect after the inflammation is gone?
12
Can blue light cause cancer? What about UVA? Where is the threshold?
4
When there is a momentum transfer between two charged particles (via a virtual particle) is that transfer instantaneous?
10
Do cephalopods control their camouflage consciously, if yes how exactly can an animals thought's change it's cells?
15
How does restricting Internet work?
11
Why can't powerbanks charge while being charged?
9
Is it a coincidence that the moons rotation around its axis matches the duration for its revolution around the earth? Or is there some scientific explanation on how these aligned in such a fashion?
7
Ask Anything Wednesday - Engineering, Mathematics, Computer Science
2
Are there any advantages to Removing Net Neutrality that the consumer can enjoy and not ISPs?
4
How does your body heal cuts?
6
How do they know 'Oumuamua is elongated vs of assymetric albedo? (Bonus Question: Is the assumed rotation stable?)
1
What changes when you break the sound barrier?
10
How, or why, do refraction and dispersion occur?
2
Are electrostatic interactions photon-mediated?
2
How does Lebesgue integral put Riemann integral and discrete sums in the same theorical mold ?
25
Why are radio waves and microwaves more damaging to the human body than light waves?
14
In my Psychology textbook it says that cortisol (a result of stress) reduces telomerase activity, therefore speeding up the aging process, however, I know that exercise also releases cortisol, yet is known to combat aging - how?
2
I measured an imaginary component of Earth's magnetic field?
3
Why does water behave like a mirror?
6
Why don't electrons in a superconductor radiate away their energy?
1
Why does the index of refraction of water change with temperature?
14
Why do planets orbit in planes?
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.