TakenItSeriously

Edit to add: Regarding the larger space, I might define a large square for populating the random positions of the universe in a cartesian coordinate system and then I would define a large circle within the boundaries of the square and call it a horizon. Then I would assign random vectors that pass only through those points within the larger circle so that the points in the corners wouldn't create a bias and the horrizon was always equidistant from the circle. This would then preclude the idea of using multiple circles of course.

The Pics didn’t get into the final draft so here they are now: I’m not sure I would call the Bertrand Paradox all that mysterious so much as confusing. I wouldn’t accept any of the three premises given as valid. Premises should be axiomatic and self evident as far as being valid and the premises given are definitely not axiomatic. My guess is that they are a problem with boundary conditions combined with conflicting properties that cannot be both defined in a non biasing way for both properties at once. It may not be possible to provide a proper definition for random chords to the circle except perhaps in an infinitely large universe which, of course is not practical. For a decent approximation, I might try picking random positions within a much larger space than that described by the circle and then assigned to them random vectors for a random distribution of lines that may or may not pass through an arbitrarily defined circle, but I would use a space that was much much larger than the given circle such that vectors that happened to intersect the circle from a long distance away would make an insignificant contribution. I might also position the circles in a random manor perhaps even using multiple circles with triangles in them. It’s just my first guess at a reasonable approximation of random that would represent an unbiased distribition or a homogenious isotropic environment FWIW. I’m not sure how well it would do in terms of convergence to a unique result.

When I first came accross the mystery of Buffon’s needle, it was presented as a mystery because, apparently, nobody could understand why it would result in the value of pi or what the problem of scattered needles had to do with a circle. You might actually do the experiment and find that the results really did statistically converge to pi as the sample size grew larger or you might find the mathematical solution would indeed result in a probability that is exactly equal to pi. You might notice that there is a cosine of the angle between the needle and the lines on the table involved. You might even be able to construct a circle to describe how the cosine function relates to a circle using trigonometry, but even then you still probably wouldn’t truly have a clear and direct physical understanding of why the problem of randomly scattered needles should be related to circles. Here, I don’t present the mathematical solution which you can look up online from a number of sources. Instead I present a simple and logical model that explains the problem in the proper physical context which in turn will make it clear why circles are related to randomly distributed needles. Once again, Once you understand the solution it will seem simple to you as all logical solutions that are properly explained will seem relatively simple compared to the math. Perhaps it will even seem like it should be obvious once you understand it and you may not understand why you didnt think of it before but unless you could physically explain it in fore-site before hearing this solution, then it clearly wasn’t really as obvious in fore-site as it may seem in hind-site. I present this solution to you not just to show off that I have a gift for solving logic problems, but to provide yet another example that shows why logic really is just as important as math and that logic and math are not the same thing. Neither is logic just an alternative method to mathematics for solving problems that can be used as a substitute for math. It actually performs a completely different function from the math as I’ve said many times before: Logic clarifies our understanding of the problem while math quantifies the numerical results of the properties involved that can then be compared to experimental results. In fact math and logic are actually complementary opposites. Another words we cannot truly understand a problem without a logical model that can explain it and we cannot truly know that our understanding is correct without validating the mathematical results with experimental test. Problem: Figure 1: Buffon’s needle is a probabilistic method that can provide a good estimate of π based on random events. Assume that you have a needle that has a length of l and a surface that has parallel lines on it that are all equally spaced at 2l distance apart. If you toss a needle in a random manor on that surface such that it can land in any arbitrary position and orientation, then the probability that the needle lands inbetween the lines divided by the number of times that the needle will intersect with a line will be equal to pi (π). Another words your results will approximate 3.14... etc. with a sufficient sample size and the larger your sample size the better your approximation of π should be. The mystery of this method is why does it approximate π which we know is a constant that must be somehow related to a circle when there seems to be no circles involved with this method of randomly scattering needles. Logical Explaination: There is actually a simple logical explaination for this mystery and to understand it more easily I will provide a probabilistically equivalent scenario to illustrate why. Instead of using needles we can use clear plastic discs that have the needle embedded in the disc such that they perfectly bisect the circumference of the discs. After all it will still represent a random position and orientation just as the needles would. In fact they would probably be more random than the needles themselves since needles are not perfectly symetrical and they may be tossed in such a way that may be biased while the disc surrounding the needle would ensure a more random or unbiased result. Given in this new context, it should now be clear that the source of pi is linked to the circular shape of the disc. Put another way, think of the position of the disks and the orientation of the needles as independant properties. It is the probability distribution of the needle’s orientation that has an even disc like distribution about their center of gravity. By taking all the angles accross the entire sample space then the orientations of all the needles would stack up to be a random sample of all angles between 0 and 2π or between 0 and π if the needle is symmetrical. So you can see that on average, the orientations of all the needles should combine to be distributed in the shape of a disk. If by some extreme long shot, they did not create a reasonable disc like distribution, then you probably would not get a reasonable approximation of pi as your result.

Betty, Carol, Dan Marketing

B & C edit to add: I find that these types of problems are often flawed with more then one valid answer.

A third person can deduce it must be July 16 using all three clues.

If my cross was red then it would be trivial for either Wombat or Breeze to know that their cross must be green. Since neither could answer, then my cross must be green.

Thanks, I really appreciate that. To answer your point, this is why I think that logical models and mathematical models are complimentary to each other. Where one is prone to intuitive error the other is not and vice-versa. Therefore you could say that math and logic are cross validating because they always follow different vectors of reasoning. edit to add: BTW, sorry about the unwieldy username. It’s based on a bit of word play. On other forums such as twoplustwo.com which is fundamentally a poker and gaming forum, I go by TakenItEasy. Lots of people there called me Taken for short.

Both twins would hear their own transponder at 1 ping/second and that never changes. When the ship is on the return leg, the earth twin would be recieving the ship’s twin’s signal at three pings per second and the ship’s twin would be recieving the Earth twin’s signal at three pings per second. So it’s still symmetrical. Both would be due to relativistic blueshift, but when frequency increases, it doesnt just mean in pitch, but in cycles per second which in this case a cycle is a ping. That doesn't mean that time would actually be sped up, for anybody. it’s only a timelag illusion where the ship is kind of racing its own light. Another words as the ship is leaving Alpha Centauri at 80% c, the light and radio signal is leaving Alpha Centauri at 100% c. So from the Earth FoR the light takes 4 years to reach Earth while the ship takes 5 years to reach Earth. With only 1 year inbetween the two. That means the ship must transmit 3 years worth of pings received in only 1 years time. On the other hand at the turn around, the ship has experienced only 1 year of pings from Earth due to that same lag time because the “now” time is still four years away back on Earth. So now the ship is racing opposite that light coming from earth from 4 years in the past plus the 5 years experienced by the Earth for the second leg of the trip so 4+5 or 9 years of Earth’s pings are crammed into 3 years of travel time for the twin on the ship. It’s confusing, I know, but I hope that makes sense.

The photo electric effect was a paper published by Einstein in 1905 which proposed that an electron could be created by light striking a surface with light The explanation for how light could cause the ejection of an electron was first postulated by Max Plank, Albert Einstein, and Niels Bohr: that light was the occurance of energy in descrete quantities or quanta (which later became known as photons) which was the first time light was proposed to be more like a particle than like a wave as it had previously been assumed to be. Heisenberg Uncertainty Principle was published in 1924 which stated that it was impossible to determine two complimentary properties of a particle at the same time. The Schrodinger Wave Equation was derrived in 1925 and published in 1926 which provided the same conslusion based on eigenstates, but interpreted properties of particles as a kind of wave probability state. The Copenhagen Interpretation which was largely devised by Werner Heisenberg and Niel’s Bohr in the years 1925-2927 was in large part about interpretating these confusing results of duality that seemed to behave sometimes like particles or sometimes like waves. The dual slit experiment that resulted in evidence of both a particle state or a wave state for light depending on wether their path through either slit was observed or not was performed by Davison and Germer in 1927 and was also the experimental basis for the superposition argument of quantum mechanics. It was later shown that electrons could also demonstrate either a particle or a wave state in the same manor. BTW, I may have been wrong when stating that the copenhagen interpretation was largely based on the dual slit experiment according to these dates which I got from Wikipedia, apparantly the dual slit experiment was in 1927 while the interpretation was developed between 1925-27 so the dates might have suggested that it was seen as more of a confirmation of the copenhagen interpretation, or perhaps it was adapted to conform to those results. I’m not sure. Entanglement was predicted in 1935 by Einstein, Podolski, and Rosen and later confirmed through experimentation. However, it was introduced as a thought expeiment that was the basis for his arguement that QM was not complete because it implied that the speed of light would be violated based upon “spooky action at a distance”. In 1964 Bells inequalities was published refuting Einsteins claims that QM was incomplete based on “spooky action at a distance” violating the speed of light, and used the EPR entanglement and the premise that classical probability and the probability of QM are different. Note that while I thought his conclusion about instantanious action at a distance was probably correct, I had strongly disagreed with his premise which was flawed. In fact it’s riddled with flaws to be honest. In my opinion Mathematicians should never try to rely on proofs using logical models. They are simply not equiped to handle logical models because they were trained to think like mathematicians not logicians which are complimentary opposites, just like position and momentum are complimentary opposites. You can’t know both at the same time. Classical probability had never been completely resolved before and was always considered to be an approximation of probability based on incomplete information. For instance the triangle pattern predicted by probability theory is only a function that is supposed to be an approximation of the actual odds, while the wave pattern predicted by QM is much like the binomial distribution pattern that statistics predicts and that the triangle fuction is supposed to estimate. So making claims that they are different and forcing some kind of conclusion from that difference is meaningless. For the record, I agree that QM as it is recognized today is incomplete. But I also agree that instantanious action at a distance is probably true. I never understood why saying that QM wasn’t complete should even be in question? To be fair, I think that Relativity as it is recognized today isn’t complete either. Clearly, neither theory can explain everything so how could anyone say that either theory is complete? Just because I admire a person doesn’t mean I will agree with him on everything. Or just because a conclusion such as instantanious action at a distance may agree with my own thinking, doesn't mean I will agree with a flawed premise such as that proposed by Bell. To do otherwise is simply corrupt thingking towards some biased agenda, just like politics. When scientists behave like politicians, why would they wonder why peole don’t trust them anymore.

Of course it has to do with the Copenhagen Interpretation because that interpretation is largely based upon the Dual Slit experiment and your arguement atttacks the conclusions from that experiment.

Well, again, I think you should take your arguements up with the origionators of the experiment which was done in the 90’s by Yoon-Ho Kim, R.Yu, S.P. Shih and Marlan O. Scully because that was their conclusion.

If you want to argue against the Copenhagen Interpretation of QM to which I am simply referring to. Don’t take it up with me. I assume the data is digitally recorded and correlated and observed after an appropriate statistical sample size has been collected. Then the patterns are determined by the filtered data. I dont have access to the origional papers, only the articles or videos that described the experiment, but I assume that it has been well documented.

Ok, so what is your definition of a quantum state?

The particle or wave nature is what’s recorded at detector DO and is correlated through their entanglement to the path information at detectors D1-D4.

It’s a very confusing setup and I must admit it took me a while to figure it out myself. It basically comes down to the particle streams are divided into entangled streams after the slits. One entangled stream always hits D0 and reveals either a dual distribution or an interference pattern. The other stream may strike one of four detectors after going through a series of splitters that will randomly determine the path of the particle. if the entangled particle hits detector D3 then we know the origional, unentangled particle went through the bottom or blue slit, or if it strikes decector D4, then we know it went through the top or red slit. Therefore, when either of those detectors are hit, their entangled partner particles at D0 exhibit a dual distribution pattern, even though the particles strike D0 before hitting any splitters that randomly determine the path of the particle! When they strike either D1 or D2, there is no way to tell which slit they traveled through, therefore they exhibit wave interference patterns at D0. Weird right?

You have dual slits first and then whatever comes out of either (or both) slits are split into entangled streams, then the Quantum eraser shows that even a delayed observation of which slit a particle passes through will determine the pattern even after the fact when the pattern is recorded before the path is or is not detected, which is why the quantum eraser is the weirdest result in QM.

A month or so ago, I was asked to provide a logical explanation to the Twin Paradox that showed why symetrical views of time was not a paradox or how was symmetrical views of time completely consistent with the time deviation experienced between the twins. So as promised I fully explain: Why length contraction is the reason why the twins experience time deviation. Why time deviation was not a paradox with the twins symmetrical views of time because length contraction is the asymetrical component that was never considered. Finally, I show how their symetrical views of time really are completely consistent for the entire journey using a trasponder solution with each other. As always, I will be using the example given in Wikipedia so that you can verify the results with those given in that example and I can skip the math for simplicity sake. I will only be providing the logical models that fully explains the paradox. BTW, this is a good example of my previous statements that while logic may be prone to intuitive errors of false premise, such as the Earth is the center of the Universe because everything appears to revolve around the Earth, math is just as prone to intuitive errors of false conclusions. The key points of the problem are: The ship carrying one of the twins goes straight to Alpha Centauri and back. Acceleration is assumed to be an insignificant factor so velocity is a constant 80% of the speed of light in both directions. Alpha Centauri is assumed to be in relativisticly static motion relative to the Earth with a proper distance of 4 light years. Each twin is equiped with a powerful transponder that pings with a source frequency of exactly once per second or 1Hz. The Earth twin sees that Alpha Centauri is a static 4 lightyears away. Therefore, he calculates the trip will take 4/0.8 = 5 years each way or 10 years total. The ships twin has a different perspective of the trip when moving at 0.8c due to length contraction, the distance is only 60% of the proper distance or 2.4 light years away. Therefore from his point of view, the trip will only last 3 light years each way or 6 years total. So when he returns, he experiences 6 years while the Earth Twin experiences 10 years, however that is not the paradox. The paradox is based on the fact that each twin should have symmetrical points of view of their brothers time which is true: When the ships twin is on the outbound leg moving away from Earth at 0.8c then each twin sees their brothers time as moving at 1/3 of normal, or they would each be receiving a transponder ping only once every 3 seconds. When the ships twin is on the return leg, then each twin sees their brothers time as moving at 3x normal or they would each be recieving 3 pings/sec. These time shifts are due to the relativistic redshift which I didnt bother working out the math again, but the formulas are pretty simple and include time dialaion plus normal doppler effect due to lagtime, so that you can verify the results yourself or just refer to the Wikipedia example which uses the exact same problem. The logical resolution to this paradox is the fact that while their views of each others time is symetrical, their views of the distance traveled is asymetrical. The reason why is that the Earth, Alpha Centari, and the space in between the two are all in the Earths inertial reference frame, while the ship plus what is inside the ship is all that is in the ship’s inertial reference frame. The Earth twin sees the ship is length contracted by 60% which has no bearing on the trip The ships twin sees the Earth’s inertial frame as length contracted and as we said, the Earth, AC and the distance inbetween is all included within that inertial reference frame. Therefore, from the ship’s twin’s point of view the distance is length contracted by 60% of 4 light years or 2.4 light years. So with 60% less distance to trave, then the trip takes 60% less time to travel from the ship twins point of view. Another words while their point of view of time is symmetrical, their point of view of distance is asymtrical which accounts for their deviation in time experienced. We can confirm this by correlating their point of view with lagtime. Another words, from the Earth twins point of view, the ships twin would take 5 years plus it would take 4 years for the light (or transponder signal) to get back to Earth from Alpha Centauri: 5 years + 4 years = 9 years That means the Earth twin would expect to witness the ship actually execute the turnaround 9 years after the ships departure. Or when the transponder signal recieved back on Earth would change from 1 ping every 3 seconds to 3 pings/second then the ship would have executed the turn which would happen 9 years after the origional launch. If you do the math and count the pings received during those 9 years at 1 ping/3 seconds adds up to: 9 years x 1/3 = 3 years which is actually what the ships clock would read at the turn around by both twins. Events that include both a time and a place must always be consistent to any inertial frame. On the trip back to Earth, the journey would only seem to take 1 year as perceived by the Earth twin so: 9 years + 1 year = 10 years total time as expected by the Earth twin. However, during that 1 year, the transponder is pinging 3 times per second so it adds up to 3 years 1 year x 3 = 3 years 3 years + 3 years = 6 years total. The Ships twin experiences something different. He hears the transponder received from Earth ping once every three seconds, and since the outbound leng only takes 3 years, he sees the Earth clock as counting only 1 year. 3/3 = 1 year On the return leg, the ship’s twin experiences three years worth of pings that are pinging at 3 pings per seconds, therefore the Earth clock advances 9 years during his 3 year return leg. 3 years x 3 = 9 years 1 year + 9 years = 10 years which is the time elapsed back on Earth. So not only is the math consistent, it sould not even be a surprise to either twin that their brother has aged differently.

Sorry for the late reply. I’ve been busy moving. The dual slit isn’t labeled and is the first component that I point out below:

OK, fair enough. I actually have proven how to explain the time paradox portion. In fact it’s another case of treating them as complimentary pairs as in: X vs ~X. I just didnt include it here because I didnt want to create multiple lines of debate. which In my view would be off topic to the op since his topic was based on the consequences of the TP not the solution. If I can find the time to squeeze it in, I will prepare an argurment and post it in a seperate thread so that this thread is not hijacked. if you dont see it in the next couple days, Ill try and post it after I move but I predict many complications in my near future, that has me feeling uncomfortable about it. Meaning I cant make any promises.

I’m not familiar with the example your citing, but logic and math can work hand in hand based on their complimentary property, in that they can cross validate each other. For example, we think up a new method for solving two unknowns using two equations, which by virtue of its origionality and its informal application is still logic.. next we formalize it applying logical properties and make it deterministic, so now its math based on logical premise, Now if we find an intuitive paradox. we can check its validity using deterministic math to prove or disprove the paradox by finding consistently correct results Since by definition, they are complimentary, they always must approach a problem from different vectors that make their cross validation possible. does any of the above explain your example? The formal logic I speak of was based on validity and falicy of a spoken language which in turn was the basis of greek philosophy.

Over enough time they should converge to both be optimal designs. Take the human brain which is about as complex a design of nature your going to get and the modern PC, the analogies were probably terrible with the first PCs, but as the PC improves its efficiency, the analogies work better and better.

Look again, its not obvious, but the blue is one slit and the red is the other slit

And by the way, since I wrote that reply on a local editor and cut and pasted that reply without typeing it in the editor, there was no way you could have read it in the two seconds it took from both downvotes. What are you guys trolls from Russia or something?

For the QT, its the simplest possible setup where we are essentially running two dual slit experiments back to back with a shared entangled source. So the setup should be trivial. If its about aligning the slits to the beams properly, since they are beams I would imagine the slits would be moved infront of the beams until they produced the interference pattern on both ends as preperations. Hmm, I think I am correlating the experiments correctly. With D3 & D4 they are only getting particles from one slit each, thats true. But thats the assumption with copenhegan interpretation, when observed its assumed the photons when slowed down to one photon at a time only goes through one slit at a time, not both. With D1 & D2, they are probably setup to make sure the any Δd = nλ such that the wave is always in phase, so in both cases, they are reading patterns from a superposition of both slits.