tar

Phi, I have spoken to many who did not want either one. Including me. However I voted, non-the-less. If people stayed home, that does not mean they wanted Hilary. It probably means we had no good choice this cycle. The electoral college gives power to the little states, so just a few people still get 2 senators. Arguments against the electoral college would be arguments against the senate, and arguments that we should just go by the house of reps or maybe just go by popular vote on each issue and bill, as we now have electronics that could quickly tally such, would be in play. But there are reasons why we have the senate, or England has the house of Lourdes. Trump won the electoral college, and such will only become official on December 19th. Some electoral college votes could still be cast for Hillary, regardless of the obligation to vote as the state voted. Nebraska and Maine split their votes according to the results of particular legislative districts, every other state does not. I am a registered Republican in a state that nearly always goes democrat in presidential elections and did in this one. If I voted Trump, my vote did not matter. I saw that news that Trump campaign had talked to Russia, but I also saw the same report said that Hilary people had as well. I am not believing that Trump is working with the Russians, and believe the Russians are just interested in getting the sanctions lifted and there is more of a chance that Putin will use Trump as a pawn, than that Trump is using Putin as an ally. Regards, TAR

Phi, I looked at the popular vote and as of a few hours ago Clinton won by 217,000. Minus California though, Trump won the popular vote, as as of now Clinton won by 26 points in California with still 1 million uncounted absentee ballots. With 55 electoral college votes, California often puts the democrat over the 270 mark, and when they don't they provide the democrat with the plurality of the popular vote. So saying that Hillary won the popular vote is true, but misleading if you wish to prove that Trump was not wanted by the American people. If California is taken out, Trump actually won the popular vote by more than 200,000. Probably closer to 800,000. So although America often goes as California and New York and Illinois goes, in this case it is obvious that America, other than California, voted, even just looking at popular vote, for Trump. So if you want to respect the popular vote, of people, respect the popular vote of the people that don't live in California, and respect their decision as to what direction they would like to see the country go in. Others on this thread have blamed the Republicans for fear and hatred and division. The Zenophobia, Racist and Sexist labels were placed on Trump and his supporters by Hilary and Reid and Warren. The fear of Trump is in their hearts, and is fostered by them in the hearts and minds of their followers. If people are to be respected, respect the people of the 49 states that voted for the man, who is now going to be our president, and support him, as he is now all of our leader, whether we like him or not. Regards, TAR

fredreload, Two thoughts. About the sphere, if you think of a sphere around a cube, the 12 edges of the cube provide a division of the sphere to where 6 Rochester cloaks could be built with equal spacing, allowing there to be at least 6 places around the sphere where you could stand to view the background without seeing the items hidden within the sphere where the light rays are not. The other thought is using fiber optic arrays. I wonder if you had a wall of ends of fiber optic strands and a similar wall of the other end of the fibers in the same orientation, to each other as the other end, whether you would see the image on the opposite side, as if you where looking through a window. If you would, then putting an item between the fibers and routing the fibers around the item would be a ray tracing analog. You would still have the distance problem, but you could set up your twelve sides of the sphere on the edges of a cube, so to speak, and effectively see the view on the other side of the device, without seeing the items you have hidden between the strands. Regards, TAR but alas I ran out of room inside the sphere for all the fibers, being that there is no circumference to go around since each of the 12 faces is actually on the circumference and each face is packed solid with fiber...oh well, maybe a combination of electronics and fibers where the signals could be recorded on the one face and regenerated on the other, maybe every other fiber being a receiver or a sender...or something...just a thought

fredreload, In the invisible four lens demo from Rochester I noticed that the grid behind is a little smaller than the grid around. Probably because the light has traveled farther than a straight line distance. In another link, the problem of phase change was brought up, which has similar cause. If you have a sphere and you are guiding the light around the sphere, the distance of travel of the light will be greater, around the circumference than through the center. Therefore the light coming from the backgrround, will be affected in two ways. Size of image seen, and phase of the light. A careful viewer or instrument would be able to pick up such irregularities in the area of the cloaking device, and such irregularities would be in the shape of the cloaking device, hence the device itself would not be invisible. It would be similar to putting something inside a box. You can't see the item, but you can see the box. Regards, TAR

fredreload, The trick is to design a "sceen" situation, that would look different from every possible different angle. That is you have to have both cameras and screens pointing in all directions. If you know the position of the observer, you can face the screen in her direction, and take a picture of the scene behind and project it toward her and be invisible. But if she moves to the left and you are still projecting the scene behind toward her former position, she will see the screen image does not match the background, in the shape and size of your cloak, thus giving you away. Like your making the cloak look black, you would not be invisible, you would be a black blob moving across the landscape, a ray tracing suit would only be affective if the camera and screen were in line to where what was behind the object, from the perspective of the viewer toward which you wish to be invisible, was projected on the front of the suit in the exact size required by the distance the observer is from both the object being cloaked, and the scene exactly behind. Perhaps this is possible through some tracking system that would identify the viewer and the position and distance of her eyes and project the appropriate image toward each of her eyes as she moved, but the system would fail, as soon as there was a second viewer. Regards, TAR Regards, TAR

fredreload, An interesting experiment to do with yourself, to understand light (RGB) and perception, as well as pigments (CMYK) and the absorbtion of light is to place a dot on a colored picture and stare at the dot for the count of 35 mississippis. Have a white sheet of paper prepared with a dot on it. After the count stare at the dot on the white sheet for about 5 seconds and you will see the image you were looking at at first appear in complementary colors. This is because the cones in your eyes responsible for picking up RGB wavelengths are somewhat fatigued after 35 seconds and the ones that where activated the most, have used up their chemicals which are quickly restored, but in the meantime, when you look at a white piece of paper, which has all the wavelengths reflected to your eye, the cones responsible for each position of the image will not be able to pump out the chemical for the color seen during the 35 seconds and you will instead experience the exact image, in terms of position and shape, in complementary colors. Magenta for Green, Yellow for Blue, and Cyan for Red. It is complicated to think through what you will see with various wavelengths of light emitted or reflected from a surface and going through various filters and bouncing off various surfaces that absorb certain frequencies and reflect others, and then enter your eye and activate various of the red and green and blue cones in your eye, but doing this experiment and thinking about light in terms of what frequencies are emitted, absorbed and reflected, will help you better understand and predict what the results will be when various filters are applied to various light sources. Regards, TAR by the way, subtractive color has to do with pigments, and pigments absorb certain frequencies, leaving the rest to reflect and reach your eye...hence those frequencies that have been absorbed, have been "subtracted" from the spectrum of wavelengths originally shone upon the object or of course a filter could "subtract" certain frequencies Or, consider what is happening when you see a green leaf or blade of grass. The sunlight which has light frequencies in the infrared-visible-ultraviolet spectrum includes the visible spectrum of rainbow colors Red, Orange, Yellow, Green, Blue, Indigo and Violet. The chlorophyll absorbs (subtracts, absorbs and utilizes the energy in the red, orange, yellow, and the blue, indigo, violet areas of the spectrum and reflects the stuff in the middle, making the thing appear green.

swansont, I understand I can not predict that sequence and then roll it. But the idea was that that sequence is made up of words, or sub sequences, or runs of one outcome, which are more likely than the run with which the 100 Heads sequence is made of. Like the 7 being a more likely outcome than the 10. It is more likely that the sequence will be made of something less than 100 in a row, because there are only 2 sequences that have this characteristic. All the others do not have this characteristic, and it is way more likely a sequence that does not have 100 in a row will be flipped than one that has 100 in a row. As there are way more ways to make sequences of small runs than sequences of large runs, the odds of having a small run sequence should be greater than having a large run sequence. Regards, TAR

swansont, well, I am talking about classes of sequences That certain sequences are more normal looking than others, and in that, their odds of occurring should be, from the beginning, considered more likely, because the law of large numbers will prevent a string of 100 from happening, whereas it will not prevent HHTTTHTHHHTTHTHTTTTHHHHTHTHTHHHTTTHHTHTHTHTHTHHHHHHTHTHTHTHTHTHTHHTTTHTHTTHTTTHHHTHTHHTTHTTHTTTHTTH from happening. I understand that getting the above sequence is just as rare as getting 100 Heads, as there are enough other arrangements to each have equal probability and still have a very small chance of getting that particular sequence, but if I were to tell you I made up the string, or I flipped the string, you would not know for sure, which was the case, because the sequence is normal looking. However, if I told you I just flipped HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHTTTTTTTTTTTTTTTTTTTTTTTTTT you would know I was lying, because the sequence laughs in the face of the law of large numbers. Regards, TAR After all, there is a REASON why the fair coin lands on either side with the same frequency. Expecting 100 Heads in a row ignores this reason. Whatever that reason may be.

Prometheus, So I probably read about that a long time ago and am considering that in my question. If there is a trial of a million, the probability of any particular sequence is just as likely as 1,000,000 heads, but the law of big numbers will not allow the 1,000,000 heads. Somewhere along the line, a tail is going to show. That particular sequence of 1,000,000 heads is working contrary to the law of large numbers, and therefore will not happen. Could happen, but will not, because the 50 50 nature of the flip is too strong to allow it. Therefore, some other particular sequence, that has the same mathematical probability of occurring, but that more closely resembles a 50 50 split will occur. Suggesting to me, that there should be an average taken to where certain sequences that deviate from the norm, or the pull of the law of large numbers should be engaged, as the number of trials increase. Maybe under 6 trials or so, it does not matter much, but as you go to 10 or 100 or 1000, the improbability of the long runs should cause one to lower the odds of those sequences that include long runs, and favor the sequences that do not. Regards, TAR Or in some way adjust the odds to include the law of large numbers. I am thinking something like a bell curve arrangement, where short run sequences will gather around the norm, and long run sequence will be the outliers.

The odds were given that the event should happen once every finite number of trials. The infinite part was just the idea that any odds that were not zero, would be sufficient to ensure that eventually the happening would happen. It was the same question in both cases...would it happen? I understand that one flip does not influence the next, except given a set of one hundred flips to study, one finds that alternation happen at close to the same rate as flipping the same thing. This likelihood that there will be about 50 heads and 50 tails in the sequence, seems to favor this class of sequences over the class of sequences that do not satisfy the likely distribution. Regards, TAR

dimreepr, A sperm whale popping into existence over the planet could not happen. You need the conditions found in the sea, and a mommy and daddy sperm whale, which you do not have over the planet. Plus whales start out as little whales. That is fiction and an example of an event with zero possibility of happening, even given an infinite amount of time. I think the universe must be finite in size because we have no evidence of matter being able to move at an infinite speed, and no matter how fast inflation was, it could not have been infinite in speed, because such a speed has no meaning. Therefore, if the universe 13.8 billion years ago was the size of a speck, it could not have grown to an infinite size, in a finite period of time. Therefore, the observable universe must be a finite percentage of the whole universe. Even if the whole universe is 100,000,000 times the size of the observable universe, it is still finite in size and the odds of everything somewhere else, happen in the exact sequence of how they happened here, with every person with exactly the same name and the exact same arrangement of elements and isotopes is beyond the realm of possibility...the number you could assign to the odds of an exact Earth existing elsewherewould be smaller than odds can be and there are not enough galaxies to cover these odds. Guaranteed. Besides, there would be at least one thing that could never be the same. When I would point to the other identical Earth, my doppelganger would be ponting in the opposite direction, disallowing the exact happenings in both places. Regards, TAR regards, TAR

swansont, Well sure the probability of a possible event happening is 1 in whatever trials. My argument is that reality is such that some things are not possible, because of the long odds. If you say it is possible, because you figured the odds and they are not zero, therefore it is possible, you have a tautology there. If when discussing probability the important thing is whether it is possible given infinite trials, or impossible given infinite trials, then the solution to the problem is given in the premises. As soon as you ascribe odds, and the odds are not 0 then you have started the problem, by saying it is possible, by ascribing odds. The suggestion was made before, that any sequence could happen next. Do you think this is anywhere near the way reality works? Are there not types of sequences that are going to happen BECAUSE each flip is either a head or a tail? What do you think of my one trial observation, that it is likely, when you flip a hundred times, that you will get 50ish runs of heads or tails and the length of the runs is going to be short, with the most runs at length of 1, then 2 then 3 then 4 then 5 with maybe on rare occasions runs of greater length? That this "type" of sequence, given 100 throws is more likely than sequences involving multiple runs of 31? Regards, TAR It is like considering that there are enough galaxies and enough planets in each galaxy to consider there must be another Earth somewhere, with exactly what is happening here, happening there. When in reality there are not enough galaxies, given a finite universe, to cover the odds.

Swansont, I always retain the right to question the validity of a premise upon which the other is going. Besides, I was using the foul shooting example within the scope of a general discussion on probability, that I was split into, I therefore cannot go off topic, if I am discussing probability in general. And in that, a discussion of the meaning of infinite trials, is certainly central to the idea that if a probability is not zero then it is one. My intuition says that there is a difference in the probability of a thing happening if it happens 1 in a million or if it happens once in a googleplex. Saying that both events could happen on the next trial, might be mathematically a true statement, but in terms of expectations, I would bet my life on the googleplex thing not happening, whereas I would not be so bold with the one in a million. someone suggested, that ANY sequence can happen, given infinity, and I think that is a thing that can happen only in one's mind in reality, there are influences that favor certain sequences over others, and when all the influences work in concert, there are some sequences where it is just unreasonable to ever expect them to occur like swansont being the sole winner of the jackpot in every lottery in the country for the next 150 years you could assign a probability and therefore it could happen...but could it? regards, TAR too many things about reality and what normally happens, would have to change for it to happen Therefore it will not happen, even if the odds are mathematically 1. and the odds instantly become 0 the first time there is a drawing where you don't have a winning ticket What happens the next 150 years does not even matter once the first loss makes the sequence impossible. Dr. Krettin, Yeah, I knew about those dice when I made the comment. They were not the set I was rolling. Regards, TAR

But there is the debate. It is not confusion. Do the numbers force reality, or does reality force the numbers? If you are using reality to come up with the odds in the first place, I think it appropriate to continue to use reality throughout the stretch of trials. It is even within the realm of the discussion, to consider if infinity ever can actually happen. By definition, you can never "get" there, so if it takes an infinite amount of time for a thing to happen, it is not going to happen. it "could", but its not going to

swansont, I understand the rule, and the idea, but in the case of PI the numbers are not random, they are coming up for a reason, that has to do with the ratio of the circumference of a circle to the diameter. The sequence I proposed has a probability of zero. And although infinity is really big and if you can assign a probability to an event, it would, given an infinite amount of trials eventually, or on the next trial, achieve the low probability arrangement, there are finite limits to certain things in reality and reasons for a thing happening or not, that would make the probability actually zero, upon inspection. For instance, no matter how many times you roll the dice, you will never get a queen of hearts. For that, you need a deck of cards. Or the chances of a particular particle being anywhere in the next nanosecond, are one thing if considered mathematically, and another thing if considered using common sense and reality, where everything must fit together. It cannot "get" further than its velocity will take it, in the time period you are considering. Or if you figure the chances of all the electrons on earth winding up in one country while all the protons wind up in another...you might be able to assign a probability, but intuition wise one would know that the integrity of the places would be destroyed if such an event were to occur, so, the probability is, for all intents and purposes, zero. Not mathematically, but when held up against reality. In the original thread for instance, the odds of missing 100 in row, were contingent on the odds you assigned to the shooter, of getting one shot in. If a shooter never missed, up to that point when you assigned the odds, then the probability for her to miss 100 in a row, would be zero. But that would not be the reality of the situation. Someone could open the door to the gym and cause a distraction or a breeze that would affect a later shot. So yes, I understand the principle, and the idea, that if you assign a probability, then the thing will eventually happen...but your probability assignment might be in error, and a condition you thought would be a constant might turn into a variable or become impossible due to other things happening in the universe over your infinite amount of trials. As in the OP of the original thread, the poster suggested that fatigue not be a factor. At one point I suggested that the gym would be torn down, before infinity could do its mathematical magic. Regards, TAR So my only point is that the numbers work, and one can "get" the reality that the numbers are after, but reality often defeats the numbers. In my old job, Six Sigma goals for a certain amount of uptime for the computer system that ran our hotline put the numbers at 99.996 or something. I forget the exact number gotten to by a certain deviation, but one time the system was down for nearly 2 days, and at the time, I calculated the amount of continuous uptime that would be required to reach the goal, and it was on the order of thousands of years, like 20 or 30 thousand. I think that the probability of reaching the goal was, at that point, effectively zero. We would not be using that system for 30 thousand years, and the next failure would push the likelihood of reaching the goal, even further down the line. In the shooting scenario, the foul shooter would likely get better given an infinite amount of practice, and the odds of missing 100 in a row would actually dwindle so that the original odds would be incorrect, and the odds would get longer and longer as you went along.

I don't know about that any other sequence thing. You cannot, for instance, expect that given enough time the first 12.1 trillion digits of PI will repeat backward as the second 12.1 with the exception of there being an 87654321 in every previous spot, where there used to be a 99999999 in the first 12.1 trillion digits. Such a sequence is way too long to expect there would be any reason for the thing to ever happen. Even given an infinite amount of digits to take PI to, your sequence is impossible to arrive at, as soon as the first digit after the 12.1 trillionith digit is not the one you were looking for.

Enough to consider the more possible patterns are as if a 100 trial run of coin toss could be expected to be like an approximately 50 character word, spelled with mostly As a few less Bs, a few less Cs a few less Ds and a few less Es. With maybe patterns that had an F and/or a G being less likely than patterns with no letters past I (9p H or T in a row.) In other words, words spelt with letters at the end of the alphabet, representing runs of 20 or more, would be less likely than patterns spelled with letters representing smaller runs. DrKrettin, But pi is neither random nor proven to be a normal number. I suppose a normal number would be what would be expected as a normal distribution of numbers and strings and combinations and such, as in a bell curve, normal distribution, where certain outcomes are more normal than others that occur in a rarer and rarer fashion, at the various deviations from the norm. If you pick 100 people at random, it is more likely you will get 68 within a standard deviation of 100 IQ points, than 68 with an IQ above 165. Regards, TAR

Thread, So I get the basic idea, that any particular outcome of 100 tosses of the coin is exactly as likely as any other, but within the 100 tosses, there are strings of 2, strings of 4, strings of 5, strings of 10, strings of 50, strings of 25, and strings of 20. The laws of probability hold for each of these strings as well, and one can consider the odds of something happening or not happening in each string, broken up into any size and starting and ending anywhere within the 100 trial set. These various influences conspire to create certain "kinds" of patterns, that are more likely then others. As in bridge, where you wind up, most of the time with suit lengths of 3 and 4 with sometimes 5 and 2 and some rarer times singletons and voids. And often you can tell something about the distribution of suits in other peoples hands based on what you have in your own. If you have 6 hearts, there are only 7 hearts in the other three hands, and most likely someone has 3 and the other two have 2. It can break other ways, but it is more common to find something close to equal distribution of all things in all ways. If there are 40 high card points to be had, for instance, it will be likely that you have close to 10 points. If you have 13 points, you know you have more high cards than average, and you open the bidding. If your partner opens and you have less than 6 points, you know that on average the opponents have as many points as your team and you will have difficulty making a high contract, and pass if you have three of your partner's suit. In other words, any possible distribution is as likely as any other, but there is more than one type of distribution being considered, and everything still has to add up. Of the four kings, each must be somewhere, on each deal. With the coin toss I did, there were more single outcome runs, a few less two in a row, a few less 3 in a row, a few less 4 in a row and a few less 5 in a row. With no runs of 6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33.... My guess is that there is something about the various probabilities that all must add up, that conspire together, to make 100 trial runs more likely consisting of internal runs of 1,2,3,4,5 and 6, than runs of 25, 50, and 5 runs of 10. Regards TAR

DrKrettin, I understand, and thought that was the answer, but I am a little confused as to the statement that any pattern is just as likely as any other. After all 100 hits or 100 misses in a row have the same probability, but other patterns, other combinations of shorter runs of hits and misses have to be more likely than 100 of just the one outcome. There must be for instance a greater likelihood of having a streak of 3 of one outcome and then a streak of two of the other outcome...and a further combination of alternating and short runs and an occasional run of more than 5 adding up to a hundred, than having a streak of 62 of the one outcome and then a streak of 38 of the other. In other words there must be an average run length of either outcome, and patterns that included several of this average run length, would be more likely than patterns that included rare run lengths. Regards, TAR for instance, I just flipped a coin 100 times. HTTHHHTTTTTHTHTHTTTTHTTHTHTTHHTHHTHTHHHTTHTHHTTTHTTTHTHHHHHTHHHTHTTTTHTHHTHHHTTTHTTTTHHHTHTHHHTTHTT 48 HEADS 52 TAILS 54 RUNS 29 RUNS OF 1 11 RUNS OF 2 9 RUNS OF 3 3 RUNS OF 4 2 RUNS OF 5 AVERAGE RUN AROUND 1.85 My expectations would be, that patterns that yielded similar stats, would be more likely than patterns that yielded widely divergent stats. That is, from the one trial, I could guess that out of a 100 flips, there would be close to 50 heads and 50 tails, and maybe about 50 runs with the most numerous run being a run of 1, then the next numerous, runs of 2, the next numerous runs of 3, then 4 then 5. Runs of 6 would happen now and again, runs of 7 less likely and 8 even less likely, etc.

Just in attempt to understand probability better, what if you are a 50 percent shooter, but you only count every other shot. Are the odds exactly the same, however you select your 100 consecutive shots that count, or does alternating the ones that count allow for a greater probability that the misses and hits will alternate, and you might count a greater number of hits, or a greater number of misses in a row?

Dr. Krettin What are the odds if you don't constrain yourself to 100 trial sets, but shoot continuously so that any streak of 100 misses count. As in you miss the last 75 of your first set and miss the first 25 of your second set? Regards, TAR

but here is where the numbers do matter Before, with the 1 in 3 shooter we knocked the odds down to 1 in 2000 which seems possible. But with the 50 50 shooter the odds are way more remote that they will miss 100 in a row. Even dividing the years it would take one 50 50 shooter to probably miss all 100 of a 100 trial set by 500,000,000, or the number of basketball players currently around, you still get a length of time required, that is 1 million times the age of the universe. So it matters greatly, in your debate with your head coach, what the caliber of player you are coaching. If you are coaching NBA players that shoot better than 50 percent then you are not going to see a trial of 100 where the guy misses all of them...unless he is injured or drunk, or otherwise compromised. On the other hand, if you are coaching a group that shoots a lot worse than 1 in three, like one in four or 1 in 5 or whatever, then you are entering a situation where a miss of 100 in a row is within the realm of possibility. That is, that the numbers would allow someone that does not shoot very well to miss 100 in a row, at some point since the beginning of basketball foul shooting. Or in terms of the OP question, it matters what kind of foul shooter you are considering, before you can calculate the odds of missing 100 in a row. Regards, TAR

7.3 septillion years of 100 shots every 5 minutes and ONE time on average during the 7.3 septillion years you should miss 100 in a row...and the numbers don't matter? Half a quadrillion times the age of the universe 'til the event is probably going to occur, and the numbers don't matter, because it could happen tomorrow? I don't know, at what point a probability is so low as that it should be considered zero...for all intents and purposes...as in, it is not likely to happen in your lifetime. Or put another way, it is not going to happen in your lifetime.

does missing 99 in a row lower the percentage of free throw shooter you are below 50 percent, and make it a little more likely you are going to miss the next shot?

so what is the probability of missing 100 free throws in a row, if you are a 50 percent free throw shooter? if you are a 50 percent free throw shooter, are the odds the same that you will miss 100 in a row, as that you will make 100 in a row? if you are a 50 percent free throw shooter, are the odds of any particular streak of misses the same as the odds of that number of makes in a row?