TakenItSeriously

The problem with general relativity is that it is hightly non-linear. You cannot simply add two solutions to get another one.

But then wouldn't that make computer modeling a more practical solution?

 

Edit to add:

Or perhaps modeling two fields prevents establishing a single inertial reference frame?

I've dealt with electromagnetic field solvers before.

 

https://en.m.wikipedia.org/wiki/Electromagnetic_field_solver

 

Though, Im not sure if they would be appropriate to use. I understand that they are based upon some kind of FEM analysts, but I'm assuming it must be dependent on anchoring a structure to some reference point which, I assume, wouldn't work for a gravity wave.

 

Edit to add:

I see your talking about gravity "fields" so, perhaps it could work as long as you establish an inertial reference frame to the massive object under study.

 

The two fields are based upon the same formulas, they are only different in magnitude.

there is a number of huge threads on coin/ball bearing weighing; including some neat proofs and algorithms.

 

here is one of my favourites if you like this sort of thing - please no open spoilers here. And apologies I should have put my answers in spoiler tags

 

 

 

http://www.xkcd.com/blue_eyes.html

When you say "please no opens spoilers here" are you referring to this this thread or the link you posted.

 

Actually, given the title of the problem, I have my doubts as to my chances for solving it though it's a rare experience for me so I wouldnt mind continuing with some questions.

 

Is the statement that everyone can see everyone else 100% of the time. Should that be taken literally? I believe I may have a solution, if such is not the case.

It is wrong because it is not right - there would be an internal contradiction if it were to be correct; ie the maths says the probability is 1/3:2/3 (stay:switch) which is not the same as 1/2:1/2

 

Why people think 50:50 (stay:switch) is correct is because they guess rather than do the maths. If you do the maths you get it right, if you use walking-ape logic you get it wrong. I think - if you really want to investigate the flawed reasoning you have to get into psych rather than maths and that your best avenue would be reading the literally hundreds (perhaps thousands) of internet threads on this very problem. There are lots of misguided souls out there who continue to bang on without the faintest glimpse of enlightenment.

 

You say "trust me" - with respect No. This is SFN - you should pony up proof that this is manifestation of a deep set internal make up. And where are the studies - must have been done a long time ago as Monty Hall is very very famous and that would completely screw the validity of any test

 

But there is no mathematical reason why people are wrong - just a lack of mathematical reasoning

You are correct, in that the reason the overwhelming majority of people thought 50:50 was correct is based upon human nature. But, that is the point of the question. Why does the 50:50 choice seem so intuitively correct?

 

It is a varidian paradox. Or a result that differs from what seems to be obvious.

 

I put that in one of the hints, after you had read the OP. Unfortunately, I couldn't think of a way to notify everyone as to when hints would get updated.

 

I generally update hints when peoples responses in the thread were touching on correct points that were on the right track. So look for more hint updates after this post.

 

You are also correct in that math is not the proper tool for finding the source of an incorrect solution. At least, not for a comprehensive proof (beyond a reasonable doubt). It's the tool for finding correct solutions.

 

When looking for the source of an incorrect response, you need to start at that response and work backwards through induction, at least initially. But that is not how most logic problems are approached. Only real world problems are approached that way.

 

For example, when solving a crime, it is always an induction process at the beginning to follow the clues that will produce all of the facts. At that point you can reassess the problem from the perspective of the past moving forward through a deduction process.

 

I had intended the following to be a separate post, unfortunately the forum structure prevents that from happening.

 

Hint update:

 

I assume everyone here is familiar with the Monty Hall problem.

I'm not looking for the solution.

I'm not looking for another proof for the solution.

I'm not even looking for a full game solution which might incidentally show how the 50:50 solution couldn't be correct.

The challenge is to directly figure out why the 50:50 answer is wrong but more importantly why it seems so axiomatically correct.

I've had the solution for some time, but wasn't sure how to present it. Since it's become a classic logic riddle, I realized this was probably the best forum. At least I hope so, Im still pretty new here.

I'll give it some time and provide a new hint every now and then, before giving the solution.

Hint:

If you find the 50:50 answer axiomatic, than you will flip over the solution.

Hint:

The answer about why we perceive the 50:50 solution as correct will tell us something about how the subconscious perceives reality.

Hint:

Don't think of this as a logic problem,its more like a human nature problem.

Hint:

See post #11 for the approach one would need to take to start trying to solve this problem.

 

It is not an easy solution. I'm pretty sure mine was the first attempt to prove it. But a 100% valid proof is not possible with regards to human nature. It can only be intrinsically proven to the point of making sense.

 

You run a popular weekly poker game and a late cancellation has left you with a seat to fill

 

You ask a friend visiting from out of town if he would like to play. He has played poker but doesn't want to be out classed as a moderately skilled player, so he asks you what the average win rate is for all of the players in the game.

 

The players have allowed you keep detailed win/loss records which you share with all of your players.

 

The game is fed by a player pool of 50 semi-regular players they each have a wide variety of hours in the game, and buy-ins cover the range. Assume all normal distributions. And 30 hand per hour

 

The game has run without fail for two years at an average of 7 hours per week. Do you have enough information to provide an accurate answer for your friend?

 

Show your work.

let cup be w and spoon z. x is tea and y is coffee. you end up with

 

(wx+zy)*(w/(w+z) in the cup that you added to and then took from

 

wy-zy+(wx+zy)*(z/(w+z)) in the cup that you took from and then added to

 

both simplify to similar expressions

 

(w(wy+zx))/(w+z)

 

and

 

(w (wx+zy))/(w+z)

 

You will notice that they are the same apart from the x and y are switched ie you end up with the same ratio in each cup - but obviously one is ratio of coffee to tea and the other tea to coffee

Correct!

 

Excellent analysis, recognizing symmetry is the key.

Intuitively - you end up with Spilt tea and Phi calling you names for messing up his carpet.

 

Heuristically - it must be the same ratio as you end up with the same amount in each cup. If you both started and ended with a cup of tea and a cup of coffee (however distributed) you must end with a cup of tea and a cup of coffee; and as each cup has same volume in at end the yo must have as much coffee in the tea cup as tea in the coffee cup

Also correct, and very quick at finding the logical shortcut. Nice job.

 

In Layperson: since both volumes started and ended up being a cup, what was missing from one, had to be replaced by the same amount of the other.

Correct!

Excellent analysis, recognizing symmetry is the key.

 

Also correct, and very quick at finding the logical shortcut. Nice job.

In Layperson: since both volumes started and ended up being a cup, what was missing from one, had to be replaced by the same amount of the other.

I'll just skip ahead to a tougher problem, have you head the riddle about finding the odd ballbearing from a set of 12 ballbearings?

Please clarify, does "a tea cup" hold "exactly 1 cup" of liquid (in this case tea), or does it hold more?

 

It will make a difference if the tea cup holds "exactly" one cup, since you'll be displacing tea out of the cup when you put an extra spoon of coffee in the tea.

Both cups have room for more liquid, and their initial volumes were equal.

 

That is quite possibly the worse answer to Monty Hall I have seen. If you simply had a 50:50 chance then why swap - the clever part of the problem is that Monty always reveals a goat and by doing so changes the information you have and thus increases your chances (you have a 1/3 stay and 2/3 switch win probality

Correct.

 

But why is the 50:50 answer wrong and why does it seem intuitively correct.

 

No proofs for the 1/3:2/3 answer please. Only direct proofs for why the 50:50 answer is wrong.

Because humans are naturally bad at probability - it is something that a huge majority must learn rather than understand intuitively. There are many things like that - many of the topics here are also unintuitive BUT they do not crop up so regularly in common world experiences.

 

Actually, even prominent mathematicians were fooled by this problem.

 

Studies have shown that for those who initially got the answer wrong it seemed to be independent of intelligence or education.

That's the incorrect answer. You can do it just marking out the possibility space with pictures of doors, cars, and goats, or you can do it the Bayesian way and you get the same answer. That answer is not 50/50.You can run actual trials (as Mythbusters did) and confirm. 50/50 is an incorrect answer.Horrible quality video to follow:https://www.youtube.com/watch?v=FAljAvR3L4s

Thats, all true but it doesn't address the 50:50 answer directly or why most people think 50:50 is correct.

 

Trust me the answer tells us important information about how the subconscious perceives reality.

I am still not entirely sure what your question is, but the 50:50 appears to be intuitively correct (whilst being wrong) as people generally dismiss the additional information provided by revealing one wrong door.

 

Edit: crossposted

Actually, they didn't dismiss the additional information, since they thought their odds changed from 1/3 to 50:50.

 

So they were wrong despite changing their odds to what they thought they knew was correct.

 

Your definitely on the right track though.

You have a coffee cup holding exactly 1 cup of coffee and a tea cup holding exactly 1 cup of tea.

 

Using a standard sized teaspoon, you transfer one teaspoon of coffee and mix it in with the tea. You then transfer a teaspoon of that mixture back into the coffee cup.

 

Question:

A) Is there more coffee in the tea cup

B) Is there more tea in the coffee cup

C) Or are the amounts the same?.

 

Justify your answer.

It isn't paradoxical the answer is that once the host opens the first door with a goat behind it you have a 50:50 chance of getting the car.

I was afraid this would happen, Im not asking for the solution or proof.

 

The challenge is to figure out why the incorrect intuitive answer is intuitive.

 

Ive cleaned up the op to hopefully clarify this point.

 

Sorry, it was a mess. My editor is acting up again and it starts becoming a chore to edit posts properly.

.

These tests strongly rely on perfect English language knowledge.

 

IMHO to truly test somebody mental acuity we need tests that will work without having to know language perfectly. That's why IQ tests looks like they look.Try beating chimps in this:

http://www.youtube.com/watch?v=zsXP8qeFF6A

 

They must love these drops..

Thanks for the video.

 

I've always had an extremely poor short term and working memory. I'd even consider it a learning disability, though it was never diagnosed, and Ive found very little over the subject matter.

 

Also I had reading comprehension issues in which I cant read any faster than I can comprehend the words in real time. And if a sentence makes no sense such as missing a reference given later, poorly written, or just unclear concepts from the author of the material, I can read the same paragraph over and over without any recollection of what I was reading.

 

So since memory and reading comprehension were such huge factors in education, it was a struggle to even finish any test. And timed tests were an even greater problem for me.

 

Ive only recently started to speculate that short term memory and reading comprehension are linked.

 

I believe, when people read, they store it in short term cache, which is then accessed by their subconscious which I believe does all of your background tasks it takes like reading

 

 

 

I always that was odd since I was strong in comprehension in general.

 

In an experiment,you shoot a bullet , down a level flat plane, and drop a bullet at the same moment.

 

A) At the exact moment bullet A) leaves the barrel of your gun, your friend dropped another bullet B) from his hand at exactly the same height and moment the bullet was expelled out of the end of your gun..

 

1) Which bullet hits the ground first?

If the gun shot was level, they hit at the same time.

 

You are rowing up river against a flow of 5 miles per hour, after 1 hour of rowing you notice you have dropped your hat and immediately turn around and row at the same rate down river to retrieve it (Discard the time needed to actually turn your boat around)

 

2) How long will it take to catch up with your hat and retrieve it from the river?

 

It's being nit picky, but if you start mixing logical riddles with word play riddles, it's just not a good mix. And people will assume the wrong meaning when looking for more word play.

For instance, it sounds like a wordplay riddle for traveling at the same speed as the hat.

 

You are in a room with just 2 unmarked doors, one door leads to the hangman and death, the other leads to freedom and life.

There are 2 guards in the room with you, one can only lie the other can only tell the truth. You have no idea which is which.

 

You are allowed just one question to one of the guards, you chose which, by just by asking this one question, you must establish exactly which door is the one leading to freedom or you die

 

3) What is the correct question?.

This one is a classic, I answered back in the 80s. I have a bunch of logical riddles from back then, though how many of them I can recall may not be considered a bunch.

I assume everyone here is familiar with the Monty Hall problem.

I'm not looking for the solution.

I'm not looking for another proof for the solution.

I'm not even looking for a full game solution which might incidentally show how the 50:50 solution couldn't be correct..

 

The challenge is to directly figure out why the 50:50 answer is wrong but more importantly why it seems so axiomatically correct.

 

I've had the solution for some time, but wasn't sure how to present it. Since it's become a classic logic riddle, I realized this was probably the best forum. At least I hope so, Im still pretty new here.

 

I'll give it some time and provide a new hint every now and then, before giving the solution.

 

 

Hint:

If you find the 50:50 answer axiomatic, than you will flip over the solution.

 

Hint:

The answer about why we perceive the 50:50 solution as correct will tell us something about how the subconscious perceives reality.

 

Hint:

Don't think of this as a logic problem,its more like a human nature problem.

 

PS, I'm posting from an iPad and don't have an editor toolbox. I'd appreciate it if someone could post a hidden text box or spoiler alert box so I can clip the proper formatting elements. Thanks.

Does anyone tell scientific facts about games for brain? In other words, I play games for brain and try to train, I believe that they help to progressing cognitive processes. Thanks in advance.

As a former poker pro, I used to play games, work on jigsaw puzzles, etc. that I found had connections to various aspects of poker.

 

I also had about 10K hours working an a suite of tools for MTT online play, so after poker was shut down in the US, I went into a pretty bad depression for a few years where I didnt do much to challenge myself.

 

One day I tried to play Freecell which I could previously beat consistently playing with a deck of cards, so there were no takebacks. I dug myself into a dead end and failed to solve the next couple of tries, having trouble focusing, a strong desire to give up, so on. I continued to fail at other games which I thought were trivial in the past. That's when I realised I wasn't as bright as I used to be.

 

That snapped me out of my funk and I first started playing Civilization which is a pretty challenging strategy game and starting at an easy level, worked my way through all of the levels and eventually managed to beat the deity level three times without using blitz tactics or anti-computer strategies. I suspect that level wasn't intended to be beatable and the next version that rolled out, cheated where an AI opponent would hand victory to another AI opponent as soon as a player win at the deity level was an otherwise strategic lock.

 

I next started working on projects, again and found a method for calculating how to bias the stub after accounting for all player ranges, in the hand or muck.

 

Since I was using weighted values instead of integers, I had to create algorithms to estimate combinatorics. When I finished I realized there wasn't any way to test my results since I had invented the method itself.

 

My next project was to develop a Montecarlo sim for a static game where the player ranges never changed, yet the deal had to remain completely random. The results matched up pretty pretty convincingly.

 

I even revived an old physics project I was too busy to work on some 20 years before, though I was formally an engineer, not a physicist.. Im used to being an autodidact but, learning all of the major branches of physics is a bit nuts.

 

Yet, ten years before I couldn't beat a game of Free Cell If I needed to. I was always a firm believer in if you dont use it you loose it. Now I don't need to believe in it, I've lived though it..

 

People are born with various gifts or talents. Yet it's still up to us to make the most of what we're given. It's not as if someone who was born gifted with rare athletic ability could expect to win in the Olympics without a life long commitment to training.

 

You don't need to become fanatic about it or become antisocial, perhaps becoming a little more disciplined would be a good first step. Jigsaw puzzles are terrific training for discipline.

Is there any property or function of a photon that would make them inconsistent with being dipoles?

 

Acting as force carriers, propagating at the speed of light, having 0 mass,...?

The traveler's distance covered when traveling to a distant planet and back again was shorter due to length contraction. than the observer witnessed back on earth. He could only observe the traveler covering the entire distance which would take longer, thus explaining the asymetrical results of time experienced by the twins due to an asymetrical experiences of distance traveled by one twin and witnessed differently by the other twin.

 

If you wish, I have a proof written up to show the numbers balance but it's pretty long.

 

BTW I believe you could provide the same arguement to show why distance appears to be expanding across the universe. In that case we would be the ones moving at relativistic speed Away from observers at the far end of the universe, so we would be experiencing length expansion, but It doesnt actually serve as a proof, I think, so much as an out to avoid the need out to avoid the need for dark energy since the observers never actually meet.

I ran into a similar problem of integers getting too large a long time ago. The first program I ever wrote in fact, I think I was a junior in highschool so it must have been 1981 and I was on one of the first macintosh computers, no HD but state of the art 31/4 floppies though ;-)

 

I was trying to use a single database that could be devided into into multiple databases where any recored could be in 1 to n databases and I didn't want to have any redundant records.

 

I assigned a prime number to each smaller DB and each record was assigned a multiple of the primes for the DBs they were assigned to. Then any DB would contain only those records where the mod of the multiple was 0.

 

The problem was I was limited to n=10 I think, before the integer became too large if a record was in all n databases. I never figured out a way around that limit, but then there was no internet back then either.

 

I recently ran into a similar issue with perfect numbers when I ran out of significant figures in Excel. VBA could work as well. Any ideas on getting around this problem would be appreciated.

No in actuality we can calculate the proper distance when the object first started emitting light and the proper distance today of any stellar object.

Granted the distance today requires assumptions that nothing out of the ordinary occured.

The universe doesnt appear larger in the past. You can't see an edge of the observable universe at any point in time.

That isnt how it works. The furthest back we can see is shortly after the dark ages at the surface of last scattering. That CMB surrounds us today.

No matter which direction you look in or how far you look you will see the universe around you. Your merely at the center of the observable universe due to your current location.

You never have a god like view of the full universe in a particular direction as were inside the universe.

You can only calculate the size of that observable portion based upon observation and redshift data with other methods such as the Sache Wolfe effect and stellar parallax. With that data we extrapolate the proper distances. The FLRW metric initially uses commoving distances ( in the past we used conformal distances prior to the cosmological constant).

These in turn allow to calculate the proper distance then and today.

The calculator in my signature does precisely that.

As far as the observable universe it will always be a sphere. When they state the universe is flat. They are not describing its shape. They are describing its actual density compared to its critical density.

This is in actuality a thermodynamic relationship that affects light paths. A perfectly flat universe without the cosmological constant is one that is static. Yet this is in itself unstable.

Our universe is extremely close to flat with a cosmological constant so will continue to expand.

I suggest reading these two articles I wrote a few years back they will help.http://cosmology101.wikidot.com/redshift-and-expansionhttp://cosmology101.wikidot.com/universe-geometry

Page two of the last article details the Flrw metric and how curvature affects light paths (in effect the null geodesics on a universal scale GR)

Here is page two on the geometry article.http://cosmology101.wikidot.com/geometry-flrw-metric/

I broke this section down to the 2d 3d and 4d metrics on all three curvatures. Positive,negative and flat cosmologies. The formulas on this page is the calculations for commoving distances.

I think I figured it out.

I realized we had to be on different pages which was my fault.

 

I had assumed we knew the size of the early universe. Specifically the age and the global size at the CMB state, which, I assumed to be the reference state for projecting lookback events into the proper time and proper distance.

 

Then I realised, that cant be logically true because we don't know if the universe is infinite.

 

Thus making my line of reasoning for comparring CMB global size totally invalid.

 

So now Im assuming the datum data is the density and time at CMB. Is this correct?

Incorrect. You can see light from further than the age of the universe. This is due to expansion.

This is tricky for many to understand how light can reach us at distances greater than the age of the universe.

What happens is that the light has already travelled part of the way. Yet during the light path the distances on the path already travelled and ahead of the light path continues to expand. Locally though that expansion per Mpc is miniscule so light will continue to make headway.

The observable universe is significantly larger than 13.7 Gly in radius.

This expansion affects the light path wavelength causing cosmological redshift

Ok but my point is that we are seeing those distant objects as they existed billions of years ago right? Yet the universe seems to be larger back then because those objects that surround us are further away.

 

Let me try this example. We create imaginary concentric spheres with us at the center every billion light years. Then we see the universe as it existed back in time a billion years ago, 2 billion years ago,...,and finally the CMB surrounds everything we can see. 13.7 billion years ago.

 

With every billion years we look back in time the universe appears to be larger, not smaller.

 

I assume this is an illusion of spacetime because we know the further back we go the smaller the universe should be.

I have seen a couple of references on EM forces creating galactic structure such as spiral arms and perhaps even intergalactic structure such as galactic filaments.

 

https://public.nrao.edu/news/pressreleases/galaxy-magnetic-field

Or in the documentary:

"The Universe Forces of Mass Construction"

 

But, it seems to me that a structure such as a spiral arm should explain the velocities.

 

Imagine EM forces tying the SMBH to stars in a spiral arms, and every star in each arm connected in a lattice work of EM forces creating a semi-rigid spiral arm structure. Then you would expect the same kind of swept back arm that we see. Then the structure, in turn would create a compliance force that should account for the added motion of the stars.

 

On the other hand gravity alone doesnt make sense. Imagine we added enough brown dwarfs in a perfect radial distribution that was the opposite from the radial distribution of visible stars to explain the flat velocity curve.

 

Then the velocities would make sense but the galactic structures wouldnt. Even if they formed arms for some reason, which would seem rather bizaar, they wouldnt be swept back, they would be spokes, because there wouldn't be any kind of resistance force to cause it.

 

I could see gravity creating a smooth disk, belts, rings or clustering into BHs like asteroids created the planets, but it's hard to imagine why gravity would create most of the structures like those found in Galaxies.

 

Perhaps this is also why we don't see DM effect planets. While the stars all have strong EM fields, the planets have relatively weak or no fields and em fields wouldnt effect the motions of planets.

 

We didnt know EM forces existed at a galactic scale when DM was calculated and couldn't have taken those forces into account. So with gravity plus structure, it seems like there is no need for DM.

 

So the question is could EM forces be strong enough to form spiral arms in a galaxy if given enough time?

It is not an illusion. You can look in any direction and see galaxies some of which will be about 13 billion light years away. Or the CMB which is 13.8 billion light years away.

 

Actually, that's not quite true. The light has taken 13 billion light years to get here. But when it was emitted, those galaxies were about 4 billion light years away. Now they are about 45 billion light years away.

If its not an illusion then the size of the universe 13.7 Billion years ago during the CMB phase would have had a diameter of 27 billion light years since it completely surrounds our observable universe which can't be true.

 

...In my opinion the answer to this question is, briefly, this: as far as the propositions of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. ...

Albert Einstein, "Geometry and Experience", 1921

Wow, Ive been looking for a quote ever since I saw that documentary but searching for quotes without knowing how it was stated is next to impossible for someone who's been quoted probably more than any man in history.

Imagine we look in one direction and see a galaxy 10 billion years away. Then we look in the opposite direction and see a different galaxy 10 billion years away It appears like they are 20 billion light years apart and we are directly inbetween these two galaxies from 10 billion years ago and the CMB looks like a big sphere of 27BLY diameter where we are at the center.

 

I understand this must be an illusion of spacetime. As a child I used to think it was because spacetime must be curved like a sphere and we were looking around all sides of the sphere to the other side. This was back when closed space was defined a cyclicle universe and not a sphere.

 

But since science has popped my bubble with a flat universe. I no longer know how to understand this illusion of an inside out universe.

 

Can someone please explain this illusion. I know that the universe is expanding.

I once heard Dr. Michio Kaku say, in a documentary, that Einstein was never comfortable with curved spacetime and said that it was just a model to demonstrate the effects of gravity but that it shouldnt be taken literally.

I've always suspected that spagettification near BHs was an observer dependant spacetime illusion, similar to length contraction at close to light speed.

 

The thinking is that the delta force between your head to feet would physically tear you apart.

 

As I see it, you dont feel a thrust when in free fall because it is spacetime that is accelerating towards the planet.

 

So you shouldnt feel the delta forces either because it is spacetime that is getting stretched not the body in free fall.