I have indicated the presence of a pentagon embedded within the two drawings of the Merseburg and Weissenstein Castles many times over several years. It has been pointed out to me recently, that ‘any geometric figure could be revealed by someone else who might draw lines on that Merseburg wheel drawing and get a hexagon or an octagon out of it!’
I think that’s a reasonable comment, although I don’t think that has happened yet. But I can provide convincing evidence that the pentagon/pentagram was deliberately included by Bessler, and with no other geometric design intended in those particular drawings, maybe that would help to focus people’s minds on the reason why.
Back in November 2021 I published a blog entitled “The Toys page, 137, 141 and 47 and the Freemasons”. Amongst other things I talked about the 47th proposition of Euclid and the Pythagorean theorem. I did not offer a link to Euclid’s 11th proposition which I now do, it was in fact ....
“ To inscribe an equilateral and equiangular pentagon in a given circle….”
I’ve abridged it somewhat to simplify my point. A diameter line is first drawn across the circle, in our Weissenstein version it is that line I call the padlock line running downwards from point A.
A second line is drawn from the upper end of the padlock line, point A, to the opposite circumference, point C in Euclid’s construction below, forming an 18 degrees angle. That one in the Weissenstein drawing I call the ‘rope line’
A third line is drawn from the same point, to the opposite circumference, point D in Euclid’s construction, again at an angle of 18 degrees but on the opposite side of the padlock line from the rope line.
A line is drawn between Points C and D. Angle CAD is 36 degrees (2 times 18 degrees) and angles C and D are twice the angle at A, 72 degrees.
“Let ABCDE be the given circle.
Set out the isosceles triangle FGH having each of the angles at G and H double the angle at F.
Inscribe in the circle ABCDE the triangle ACD (blue) equiangular with the triangle FGH, so that the angles CAD, ACD, and CDA equal the angles at F, G, and H respectively. Therefore each of the angles ACD and CDA is also double the angle CAD.
6Now bisect the angles ACD and CDA respectively by the straight lines CE and DB, and join AB, BC, DE, and EA.
Then, since each of the angles ACD and CDA is double the angle CAD, and they are bisected by the straight lines CE and DB, therefore the five angles DAC, ACE, ECD,CDB, and BDA equal one another.
But equal angles stand on equal circumferences, therefore the five circumferences AB, BC, CD, DE, and EA equal one another.
But straight lines that cut off equal circumferences are equal, therefore the five straight lines AB, BC, CD, DE, and EA equal one another. Therefore the pentagon ABCDE is equilateral.
I say next that it is also equiangular.”
With thanks to http://aleph0.clarku.edu/~djoyce/elements/bookIV/propIV11.
What features of Euclid’s construction could be found in the two drawings being examined, and clearly identified as a clue to it being part of the pentagon, and nothing else?
This is the Weissenstein drawing with some existing lines coloured by me!
The blue line exists as the padlock line from A. Although it isn’t in this particular construction it is used in alternative constructions.
The red line is the rope line A to C. These two are 18 degrees apart. This should spark the thought of a pentagon on its own.
The purple line A to D is also 18 degrees from the blue padlock line. These two angles total 36 degrees, another hint at the presence of a pentagon.
The yellow line C to D matches the green one and is aligned with the hatching lines in the wheel drawings. Just in case you think that you B and E should also align with the hatching lines, you’re right they should, but I did not measure the bisected angles when I drew this with my mouse, so on the Weissenstein drawing my positioning was slightly out - but it doesn’t affect the conclusion.
The two white lines, DB and CE bisect the angles at ACD and ADC to provide the final two points of the pentagon.
Remember every single angle in the pentagram is a multiple of 18. Hence there are these angles 18, 36, 54, 72, 90 and 108.
Also the letter ‘R’ is the 18th letter of the alphabet. It also forms a major part of Bessler’s logo and his initials, J for Johann, to become R through the ROT13 cipher.
To summarise. The two lines of interest in the Bessler wheel drawings are the rope line and the padlock line. These two lines form the basis for suspecting the presence of the pentagon. They’re 18 degrees apart.
JC.
© John Collins 2022
Dear Mr. J. Collins.
ReplyDeleteTwo little mistake in your writings I need to mention now:
"Then, since each of the angles ACD and CDA is double the angle CAD, and they are bisected by the straight lines CE and DB, therefore the five angles DAC, ACE, ECD,CDB, and BDA equal one another."
Correction should be: ... the five angles DAC, ACE, EBD, CEB, and BDA equal one another."
Thank you for attention, the number 5 and this geometrical solution.
I hope you can solve your search this year.
Stay healthy and have good luck.
If we could help in any way, let us know.
Yours sincerely
Marco Z.
Thank you Marco. I think that you are wrong because the angles you quoted are not present, no lines linking them were included. The angles they quoted ( and I did copy and paste the italicised text) are correct but I see how you came to that conclusion. I wish you and your loved ones good health and happiness.
DeleteJC
JC
Mr. Collins, I have to apologize.
DeleteI ignored the straight lines CE and DB. So you are absolutely right.
The angle 36 degree is everywhere :-) (BCD=CDE=3x36°=108°).
Thank you for the answer.
All the best for the quest.
Marco Z.
John, there is a significance to the angle of the Rope and yes, Bessler is trying to make a point of it. He is directly communicating from his time to ours. It is really rather simple once you understand the spinning egg point. The egg represents potential philosophically also the Earth. He also shows an elliptical shape on the equator, on the toy page between parallel lines indicating a corridor. There is, however, another parallel. You seem to be hung up on its relationship to the number five. The relationship to the number five comes from the eight spoked wheel; it is a symbol comprised of five Greek letters overlaid one upon another, spelling the word for fish in Greek, which is an acrostic. "Ἰησοῦς Χρῑστός Θεοῦ Υἱός Σωτήρ"in English, translates to “Jesus, Christ, Son, of God, savior.” do I now make myself clear and succinct enough for you when I say,” I know, I know, what bears significance to the design.” All of this is important to a degree. Are you an angel or a demon?Do you appreciate poetic truth or not! Knit one Purl two, see what I did there? There the end is at the beginning, and the beginning is at the end, either pull out the plum or get out of the corner! What's it going to be Jack? You either own the field work in the field, or glean the field; stealing is not permitted, greed is an evil root! Stop hedging your bets, you either understand it or you don't. The universe is trying to tell you something John. You'll wind up sitting on your laurels broken, or you'll get to the point of all this; which is a Cooperative effort for salvation of this world. Please John, don't get stuck on an island, everyone has something to contribute! To all those here who glean; Take freely to sustain your needs, and give thanks for all the gifts to the Creator who resides everywhere!
DeleteIt's not about conquering gravity it's about concurring with gravity. The weight do not fall they follow a path it is a beautiful dance too much of our technology is based on destruction and from that comes instability. Try everyday to see the world optimistically and take part in its healing through Jesus Christ's sacrifice it is never impossible. Those who separate spirituality from the physical world we live in are an error just because you don't understand something doesn't mean it doesn't exist and those who would judge you based upon they're bias and not truth are also an error I have searched and I have found truth there is still more work to be done let us know have a discussion of cooperation any plan of action I propose that we speak in a more fluid forum does anyone else have anything to contribute to this proposal.
DeleteUh oh! Looks like SG "done got religion"! That's all we need around here. However, maybe it's just some new ploy of his to recruit followers? Possibly he's envious of the sudden showing of Ken B disciples in the last blog's comments and wants to desperately catch up?
DeleteIf he really wants to do that, then he needs to stop writing what HE thinks are clever riddles and start SHOWING us something in the form of drawings, photos, animations, or sims of what design he thinks Bessler used. These will all speak much louder than riddles and will gather many loyal disciples unto himself. Damn! Now he's even got me now starting to sound like some kooky religious leader!
Ken B & SG are a match made in heaven. They have both said they have sims that are runners.
ReplyDeleteKen B's claim I trust...SG's claim I definitely do NOT trust! In the last blog's comments SG was claiming he had a sim showing a ONE lever wheel running!
DeleteHe won't even say what program he is using lol.
ReplyDeleteIt's probably Algodoo and he's managed to accidentally create something with it that only keeps going because of some glitch he's not aware of. This happens to newbie simmers all the time. He dares not show it to us because if he did he would run the risk of a more experienced Algodoo user showing it's not really a runner. Then he wouldn't have anything to brag about and would lose the "bright shiny object" he wants to use to attract potential followers to himself.
DeleteOh I see. The same reason KB won't share his WM2D file of his self proclaimed runner sim.
DeleteKen, stop mentioning yourself to make it seem like you have followers here! Go push your crap in the comments of your YouTube videos or your crackpot website. And WM2D doesn’t give you any more credentials than Algodoo. You still don’t have anything more than claims and no proof!
DeleteYou can go and follow his comments on youtube and discover how he goes about commenting on various youtubers perpetual motion videos , where he would act smarty pants disproving their videos with physics .
DeleteThe funny thing about that , is he went on youtube posted an animation , and wrote a book , claiming that he has solved perpetual motion but suddenly he lacks the ability to provide proof for the physics involved which he himself went about disproving on other youtubers videos.
Putting comedy and distraction aside , JC if it was designed on purpose to be there , what do you think it means ?
Hi 11.31, I’d like to tell you all about what I think it means but I’d prefer to wait until I have some additional evidence that I’m right. I believe I have the answer but I’ve been caught out too many times in the past to put myself back in the firing line too soon! But it won’t be long.
DeleteJC
@anon11:31
DeleteKen B didn't post an "animation" on YT. It's an actual wm2d simulation and it took him two thousand tries to finally find after studying Bessler for a half century. How many simulations have you made? His book is the largest one ever devoted to Bessler in history. How many books about Bessler have you written?
He gives complete info in his book that anyone can use to make his own sims of the design or make a real world build of it if he chooses to so that he can verify for himself if it is actually the long sought secret of Bessler's wheels. Ken's not really hiding anything from anyone. If others are too lazy to read the results of his decades of research, then that is not his fault.
Those who have the most serious interest in seeing a solution to Bessler's wheels will get at least a download of his book and actually read it and will then have the maximum chance of successfully building a reproduction of one of Bessler's wheels if they want to. Those who can't be bothered doing that will continue to do what they've always done...tinker away in their basements and garages on no hope designs until the day they finally quit in disgust or drop down dead. They will then join the tens of thousands of others who did the exact same things over the last three centuries whoever they were.
Ken's book is really meant for those that are ready for a fresh approach and don't want to share the same dismal fate of all those other failed Bessler pm wheel chasers. It's probably best for younger people with plenty of enthusiasm and energy than for burned out oldtimers who haven't built anything in years and probably never will again.
Moe Larry shamp and Curly
ReplyDeleteThe three stooges, but I had to google it. JC
Delete@SG. I appreciate your comments although sometimes I find them somewhat wide of the mark, my mark not yours. But today we seem to be on two different planets. You seem very knowledgeable about what you write but I am unable to connect the starting point to the conclusions you reach. I shall continue on my way blindly blundering ahead hoping against hope to hit this moving target in spite of your efforts to help.
DeleteJC
"...we seem to be on two different planets."
DeleteNo, John, you two are in actually in different parallel universes. You are still in our real and rational universe (I hope!) and he is in the "bizarro" parallel universe where 2 + 2 never equals 4 and one lever wheels provide pm. If you ever do need to go to him for help, that will be a sure sign that your own B wheel research is in BIG trouble!
Shemp (I hate it when bizarro world inhabitants misspell my name!)
I have to admit that I had a lot of trouble trying to understand how John decided that Bessler's wheels contained pentagons and five levers even after reading the blog topic above several times. It's too complicated mathematically, imo, for this blog.
ReplyDeleteHowever, I decided to use a clear plastic protractor and an enlarged MS Paint image of the Merseburg wheel on my laptop screen to check the angle that John's rope line makes with his padlock line. He claims it's 18 degrees and considers that as evidence that a pentagon can be drawn inside of the Merseburg wheel. I noticed that if you multiply 18 degrees by 6 you will get 108 degrees which just happens to be the interior angle of a pentagon. Perhaps that is evidence that Bessler was using five levers inside of his wheels?
I can confirm that you will indeed get 18 degrees IF you draw your padlock line the way John did. He even points out the letter "R" in Bessler's logo which is the 18th letter of the alphabet as further evidence that Bessler deliberately hid this angle of 18 degrees in the Merseburg wheel drawing because his wheels contained five levers with weights. That certainly seems to make some sense.
I discovered, however, that there is considerable variability in the angle you get depending on HOW you draw your padlock line.
He draws his padlock line starting from the BOTTOM point of the triangular padlock up through the center of the axle pivot and then up to a point where it intersects the rope line which looks like it's just outside of the upper right side rim of the drum. I decided to draw my padlock line starting from a DIFFERENT part of the triangular padlock.
I drew my padlock line from the LEFT corner point on the triangular padlock up through the center of the axle pivot and then up to the point were it intersects the rope line outside of the upper right side rim of the drum. That intersection point is actually located ON the upper vertical part of the cross shaped window frame (where Jesus' head would have been located during his crucifixion on his actual cross!). When I then measured the angle between the rope line and the padlock line I got an angle that looks like it's EXACTLY 15 degrees. Is this the angle that Bessler was really hiding in his Merseburg wheel drawing?
Those who think it might be could also look at Bessler's logo and point out that it actually contains two "O" letters...a small one inside of a larger one. "O" is the 15th letter of the alphabet! How could anyone ignore such an obvious clue like that they would ask?
If you multiply 15 degrees by 6 you will get 90 degrees which is one of the interior angles of a square. That could then be considered as evidence that one could also draw a square inside of the Merseburg wheel and that Bessler only used four levers in his wheels.
If you multiply 15 degrees by 8 you will get 120 degrees which is one of the interior angles of a hexagon. That could then be considered as evidence that one could also draw a hexagon inside of the Merseburg wheel and that Bessler used six levers in his wheels.
If you multiply 15 degrees by 9 you will get 135 degrees which is one of the interior angles of an octagon. That could then be considered as evidence that one could also draw a octagon inside of the Merseburg wheel and that Bessler used eight levers in his wheels.
Finally, if you multiply 15 degrees by 10 you will get 150 degrees which is one of the interior angles of an dodecagon. That could then be considered as evidence that one could also draw a dodecagon inside of the Merseburg wheel and that Bessler used twelve levers in his wheels.
Who can ever know with any certainty how many levers Bessler actually used inside of his wheels? We may never know for sure. It's really all guesswork, imo. However, I would quickly change my mind about Bessler's wheels using five levers if someone could just find a WRITTEN mention somewhere about five impact sounds being heard per wheel rotation. Show me that and I will gladly hop aboard John's five levers per wheel train.
If you take a closer look , the line drawn by john at the padlock C is 11 to 12 dots on the rim away from the line drawn on the rope , and also 11 to 12 dots away on the rim from the line drawn at D.
DeleteSo to just go about drawing your line to random positions on the padlock and then stipulating the theory that you can produce anything does not hold up and concur with the validity of the symmetrical equidistant points of intersection as proposed by John to back up what he is showing.
jb
Anonymous 18:35 quite a detailed analysis very good train of thought unfortunately you're just gleaning you have gifts but still you glean it's not too late all of this here is merely a distraction go out and be someone and maybe someday we'll meet then you could tell me a wild story and I'll believe you!
ReplyDeleteTo mow Larry shamp curly oh I forgot one more JC or shall I call you the last of the Stooges Joe and again 18:35 don't forget It's All Greek To Me the one thing everyone seems to not see in the drawing of the wheel the biggest Greek letter of all capital Phi
ReplyDeleteInteresting that it can be found in the drawing , i have no idea what implications that would have for me , nothing comes to mind.
ReplyDeletegood luck john.
JB
Excellent analysis, anon 18:35! I had no trouble understanding what you were describing.
DeleteLike you, I'm not ready to jump aboard John's five lever per wheel train yet, but for different reasons. In fact, I find myself slowly drifting toward the Ken B train whose passengers/disciples seem to think that ALL of Bessler's one way wheels used exactly 8 levers with weights at their ends. Some on this blog think it is possible for Bessler's smaller than 12 foot diameter wheels at least to have had less than 8 levers in them and maybe even the 5 that John is convinced they had. I've found some evidence, however, that suggests to me that was unlikely.
Here's a quote from section XXIX of Christian Wagner's "First Critique" pamphlet of Bessler's wheels published in 1716:
"Almost no clatter and rattle was to be heard with the Draschwitz wheel; the wheel was made up of 8 spokes and was completely empty near the circumference, as one could see through the various cracks in the casing made of thin splinters, but there was not the slightest trace of a rising and falling weight to be heard or seen."
This wheel, which was the last one direction wheel that Bessler made and then destroyed before moving on to Merseburg and building his first two directional wheel there, was probably stationary when Wagner first viewed it so it did not make any noise then. However, there was enough of the interior visible to him through the small gaps between the thin boards nailed to its drum's radial frame pieces so he could just make out EIGHT of those frame pieces on ONE side of the drum.
The levers in this wheel would have had lead weights attached to their ends and Bessler would most logically have placed their pivots between parallel pairs of those radial frame pieces because of the added strength they had. Since there were eight radial frame pieces visible on one side of the drum (there would also have been another set of eight different radial frame pieces visible on the drum's other side) that implies that the Draschwitz wheel used 8 levers and not 5 or any other number.
Of course, if the wheel was stationary as Wagner viewed it, then he would not have seen any lever motions taking place inside of it or heard any impact sounds. What is meant by the drum being described as "completely empty near the circumference"? Maybe only that Wagner could just make out the drum's radial frame pieces, but the rest of the drum's interior was too dark for him to see any of the eight levers and their attached weights. If he could actually have seen the levers, then one would expect him to have described them in his critique, but he doesn't.
jason
@Jason
DeleteI think you're right about the Draschwitz wheel's drum being too dark to see into. Bessler was so obsessed with secrecy that I don't think he would have let anybody near that wheel if he could easily see into the interior of its drum. Maybe he had placed dark cloth around the inside of the drum near the outer circumference to prevent anyone from seeing the levers and their weights there?
I read somewhere that Bessler used felt as a cushioning material in various places inside of the drum to deaden the sounds of the lever weights as they hit their stops while the wheel was running. That was to prevent anyone inspecting the wheel from analyzing how it worked based on the sounds coming out of it.
Jason, I’m beginning to wonder who you are? Quoting Wagner as a reliable witness seems odd, given that he was a sworn enemy of Bessler’s.
DeleteBessler describes Wagner’s visit as only long enough to swallow the breakfast Bessler provided. He also questions Wagner’s claimed knowledge of the machine as they only met once and very briefly.
But there are other more trustworthy witness to the Draschwitz wheel which you would be aware of if you read my book.
I’ll quote very briefly, from a letter sent to Gottfried Leibniz- “ Having made an appointment with the inventor, we approached the machine and noticed that it was secured by a cord to the rim of the wheel. Upon the cord being released, the machine began to rotate with great force and noise, maintaining its speed with out increasing or decreasing it for some considerable time. To stop the wheel and retie the cords required tremendous effort. The inventor is asking for one hundred thousand Thalers to reveal the mechanism or sell the machine.”
There are other reliable witnesses who also mention the sounds produced by the wheel.
JC
I warned you about posting here Ken. Deletion in progress. JC
DeleteLooks like John is furiously deleting comments from anyone who offers evidence that can debunk his five lever theory assuming he must be either Ken B or one of his disciples. Some of them probably are from his disciples, but I doubt if any are from Ken B himself.
DeleteAnyway, I recently figured out a way to save John's theories despite that mention Wagner made of the Draschwitz wheel having 8 radial pieces in its drum that Wagner counted.
Maybe what Wagner meant was that he saw the 8 radials on BOTH sides of the drum which means there were only 4 on each side. Now, maybe because of the angle from which he viewed the wheel during a public demo, there was another radial that was hidden from his view by one of the axle's vertical wooden supports. That would mean there were actually 5 radials on each side of the drum and they would have held a total of 5 levers!
There John's theory saved.
IIRC there was a photo that appeared here years ago of a full size model of the pm wheel Bessler unveiled in Gera in 1712 that was used for an exhibit on pm in a museum in Gera. It was just a mock up made of wood that visitors could rev up by turning a crank handle attached to the end of its axle, but it had 5 radials on its drum! I'm wondering where the museum got the information they used for that model. Did they have some information we don't have that said its drum actually had 5 radials?
This blog was originally somewhere for me to discuss Bessler with like-minded people, for us to try and get to the truth, but now it’s just a game to some people who have nothing worth contributing unless it’s to mock others. I think it’s time to close comments and for me to stop posting. I’ll decide what to do tomorrow.
DeleteJC
I've been reading a lot of good comments on these blogs of yours and hope we can all keep reading them long into the future.
DeleteI think some mock the beliefs of others because they have a need to get those others to agree 100% with their beliefs. If that happens, then it will validate the beliefs of the mockers and help remove their own secret doubts about them. Such mockery only shows how really insecure the mockers feel about their beliefs. Once I realized how this works, I found being mocked less upsetting. I don't enjoy it, but I don't lose any sleep over it either.
PM Dreamer
JC wrote "This blog was originally somewhere for me to discuss Bessler with like-minded people, for us to try and get to the truth, but now it’s just a game to some people who have nothing worth contributing unless it’s to mock others. I think it’s time to close comments and for me to stop posting. I’ll decide what to do tomorrow.
DeleteJC"
Anonymity is a breeding ground for decline & contempt which eventually leads to societal decay & lowest common denominator when there is no fear of consequences. The human condition played out daily in all social media experiments that are also works in progress.
Hey, anon 21:11
DeleteYou were right about that Gera wheel model they had at the museum over in Gera.
You can see it in this short youtube video:
https://www.youtube.com/watch?v=5lKTN35SPZw
It appears at times 1:15 and 2:42. It's even making five noises per rotation as it turns!
You think! John Anonymity might be causing a communication problem really! What a shock I had to read that three times John did you make that statement or is someone using anonymous to put words in your mouth we must get to the bottom of this don't you think!
Delete"It's even making five noises per rotation as it turns!"
DeleteThat's music to John's ears! Lol!
I agree with Stephen Glorioso, anonymity is probably contributing to the problem.
DeleteBefore closing comments, would it not be worth a try to not allow anonymous comments?
Here is a theory that saves Johns pentagon theory, while respecting the 8 knocks per revolution.
Deletehttps://youtu.be/fC460pcXgWg
Sorry about the quality of the simulation, i have a crappy computor and connection internet.
And it's so simple that even a carpenter's boy could understand it!
DeleteNice try, but you seem to forget the Bessler wrote that he allowed people to reach into the cloth sided drums of his wheels and feel their axles. If what you suggest was used, then they surely would have felt all of those pieces piercing (and weakening!) the axle. I think John's five lever approach is still on very shaky ground.
Good one funny! funny! ? RH46
ReplyDelete?John
ReplyDeleteI’ve tried requiring people to sign in but most people find it a drag to have to sign in so they don’t bother, but given the choice of no blog and few comments or what is already here, I’ll try the sign in method and see how it goes. I’m sorry for those who like the anonymity but it’s just getting too bad. Good luck🤞
Delete