I sometimes wonder if Bessler had any qualms about publishing his Apologia Poetica and his Das Triumphans books. Did he fear that he had provided clues that were too easy to decipher? I know I am reluctant to give any hints about my current thinking for fear of giving anything away and I suspect most of us are of a similar mind.
However, I think he must have been pretty confident that the clues were too difficult to decipher otherwise he would never have published them. But that raises the question are they too difficult for us too? He must have thought that at some point people would work on his books in an effort to extract the original meaning he intended us to grasp; but that this should begin to happen three hundred years after his death was probably not something that occurred to him.
He published the books when he was at the height of his fame and confident that his wheel would be sold, in which case the books were just there to allow him to reveal that the clues had been there all along and only his own cleverness had kept them invisible.
I have been criticised in the past for publishing speculation without labelling it as such, thereby giving the impression that my speculations were factual. I hope I corrected that impression but I think there is a thin wall between what we think is fact, speculation, following a hunch and guessing.
Speculation is the consideration of some subject which leads to a conclusion or opinion reached by such contemplation. Often such speculations are impossible to verify, and one can say that it is the forming of a theory or conjecture without firm evidence.
Besides speculating, I have followed many hunches over the years most of which ended in a firm conviction that my hunch was wrong. Other hunches I chased have led me to believe they were correct or true, even though I did not have any proof. Like all hunches these were based on a feeling or guess, based on intuition rather than fact.
Guessing combines elements of hunches and speculation but is broader based. For example you can guess the next roll of a dice but you can't speculate what it would be. It won't be accurate at all because the dice has no memory of previous rolls, but you can speculate what the dice roll will be, based on, for example, looking at the statistical distribution of past rolls and so forth. But it just won't be very accurate.
So I think that speculation is an informed guess. But a hunch is something extra; some unconscious conclusion about the way to the solution. I often awaken in the night having had a sudden revelation about something I had been thinking about during the previous day or week. Often it it proves unfounded in the cold light of dawn, on the other hand I have made some major discoveries which I was able to verify subsequently.
But some of the most interesting revelations have come to me as I was writing descriptions of my various discoveries. These have confirmed what I considered was hardly more than speculation at the time and thus became facts.
So revelations can materialise out of the blue and I'm sure they stem from unconscious activity in a part of the brain which appears to be able to work unsupervised, independently and in a focussed way.
JC
10a2c5d26e15f6g7h10ik12l3m6n14o14r5s17tu6v5w4y4-3,’.
So revelations can materialise out of the blue and I'm sure they stem from unconscious activity in a part of the brain which appears to be able to work unsupervised, independently and in a focussed way.
JC
10a2c5d26e15f6g7h10ik12l3m6n14o14r5s17tu6v5w4y4-3,’.
The possibility of some kind of Mendeleyevian revelation one dark and stormy night ought not to be scoffed at - just this last week, research has been published demonstrating that late-night inspirations can provide real breakthroughs; the researchers concluding that we may do some of our best thinking when tired.
ReplyDeleteAlso of course, it's been shown time and time again that much problem solving occurs unconsciously during sleep.
All of which ties in with another, related line of research in recent years which has focused on the apparently savant-like abilities some subjects acquire following brain injuries, or lesions caused by brain surgery - again, in the last week there was such an example in the news, of a man suffering from a form of temporal lobe dementia who, consequently, rapidly developed virtuoso musicianship on the saxaphone.
A fascinating tool for studying these effects has been the development of a technology called TMS (trans-cranial magnetic stimulation) - something of a misnomer, since it works not by stimulating targetted brain regions, but rather by knocking them out. However, this has the surprising effect of kicking the remaining active brain regions into overdrive. The tech works by inducing epiliptic-type disruptions in a kind of reverse EEG effect through the scalp, in highly localised areas, temporarily preventing that part of cortex from contributing to the conscious whole. Volunteer subjects typically perform a series of 'before and after' tesst exercises, such as a spelling bee or sketching wild animals from memory, with often profound results - some of the resulting drawings have been likened to the sublimely fluid depictions of animals in cave paintings, many of which are now widely believed to have actually been drawn by Neanderthals rather than modern man.
It thus seems that we all have an inner Rainman, waiting to be untethered from the distracting hustle and bustle of everyday cognitive tedium. A late night, a stiff drink or three, or even perhaps an Emmet Brown-esqe crack on the nut might yet prove just the ticket for cracking this nut..
Interesting and informative response Vibe. It seems as though the ideas which have come down to us using meditation, yoga etc, about ways of shutting off the brain's conscious activity is supported by those findings you have mentioned. Even though the accounts many of us provide both here and in many other forums about night time revelations may seem apocryphal, to each individual it seems a genuine experience and one which we may recount in a slightly self-conscious way, as if we know it's utter rubbish, and yet internally we know it has validity and should not be dismissed without thought.
DeleteJC
Interesting blog topic, John. Speculation is just another name for guessing. My current view of Bessler's wheels is the product of a long series of guesses and I believe that I now have all of the secret mechanism he used except for the placement of a single spring on his levers. I'm currently beginning to work my way through all of the possible placements of that spring until I finally find the one that works. I "know" it will happen. How? Hard to say, but I do believe that my unconscious mind, as Vibrator stated above, is really working on the problem 24/7. Sort of like anti-virus software that works "in the background" while your computer is in use. When I do a test of a wheel design that fails, I tend to give it a rest for a while, but my unconscious mind takes it all in and begins looking for alternate approaches to try. When it's ready, it then creates an "urge" in me to return to my wm2d models and make a modification and prepare for another test. I said in previous blogs that I had set a limit of 1200 models and that, if I failed to achieve success by then, I would call it quits. However, I think I now know why I selected this particular number. I believe it was actually selected by my unconscious mind because it "knows" that I will achieve success before that number is reached! In other words that limit is not a prediction of coming failure, but, rather, one of coming success. How can my unconscious mind possibly "know" that success will happen before the 1200th model? Hard to say, but I suspect that it has already analyzed how many possible spring placement combinations I can make and, knowing the pace at which I modify and test models, has predicted this number. I'm now up to about model #1120 so that means success is getting a little closer with each passing day. I'm feeling that I will finally find it by the beginning of summer. Let's see if I or, rather, my unconscious is right about this in the coming months.
ReplyDeleteI get the impression, Ken, that you are a trial and error man, trying an infinite series of small adjustments in the hope that you will strike the right combination. I know you are certain about the need for springs, but suppose there isn't any need for springs? Doesn't that mean your subconscious is on the wrong track? I'm not trying to be facetious Ken, I respect what you are trying to achieve, but if I'm right and you don't need springs, and my subconscious is right then you will fail and I still might! May the best subconscious win.
DeleteJC
One of the many things that convinces me that springs were critical to the operation of Bessler's wheels was that incident that occurred after the moving of the Merseberg wheel to a secondary set of upright supports during its official test. As Bessler was putting the lead weights back on the ends of their levers, there was a sudden loud cracking sound which startled everyone. Apparently, one of the levers slipped out of his hand and smacked into the part of the drum that it occupied. Supposedly, there was also the sound of a spring making some sort of noise. From this it's obvious to me, at least, that each lever had one or more springs directly attached to it and these springs were able to apply much force to a lever as it swung away from the rim and toward the axle on a wheel's ascending side. Many have constructed imbalanced wheels that use levers with weights on their ends, but few that I know of also "enhanced" the operation of their levers with springs. If I can figure out how Bessler used the springs attached to his levers, then I believe I can, finally, duplicate his mechanism. I think I'm very close at this point.
DeleteI agree with Ken, good blogg topic John Collins.
ReplyDeleteI moment I became seriously involved in looking for Bessler’s wheel was back in 2007 when my copy of MT arrived. Flicking through the book for the first time something immediately jumped out at me; what was Bessler up to with his two types of letter A? Then, upon reading the book properly for the first time I saw that you had written on page 18, Drawing number 12 is the first to label the parts with letters, and it is interesting to point out that the letter ‘A’ appears in two guises; sometimes, as here with a straight cross-bar, and sometimes with a bent one. This appears to be a deliberate variation, and I think is intended to be a hint as to some part of the mechanism.
I think there may be a lot less guessing going on than some suppose.
There has been a lot of guessing but I think, (or my subconscious thinks) I understand its use. My own feeling is that the meaning of the 'A's is not as important as much as their form. Bessler talks about the importance of form in Das Triumphans, and what he says seems fairly obvious but as in all of Bessler's clues there is a subtext which he intends we should apply to all of his clues.
DeleteSo although the two 'A's seem an interesting mechanical arrangement we need to look at them with fresh eyes to see what other form they could represent.
JC
Yes JC, as you say, "the two 'A's seem an interesting mechanical arrangement" is exactly right. They 'fall open'' at the 12 o'clock position and 'snap shut' at the 6 o'clock position. A couple of storks bills or students forceps (or something similar?) in combination with them has always looked rather promising and useful to me......
DeleteThe form of the letter 'A's' in Bessler's clues have an uncanny resemblance to the form of the bellows motif in his clues, don't you think? Could these be The Bellows of the machine?
DeleteI'm not quite so sure about your "subtext" idea/observation, I think you may be overcomplicating things. To me this thing needs to work, from Bessler's point of view, in a very obvious and straightforward way. 'No recognition, No posthumous recognition' has long been a mantra of mine. I believe that when we finally get to see a gravity wheel running, instantly recognisable elements of the mechanism will jump of the pages of MT and slap us in the face, just as Bessler intended.
"... instantly recognisable elements of the mechanism will jump of the pages of MT and slap us in the face, just as Bessler intended."
DeleteOh yes, I do agree. I believe the elements of his secret mechanism are found in MT 9, 10, 11, and 18. But, these four figures are the only ones I think are significant.
I guess if my name was Quasimodo, I might have a hunch, is that something I should speculate about ?
ReplyDeleteI think if you had a hunch, Stevo, you'd know it!
DeleteJC
Interesting that you should make this post at this time, John. I, too, seem to be one of those people that wake up with 'answers' (for lack of a better term). Sunday morning, March 1st, I woke up with a physical concept in my avenue of research, which eliminates the springs, if so desired.
ReplyDeleteIt is very simple, answers 'yes' to all the known clues and hints left regarding the wheel, and interestingly enough, NO ONE is working using this principle, or even discussing it! In fact, in all the Bessler material that I've studied, I've never seen it mentioned, discussed, or tried. Also, it can't be simulated with two-dimensional simulation software. So, I'm building it now. Time will tell .....................
Wow, sounds good Hutch. Don't be over confident that no one else is working and using this principle, just because you haven't heard about it. Your description could also apply to me, although I don't actually know if it does because, like you, I haven't shared it with anyone else yet.
DeleteGood luck and keep us informed of your progress.
JC
Further to my last, Hutch. If it can't be simulated with 2D simulation software then I think you might just have a winner - good luck!
DeleteJC
Hutch — if the issue is just that you need a good 3D simulation program, you might like to look at Universal Mechanism, see http://www.universalmechanism.com/en/pages/index.php?id=1
DeleteI've been using it for a while. I'd still prefer a decent 3D finite-differences program, but for finite-elements, it's pretty good, and far cheaper than comparable Western software.
It looks like being able to focus 100% on my Bessler research is beginning to pay off. Late yesterday I found a very obscure clue in the first DT portrait that may help resolve a problem I'm having trying to decide where to attach the second spring to the levers and what k value to give it. I made a quick preliminary model and saw a rate of ascending side shifting taking place in the model's levers that was more rapid than I've ever seen before! However, I still need to do a lot more work with this new information to see if, once again, I'm heading down another dead end or if, hopefully, my quest will finally end in success. But, so far, it's looking very interesting.
ReplyDeleteAs far a using 3D software to model Bessler's wheels is concerned, I dismissed that possibility a long time ago. It's also known as the "Z Axis Hypothesis" and posits that there were actions taking place inside of his wheel's drums that involved motions parallel to their axles. Because of the extreme thinness of his drums relative to their diameters, that seems unlikely. All motions were basically levers swinging about pivots and were confined to the plane of the drum (and there were a lot more levers inside of his wheels than just the main ones that had weights attached to their ends). I remember one estimate that the amount of free space inside of the Gera wheel was actually less than 2 inches wide! That's very tight and would seem to preclude any extensive motions taking place along the Z axis.
I would like to suggest that the reason why the solution has eluded us is, the first line of the apologia poetica...." Greed is an evil root".
ReplyDeleteYou will see what I mean when you see the working wheel.
You could be right Trevor. I too have often thought about this statement. Of course you have to know the correct meaning of 'Greed'.
DeleteWho has a working wheel?
ReplyDeleteI have a machine that runs but you have to push it to start. So I'll been informed it's not a Blessler's wheel, so it doesn't count.
ReplyDeleteHowever I'm trying to convert it into a bessler wheel. I will keep in touch.
Bessler's later wheels were not self-starters. They needed a push to get started, then sped up to around 20rpm. If your wheel continues to run after an initial push, then you may indeed have a genuine Bessler wheel.
DeleteOf course we won't know what a Bessler wheel is until someone builds a 'working wheel' based on clues left by Bessler in his written works or portraits.
DeletePeople are looking into its performance. I will in touch.
DeleteIt does not matter if it's not a Bessler wheel in the pure sense of the word, if it runs by itself after a push it is still Perpetual motion so what are you waiting for,... Announce it!
DeleteWe want to see your working wheel first, Trevor, what are you waiting for?, video it and put it up on youtube.
Delete-TGIIAOTWEU-
Oh, yes, that line from AP about greed being an "evil root". The original German is:
ReplyDelete"Der Geitz ist eine Wurtzel Böß"
Note that it contains the letters G, W, and B which just happen to be those in the surnames of three of Bessler's most annoying detractors: Gärtner, Wagner and Borlach
I think this was Bessler's way of saying that his detractors were greedy in that they wanted to know the secret of his wheels without paying for it. However, there is another possible interpretation for it. By "greed", Bessler could be referring to the search for pm since pm, as understood in Bessler's times, would be, literally, getting something (energy) for nothing. Perhaps Bessler is using this line to describe the search for pm as evil because it is an obsession driven by one's desire to make a fortune, become famous, etc. And, the pursuit is one that actually drains one's physical and mental strength, his time and financial resources, and undermines his interpersonal relationships. I think Bessler's wife complained that all he thought about was his wheels! In today's world, he would have been quickly divorced and spent most of his life as a loner type. Anyway, I think Bessler derived much pleasure from having succeeded in building a working imbalanced pm wheel while everyone else had failed. But, the pursuit also caused him much anguish. At times he might even have felt like he was possessed by a demon and that, of course, would be disgusting to a man as religious as Bessler was.
Personally, if I am lucky enough to successfully reverse engineer Bessler's invention, I don't expect to make any "serious" money off of it. In fact, presenting the material will actually cost me some money. Right now I don't know how many thousands of hours I've invested in this pursuit over the decades and I know I'll never see a penny in compensation for any of that. I can well appreciate why Bessler was so concerned about receiving such a huge sum of money for his invention. The best that he will ever get from his efforts is to have future researchers finally prove that he did what he said he had done and, finally, clear his name of any "hint or suspicion" of fraud. He needs to get far more historical recognition than he currently has, imo.
Something I've been meaning to say for several years in connection with the phrase "Der Geitz ist eine Wurtzel Böß", is that when ever I've tested the translation, the meaning comes out as " that meanness is a an evil root", or "Stinginess is the root of evil". I suspect that Bessler used the word 'meanness' to incorporate the initial letter in Gartner's last name. Having said that there are two other words which mean greed and both begin with 'G' - 'Gier', and 'Geldgier'. ????
DeleteJC
I'm content with translating "der Geitz" as "greed" although it can have other slightly different meanings depending upon context. Obviously, Bessler did not perceive himself as greedy despite the huge payment he demanded for his secret pm design. After all, he had earned that amount because of the enormous effort he had to make to achieve success. But, a greedy person wants to obtain wealth he did not earn and that would apply to those trying to coax the secret out of Bessler without compensating him for it. By Bessler's standards, his detractors fit into that evil category because they seemed to be trying to infuriate him to the point where he would openly reveal the secret just to prove that they were wrong. At that point, of course, they would then immediately begin copying his design and, perhaps, modifying it a bit to make it "theirs" without giving him any credit or money. Fortunately for Bessler, he had a very powerful person backing up his claim to having a genuine pm wheel. I've often wondered, however, what would have happened if Bessler had sold his invention and it was then demonstrated to the world of science at the time that it was, in fact, genuine. It would be nice to see what Bessler's detractors would say then. Most likely they would have apologized for doubting his word, but excused themselves on the grounds that they had not seen enough demonstrated to prove to them that the wheels were genuine.
DeleteKen I took it literally on face value, meaning that if you try to design something that is too focussed on lifting heavy weights, you are going to end up with wheel that keels at the root.
ReplyDelete"One man will not change the world, but one man can communicate information ...
ReplyDeletewhich will change the world. "
Lifting weights ! Weights are always falling, he said so himself .
ReplyDelete- TGIIAOTWEU -
Weights were lifted by the wheel outside the wheel using ropes and pulleys, he never said weights were being lifted inside the wheel .
ReplyDeleteNothing was being lifted inside the bessler wheels . The truth is weights were always fallling .
- TGIIAOTWEU -
Weights can only fall to their lowest point in the wheel once! After that, they have to be lifted.
ReplyDeleteActually, in order to produce a net external torque, the center of mass of the weights and levers inside of one of Bessler's one directional wheels had to continuously fall. But this falling process as no ordinary one, because, just as soon as the center of mass fell even a tiny amount, it was again lifted back to its starting position. The energy necessary for that instantaneous resetting was provided by weights that swung about the pivots of their levers on the wheel's ascending side as they traveled from a drum's 6 o'clock to 9 o'clock positions. As a wheel turned and delivered mechanical energy to its environment, the mass of the weights and levers would slowly diminish over time. In order to produce the pm effect or to keep the center of mass of the weights and levers always on the descending side of a wheel as it rotated, certain precise conditions had to be achieved. The levers had to have an exact shape, the sets of coordinating ropes had to each have an exact length, and the springs attached to each lever had to have an exact spring constant value and be attached to certain points inside of the drum and on the levers. If these conditions were not all achieved, the the center of mass of the weights and levers would rapidly sink to a location below the axle (also known as "keeling") as the axle torque dropped to zero. The challenge for anybody trying to reverse engineer Bessler's secret wheel mechanism is to find all of these factors and then incorporate them into a model, either real or virtual, of a wheel. I can personally attest to the extreme difficulty of finding out what all of these factors are. If a single factor is not known, then one can not find success...ever! But, by the grace of God and Bessler, there is, I believe, a single source of information about these factors in the Bessler literature. No, it is not in GB, AP, or MT. But it is in DT and is provided the minute you open the work. We must remember that DT is different from Bessler's other works in a certain sense. He apparently wrote it at the request of Count Karl who wanted Bessler to "explain" how his wheels worked. That explanation went far beyond the usual vague descriptions of performance and mechanics that Bessler delivers in his other works and extends into the very heart of the secret mechanism he found. No, you will not find a working schematic in DT that you can run to your shop and begin using as a guide for you next built. What you will find, however, are sets of numbers that represent angles, distances, and spring tensions. Everything one needs to build one of Bessler's wheels is there. But, it is there in highly symbolic form that will require much, much effort to accurately decode and one will have no hope of doing that unless he is tirelessly building and rebuilding wheels during the process. To expedite matters, I do my "building" on a computer monitor. If I find success and decide to do a book on the subject, about half of it will be devoted to a clear and accurate description of the secret pm mechanism Bessler found and the other half will be devoted to an analysis of the many DT clues that led me to the rediscovery. Those clues are almost as fascinating as the wheels themselves!
ReplyDeleteKen said:
ReplyDelete"The levers had to have an exact shape, the sets of coordinating ropes had to each have an exact length, and the springs attached to each lever had to have an exact spring constant value and be attached to certain points inside of the drum and on the levers."
And yet, Bessler said:
"design has, in fact, progressed to the point where there is nothing supercritical about the exact disposition of the weights - an ounce more or less, here or there, makes not a scrap of difference to the Wheel, which will hold its course serenely without 'turning a hair'."
If an ounce more or less here or there doesn't matter, it follows that there would be more than one shape, length, locations, and constants that would work. If the weights themselves are the pm device, and they don't need to be an exact value, then neither would the levers, ropes, and springs. My hunch is you're on the "wrong track" like other pm researchers.
Good luck with your model.
Bessler's design does allow for slight variations in the masses of the weights about a precise value. As we all know by now, that precise value for the Merseberg wheel was 4 lbs per weight. Any variations in the weight masses will average out to this value, but one should try to make his weights as close to this value as possible. However, all other parts of the wheel must have precise values. Some of the clues Bessler gives specify distances accurate to three decimal places! I believe these values were derived from his many geometrical calculations that went into the design he used and were probably not attainable in practice despite his skills as a clockmaker. When building my computer models, I do aim for three decimal place accuracy and believe the closer one gets to this, either directly or through averaging, the closer one will get to a wheel that is as efficient as possible. The bottom line is that, if one makes a wheel with sloppy parameters, then they'd better average out to the required precise values. Or, better yet, aim for the precise values and then one will not have to worry about averaging having to take place.
DeleteWe don't know if they were exactly 4 lbs. They weren't put on scales.
ReplyDeleteMy hunch is Bessler had no way of measuring anything to 3 decimal places. That is to the nearest 1/1000th. A tape measure has 1/16ths marked on it. It wouldn't make sense to calculate that precisely if he couldn't turn around and build it that precisely. My hunch is he didn't leave any clues that specified distances to 3 decimal places. But whatever floats your boat as they say.
Also, I think I mentioned this long ago, geometry tells one if a certain model doesn't work, then any variation of it isn't going to work either. Bessler came up with his principle first, and the model was the easy part.
All I can say in response is that there are multiple clues that indicate the weights in the Merseberg wheel were 4 lbs, but they were the "pounds" that Bessler used locally. They were not identical to our present day English pounds. However, interestingly that does not affect the operation of his wheels. He does give distances to three decimal places, but I am convinced these were theoretical values derived from geometric computations. I agree that when one looks at static diagrams of Bessler's wheels' mechanics, it is easy to conclude that they can not work. However, the picture changes when one considers what is going on dynamically. Bessler, by using spring tension, managed to produce an array of interconnected weights whose center of mass was, when the wheel was stationary, located to one side of the wheel's axle. As rotation began, the weights would automatically shift themselves so that their center of mass always remained on one side of the axle. It takes energy to do that and that energy always came from the inward swinging of weights on the ascending side of the wheel and between the 6 o'clock and 9 o'clock positions. When one studies Bessler's approach, one realizes that it is the simplest and most logical approach to constructing an imbalanced pm wheel. I, too, believe that Bessler conceived the principle first, but finding the exact mechanics that would use it was anything by easy. It took him a decades and hundreds of attempts. The average pm wheel builder today has, imo, no idea of the amount of effort he made to achieve success. He truly was one of the most tenacious inventors in history. He needs to be vindicated and receive the recognition he deserves.
DeleteI disagree that he gave distances to 3 decimal places. it wouldn't be necessary for the operation of his wheels, just as the English pound vs. the local pound wouldn't affect their operation. If values for the weights can have a range, logic tells us that any parts that the weights are attached to have a range of values. What you're not seeing is that if your principle doesn't work on the first try, you're working on the wrong principle. No amount of tweaking spring constants or attachment points or lever shapes or lengths or number of connecting ropes is going to all of a sudden make it work. But you'll find that out soon enough on your 1200th sim. Good luck.
ReplyDeleteAt this point I am tempted to reveal some of the DT clues that show three decimal place accuracy, but this is not the right time or place for that. Yes, some variation in weight mass is acceptable, but it is a small variation. Bessler mentions the weights being an ounce more or less. For a four pound weight, one ounce represents a variation of one part in sixty four or +/- 1.56%. A frequency distribution of the variations of all of the weights in one of Bessler's one directional wheels would have a peak at almost exactly four pounds per weight. Yes, it's probably the case that the other parameters involved in his design could also have a little variation as well. But, if there is too much, like more than a few percent, wheel performance will begin to deteriorate sharply. Thanks for the well wishes. I'm close to having a runner currently. My levers are shifting smoothly, but still not rapidly enough on the ascending side. The center of mass of the weights and levers, however, is starting to sink at slower and slower rates toward the "punctum quietus". When (if) it stays steady throughout a forty five degree segment of drum rotation, I will know that I have arrived at long last. I'm praying it happens before I reach model #1200.
DeleteMore research published today demonstrating that the brain's "default mode network" - one of its most energy intensive systems - remains engaged during rest and sleep, showing much the same kinds of activity as when consciously focused on a specific task:
ReplyDeletehttp://medicalxpress.com/news/2015-04-deciphers-noise-human-brain.html
This would doubtless be the engine behind those legendary bolt-from-the-blue "Eureka!" moments..
I agree completely, of course. I've always felt that what I'm trying to do consciously somehow would program my unconscious mind to continue working on a problem while my conscious mind was asleep or directed elsewhere. The powers of the human mind are truly amazing and it's difficult to think something like the brain could come into existence through evolution. Yet, science assures us that this miracle did happen that way. If humans are capable of this today, I wonder what, say, an alien being with a brain several times the volume of a human one might be capable of. Perhaps they have evolved beyond the need to any sort of "formal" mathematical research into physics and just use their unconscious abilities to consciously "intuit" their theories.
Delete