I HOPE that the reality is near the last option! Is it actually likely that I totally understand all these subjects? Probably not! Many of these subjects have been attacked by the world's greatest minds for hundreds of years! The likelihood that a single person could solve even one would be significant . . . solving many of them, pretty close to inconceivable.
So why all these pages?
It has long been my observation that the bulk of intelligent minds tend to approach problems from pretty much the same directions. There is a tendency to climb on the backs of scholars that have gone before. This is certainly a good concept, and it represents the vast majority of advances in science and society in recent centuries. However, I think it sometimes causes later researchers to funnel their thinking along the same lines as those earlier giants. I think that this can unintentionally introduce limitations and biases on their later assumptions and conclusions. Hey, for 1800 years, the ancient Greek Aristotle's view of science prevailed! I have to think that many of the later people who followed him must have contemplated things like a non-flat Earth and maybe even one that could move! But nobody dared question the great Aristotle, who everyone knew could not possibly be wrong about anything!
Even inside the field of Nuclear Physics (the field for which I was educated in College), I think the same thing sometimes occurs. Around 1935, a Physicist named Hideki was thinking about the nucleus of atoms and that they certainly contained many positively charged protons, which all electrically repelled each other. It was already known that there was more material in the nucleus of nearly all atoms, and earlier (1930) Physicists had concluded that they must be "neutrons", electrically neutral objects that pretty much just take up space to separate the protons. Hideki did the simple calculations and found that no known force could counteract the repulsion of the protons from each other, so he described a "Strong Nuclear Force" which MUST exist to allow atomic nuclei to avoid instantly coming apart! Recently, in some investigations on some other matters inside the nucleus, I believe I have come upon extremely strong evidence that neutrons probably do NOT exist inside the nucleus, and that a Strong Nuclear Force is unnecessary in describing the stability of atomic nuclei!I now have the impression that Hideki had ASSUMED that neutrons existed inside the nucleus, since all Physicists of the time had accepted that concept, and so he saw the need to find some way of explaining stability. And ALL Physicists (apparently) who have followed have simply accepted that he was right! I no longer think he was! I see this as an example where things seem really "obvious" (neutrons seem to exist inside the nucleus) (a Strong Nuclear force MUST exist to keep protons from flying apart), while a different explanation might have equally explained the evidence that had been found.
In this case, I believe the evidence actually supports a structure where "loose" protons and electrons exist inside the nucleus instead of neutrons, which are essentially a proton and electron stuck together.
I'll give a few examples:
With 99 addition problems to do, clearly the class would be occupied for a LONG time. And, the odds were, that the 6-year old kids would make mistakes along the way, and probably have to do it all over! Her next hour should be calm, right? Wrong!
Maybe half a minute after getting us started, I raised my hand. She thought I wanted to leave the room for the bathroom. I said, "No, I have the answer." She was NOT happy! She stormed to my desk. I had my hand over my answer, but she saw the sheet basically blank. She started going ballistic in not liking to be annoyed like that. When I raised my hand, she saw the correct answer! She made some weird sounds, and then shouted that I had cheated, that I had copied the answer from someone else!
It's tough when a 6-year old kid gets accused like that, and I didn't even try to point out that the other kids were probably only up to adding the 4! That night, my parents got a call to come in to the school to see the Principal (and to bring me).
At that meeting, she went through the Riot Act to describe to the Principal (Mr. Galliher) and my parents, the problem and that she couldn't figure out how I "cheated" but that I certainly did. She apparently concluded that I somehow had seen the answer on her desk, even knowing that I had not been near her desk. This was pretty intense for a shy little kid. (I still remember it all VERY vividly!)
After she was done, and after a pause, the Principal (a REALLY nice man) came over to me to ask how I got the answer so fast. That was really nice, as he didn't seem to be automatically accusing me. I told him that I knew that you didn't have to add numbers in any special order. (I think the teacher might have taught us that.) I told him that I had noticed that 1+100=101, and 2+99=101, and 3+98=101, and so on, all the way to 50+51=101. It had seemed obvious that there were 50 pairs like that, each of which equaled 101. So the answer had to be 50 * 101 or 5050. If you see the pretty simple logic of this, you can see that nothing much would have to be written down! Not because I was smart or anything, but because those particular numbers made it easy.
The next day, I was in Second Grade! For many years after, I didn't think that was a compliment, but just a way that that teacher found to get rid of me so she wouldn't have to deal with me any more!
(There is a recent footnote to this anecdote! SEVERAL people who have read these foregoing paragraphs have torn into me! EACH of these individuals has accused me of having "stolen" this event from some other (famous) person's life! Wow! Each has also expressed tremendous disgust at me for "having stolen that anecdote from a famous person AND still had the audacity to mention my Christian aspects!
Around 25 years after my "incident", I happened to hear a momentary comment on some PBS educational program about a similar problem and some mathematician as a kid. A few months later, the program was re-run, so I listened this time. It turns out that Gauss, the guy who I then knew was famous for his magnetism and electricity researches, was also a famous mathematician. When he was a kid, around 1784, he quickly got the answer to essentially that same problem. My impression was that he was 5 at the time, and not in school, and just doing his own studying, but I'm not sure about that.
I went to the library and checked out several Gauss biographies, and finally found one that mentioned that incident in his life. It turns out that he DID solve the very same problem, but he did it in a slightly different, and much more elegant, way. Actually, the way he used is now used by professional mathematicians to solve that sort of problems, so it was a LOT classier than my crude way.
Yet, these current critics tell me that statistically it is ABSOLUTELY IMPOSSIBLE for two different people to have such a similar incident, and that I should ADMIT that I somehow "stole" it from Gauss. This would be an interesting idea, but SOMETHING definitely caused me to skip most of First Grade, and some fantasy wouldn't have done that!
Even MORE interesting to me (as I have a peculiar sense of humor) is that a couple of these people who have hurled accusations at me, have accused me of stealing the incident from a DIFFERENT mathematician, somebody named Cantor, who apparently lived in the 1800s! Well, not even counting me, how do these critics explain the ABSOLUTE IMPOSSIBILITY of two people having the similar experience when two of their heroes both seem to? (Pretty funny, huh?)
In all the other wild accusations they have thrown at me, attacking my character, my honesty, my Faith, and a variety of other things, each has been aghast that I "dared" compare myself with their hero (whichever one that was!). I did nothing of the sort. Actually, I see no REASON for even TRYING to do such a comparison. All I did was describe what I thought was an interesting little anecdote (from MY life!!!) that fit in with this "unique perspectives" discussion. And, actually, I tend to wonder about little kids who somehow establish great "documentation" for such things. (My critics emphasize that the famous mathematicians are well documented as having done such things, where I, a mere impostor, have no such documentation. Of course, there might actually be some record of why a First Grader was suddenly promoted to Second Grade in that school's records!) (I KNEW my [poor] parents messed up in not hiring a team of reporters to follow their little kid around!)
Finally, I would like to think that IF I had wanted to try to "impress" anyone, I would have chosen one of several "adult" accomplishments, like maybe inventing a truly advanced woodstove and then, starting with $3100, manufacturing and selling about $11 million of them, rather than something that happened when I was six. (Otherwise, I've been going downhill since First Grade!)
Apparently, a student ignored this "obvious" solution and submitted a paper with TWO alternative solutions. (1) The barometer could be carried to the roof of the building and dropped off, carefully timing the interval until it smashed on the ground. A simple gravitational equation would then give the building's height. (2) Take the (expensive) barometer to the building's owner and say "I'll give you this barometer if you tell me how tall the building is!"
Seems to me that there are a bunch more possibilities. (1) If it was sunny, and the ground was level, set the barometer on the ground and measure the length of its shadow, and also measure its height. Then count your footsteps in the length of the building's shadow, to determine how long it is. A simple proportion (of similar triangles) would give the height of the building. (2) The building is REQUIRED to have a fire escape stairway, which is likely to have steps that are all the same height. Walk up the steps, carving a notch in the barometer for every ten steps you climb. You would soon know the building height.
Think of a cube. Draw a diagonal line from corner to corner on one
surface of the cube. From one of those end corners, draw another
diagonal across a different face of the cube. (Like in the drawing)
What is the ANGLE (in space, inside the cube) between those two lines?This is an immensely NASTY mathematical problem! It would take a LOT of effort to solve it, using any traditional approach.
It turns out that there is a VERY different approach that can be used. The outboard ends of the diagonal lines happen to be at opposite corners of one of the OTHER sides of the cube. Imagine drawing a diagonal line on that side connecting them. You now have a triangle inside the cube, at some weird angle. Since a cube's sides and edges and angles are all identical, that triangle must have sides that are exactly the same length! That means that it HAS TO BE an equilateral triangle. That means the included angle (what we want) HAS TO BE 60 degrees!
Then, a creative forester was one day in such a grove, watching the trees sway in the constant moderate wind that day. He noticed that one single tree was swaying at a different rate than all the others. He realized this was a situation where Physics was useful, and that the trees were resonating like tuning forks (but at VERY low frequencies). The one with a different resonant frequency clearly had a (hidden) internal difference, which he realized was probably a flaw as a result of the disease. He painted a mark on that tree and had it cut down, and the disease was clearly there!
As it happened, one plane was on a path to pass almost directly over me. When I saw the airplane directly above me, the sound seemed to be coming from a spot well behind it. I didn't have an entire plan at that moment, but I decided to count the seconds until the sound got to the point directly above me, which was 31 seconds. At that point, the image of the airplane was in the sky about a 30° angle farther ahead of it.
It turns out that that's enough information to be able to figure out how high the plane was and how fast it was moving! Isn't that cool? Virtually no information, and yet it's possible to figure out some things that would seem impossible! Try thinking it through. It's pretty logical!
Here's the way I looked at it. From the moment the plane's image was overhead until the sound was, was 31 seconds. That means that the sound that was created up there, when the plane was actually overhead, took 31 seconds to get down to me. Sound travels about 1100 feet per second in air. Therefore, the plane must have been 31 * 1100 or about 34,000 feet above me when it passed overhead! That's a pretty common height for long-range passenger aircraft, so I felt that was a reasonable answer.
Now think about that triangle when the plane was actually overhead: me: the plane overhead, and the plane's location when the sound got down to me, and me. That was a right triangle, with a 30° angle. Geometry or trigonometry can tell you that the two legs of that triangle are in the ratio of 1 to the square root of three (about 1.73). I already know that the long leg is 34,000 feet, so the short one (the horizontal one that was the path of the airplane) must have been a little under 20,000 feet. That means the plane must have traveled about 20,000 feet in the 31 seconds. So it had to have been traveling at 635 feet per second (or 430 mph). The airliner was probably slowing down to land at either Chicago or Indianapolis, so that answer made sense, too.
Wouldn't it seem impossible to know those things? But they were reasonably simple to estimate, using minimal information.
The computer analysis could be pre-programmed for any location where the necklace would be unlikely to ever be. If this would work, it might be the ultimate in a personal safety monitor, for elderly people who lived alone!
These examples are meant to show that the "obvious" approach to a problem is not always the ONLY approach. More than that, an alternate approach might exist that more simply or easily or quickly offers a solution to the problem. It might even turn out that the "traditional" answer is not correct, and that only some alternate approach is capable of coming up with the correct answer.
For some reason, throughout my life, I have tended to see the world from such different perspectives! Combined with a College Degree in Physics, and a natural curiosity, I have always had a tendency to explore many subjects. Since these unusual approaches often occur to me, I then often find it necessary to study some new field, in order to determine if my approach might be valid and if it gives a solution that matches the traditional solution to the question. Usually, I find that they match up fine, and I had just found some unique way of confirming something that people already knew. I suppose that represents a lot of wasted effort. Friends sure seem to think so! But I think there has been value to me in doing this sort of thing. The fact that, usually, my conclusions perfectly matches things already known (by other methods) has tended to give me confidence that my approach has some validity.
THEN, when I get results that do NOT match accepted knowledge, I have to consider two possibilities. They really are right, and I made some blunder of assumption or logic or mathematics; or there might be a new insight like those included in these pages. As mentioned above, it would be awfully arrogant to seriously think that my solutions for these many subjects are better than those of the "experts" in those fields. Many of these pages have been included here because I just cannot figure out where my error must be, as to why my results don't match the accepted knowledge. In each case, I attempt to present the logic and arguments and assumptions that I used in arriving at my results. It seems likely to me that, in some of these specific subject areas, an expert will someday come along and explain where my error lies. No problem, there!
Are these pages all right? Not a chance! That's not my intent. I hope to offer alternate approaches for analyzing some subjects or problems. In many cases, these are problems that are generally considered enigmas. In some cases, I have already found that they DO work! In other cases, experimental confirmation of benefit has not yet been done. In yet other of these presentations, particularly the Theoretical Physics and Geophysics and Astrophysics presentations, ultimate confirmation of one theory over another may elude mankind for Centuries!
In addition, if kids and teens (who often think like I do!) get confidence in knowing that there is someone else who generally thinks outside the box, wonderful!
Shortly after college, and a degree in Nuclear Physics, I wound up living in a hundred year old farmhouse that had been abandoned for about 7 years. It had no insulation and 11 major rooms, in a NASTY climate of northern Indiana. After getting large Propane bills, for heating only part of the first floor of that house, I designed a woodstove with all the sophistication that a creative Physicist could manage. I never wanted to be in that business or any business. My intent was to make a grand total of ONE woodburner! I expected that my life work would involve doing research in some lab somewhere.
After the woodstove worked so well that I heated the entire large house while using a total of one gallon of Propane during an entire winter (and that was for kitchen cooking), word got out. I eventually built a few, just to get people to leave me alone, and sold them at exactly what the materials cost me, $365.08. When those people told their friends, I eventually realized that I was in business. Within a year, I was 1600 units behind on production!
I didn't really enjoy being in business, but I knew that I was enhancing the lives of all the families that got them, and I thought that maybe that's what I was born to do. My company made a BUNCH of them, well over 25,000!
That motivation, and my creativity and my Physics background, combined with a financial freedom (because of the stoves) to explore such areas, allowed me to pursue many projects and therefore learn about many subjects. Many more ideas had occurred to me over the years, but I just have little interest pursuing anything that does not clearly have potential benefit to society, to Nature, or to God in some way. (A few of the projects described in my Public Service lists are a little borderline on this, but there were many other projects that had even less redeeming value, and I basically dismissed them. They tended to be things that would likely make lots of money, with that as their only goal.)
I was saved as a Christian when I was 19. Ever since then, my religion has been important to me. I became a Pastor of a tiny non-denominational Christian Church in 1996. I soon realized that my unique set of motivations and talents would allow me to be an Instrument in His Work, by creating the BELIEVE site on the InterNet. (I had previously created a smaller version of it, that fit on a floppy disk, to give to anyone who wanted it. In 1994, I tried to get Willow Creek Community Church to make 22,000 duplicate diskettes, so they could be given to all the congregation members as a Christmas present that year! How often does a Church give Christmas presents to its Congregation? Unfortunately, Bill Hybels and his staff did not see value in what I proposed. But I still have great respect for them!)
It took me about 2.5 years of more than full-time effort to assemble and initially program the entire BELIEVE structure. Having done all that, my hopes were modest. My ultimate hope was that a single person found enough value from BELIEVE to either renew his/her own Christianity or to become a Christian. THAT would have made it all worth while!
I had long been distressed by the bias of information presented by many of the Churches I was aware of. Each one seems to be so terrified that someone would leave their Church and go somewhere else, they tend to say bad things about all competing organizations (and their beliefs). I truly hope their motivation was other than the income in the collection plate, but I worry about that.
As a result, I went to extreme effort to select the BELIEVE presentations to be informative, honest, accurate, complete, and as unbiased as possible. This will certainly be an ongoing activity for the rest of my life, and it is a joy! As BELIEVE is getting better known (now about 10,000 visitors each day), the responsibility feels even greater.
There are at least a dozen more projects that have not yet been included in the Public Service pages. Hey, there's only one of me! And, as long as BELIEVE exists, and is supported financially by my projects so it can continue (forever???), I am one happy camper!
Regarding BELIEVE, I feel strongly that any Instrument of the Lord should remain in the background, if possible, to allow the Glory of His Word to have the stage. That's why I didn't make a big production of who I am in the BELIEVE web-site.
I also hope that this text doesn't make it sound like I think I'm anyone unusually important. We're all the same, really, we just have different talents or skills, that's all. It seems that I have just put mine out on the table! Kind of scary!
And, if you have tried to work your way through any of my presentations, you already know that I have extreme limitations regarding compositional and literary skills! I hear endless criticisms about that, and all I can say is that I do the best I can, to present these assorted concepts.
C Johnson
( http://mb-soft.info/public4/index.html )