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Sci Tech    H4'ed 4/28/19

Daily Inspiration — Whoa, man, that’s like some heavy-duty physics!

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I know I've said this before, but I feel a need to formulate it anew, so I'm asking you to indulge me. It's about identical particles, Bosons and Fermions, and why the world seems solid when we kick it and how physics tells us that everything is really one thing.

Alice and Bob are both people, but you would never confuse them--they're not identical. "Identical twins" are a lot closer. Some people can't tell them apart, but their mother can, their spouses can. Imagine opening a box from the Acme Ball Bearing Company, picking out two stainless steel balls that look exacly alike. You really can't tell them apart. Maybe looking for pits and scratches with a microscope, or with a scale that weighs accurate to a microgram you might be able to distinguish them; but even if you couldn't tell them apart at all, you would always think it's a meaningful question to ask, 'is this ball number one or ball number two?'

We think of two electrons or two photons (light particles) with an extension of our common sense from larger objects. They have no nicks or scratches, and even the most sensitive measurement apparatus can't detect a difference in their mass or any other properties. But we think of them as distinct in principle. You, me, and the physics professor, we all think that this electron is the one over here, and that is the one over here. In fact, micro manipulation technology has allowed us to line up individual atoms in a pattern, and they stay put!


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This picture is made of individual atoms (courtesy of IBM)

But (you knew there was a "but" coming after this long-winded explanation of what everyone knows) the formalism of quantum mechanics tells a very different story. Actually, it's two very different stories, very different from what we imagine and very different from one another. These are the stories of Bosons and Fermions.

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Light is made of photons, which are Bosons. The equation that governs the movement of a collection of photons, is explicitly symmetrized to account for the fact that the photons are identical in principle. What I mean by 'symmetrized' is that you write down the equation with photon #1 over here and photon #2 over there, then you write the same equation with photon #1 over there and photon #2 over there, you add up the equations and divide by two. So, what difference does it make to go through this Chinese fire drill, averaging up the two terms that are really no different from one another? Why bother? Yes it makes a difference, it makes a big difference. Technically, it's because the wave function for the photons is squared before you evaluate the intensity of the light, so that factor of 2 in the average doesn't come out in the wash. The probability is twice is high for two photons to be coupled together, moving in lockstep, acting like one big photon. And for a million photons, the probability is a million times as big. Once you get a large number of photons all moving in lockstep, the probabilty for the next photon to join them is very high. The upshot is that lasers are possible. Just a tiny crystal and an LED is enough to line up the photons, all moving in lockstep. (When I was in college, a laser cost $100,000, but now they're cheap enough that people buy them just to amuse their cats.) Lasers work because of the way that identical Bosons behave in quantum mechanics.

Electrons are Fermions, the opposite of Bosons in quantm lingo. Instead of adding up their wave functions and dividing by two, you subtract them and divide by two.

[particle #1 here, particle #2 there] - [particle #2 here, particle #1 there]

This minus sign is entirely responsible for the illusion of separateness which is so deeply embedded in our perception of the physical world. It's because for the special case where "here" and "there" are the same place, the two terms cancel out and the probability is zero. For two Bosons to be in the same place at the same time, the probabiliy is doubled; but for two Fermions, the probability is zero. Never happens. (This is called the Pauli exclusion principle.) And as the two Fermions get too close together, they start to sense this and they get antsy. They can only be brought very close together by giving them a great deal of energy.

When "here" and "there" are far apart, we imagine that particle #1 is over here and particle #2 is over there. Applying our experience from everyday life, we think of them as separate and distinct, but the QM equations are telling a different story. Both electrons are here, and simultaneously both electrons are there, and the two electrons are conspiring to keep a distance between "here" and "there" - not because they are different electrons, but precisely because their fates are locked perfectly together in this weird way, with the minus sign.

So, why is the rock hard when you kick it? Maybe you thought that the atoms in your shoe take up space and the atoms in the rock take up space and they can't be in the same space at the same time. That would be wrong. Or maybe you thought the electrons in your shoe have a negative charge and the electrons in the rock have a negative charge, and the two negatives strongly repel each other when they get close together. That's a very educated guess, but it's also wrong.

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The reason that the electrons in your shoe and the electrons in the rock kick up a fuss when they are in very close proximity is that the electrons in the rock and in your shoe are, at the most fundamental level, the same electrons, part of the same wave function. The lowest energy state of that electron pair has two lobes, with empty space between them, and unless you have a whole lot of energy to bring those electrons up to the next higher energy state, they are going to conspire to maintain that empty space between them.

But there are more than two electrons in the world

How would you write the wave function for 3 or 4 or 1080 electrons? This part gets technical, but I'll write it down for those who find it fun.

Let's say there are 3 electrons and three different places. Call the places One, Two and Three, and call the electrons 1, 2, and 3. Then

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Josh Mitteldorf, a senior editor at OpEdNews, blogs on aging at http://JoshMitteldorf.ScienceBlog.com. Read how to stay young at http://AgingAdvice.org.
Educated to be an astrophysicist, he has branched out from there to mathematical (more...)
 

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David Watts

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This is what Richard Feynman said about a phone call I made to him in, I think I recall, the early sixties:

"I received a telephone call one day at the graduate college at Princeton from Professor Wheeler, in which he said, "Feynman, I know why all electrons have the same charge and the same mass." "Why?" "Because, they are all the same electron!" And, then he explained on the telephone, "suppose that the world lines which we were ordinarily considering before in time and space - instead of only going up in time were a tremendous knot, and then, when we cut through the knot, by the plane corresponding to a fixed time, we would see many, many world lines and that would represent many electrons, except for one thing. If in one section this is an ordinary electron world line, in the section in which it reversed itself and is coming back from the future we have the wrong sign to the proper time - to the proper four velocities - and that's equivalent to changing the sign of the charge, and, therefore, that part of a path would act like a positron."

If I remember correctly -- my memory ain't what it used to be cracked up to be -- I think I was telling Feyman there is only one electron in the universe. By the way, I changed my name from Professor Wheeler to David Watts a lot of years ago.

Josh, very interesting article that seems to be a bit more than well beyond my comprehension. I do respect people like you and Richard Feynman that can put two and two together on stuff like this.

Submitted on Monday, Apr 29, 2019 at 12:22:42 AM

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Reply to David Watts:   New Content

So, David, in this picture wouldn't there have to be exactly as many positrons as electrons? (Last I looked, there were more electrons.)

Submitted on Monday, Apr 29, 2019 at 1:21:38 AM

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Reply to Josh Mitteldorf:   New Content

To be honest, I have absolutely no idea and I have not counted. My comment was just saying stupid stuff to entertain myself like I do all of the time -- I just copied the bit about the conversation from some website.

Your article like I said, is very interesting, but I am nowhere near at that level. I enjoy reading your science postings because even if I don't completely understand, I have just enough -- not really very much -- science knowledge that I like thinking about these kinds of things.

Actually, my answer to what you asked is yes, there have to be exactly the same number of electrons as positrons. And when you add the two numbers together the sum is exactly ... 1! There is exactly only one of each and they are the same one! How simple. :)

When I was reading the article I remembered something from the book, "Genius." The book is about Richard Feynman. I remember it talked about the idea of there being just one electron in the universe. Then, I read the link in your article that said, "A third way: there is only one electron in all the universe, and it travels forward and backward in time*, appearing in different circumstances as though it were a different electron."

I am sure in the book about Feynman, the reference to the idea of there being only one electron came no doubt from what Feynman said about the phone conversation I referred to with John Archibald Wheeler, a theoretical physicist.

Submitted on Monday, Apr 29, 2019 at 2:34:04 AM

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Reply to David Watts:   New Content

John Archibald Wheeler? I'm sure Feynman knew him, but didn't he die some time ago?

I remember a fine little book on special relativity by Taylor and Wheeler called "Spacetime Physics" that I haven't laid eyes on for many decades.

Submitted on Monday, Apr 29, 2019 at 6:47:25 PM

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Reply to Maxwell:   New Content

Wheeler was Feynman's PhD advisor. He outlived Feynman, productive to the end, and died in 2008 at the age of 96.

Submitted on Monday, Apr 29, 2019 at 9:05:48 PM

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I say no doubt 1080 is greater than a googol. And because you asked the question I suspect it is even greater than a googolplex. But I will take a guess that it is not greater than a googolplex.


Along those lines, rank in order the number googol, the estimated # of atoms in the universe, and the number of estimated possible moves in a game of chess.

Submitted on Monday, Apr 29, 2019 at 12:31:31 AM

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Reply to David Watts:   New Content

Actually 10^80 is less than a googol (=10^100), but he's talking about (10^80)! Yes! Huge number!

Submitted on Monday, Apr 29, 2019 at 6:55:13 PM

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Reply to Maxwell:   New Content

Thanks Maxwell. Yes I knew that 10^80 is less than a googol (=10^100).

I did not state it correctly. What Josh said was How big a number is 1080 factorial? So that is what I was referring to.

So, what do you think, is 1080 factorial greater than or lesser than a googolplex?

Submitted on Monday, Apr 29, 2019 at 9:05:49 PM

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One more thing, I am pretty much agnostic. But just last night I found out there really is a God; she exists. How did I find out? Last night in a feminine whisper, God whispered into my ear how quantum mechanics really works. Proof positive, god exists. :)

Submitted on Monday, Apr 29, 2019 at 12:43:06 AM

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I hang on to articles like this by the skin of my teeth, but do appreciate how it gets me thinking. As I've noted I watch many videos on these things, and find all of them fascinating, usually comprehensible at some level, but also some far better than most.

E.g. My recommend of Wonders of the Universe by Brian Cox, and Curiosity Stream in general, the other day. Jim" Al-Khalili has done more for me than say Brian Greene in quantum physics generally, but even the latter has helped much, starting with his--I was going to say Dancing Wu Li Masters, but I see that was by Gary Zukav click here . Here are some others worth taking a look at in general click here

Submitted on Monday, Apr 29, 2019 at 6:59:27 PM

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I know Brian Greene. I bought his video "The Elegant Universe" some number of years ago. It is late but I think I will start watching it again now. I mean, what else am I going to do. Do I need to read even more about all of the crap going on and learn even more about the fact we stand no chance? I am sure I will tomorrow but my consciousness has already been raised, and I have enough trouble sleeping already.

So, watching The Elegant Universe sounds right now ... pretty elegant ...

Submitted on Tuesday, Apr 30, 2019 at 9:30:57 AM

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So, I think if you had just one electron, in a large enough space that you could be pretty sure where it was and how fast it was moving, and it's wave function didn't overlap significantly with any other electron (a nice trick since as Josh says and contrary to what "Wheeler" says there are a hell of a lot of electrons in the universe) then you could pretty well tell that it was "your" electron. But if someone snuck up and swapped it with another one you wouldn't be able to tell. The composite wave function of every electron in the universe would change sign but the only observable thing is the square of the wave function, so no change. But it still doesn't "explain" why spin 1/2 particles have to be anti-symmetric and spin 1 particles symmetric.

If you're suggesting,though, that electrons in the universe are constantly changing places, that may help get a handle on "non-locality". If an electron on earth suddenly found itself in the spot on Alpha Centauri where another electron was, and vice versa, that would technically violate Einstein causality, but there would be no observable result. Same thing with Alice and Bob trying to exchange information by measuring entangled particles at those locations. One state may affect another instantaneously but there'd be no way to exchange hard information, at least nothing observable.

Submitted on Monday, Apr 29, 2019 at 7:22:45 PM

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Reply to Maxwell:   New Content

What I was trying to say is that what we call an electron is this wave function localized in space, but, according to standard quantum theory, this is an antisymmetric wave function that ties together all electrons in the universe, and the only thing local about it is that the wave function is confined locally.

Are there any observable consequences to the shorthand that we adopt when we talk about "an electron"? I haven't thought deeply enough to have an answer to that.

Submitted on Monday, Apr 29, 2019 at 9:15:30 PM

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Maxwell, I agree with you wholeheartedly. But what you wrote brought a question to my mind that I would guess you will know the answer to. The reason I make that guess is that you obviously know a hell of a lot about this stuff.

My question, what would happen if you collapsed the wave function of all electrons in the universe at the same time whether there be only one electron or a googolplex of them? Try to keep your answer brief please. :)

(By the way, my understanding of wave functions is little more than my holding my hand up and waving goodbye.)

Submitted on Monday, Apr 29, 2019 at 9:22:30 PM

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Briefly, in order to collapse the wave function of all the electrons in the universe you would have to include the ones in your own body. The whole "measurement problem" happens when you assume an external agent is doing the measurement.

Submitted on Tuesday, Apr 30, 2019 at 2:42:20 PM

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So to answer the truly nerdy question, a good approximation for the natural logarithm of the factorial of a huge number is ln(x!)=x*ln(x) - x. The natural log is about 2.3 times the base 10 log which in turn is about the number of zeros it takes to write it. Using those factoids and a back of the envelope calcultion the factorial of 10^80 works out to be more than googolplex.

If I remember correctly googol is 10^100 and googolplex is 10^(10^100). I'd be dead long before I counted that many sheep.

Submitted on Monday, Apr 29, 2019 at 7:31:06 PM

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Yes! I used the same method you did, but I decided (10^80)! is less than a googolplex.

Submitted on Monday, Apr 29, 2019 at 9:11:54 PM

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Well, the envelope was already full (from proving Fermat's last conjecture) so maybe I mad a mistake.

Submitted on Tuesday, Apr 30, 2019 at 2:38:02 PM

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You said, "If I remember correctly googol is 10^100 and googolplex is 10^(10^100)." I say you remember correctly. Another way to express a googolplex would be, googol^googol.

Submitted on Monday, Apr 29, 2019 at 9:29:03 PM

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Reply to David Watts:   New Content

David - not so fast. Check your calc, please.

10^googol is not the same as googol^googol.

Submitted on Tuesday, Apr 30, 2019 at 1:13:38 PM

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Reply to Josh Mitteldorf:   New Content

oops. What was I thinking? I must have been thinking of a googolsuperplex. After all googol^googol is a super big number. Even so, it is not as big as googol^googol + 1. Anyway, a number that big is kind of irrational to spend much time thinking about.

Thanks for the correction.

Submitted on Tuesday, Apr 30, 2019 at 5:14:38 PM

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Reply to David Watts:   New Content

The number itself is perfectly rational, though. Has to be. Also composite--lots of 2's and 5's in the factorization--so you can't use it to derive an RSA key.

Googol^googol + 1 might be prime, not sure. I think there's some theorem about that. Googol^googol -1 is the difference of two squares, so not prime.

Submitted on Tuesday, Apr 30, 2019 at 6:48:18 PM

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Josh, I just redid my thinking. I realize now why I was mistaken ... I forgot to carry the two.

Submitted on Wednesday, May 1, 2019 at 6:37:20 AM

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This conversation makes me so glad I'm just a garden variety wizard and not a math wizard! :)

Submitted on Wednesday, May 1, 2019 at 4:52:39 AM

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David Watts

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Reply to Janet Supriano:   New Content

You are not being straight with us Janet. You told me, and I know you remember, that you are a "Certified Quantum Theorist" or something like that. You said you framed the certificate and were going to post a picture of it here at OEN. I have not seen you post it so maybe it just slipped your mind. But I believe you and hope to god you are being honest with me because I have been bragging to people I know a "Certified Quantum Physicist" ... or something like that.

Submitted on Wednesday, May 1, 2019 at 6:34:21 AM

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David Watts

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Josh, I know I sometimes say stupid stuff in comments on your articles. It is merely an attempt to entertain myself while hoping others are entertained as well. But with your science articles, I try to do it with at least some sort of reference or relevance to the science in your articles. I hope that is ok.

Josh, I hope you have a sense of humor. :)

Submitted on Wednesday, May 1, 2019 at 6:40:33 AM

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Janet Supriano

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Reply to David Watts:   New Content

As a recently certified Quantum Theorist, I most definitely have a sense of humor. (secretly fostered in Catholic school) I find it important to not take myself too seriously... because if I do, I will have a mountain of crow to swallow if I ever forget to carry the 2 while the world watches. Besides, a touch of humility is kinder; and nobody's head has to explode.

BTW, I have a knock-knock joke for you. Go ahead, you start it. :)

Submitted on Wednesday, May 1, 2019 at 2:57:25 PM

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Josh Mitteldorf

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Reply to Janet Supriano:   New Content

knock-knock

Submitted on Wednesday, May 1, 2019 at 7:55:59 PM

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Josh Mitteldorf

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Reply to David Watts:   New Content

Is there anything I've written in anywhere at OpEdNews or on my blog or my poetry, or my books, or in academic journals -- anything at all that would indicate to you that I might be anything other than 100% dead serious about the facts, the truth, and pure logic?


I rest my case.

Submitted on Wednesday, May 1, 2019 at 8:33:20 PM

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David Watts

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Reply to Josh Mitteldorf:   New Content

No, but does that necessarily mean you don't have a sense of humor?

I will take what you said to mean you don't appreciate my attempts to be lighthearted. I shall refrain from doing so in the future.

But here is my "forgot to carry the two" explanation which I think is pretty darn funny. I have never forgotten this "Bloom County" cartoon. The star of the comic strip is a flightless-waterfowl Penguin named Opus.

The words are very hard to make out but this is what they are. The one talking is the little guy.

1st frame: "That's it. I've finished it. "The grand Unification Theory.""

2nd frame: "Quantum Mechanics and Relativity Reconciled! Everything in the universe can be explained! The Big Bang! The Galaxies! Earth! People! Trees! Everything except ... "

3rd frame: "Flightless Waterfowl. There is nothing here to explain flightless waterfowl." (Meanwhile Opus hearing this starts to panic and fade away.)

4th frame: "If this is right they just shouldn't exist at all." (As Opus is disappearing he pleads, "HELLO?")

5th frame: "I simply don't understand." (All that is left of Opus is his hand and arm holding an ice cream cone.)

6th frame: "Uh Oh. Wait a minute." (Opus has evaporated away.)

7th frame: The little guy is on the floor erasing some of his work, "Erase Erase Erase"

8th frame: "Didn't carry the two." Opus reappears and says, "NOW CUT THAT OUT!!""


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Josh, I meant what I said about my stupid stuff being science related. Even the cartoon has "quantum mechanics" and "relativity" in it!

Josh, I am hoping I can get at least a little smile out of you. And actually, your sense of humor did come out a little when you said to Janet, "knock-knock." :)

Submitted on Wednesday, May 1, 2019 at 11:12:04 PM

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David Watts

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Reply to David Watts:   New Content

Darn it. I left one thing out which is funny.

When the little guy says, "Quantum Mechanics and Relativity Reconciled! Everything in the universe can be explained! The Big Bang! The Galaxies! Earth! People! Trees! Everything except ... "

Opus then says "Except what?"

Then the little guy says, "Flightless waterfowl."

Submitted on Wednesday, May 1, 2019 at 11:38:17 PM

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Josh Mitteldorf

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Reply to David Watts:   New Content

Smiling takes energy that can be put to better use solving equations!

Submitted on Thursday, May 2, 2019 at 10:43:01 PM

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David Watts

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Reply to Josh Mitteldorf:   New Content

That did to me what I had hoped to do to you. It made me smile. Thanks.

The only equations I remember are E = mc2 and something called a quadratic equation or something that went something like -b ┬▒ the square root of (b2 - 4ac) all over b2. Pretty high level math if you ask me. But, I will leave the hard stuff to you.

I think it would be very enjoyable and fun and gratifying to understand at the level you do, all the science and math and physics, etc., that you know and understand.

Submitted on Friday, May 3, 2019 at 1:01:22 AM

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Brian Giffin

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Reply to David,

This is fascinating, thanks to all. My math got stuck back at a/b = c/x which I find very useful. On the other hand I did catch onto Uber (awesome) which rely's on GPS which I'm told needs Quantum Theory math in order to work.

From what I'm reading, if there is only one electron it must be the God Particle. That simplifies a lot.

Newton helps me with manufacturing stuff, but I thought I was using a lot of electrons thinking about stuff and then making up CNC programs for cutting materials. If there is only one electron, then how come I have to make so many copies of the same idea to pay the mortgage over and over?

I've concluded I'm stuck roaming with the Bosons, that's OK. I always liked Bosons better than Fermions. 3-D seemed more secure than say politics or science, until Daniel Geery led me off the cliff in the past few months. I feel like a Ghost Dancer.

So I'm looking for a Universal Theory of Everything, that leaves me someplace pleasant to get born in again. My oneness isn't completed. That is, if I'm a universal being like everything else that gets reincarnated over and over. This Theory seems to need parallel universes, that's obviously a good idea. I want to go to the parallel where the birds and the bugs and the fish all went.

Submitted on Friday, May 3, 2019 at 4:23:58 PM

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Janet Supriano

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Reply to Brian Giffin:   New Content

Fantastic (and deep) reply, Brian! I felt it and I'm with ya'

You also made me laugh. I got lost in math before you did.

I like the idea of roaming with Bosons, tho' on occasion it can get scary lonely.

Daniel, whom I love to pieces, led me off that cliff, too. (just ask David Watts) Everyone became a Ghost Dancer, which maybe we are anyway, with or without climate spooks. But been clawing my way back to smiling again.

Your comment made me smile. :)

Submitted on Friday, May 3, 2019 at 8:13:23 PM

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Brian Giffin

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Reply to Janet Supriano:   New Content

Thanks Janet,

I've been a fan of yours for years. You keep me smiling. But, this thing that if we reduce our CO2 output, it only gets the warming going worse, this is bugging me a lot.

I hate feeling trapped and get like a wild animal. We that worry about it all, need an improved outlook, something to grasp hold of. Some Theory with a sliver of daylight at the end of the tunnel.

Submitted on Saturday, May 4, 2019 at 1:55:49 AM

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Janet Supriano

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Reply to Brian Giffin:   New Content

Gosh, I feel the same way, Brian. It ALL bugs me a lot. Yeh, I get scared, and I worry for the younger ones; but mostly I get furious. I hate being tricked as well as feeling trapped.

I've read that depression is the aftermath of anger. I admit to both.

For that sliver of daylight, I've been paying more attention to Molly Cruz's posts.

I can't say if I agree with her philosophy and trust; I simply don't know. But it is nice to think humanity could have a higher purpose than mere self-destruction. And that it's possible both Earth and humanity will continue and flourish.

I do think there is evil at play; in what form, I don't know. But I grew up on the Lone Ranger, Hopalong Cassidy and religious ideas, so I choose to think the White Hats win in the end. (that would be us)

It's true we weren't promised a rose garden (we have to grow our own and thorns hurt), but we sure heard a lot of 'Happily Ever After'. I'll go with that.

We're not going to figure this one out, Brian, hard as we try. Too many rabbit holes. We can enjoy the puzzle until we don't, and just ride it out....and relish the smiles. :)

Submitted on Saturday, May 4, 2019 at 3:41:32 PM

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