Bozo's Last Number Theorum

surprise I am amazed by the rich texture of numbers.  I mean who would expect that just adding the same unit, again and again, would generate beautiful features … why didn’t it just generate a long list of names of the next stretching boringly forever.   Famous mathematicians have studied this beauty as Number Theory to depths that i can barely fathom.   Me, i am a dilettante having merely sniffed around the edges and see only that which smacks me personally right in the face.   “Bozo's Last Number Theorum”  is a case in point. 
 

Two numbers added together will exclude their prime factors from their sum. 

Now obviously we need to factor any primes which they already share, for a + a = 2a regardless of whatever else is present.

Note the similarity with Fermat’s last theorum, which also excludes certain integers from appearing in a sum. 

Here are some examples … Now go ahead … i dare you!  Find an example of adding two numbers together, which have no common prime factors, and any of their prime factors are contained in their sum. 

But i rather doubt that you can ...
 

Proof by contradiction: 
Assume:
1) x + y = z
2) x,y,z are integers
3) there are no common factors of x, y
Now contra factually assume that a factor in an addend also appears in the sum.
If that is the case then (1) can be rewritten in the form:
4) x + ab = ac 
5) by algebra:
x = ab – ac
x = a(b – c)
6) x/a = b – c
7) b – c must be an integer as given by (2) – the difference of integers must be an integer.
8) x/a must also be an integer because it is equal to an integer.
9) therefore x must contain “a” as a factor.
10) but x cannot contain “a” as a factor as given by (3).
11) Therefore there is no “a” which will satisfy (4).
QED
 

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Tags

  1. number theory
  2. prime

Comments


Seth says


Fastblogit’s Bozomic Decomposition of this thought.

my interpertation … contradiction squared leading to transition to something new yet to be named ← which is what the the theorum discovers laughing

Seth says
Seth 2016-06-20 08:09:27 [item 21036#53113]
the more i think about this proof, the more i am unconvinced by step 10.  that step needs elaboration. 
the proof rests on the realization in step 10 that since the integer “a” ...
  • is not contained is x, y and z, 
  • and if we suppose that it is contained in y and z
  • then it can not be contained in x (otherwise we have contracicted ourself)

Seth says
Mark de LA 2016-06-21 09:53:07 [item 21036#53166]
A little bird told me this AM when I was waking up that Bozo is trying to create thotons; perhaps ones he could find again or got sticky. So far they are as automatic as tags laughing – I don’t  quite get the prime numbers yet.
primes have characteristics of thoughts …

objectively we can share that ...
  • there are an infinity of them
  • they combine together
  • they expand spirarially in complexity
subjectively anyone can associated them to any meaning of their choice  … they are a perfect medium.

so carrying on a tradition i gleaned from GW who learned it from the ancients, i can notice coincidences happening  reflected in a peculiar network of primes that i can build up just as very intensly as i pay it attention.  it is a fun game … me i do not take it seriously.  So far i have stopped at 11.  There is a long way to go to 23 … think what could emerge were i get deep as 1753 … and there is no limit, like 64, as to how deep i can go. 

 

Seth says
Mark de LA 2016-06-22 07:39:38 [item 21036#53203]
pondering I wonder if the RWG is a fundamental thought.
i think it is … maybe 2^4 + ego ? or something like that.  in my ontology-game i have yet to assigned even ego to a prime

… though for ego 7 + 11 + 5  = 23 ← (a beautiful prime indeed) seems would be close pondering ← just now written out loud

Why 7 + 11 you might have asked laughing

Seth says
hmmm …  2^2 + 23 = 27 = 3^3  might make RWG zen … we can not have that in my ontology. 

2^3 + 23 = 31 would make RWG a prime … that works for me smuglaughing

Seth says
Mark de LA 2016-06-22 08:14:38 [item 21036#53213]
In the Cosmic Trigger , Wilson mentions the oddities of coincidence regarding the number 23.  I reference a PDF so they are searchable if you are interested.  Of course Hex 23 is “gnaw through” & gnaw through is also the title of one of GW’s little projective geometry books.
Seth 2016-06-22 08:18:06 [item 21036#53216]
strangely enought i noticed 23 in the Cosmic Trigger too, based on your previous post …. probably why i glomed on to it here as ego … especially for the coincidence that 7 + 11 + 5 equals it laughing

this shit keeps comming
nathan 2016-06-22 08:21:43 [item 21036#53218]
LOL … your number game sounds intriguing … though I don’t have time to focus on it right now.  

Of course the shit keeps coming!  You are focused on it, and whatever you focus on will become something. It will happen in your reality. Now, in these times, more than ever before!
Seth 2016-06-22 08:26:19 [item 21036#53219]
true thumbs up 

however it will not happen in the world that share, unless we in fact do share it.   that happening is not just up to my personal focus. 
Mark de LA 2016-06-22 08:29:48 [item 21036#53220]
Lots of people have the same ideas without communicating with each other otherwise the patent & copyright offices would run out of business & why in politics there are no new ideas. laughing
partually true thumbs up.  

here i concern myself with that singular pecular one … and not all of them in some munged generality.

Si says
Mark de LA 2016-06-22 08:14:38 [item 21036#53213]
In the Cosmic Trigger , Wilson mentions the oddities of coincidence regarding the number 23.  I reference a PDF so they are searchable if you are interested.  Of course Hex 23 is “gnaw through” & gnaw through is also the title of one of GW’s little projective geometry books.
Seth 2016-06-22 08:18:06 [item 21036#53216]
strangely enought i noticed 23 in the Cosmic Trigger too, based on your previous post …. probably why i glomed on to it here as ego … especially for the coincidence that 7 + 11 + 5 equals it laughing

this shit keeps comming
Mark de LA 2016-06-22 08:20:15 [item 21036#53217]
As someone said “shit happens” ! laughing
?

Mark de LA says
Seth 2016-06-22 08:34:55 [item 21036#53223]
incidentally, even in politics, there are always new ideas … else the game would not match the medium of primes … look see for yourself … the primes are infinite as are their combinations.
Yeah, that was mostly my joke. Although, I would like to see just one new idea in the politics of today that has not already been expressed in the last 2000 years.
 

Si says
Mark de LA 2016-06-22 08:14:38 [item 21036#53213]
In the Cosmic Trigger , Wilson mentions the oddities of coincidence regarding the number 23.  I reference a PDF so they are searchable if you are interested.  Of course Hex 23 is “gnaw through” & gnaw through is also the title of one of GW’s little projective geometry books.
Seth 2016-06-22 08:18:06 [item 21036#53216]
strangely enought i noticed 23 in the Cosmic Trigger too, based on your previous post …. probably why i glomed on to it here as ego … especially for the coincidence that 7 + 11 + 5 equals it laughing

this shit keeps comming
nathan 2016-06-22 08:21:43 [item 21036#53218]
LOL … your number game sounds intriguing … though I don’t have time to focus on it right now.  

Of course the shit keeps coming!  You are focused on it, and whatever you focus on will become something. It will happen in your reality. Now, in these times, more than ever before!
Seth 2016-06-22 08:29:58 [item 21036#53221]
true thumbs up 

however it will not happen in the world that we share, unless we in fact do share it.   that happening is not just 100% up to my personal focus.  

“Shrodenger’s cat does not live unless the poor creature is let out of the box.”   ← i wonder how many people have ever thought that peculair thought smugsurpriselaughingcool
Mark de LA 2016-06-22 08:37:39 [item 21036#53226]
Or that in reality a cat can’t be both alive & dead at the same time.  Or that maybe the cat can be revived if the poison only makes it sick. Or maybe the poison kills the observer. Or … laughing Failure to focus on reality is the real problem of Shrodinger’s Cat “problem”
.
nathan 2016-06-22 08:41:29 [item 21036#53227]
All of those do exist Mark. It is failure to focus your choice so that you manifest your desired experience out of all of those that are possible and exist at the quantum level that is the real problem.  The observer selects the outcome by the micro effects of their own thoughts on the quantum possibilities.
Mark de LA 2016-06-22 08:55:41 [item 21036#53230]
Experience with real dogs tells me that it is in one state or the other & not both.  If your focus is confused between reality & possibility then maybe you think dual opposing states can go simultaneously, not me!
cool
Humm, well clearly science things dual opposing states can and do exist. I am not a look-up junkie, but I remember reading articles about quantum tunneling of particles that proved both states do exist at the same time.

Expriements with dogs would be dependant on the thoughts of the observer. If the observer thought the results should be random and that was their propensity of focus, then the results would be, of course. This is why things like this, and even things like ESP, cannot be tied down with hard science … because they depend on the thoughts of the observer even more so than the higher level physical realm, which we all have millions of years of common thought and agreement about so the physical realm seems somewhat similar to us all and science can tie an aspect of it down by consensus of scientific opinion. 

Si says
Mark de LA 2016-06-22 08:14:38 [item 21036#53213]
In the Cosmic Trigger , Wilson mentions the oddities of coincidence regarding the number 23.  I reference a PDF so they are searchable if you are interested.  Of course Hex 23 is “gnaw through” & gnaw through is also the title of one of GW’s little projective geometry books.
Seth 2016-06-22 08:18:06 [item 21036#53216]
strangely enought i noticed 23 in the Cosmic Trigger too, based on your previous post …. probably why i glomed on to it here as ego … especially for the coincidence that 7 + 11 + 5 equals it laughing

this shit keeps comming
nathan 2016-06-22 08:21:43 [item 21036#53218]
LOL … your number game sounds intriguing … though I don’t have time to focus on it right now.  

Of course the shit keeps coming!  You are focused on it, and whatever you focus on will become something. It will happen in your reality. Now, in these times, more than ever before!
Seth 2016-06-22 08:29:58 [item 21036#53221]
true thumbs up 

however it will not happen in the world that we share, unless we in fact do share it.   that happening is not just 100% up to my personal focus.  

“Shrodenger’s cat does not live unless the poor creature is let out of the box.”   ← i wonder how many people have ever thought that peculair thought smugsurpriselaughingcool
nathan 2016-06-22 08:35:13 [item 21036#53224]
Well, it is created in your reality, at least that part that is created from your continuing thoughts. Once created, it is instantly available for including in any reality. It becomes part of the reality matrix that all can draw upon, the multiverse. Even if no version of anyone ever includes it (which probably never happens), it is still there, created, and available.

Now, what I think you are looking for, is the idea that you can also create an experience of sharing it with someone, of them including it in their reaity and you including that experience of theirs in your reality, and that is what is important and desirable to you. And yes, if you don’t create that sharing experience in your reality, it does not exist.  
Seth 2016-06-22 08:43:38 [item 21036#53228]
well i actually disagree with your first paragraph here.   an idea conceived in a private mind that never gets represented externally dies with that mind.  ← a thought dreaded by you, i have no doubt.  now certainly it can become reborn in another mind (i think mark refered to that above) ← but that rebirth is not connected at all with the idea which died.  which connection might be some outrageous coincidence ← which me, i will not await.

 
nathan 2016-06-22 08:50:03 [item 21036#53229]
I really have no care or vested interest in my thoughts dieing or not. What I care about is my experience. I know that all thoughts by everyone do exist by my own experimentation and living. But I don’t care if mine do or not … that is not part of my experience.

What I am more interested in is your thoughts on the idea that you not only create new stuff in your reality, but that you also create the experience of sharing, which is the experience that you use to validate stuff. Of course, sharing is a particular type of experience. It is also being created by another and both (or more) are aware of the other’s experience while continuing to create their own experience. But really, this is just a type of experience, it is not the root of if something does exist or not, right?
Seth 2016-06-22 09:01:23 [item 21036#53232]
well i call ideas that i cannot represent externally … AND … do not get picked up and vibrate (as it were) external to myself,  “not shared”.   the first term of that equation is pretty much 100% my doing and my experience.  the second term is not something that i have much control of.   so no, i cannot unilaterally create the experience of sharing ← althought i can imagine that i do. 

so for me the “The Wet Noodle Effect” is very much part of my reality … and no i can not wish it away … even if it might be fun.    apparently you have done it internally.  the trick, however, would be to do it externally. 
I agree. The trick IS to do it internally, with a degree of consistency. Then, it starts popping up externally, rather quickly in these times in fact. The external is a mirror of the internal. When the internal has sufficient amount of focus in the right way, the external cannot help but mirror it and no other apparent external circumstance can suppress the external manifestation (mirroring).

We each develop our own relationship to the process of this internal focus and external mirroring as we develop from birth. For some it is more concrete, for others, perhaps more like pushing a wet noodle. But surely, with the right technique, even a wet noodle can be pushed and similarly anyone can learn to push their internal into the external as well … and with with conscious design, not random happening by taking clues from others reality. It’s really fun to include others reality and meld it with our own, but it is only a kind of experience, not what reality is made of.  

Si says
Mark de LA 2016-06-22 09:05:55 [item 21036#53234]
Science fiction is full of it: mostly elaborate mathematics. Experiments where the observer observes something & then tells a fantastic story fill the quantum space of multiverses of multiple personalities.
Yes it is. I would take that as proof that what is thought out as science fiction does exist. After all, by the odds, more that started as science fiction has come into material existence than that which was thought out as science fact firstly.  If I were a betting man, I would bet on science fiction before science fact. There is a good reason for that too. Science fiction is read and thus thought by many, often a huge many. So it is more likely to become than science fact which is often only thought about by a small few.

Mark de LA says
Seth 2016-06-22 09:33:46 [item 21036#53237]
well, it is absolutely true that the cat in Schrodinger’s thought problem is never in a dual-state of being both alive and dead at the same time.   That is not something that can ever happen and be shared.   Mark, imho, has that absolutely right.

Now stastically it can look as if that dual state exists –  and physical experiments bear out that model.  but that is only in the thought dimension – we can never share a happening of the cat being both dead and alive.  Which is why i think this term,  “what happens that we can share”, is a better one than the ancient term called “physical”. 

I’d actaully like to run that by eric rieter … he has much more hands on experence with this kind of thing.
nathan 2016-06-22 09:41:25 [item 21036#53238]
As I said, there are real science experiments that do have particles being both dead and alive at the quantum particle level as well as in two places at the same time in this physical reality. Can that happen to the complexity of an entire cat? I suspect that someday it can. Someday our understanding of complex structures will be up to the task while today we can only observe it at the particle level.

Perhaps, that will be exactly how the Star Trek transporter works someday, for surely we will eventually make one, so much thought energy and momentum has pored into it already … perhaps it will work by making an entire complex physical structure exist in two places at once at the same time in the same physical verse.
Seth 2016-06-22 10:02:02 [item 21036#53245]
nathan, i don’t think you are appreciating the statical nature of these science experiments to which you refer.   stastics are entirely in some mind.  we never experience stastics .. rather we experience discrete particulars.  me thinks to gork this distinction i am drawing between statical models which are merely consistent with  experience and what actually happens that we can share, you would need to delve hands on into the physical experiments themselves, rather than just go with popular stories in the media.
Statistics are usually based on a matrix of all the possibilities of what can happen. Some have zero probability. Some have some fraction of the whole as probability. Eg. a coin toss has ½ heads & ½ tails. A dodecahedron has 1/12 for each face.  More complex events have more complex scenarios.  So far climate change is mostly modeling complexities toward simplicity. etc.

Mark de LA says
Seth 2016-06-22 09:33:46 [item 21036#53237]
well, it is absolutely true that the cat in Schrodinger’s thought problem is never in a dual-state of being both alive and dead at the same time.   That is not something that can ever happen and be shared.   Mark, imho, has that absolutely right.

Now stastically it can look as if that dual state exists –  and physical experiments bear out that model.  but that is only in the thought dimension – we can never share a happening of the cat being both dead and alive.  Which is why i think this term,  “what happens that we can share”, is a better one than the ancient term called “physical”. 

I’d actaully like to run that by eric rieter … he has much more hands on experence with this kind of thing.
nathan 2016-06-22 09:41:25 [item 21036#53238]
As I said, there are real science experiments that do have particles being both dead and alive at the quantum particle level as well as in two places at the same time in this physical reality. Can that happen to the complexity of an entire cat? I suspect that someday it can. Someday our understanding of complex structures will be up to the task while today we can only observe it at the particle level.

Perhaps, that will be exactly how the Star Trek transporter works someday, for surely we will eventually make one, so much thought energy and momentum has pored into it already … perhaps it will work by making an entire complex physical structure exist in two places at once at the same time in the same physical verse.
Mark de LA 2016-06-22 10:00:37 [item 21036#53244]
Or maybe science & the scientific method will replace fiction for the purpose of making scientific headlines & keeping job security going for researches.  What is actually observed is a lot different than the story told in most of the subatomic world. What we see in a LHC  is an impressive bunch of magnets & a lot of energy put into a mass of circulating gas targeting a small object . Also some sort of cloud chamber with curlicues of presumably energy & particles in it. I saw a cloud chamber detecting so called cosmic rays at the Exploritorium in SF during one visit.  It was a super cooled, high pressure ether of some kind in a sealed chamber & the waves of “cosmic rays” formed penetrating the chamber with what looked like the edges of waves at the beach.  The rest is the story the so-called scientists tell.  These days the stories are not the same for all the scientists. 
nathan 2016-06-22 10:04:47 [item 21036#53246]
These days the stories are not the same for all the scientists. I fully agree … and understand why. It is because these days people are becoming aware that each of us lives entirely in our own reality. Most children today understand that intuitively at a very solid gut level and when they someday become scientists science will be very different … not the same for everyone.

But even adult scientists today have an awareness of the ludicrouscy that we all live in the same world with the same rules … their own experiments just don’t consistently support that, and they often take different paths from each other instead of going with the status quo and consensus as was done in the past.
Mark de LA 2016-06-22 10:10:06 [item 21036#53247]
Sounds like the death of Science! sad Experiments which can’t be shared or duplicated aren’t science!thumbs down
nathan 2016-06-22 10:16:33 [item 21036#53249]
Sounds like the birth of utopia. Instead of everyone putting all their effort and energy into trying to create one same reality, people will instead realize that there is no one reality, we each create our own, and will put all that energy and effort into consciously selecting the aspects of others realities they want to include in their own. Life will get seriously interesting, exciting, and fun!
 
I don’t “believe” in Utopias. Sounds like you’re closer to it.  Just emote,excite, & focus the right vibes in a vortex somewhere & you get what you want, eh? own private worlds notwithstanding ?

Seth says
Seth 2016-06-22 09:33:46 [item 21036#53237]
well, it is absolutely true that the cat in Schrodinger’s thought problem is never in a dual-state of being both alive and dead at the same time.   That is not something that can ever happen and be shared.   Mark, imho, has that absolutely right.

Now stastically it can look as if that dual state exists –  and physical experiments bear out that model.  but that is only in the thought dimension – we can never share a happening of the cat being both dead and alive.  Which is why i think this term,  “what happens that we can share”, is a better one than the ancient term called “physical”. 

I’d actaully like to run that by eric rieter … he has much more hands on experence with this kind of thing.
nathan 2016-06-22 09:41:25 [item 21036#53238]
As I said, there are real science experiments that do have particles being both dead and alive at the quantum particle level as well as in two places at the same time in this physical reality. Can that happen to the complexity of an entire cat? I suspect that someday it can. Someday our understanding of complex structures will be up to the task while today we can only observe it at the particle level.

Perhaps, that will be exactly how the Star Trek transporter works someday, for surely we will eventually make one, so much thought energy and momentum has pored into it already … perhaps it will work by making an entire complex physical structure exist in two places at once at the same time in the same physical verse.
Seth 2016-06-22 09:55:57 [item 21036#53242]
nathan, i don’t think you are appreciating the statical nature of these science experiments to which you refer.   stastics are entirely in some mind.  we never experience stastics .. rather we experience discrete particulars.  me thinks to gork this distinction i am drawing between statical models which match exprience and what actually happens that we can share, you would need to delve hands on into the physical experiments themselves, rather than just go with popular stories in the media.
nathan 2016-06-22 10:00:13 [item 21036#53243]
I really don’t like going and looking these things up. My time is better spent. But I really did read more than one article about actual particles that were caused to exist and be measured in two different places at the same time. It was a breakthrough of sorts and not stistical, but actually observed.

Also realize that statistical is simply how we represent things in matimatical language that we are becoming aware of but do not yet know fully. As our knowledge grows, statistical representations tend to get replaced with solid understanding.
Seth 2016-06-22 10:17:54 [item 21036#53250]
yes i read the same articles … probably as a result of your provocation … and i even delved to some of the scientific peer reviewed papers which were being hyped on the internet as “proving” that which you seem  so keen to “prove” to yourself.

Your second paragraph hangs together very well here indeed thumbs up.

Yet i can not use its generality as justification in this particular case to believe that the statical models are anything but a map in a different dimension from what actually happens …especially that which we can share.  All such maps necessarily diverge from the territory of which they map,  me thinks it is better not to take them all so very seriously, for they must be revised just according to what actually happens. 
nathan 2016-06-22 10:28:31 [item 21036#53252]
I know the ones you are reffering to that I talked about more reciently and those have aspects of what we are talking about but are not so clear. The ones I am thinking of I remember reading around the time of 911, when I live in Ohio … well before FB and FBI. I do remember that it was very clear that the same particle was in both places at the same time. But in any case, even one of those later ones showed that you could have paired particles such that you could affect one and it affected the other … and that is a similar kind of thing.

And really, it just doesn’t matter. The science of tomorrow will be the cumulative thoughts of the people of today. There is infinite flexibility in what that actually will be. Haggling over the uncertainties in the thoughts of the thinkers of today won’t prove anything. Science itself doesn’t prove anything, it just map's what has become. It is not even about the now … it map's the past, what was thought up to the current moment. Anything is possible now.
Seth 2016-06-22 10:45:57 [item 21036#53253]
well the thing about stories, even like that one above,  is that “All stories obtain”.   which is why i go with what happens that we can share.   i don’t think i am attempting to force everybody into the same story … it sure doesn’t feel that way to me … especially because i can still trip on your story, which like i thunk in 19780,  must necessarily be one which optains. 


here i because i flashed 19780 in response, i will also flash it’s game, even now with my interpertation.

this is Contradiction Squared combined with Human Ego and 43 which is new to me now. 

pondering
nathan 2016-06-22 10:50:43 [item 21036#53254]
Yes. Our language almost even agrees on the what obtains part of it all.

The only substantial difference is that I look at shared experience as a kind of experience available. One that is delicious, but only a kind, not a basis. Where you seem to see shared experience as the most desirable goal, so much so, that you seem to see it as the thing reality is.
Seth 2016-06-22 11:07:03 [item 21036#53257]
thumbs up thumbs up YES, YES definitely, HELL YES.  I have actually chosen in my life that what happens that we can share is the most valuable thing to me and to humanity.  To you it seems merely an option … perhaps delicious … but not impelling enough to have chosen it for yourself. 

smug it is fun to know where we mutually agree that we are different and now know almost clearly that each other knows as well.  heart  ← nor does that difference even ever need to be erased idea newcool
nathan 2016-06-22 11:10:11 [item 21036#53258]
?
nathan 2016-06-22 11:14:02 [item 21036#53260]
I do choose shared experiences often. I just know that it is a choice and that I am creating that experience for my part and reflecting it in my creation for the other’s part. You don’t seem to want to know that, true or not, as the knowing of it may possibly distract you from your prime choice of diving in fully to shared reality.
true, i cannot break: “the part not actually being the whole”.  ← not that i even want to. 

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