Once had my own method for calculating the modular inverse gained a LOT more perspective on my situation. So yeah there's a recursive method for calculating the modular inverse which I discovered.
Meaning now there are three primary ways to figure out a modular inverse versus only two PRIMARY ways, before. Putting me in company with Euler and oddly enough, Euclid.
One of my best posts deriving: Meta and my modular inverse method
Where stepped through in more detail than had prior. Which was good! And gave an example calculating modular inverse of 35 mod 101, which is 26. So yeah, thankfully verified what I already had, and helped me understand better.
Where will edit to add realized the key expression is: F = r(r + 2my) mod N
And have F self-referencing itself with two added control variables n and d, where F0 is initial F value, and y0 is initial y. So yeah, while I derive to there from another key expression turns out the above is technically all I need.
So yeah I do yet another thing NOT intuitive in adding two variables for control purposes. Yet I did, and that's why I have the result. Often just wonder and wonder at simple answers, after. Will admit is a fun thing to find puzzling.
Also have talked SOME big picture things even more recently:
Thoughts on my modular inverse derivation and possible algorithm
Where realized how fast potentially it might be.
Have noted before that math and emotion do not mix well. And for me can end up on a roller coaster of emotions where thankfully have been through it before, with prior major discoveries.
Still this time...yeah, math and emotion do not mix well.
Is weird, to some extent will run away from results like this discovery. Then come back to it, eventually. Study a bit, run away again. And ponder. Run away again. Until finally is acceptance and am like, is cool.
Yeah, math and emotion do not mix well.
Can be overly dramatic I think. Where also should emphasize the wonder that is math as regardless of your feelings? You can check. And readily admit going over arguments over and over and over again. Where part of you is like, nothing is going to change here.
But also finding new ways to explain, or making sure to explain in EXTREME detail, to the point of using my own definition of mathematical proof...ok, I always do that one. As how else can I be sure?
Yeah at some point, will check to be sure began with a truth, then will check EACH step from there as to logic of it, until get to conclusion which I then know must be true, intellectually.
James Harris
Wednesday, November 13, 2019
Sunday, March 17, 2019
Why math discovery is fun
Have been pushing myself to focus more on folks who can check the math and may be confident is correct which does allow for a post that focuses more on fun things. While I really am glad for SO many posts that tried to explain in as much detail as possible and as simply as I could as those helped me immensely as well.
So yeah there may be folks who were aware from my original paper back to its appearance in 2004 that I'd shown that established mathematical ideas could lead to apparent contradiction. Where now I explain simply as: you can declare the ring to be algebraic integers, use statements correct in that ring and ring operations yet get to a conclusion NOT true in THAT ring. Which is wild.
But oh yeah, so my path of discovery has given LOTS to human mathematics.
So now we have an explanation for prime counts close to continuous functions. Like count of primes up to 10 is 4: 2, 3, 5 and 7. And 10/ln 10 equals approximately 4.34.
While is 25 primes to 100 and 100/ln 100 is about 21.7. While 168 primes to 1000 and 1000/ln 1000 is about 144.7 and that growing lag I can easily explain. And one of my more popular posts talks:
Differential equation and prime counting
Where that is at the end of the post. And yeah for me for over a decade as figured out my way to count primes back summer of 2002 have wondered how that could apparently sit. But also yeah, have garnered global interest as have discussed. So is more like mysteriously to me there hasn't been discussion I noticed as expected.
But also now the world has a primary way to calculate the modular inverse which to me is probably THE way to do it, where talked that quite a bit including a recent post where stepped through my derivation with more reflection.
Still my biggest result by far is finding out there were more numbers to catalog!!! Which goes back to that apparent contradiction thing. And feel like give a good overview with a recent post:
Why new numbers, really?
Where there has been LOTS of other discovery as well. Will admit that while proof is great there are times I like to look at some numbers behaving as expected, so here is a link to one of my favorite posts where I collect cases where they DO, which I did just to feel better:
Some number examples
And yeah, thanks to my need to be sure of my own research came up with a functional definition of mathematical proof. Also have used my advanced methods to figure out a simpler way to reduce two variable quadratic equations, where could also get far with a special case of a three variable quadratic, plus much more!!!
Yeah am getting tired of typing. And trying not to link to tons of things. But we're talking about over two decades of discovery. This blog covers THAT and yeah you can find all of the above, if you're interested.
So why do I think math discovery is fun?
There is a joy in the answers.
We get to know things that are answers for things some of the greatest mathematicians in human history puzzled over, as they laid the foundations upon which the answers could be found. Especially appreciate Gauss of course and Euler as they had so much to do with much, but also with modular.
Modular algebra is just such a gift to humanity. Can even do algebra for us, and better than we can on our own. Yes, discovery is fun.
Am so glad for the knowledge really.
Where also yeah, there cannot be a rush with things with such impact.
Humanity will take whatever time it needs, which includes me. As years go by, feel less shocked myself. And more and more I wonder about knowledge, and how we know--or think we know things, as a species or as individuals.
James Harris
So yeah there may be folks who were aware from my original paper back to its appearance in 2004 that I'd shown that established mathematical ideas could lead to apparent contradiction. Where now I explain simply as: you can declare the ring to be algebraic integers, use statements correct in that ring and ring operations yet get to a conclusion NOT true in THAT ring. Which is wild.
But oh yeah, so my path of discovery has given LOTS to human mathematics.
So now we have an explanation for prime counts close to continuous functions. Like count of primes up to 10 is 4: 2, 3, 5 and 7. And 10/ln 10 equals approximately 4.34.
While is 25 primes to 100 and 100/ln 100 is about 21.7. While 168 primes to 1000 and 1000/ln 1000 is about 144.7 and that growing lag I can easily explain. And one of my more popular posts talks:
Differential equation and prime counting
Where that is at the end of the post. And yeah for me for over a decade as figured out my way to count primes back summer of 2002 have wondered how that could apparently sit. But also yeah, have garnered global interest as have discussed. So is more like mysteriously to me there hasn't been discussion I noticed as expected.
But also now the world has a primary way to calculate the modular inverse which to me is probably THE way to do it, where talked that quite a bit including a recent post where stepped through my derivation with more reflection.
Still my biggest result by far is finding out there were more numbers to catalog!!! Which goes back to that apparent contradiction thing. And feel like give a good overview with a recent post:
Why new numbers, really?
Where there has been LOTS of other discovery as well. Will admit that while proof is great there are times I like to look at some numbers behaving as expected, so here is a link to one of my favorite posts where I collect cases where they DO, which I did just to feel better:
Some number examples
And yeah, thanks to my need to be sure of my own research came up with a functional definition of mathematical proof. Also have used my advanced methods to figure out a simpler way to reduce two variable quadratic equations, where could also get far with a special case of a three variable quadratic, plus much more!!!
Yeah am getting tired of typing. And trying not to link to tons of things. But we're talking about over two decades of discovery. This blog covers THAT and yeah you can find all of the above, if you're interested.
So why do I think math discovery is fun?
There is a joy in the answers.
We get to know things that are answers for things some of the greatest mathematicians in human history puzzled over, as they laid the foundations upon which the answers could be found. Especially appreciate Gauss of course and Euler as they had so much to do with much, but also with modular.
Modular algebra is just such a gift to humanity. Can even do algebra for us, and better than we can on our own. Yes, discovery is fun.
Am so glad for the knowledge really.
Where also yeah, there cannot be a rush with things with such impact.
Humanity will take whatever time it needs, which includes me. As years go by, feel less shocked myself. And more and more I wonder about knowledge, and how we know--or think we know things, as a species or as individuals.
James Harris
Sunday, March 03, 2019
Thoughts on my modular inverse derivation and possible algorithm
Thankfully went through a more stepped out derivation of my method for calculating the modular inverse with post: Meta and my modular inverse method
There I finally paid more attention to the requirement from my derivation:
nF0 = F+1 mod N
Which I noted puts pressure on the math. Which can happen if F0 shares prime factors with N, as then those have to divide off, for n to exist.
That situation actually occurs in my long example where I didn't realize why then, but simply thought it was an irritation without knowing the why of it happening. And discussed a bit in this post, where now also can talk how to avoid.
Of course F0 = r(r+2my0) mod N, so you actually have control there, as you choose m and y0, which means for an algorithm can actually pick such that F0 does NOT share prime factors by preventing r+2my0 = N mod p, for any prime factor p of N. Where of course r has to be coprime already which is a tidbit I've tended to leave out stating as that is obviously required.
Oh yeah, so the derivation is focusing on F = x2 - Dy2 mod N, as a key equation and finding I can focus on r, and get to F = r(r+2my) mod N, and then self-reference using added variables n and d to get to a solution for the modular inverse:
r-1 = (n-1)(r + 2my0) - 2md mod N
With the control equation:
2mdF0 = [F0(n-1) - 1](r+2my0) mod N
And again my baseline derivation is here.
Importantly my post on the meta aspect also covered how you get to recursion, and emphasized that with next iteration the modulus must be smaller, and can cut at least in half, guaranteed--with each recursion.
Which is really cool.
Now with it figured out, to me is kind of weird how easy it all is.
James Harris
There I finally paid more attention to the requirement from my derivation:
nF0 = F+1 mod N
Which I noted puts pressure on the math. Which can happen if F0 shares prime factors with N, as then those have to divide off, for n to exist.
That situation actually occurs in my long example where I didn't realize why then, but simply thought it was an irritation without knowing the why of it happening. And discussed a bit in this post, where now also can talk how to avoid.
Of course F0 = r(r+2my0) mod N, so you actually have control there, as you choose m and y0, which means for an algorithm can actually pick such that F0 does NOT share prime factors by preventing r+2my0 = N mod p, for any prime factor p of N. Where of course r has to be coprime already which is a tidbit I've tended to leave out stating as that is obviously required.
Oh yeah, so the derivation is focusing on F = x2 - Dy2 mod N, as a key equation and finding I can focus on r, and get to F = r(r+2my) mod N, and then self-reference using added variables n and d to get to a solution for the modular inverse:
r-1 = (n-1)(r + 2my0) - 2md mod N
With the control equation:
2mdF0 = [F0(n-1) - 1](r+2my0) mod N
And again my baseline derivation is here.
Importantly my post on the meta aspect also covered how you get to recursion, and emphasized that with next iteration the modulus must be smaller, and can cut at least in half, guaranteed--with each recursion.
Which is really cool.
Now with it figured out, to me is kind of weird how easy it all is.
James Harris
Monday, February 25, 2019
Considering the long haul is better
Knew I probably had a long journey ahead back I guess in 2003. Had been working at trying to prove Fermat's Last Theorem which was exasperating but fun--with TONS of errors. But had my approach to the packing of spheres from 1996, which hadn't made it past an editor, and in my mind seemed too simple like he had said.
Now I realize I'd used a spatial modular approach, and modular is the most powerful...how best to describe? Now of course I have lots more modular but still can be hard to grasp how changes entire field of mathematics.
Oh, so yeah, was chasing Fermat's Last Theorem with lots of frustration, but had also found my own way to count primes with a clever thing. I now know that thing is:
ΔS(x,pj) = [x/pj] - 1 - (j-1) - S(x/pj, pj-1)
That is the count of composites for a particular prime excluding composites that are products of lesser primes.
Which I copied from this post which I noticed was trending highly. Is so weird how something so short, and simply presented can change so much. That is the key to questions that Gauss, and Euler and so many others had about prime numbers. And we've had the answers now for over 16 years. But yeah I knew I had a long haul ahead, but not because of THAT result.
My heart sunk when I realized what I would call for a bit the coverage problem. When came across a way to present what looked like a perfect mathematical contradiction--within accepted rules. I could declare the ring as algebraic integers, use expressions valid in that ring, and valid ring operations, and nonetheless get to a conclusion not true in THAT ring.
Is kind of funny now. I just felt like the result was too big. Couldn't comprehend why was mine, and back then also hadn't yet resolved fully in my mind that the foundations of mathematics weren't maybe flawed. So I did try, and did my best to write a paper as close as I could to some standard format. And even shopped journals which I hadn't bothered to do with my spherical packing paper.
Even visited my alma mater Vanderbilt University to pitch the paper in person to a math professor who was an editor of some journal.
But it was later found a journal that would publish as have talked so much. And yeah was in conversation by email with editors at that journal for nine months before got word my paper would be published. My first correction to them was to stop them from giving me the title of Dr. Harris in correspondence. Emphasized was not a mathematician and I don't have a doctorate degree.
For me 2004 was not a year when felt well much of that year. Went from that elation and preparation for the world press when knew my paper would be published to the consternation and disappointment as drama played out instead. And then calm resignation as yeah, would be the long haul I feared.
Now appreciate how lucky I was. I DID get a publication. And then was left to myself to pursue mathematical truth. Eventually figuring out all the details which intrigued me so much. Back then I had inklings and intuition. Figured there had to be these other numbers, but how could I be sure?
Without help from the mathematical establishment, realized I needed a functional definition of mathematical proof. So I could know. And built so many others things. Until the activity was my new normal. And later would also accept being a global figure in my own right, where have puzzled there as well.
Now an authority in my own right on my math and I ponder what I owe my world or my species. I think about what I want for mathematics itself globally, and I wonder.
Is better to know. That I firmly believe. Have been so blessed I wonder why. But then again, so much I know now because have been--always with the questions.
And actually got some really cool answers thank God.
James Harris
Now I realize I'd used a spatial modular approach, and modular is the most powerful...how best to describe? Now of course I have lots more modular but still can be hard to grasp how changes entire field of mathematics.
Oh, so yeah, was chasing Fermat's Last Theorem with lots of frustration, but had also found my own way to count primes with a clever thing. I now know that thing is:
ΔS(x,pj) = [x/pj] - 1 - (j-1) - S(x/pj, pj-1)
That is the count of composites for a particular prime excluding composites that are products of lesser primes.
Which I copied from this post which I noticed was trending highly. Is so weird how something so short, and simply presented can change so much. That is the key to questions that Gauss, and Euler and so many others had about prime numbers. And we've had the answers now for over 16 years. But yeah I knew I had a long haul ahead, but not because of THAT result.
My heart sunk when I realized what I would call for a bit the coverage problem. When came across a way to present what looked like a perfect mathematical contradiction--within accepted rules. I could declare the ring as algebraic integers, use expressions valid in that ring, and valid ring operations, and nonetheless get to a conclusion not true in THAT ring.
Is kind of funny now. I just felt like the result was too big. Couldn't comprehend why was mine, and back then also hadn't yet resolved fully in my mind that the foundations of mathematics weren't maybe flawed. So I did try, and did my best to write a paper as close as I could to some standard format. And even shopped journals which I hadn't bothered to do with my spherical packing paper.
Even visited my alma mater Vanderbilt University to pitch the paper in person to a math professor who was an editor of some journal.
But it was later found a journal that would publish as have talked so much. And yeah was in conversation by email with editors at that journal for nine months before got word my paper would be published. My first correction to them was to stop them from giving me the title of Dr. Harris in correspondence. Emphasized was not a mathematician and I don't have a doctorate degree.
For me 2004 was not a year when felt well much of that year. Went from that elation and preparation for the world press when knew my paper would be published to the consternation and disappointment as drama played out instead. And then calm resignation as yeah, would be the long haul I feared.
Now appreciate how lucky I was. I DID get a publication. And then was left to myself to pursue mathematical truth. Eventually figuring out all the details which intrigued me so much. Back then I had inklings and intuition. Figured there had to be these other numbers, but how could I be sure?
Without help from the mathematical establishment, realized I needed a functional definition of mathematical proof. So I could know. And built so many others things. Until the activity was my new normal. And later would also accept being a global figure in my own right, where have puzzled there as well.
Now an authority in my own right on my math and I ponder what I owe my world or my species. I think about what I want for mathematics itself globally, and I wonder.
Is better to know. That I firmly believe. Have been so blessed I wonder why. But then again, so much I know now because have been--always with the questions.
And actually got some really cool answers thank God.
James Harris
Sunday, February 24, 2019
Why new numbers, really?
Feel is important to continue to emphasize what is actually I guess my most dramatic discovery, which is easy to prove with elementary methods. So yeah back in 2003, realized that there were more important numbers than had previously been catalogued.
Eventually, thankfully, came across a very simple way to show their existence, with quadratics.
In the complex plane, consider:
P(x) = (g1(x) + 1)(g2(x) + 2)
where P(x) is a primitive quadratic with integer coefficients, g1(0) = g2(0) = 0, but g1(x) is not equal to 0 for ALL x.
The simplest example is: P(x) = x2 + 3x + 2
And that is the end of things just casually making sense. As by the time I knew to use this expression around 2010, also knew I NEEDED to multiply it by an additional, added factor I call k.
So, introduce k, where k is a nonzero, and new functions f1(x), and f2(x), where:
g1(x) = f1(x)/k and g2(x) = f2(x) + k-2
Multiply both sides by k, and substitute for the g's, which gives me the now symmetrical form:
k*P(x) = (f1(x) + k)(f2(x) + k)
Getting to symmetry lets me solve for the f's, and do so as roots of a monic polynomial with integer coefficients, so I can make them be algebraic integers!
So yeah it is all a way to flip things cleverly. Is like building backwards. Then I get the crucial result which follows.
But for one of the f's: f1(x) = kg1(x)
Where now is built front and notice result NOW will apply in a ring.
And we have a problem if the f's are not rational. We do but the math doesn't. The algebra is straightforward. Is weird how easy it is really.
Of course indices are arbitrary so we simply know that one of the solutions has k as a factor. If you wonder why that is a problem, consider 3+sqrt(-26), as it can be shown that one of its two solutions has 7 as a factor!
Confused? Consider 1+sqrt(4) = 3 or -1. Tend to gloss over that quickly but it is bizarre that people might be taught any other way. It is actually simply mathematically incorrect to say that sqrt(4) is JUST 2, as -2 is a solution. You can't just wish away.
Oh yeah, so of course then 1 - sqrt(4) = -1 or 3. So has 3 as a factor for one of its two values.
But it can be proven that 3+sqrt(-26) also does NOT have 7 as a factor in the ring of algebraic integers.
Well yeah one of the g's cannot be an algebraic integer if k is some nonzero integer other than 1 or -1, when they are NOT rational. (Let them be integers like with simple example noted to notice how easy the math actually is.)
So yeah, my trick is forcing the f's to be algebraic integers, when I multiplied times some prior numbers, and that blows up LOTS of prior number theory when not rational. And then reveals new numbers! Yay!
The situation is like, if people knew of evens and did NOT know of odds, so you caught someone exasperated by the notion that 6 and 2 share 2 as a factor, because they don't know 3 exists.
Well there isn't a unit there which is a big difference. But situation is exactly the same with ring of algebraic integers except there are units.
But if you don't know there are those other numbers, yeah can get apparent contradictions which I exploited in my pivotal paper like to talk so much.
Like with this post: Publication does matter
Are these numbers a big deal? Of course. We're talking about number theory where MOST of the numbers, like an infinity of them, were previously unknown to exist! And I found them. Is cool.
(Oh my God is just so freaking amazing. Why me? How me? Oh my God, oh my God, oh my God.)
Am much better at handling that information now than in the past. See? I'm maturing as a human being.
James Harris
Eventually, thankfully, came across a very simple way to show their existence, with quadratics.
In the complex plane, consider:
P(x) = (g1(x) + 1)(g2(x) + 2)
where P(x) is a primitive quadratic with integer coefficients, g1(0) = g2(0) = 0, but g1(x) is not equal to 0 for ALL x.
The simplest example is: P(x) = x2 + 3x + 2
And that is the end of things just casually making sense. As by the time I knew to use this expression around 2010, also knew I NEEDED to multiply it by an additional, added factor I call k.
So, introduce k, where k is a nonzero, and new functions f1(x), and f2(x), where:
g1(x) = f1(x)/k and g2(x) = f2(x) + k-2
Multiply both sides by k, and substitute for the g's, which gives me the now symmetrical form:
k*P(x) = (f1(x) + k)(f2(x) + k)
Getting to symmetry lets me solve for the f's, and do so as roots of a monic polynomial with integer coefficients, so I can make them be algebraic integers!
So yeah it is all a way to flip things cleverly. Is like building backwards. Then I get the crucial result which follows.
But for one of the f's: f1(x) = kg1(x)
Where now is built front and notice result NOW will apply in a ring.
And we have a problem if the f's are not rational. We do but the math doesn't. The algebra is straightforward. Is weird how easy it is really.
Of course indices are arbitrary so we simply know that one of the solutions has k as a factor. If you wonder why that is a problem, consider 3+sqrt(-26), as it can be shown that one of its two solutions has 7 as a factor!
Confused? Consider 1+sqrt(4) = 3 or -1. Tend to gloss over that quickly but it is bizarre that people might be taught any other way. It is actually simply mathematically incorrect to say that sqrt(4) is JUST 2, as -2 is a solution. You can't just wish away.
Oh yeah, so of course then 1 - sqrt(4) = -1 or 3. So has 3 as a factor for one of its two values.
But it can be proven that 3+sqrt(-26) also does NOT have 7 as a factor in the ring of algebraic integers.
Well yeah one of the g's cannot be an algebraic integer if k is some nonzero integer other than 1 or -1, when they are NOT rational. (Let them be integers like with simple example noted to notice how easy the math actually is.)
So yeah, my trick is forcing the f's to be algebraic integers, when I multiplied times some prior numbers, and that blows up LOTS of prior number theory when not rational. And then reveals new numbers! Yay!
The situation is like, if people knew of evens and did NOT know of odds, so you caught someone exasperated by the notion that 6 and 2 share 2 as a factor, because they don't know 3 exists.
Well there isn't a unit there which is a big difference. But situation is exactly the same with ring of algebraic integers except there are units.
But if you don't know there are those other numbers, yeah can get apparent contradictions which I exploited in my pivotal paper like to talk so much.
Like with this post: Publication does matter
Are these numbers a big deal? Of course. We're talking about number theory where MOST of the numbers, like an infinity of them, were previously unknown to exist! And I found them. Is cool.
(Oh my God is just so freaking amazing. Why me? How me? Oh my God, oh my God, oh my God.)
Am much better at handling that information now than in the past. See? I'm maturing as a human being.
James Harris
Monday, February 11, 2019
Better defining what I call the social problem
Back last year noted in a post was turning away from what I call the social problem until 2028. By that phrase mean working to get the acceptance by the established mathematical community of my research.
And that's it.
For years tried various things from working to getting another paper published after my pivotal one got through, and then all that weird happened, to direct contacts with mathematicians like by email. And would do posts at times I felt were targeted to various levels of the mathematical community, to no avail.
Which raises the question then of, to whom are my posts directed now?
Which to me is where the fun is. But my resolve to not focus on the social problem till 2028 was primarily to get me out of a rut, and besides it's kind of embarrassing. Makes me look desperate. Now I just don't bother.
James Harris
And that's it.
For years tried various things from working to getting another paper published after my pivotal one got through, and then all that weird happened, to direct contacts with mathematicians like by email. And would do posts at times I felt were targeted to various levels of the mathematical community, to no avail.
Which raises the question then of, to whom are my posts directed now?
Which to me is where the fun is. But my resolve to not focus on the social problem till 2028 was primarily to get me out of a rut, and besides it's kind of embarrassing. Makes me look desperate. Now I just don't bother.
James Harris
Saturday, February 02, 2019
Abstract reductionism and simpler rules
Debate with myself often my responsibility in making certain things clear. This post is meant to help clarity while also showing the logical framework around my work, especially with regards to what I like to call abstract reductionism.
The most dramatic discovery I made was over 15 years ago, when realized could create a mathematical argument correct by the accepted rules of the mathematical community which nonetheless lead to an incorrect result. So I wrote a paper which was published demonstrating.
So yeah you have this HUGE result which brings into question mathematical consistency. Where the paper demonstrates inconsistency--so stands on its own regardless of anything else.
When the mathematical community did not behave as expected, I realized there was serious corruption as no real mathematicians would leave something like that undiscussed at very high levels and especially not, unresolved.
Which was an opportunity for me as have admitted as discovered problem was JUST with ring of algebraic integers, so a proper ring had to exist--for mathematical consistency. To be sure I also studied logic and concluded that mathematics is a subset of logic. That forced me to resolve the oxymoron of a "logical contradiction" and did that early on this blog.
From the logic axioms linked there established what I called: Three Valued Logic
That was HUGE for me and necessary for later when defined mathematical proof.
And I had mathematical consistency back. Had mathematics as a subset of logic. And had begun abstracting to simpler things, in a way I now call abstract reductionism. Where also focused modular often, and one of my most powerful tools had lead me to the problem with algebraic integers, when focused on x+y+vz = 0(mod x+y+vz). (And I don't use congruence symbol.)
So fifteen years ago, by this time knew that my paper could pass formal peer review and was published but things got weird after. And realized mathematicians as a community were corrupted. And began a distancing which has continued. As of course people with a title of mathematician who don't behave as mathematicians are useless to me.
But abstract reductionism is a logical tool. And importantly went on to use it to functionally define science, and also to functionally define entertainment. That latter was less than four years ago. And world is already in flux as global entertainment has changed rapidly with the US leading those changes with dramatic impact for example with movies with the US box office.
I think it is all SO COOL where have defined cool, of course. Not linking to too much here and trying to keep this post short. The gist of it for those interested in mathematics is to establish much is certain while the world is just taking its time to handle certain things.
To the human species, fifteen years is barely a blink.
While I'm enjoying the ride more and more.
So this post covered logic from axioms to actual Three Valued Logic. Established how mathematical inconsistency appeared with use of ring of algebraic integers, demonstrated with my pivotal paper. And talked abstract reductionism as a logical tool and process which handles mathematics--and beyond.
James Harris
The most dramatic discovery I made was over 15 years ago, when realized could create a mathematical argument correct by the accepted rules of the mathematical community which nonetheless lead to an incorrect result. So I wrote a paper which was published demonstrating.
So yeah you have this HUGE result which brings into question mathematical consistency. Where the paper demonstrates inconsistency--so stands on its own regardless of anything else.
When the mathematical community did not behave as expected, I realized there was serious corruption as no real mathematicians would leave something like that undiscussed at very high levels and especially not, unresolved.
Which was an opportunity for me as have admitted as discovered problem was JUST with ring of algebraic integers, so a proper ring had to exist--for mathematical consistency. To be sure I also studied logic and concluded that mathematics is a subset of logic. That forced me to resolve the oxymoron of a "logical contradiction" and did that early on this blog.
From the logic axioms linked there established what I called: Three Valued Logic
That was HUGE for me and necessary for later when defined mathematical proof.
And I had mathematical consistency back. Had mathematics as a subset of logic. And had begun abstracting to simpler things, in a way I now call abstract reductionism. Where also focused modular often, and one of my most powerful tools had lead me to the problem with algebraic integers, when focused on x+y+vz = 0(mod x+y+vz). (And I don't use congruence symbol.)
So fifteen years ago, by this time knew that my paper could pass formal peer review and was published but things got weird after. And realized mathematicians as a community were corrupted. And began a distancing which has continued. As of course people with a title of mathematician who don't behave as mathematicians are useless to me.
But abstract reductionism is a logical tool. And importantly went on to use it to functionally define science, and also to functionally define entertainment. That latter was less than four years ago. And world is already in flux as global entertainment has changed rapidly with the US leading those changes with dramatic impact for example with movies with the US box office.
I think it is all SO COOL where have defined cool, of course. Not linking to too much here and trying to keep this post short. The gist of it for those interested in mathematics is to establish much is certain while the world is just taking its time to handle certain things.
To the human species, fifteen years is barely a blink.
While I'm enjoying the ride more and more.
So this post covered logic from axioms to actual Three Valued Logic. Established how mathematical inconsistency appeared with use of ring of algebraic integers, demonstrated with my pivotal paper. And talked abstract reductionism as a logical tool and process which handles mathematics--and beyond.
James Harris
Monday, January 28, 2019
Better when the math convinces
YEARS ago actually went through a period when said I didn't want to be credible with my mathematics as wanted to be sure the math was correct! Which actually makes sense though back then didn't go over well in what too often tended to be arguments on math news groups.
But like I went through a period of around 6 MONTHS where was certain had proven Fermat's Last Theorem when I simply had not. And had failed with a basic math error which a bunch of folks saw, but refused to tell me. By then had had more than one such failure, where they HAD gleefully informed me.
Eventually realized the error and was appropriately...let's just say was emotional. But later came up with more things.
So should that matter? With math? It should be just about the math. But we're human beings so I guess it can be hard for people to rely on the math even when by the rules they should.
Like later got published, with a paper demonstrating that starting with expressions valid in ring of algebraic integers and using only ring operations could still get to a result invalid in the ring of algebraic integers. So using all accepted rules could get to a seeming contradiction with the math.
The paper is dated December 2003 and actually got published late by the now defunct journal in 2004. And now 15 years later is clear mathematicians didn't want to deal with it. The chief editor deleted my paper out of the journal, claiming was withdrawn. Journal managed one more edition before shutting down, and being scrubbed COMPLETELY from its hosting university's web site.
While EMIS thankfully maintained a copy, which let's me link to my paper from a solid source.
And mathematicians moved to a fake result reality which is the situation to this day. I find it curious.
Yeah am glad I realized my credibility was irrelevant. What matters only--is the math.
Of course person who could find such a thing might be person who could do MUCH more as I have as kept piling on major mathematical results, which I did. Which actually intrigues me more.
However, my biggest result is that demonstration actually. Showing that the entire mathematical field could lead to contradiction at its base. Which is easy to check with elementary methods.
So yeah, for that reason is definitely one of the greatest intellectual demonstrations in ALL of human history. Which have pondered for years. And I keep wondering about it.
Anyone who can do basic algebra and knows a little number theory can verify it. Use of the ring of algebraic integers quite simply leads to contradiction. But does that mean math contradicts itself?
No. Of course not.
Yeah I fixed the problem also by discovering what I like to call the ring of objects which is given in the FIRST post on this blog. Which to me is telling.
How do people go on with error? They've given up on their future. Eventually humanity will go with the truth. Is just a matter of time.
So why would modern mathematicians for so long continue to waste time and energy on bad math research?
Talk to social psychologists or folks in that arena of science, but I say, is like with religions that keep going with claims debunked by science. In essence world kept going with what had been shown to be equivalent of a mathematical religion debunked by the math itself.
I DO find that curious as well.
James Harris
But like I went through a period of around 6 MONTHS where was certain had proven Fermat's Last Theorem when I simply had not. And had failed with a basic math error which a bunch of folks saw, but refused to tell me. By then had had more than one such failure, where they HAD gleefully informed me.
Eventually realized the error and was appropriately...let's just say was emotional. But later came up with more things.
So should that matter? With math? It should be just about the math. But we're human beings so I guess it can be hard for people to rely on the math even when by the rules they should.
Like later got published, with a paper demonstrating that starting with expressions valid in ring of algebraic integers and using only ring operations could still get to a result invalid in the ring of algebraic integers. So using all accepted rules could get to a seeming contradiction with the math.
The paper is dated December 2003 and actually got published late by the now defunct journal in 2004. And now 15 years later is clear mathematicians didn't want to deal with it. The chief editor deleted my paper out of the journal, claiming was withdrawn. Journal managed one more edition before shutting down, and being scrubbed COMPLETELY from its hosting university's web site.
While EMIS thankfully maintained a copy, which let's me link to my paper from a solid source.
And mathematicians moved to a fake result reality which is the situation to this day. I find it curious.
Yeah am glad I realized my credibility was irrelevant. What matters only--is the math.
Of course person who could find such a thing might be person who could do MUCH more as I have as kept piling on major mathematical results, which I did. Which actually intrigues me more.
However, my biggest result is that demonstration actually. Showing that the entire mathematical field could lead to contradiction at its base. Which is easy to check with elementary methods.
So yeah, for that reason is definitely one of the greatest intellectual demonstrations in ALL of human history. Which have pondered for years. And I keep wondering about it.
Anyone who can do basic algebra and knows a little number theory can verify it. Use of the ring of algebraic integers quite simply leads to contradiction. But does that mean math contradicts itself?
No. Of course not.
Yeah I fixed the problem also by discovering what I like to call the ring of objects which is given in the FIRST post on this blog. Which to me is telling.
How do people go on with error? They've given up on their future. Eventually humanity will go with the truth. Is just a matter of time.
So why would modern mathematicians for so long continue to waste time and energy on bad math research?
Talk to social psychologists or folks in that arena of science, but I say, is like with religions that keep going with claims debunked by science. In essence world kept going with what had been shown to be equivalent of a mathematical religion debunked by the math itself.
I DO find that curious as well.
James Harris
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