| Topic: |
Science > Physics |
| User: |
"Mike Fleagle" |
| Date: |
21 Jan 2008 10:01:56 PM |
| Object: |
Re: JSH: What are you people? |
"JSH" <jstevh@gmail.com> wrote in message
news:2d71f112-59e8-46e9-8a0a-8229fa483ec5@i12g2000prf.googlegroups.com...
Can someone explain to me how nothing matters at all with you people?
One of the simplest algebraic proofs in mathematical history solves
the factoring problem, and you have independent validation from
someone other than me, but still some of you misinterpret the results
and insult me, while the rest of you are quiet, as always.
you like to be insulted, *crackpot*, it is your "fix"
I wondered for a while if some alien species had taken over the planet
and sought to end the future of the human race by keeping it from
getting its math right, but I've recently concluded that many of you
just have no clue what mathematics is.
So you think we are all scientologiests?
To you it's a style, and agreement, and lots of results from the
"smart people" as determined by some vague rules who tell you what to
think.
And God help anyone you don't like, as you'll reject anything they
discover, which is like diamond merchants looking the prospector up
and down and rejecting a HUGE major diamond because they don't like
the guy.
it was not a diamond, but half ***** troll poop, who is gonna like you now ?
The only conclusion available is that most of you do not do any real
mathematics.
you don't, that is for sure.
You're playing pretend. And I've come to that conclusion repeatedly
as I've confronted you through the years and considered your
stranglehold on the current mathematical field.
yes you remain blocked by sci.math group, they control the newsgroups for
Math content.
The mathematical field has been taken over by actors pretending to be
mathematicians.
Is that what you do? Projecting again ?
That is the only conclusion available at this point. I am sure there
are some people out there doing real mathematics, and I feel sorry for
them, because the field is clearly dominated by the bulk of you who
are not. And you are some vicious, nasty people who think that
telling a person they're insane is just a normal way to do business.
you are not insane at all, you only know high school algebra, and you are a
crackpot.
You are quite capable of being very vicious to get what you want. So
you dominate the poor people who actually do real mathematics who are
the sad minority among you.
there are no rich people posting in newsgroups, delusional DA.
Insults are what you do because that is who you are. There is nothing
more to you.
factor an RSA, provide a proof, or STFU, troll.
You have nothing without belief against mathematical proof.
your engrlish is getting tweaked, are you tweaked too ?
It's like if arsonists took over the fire station pretending to be
firefighters.
Take your JSH Monkey-Math and bury it, it stinks really really bad.
HUGE Monky Math Turdlets on the internet for YEARS and YEARS, what a DA.
James Harris
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| User: "Bob Cain" |
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| Title: Re: JSH: What are you people? |
25 Jan 2008 03:06:39 AM |
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Mike Fleagle wrote:
your engrlish is getting tweaked, are you tweaked too ?
Ah, of course he is! Now it all makes a kind of sense. Not technical sense,
but that mental state and paranoia is a logical and common consequence of meth
tweaking.
Bob
--
"Things should be described as simply as possible, but no simpler."
A. Einstein
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| User: "Fredrico Juarrez" |
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| Title: Re: JSH: What are you people? |
25 Jan 2008 04:27:27 AM |
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Bob Cain wrote:
Mike Fleagle wrote:
your engrlish is getting tweaked, are you tweaked too ?
Ah, of course he is! Now it all makes a kind of sense. Not technical
sense, but that mental state and paranoia is a logical and common
consequence of meth tweaking.
That's interesting. I thought it was either the medication, or the lack
thereof.
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| User: "JSH" |
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| Title: Re: JSH: What are you people? |
21 Jan 2008 10:09:12 PM |
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On Jan 21, 8:01 pm, "Mike Fleagle" <dd...@yahoo.com> wrote:
"JSH" <jst...@gmail.com> wrote in message
news:2d71f112-59e8-46e9-8a0a-8229fa483ec5@i12g2000prf.googlegroups.com...
Can someone explain to me how nothing matters at all with you people?
One of the simplest algebraic proofs in mathematical history solves
the factoring problem, and you have independent validation from
someone other than me, but still some of you misinterpret the results
and insult me, while the rest of you are quiet, as always.
you like to be insulted, *crackpot*, it is your "fix"
Nope. I have multiple major mathematical proof discoveries.
I even had publication until people like you showed how broken the
modern system of journal peer review is.
Now I have an easy algebraic solution to the factoring problem and the
ability to let this drag out for a little while, as I wait for others
to demonstrate the value of the research.
That's how it's done. Valuable research gets picked up by others.
It is so weird though. Here I am arguing with some mental midget,
when I've had a simple algebraic proof of the factoring problem out
there for days.
Anyone else suppose that the human race is devolving? Rapidly?
James Harris
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| User: "Duatcher" |
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| Title: Re: JSH: What are you people? |
21 Jan 2008 11:15:55 PM |
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"JSH" <jstevh@gmail.com> wrote in message
news:2ed38249-5ad0-4a65-a9b5-8b1197701755@v4g2000hsf.googlegroups.com...
On Jan 21, 8:01 pm, "Mike Fleagle" <dd...@yahoo.com> wrote:
"JSH" <jst...@gmail.com> wrote in message
news:2d71f112-59e8-46e9-8a0a-8229fa483ec5@i12g2000prf.googlegroups.com...
Can someone explain to me how nothing matters at all with you people?
One of the simplest algebraic proofs in mathematical history solves
the factoring problem, and you have independent validation from
someone other than me, but still some of you misinterpret the results
and insult me, while the rest of you are quiet, as always.
you like to be insulted, *crackpot*, it is your "fix"
Nope. I have multiple major mathematical proof discoveries.
Nope. you dont have any.
I even had publication until people like you showed how broken the
modern system of journal peer review is.
you never published anything, they rejected your "paper"
Now I have an easy algebraic solution to the factoring problem and the
ability to let this drag out for a little while, as I wait for others
to demonstrate the value of the research.
why cant you validate it ? Because it dosen't work.
That's how it's done. Valuable research gets picked up by others.
and Worthless research is Discarded, Rejected, Ignored, Blocked, Ridiculed.
quit trying to shove your Monkey Math into peoples faces, it is still Monkey
math poop.
It is so weird though. Here I am arguing with some mental midget,
when I've had a simple algebraic proof of the factoring problem out
there for days.
Bet you discover your own arrss every morning.
Anyone else suppose that the human race is devolving? Rapidly?
You say that to give yourself a feeling of superiority, however it keeps you
from realizing you are only protecting your ego, and you can't take the
heat, so stay out of the kitchen.
James Harris
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| User: "Mike Fleagle" |
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| Title: Re: JSH: What are you people? |
05 Feb 2008 07:10:44 PM |
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" A person who says: "I
am neither for nor against"; we ought to reply to him...
900. He who will give the meaning of Scripture, and does not take it from
Scripture, is an enemy of Scripture. (St. Augustine, Of Christian Doctrine.)
901. Humilibus dat gratiam;223 an ideo non dedit humilitatem?224
Sui eum non receperunt; quotquot autem non receperunt,225 an non erant
sui?226
902. "It must indeed be," says Feuillant, "that this is not so certain; for
controversy indicates uncertainty (Saint Athanasius, Saint Chrysostom,
morals, unbelievers)."
The Jesuits have not made the truth uncertain, but they have made their own
ungodliness certain.
Contradiction has always been permitted, in order to blind the wicked; for
all that offends truth or love is evil. This is the true principle.
903. All religions and sects in the world have had natural reason for a
guide. Christians alone have been constrained to take their rules from
without themselves, and to acquaint themselves with those which Jesus Christ
bequeathed to men of old to be handed down to true believers. This
constraint wearies these good Fathers. They desire, like other people, to
have liberty to follow their own imaginations. It is in vain that we cry to
them, as the prophets said to the Jews of old: "Enter into the Church;
acquaint yourselves with the precepts which the men of old left to her, and
follow those paths." They have answered like the Jews: "We will not walk in
them; but we will follow the thoughts of our hearts"; and they have said,
"We will be as the other nations."
904. They make a rule of exception.
Have the men of old given absolution before penance? Do this as exceptional.
But of the exception you make a rule without exception, so that you do not
even want the rule to be exceptional.
905. On confessions and absolutions wit
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| User: "Mike Fleagle" |
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| Title: Re: JSH: What are you people? |
05 Feb 2008 09:11:29 PM |
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China. The conflicting views thus presented are but a
reproduction of conflicting testimony in reference to negro
slavery in the West Indies, and more lately in the United States.
Very benevolent persons, some my own friends, looking at facts
from the respectable standpoint, thought that such slavery was
based on human nature, and conduced to the spread of Christianity.
But the contrary view prevailed. I am quite satisfied that the
right view on this question will ultimately prevail. As a man I
have very decided views on these subjects, but as a judge I feel
it is not for me further to debate them. I expressly retired from
doing so on the 27th of October, 1879, although I thought it
necessary in March last to comment on what I thought to be an
erroneous view of the _patria potestas_."
Later, in response to a suggestion on the part of the Governor, for a
more explicit statement as to wherein his views differ from those of
the Chinese and of Dr. Eitel, the Chief Justice says, among other
things:
"I do not admit the statements of Dr. Eitel. They do not apply
to Hong Kong, but they may, and probably do, apply to certain
respectable classes in China proper, where China family life
proper exists. What I assert is that family life does not, in the
proper Chinese sense, exist in Hong Kong, and that although, under
certain very restricted conditions, the buying and selling, and
adopting and taking as concubines, boys and girls in China proper,
is permitted as exceptions to the penalties inflicted by Chinese
law in China proper, these conditions do not exist in Hong Kong;
and that the conditions necessary to these exceptions in their
favor in the Chinese Criminal Code do not exist in Hong Kong,
and that
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| User: "JSH" |
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| Title: Re: JSH: What are you people? |
21 Jan 2008 11:24:38 PM |
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On Jan 21, 9:15 pm, "Duatcher" <nos...@nospam.com> wrote:
"JSH" <jst...@gmail.com> wrote in message
news:2ed38249-5ad0-4a65-a9b5-8b1197701755@v4g2000hsf.googlegroups.com...
On Jan 21, 8:01 pm, "Mike Fleagle" <dd...@yahoo.com> wrote:
"JSH" <jst...@gmail.com> wrote in message
news:2d71f112-59e8-46e9-8a0a-8229fa483ec5@i12g2000prf.googlegroups.com...
Can someone explain to me how nothing matters at all with you people?
One of the simplest algebraic proofs in mathematical history solves
the factoring problem, and you have independent validation from
someone other than me, but still some of you misinterpret the results
and insult me, while the rest of you are quiet, as always.
you like to be insulted, *crackpot*, it is your "fix"
Nope. I have multiple major mathematical proof discoveries.
Nope. you dont have any.
I even had publication until people like you showed how broken the
modern system of journal peer review is.
you never published anything, they rejected your "paper"
Now I have an easy algebraic solution to the factoring problem and the
ability to let this drag out for a little while, as I wait for others
to demonstrate the value of the research.
why cant you validate it ? Because it dosen't work.
I did validate it.
Mathematical proof.
And it's an easy proof so all this arguing shows that a lot of you
really don't get what a mathematical proof is.
I guess you think it's some delicate or wishy-washy thing.
You really can't comprehend that a person can prove something
mathematically and just sit back with certainty?
Or you think I have to demonstrate it with some big factorization to
know what mathematical proof already told me?
Ok, here's an important question: do you think if I really knew that
mathematical proof meant that I'd solved the factoring problem that
I'd quickly demonstrate it, wait on others to show it, or just write a
paper and send it to a journal?
James Harris
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| User: "Mike Fleagle" |
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| Title: Re: JSH: What are you people? |
21 Jan 2008 11:35:54 PM |
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"JSH" <jstevh@gmail.com> wrote in message
news:56f84bce-d165-4959-8de4-b4c072a67524@e32g2000prn.googlegroups.com...
On Jan 21, 9:15 pm, "Duatcher" <nos...@nospam.com> wrote:
"JSH" <jst...@gmail.com> wrote in message
news:2ed38249-5ad0-4a65-a9b5-8b1197701755@v4g2000hsf.googlegroups.com...
On Jan 21, 8:01 pm, "Mike Fleagle" <dd...@yahoo.com> wrote:
"JSH" <jst...@gmail.com> wrote in message
news:2d71f112-59e8-46e9-8a0a-8229fa483ec5@i12g2000prf.googlegroups.com...
Can someone explain to me how nothing matters at all with you
people?
One of the simplest algebraic proofs in mathematical history solves
the factoring problem, and you have independent validation from
someone other than me, but still some of you misinterpret the
results
and insult me, while the rest of you are quiet, as always.
you like to be insulted, *crackpot*, it is your "fix"
Nope. I have multiple major mathematical proof discoveries.
Nope. you dont have any.
I even had publication until people like you showed how broken the
modern system of journal peer review is.
you never published anything, they rejected your "paper"
Now I have an easy algebraic solution to the factoring problem and the
ability to let this drag out for a little while, as I wait for others
to demonstrate the value of the research.
why cant you validate it ? Because it dosen't work.
I did validate it.
you just said you are waiting for others to validate it, they found grevious
errors in it.
you fail to remember that ?
Mathematical proof.
And it's an easy proof so all this arguing shows that a lot of you
really don't get what a mathematical proof is.
you do spoof's , not proofs. .
I guess you think it's some delicate or wishy-washy thing.
you admitted that it was already, dont you remember ? How is your thought
process ? Ever take one of those on line tests to see if you are really
sane ?
You really can't comprehend that a person can prove something
mathematically and just sit back with certainty?
you have proved nothing, just 3 dilbert equations, a hack at a hack, that do
so little you cant even factor a 70 digit number with it in less than 1
second.
Or you think I have to demonstrate it with some big factorization to
know what mathematical proof already told me?
listen to your spoof, Monkey Math Boy, it is REJECTED.
Ok, here's an important question: do you think if I really knew that
mathematical proof meant that I'd solved the factoring problem that
I'd quickly demonstrate it, wait on others to show it, or just write a
paper and send it to a journal?
Goverment and Banks do not use RSA or factoring, that is 80's technology.
and you do not know what a proof is, you could google for it too.
James Harris
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| User: "Gordon Burditt" |
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| Title: Re: JSH: What are you people? |
05 Feb 2008 07:40:59 PM |
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733. That He would teach men the perfect way.
And there has never come, before Him nor after Him, any man who has taught
anything divine approaching to this.
734.... That Jesus Christ would be small in His beginning, and would then
increase. The little stone of Daniel.
If I had in no wise heard of the Messiah, nevertheless, after such wonderful
predictions of the course of the world which I see fulfilled, I see that He
is divine. And, if I knew that these same books foretold a Messiah, I should
be sure that He would come; and seeing that they place His time before the
destruction of the second temple, I should say that He had come.
735. Prophecies.--That the Jews would reject Jesus Christ, and would be
rejected of God, for this reason, that the chosen vine brought forth only
wild grapes. That the chosen people would be fruitless, ungrateful, and
unbelieving, populum non credentem et contradicentem.141 That God would
strike them with blindness, and in full noon they would grope like the
blind; and that a forerunner would go before Him.
736. Transfixerunt.[142] Zech. 12:10.
That a deliverer should come, who would crush the demon's head, and free His
people
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| User: "Gordon Burditt" |
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| Title: Re: JSH: What are you people? |
03 Feb 2008 01:04:34 PM |
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I did validate it.
Mathematical proof.
I can come up with a method of factoring, easily.
I'm trying to factor x.
For each integer i between 2 and x-1, inclusive
Try dividing x by i.
If I get a zero remainder, I've found two factors, i and x/i.
Next i
If I get here without finding any factors, it must be prime.
Now, is this fast enough to be a practical threat to RSA as it is
used today? No.
And it's an easy proof so all this arguing shows that a lot of you
really don't get what a mathematical proof is.
We do get what factoring is. Try factoring 6 if larger numbers are
too hard.
I guess you think it's some delicate or wishy-washy thing.
You really can't comprehend that a person can prove something
mathematically and just sit back with certainty?
How did you mathematically prove that you can factor *FAST ENOUGH TO
THREATEN RSA AS IT IS USED TODAY*?
Or you think I have to demonstrate it with some big factorization to
know what mathematical proof already told me?
Yes, because it didn't tell me that. I'm not a mathematician.
Ok, here's an important question: do you think if I really knew that
mathematical proof meant that I'd solved the factoring problem that
I'd quickly demonstrate it, wait on others to show it, or just write a
paper and send it to a journal?
Well, a sane person would demonstrate it. Especially if other
people didn't show any interest in a proof from someone they perceive
as a crackpot.
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| User: "=?ISO-8859-1?Q?Jos=E9_Carlos_Santos?=" |
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| Title: Re: JSH: What are you people? |
22 Jan 2008 06:27:49 AM |
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Em 22-01-2008 5:24, JSH escreveu:
Now I have an easy algebraic solution to the factoring problem and the
ability to let this drag out for a little while, as I wait for others
to demonstrate the value of the research.
why cant you validate it ? Because it dosen't work.
I did validate it.
Mathematical proof.
And it's an easy proof so all this arguing shows that a lot of you
really don't get what a mathematical proof is.
You also had a proof of the fact that, given a prime p, if p - 1 has 3
as a factor, then it must be true that if f is a factor of p - 2,
f < p^{1/3}, or f > sqrt(x), or f may equal the largest prime less than
sqrt(x). Remember that? You wrote here:
http://groups.google.com/group/alt.math.undergrad/msg/8ee7652d25321447
the sentence "I do have the proof." Why should we suppose that now you
*really* do have a proof but back then you didn't?
Best regards,
Jose Carlos Santos
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| User: "mike3" |
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| Title: Re: JSH: What are you people? |
21 Jan 2008 11:36:34 PM |
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On Jan 21, 10:24 pm, JSH <jst...@gmail.com> wrote:
<snip>
I did validate it.
Then what is the factorization of the challenge numbers?
Mathematical proof.
The "proof" though says _nothing_ about the efficiency of your
algorithm. Can you prove it factors in POLYNOMIAL time, or at
least fast enough to enable the breaking of all the unbroken
RSA challenge numbers?
And it's an easy proof so all this arguing shows that a lot of you
really don't get what a mathematical proof is.
But it does not prove what you need it to prove, even if it's
right.
I guess you think it's some delicate or wishy-washy thing.
You really can't comprehend that a person can prove something
mathematically and just sit back with certainty?
Or you think I have to demonstrate it with some big factorization to
know what mathematical proof already told me?
The proof _doesn't_ say anything about the efficiency! That's
what we're after and that's what a factorization would show.
Ok, here's an important question: do you think if I really knew that
mathematical proof meant that I'd solved the factoring problem that
I'd quickly demonstrate it, wait on others to show it, or just write a
paper and send it to a journal?
James Harris
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| User: "marcus_b" |
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| Title: Re: JSH: What are you people? |
22 Jan 2008 12:22:23 PM |
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On Jan 21, 11:24 pm, JSH <jst...@gmail.com> wrote:
On Jan 21, 9:15 pm, "Duatcher" <nos...@nospam.com> wrote:
"JSH" <jst...@gmail.com> wrote in message
news:2ed38249-5ad0-4a65-a9b5-8b1197701755@v4g2000hsf.googlegroups.com...
On Jan 21, 8:01 pm, "Mike Fleagle" <dd...@yahoo.com> wrote:
"JSH" <jst...@gmail.com> wrote in message
news:2d71f112-59e8-46e9-8a0a-8229fa483ec5@i12g2000prf.googlegroups.com=
....
Can someone explain to me how nothing matters at all with you peopl=
e?
One of the simplest algebraic proofs in mathematical history solves=
the factoring problem, and you have independent validation from
someone other than me, but still some of you misinterpret the resul=
ts
and insult me, while the rest of you are quiet, as always.
you like to be insulted, *crackpot*, it is your "fix"
Nope. I have multiple major mathematical proof discoveries.
Nope. you dont have any.
I even had publication until people like you showed how broken the
modern system of journal peer review is.
you never published anything, they rejected your "paper"
Now I have an easy algebraic solution to the factoring problem and the=
ability to let this drag out for a little while, as I wait for others
to demonstrate the value of the research.
why cant you validate it ? Because it dosen't work.
I did validate it.
Mathematical proof.
And it's an easy proof so all this arguing shows that a lot of you
really don't get what a mathematical proof is.
I guess you think it's some delicate or wishy-washy thing.
You really can't comprehend that a person can prove something
mathematically and just sit back with certainty?
Or you think I have to demonstrate it with some big factorization to
know what mathematical proof already told me?
Ok, here's an important question: do you think if I really knew that
mathematical proof meant that I'd solved the factoring problem that
I'd quickly demonstrate it, wait on others to show it, or just write a
paper and send it to a journal?
James Harris
Here is what you say on your blog:
[Quote]
Given nonzero integer factors f1 and f2 where f1f2 =3D nT,
75% of the time the following relations are true for each
unique factorization of nT:
f1 =3D =E1k mod p
and
f2 =3D =E1^(-1)(1 + =E1^2)k mod p
where
k^2 =3D (=E1^2+1)-1(nT) mod p
where =E1 is found non-zero such that k exists.
[End of quote]
There is some ambiguity about this. However, when
you say "75% of the time", it would appear that you are
saying that for T =3D f1*f2, and p an unspecified prime,
and n an unspecified (positive) integer, then if you
randomly choose positive integers =E1 which are such
that
(=E1^2 + 1)^(-1) * nT mod p
is a quadratic residue, the probability is at least 0.75 that
the formulas given above for f1 and f2 yield a nontrivial
factorization of T.
Enrico presented data which unquestioningly showed that
this is false. So one of two things must be true:
1. The interpretation above of what you claim to
have proved is wrong - in which case, you should try
to state it clearly and unambiguously; or
2. Your claimed proof is not a proof.
You can easily straighten this out. Why not
do it?
Marcus.
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| User: "Rotwang" |
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| Title: Re: JSH: What are you people? |
22 Jan 2008 12:47:48 PM |
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On 22 Jan, 18:22, marcus_b <marcus_bruck...@yahoo.com> wrote:
Here is what you say on your blog:
[Quote]
Given nonzero integer factors f1 and f2 where f1f2 =3D nT,
75% of the time the following relations are true for each
unique factorization of nT:
f1 =3D =E1k mod p
and
f2 =3D =E1^(-1)(1 + =E1^2)k mod p
where
k^2 =3D (=E1^2+1)-1(nT) mod p
where =E1 is found non-zero such that k exists.
[End of quote]
There is some ambiguity about this. However, when
you say "75% of the time", it would appear that you are
saying that for T =3D f1*f2, and p an unspecified prime,
and n an unspecified (positive) integer, then if you
randomly choose positive integers =E1 which are such
that
(=E1^2 + 1)^(-1) * nT mod p
is a quadratic residue, the probability is at least 0.75 that
the formulas given above for f1 and f2 yield a nontrivial
factorization of T.
Enrico presented data which unquestioningly showed that
this is false. So one of two things must be true:
1. The interpretation above of what you claim to
have proved is wrong - in which case, you should try
to state it clearly and unambiguously; or
2. Your claimed proof is not a proof.
Having looked over James' recent replies to Enrico, I think that your
interpretation (which was my first guess too - James, couldn't you at
least try to learn to write in a mathematically unambiguous manner?
You could start by learning the phrases "there exists ... such
that ..." and "for all ... such that ...") is wrong. In a reply in the
thread "JSH: Counting a's" he wrote
*** begin quote ***
Excellent experimental results which some posters have been confused
by, as experiment is in line with my original post.
So the theory is being validated by experiment.
Sample - larger P
P=3D839 f1 =3D 773 f2 =3D 997
first a found =3D 276
f1 mod p =3D 773
f2 mod p =3D 158
Enrico
Looks like Enrico has started on seeing what happens with larger
primes to see if there is something different.
To me it's kind of amazing seeing some posters go off, on the results,
completely mis-interpreting them.
The result is that the algebra counts the number of integer
factorizations and 75% of the time gives a's equal to that count in
two groups: the exact count and twice that count.
So with two primes you have two a's that will work or four a's, or
none.
*** end quote ***
So it looks like what he means his theorem to say is that, for a given
factorisation of T given by z^2 - y^2 =3D T and a given prime p, there
is a 75% probability that there exist alpha and k satisfying his other
two equations (James: can you confirm?). Of course if this is true
then I don't see how it is supposed to solve the factoring problem at
all; he correctly states that knowing z mod p when p > sqrt(T) will
enable us to factor T, but if there are only a small number of alphas
from 0 to p - 1 which work then, in the absence of further
information, we simply have to search that range until we find the
right value of alpha. And James has offered no reason to believe that
this will be faster than simply checking whether each number in the
same range is a factor of T, which will find a non-trivial
factorisation of T 100% of the time.
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| User: "marcus_b" |
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| Title: Re: JSH: What are you people? |
22 Jan 2008 03:35:00 PM |
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On Jan 22, 12:47 pm, Rotwang <sg...@hotmail.co.uk> wrote:
On 22 Jan, 18:22, marcus_b <marcus_bruck...@yahoo.com> wrote:
Here is what you say on your blog:
[Quote]
Given nonzero integer factors f1 and f2 where f1f2 =3D nT,
75% of the time the following relations are true for each
unique factorization of nT:
f1 =3D =E1k mod p
and
f2 =3D =E1^(-1)(1 + =E1^2)k mod p
where
k^2 =3D (=E1^2+1)-1(nT) mod p
where =E1 is found non-zero such that k exists.
[End of quote]
There is some ambiguity about this. However, when
you say "75% of the time", it would appear that you are
saying that for T =3D f1*f2, and p an unspecified prime,
and n an unspecified (positive) integer, then if you
randomly choose positive integers =E1 which are such
that
(=E1^2 + 1)^(-1) * nT mod p
is a quadratic residue, the probability is at least 0.75 that
the formulas given above for f1 and f2 yield a nontrivial
factorization of T.
Enrico presented data which unquestioningly showed that
this is false. So one of two things must be true:
1. The interpretation above of what you claim to
have proved is wrong - in which case, you should try
to state it clearly and unambiguously; or
2. Your claimed proof is not a proof.
Having looked over James' recent replies to Enrico, I think that your
interpretation (which was my first guess too - James, couldn't you at
least try to learn to write in a mathematically unambiguous manner?
You could start by learning the phrases "there exists ... such
that ..." and "for all ... such that ...") is wrong. In a reply in the
thread "JSH: Counting a's" he wrote
*** begin quote ***
Excellent experimental results which some posters have been confused
by, as experiment is in line with my original post.
So the theory is being validated by experiment.
Sample - larger P
P=3D839 f1 =3D 773 f2 =3D 997
first a found =3D 276
f1 mod p =3D 773
f2 mod p =3D 158
Enrico
Looks like Enrico has started on seeing what happens with larger
primes to see if there is something different.
To me it's kind of amazing seeing some posters go off, on the results,
completely mis-interpreting them.
The result is that the algebra counts the number of integer
factorizations and 75% of the time gives a's equal to that count in
two groups: the exact count and twice that count.
So with two primes you have two a's that will work or four a's, or
none.
*** end quote ***
So it looks like what he means his theorem to say is that, for a given
factorisation of T given by z^2 - y^2 =3D T and a given prime p, there
is a 75% probability that there exist alpha and k satisfying his other
two equations (James: can you confirm?). Of course if this is true
then I don't see how it is supposed to solve the factoring problem at
all; he correctly states that knowing z mod p when p > sqrt(T) will
enable us to factor T, but if there are only a small number of alphas
from 0 to p - 1 which work then, in the absence of further
information, we simply have to search that range until we find the
right value of alpha. And James has offered no reason to believe that
this will be faster than simply checking whether each number in the
same range is a factor of T, which will find a non-trivial
factorisation of T 100% of the time.
If that is all he is saying, and you may be right, he
is getting things exactly backward, and my interpretation
is the more charitable.
That is, if he is saying, if you have a factorization
then you can find alpha and k satisfying his equations
75% of the time. A gigantic so what? If you start
with a factorization the game is over before it's
begun. In "real life", what you start with is T,
n, and p. You need to find alpha and k, and then
you use those (via his formulas) to find y and z. But
that's still not enough. The resulting factorization
may well be trivial.
What I think he does not understand is that going
from y, z to alpha is not reversible. He appears to
think that the correspondence is one-to-one - that is,
a given alpha is associated with only the nontrivial
factorization pair y, z. That is of course not true.
I believe it is the case that most alpha will be found
to correspond to trivial factorizations. That it
seems to me was the point of what Enrico posted,
where he I think he was saying that 276 trials of alpha
were necessary to come up with the nontrivial
factorization.
If Harris is saying what you think he is saying,
there is essentially no point in even saying it.
I gave him the benefit of the doubt and assumed
he was saying more, but that Enrico's results
indicated he was wrong.
Marcus.
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| User: "amzoti" |
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| Title: Re: JSH: What are you people? |
21 Jan 2008 11:28:21 PM |
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On Jan 21, 9:24=A0pm, JSH <jst...@gmail.com> wrote:
On Jan 21, 9:15 pm, "Duatcher" <nos...@nospam.com> wrote:
"JSH" <jst...@gmail.com> wrote in message
news:2ed38249-5ad0-4a65-a9b5-8b1197701755@v4g2000hsf.googlegroups.com...
On Jan 21, 8:01 pm, "Mike Fleagle" <dd...@yahoo.com> wrote:
"JSH" <jst...@gmail.com> wrote in message
news:2d71f112-59e8-46e9-8a0a-8229fa483ec5@i12g2000prf.googlegroups.com=
....
Can someone explain to me how nothing matters at all with you peopl=
e?
One of the simplest algebraic proofs in mathematical history solves=
the factoring problem, and you have independent validation from
someone other than me, but still some of you misinterpret the resul=
ts
and insult me, while the rest of you are quiet, as always.
you like to be insulted, *crackpot*, it is your "fix"
Nope. =A0I have multiple major mathematical proof discoveries.
Nope. you dont have any.
I even had publication until people like you showed how broken the
modern system of journal peer review is.
you never published anything, they rejected your "paper"
Now I have an easy algebraic solution to the factoring problem and the=
ability to let this drag out for a little while, as I wait for others
to demonstrate the value of the research.
why cant you validate it ? =A0Because it dosen't work.
I did validate it.
Mathematical proof.
And it's an easy proof so all this arguing shows that a lot of you
really don't get what a mathematical proof is.
I guess you think it's some delicate or wishy-washy thing.
You really can't comprehend that a person can prove something
mathematically and just sit back with certainty?
Or you think I have to demonstrate it with some big factorization to
know what mathematical proof already told me?
Ok, here's an important question: do you think if I really knew that
mathematical proof meant that I'd solved the factoring problem that
I'd quickly demonstrate it, wait on others to show it, or just write a
paper and send it to a journal?
James Harris- Hide quoted text -
- Show quoted text -
Given that you have not done any of those - I'd surmise you are a
troll!
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| User: "Gordon Burditt" |
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| Title: Re: JSH: What are you people? |
05 Feb 2008 08:54:49 PM |
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the low-roofed house on Spofford alley. With Sergeant Ross leading
and our courageous young interpreter at our side, we stealthily
ascended the dark, narrow stairs to the second floor, where a
heavy door barred the way, but for such obstacles our good officer
was prepared. A few blows of his strong hammer made bolts and bars
yield. We passed through into a small dark passage. From there
could be heard on all sides sounds of excitement; light feet
running hither and thither to places of escape, only to be turned
back by the sight of our guards, who stood on watch. As we
cautiously felt our way further in we were met by the baffled and
angry keeper of the den--a woman, but not worthy the name. She
fiercely demanded our business--there was no need to tell it,
for she knew as well as we; but she wished to find some means of
hindering our search for her newest and most valuable slave. A
room was at length discovered in which we felt sure the treasure
was hidden. Again Sergeant Ross had to force open a door. As it
gave way, a small, dimly-lighted room opened before us. In the
center cowered a Chinese girl. It needed not a second look to
recognize in the frightened, anxious face before me Kum Ping of
the steamer. Our talisman had worked its charm. She had proved
to the depths the terrible truth of our warning, and now gladly
entrusted herself to our care, while her almost frantic owner
stormed, threatened and at last laid violent hands on the officer
who was helping us. As we led the trembling Kum Ping out, a
greatly excited crowd of chattering Chinese met us at the end of
the passage at Spofford alley, and the news passed from lip to
lip, "The Mission people have taken Woon Ha's new slave girl!" We
would be glad to end the story of our little friend's troubles and
safe escape with her arrival at last in the Mission Home that day.
But how few rescues eve
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| User: "gjedwards" |
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| Title: Re: JSH: What are you people? |
22 Jan 2008 05:45:45 PM |
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I even had publication until people like you showed how broken the
modern system of journal peer review is.
Wow, a rare insight from JSH. Yes the review system at SWJPAM was a
complete mess. Care to post the reviewers comments on your paper? No?
Thought not, you don't have any, because nobody read the thing.
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| User: "Mike Fleagle" |
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| Title: Re: JSH: What are you people? |
22 Jan 2008 08:58:15 PM |
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"gjedwards" <gjedwards@gmail.com> wrote in message
news:9fc7a892-843c-44fa-bce0-2ba2201ac1d1@c23g2000hsa.googlegroups.com...
I even had publication until people like you showed how broken the
modern system of journal peer review is.
Wow, a rare insight from JSH. Yes the review system at SWJPAM was a
complete mess. Care to post the reviewers comments on your paper? No?
Thought not, you don't have any, because nobody read the thing.
It was never in print on paper. He posted it one time, and it was 1/2 page
of garbage no conclusion.
BUT HE COULD POST IT HERE !!!
and let us read it.
Then we would really know.
the truth.
and the truth, hurts.
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| User: "Mike Fleagle" |
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| Title: Re: JSH: What are you people? |
05 Feb 2008 08:23:30 PM |
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but,
on the other hand, if this meaning had been so hidden as not to appear at
all, it could not have served as a proof of the Messiah. What then was done?
In a crowd of passages it has been hidden under the temporal meaning, and in
a few been clearly revealed; besides that, the time and the state of the
world have been so clearly foretold that it is clearer than the sun. And in
some places this spiritual meaning is so clearly expressed that it would
require a blindness, like that which the flesh imposes on the spirit when it
is subdued by it, not to recognise it.
See, then, what has been the prudence of God. This meaning is concealed
under another in an infinite number of passages, and in some, though rarely,
it is revealed; but yet so that the passages in which it is concealed are
equivocal and can suit both meanings; whereas the passages where it is
disclosed are unequivocal and can only suit the spiritual meaning.
So that this cannot lead us into error and could only be misunderstood by so
carnal a people.
For when blessings are promised in abundance, what was to prevent them from
understanding the true blessings, but their covetousness, which limited the
meaning to worldly goods? But those whose only good was in God referred them
to God alone. For there are two principles, which divide the wills of men,
covetousness and charity. Not that covetousness cannot exist along with
faith in God, nor charity with worldly riches; but covetousness uses God and
enjoys the world, and charity is the opposite.
Now the ultimate end gives names to
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| User: "Mike Fleagle" |
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| Title: Re: JSH: What are you people? |
05 Feb 2008 06:41:14 PM |
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sound and that thus, since
all these vanities are well founded, the people are not so foolish as is
said. And so we have destroyed the opinion which destroyed that of the
people.
But we must now destroy this last proposition and show that it remains
always true that the people are foolish, though their opinions are sound
because they do not perceive the truth where it is, and, as they place it
where it is not, their opinions are always very false and very unsound.
329. The reason of effects.--The weakness of man is the reason why so many
things are considered fine, as to be good at playing the lute. It is only an
evil because of our weakness.
330. The power of kings is founded on the reason and on the folly of the
people, and specially on their folly. The greatest and most important thing
in the world has weakness for its foundation, and this foundation is
wonderfully sure; for there is nothing more sure than this, that the people
will be weak. What is based on sound reason is very ill-founded as the
estimate of wisdom.
331. We can only think of Plato and Aristotle in grand academic robes. They
were honest men, like others, laughing with their friends, and, when they
diverted themselves with writing their Laws and the Politics, they did it as
an amusement. That part of their life was the least philosophic and the
least serious; the most philosophic was to live simply and quietly. If they
wrote on politics, it was as if laying down rules for a lunatic asylum; and
if they presented the appearance of speaking of a great matter, it was
because they knew that the madmen, to whom they spoke, thought they were
kings and emperors. They entered into their principles in order to make
their madness as little harmful as possible.
332. Tyranny consists in the desire of universal power beyond its scope.
There are different as
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| User: "Mike Fleagle" |
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| Title: Re: JSH: What are you people? |
05 Feb 2008 07:43:16 PM |
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the Lord will come with fire, and with his chariots like a
whirlwind, to render his anger with fury, and his rebuke with flames of
fire." And in many other places. So, Rev. 19:15, we read of "the wine
press of the fierceness and wrath of Almighty God." The words are
exceeding terrible. If it had only been said, "the wrath of God," the
words would have implied that which is infinitely dreadful: but it is
"the fierceness and wrath of God." The fury of God! the fierceness of
Jehovah! Oh, how dreadful that must be! Who can utter or conceive what
such expressions carry in them! But it is also "the fierceness and wrath
of almighty God." As though there would be a very great manifestation of
his almighty power in what the fierceness of his wrath should inflict,
as though omnipotence should be as it were enraged, and exerted, as men
are wont to exert their strength in the fierceness of their wrath. Oh!
then, what will be the consequence! What will become of the poor worms
that shall suffer it! Whose hands can be strong? And whose heart can
endure? To what a dreadful, inexpressible, inconceivable depth of misery
must the poor creature be sunk who shall be the subject of this!
Consider this, you that are here pres
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| User: "Mike Fleagle" |
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| Title: Re: JSH: What are you people? |
05 Feb 2008 06:46:06 PM |
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they have not humbled
themselves, but...
Quo quisque optimus est, pessimus, si hoc ipsum, quod optimus est, adscribat
sibi.93
550. I love poverty because He loved it. I love riches because they afford
me the means of helping the very poor. I keep faith with everybody; I do not
render evil to those who wrong me, but I wish them a lot like mine, in which
I receive neither evil nor good from men. I try to be just, true, sincere,
and faithful to all men; I have a tender heart for those to whom God has
more closely united me; and whether I am alone, or seen of men, I do all my
actions in the sight of God, who must judge of them, and to whom I have
consecrated them all.
These are my sentiments; and every day of my life I bless my Redeemer, who
has implanted them in me, and who, of a man full of weakness, of miseries,
of lust, of pride, and of ambition, has made a man free from all these evils
by the power of His grace, to which all the glory of it is due, as of myself
I have only misery and error.
551. Dignior plagis
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| User: "Randy Poe" |
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| Title: Re: JSH: What are you people? |
22 Jan 2008 08:59:30 AM |
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On Jan 21, 11:09 pm, JSH <jst...@gmail.com> wrote:
On Jan 21, 8:01 pm, "Mike Fleagle" <dd...@yahoo.com> wrote:
"JSH" <jst...@gmail.com> wrote in message
news:2d71f112-59e8-46e9-8a0a-8229fa483ec5@i12g2000prf.googlegroups.com...
Can someone explain to me how nothing matters at all with you people?
One of the simplest algebraic proofs in mathematical history solves
the factoring problem, and you have independent validation from
someone other than me, but still some of you misinterpret the results
and insult me, while the rest of you are quiet, as always.
you like to be insulted, *crackpot*, it is your "fix"
Nope. I have multiple major mathematical proof discoveries.
I even had publication until people like you showed how broken the
modern system of journal peer review is.
Now I have an easy algebraic solution to the factoring problem and the
ability to let this drag out for a little while, as I wait for others
to demonstrate the value of the research.
That's how it's done. Valuable research gets picked up by others.
It is so weird though. Here I am arguing with some mental midget,
when I've had a simple algebraic proof of the factoring problem out
there for days.
A "proof of the factoring problem"?
I think you mean a proof that keys based on products of
large primes are insecure. But such a proof would involving
proving that those keys could be factored in reasonable
time.
In other words, if you had such a proof, runtime (technically,
algorithmic complexity) would be the thing you were proving.
And you refuse to make any claim whatsoever about
algorithmic complexity. So you do NOT have a proof of
improved algorithmic complexity, and so you do NOT have
a proof of the factoring problem which by definition is
to find a factoring method of lower complexity than
current methods.
- Randy
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| User: "Duatcher" |
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| Title: Re: JSH: What are you people? |
05 Feb 2008 06:55:39 PM |
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--I believe only the histories, whose witnesses got
themselves killed.
Which is the more credible of the two, Moses or China?
It is not a question of seeing this summarily. I tell you there is in it
something to blind, and something to enlighten.
By this one word I destroy all your reasoning. "But China obscures," say
you; and I answer, "China obscures, but there is clearness to be found; seek
it."
Thus all that you say makes for one of the views and not at all against the
other.
So this serves, and does no harm.
We must, then, see this in detail; we must put the papers on the table.
594. Against the history of China.--The historians of Mexico, the five suns,
of which the last is only eight hundred years old.
The difference between a book accepted by a nation and one which makes a
nation.
595. Mahomet was without authority. His reasons, then, should have been very
strong, having only their own force. What does he say, then, that we must
believe him?
596. The Psalms are chanted throughout the whole world.
Who renders testimony to Mahomet? Himself. Jesus Christ desires His own
testimony to be as nothing.
The quality of witnesses necessitates their existence always and everywhere;
and he, miserable creature, is alone.
597. Against Mahomet.--The Koran is not more of Mahomet than the Gospel is
of Saint Matthew, for it is cited by many authors from age to age. Even its
very enemies, Celsus and Porphyry, never denied it.
The Koran says Saint Matthew was an honest man. Therefore Mahomet was a
false prophet for calling honest men wicked, or for not agreeing with what
they have said of Jesus Christ.
598. It is not by that which i
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| User: "Tim Peters" |
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| Title: Re: JSH: What are you people? |
22 Jan 2008 11:37:07 AM |
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[JSH <jstevh@gmail.com>]
...
It is so weird though. Here I am arguing with some mental midget,
when I've had a simple algebraic proof of the factoring problem out
there for days.
[Randy Poe <poespam-trap@yahoo.com>]
A "proof of the factoring problem"?
I think you mean a proof that keys based on products of
large primes are insecure. But such a proof would involving
proving that those keys could be factored in reasonable
time.
In other words, if you had such a proof, runtime (technically,
algorithmic complexity) would be the thing you were proving.
And you refuse to make any claim whatsoever about
algorithmic complexity. So you do NOT have a proof of
improved algorithmic complexity, and so you do NOT have
a proof of the factoring problem which by definition is
to find a factoring method of lower complexity than
current methods.
Part of James's problem is that his technical writing is so poor. His
gibberish "proof of the factoring problem" here is typical. Whether
that reflects equally confused thinking is left for the reader to decide
;-)
James doesn't have the technical vocabulary to say it, but if he did he
would claim that while his current approach has a probabilisitic
component, it will factor a composite T using a number of arithmetic
operations independent of T's size -- provided only that scumbag
mathematicians stop lying about his research and take the few hours
needed to transform his brilliant congruences into a concrete algorithm.
IOW, in his addled brain, he already addressed the complexity issue (as
he said several times, and because he thinks it's obvious at this point,
his current approach will factor public keys in less time than it takes
to generate them). That you're still questioning it means you're either
too stupid for him to bother with, or you know that he's right (hey,
it's simple math, dude -- you may as well pretend not to understand the
distributive property) so are lying about his research.
As always with these things, the only sure way for James to find out
that he hasn't "proved the factoring problem" is for him to simply try
it on all composites less than, say, 10000. If he did, he'd find case
after case that doesn't work out the way he insists he's "proved" it
must work. And also as always, James will invent endless bizarre
excuses for refusing to do such basic numeric sanity checks anyone else
would perform before making a public claim.
Then again, most other people are averse to being considered insane ;-)
.
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| User: "Duatcher" |
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| Title: Re: JSH: What are you people? |
22 Jan 2008 08:48:48 PM |
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"Tim Peters" <tim.one@comcast.net> wrote in message
news:Xns9A2D805C776C1tim111one@216.196.97.136...
[JSH <jstevh@gmail.com>]
Part of James's problem is that his technical writing is so poor. His
gibberish "proof of the factoring problem" here is typical. Whether
that reflects equally confused thinking is left for the reader to decide
;-)
James doesn't have the technical vocabulary to say it, but if he did he
would claim that while his current approach has a probabilisitic
component, it will factor a composite T using a number of arithmetic
operations independent of T's size -- provided only that scumbag
mathematicians stop lying about his research and take the few hours
needed to transform his brilliant congruences into a concrete algorithm.
IOW, in his addled brain, he already addressed the complexity issue (as
he said several times, and because he thinks it's obvious at this point,
his current approach will factor public keys in less time than it takes
to generate them). That you're still questioning it means you're either
too stupid for him to bother with, or you know that he's right (hey,
it's simple math, dude -- you may as well pretend not to understand the
distributive property) so are lying about his research.
As always with these things, the only sure way for James to find out
that he hasn't "proved the factoring problem" is for him to simply try
it on all composites less than, say, 10000. If he did, he'd find case
after case that doesn't work out the way he insists he's "proved" it
must work. And also as always, James will invent endless bizarre
excuses for refusing to do such basic numeric sanity checks anyone else
would perform before making a public claim.
Then again, most other people are averse to being considered insane ;-)
excellent summery of the JSH space.
.
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| User: "Randy Poe" |
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| Title: Re: JSH: What are you people? |
22 Jan 2008 12:26:23 PM |
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On Jan 22, 12:37 pm, Tim Peters <tim....@comcast.net> wrote:
[JSH <jst...@gmail.com>]
...
It is so weird though. Here I am arguing with some mental midget,
when I've had a simple algebraic proof of the factoring problem out
there for days.
[Randy Poe <poespam-t...@yahoo.com>]
A "proof of the factoring problem"?
I think you mean a proof that keys based on products of
large primes are insecure. But such a proof would involving
proving that those keys could be factored in reasonable
time.
In other words, if you had such a proof, runtime (technically,
algorithmic complexity) would be the thing you were proving.
And you refuse to make any claim whatsoever about
algorithmic complexity. So you do NOT have a proof of
improved algorithmic complexity, and so you do NOT have
a proof of the factoring problem which by definition is
to find a factoring method of lower complexity than
current methods.
Part of James's problem is that his technical writing is so poor. His
gibberish "proof of the factoring problem" here is typical. Whether
that reflects equally confused thinking is left for the reader to decide
;-)
James doesn't have the technical vocabulary to say it, but if he did he
would claim that while his current approach has a probabilisitic
component, it will factor a composite T using a number of arithmetic
operations independent of T's size -- provided only that scumbag
mathematicians stop lying about his research and take the few hours
needed to transform his brilliant congruences into a concrete algorithm.
IOW, in his addled brain, he already addressed the complexity issue (as
he said several times, and because he thinks it's obvious at this point,
his current approach will factor public keys in less time than it takes
to generate them). That you're still questioning it means you're either
too stupid for him to bother with, or you know that he's right (hey,
it's simple math, dude -- you may as well pretend not to understand the
distributive property) so are lying about his research.
As always with these things, the only sure way for James to find out
that he hasn't "proved the factoring problem" is for him to simply try
it on all composites less than, say, 10000. If he did, he'd find case
after case that doesn't work out the way he insists he's "proved" it
must work. And also as always, James will invent endless bizarre
excuses for refusing to do such basic numeric sanity checks anyone else
would perform before making a public claim.
Then again, most other people are averse to being considered insane ;-)
I made a reference to the movie "Sneakers" (which I
like a lot, actually. Any movie with a math-based plot
starts out with a plus in my book, and this one does
a very nice job with a very good cast).
I suspect that James has seen this movie and really
is thinking of himself as having made it a reality.
The plot involved a mathematician who had solved the
factoring problem, and was immediately murdered by
somebody's spy agency for his trouble. However, as
I recall, the plot also included an implementation
which as I said is the whole point. I believe there
was an implementation on a chip which everybody
was fighting over.
I don't recall the resolution. It seems to me that
our free-spirited hacker heroes escaped all the
killers and made the chip public domain, but my
memory might be defective. And it was
not implied that the end of civilization resulted,
just the end of evil government secrets (encryption
being portrayed as inherently a Bad Thing).
- Randy
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| User: "Duatcher" |
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| Title: Re: JSH: What are you people? |
05 Feb 2008 09:42:01 PM |
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from it, since there is always some advantage in
making men love us. Human life is thus only a perpetual illusion; men
deceive and flatter each other. No one speaks of us in our presence as he
does of us in our absence. Human society is founded on mutual deceit; few
friendships would endure if each knew what his friend said of him in his
absence, although he then spoke in sincerity and without passion.
Man is, then, only disguise, falsehood, and hypocrisy, both in himself and
in regard to others. He does not wish any one to tell him the truth; he
avoids telling it to others, and all these dispositions, so removed from
justice and reason, have a natural root in his heart.
101. I set it down as a fact that if all men knew what each said of the
other, there would not be four friends in the world. This is apparent from
the quarrels which arise from the indiscreet tales told from time to time. I
say, further, all men would be...
102. Some vices only lay hold of us by means of others, and these, like
branches, fall on removal of the trunk.
103. The example of Alexander's chastity has not made so many continent as
that of his drunkenness has made
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| User: "Duatcher" |
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| Title: Re: JSH: What are you people? |
05 Feb 2008 07:41:03 PM |
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know
their own wretchedness, but not the Redeemer.
And, as it is alike necessary to man to know these two points, so is it
alike merciful of God to have made us know them. The Christian religion does
this; it is in this that it consists.
Let us herein examine the order of the world and see if all things do not
tend to establish these two chief points of this religion: Jesus Christ is
end of all, and the centre to which all tends. Whoever knows Him knows the
reason of everything.
Those who fall into error err only through failure to see one of these two
things. We can, then, have an excellent knowledge of God without that of our
own wretchedness and of our own wretchedness without that of God. But we
cannot know Jesus Christ without knowing at the same time both God and our
own wretchedness.
Therefore I shall not undertake here to prove by natural reasons either the
existence of God, or the Trinity, or the immortality of the soul, or
anything of that nature; not only because I should not feel myself
sufficiently able to find in nature arguments to convince hardened atheists,
but also because such knowledge without Jesus Christ is useless and barren.
Though a man should be convinced that numerical proportions are immate
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