# Scientific evidence of God by an atheist (mankind is one likely type)

119 posts / 0 new

ProgrammingGodJordan,

You are quoting stuff without understanding it. A lemma is a theorem, and a theorem is a proven mathematical result. It's called a "lemma" because it is a lightweight spin-off (proof-wise) of a theorem and is used to reach other theorems. That's generally how the label is used in mathematical textbooks.

One shall promptly observe : 'Theorem versus Lemma'

Alternatively, it is perhaps pertinent that one reviews:

https://en.wikipedia.org/wiki/Lemma_(mathematics)

https://en.wikipedia.org/wiki/Theorem#Terminology

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('A')

('A.1')

Greensnake Stipulation:

It's called a "lemma" because it is a lightweight spin-off (proof-wise) of a theorem and is used to reach other theorems.

Such is but inconsequential, for I had but stipulated such amidst my prior response:

ProgrammingGodJordan Stipulation:

LEMMA DEFINITION: In mathematics, a "HELPING THEOREM" or lemma (plural lemmata or lemmas) is a PROVED PROPOSITION which is USED AS A STEPPING STONE TO A LARGER RESULT rather than AS A STATEMENT OF INTEREST BY ITSELF.

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('A.2')

Greensnake Stipulation:

You are quoting stuff without understanding it.
A lemma is a theorem, and a theorem is a proven mathematical result.
That's generally how the label is used in mathematical textbooks.

Such is quite the irony; quite the nonsensical sequence.

RATHER, a LEMMA is proven proposition, "USED AS A STEPPING STONE TO A LARGER RESULT **rather than** AS A STATEMENT OF INTEREST BY **ITSELF**" (Wikipedia).

A THEOREM is quintessentially the CONTRAST; **INDEPENDENT**. (Wikipedia: "...a theorem is usually RESERVED for the MOST IMPORTANT RESULTS OR THOSE WITH LONG OR DIFFICULT PROOFS.")

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RECALL AN INITIAL DESCRIPTION OF MINE:

ProgrammingGodJordan Stipulation:

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('B')

Nyarlathotep Stipulation:
[0]
See the thing is, a lemma is a PROOF. That is why what you posted isn't a lemma. But forget the semantics and the proof; **I just want to see a single example of it.**

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[1]
See the thing is, a lemma is a PROOF.

THEREAFTER,

(1) The request of Nyarlathotep, amid the requirement of mine, such that I postulate extended data (See Stipulation[0] via Nyarlathotep) is but invalid.

(2) The postulation of Nyarlathotep, amid the incongruousness of the definition as I had priorly initially referenced, is but, starkly invalid.

Special cases aside, posts with hard to read type fonts will not be addressed by myself.
Special cases aside, posts that just send me to web sites will not be addressed by myself.
Special cases aside, massive pastes of off-site material will not be addressed by myself, especially if I get the feeling that the poster never read it.

What I expect to see, in normal type font, is a careful, intact, thorough summary of the argument in the poster's own words. That tells me that he or she is doing more than just flipping sites at me. That tells me that he or she is reasonably familiar with the argument and can answer intelligent questions. I don't want to deal with morons who have no clue as to how the arguments in their off-site references work, who probably never even read the material, who would not be able to answer serious questions if I put in the time.

Dear advocate, If you want to suggest an interesting site that presents the details or added background, that's fine, but don't expect us to invest serious time in a reply unless you have demonstrated that you understand the argument enough (and have the courtesy) to conveniently summarize it in some detail.

I'll call this the DEBATE FORUM BILL OF RIGHTS for those of us who continually deal with newbies and their infallible "proofs."

Greensnake Stipulation: I'll call this the DEBATE FORUM BILL OF RIGHTS for those of us who continually deal with newbies and their infallible "PROOFS."

(1)
The response-BASEIS/entirety of THINE, ("PROOF") collapses amidst a RATHER profound ERROR of thine; for the initial stipulation OF MINE , consisted NOT OF ANY PROOF, but RATHER acute EVIDENCE, (on the horizon of FACTS) ~ (as observed amidst the title)

'Proof versus Evidence'

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(2)

Perhaps, it is exigent that one absorbs mathematically, at minimum, the premise par QUANTUM COMPUTING.

Herein, is a 4-line mathematical QUANTUM COMPUTING summary of mine: https://www.quora.com/How-does-quantum-computing-work/answer/Jordan-Benn...

Any other sufficiently complex sequence of maths is feasible. Larger complexities are likewise feasible.﻿

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(3)

Greensnake Stipulation/Self:
"My degree in MATHEMATICS is very helpful here."
"In fact, MOST OF MY TIME lately has been spent PHOTOGRAPHING WILD-FLOWERS and organizing the zillions of resulting photos!"

Perhaps, one shall RATHER encounter neural modelling.

As such, I but bequest thine (on the scope of the calculation-bound field of thine):

(a)
It is likely that life's meaning arises amidst thermodynamics.

(b)
SEPARATELY, life perhaps exists, such that matter shall manifest as some disparate time-space complex optimal fabric , on the order of algorithmic analysis.

PGJordan,

"1)
The response-BASEIS/entirety of THINE, ("PROOF") collapses amidst a RATHER profound ERROR of thine; for the initial stipulation OF MINE , consisted NOT OF ANY PROOF, but RATHER acute EVIDENCE, (on the horizon of FACTS) ~ (as observed amidst the title)" - PGJordan

The error is thine! I never said you had a proof. The Debate Forum Bill of Rights is a general document that applies to newbies offering "proof" or its equivalents.

Define "disparate time-space complex optimal fabric."

I don't know what you are smok'n, but you are clearly lost in your own aggrandizement. Putting scientific-sounding words together in a random babble does not impress us. Since sober communication with you is quite impossible given your tenancy to take off in flights of pretentious, nonsensical babble, a mental fog with nothing profound at its core to explore, I have no choice but to move on to more coherent pastures.

('A')

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Greensnake Stipulation [0]
The error is thine! I never said you had a proof. The Debate Forum Bill of Rights is a general document that applies to newbies offering "proof" or its equivalents.

Nonsense; for thou had stipulated of my ERRONEOUS expression of PROOF prior, as observed amidst said prior stipulations of THINE.
I MAINTAIN, that I had but not postulated any such process, of proof.

Greensnake Prior Stipulation [0]

Nyarlathotep,
I take it that you are getting in a bit of recreation here. Indulging, as it were, in the sheer joy of popping pretentious bubbles! That probably explains why you are even addressing this stuff. (In another post on this thread I've formulated a Debate Forum Bill of Rights for those of us who are constantly bombarded by canned "proofs" by newbies.)

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Greensnake Prior Stipulation [0]
I'll call this the DEBATE FORUM BILL OF RIGHTS for those of us who continually deal with newbies and their infallible "proofs."

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('B')

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Greensnake Stipulation [1]:
Define "disparate time-space complex optimal fabric."

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...for I stipulate not of any non-standard baseis.

PGJordan,

I know what the words mean, except for "time-space" which I assume is a clumsy reference to "spacetime." Anybody can look the words up! You gave me a non-definition consisting of trivial components. Tell us in plain English what you are referring to with these 5 words. If it is an object of scientific interest, then cite a reference or two in refereed scientific journals.

I thereafter maintain my priorly promptly expressed response.

Still waiting for you to use the results of your lemma to calculate the value of that simple integral, based on the example you gave! Shouldn't take more than a minute or two...www.atheistrepublic.com/comment/45798

ProgrammingGodJordan Stipulation:

I had long demonstrated the accuracy of said lemma, amidst the University of the West Indies (abound a diplo-presence of professors of Calculus), 4 years prior.

Albeit, you need:

Construct the form "∫ [ xⁿ · dx / d theta · dx ]", on the horizon of the aforesaid value sequence...

http://www.atheistrepublic.com/comment/45799

"I just want to see a single example of it! In the time you took to write that post, you should have been able to do it ... I'm still waiting."

PGJordan,

Why the hesitation? Nyarlathotep asked you to apply yourself and evaluate the integral. It takes more than gaseous words to do real math! Show us how to use your lemma to get the results!

So, you "demonstrated the accuracy of said lemma, amidst the University of the West Indies (abound a diplo-presence of professors of calculus)..." Wow! That must have been one, important demo to draw such a distinguished crowd! I assume that your results were written up in one or more mathematical journals. Would you kindly give a proper citation or two so that we can follow it for ourselves?

Still waiting for you to use the results of....

Therein, it is perhaps pertinent that one observes the facing sequence: https://www.youtube.com/watch?v=t4kyRyKyOpo

Subsequently, one shall promptly encounter: Source [2]

Still waiting....................

PGJordan,

Do the integration, please! You can do it, can't you?

MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\$','\$']]}, displayAlign: "left"});

ProgrammingGodJordan - I maintain my priorly promptly expressed response.

Fine, I'll do it for you.
Let's consider a simple case of your first example:
$$\int_0^1 x^n \sqrt{a^n - x^n}dx\bracevert a=1, n=1 \rightarrow \int_0^1 x \sqrt{1 - x}dx \tag{1}$$
$$\int_0^1 x \sqrt{1 - x}dx = \int_{x=0}^{x=1} x \frac{dx}{d\theta} dx\bracevert x = \sqrt{ sin(\theta)}\tag{2}$$
The left hand integral can be approximated already, and lets find dx/dθ and dx:
$$0.26667 \approx \int_{x=0}^{x=1} x \frac{dx}{d\theta} dx\bracevert x = \sqrt{ sin(\theta)}, \frac{dx}{d\theta}=\frac{cos(\theta)}{2\sqrt{sin(\theta)}}, dx = \frac{cos(\theta)}{2\sqrt{ sin(\theta)}}d\theta\tag{3}$$
Let's make those substitutions:
$$0.26667 \approx \int_{x=0}^{x=1} \sqrt{ sin(\theta)}*\frac{cos(\theta)}{2\sqrt{ sin(\theta)}}*\frac{cos(\theta)}{2\sqrt{ sin(\theta)}}d\theta\tag{4}$$
Cleaned up a bit:
$$0.26667 \approx \int_{0}^{\frac{\pi}{2}} \frac{cos^2(\theta)}{4\sqrt{ sin(\theta)}}d\theta\tag{5}$$
We can now approximate the right hand side:
$$0.26667\approx0.43701\tag{6}$$
No amount of your word salad is going be able to make 0.26667 equal 0.43701; your "lemma" is false.

I maintain my priorly promptly expressed response.

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NOTE:

Nyarlathotep Stipulation:

There is but an error sequence amidst YOUR computation:

http://www.wolframalpha.com/input/?i=integrate+sqrt(1-x)

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RESOURCE:

PGJordan,

Nyarlathotep's calculation looks good to me! We may conclude that, for the values he assigned to the constants, your lemma has failed! Hence, your lemma has failed. Look to thyself for thine error.

There exists, quite a many integral-bound paradigm strings, unbeknownst betwixt thine/Nylartothep, as is observable amid the definite/indefinite-aligned nescience instance, of thine, prior.

I thereafter, maintain, that Nylartothep has but misapplied the aforesaid lemma of mine; for there persists an error sequence amidst that of the computation/interpretation of thine, vis a vis TRcS.

INTIMATION: My lemma collapses said process, such that a MONO-line-construction occurs.

Nyarlathotep,

Nice exercise of basic calculus! Too bad our "learned" friend couldn't handle it. Of course, if he did he would have quickly retracted his lemma. His lemma turned out to be a lemon!

By the way, how do you get all those nice symbols posted?

Well as you surely know; there is no way to make a universal formula like that to reduce something as complicated as sqrt(1-x^n) because how you deal with it is heavily influenced by the value of n. Or in other words; what works for n=1 won't work for n=10; so a universal formula is a pipe dream.

And you are right; it is very basic stuff. I'm sure to those who haven't had the luxury of learning this material it might look hard but it really isn't. Trust me, if it was hard; I wouldn't be able to do it.

There exists, quite a many integral-bound paradigm strings, unbeknownst betwixt thine, as is observable amid the definite/indefinite-aligned nescience instance, of thine, prior.

I thereafter, maintain, that thou has but misapplied the aforesaid lemma of mine; for there persists an error sequence amidst that of the computation/interpretation of thine, vis a vis TRcS.

INTIMATION: My lemma collapses said process, such that a MONO-line-construction occurs.

INTIMATION: My lemma collapses said process, such that a MONO-line-construction occurs.

There exists, quite a many integral-bound paradigm strings, unbeknownst betwixt thine/Nylartothep, as is observable amid the definite/indefinite-aligned nescience instance, of Nylartothep, prior.

I thereafter, maintain, that Nylartothep has but misapplied the aforesaid lemma of mine; for there persists an error sequence amidst that of the computation/interpretation of thine, vis a vis TRcS.

INTIMATION: My lemma collapses said process, such that a MONO-line-construction occurs.

ProgrammingGodJordan - There is but an error sequence amidst YOUR computation:

While it is always possible I made a mistake somewhere; your criticism is troubling for two reasons:

• Your link to Wolfram is for an indefinite integral, I only did definite integrals; so it is impossible for me to have made this mistake.
• Your link to Wolfram is for the function sqrt(1-x) (notice the bold above in the url); the function I integrated was x*sqrt(1-x). So again, it is impossible for me to have made the mistake you described.

You would think these points would be painfully obvious to someone who is authoring ground breaking calculus "lemmas".

('A')

Your link to Wolfram is for an indefinite integral, I only did definite integrals; so it is impossible for me to have made this mistake.

{ DEFINITE : ∫(1,0) x sqrt(1-x) [a=1,n=1] } ↔ { 'DEFINITE' : ∫(∞,0) x sqrt(1-x) [a=1,n=1] } ↔ { INDEFINITE : ∫ x sqrt(1-x) [a=1,n=1] }

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{ BOUNDED : x = [0 to 1] }

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{ 'UNBOUNDED' } ↔ { BOUNDED : x = [0 to ∞] }

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**************************************************************************************
SO, { BOUNDED : x = [0 to 1] } ↔ { BOUNDED : x = [0 to ∞] } ↔ { UNBOUNDED/INDEFINITE. }
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('B')

Your link to Wolfram is for the function sqrt(1-x) (notice the bold above in the url); the function I integrated was x*sqrt(1-x). So again, it is impossible for me to have made the mistake you described.

Indeed, a WOLFRAM-bound typographical error of mine:

PRIOR: ∫ sqrt(1-x)
ERRATUM: ∫ x*sqrt(1-x)

ALBEIT, I maintain, that you have but misapplied the aforesaid lemma of mine, such that 0.43701 is erroneously derived.

INTIMATION: My lemma collapses said process, such that a MONO-line-construction occurs.

ProgrammingGodJordan - ALBEIT, I maintain, that you have but misapplied the aforesaid lemma of mine

I didn't apply your lemma; I used the result you posted in your example! That is where the problem is!

I have but not expressed any such RESULT.

I thereafter, maintain, that you have but misapplied the aforesaid lemma of mine; there persists an error sequence amidst YOUR computation/interpretation, vis a vis TRcS.

MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\$','\$']]}, displayAlign: "left"});

ProgrammingGodJordan - I have but not expressed any such RESULT.

You did! Let's have a look!

ProgrammingGodJordan PROBLEM: ∫ [ xⁿ · √ ( aⁿ - xⁿ ) ]
DERIVE X: x = √ aⁿ · sin(θ))
SOLVING (TRcS): Rewrite as ∫ [ xⁿ · dx/d theta · dx ]

V.S.

Nyarlathotep:$$\int_0^1 x^n \sqrt{a^n - x^n}dx\bracevert a=1, n=1 \rightarrow \int_0^1 x \sqrt{1 - x}dx \tag{1}$$
$$\int_0^1 x \sqrt{1 - x}dx = \int_{x=0}^{x=1} x \frac{dx}{d\theta} dx\bracevert x = \sqrt{ sin(\theta)}\tag{2}$$

It is your result. And it is one of the many reasons I knew your "lemma" was garbage with just a glance.

There exists not any prior 'result' stipulation of mine; for there persisted solely frame|template distributions.

There exists, quite a many integral-bound paradigm strings, unbeknownst betwixt thine, as is observable amid the definite/indefinite-aligned nescience instance, of thine, prior.

I thereafter, maintain, that thou has but misapplied the aforesaid lemma of mine; for there persists an error sequence amidst that of the computation/interpretation of thine, vis a vis TRcS.

INTIMATION: My lemma collapses said process, such that a MONO-line-construction occurs.

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