How about some mathematic?

[Hagnismos]

Can I persuade the mods to create a Mathematics and Statistics forum in society with the following rules.

1) the rules of logic and the literature pertaining to math and logic shall be the final judge of what is right in answering any math problem

2) apparent conflicts between math and Scripture defer to Scripture (there are'nt any that cannot be explained using Godel, on the math side, and of the Bible on the God side, but just for good measure)

3) no homework or test questions will be answered the forum is for talking about math and enjoying it with fellow Christians

Add to or modify as you see fit.

Thanks,

Hagnismos

 

[Hagnismos]

Here is a classic. We will have to get LaTex here eventually if this thing is going to work.

Parametrizing Pythagorean Triples.

Definition 1.1 - A Pythagorean Triple is a triple of positive integers a,b,c such that a^2+b^2=c^2. A well known example is 3^2+4^2=5^2.

Theorem 1.1 All pythagorean triples produce right triangles when the values are used as lengths of the sides of a triangle.

Proof
Knowing that the sum of the angles of a triangle is 180 degrees or Pi radians we can find the size of the other two angles using basic trigonometry. The law of cosines says that for any triangle

c^2 = a^2 + b^2 - 2ab cos C

where C is the angle between sides a and b.

Given a pythagorean triple we have c^2 = a^2 + b^2 therefore

2ab cos C = 0

we know a and b are greater than zero so cos C = 0 and C must be equal to nPI/2 radians for some n. But the sum of the angles is PI radians (180 degrees), this means that n must equal 1 and C = PI/2 radians (90 degrees).

This was easy to get at since we already nkow the Law of Cosines, it would be harder if we had to prove the Law of Cosines from scratch.

So now we know pythagorean triples correspond to right triangles with integer side lengths.

To parametrize all pythagorean triples actually requires two dimensions and fleshes out like this. we seek parameters u and v integers such that

c = C(u,v)
a = A(u,v)
b = B(u,v)

and C^2 = A^2 + B^2

Let a = 2uv, b = u^2 - v^2 and c = u^2+v^2

Clearly

4u^2v^2 + v^4 + u^4 - 2u^2v^2 = u^4 + 2u^2v^2+ v^4

What parameters correspond to the pythagorean triple (3,4,5)?

we require a = 2uv the even element so uv must equal 2, let v = 1 and u = 2 to get

2uv =2*2*1 = 4, u^2 - v^2 = 4 - 1 = 3, and u^2 + v^2 = 2^2 + 1 = 5

[The parametrization comes from 'Elementary Number Theory in Nine Chapters' by Tattersall]

The whole thing is quite amazing. The pythagorean triples are points on a parabaloid, like a cup with a round bottom c = sqrt(a^2+b^2) for any value c is a circle. Think of the c direction as going up and a and b in the plane. And yet we can assign to everyone of those pythagorean triples a pair of integers? one reason it is possible at all is that the paraboloid c = sqrt(a^2+b^2) is really a deformation of the plane, it is in fact a plane that has been stretched in a special way.

Compare distance in the two spaces that are mapped. In the (u,v) plane the distance between two pythagorean triples is d((u[1],v[1]),(u[2],v[2])) = SQRT((u1]-u[2])^2+(v[1]-v[2])^2)

In the c,a,b cube the distance is

d((c[1],b[1],a[1]))= SQRT((c[1]-c[2])^2+(a[1]-a[2])^2+(b[1]-b[2])^2))

Using the 3,4,5 and 5,12,13 example we have d[u,v]^2 = (2-1)^2+(3-1)^2 = 2, the distance is root two which is the point are diagonal to each other.

d[c,a,b] ^2 = (3-5)^2 + (12-4)^2 + (13-5)^2 = 4 + 64 + 81 = 149. greater than 12 units apart by a straight line distance.

If you take the triple (a,b,c) = (u,v) (3,4,5) = (u,v) as a reference point you can plot the distance between this point and every other pythagorean triple as an ordered pair. the above example gave (12,2) as the ordered pair showing the distance between the points in a,b,c space and u,v space. notice that the distances 3,4,5 is away from itself in both spaces is zero so the point (0,0) in your graph would correspond to that.

Try doing this for u and v up to say twenty and look at the pattern that emerges.

God blesses those who seek knowledge, understanding and wisdom. Yours in Christ, Hagnismos

 

[decoytdtc]

So, for a statistical physics/mechanics problem the other day, we had this utterly ridiculous problem where our answer had a weird gaussian integral we had to look up in 1000 page book of integrals...

The answer was basically a Bessel function of the second kind


Anyway, it was really annoying to have to go through that book to get the right integral and that's when we thought it'd be a great idea to be able to use LaTex to search a database of integrals

I don't think even wiki or wolframs do that

 

[ArnautDaniel]

2) apparent conflicts between math and Scripture defer to Scripture (there are'nt any that cannot be explained using Godel, on the math side, and of the Bible on the God side, but just for good measure)

I've got to wonder how Goedel's theorems could ever apply to any such question.

 

[Hagnismos]

I've got to wonder how Goedel's theorems could ever apply to any such question.

So if you are wondering, why not fill out your thoughts a bit so we can have a discussion. Please, let us consider the implications of Godel on human attempts to understand God.

 

[Hagnismos]

So, for a statistical physics/mechanics problem the other day, we had this utterly ridiculous problem where our answer had a weird gaussian integral we had to look up in 1000 page book of integrals...

The answer was basically a Bessel function of the second kind


Anyway, it was really annoying to have to go through that book to get the right integral and that's when we thought it'd be a great idea to be able to use LaTex to search a database of integrals

I don't think even wiki or wolframs do that

Knowledge puffs up but love edifies. I challenge everyone who comes here to despise the pride that mathematicians try to teach us, but to love the knowledge gained and use it for God's glory.

I like the idea of creating a database for looking up integrals, however why not just use numerical integration? Isn't that what most of the computer math systems do anyways? Then when you write your paper you can simply use the integral notation itself with that understanding, you don't need to explicitly write out the result.

[Note: I expect in this thread to have pride become an argument before we reach 20 posts. I will place anyone who starts casting such insults or who starts vaunting themselves on my ignore list immediately. I do not know everything about math and I am teachable, but I will not sit under someone who is as proud as a peackock or someone who treats mathematics as sacrosanct. The Lord is God, not the articulations of the human mind. Once we honestly learn this and submit to it our knowledge can be used for good.]

Have at er boys! Show me how smart you are!

 

[ArnautDaniel]

So if you are wondering, why not fill out your thoughts a bit so we can have a discussion. Please, let us consider the implications of Godel on human attempts to understand God.

I don't think it would have any implication whatsoever.

Goedel's theorems are simply theorems about formal systems which contain arithmetic.

Why would a formal system containing arithmetic ever have any effect on one's understanding of God?

 

[ArnautDaniel]

Knowledge puffs up but love edifies. I challenge everyone who comes here to despise the pride that mathematicians try to teach us, but to love the knowledge gained and use it for God's glory.

I like the idea of creating a database for looking up integrals, however why not just use numerical integration? Isn't that what most of the computer math systems do anyways? Then when you write your paper you can simply use the integral notation itself with that understanding, you don't need to explicitly write out the result.

[Note: I expect in this thread to have pride become an argument before we reach 20 posts. I will place anyone who starts casting such insults or who starts vaunting themselves on my ignore list immediately. I do not know everything about math and I am teachable, but I will not sit under someone who is as proud as a peackock or someone who treats mathematics as sacrosanct. The Lord is God, not the articulations of the human mind. Once we honestly learn this and submit to it our knowledge can be used for good.]

Have at er boys! Show me how smart you are!

I believe he wants the formula rather than the numeric solution.

He should be able to use some computer algebra system to get that answer though.

 

[Hagnismos]

I don't think it would have any implication whatsoever.

Goedel's theorems are simply theorems about formal systems which contain arithmetic.

Why would a formal system containing arithmetic ever have any effect on one's understanding of God?

A man made religion is not dissimilar to a formal system. Bear with me here. I have a degree in math and some graduate level math experience so I understand rigor. Look a philosophical system has to have undefinable terms, it has to have something like axioms, and it has to have rules that are more less strongly enforced when one tries to apply it to life or cosmology or whatever.

Here might be axioms for Biblical faith (knowing that true faith is deeper than this but I'm just saying)

Axioms

1) God exists

2) There is One God

3) God is Good

4) God is Omnipotent

5) God is Omniscient

6) God is Omnipresent

Each of these has the undefined term God in them, and all of the descriptive words can be at least qualified.

Taken together with some descent qualifiers for the terms, love, omnipotent, omnipresent, omniscient, person, exists we have a 'definition' of God.

Now notice that if my faith were simply a human exercise I could construct an entire religion from those 'axioms' and say things like,

because God is good He will not hurt me

It is a weak theorem of sorts that may or may not be true in reality but depending on how I interpret 'good' I may believe this.

I am not submitting that Christians should pursue God this way, but that rather those who do not know God often do. Their faith is not trust in a person they know, rather it is mental assent, based upon a set of a priori beliefs that continue to make sense perhaps only becuase they have never been contradicted.

Other religions then we simply alter axiom 2 from There is One God to

The most general set of axioms, maybe pseudo-axiom is better because in modern math we have completely divorced ourselves from the close ties to philosophy that men like Liebnitz enjoyed. We can protect our backs by agreeing we aren't really trying to involve mathematics here.

What the development it is straight forward.

A1) There is no god.[atheism]

It matters not what the definition for a 'god' is. it simply is true or is not true as a statement about a term that does not need to be defined.

B1) There exists at least one god [agnosticism?]

Again, now maybe we need more axioms

D1) there exists many gods [pantheism]

E1) there exists one God (God is One) [monotheism]

E2) God is Triune [christian monotheism]

What I am saying is that comparative religion is at it's heart axiomatic since at some point those who think about religion must accept some statement as true without knowing it is true. This is not faith in the Biblical sense of the greek word pistis. It is a very human assumption.

There is no reason to believe that human perspectives on society, life, right and wrong, the afterworld, love, war, peace etc. are not all ultimately based upon lists of axioms, with many undefined terms, and some rules of logic that they use to argue for things, to reason or divine our way though life.

I believe that Christiniaty differs in that one knows God, that would be the phrase 'you must be born again.' But some would argue that is an evangelical creation not to be taken seriously. I would beg to differ but would not try to force that since how could you.

Now the rules of logic that people use, we have to fuzzy that up to understand the rules they use.

Mathematicians like to use If/then statements to get everywhere. If this is true then do this unless this and then do this, but why? The why references back to supposedly deeper motivations and supporting arguments, 'I want to', 'God told me to', 'I feel like it', 'It will help someone I love.'

So motivation is part of it all too.

How often has you heard someone say this.

'Why did you did'nt you do this or that?'

'It just does'nt make sense to do that.'

Anyways, I am laying all this out there in the spirit of discussion so I will wait and see what you guys come up with.

I would say that I agree that in order to even consider this we have to fuzzy up our notions of definition, undefined, rules of logic and broaden them to include all human experience, that said we can investigate alot of things this way.

For instance consider this tenet of the Christian faith

C56) God is good

What if God is not good? What if what God does does not seem good to us? What if we do not know what good means? Is good in God's mind exactly the same as good in our mind? Why or why not?

It has long been accepted that the basic threefold purpose of the church is worship, fellowship, and discipleship.

In the matter of discipleship Isaiah said

'My people perish for lack of knowledge.' chapter 5

'Order on order, order on order,
Line on line, line on line,
A little here, a little there.' 28:9

As mathematicians we do have definitions that allow several things here. We can register ageement or disgreement on particular points of doctrine between denominations or philosophies and then create a distance measure. a weighted graph, trees that show relationships.

That is all sort of geek stuff I guess, but some people fear the application of statistics and structural modeling to society, and I think rightly so to some extent.

But when God says 'My people perish for lack of knowldge.' if we hold the Bible to be authoritative we have to wonder what that means.

Not every pursuit of knowledge is right in God's eyes, and I would not dare reverse the stakes and turn God into a lab rat. What I would say is that exhaustive resources documenting the differences between belief systems in a variety of ways might aid in peoples understanding of the issues we all face.

I think if we consider it carefully there are areas of everyone's life where we use terms for which we have no definition, or for which the definition we have leads only to more questions.

Imagine a website where I can learn about Christianity. I choose to look at the question of Trinitarian churches so I click under issue and choose trinity, immediately a rich mutimedia page comes up with links to lists of Trinitarian and non-Trinitarian churches, videos, history, important persons, etc.

What if we were studying a history of schism in the church and presented it as a graphic, a zoomable tree where each node had a link to complete background on the issue, the dates and the persons, the politics?

I realize that is a lot of sort of scattered ideas, but I get excited about this. How many Christians would have closer fellowship with others if they could understand how their church is like or different from the one next to them?

That's enough.

A simple distance between to faith's determined by agreement/disagreement on major points of doctrine might be interesting. A cluster analysis of survey responses related to social issues where the identifying flag was denominational affiliation, we would want to test for spatial variation as well.

For a believer what would the point be? The point is knowledge is a tool in the hands of a master builder. Paul used his knowledge to build the early church, the more knowledge have to day of the world in which we live the more effective we can potentially be, the more shrewd in our arguments and actions.

So here is a challenge of sorts.

Define the term 'God.' Give justification if you can.

 

[Hagnismos]

Ok,

Now I am going to get a little goofy, butsomeone will get it. Let me note beforehand that I am a Nicene Christian, a Bible believing Christian, so I hope that will help stay the hearts and minds of some who might feel swayed by an imaginary wind of doctrine that is not present in this note.

Axioms

1) G exists uniquely

2) G exists in all space and time (weak omnipresence)

3) G knows the value of all things at any given place in all of space and time (weak omniscience)

4) G can operate on any value at any place in space and time (weak omnipotence)

5) G has a property called 'goodness' that defines properties and methods, locally and globally that are unique to G (weak pseudo-character)


We could capture most of this by defining a field G everywhere in space and time that has at least two parts, a universal operator called G which encapsulates 2,3, and 4 and a property called g (goodness)

Someone may suspect I am about to try to show a similarity between gravity and God, but actually the gravity at any point in space time is a sum of gravity over all space relative to that point expressed as a vector (one concept of gravity anyways.) It does not actually contain information about every other point in space, that is we cannot expand the gravity vector at some point (x,y,z,t) into a complete description of the universe. The G field is greater than this. The G-field has a property such that it knows the value of everything everywhere all the time (weak omniscience.) The G-field further can change the value of anything anywhere at anytime (weak omnipotence.) The G-field is present everywhere, all the time (weak omnipresence.)

Let me play this game to completion. What is the purpose or usefulness of this hypothetical field of apparently unknown substance?

If it is an unintelligent agent then what? Either it obeys rules that we can understand or it does not. You see when you strip your notion of God of the intelligent personal aspects you end up with something like New Age theology, or the Force or something. But when you define G to be a rational being, having the stated properties, everything changes because now there is the question of the will of God. This living person G(od) can do anything, knows everything, and is everywhere. But does He just do anything, everywhere, all the time? No. Can we make Him do what we want anywhere at anytime? According to the Bible no, with some qualification. According to other religions, maybe.

I arrive then at a difference. When a person thinks they have the right to create God in their own image according to their own likes and dislikes this supposes a profound arrogance or a profound deception if one recognizes the properties the Bible attributes to God. Those who seek to manipulate God, or are indifferent to Him and His will, are also doomed to failure.

There is no way to escape from the authority of a God who is a rational being, and who is omnipotent (which we can argue presumes omniscience and omnipresence in some vague sense.)

Remember these discussion get fuzzy, but then after a little bit of adjusting the lens, sometimes things get very clear all of a sudden. If there is but one church, and one hope of our calling, one Lord, then it is vanity and striving after the wind to entertain notions of God that are not express truths about that One Lord, except perhaps to prepare oneself to minister to others.

So what is next? How does one come to the conviction that God is the 'God' of the Bible? If we arrive at that place, and even better that God's will is now revelaed in the New Testament, do you see how lcose we are now to actually knowing God.

Human reason (CS Lewis believed this as well) can be argued both closer and further away from a correct understanding of God. That of course may be small consolation since even the demons know these things and shudder (James.) And yet being able to give a decent response is important. Christians should not neglect the cognitive arts simply because of the temptation to vanity anymore than they should neglect any field because of it's peculiar temptations. Mature Christians are not pushed about by every wind of doctrine.

'And He gave some as apostles, and some as prophets, and some as evangelists, and some as pastors and teachers, for the equipping of the saints for the work of service, to the building up of the body of Christ; until we all attain to the unity of the faith, and the knowledge of the Son of God, to a mature man, to the measure of the stature which belongs to the fulness of Christ.

As a result, we are no longer to be children, tossed here and there by waves, and carried about by every wind of doctrine, by the trickery of men, by craftiness in deceitful scheming; but speaking the truth in love we are to grow up in all aspects into Him, who is the head even Christ, from whom the whole body, being fitted and held together by that which every joint supplies, according to the proper working of each individual part, causes the growth of the body for the building up of itself in love.'

Ephesians 4:11-16

Notice the emphasis I am placing there. If there be God appointed leadership among us, they are to be working to see us all attain to the measure of the stature which belongs to the fulness of Christ. Is that a corporate stature only? Or is it also in regard to each individual through discipleship that brings each one to their greatest fruitfulness in the body of Christ and in the service of the Lord?

We should not neglect to develop any gift that God has given us and use it against our adversary the devil. We should hope to see minds disciplined by knowledge and hearts empowered by faith and hearts healed by love, and the public square influenced by sincere testimony, and we should do this until we are interrupted by the arrival of the Lord Himself, after such time we shall forever be with Him.

 

[ArnautDaniel]

A man made religion is not dissimilar to a formal system. Bear with me here. I have a degree in math and some graduate level math experience so I understand rigor. Look a philosophical system has to have undefinable terms, it has to have something like axioms, and it has to have rules that are more less strongly enforced when one tries to apply it to life or cosmology or whatever.

Here might be axioms for Biblical faith (knowing that true faith is deeper than this but I'm just saying)

Axioms

1) God exists

2) There is One God

3) God is Good

4) God is Omnipotent

5) God is Omniscient

6) God is Omnipresent

Each of these has the undefined term God in them, and all of the descriptive words can be at least qualified.

Taken together with some descent qualifiers for the terms, love, omnipotent, omnipresent, omniscient, person, exists we have a 'definition' of God.

Now notice that if my faith were simply a human exercise I could construct an entire religion from those 'axioms' and say things like,

because God is good He will not hurt me

It is a weak theorem of sorts that may or may not be true in reality but depending on how I interpret 'good' I may believe this.

I am not submitting that Christians should pursue God this way, but that rather those who do not know God often do. Their faith is not trust in a person they know, rather it is mental assent, based upon a set of a priori beliefs that continue to make sense perhaps only becuase they have never been contradicted.

Other religions then we simply alter axiom 2 from There is One God to

The most general set of axioms, maybe pseudo-axiom is better because in modern math we have completely divorced ourselves from the close ties to philosophy that men like Liebnitz enjoyed. We can protect our backs by agreeing we aren't really trying to involve mathematics here.

What the development it is straight forward.

A1) There is no god.[atheism]

It matters not what the definition for a 'god' is. it simply is true or is not true as a statement about a term that does not need to be defined.

B1) There exists at least one god [agnosticism?]

Again, now maybe we need more axioms

D1) there exists many gods [pantheism]

E1) there exists one God (God is One) [monotheism]

E2) God is Triune [christian monotheism]

What I am saying is that comparative religion is at it's heart axiomatic since at some point those who think about religion must accept some statement as true without knowing it is true. This is not faith in the Biblical sense of the greek word pistis. It is a very human assumption.

There is no reason to believe that human perspectives on society, life, right and wrong, the afterworld, love, war, peace etc. are not all ultimately based upon lists of axioms, with many undefined terms, and some rules of logic that they use to argue for things, to reason or divine our way though life.

I believe that Christiniaty differs in that one knows God, that would be the phrase 'you must be born again.' But some would argue that is an evangelical creation not to be taken seriously. I would beg to differ but would not try to force that since how could you.

Now the rules of logic that people use, we have to fuzzy that up to understand the rules they use.

Mathematicians like to use If/then statements to get everywhere. If this is true then do this unless this and then do this, but why? The why references back to supposedly deeper motivations and supporting arguments, 'I want to', 'God told me to', 'I feel like it', 'It will help someone I love.'

So motivation is part of it all too.

How often has you heard someone say this.

'Why did you did'nt you do this or that?'

'It just does'nt make sense to do that.'

Anyways, I am laying all this out there in the spirit of discussion so I will wait and see what you guys come up with.

I would say that I agree that in order to even consider this we have to fuzzy up our notions of definition, undefined, rules of logic and broaden them to include all human experience, that said we can investigate alot of things this way.

For instance consider this tenet of the Christian faith

C56) God is good

What if God is not good? What if what God does does not seem good to us? What if we do not know what good means? Is good in God's mind exactly the same as good in our mind? Why or why not?

It has long been accepted that the basic threefold purpose of the church is worship, fellowship, and discipleship.

In the matter of discipleship Isaiah said

'My people perish for lack of knowledge.' chapter 5

'Order on order, order on order,
Line on line, line on line,
A little here, a little there.' 28:9

As mathematicians we do have definitions that allow several things here. We can register ageement or disgreement on particular points of doctrine between denominations or philosophies and then create a distance measure. a weighted graph, trees that show relationships.

That is all sort of geek stuff I guess, but some people fear the application of statistics and structural modeling to society, and I think rightly so to some extent.

But when God says 'My people perish for lack of knowldge.' if we hold the Bible to be authoritative we have to wonder what that means.

Not every pursuit of knowledge is right in God's eyes, and I would not dare reverse the stakes and turn God into a lab rat. What I would say is that exhaustive resources documenting the differences between belief systems in a variety of ways might aid in peoples understanding of the issues we all face.

I think if we consider it carefully there are areas of everyone's life where we use terms for which we have no definition, or for which the definition we have leads only to more questions.

Imagine a website where I can learn about Christianity. I choose to look at the question of Trinitarian churches so I click under issue and choose trinity, immediately a rich mutimedia page comes up with links to lists of Trinitarian and non-Trinitarian churches, videos, history, important persons, etc.

What if we were studying a history of schism in the church and presented it as a graphic, a zoomable tree where each node had a link to complete background on the issue, the dates and the persons, the politics?

I realize that is a lot of sort of scattered ideas, but I get excited about this. How many Christians would have closer fellowship with others if they could understand how their church is like or different from the one next to them?

That's enough.

A simple distance between to faith's determined by agreement/disagreement on major points of doctrine might be interesting. A cluster analysis of survey responses related to social issues where the identifying flag was denominational affiliation, we would want to test for spatial variation as well.

For a believer what would the point be? The point is knowledge is a tool in the hands of a master builder. Paul used his knowledge to build the early church, the more knowledge have to day of the world in which we live the more effective we can potentially be, the more shrewd in our arguments and actions.

So here is a challenge of sorts.

Define the term 'God.' Give justification if you can.

Okay, so I'm still missing where the system contains arithmetic so that Goedel's theorems can have any relevance...

 

[ArnautDaniel]

Axioms

1) G exists uniquely

2) G exists in all space and time (weak omnipresence)

3) G knows the value of all things at any given place in all of space and time (weak omniscience)

4) G can operate on any value at any place in space and time (weak omnipotence)

5) G has a property called 'goodness' that defines properties and methods, locally and globally that are unique to G (weak pseudo-character)

You see, the thing about formal systems is that the terms have no meaning whatsoever aside from their relations among themselves within the scope of the system.

Thus, for example, one can take the axioms of geometry and interpret the "line" from the axioms as something most people would call a "point" in the model, and vice versa and still have a perfectly good system.

The terms are nothing more than place holders.

So your system might be consistent, but in a model where the terms don't mean what you want them to mean.

It stikes me you are relying on understandings of some terms that aren't specified in the axioms.

Anyway, the basic problem with these sorts of things is smuggling things in the back door.

So "god" gets defined in some formal way to prove "god exists" but then one wants to get all the theist jargon without specifying it.

A formal system is simply a contentless structure, but you are relying on particular content mattering.

 

[Hagnismos]

You see, the thing about formal systems is that the terms have no meaning whatsoever aside from their relations among themselves within the scope of the system.

Thus, for example, one can take the axioms of geometry and interpret the "line" from the axioms as something most people would call a "point" in the model, and vice versa and still have a perfectly good system.

The terms are nothing more than place holders.

So your system might be consistent, but in a model where the terms don't mean what you want them to mean.

It stikes me you are relying on understandings of some terms that aren't specified in the axioms.

Anyway, the basic problem with these sorts of things is smuggling things in the back door.

So "god" gets defined in some formal way to prove "god exists" but then one wants to get all the theist jargon without specifying it.

A formal system is simply a contentless structure, but you are relying on particular content mattering.

'he who comes to God must believe that He is and that He is a rewarder of them who seek Him.' Hebrews 11:6

How do we come to these prerequisites?

Also have you read 'Godel, Escher, Bach'? The idea that Godel only applies to arithmetic seems a little restrictive, but I appreciate your point of view.

Also, I would not dream of trying to prove God's existence, I am certain that only experience can do that. And of course since He does exist He can speak for Himself. However we do have evidence that faith is intended to be more like trusting in someone you know than some vague ethereal half hope in a person that you rarely see or someone just told us about.

I really do not see where we could deny that

1) God exists uniquely

Could possibly be anything other than an assumption unless God Himself had at some point told someone that.

Why would we even tacitly assume that God is good, when we look everyday at a world filled with evil.

Spinoza suggested that comprehension of something required the tacit assumption of it's truth or existence and recent studies have seemed to bear this out. Those who hold prejudices cannot see the objects of those prejudices as people unless they first tacitly assume that the arguments supporting the prejudice are wrong.

those who do not know Christ build their lives around assumptions and fuzzy rules for turnig assumptions into 'theorems'

Now, how do we turn that into arithmetic. Let me think about that one for a little bit.

In the mean time consider Paul in this light,

'for the weapons of our warfare are not of the flesh, but divinely powerful for the destruction of fortresses. We are destroying speculations and every lofty thing raised up against the knowledge of God.'

2 Corinthians 10:4,5

Is it possible that a peson can know all the right things to say about God, can know all the premises (axioms of the faith) and argue persuasively as a Christian and still be only speculating? I think so. Remember what the people thought of Jesus' teaching

'The result was that when Jesus had finished these words, the multitudes were amazed at His teaching; for He was teaching them as one having authority, and not as their scribes.' Matthew 7:28-29

There are many scribes in America today. I pray God that none of us ever be found among them.

Those are all interesting points. I still think it would useful to list major points of doctrine for every denomination then use binomial variables , one if the group holds the doctrin, zero if it does not and, then calculate some kind of a distance between them in that space. I'm certain we would find for instance that the protestant churches are far removed from the catholic church etc. Which points of belief should we include? The official list from each church should be included, whatever that group calls their distinctives, each point should be given it's own variable. It would be a graphical way of understanding proximity in major tenets and in clustering denominations. The next level would then be to attach weights to certain issues, since some differences would be of less importance than others, and see how that effects the picture of who is nearby and who is far away. Maybe we would want to try to investigate how people change denominations by looking at how they bridge the gap, or transition from groups. Do people tend to make large numbers of adjustments, none at all, just switch churches. I think there is alot that could be learned about Christianity in America by something like that.

Thanks for your input. I started this thread to talk about math, please feel free to put some brain teasers in here. I'll keep thinking about how to turn a religious system into arithmetic.

 

[ArnautDaniel]

'he who comes to God must believe that He is and that He is a rewarder of them who seek Him.' Hebrews 11:6

How do we come to these prerequisites?

Also have you read 'Godel, Escher, Bach'? The idea that Godel only applies to arithmetic seems a little restrictive, but I appreciate your point of view.

Have you read Goedel's original paper?

The proof assumes arithmetic to reach the conclusion.

The proof is constructed entirely using arithmetic, and carried out using arithmetic.

So nothing has been proven for systems not containing arithmetic.

That is unless you want to assert that a proof using the Halting Problem is somehow more general (which I do not believe to be true).

Also, I would not dream of trying to prove God's existence, I am certain that only experience can do that. And of course since He does exist He can speak for Himself. However we do have evidence that faith is intended to be more like trusting in someone you know than some vague ethereal half hope in a person that you rarely see or someone just told us about.

I really do not see where we could deny that

1) God exists uniquely

Could possibly be anything other than an assumption unless God Himself had at some point told someone that.

Why would we even tacitly assume that God is good, when we look everyday at a world filled with evil.

Spinoza suggested that comprehension of something required the tacit assumption of it's truth or existence and recent studies have seemed to bear this out. Those who hold prejudices cannot see the objects of those prejudices as people unless they first tacitly assume that the arguments supporting the prejudice are wrong.

those who do not know Christ build their lives around assumptions and fuzzy rules for turnig assumptions into 'theorems'

Now, how do we turn that into arithmetic. Let me think about that one for a little bit.

In the mean time consider Paul in this light,

'for the weapons of our warfare are not of the flesh, but divinely powerful for the destruction of fortresses. We are destroying speculations and every lofty thing raised up against the knowledge of God.'

2 Corinthians 10:4,5

Is it possible that a peson can know all the right things to say about God, can know all the premises (axioms of the faith) and argue persuasively as a Christian and still be only speculating? I think so. Remember what the people thought of Jesus' teaching

'The result was that when Jesus had finished these words, the multitudes were amazed at His teaching; for He was teaching them as one having authority, and not as their scribes.' Matthew 7:28-29

There are many scribes in America today. I pray God that none of us ever be found among them.

Those are all interesting points. I still think it would useful to list major points of doctrine for every denomination then use binomial variables , one if the group holds the doctrin, zero if it does not and, then calculate some kind of a distance between them in that space. I'm certain we would find for instance that the protestant churches are far removed from the catholic church etc. Which points of belief should we include? The official list from each church should be included, whatever that group calls their distinctives, each point should be given it's own variable. It would be a graphical way of understanding proximity in major tenets and in clustering denominations. The next level would then be to attach weights to certain issues, since some differences would be of less importance than others, and see how that effects the picture of who is nearby and who is far away. Maybe we would want to try to investigate how people change denominations by looking at how they bridge the gap, or transition from groups. Do people tend to make large numbers of adjustments, none at all, just switch churches. I think there is alot that could be learned about Christianity in America by something like that.

Thanks for your input. I started this thread to talk about math, please feel free to put some brain teasers in here. I'll keep thinking about how to turn a religious system into arithmetic.

 

[Washington]

1) the rules of logic and the literature pertaining to math and logic shall be the final judge of what is right in answering any math problem

2) apparent conflicts between math and Scripture defer to Scripture (there are'nt any that cannot be explained using Godel, on the math side, and of the Bible on the God side, but just for good measure)

Evidently the humor here has eluded you.

 

[decoytdtc]

I believe he wants the formula rather than the numeric solution.

He should be able to use some computer algebra system to get that answer though.

Well, Maple and other programs cost a lot of money...the point is to have a free and easy-to-use integral database so that people don't have to shell out hundreds of dollars for a difficult book or program

Knowledge puffs up but love edifies. I challenge everyone who comes here to despise the pride that mathematicians try to teach us, but to love the knowledge gained and use it for God's glory.



[Note: I expect in this thread to have pride become an argument before we reach 20 posts. I will place anyone who starts casting such insults or who starts vaunting themselves on my ignore list immediately. I do not know everything about math and I am teachable, but I will not sit under someone who is as proud as a peackock or someone who treats mathematics as sacrosanct. The Lord is God, not the articulations of the human mind. Once we honestly learn this and submit to it our knowledge can be used for good.]

Ohohoho... I see what you did there

 

[ArnautDaniel]

Well, Maple and other programs cost a lot of money...the point is to have a free and easy-to-use integral database so that people don't have to shell out hundreds of dollars for a difficult book or program

Maxima, however, is free!



There are several other similar freely available mathematics software packages as well.