I suppose add it anywhere you can. The little hole might work. Otherwise, if the result is horrid- just toss a few teaspoons directly into the pot. Now as for removing lipstick stains- that is another kettle of fish, so to speak.
Yowzah, Waysider ! Thanks for that… William Clarke was a smokin’ hot blues harmonica virtuoso! I can see how that kinda relates to this thread on PFALT…develops more harmonica in the home… unfortunately I’m here all week folks.
Learning is pretty much Axiomatic. Sounds complicated, but not really- one assumes that a few set of rules or tenets are true, or commonly agreed upon. And include agreeable assumptions. Then you build your whole existence or Theology based on these few "irrefutable" truths.. Euclid's successors figured that they could explain it all without being able to draw a straight line.. they abandoned the parallel postulate.
Some fantastic results followed. But it did not explain everything.
Then come Godel. The tenets of any closed mathematical system cannot be proved by the axioms of the system. Some among us are trying to do the impossible here..
Some think that the Axioms are sacrosanct. But Axioms are pretty much self-assured truths. They only have relevance if one assigns it to them.
Religion is not math. Or necessarily a set of postulates. Is math a tool or a guide?
Religion stems from the psyche. Which is biological in origin.
In a weird sense, I think Math might be Religion. Certainly has a lot of the same characteristics. Now the Postulates of Religion. There is one God. I don't necessarily think that the Creator of the universe is a projection of my psyche..
Is Math a tool or guide. I think neither. It provides tools.. and maybe logical guidance.
Religion. Is it a tool or guide? Definitely a guide.
There are a definite number of Postulates and common assumptions one must agree with in order to proceed to the Next Phase of the Operation..
I hope that the audience does not object to this Stream of Consciousness one post after another proceeding.. :L)
You know.. human nature and understanding is so what's the word.. depraved? Merely by agreeing to some definition of God or reality we seem to alter the rules of the game. Usually not for the better. Even trying to improve this existence.
I like the simpler questions, like Where did we all come from? I kind of like the idea that we were all one, at least at one time. Yep, here comes more new age stream of consciousness BS.
Imagine a World where one can Magically summon whatever one desires- law of believing.
I like to give the reply to the question, "what do you want" with "Nothing. I already have far more that than I need."
Learning is pretty much Axiomatic. Sounds complicated, but not really- one assumes that a few set of rules or tenets are true, or commonly agreed upon. And include agreeable assumptions. Then you build your whole existence or Theology based on these few "irrefutable" truths.. Euclid's successors figured that they could explain it all without being able to draw a straight line.. they abandoned the parallel postulate.
Some fantastic results followed. But it did not explain everything.
Then come Godel. The tenets of any closed mathematical system cannot be proved by the axioms of the system. Some among us are trying to do the impossible here..
Some think that the Axioms are sacrosanct. But Axioms are pretty much self-assured truths. They only have relevance if one assigns it to them.
Same works for Religion.
You are so right about a lot there. I have studied these things, non-Euclidean Geometry and Godel's theorem on-and-off for 50 years. I love how you put it. Untouchable axioms are a must to any logic at it's beginnings.
Axioms are similar to "our only rule for faith and practice." and are untouchable. In math axioms are the "only set of rules for cranking out math."
Selecting one's axioms is critical for everything in life.
For those unfamiliar, axioms also called postulates and assumptions.
*/*/*/*/*/*/*
Bolshevik is partially right, though, I think.
The tight RESULTS of Godel's theorems apply only to "formal systems" in mathematics, and should be ONLY cautiously applied to other areas, bearing in mind that the PROOF of Godel only works for the formal systems.
Saying the Godel applies to anything outside a formal system is a little like saying Einstein proved that everything is relative.
The ideas may apply outside a formal system, but not the proofs.
Formal systems were devised in the early 20th Century by mathematicians to try and make a machine that proves math theorems. The machine only pays attention to the FORMS of the symbols that are used. The word "formal" does not imply the mathematicians wear tuxedos while they crank the proving machine.
Ham, would you say I got those details right? I dropped Godel about 8 years ago after Hofstadter's second book on it. I'm already getting a little rusty on it.
You are so right about a lot there. I have studied these things, non-Euclidian Geometry and Godel's theorem for 50 years. I love how you put it. Untouchable axioms are a must to any logic at it's BEGINNINGS.
Axioms are similar to "our only rule for faith and practice." and are untouchable. In math axioms are the "only set of rules for cranking out math."
Selecting one's axioms is critical in everything in life.
For those unfamiliar, axioms also called postulates and assumptions.
*/*/*/*/*/*/*
Bolshevik is partially right, though, I think.
The tight RESULTS of Godel's theorems apply only to "formal systems" in mathematics, and should be ONLY cautiously applied to other areas, bearing in mind that the PROOF of Godel only works for the formal systems.
Formal systems were devised in the early 20th Century by mathematicians to try and make a machine that proves math theorems. The machine only pays attention to the FORMS of the symbols that are used. The word "formal" does not imply the mathematicians wear tuxedos while they crank the proving machine.
Ham, would you say I got those details right? I dropped Godel about 8 years ago after Hofstadter's second book on it. I'm already getting a little rusty on it.
Bertrand Russel tried the approach of Logic and some kind of basis of only rule for Faith and Practice- mathematically speaking. But his research came up with one Paradox after another. Whos career did he ruin at the last moment.. just as the book was ready for press. Can't remember the name at the moment. I think Christians regard him as some kind of heretic, Godless unbeliever. History shows he hated violence and Mob Rule. Would not follow a politically motivated mob to embrace yet one more Godless War. I think that he was a true Christian.
I think that Godel shows us the way out of all of this, Philosophically, Theologically and Mathematically.
How do we apply this to Biblical Truth. I don't entirely know. There is a Larger System than Us.
Before Godel, there was Cantor. Cantor rattled their cages.
In a weird sense, I think Math might be Religion. Certainly has a lot of the same characteristics. Now the Postulates of Religion. There is one God. I don't necessarily think that the Creator of the universe is a projection of my psyche..
Is Math a tool or guide. I think neither. It provides tools.. and maybe logical guidance.
Religion. Is it a tool or guide? Definitely a guide.
There are a definite number of Postulates and common assumptions one must agree with in order to proceed to the Next Phase of the Operation..
Well, if we're arguing Math is not a cognitive exercise, maybe so.
Math carries the characteristics of the “ethical cult” that is discussed in another thread. No direct human hierarchy. But a code and pattern that all mathematicians worldwide follow.
You are so right about a lot there. I have studied these things, non-Euclidean Geometry and Godel's theorem on-and-off for 50 years. I love how you put it. Untouchable axioms are a must to any logic at it's beginnings.
Axioms are similar to "our only rule for faith and practice." and are untouchable. In math axioms are the "only set of rules for cranking out math."
Selecting one's axioms is critical for everything in life.
For those unfamiliar, axioms also called postulates and assumptions.
*/*/*/*/*/*/*
Bolshevik is partially right, though, I think.
The tight RESULTS of Godel's theorems apply only to "formal systems" in mathematics, and should be ONLY cautiously applied to other areas, bearing in mind that the PROOF of Godel only works for the formal systems.
Saying the Godel applies to anything outside a formal system is a little like saying Einstein proved that everything is relative.
The ideas may apply outside a formal system, but not the proofs.
Formal systems were devised in the early 20th Century by mathematicians to try and make a machine that proves math theorems. The machine only pays attention to the FORMS of the symbols that are used. The word "formal" does not imply the mathematicians wear tuxedos while they crank the proving machine.
Ham, would you say I got those details right? I dropped Godel about 8 years ago after Hofstadter's second book on it. I'm already getting a little rusty on it.
Hi. I find it a bit disingenuous when someone claims to be an armchair mathmetician for two decades without pursuing education. I do have a degree in math.
Godel was instrumental in tying the concepts involved in mathematical proofs together from previous threads. I find it hilarious for people to be discussing derived systems from Godel without discussing his incompleteness theorem. What are your thoughts on his incompleteness theories and writings as a 50 year student? It is very on topic btw.
Bertrand Russel tried the approach of Logic and some kind of basis of only rule for Faith and Practice- mathematically speaking. But his research came up with one Paradox after another. Whos career did he ruin at the last moment.. just as the book was ready for press. Can't remember the name at the moment. I think Christians regard him as some kind of heretic, Godless unbeliever. History shows he hated violence and Mob Rule. Would not follow a politically motivated mob to embrace yet one more Godless War. I think that he was a true Christian.
I think that Godel shows us the way out of all of this, Philosophically, Theologically and Mathematically.
How do we apply this to Biblical Truth. I don't entirely know. There is a Larger System than Us.
Before Godel, there was Cantor. Cantor rattled their cages.
You have a point about Godel. His work did tie together a lot of the philosophy of the time together and he could be called a father of the modern proof so to speak with his work used to improve the logical proof process.
Hi. I find it a bit disingenuous when someone claims to be an armchair mathmetician for two decades without pursuing education. I do have a degree in math.
Godel was instrumental in tying the concepts involved in mathematical proofs together from previous threads. I find it hilarious for people to be discussing derived systems from Godel without discussing his incompleteness theorem. What are your thoughts on his incompleteness theories and writings as a 50 year student? It is very on topic btw.
Not to accuse you of jealousy, but I do have that knee-jerk reaction to degree people who think their "official" path to intense knowledge is the only path. I have often encountered undisguised and overt jealousy at my lack of formal credentials. Jealousy because I sometimes got to sit and brainstorm with academic prizewinners including Nobel and MacArthur.
If I worded anything inaccurately about Godel above, THAT should be the target of your criticism, not my credentials. I will ignore now your opening as trivial and disingenuous itself.
God was very instrumental in opening doors for me to sit with great leaders in academia. This has happened over and over, and the only reason I can figure out why is that I have a job to do in applying my good fortune to bless others.
As for Godel, I had first heard about his stuff in High School, and thought it may be a key to solving mysteries of consciousness and free will. I was not looking for a job in mathematics, just help in working Neuroscience, where I am also a Rogue Scholar. I don't want to be a neuroscientist either; just need info to bless grads and then others.
As for Godel I searched out the best authors on his 2 famous theorems, which were few in 1966 when I started. Then Hofstadter wrote his Pulitzer Prize winning "Godel Escher and Bach." Soon more authors joined the exposition.
The most authoritative treatment of Godel I knew of in the 1990s from Nobel Prize winning physicist two books on consciousness and the mind, starting with The Emperor's New Clothes. I had been waiting for the top level to pick up where Schrodinger's tiny booklet "What is Life?" had left off in the 1930s, and Penrose went full bore on it. But I was still far from anything that could directly help me with the mystery of free will.
Then Hofstadter wrote another Godel book at the 30th anniversary of "Godel Escher and Bach" because he felt no one really got what he was aiming at. This book is "I AM a Strange Loop."
Although his Godel exposition here is superb, and I got some questions answered about Godel numbering, Hofstadter mostly taught me that Godel was NOT going to help me with free will. I loved what I learned about Godel, and can rub shoulders with any person with a degree in it for mutual learning.
If you haven't yet read "I AM a Strange Loop' then I highly recommend it. It has all sorts of surprises in it, and Hofstadter gets surprisingly personal about his private life and emotions than I was expecting. His main focus there is consciousness, and Godel is but one tool in the inquiry.
Soooo, you're basing your assertion on 40 year old, secondhand hearsay?
It would appear so. One thing is for certain, when challenged in any meaningful way Mike starts moving the goal posts and employing any method he can use to avoid staring at the obvious truth.
Obvious truth: When VPW said "Not all of his writings are necesarily God breathed" he was doing one of two things if not both. Including himself amongst men like Calvin, Luther, and Wesley - clearly he is not a man amongst those men.
Or....or....he chose his wording carefully to bait people into thinking that some of his writings were God breathed by saying that "not all of his writings are necessarily God breathed". That must leave room for occasional God breathed writings penned by wierwille. And of course the collateral damage with such a statement is well meaning people like you are stuck looking for easter eggs and obscured meaning in his words. That's a sad place to be my friend. Kinda smacks of mystiscism where you have to understand the inner depths of some esoteric meaning to get to the real hidden truths that are buried deep inside. Perhaps you would enjoy following Kabbalah with it's Gemetria and other methods of divining hidden meanings that are reserved for the initiated.
It would appear so. One thing is for certain, when challenged in any meaningful way Mike starts moving the goal posts and employing any method he can use to avoid staring at the obvious truth.
Obvious truth: When VPW said "Not all of his writings are necesarily God breathed" he was doing one of two things if not both. Including himself amongst men like Calvin, Luther, and Wesley - clearly he is not a man amongst those men.
Or....or....he chose his wording carefully to bait people into thinking that some of his writings were God breathed by saying that "not all of his writings are necessarily God breathed". That must leave room for occasional God breathed writings penned by wierwille. And of course the collateral damage with such a statement is well meaning people like you are stuck looking for easter eggs and obscured meaning in his words. That's a sad place to be my friend. Kinda smacks of mystiscism where you have to understand the inner depths of some esoteric meaning to get to the real hidden truths that are buried deep inside. Perhaps you would enjoy following Kabbalah with it's Gemetria and other methods of divining hidden meanings that are reserved for the initiated.
What you are saying makes a lot of sense IF it were the case that God was not involved and truly interested in blessing the world with fresh God-breathed writings in English.
Do really wan to forbid God from working with sinful men to bless other sinful men with His pure Word?
There were several times in the OT when God's Word was lost or destroyed. God always moved to restore it, sometimes immediately (Jer. 36) and sometimes after a span of time. I don't know why God waited so long to have the scriptures AUTHORITATIVELY restored, but who am I to question God's timing? Remember, translations and versions are void of authority. Change one word and you no longer have the Word, so even many early copies of the originals, which were notoriously inaccurate, are void of authority.
Math carries the characteristics of the “ethical cult” that is discussed in another thread. No direct human hierarchy. But a code and pattern that all mathematicians worldwide follow.
I understand math as a language. It's used to communicate, understand, explain, make predictions.
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Bolshevik
Scripture, The Bible, is not *a* language. "It interprets itself", though.
T-Bone
Excerpts from the first draft for a totally revised burnt orange book “Power For Materialistic Living Today”, page 3, Introduction: The Materialistic Life …This post literally changed my life. My
Raf
It is almost impossible to overstate how much this reeks of bullcrap. I'll be gentle: If Euclidian geometry were wrong on one point, Euclidian geometry would be perfectly content to remove
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Ham
I suppose add it anywhere you can. The little hole might work. Otherwise, if the result is horrid- just toss a few teaspoons directly into the pot. Now as for removing lipstick stains- that is another kettle of fish, so to speak.
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T-Bone
Yowzah, Waysider ! Thanks for that… William Clarke was a smokin’ hot blues harmonica virtuoso! I can see how that kinda relates to this thread on PFALT…develops more harmonica in the home… unfortunately I’m here all week folks.
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Ham
Learning is pretty much Axiomatic. Sounds complicated, but not really- one assumes that a few set of rules or tenets are true, or commonly agreed upon. And include agreeable assumptions. Then you build your whole existence or Theology based on these few "irrefutable" truths.. Euclid's successors figured that they could explain it all without being able to draw a straight line.. they abandoned the parallel postulate.
Some fantastic results followed. But it did not explain everything.
Then come Godel. The tenets of any closed mathematical system cannot be proved by the axioms of the system. Some among us are trying to do the impossible here..
Some think that the Axioms are sacrosanct. But Axioms are pretty much self-assured truths. They only have relevance if one assigns it to them.
Same works for Religion.
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Ham
I have watched at least one professor try to justify the Pythagorean Theorem from Trigonometric Identities. Pretty much circular logic.
If one takes the formula for distance as an Axiom, the problem is supposedly solved..
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Bolshevik
Religion is not math. Or necessarily a set of postulates. Is math a tool or a guide?
Religion stems from the psyche. Which is biological in origin.
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Ham
Math is EASY compared to this argument. Far easier to watch someone go through a circular pattern of logic uses the conclusion to prove the premises.
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Ham
In a weird sense, I think Math might be Religion. Certainly has a lot of the same characteristics. Now the Postulates of Religion. There is one God. I don't necessarily think that the Creator of the universe is a projection of my psyche..
Is Math a tool or guide. I think neither. It provides tools.. and maybe logical guidance.
Religion. Is it a tool or guide? Definitely a guide.
There are a definite number of Postulates and common assumptions one must agree with in order to proceed to the Next Phase of the Operation..
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waysider
That's what I was afraid of.
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Ham
I hope that the audience does not object to this Stream of Consciousness one post after another proceeding.. :L)
You know.. human nature and understanding is so what's the word.. depraved? Merely by agreeing to some definition of God or reality we seem to alter the rules of the game. Usually not for the better. Even trying to improve this existence.
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Ham
Heh...me too.
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Ham
I like the simpler questions, like Where did we all come from? I kind of like the idea that we were all one, at least at one time. Yep, here comes more new age stream of consciousness BS.
Imagine a World where one can Magically summon whatever one desires- law of believing.
I like to give the reply to the question, "what do you want" with "Nothing. I already have far more that than I need."
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Mike
You are so right about a lot there. I have studied these things, non-Euclidean Geometry and Godel's theorem on-and-off for 50 years. I love how you put it. Untouchable axioms are a must to any logic at it's beginnings.
Axioms are similar to "our only rule for faith and practice." and are untouchable. In math axioms are the "only set of rules for cranking out math."
Selecting one's axioms is critical for everything in life.
For those unfamiliar, axioms also called postulates and assumptions.
*/*/*/*/*/*/*
Edited by MikeBolshevik is partially right, though, I think.
The tight RESULTS of Godel's theorems apply only to "formal systems" in mathematics, and should be ONLY cautiously applied to other areas, bearing in mind that the PROOF of Godel only works for the formal systems.
Saying the Godel applies to anything outside a formal system is a little like saying Einstein proved that everything is relative.
The ideas may apply outside a formal system, but not the proofs.
Formal systems were devised in the early 20th Century by mathematicians to try and make a machine that proves math theorems. The machine only pays attention to the FORMS of the symbols that are used. The word "formal" does not imply the mathematicians wear tuxedos while they crank the proving machine.
Ham, would you say I got those details right? I dropped Godel about 8 years ago after Hofstadter's second book on it. I'm already getting a little rusty on it.
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Ham
Bertrand Russel tried the approach of Logic and some kind of basis of only rule for Faith and Practice- mathematically speaking. But his research came up with one Paradox after another. Whos career did he ruin at the last moment.. just as the book was ready for press. Can't remember the name at the moment. I think Christians regard him as some kind of heretic, Godless unbeliever. History shows he hated violence and Mob Rule. Would not follow a politically motivated mob to embrace yet one more Godless War. I think that he was a true Christian.
I think that Godel shows us the way out of all of this, Philosophically, Theologically and Mathematically.
How do we apply this to Biblical Truth. I don't entirely know. There is a Larger System than Us.
Before Godel, there was Cantor. Cantor rattled their cages.
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Mike
Yes we can't forget Cantor.
However, I can't think of any possible applications for his infinities.
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Bolshevik
Well, if we're arguing Math is not a cognitive exercise, maybe so.
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chockfull
Math carries the characteristics of the “ethical cult” that is discussed in another thread. No direct human hierarchy. But a code and pattern that all mathematicians worldwide follow.
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chockfull
Hi. I find it a bit disingenuous when someone claims to be an armchair mathmetician for two decades without pursuing education. I do have a degree in math.
Godel was instrumental in tying the concepts involved in mathematical proofs together from previous threads. I find it hilarious for people to be discussing derived systems from Godel without discussing his incompleteness theorem. What are your thoughts on his incompleteness theories and writings as a 50 year student? It is very on topic btw.
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waysider
I still struggle with fractions at least 2/7 of the time.
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chockfull
You have a point about Godel. His work did tie together a lot of the philosophy of the time together and he could be called a father of the modern proof so to speak with his work used to improve the logical proof process.
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Mike
Not to accuse you of jealousy, but I do have that knee-jerk reaction to degree people who think their "official" path to intense knowledge is the only path. I have often encountered undisguised and overt jealousy at my lack of formal credentials. Jealousy because I sometimes got to sit and brainstorm with academic prizewinners including Nobel and MacArthur.
If I worded anything inaccurately about Godel above, THAT should be the target of your criticism, not my credentials. I will ignore now your opening as trivial and disingenuous itself.
God was very instrumental in opening doors for me to sit with great leaders in academia. This has happened over and over, and the only reason I can figure out why is that I have a job to do in applying my good fortune to bless others.
As for Godel, I had first heard about his stuff in High School, and thought it may be a key to solving mysteries of consciousness and free will. I was not looking for a job in mathematics, just help in working Neuroscience, where I am also a Rogue Scholar. I don't want to be a neuroscientist either; just need info to bless grads and then others.
As for Godel I searched out the best authors on his 2 famous theorems, which were few in 1966 when I started. Then Hofstadter wrote his Pulitzer Prize winning "Godel Escher and Bach." Soon more authors joined the exposition.
The most authoritative treatment of Godel I knew of in the 1990s from Nobel Prize winning physicist two books on consciousness and the mind, starting with The Emperor's New Clothes. I had been waiting for the top level to pick up where Schrodinger's tiny booklet "What is Life?" had left off in the 1930s, and Penrose went full bore on it. But I was still far from anything that could directly help me with the mystery of free will.
Then Hofstadter wrote another Godel book at the 30th anniversary of "Godel Escher and Bach" because he felt no one really got what he was aiming at. This book is "I AM a Strange Loop."
Although his Godel exposition here is superb, and I got some questions answered about Godel numbering, Hofstadter mostly taught me that Godel was NOT going to help me with free will. I loved what I learned about Godel, and can rub shoulders with any person with a degree in it for mutual learning.
If you haven't yet read "I AM a Strange Loop' then I highly recommend it. It has all sorts of surprises in it, and Hofstadter gets surprisingly personal about his private life and emotions than I was expecting. His main focus there is consciousness, and Godel is but one tool in the inquiry.
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OldSkool
It would appear so. One thing is for certain, when challenged in any meaningful way Mike starts moving the goal posts and employing any method he can use to avoid staring at the obvious truth.
Obvious truth: When VPW said "Not all of his writings are necesarily God breathed" he was doing one of two things if not both. Including himself amongst men like Calvin, Luther, and Wesley - clearly he is not a man amongst those men.
Or....or....he chose his wording carefully to bait people into thinking that some of his writings were God breathed by saying that "not all of his writings are necessarily God breathed". That must leave room for occasional God breathed writings penned by wierwille. And of course the collateral damage with such a statement is well meaning people like you are stuck looking for easter eggs and obscured meaning in his words. That's a sad place to be my friend. Kinda smacks of mystiscism where you have to understand the inner depths of some esoteric meaning to get to the real hidden truths that are buried deep inside. Perhaps you would enjoy following Kabbalah with it's Gemetria and other methods of divining hidden meanings that are reserved for the initiated.
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Mike
What you are saying makes a lot of sense IF it were the case that God was not involved and truly interested in blessing the world with fresh God-breathed writings in English.
Do really wan to forbid God from working with sinful men to bless other sinful men with His pure Word?
There were several times in the OT when God's Word was lost or destroyed. God always moved to restore it, sometimes immediately (Jer. 36) and sometimes after a span of time. I don't know why God waited so long to have the scriptures AUTHORITATIVELY restored, but who am I to question God's timing? Remember, translations and versions are void of authority. Change one word and you no longer have the Word, so even many early copies of the originals, which were notoriously inaccurate, are void of authority.
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waysider
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Bolshevik
I understand math as a language. It's used to communicate, understand, explain, make predictions.
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