- #71
Mentat
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For a simple definition: The ability to exchange energy, and interact physically with other physical objects.
What is the Nature of Mathematics?
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In summary, Alexander's mysticism is deep and rich, not unlike a twelve layer chocolate cake or a fresh cowpie. However, we already have a bulletin board dedicated to mysticism and I try not to encourage him to get to deep into it on the philosophy bulletin board.
For a simple definition: The ability to exchange energy, and interact physically with other physical objects.
- #72
Mentat
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Why can't you just get to the point, without condesceding comments? If it's so simple to you, you should have no problem convincing me.
Force doesn't exist, but the curvature of spacetime does. According to a lot of the candidates for the T.O.E., all of the "forces" can be explained as curvatures of spacetime itself. That doesn't mean that it is only a mathematical phenomenon, it means that it requires different mathematics (Riemann Geometry, for example) to describe it.
So what? The "interaction of objects" is still a physical process, that is described by mathematical symmetries.
I know that this is your opinion, but that doesn't mean it's true. In fact, you are contradicting yourself, as you said that there were no physical phenomena (just mathematical properties), and then you said that mathematics is the way that these "physical phenomena" came into existence.
No, if there were no "forces" in our Universe, then the rate of change of momentum would be zero.
- #73
Mentat
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Why are you construing a "why" question as though it were scientific? Science doesn't answer "why" questions.
- #74
Mentat
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Thanks Tom! This is the biggest "hurdle", in my opinion, and cannot be overcome.
You see, Alexander, if you deny that there is a difference between the abstract and the concrete, then you make known that you are an idealist, not a scientist.
- #75
Mentat
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You don't need to weaken your position any further with these kind of comments, Alexander. Lifegazer was just recently banned, and he didn't start out so many of his posts with condescending comments, like you.
- #76
Alexander
You don't like thinking? I do. It never hurts to think, to analyse, to investigate in depth cause(s) and reason(s) things behave certain way.
Say, what is the definition of a force?
Say, what is the definition of a force?
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- #77
ahrkron
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Drop the attitude.
- #78
Perspectives
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Mathematics and its relivance
Mathematics is an explanation of existence. Its complexity and level of relevance depends on need. Mathematics is to existence what the footprint is to the foot. Everthing discovered or not discovered that is cannot have been constructed from nothing. Therefore mathematics is, was and has always existed.
Mathematics is an explanation of existence. Its complexity and level of relevance depends on need. Mathematics is to existence what the footprint is to the foot. Everthing discovered or not discovered that is cannot have been constructed from nothing. Therefore mathematics is, was and has always existed.
- #79
wuliheron
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Mathematics is symbolic of the footprint itself from a classical viewpoint. No matter how accurate our mathematical description of something might be, we cannot prove beyond a shadow of a doubt the thing itself really exists except by pointing our finger at it. When all is said and done, we can only point to a real footprint to prove they exist. Mathematics alone cannot prove anything exists in reality, thus it is considered symbolic.
A bird in the hand is worth two in the bush
And, in turn, the two in the bush are (for all I can determine) worth an infinite number of mathematical white rabbits.
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- #80
Perspectives
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Mathematics, the object and Reality
Mathematics in its finest detail are composed of symbols and relationships between them. It is truly an expression of the tangible. However, most proven things cannot be held in the hand or seen by the eye but due to things in existence that can, we believe. These things are a model of what is from our perspective and while they are not the things, they like an echo are a part of it. Our existence is composed of all the things that are and the Mathematics are revealed to describe them. Without an object to examine we cannot apply math to it.
Mathematics in its finest detail are composed of symbols and relationships between them. It is truly an expression of the tangible. However, most proven things cannot be held in the hand or seen by the eye but due to things in existence that can, we believe. These things are a model of what is from our perspective and while they are not the things, they like an echo are a part of it. Our existence is composed of all the things that are and the Mathematics are revealed to describe them. Without an object to examine we cannot apply math to it.
- #81
Royce
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Ever notice how when Alexander feels he's being ganged up on and he thinks he's losing and arqument or debate he starts getting insulting. Very mature for a materialistic scientist, don't you think.
- #82
FZ+
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Royce: It is also immature to make wry comments as to someone else's maturity from the sidelines.
Hmm...
(FZ+, now aged 4 [mental age])
Hmm...
(FZ+, now aged 4 [mental age])
- #83
Mentat
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I don't like someone's insinuating that I, or any other member here, is not doing so. Insulting others, in this way, serves absolutely no purpose, except to irritate others.
- #84
Mentat
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Very good post. I like the analogy (of the foot and the footprint) too. I've been trying to defend a similar position against the belief that mathematics can actually "tell the Universe how to behave", or that there is no physical reality, but rather just mathematics.
- #85
Perspectives
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Mathematics, Existence and Reality
What is possible and not is an enigma. I’m not speaking of why a person cannot flap its arms and fly like a bird. That we know is not possible. Why? We’re not equipped to do so and no one has reported it. Surely I would shout at the top of my lungs, ”I can fly like a bird, if I could.”
No, this is about the impossible being created out of nothing. On the one hand something that has not been discovered before, or should I say created, is new. Since it is new and a construct of the mind. Can we claim it never was therefore it is ours, created out of nothing? If we say YES, then we can say we operate outside of that which has been divined as ours back yard, our existence. If we say NO it has always been and it is predefined and impossible not to find if we exercise our mental ability.
When a lion drags down a deer, it does not empirically measure the deer’s health, size or weight. For the lion it is food and it will last how ever long it lasts. That is the lions existence and it’s mental extension to food. We on the other hand have selected the entire world as our food stores. We select a 32 oz. Steak, a baked potato, sour cream and a salad. That’s supper and we are satisfied. We check our mental pockets or our actual pockets and know how much money we have. We can eat till Thursday and we get paid Friday therefore we have a day of hunger or we can eat less expensive meals. I guess we should have had a hot dog instead of that large steak. We think of these things, our food supply in abstract terms days, money, where and what we eat. We developed these concepts out of want, not need. We could have still bartered or been self-sufficient. But we wanted more therefore we developed a system and nurtured friendly relations. We developed concepts that are extensions of more primitive existences. Families of Hippos allow little birds to pick parasites from their bodies, cooperation.
Where do we draw the line between saying “I did this out of nothing, it never was and it never could be at this time in this place except by me?” I claim this victory for myself at this point in existence. All may be true, except and it was specified, someone else could have discovered it, somewhere or sometime different.
But the essential point is not that it was discovered but that “what claim may be made regarding its preexistence?” Did these things exist before creation or were they there to create?
Mathematics is an expression of our existence as is physically portrayed through the universe. We merely model and explain what it is doing. If we developed a model of something that never was, or could not ever have been and has no relevance in existence then it can never be.
I believe existence and our comprehension of it as is called Reality, is only limited by our ability to emulate it through our mental constructs and exposure to others for consideration.
What is possible and not is an enigma. I’m not speaking of why a person cannot flap its arms and fly like a bird. That we know is not possible. Why? We’re not equipped to do so and no one has reported it. Surely I would shout at the top of my lungs, ”I can fly like a bird, if I could.”
No, this is about the impossible being created out of nothing. On the one hand something that has not been discovered before, or should I say created, is new. Since it is new and a construct of the mind. Can we claim it never was therefore it is ours, created out of nothing? If we say YES, then we can say we operate outside of that which has been divined as ours back yard, our existence. If we say NO it has always been and it is predefined and impossible not to find if we exercise our mental ability.
When a lion drags down a deer, it does not empirically measure the deer’s health, size or weight. For the lion it is food and it will last how ever long it lasts. That is the lions existence and it’s mental extension to food. We on the other hand have selected the entire world as our food stores. We select a 32 oz. Steak, a baked potato, sour cream and a salad. That’s supper and we are satisfied. We check our mental pockets or our actual pockets and know how much money we have. We can eat till Thursday and we get paid Friday therefore we have a day of hunger or we can eat less expensive meals. I guess we should have had a hot dog instead of that large steak. We think of these things, our food supply in abstract terms days, money, where and what we eat. We developed these concepts out of want, not need. We could have still bartered or been self-sufficient. But we wanted more therefore we developed a system and nurtured friendly relations. We developed concepts that are extensions of more primitive existences. Families of Hippos allow little birds to pick parasites from their bodies, cooperation.
Where do we draw the line between saying “I did this out of nothing, it never was and it never could be at this time in this place except by me?” I claim this victory for myself at this point in existence. All may be true, except and it was specified, someone else could have discovered it, somewhere or sometime different.
But the essential point is not that it was discovered but that “what claim may be made regarding its preexistence?” Did these things exist before creation or were they there to create?
Mathematics is an expression of our existence as is physically portrayed through the universe. We merely model and explain what it is doing. If we developed a model of something that never was, or could not ever have been and has no relevance in existence then it can never be.
I believe existence and our comprehension of it as is called Reality, is only limited by our ability to emulate it through our mental constructs and exposure to others for consideration.
- #86
wuliheron
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Mathematics is meaningless unless we translate it into natural language. Ask yourself, "What is five?" Without reference to natural language concepts and the ability to physically point to "five" of something the word has no meaning. Thus the interpretation of mathematics and, indeed, logic itself has no meaning outside of natural language.
Natural language is repleate with vague terms and contradictions. Unless you can clarify these terms and contradictions, at least those that apply to mathematics and logic, any assertions you can make about mathematics and how it applies to the real world are pure speculation. Considering the evidence of the last century especially, the idea that any single view of mathematics covers everything is patently absurd.
- #87
Perspectives
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Mathematics in all its form reveals all
While it is true mathematics is the chosen tool for the formal expression of physical phenomena, to most if it ‘s implications and indeed it’s implied consequences are not revealed through words and a story then it will not matter. I am most familiar with Einstein’s Special Theory of Relativity in both the math and his eloquent verbal expression of it. However his General Theory of Relativity is Mathematically beyond me at present and after that the implications that I must derive from it and finally I will not be able to express it verbally till I get the other two straight.
So considering the bridge that must be created between the abstractions of mathematics to the verbalization of its consequences, I agree with you. We do need to be able to properly express in non-mathematical terms the things revealed by mathematics.
Regarding why mathematics can be used to express all phenomena, I hold despite the many varied branches that may be needed, mathematics is a tool that is intrinsic to humans. And that it is very much applicable to all physical phenomena. We may need to create new abstract tools in the future that are mathematical in nature but nonetheless they will be mathematics. I therefore submit, formally expressed notation will be used that abstractly represent the relations in nature and it will perform the service of revealing nature’s inner workings. Mathematics and only mathematics in all its form is necessary and implicit in discovering nature’s mechanisms.
While it is true mathematics is the chosen tool for the formal expression of physical phenomena, to most if it ‘s implications and indeed it’s implied consequences are not revealed through words and a story then it will not matter. I am most familiar with Einstein’s Special Theory of Relativity in both the math and his eloquent verbal expression of it. However his General Theory of Relativity is Mathematically beyond me at present and after that the implications that I must derive from it and finally I will not be able to express it verbally till I get the other two straight.
So considering the bridge that must be created between the abstractions of mathematics to the verbalization of its consequences, I agree with you. We do need to be able to properly express in non-mathematical terms the things revealed by mathematics.
Regarding why mathematics can be used to express all phenomena, I hold despite the many varied branches that may be needed, mathematics is a tool that is intrinsic to humans. And that it is very much applicable to all physical phenomena. We may need to create new abstract tools in the future that are mathematical in nature but nonetheless they will be mathematics. I therefore submit, formally expressed notation will be used that abstractly represent the relations in nature and it will perform the service of revealing nature’s inner workings. Mathematics and only mathematics in all its form is necessary and implicit in discovering nature’s mechanisms.
- #88
wuliheron
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Mathematics can be highly accurate and precise, but whether or not this implies it reflects reality in some sense is unknown. Its a bit like saying my yardstick is highly accurate and precise, therefore existence must be a yardstick, and everything must be capable of being measured by a yardstick. I should be able to measure my mother's love for me using my yardstick, or even the value of life itself.
Note that within mathematics itself, there is no clearly superior form of mathematics which describes reality better than another. In physics, Quantum Mechanics does a good job but only on a statistical basis that does not make any conclusive statement about the ultimate nature of existence. In other words, the evidence is against the idea no matter which way you turn. The only way available currently for this idea to hang on by a toe nail, is through the undifferentiated or indeterminate nature of existence we observe. If we cannot determine the precise nature of reality, then at least a small chance exists all our other observations are misleading due to our limited perspective.
- #89
Perspectives
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Math, Man and Reality
Post from: Wuliheron
“Mathematics can be highly accurate and precise, but whether or not this implies it reflects reality in some sense is unknown.”….
”Note that within mathematics itself, there is no clearly superior form of mathematics which describes reality better than another.”…
“The only way available currently for this idea to hang on by a toe nail, is through the undifferentiated or indeterminate nature of existence we observe.”…
“If we cannot determine the precise nature of reality, then at least a small chance exists all our other observations are misleading due to our limited perspective.”…
___________________________________________________________________
I agree with you, we cannot know the precise nature of Reality since it is variable and interpreted from our perspective. Indeed our interpretation of Reality is subjective though the use of our Mathematics.
Mathematics can be the cause of two forms of interpretation, one a perspective and two a thoroughly incorrect application. I’m not sure there is much difference between them but there is a surety involved here, our observation of Reality in itself affects the outcome.
The interpretation of Reality is one point in the search and Mathematics is the other. It is difficult enough to, by some mystical event, discover a new or corrected view of reality, prove it in-principle through formal methodology, and then interpret what you’ve got. Lesley Groves has been quoted as having said upon viewing the first detonation of the atomic bomb, “ We’ve won the war, we have the biggest stick on the block,” whereas Robert Openheimer was quoted as reciting a passage from the Gita Bhagwat, “ I am become death…”
This is not math or science but a demonstration of perspectives regarding a pivotal event in history. After all the math and science two men regard the result from two entirely different perspectives.
There are times Mathematics, Reality and Humankind are as disparate as wind, rain, and Earth and sometimes, maybe as close as the tree that gains the benefits of the three.
Post from: Wuliheron
“Mathematics can be highly accurate and precise, but whether or not this implies it reflects reality in some sense is unknown.”….
”Note that within mathematics itself, there is no clearly superior form of mathematics which describes reality better than another.”…
“The only way available currently for this idea to hang on by a toe nail, is through the undifferentiated or indeterminate nature of existence we observe.”…
“If we cannot determine the precise nature of reality, then at least a small chance exists all our other observations are misleading due to our limited perspective.”…
___________________________________________________________________
I agree with you, we cannot know the precise nature of Reality since it is variable and interpreted from our perspective. Indeed our interpretation of Reality is subjective though the use of our Mathematics.
Mathematics can be the cause of two forms of interpretation, one a perspective and two a thoroughly incorrect application. I’m not sure there is much difference between them but there is a surety involved here, our observation of Reality in itself affects the outcome.
The interpretation of Reality is one point in the search and Mathematics is the other. It is difficult enough to, by some mystical event, discover a new or corrected view of reality, prove it in-principle through formal methodology, and then interpret what you’ve got. Lesley Groves has been quoted as having said upon viewing the first detonation of the atomic bomb, “ We’ve won the war, we have the biggest stick on the block,” whereas Robert Openheimer was quoted as reciting a passage from the Gita Bhagwat, “ I am become death…”
This is not math or science but a demonstration of perspectives regarding a pivotal event in history. After all the math and science two men regard the result from two entirely different perspectives.
There are times Mathematics, Reality and Humankind are as disparate as wind, rain, and Earth and sometimes, maybe as close as the tree that gains the benefits of the three.
- #90
drag
Science Advisor
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Hmmm...
Alexander doesn't want to play with me...
Alexander doesn't want to play with me...
- #91
Mentat
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Originally posted by drag
Hmmm...
Alexander doesn't want to play with me...
Yeah, I'm getting the same feeling.
- #92
wimms
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Give him a break. Hes becoming impatient and took some time to chill.
Question to ask may be - is there anything AT ALL that mathematics isn't able to describe, including however wild acausally looking relations?
When I first encountered Fourier series I was baffled, you can dismantle wavesignal of any shape whatsoever into finite number of components, that can sometimes be awfully compact equation. Any kind of patterns in signal results in reduction of complexity of equation. The more repetitions, the simpler it becomes. Complexity of equations increase only in case when signal approximates towards completely acausally random noise.
Math is so powerful these days, that they seek for methodology to actually find equation for any given photo of any complexity. Its all about compression ala DNA. Given space of nearly infinite possibilities, find equation that produces exactly that given image.
I guess one could describe in full detail, shape, colors, smell and all, actual bull's shjt floating in the waterpool with wave equations. Some QM is 'piece of cake' in comparison. Question is merely in finding which of infinite possible equations best fits observable reality. Thus impression creeps in, if math is so powerful that it can describe about anything, how can math be actually cause for anything? What then constrains its infinite flexibility? And most importantly, why in this particular way?
Then, equations are merely dormant relations, 'curvature'. To make them alive, one needs to put in some values, 'matter'. Only then can equations 'take off'. Only if 'matter' and 'curvature' were in mutual interaction, creating and changing each other, like mass and spacetime, could there be some justification to why we observe only small subset of possibilities. In that sense, theories of chaos are fascinating. As I understand it, they have capacity to actually create new math from dumbsimple initial conditions, upto complexification beyond imagination.
Question to ask may be - is there anything AT ALL that mathematics isn't able to describe, including however wild acausally looking relations?
When I first encountered Fourier series I was baffled, you can dismantle wavesignal of any shape whatsoever into finite number of components, that can sometimes be awfully compact equation. Any kind of patterns in signal results in reduction of complexity of equation. The more repetitions, the simpler it becomes. Complexity of equations increase only in case when signal approximates towards completely acausally random noise.
Math is so powerful these days, that they seek for methodology to actually find equation for any given photo of any complexity. Its all about compression ala DNA. Given space of nearly infinite possibilities, find equation that produces exactly that given image.
I guess one could describe in full detail, shape, colors, smell and all, actual bull's shjt floating in the waterpool with wave equations. Some QM is 'piece of cake' in comparison. Question is merely in finding which of infinite possible equations best fits observable reality. Thus impression creeps in, if math is so powerful that it can describe about anything, how can math be actually cause for anything? What then constrains its infinite flexibility? And most importantly, why in this particular way?
Then, equations are merely dormant relations, 'curvature'. To make them alive, one needs to put in some values, 'matter'. Only then can equations 'take off'. Only if 'matter' and 'curvature' were in mutual interaction, creating and changing each other, like mass and spacetime, could there be some justification to why we observe only small subset of possibilities. In that sense, theories of chaos are fascinating. As I understand it, they have capacity to actually create new math from dumbsimple initial conditions, upto complexification beyond imagination.
- #93
wuliheron
- 2,155
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Paradox.
- #94
drag
Science Advisor
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Greetings !
discribe. In fact, modern mathematics is
full of approximations of nature with few
direct discriptions. The simplest example
I offered Alexander and got no response is
that of 3+ bodies orbiting each other due to
the force of gravity.
Live long and prosper.
Of course there are things math fails to
discribe. In fact, modern mathematics is
full of approximations of nature with few
direct discriptions. The simplest example
I offered Alexander and got no response is
that of 3+ bodies orbiting each other due to
the force of gravity.
Live long and prosper.
- #95
Perspectives
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- 0
Math is a reflection and our mind the Mirror
The universe is an orderly and predictable environment that is reality. I’m sure the O and P statement will bring howls. Our attempt to emulate and capture the rules of the environment is through the discovery of the interrelationships that exist. We do this by creating symbolic relationships that when applied are predictive in nature, we call this mathematics. If math predicts in any reasonable manor the mechanics and mechanisms of the universe then we are merely illuminating that which is from the logic that is already there.
As regards what we call Reality, it is a subjective interpretation, verbal as much as logical, of our formal proofs. Half empty or half full, which is right?
The universe is an orderly and predictable environment that is reality. I’m sure the O and P statement will bring howls. Our attempt to emulate and capture the rules of the environment is through the discovery of the interrelationships that exist. We do this by creating symbolic relationships that when applied are predictive in nature, we call this mathematics. If math predicts in any reasonable manor the mechanics and mechanisms of the universe then we are merely illuminating that which is from the logic that is already there.
As regards what we call Reality, it is a subjective interpretation, verbal as much as logical, of our formal proofs. Half empty or half full, which is right?
- #96
wuliheron
- 2,155
- 0
Both are true, the glass is half empty and half full and that is the paradox. The universe is incredibly predictable and inordinately unpredictable else we would not be discussing the issue. Your argument is nothing less than a variation on the Anthropic Principle. That in itself is as humorous as it gets for the sciences and philosophy.
- #97
Eh
- 746
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Why does this remind me of Lifegazer threads?
- #98
Alexander
Small but impotrant correction: Behavior of existing objects is to mathematics what the footprint is to the foot.
- #99
Alexander
Wulli - no offense - how much expertise in math do you have?
The reason I am asking is that sometimes people with no or little expertise in some field try to judge that field and get wrong conclusion.
- #100
Perspectives
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Mathematics any conclusions?
The qualifications for evaluation of the subject matter is elusive and every bit as consensus as the subject it’s self. We’re examining philosophy, theoretical physics, theology if you’re inclined, and of course mathematics.
I think, like the blind men each describing an elephant, the allegory fails to bring into account their area of expertise. It seems the most important part of the story is that they are blind, as if they could see they would immediately know what they see. Since all humans have some unique attributes that color their judgment each man would probably see something different. Scientific methodology tries to eliminate subjectivity from the evaluative process; therefore man should see the same thing. Yet we may have asked a subjective question, too unscientific to use an objective measure.
Mathematics without question is a methodology, just like a man is male. Math is a tool to assist our understanding of the Universe and a tool to assist us to build a house. We don’t care about the Universe when we build our house and we don’t think of houses when we consider the Universe. We just use it to justify our work. Especially at those levels we’re not standing far enough from the subject to illuminate it.
I believe that we have touched on many of the important points of the argument and as is equally important assisted each other in understanding individual perspective. At various levels we’re all right to some degree. This subject is important and not just an academic exercise since it’s conclusions could lead to innovation. Especially if one can get our mind around what Mathematics is. Then we can consider what it isn’t.
The qualifications for evaluation of the subject matter is elusive and every bit as consensus as the subject it’s self. We’re examining philosophy, theoretical physics, theology if you’re inclined, and of course mathematics.
I think, like the blind men each describing an elephant, the allegory fails to bring into account their area of expertise. It seems the most important part of the story is that they are blind, as if they could see they would immediately know what they see. Since all humans have some unique attributes that color their judgment each man would probably see something different. Scientific methodology tries to eliminate subjectivity from the evaluative process; therefore man should see the same thing. Yet we may have asked a subjective question, too unscientific to use an objective measure.
Mathematics without question is a methodology, just like a man is male. Math is a tool to assist our understanding of the Universe and a tool to assist us to build a house. We don’t care about the Universe when we build our house and we don’t think of houses when we consider the Universe. We just use it to justify our work. Especially at those levels we’re not standing far enough from the subject to illuminate it.
I believe that we have touched on many of the important points of the argument and as is equally important assisted each other in understanding individual perspective. At various levels we’re all right to some degree. This subject is important and not just an academic exercise since it’s conclusions could lead to innovation. Especially if one can get our mind around what Mathematics is. Then we can consider what it isn’t.
- #101
Alexander
So, if a laymann walked into physics conference and said: "I am not an expert in general relativity, but general relativity is clearly wrong", then what? Shall GR be discarded then?
- #102
Mentat
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Step outside of your religious hold to this unproven idea, and you will realize that you are preaching against the definitive notion of mathematics itself. I've been doing research into what mathematics is, and it seems that everyone (including expert mathematicians) recognizes mathematics as a tool for understanding physical reality.
- #103
Mentat
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And herein lies one of your greatest character flaws. An Indian mand (from India), revolutionized Mathematics, after having only read a basic mathematics textbook (I forget his name, but I'm sure you're familiar with him). It doesn't take an extensive education in a field, to question an "expert's" of understanding of it.
- #104
quantumdude
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This has nothing to do with anything in the discussion. No one is saying that accepted physical theories are "wrong".
- #105
FZ+
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In an ideal would, they would nod in agreement, but not discard GR. Rather, they would agree that inevitably there would be improvements to the theory, but it's the best around at the moment.
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