Philosophy of Cosmology

[SoAMadDeathWish]

My point is that, just because no one understands some equation or other on an intuitive level, it doesn't mean that QM is a bad theory. Which is what I think you were trying to say in the OP.

SoAMadDeathWish,

What does understand "some equation or other on an intuitive level" mean?

I've got nothing against equations and nothing against intuition, but I'm having trouble groking this.

MIchael

By that I mean to be able to connect the equation to some basic, concrete experience. For example, e^(i*(pi)) = -1 can be understood as a rotation of a unit length through 180 degrees around one of its ends.

[Michael Stuart Kelly]

SoAMadDeathWish,

That's intuition?

I still don't understand.

I'm not busting on you. I'm serious.

I don't get what part of this is intuition.

Michael

[SoAMadDeathWish]

SoAMadDeathWish,

That's intuition?

I still don't understand.

I'm not busting on you. I'm serious.

I don't get what part of this is intuition.

Michael

Here's a definition from wikipedia:

Intuition is the ability to acquire knowledge without inference and/or the use of reason.

To illustrate further, you could use your understanding of the equation in my previous post to automatically intuit that e^(i*(pi/2)) = i, e^(i*(3pi/2)) = -i, e^(i*(pi/4)) = Sqrt(2)/2 + i*Sqrt(2)/2, etc. simply by fixing a unit length at the origin of the complex plane and rotating it by the apporpriate angle. You can therefore know a true statement without having to prove it rigorously first.

This is how mathematicians work. They intuit a theorem first, and then try to prove it.

[dennislmay]

SoAMadDeathWish,

That's intuition?

I still don't understand.

I'm not busting on you. I'm serious.

I don't get what part of this is intuition.

Michael

Here's a definition from wikipedia:

Intuition is the ability to acquire knowledge without inference and/or the use of reason.

To illustrate further, you could use your understanding of the equation in my previous post to automatically intuit that e^(i*(pi/2)) = i, e^(i*(3pi/2)) = -i, e^(i*(pi/4)) = Sqrt(2)/2 + i*Sqrt(2)/2, etc. simply by fixing a unit length at the origin of the complex plane and rotating it by the apporpriate angle. You can therefore know a true statement without having to prove it rigorously first.

This is how mathematicians work. They intuit a theorem first, and then try to prove it.

http://en.wikipedia.org/wiki/Visual_reasoning

Never underestimate non-verbal reasoning.

The best example I've run into in my life was in 1987-1988 in a graduate class on complex variables. The professor used the example of complex variable

integration around a hole - expanding the results outward giving an Airy disk-like result.

http://en.wikipedia.org/wiki/Airy_disk

In his mind this "proved" that everything relating to quantum mechanics as far as diffraction and interference was already well understood - this

was his mathematical intuition at work,

His level of understanding was already more than a century old and neglected all of the interesting physics but it could be presented in the form

of a "proof". A proof of course is only as good as its underlying assumptions and your level of understanding of the subject matter.

Speaking of interesting questions:

Agree or disagree and why?: The real results of all complex variable problems can in theory be arrived at without the use of complex variables.

Dennis

[SoAMadDeathWish]

http://en.wikipedia.org/wiki/Visual_reasoning

Never underestimate non-verbal reasoning.

The best example I've run into in my life was in 1987-1988 in a graduate class on complex variables. The professor used the example of complex variable

integration around a hole - expanding the results outward giving an Airy disk-like result.

http://en.wikipedia.org/wiki/Airy_disk

In his mind this "proved" that everything relating to quantum mechanics as far as diffraction and interference was already well understood - this

was his mathematical intuition at work,

His level of understanding was already more than a century old and neglected all of the interesting physics but it could be presented in the form

of a "proof". A proof of course is only as good as its underlying assumptions and your level of understanding of the subject matter.

Speaking of interesting questions:

Agree or disagree and why?: The real results of all complex variable problems can in theory be arrived at without the use of complex variables.

Dennis

It's not clear to me what point you're trying to make with your professor anecodte....

But to answer your question... I think the answer depends on what you mean by "complex variables". If you regard C as a real vector space, then it is isomorphic to R^2, and then I think that you can do physics without using complex variables. However, if you regard C as a complex vector space, then I'd have to say the answer is that you can't.

[Michael Stuart Kelly]

Here's a definition from wikipedia:

Intuition is the ability to acquire knowledge without inference and/or the use of reason.

To illustrate further, you could use your understanding of the equation in my previous post to automatically intuit that e^(i*(pi/2)) = i, e^(i*(3pi/2)) = -i, e^(i*(pi/4)) = Sqrt(2)/2 + i*Sqrt(2)/2, etc. simply by fixing a unit length at the origin of the complex plane and rotating it by the apporpriate angle. You can therefore know a true statement without having to prove it rigorously first.

This is how mathematicians work. They intuit a theorem first, and then try to prove it.

SoAMadDeathWish,

I have to apologize. I thought you were interested in ideas and I was taking you seriously at first.

You give a definition of intuition from psychology and say this is a math procedure--as you conveniently leave out the link? Go on. Click on it and read the big honking word "psychology" in the title.

I wonder why you left that out, I wonder.

Then you even use a definition that says "acquire knowledge" and talk about "intuiting a theorum"--which is not knowledge, but the attempt to gain it?

You're faking it.

So I'm not going to waste your time or mine. I'll let others engage you. I'm not interested in phoney-baloney games presented as intellectual largesse to bestow upon the unwashed. If you want to play that game, at least have something solid behind it, not faking for God's sake. (That's a freebie suggestion, but you don't have to accept it.)

Enjoy the forum and please stay within the posting guidelines.

Michael

[SoAMadDeathWish]

SoAMadDeathWish,

I have to apologize. I thought you were interested in ideas and I was taking you seriously at first.

You give a definition of intuition from psychology and say this is a math procedure--as you conveniently leave out the link? Go on. Click on it and read the big honking word "psychology" in the title.

I wonder why you left that out, I wonder.

Then you even use a definition that says "acquire knowledge" and talk about "intuiting a theorum"--which is not knowledge, but the attempt to gain it?

You're faking it.

So I'm not going to waste your time or mine. I'll let others engage you. I'm not interested in phoney-baloney games presented as intellectual largesse to bestow upon the unwashed. If you want to play that game, at least have something solid behind it, not faking for God's sake. (That's a freebie suggestion, but you don't have to accept it.)

Enjoy the forum and please stay within the posting guidelines.

Michael

Michael, yes the definition I gave was from psychology. Appropriate, I think, since I was in fact talking about the psychological phenomenon of intuition. You're making it seem like I'm trying to hide something. I'm not.

I have never called intuition a math procedure. I merely said that that's how actual people think about math.

Again, I don't understand what I've done to you to earn your enmity. This is the second time you've accused me of "playing games" or some such.

[dennislmay]

http://en.wikipedia.org/wiki/Visual_reasoning

Never underestimate non-verbal reasoning.

The best example I've run into in my life was in 1987-1988 in a graduate class on complex variables. The professor used the example of complex variable

integration around a hole - expanding the results outward giving an Airy disk-like result.

http://en.wikipedia.org/wiki/Airy_disk

In his mind this "proved" that everything relating to quantum mechanics as far as diffraction and interference was already well understood - this

was his mathematical intuition at work,

His level of understanding was already more than a century old and neglected all of the interesting physics but it could be presented in the form

of a "proof". A proof of course is only as good as its underlying assumptions and your level of understanding of the subject matter.

Speaking of interesting questions:

Agree or disagree and why?: The real results of all complex variable problems can in theory be arrived at without the use of complex variables.

Dennis

It's not clear to me what point you're trying to make with your professor anecodte....

But to answer your question... I think the answer depends on what you mean by "complex variables". If you regard C as a real vector space, then it is isomorphic to R^2, and then I think that you can do physics without using complex variables. However, if you regard C as a complex vector space, then I'd have to say the answer is that you can't.

The correct answer: complex variables [imaginary numbers in any form] are not required to produced real results. Imaginary numbers may provide mathematical methodology difficult to achieve

in closed form otherwise but they add nothing in information content - any of their forms can be expressed using only real numbers if the beginning and end results are also a real numbers.

If you have not been taught this don't feel bad, In 1979 I encountered a professor of applied mathematics at Drake University who didn't know it either. I suspect very few people are aware of this

non controversial fact - simply because the entire educational system does want to have to explain it in class a billion times - so sweep it under the rug and keep on plugging what we tell you to

plug.

Why is it important? Because when you get into graduate school you will run into professors who will roadblock progress in physics because they have come to believe imaginary numbers

are in fact required - problems like the Airy disk can't be solved without them - they were taught wrong so it is their job to make sure you think the "right" way too. This is just a simple example

of a problem which stretches across countless issues in our educational system.

Beauty and intuition in mathematics do not necessarily translate in any form once physics is involved. A beautiful equation [or even closed forms] in physics is the extremely rare exception. When

mathematicians try pushing beauty onto physics you can with very very few exceptions be sure that beauty came at the cost of neglecting some of the physics - perhaps even the most important

parts. When you take short cuts for the sake of beauty you can only stunt progress - likely for generations.

Dennis

[SoAMadDeathWish]

Dennis, how is any of this at all relevant right now?

[dennislmay]

Dennis, how is any of this at all relevant right now?

Every day right now students and the public are being mis-educated concerning the kinds of mathematics required to do physics, the foundations of physics required to understand

cosmology and future physics advances, the requirements of the scientific method, and what is and is not actual science being touted as science in the public arena. These errors

have a direct impact in our daily lives.

Dennis

[SoAMadDeathWish]

Every day right now students and the public are being mis-educated concerning the kinds of mathematics required to do physics, the foundations of physics required to understand

cosmology and future physics advances, the requirements of the scientific method, and what is and is not actual science being touted as science in the public arena. These errors

have a direct impact in our daily lives.

Dennis

Ok, but, what does that have to do with our discussion?

[Peter]

SoAMadDeathWish wrote:

Ok, but, what does that have to do with our discussion?

end quote

Let us get the inevitable out of the way: the name your parent’s did not give you. Its length will mean responders will not use your pen name. They may start shortening it to “So.” Or since each first letter of every word is capitalized, that means the shortest word, “A” has added significance. “Ay?” hmmm? I can’t get “Ayn” out of that. The capitalized letters are “SAMDW.” Ah ha. Is your real name, Samantha Dwyer?

No? That leaves the un-capitalized letters: “oadeathish.” Oh a death wish? Why the heck would you have a death wish? Why would you broadcast that? Why are you mad? “Mad” as in angry or “mad” as in insane?

An alternative *affect* you may wish to *cause* is something mathematical. No answer required. I will imagine the worst.

edit.

I investigated, and you list your name as “Naomi Ludenberg.” “Naomi?” is obviously jumbled. Amino? “Ludenberg? Blunder, blender, bundler, bungled, burgled? “Amino Blender” could be a nice name for bio-scientist. I won't bother you any more.

[BaalChatzaf]

Dennis, how is any of this at all relevant right now?

Every day right now students and the public are being mis-educated concerning the kinds of mathematics required to do physics, the foundations of physics required to understand

cosmology and future physics advances, the requirements of the scientific method, and what is and is not actual science being touted as science in the public arena. These errors

have a direct impact in our daily lives.

Dennis

Right now we are in the midst of a "beauty is truth" crisis in physics. Some physicists have even talked about entering a post-empirical era! When physics become post-empirical it will be the restoration of platonic and Aristotelian nonsense. Back in 1609 Galileo began digging us out from under Aristotle's nonsense and in 2014 Max Tegmark is reburying us under Platonic effluence.

Ba'al Chatzaf

[dennislmay]

Dennis, how is any of this at all relevant right now?

Every day right now students and the public are being mis-educated concerning the kinds of mathematics required to do physics, the foundations of physics required to understand

cosmology and future physics advances, the requirements of the scientific method, and what is and is not actual science being touted as science in the public arena. These errors

have a direct impact in our daily lives.

Dennis

Right now we are in the midst of a "beauty is truth" crisis in physics. Some physicists have even talked about entering a post-empirical era! When physics become post-empirical it will be the restoration of platonic and Aristotelian nonsense. Back in 1609 Galileo began digging us out from under Aristotle's nonsense and in 2014 Max Tegmark is reburying us under Platonic effluence.

Ba'al Chatzaf

Ba'al Chatzaf is correct about this crisis - when science is no longer science. I remember recoiling in horror when I was about 15-16 and I first understood what

"scientists" were saying when they kept talking about beautiful equations. It made me sick then and it has only grown worse since.

Dennis

[SoAMadDeathWish]

Ba'al Chatzaf is correct about this crisis - when science is no longer science. I remember recoiling in horror when I was about 15-16 and I first understood what

"scientists" were saying when they kept talking about beautiful equations. It made me sick then and it has only grown worse since.

Dennis

Dennis,

I understand your concern. I sincerely hope that no physicists actually believe that beauty determines truth. I think that the whole "beauty is truth" idea is just hyperbole. From what I know, Einstein and other physicists have only ever used beauty as a heuristic for picking out interesting hypotheses from a large (possibly infinite) pool of possibilities.

For example, there is no rigorous deduction of the Einstein field equations anywhere in GR from first principles. GR allows for an infinity of field equations. Einstein simply chose the one form that fit Newtonian gravity at low energies and that was the simplest, and that form has turned out to be the correct one. Nobody, as far as I know, has said that the beauty of the field equations alone is enough to establish them as a truth. Many alternative field equations have been proposed over the years and only Einstein's have passed all the tests.

[BaalChatzaf]

Ba'al Chatzaf is correct about this crisis - when science is no longer science. I remember recoiling in horror when I was about 15-16 and I first understood what

"scientists" were saying when they kept talking about beautiful equations. It made me sick then and it has only grown worse since.

Dennis

There is nothing wrong with a beautiful or elegant theory as long as it holds up under rigorous empirical testing.

It is easier to love a beautiful correct theory than an ugly correct theory.

Order of precedence. 1- correct 2 - elegant and economical but one cannot infer truth from beauty.

Ba'al Chatzaf

[dennislmay]

Ba'al Chatzaf is correct about this crisis - when science is no longer science. I remember recoiling in horror when I was about 15-16 and I first understood what

"scientists" were saying when they kept talking about beautiful equations. It made me sick then and it has only grown worse since.

Dennis

Dennis,

I understand your concern. I sincerely hope that no physicists actually believe that beauty determines truth. I think that the whole "beauty is truth" idea is just hyperbole. From what I know, Einstein and other physicists have only ever used beauty as a heuristic for picking out interesting hypotheses from a large (possibly infinite) pool of possibilities.

For example, there is no rigorous deduction of the Einstein field equations anywhere in GR from first principles. GR allows for an infinity of field equations. Einstein simply chose the one form that fit Newtonian gravity at low energies and that was the simplest, and that form has turned out to be the correct one. Nobody, as far as I know, has said that the beauty of the field equations alone is enough to establish them as a truth. Many alternative field equations have been proposed over the years and only Einstein's have passed all the tests.

Beginning in late 2010 [others] and early 2011 with this paper of Stacy McGaugh:

http://arxiv.org/pdf/1102.3913.pdf

the entire Dark Matter/General Relativity explanation of the velocity curves

of spiral galaxies unraveled and should now enjoy the status of junk science.

Start with McGaugh's paper and you will find 3-4 versions of GR different from

Einsteins which give better results than regular GR - plus MOND which is also

better within certain ranges found in spiral galaxies. John Moffat is a researcher

with a version of GR superior to Einstein's:

http://arxiv.org/pdf/1110.5420.pdf

General Relativity is constantly praised for its beauty but since 1932 it has been

at odds with observation:

http://en.wikipedia.org/wiki/Dark_matter

So General Relativity had a 16 year run before it was shown to be observationally

incorrect. 13 of those years it enjoyed provisional observational support.

It wasn't until the 1960's that GR saw much application in cosmology - years after

it had already been observed to be incorrect.

Outside of the solar system GR has been found to be observationally inferior to at

least 4-5 competing theories. 3-4 of them give the same or better results on all

scales.

Within our solar system the value of "G" evades a consensus value and has

been the subject of continuing evasion since I was in high school. I don't believe

this is just plain error upon error but a misunderstanding of the physics involved.

http://www.scientificamerican.com/article/puzzling-measurement-of-big-g-gravitational-constant-ignites-debate-slide-show/

So I do disagree with several of your statements concerning GR. As a student I observed the religious figure worship

of Einstein and the beauty of his equations was a subject of much discussion which left a bad taste in my mouth. His

GR work has been found lacking and the Dark Matter fix is incorrect by observation. The fixes to GR to give better

results are also without foundation from any first principles. I have observed beauty of formula worship and it is a real

problem.

Dennis

[BaalChatzaf]

Dennis,

I understand your concern. I sincerely hope that no physicists actually believe that beauty determines truth. I think that the whole "beauty is truth" idea is just hyperbole. From what I know, Einstein and other physicists have only ever used beauty as a heuristic for picking out interesting hypotheses from a large (possibly infinite) pool of possibilities.

For example, there is no rigorous deduction of the Einstein field equations anywhere in GR from first principles. GR allows for an infinity of field equations. Einstein simply chose the one form that fit Newtonian gravity at low energies and that was the simplest, and that form has turned out to be the correct one. Nobody, as far as I know, has said that the beauty of the field equations alone is enough to establish them as a truth. Many alternative field equations have been proposed over the years and only Einstein's have passed all the tests.

Einstein got his General Theory from two principles. 1. The Equivalence Principle and 2. The desirability of a covariant theory where the laws are not dependent on the frame of references. He busted his head for 8 years pursuing this and and had a mini-nervous breakdown in the process.

Einstein's concept of space and time were quite different that that of Isaac Newton so General Theory is not a mere refinement of Newton's Theory. It is a replacement.

Ba'al Chatzaf

[SoAMadDeathWish]

Einstein got his General Theory from two principles. 1. The Equivalence Principle and 2. The desirability of a covariant theory where the laws are not dependent on the frame of references. He busted his head for 8 years pursuing this and and had a mini-nervous breakdown in the process.

Einstein's concept of space and time were quite different that that of Isaac Newton so General Theory is not a mere refinement of Newton's Theory. It is a replacement.

Ba'al Chatzaf

I know. I never said otherwise.

[BaalChatzaf]

Einstein got his General Theory from two principles. 1. The Equivalence Principle and 2. The desirability of a covariant theory where the laws are not dependent on the frame of references. He busted his head for 8 years pursuing this and and had a mini-nervous breakdown in the process.

Einstein's concept of space and time were quite different that that of Isaac Newton so General Theory is not a mere refinement of Newton's Theory. It is a replacement.

Ba'al Chatzaf

I know. I never said otherwise.

You wrote "For example, there is no rigorous deduction of the Einstein field equations anywhere in GR from first principles."

WRONG. The first principles were the equivalence principle and covariance. And his inference from those two principle were very rigorous. So rigorous that Hilbert nearly scooped Einstein by purely mathematical procedures. Hilbert used Langrangians and Hamiltonians to get the Field Equations.

Ba'al Chatzaf

[SoAMadDeathWish]

You wrote "For example, there is no rigorous deduction of the Einstein field equations anywhere in GR from first principles."

WRONG. The first principles were the equivalence principle and covariance. And his inference from those two principle were very rigorous. So rigorous that Hilbert nearly scooped Einstein by purely mathematical procedures. Hilbert used Langrangians and Hamiltonians to get the Field Equations.

Ba'al Chatzaf

Ok, but, the deduction picked out a large class of field equations, not the specific ones Einstein believed were true. This is important because there are different sets of field equations, each that fit the equivalence principle and covariance principle but which yield different predictions.

[SoAMadDeathWish]

Dennis,

GR itself has been tested many times, and many alternative theories have been proposed and tested as well. This abundance of active scientific research directly contradicts your claim that Einstein is worshiped as a religious figure and that his ideas are above criticism.

Perhaps you're right that STVG theory is the one true faith, but none of what you've posted supports your claims about Einstein worship.

[dennislmay]

Dennis,

GR itself has been tested many times, and many alternative theories have been proposed and tested as well. This abundance of active scientific research directly contradicts your claim that Einstein is worshiped as a religious figure and that his ideas are above criticism.

Perhaps you're right that STVG theory is the one true faith, but none of what you've posted supports your claims about Einstein worship.

http://www.everythingimportant.org/Einstein_worship/

Scientists are not going to openly admit their worship of Einstein or their blindness to alternatives because they see

the "beauty" in his formulation. You have to experience seeing it first hand - there will be no valid survey unless done

in a clandestine manner.

There is however the competing church of indetermistic QM with Feynman as its last idol of worship. No different in

kind - the competing religions do battle to this day.

Both are overshadowed by the newer climate change religion which enjoys unlimited funding and a wider less educated

audience.

Dennis

[SoAMadDeathWish]

Dennis,

Scientists are not going to openly admit their worship of Einstein or their blindness to alternatives because there isn't any to begin with. Like I said before, it is a fact that alternatives to GR have been proposed and tested ever since at least the sixties. This fact directly contradicts your claim.

[dennislmay]

Dennis,

Scientists are not going to openly admit their worship of Einstein or their blindness to alternatives because there isn't any to begin with. Like I said before, it is a fact that alternatives to GR have been proposed and tested ever since at least the sixties. This fact directly contradicts your claim.

Yes a handful of people have worked on alternatives - and GR has been found lacking and wrong. You clearly were not aware of that superior alternatives have existed since late 2010. You didn't know about it because the dominant science media and educational institutions continue to take the view that Einstein can do no wrong - if not openly then by their silence. Dennis