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Responsible Quantum Speculation

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Responsible Quantum Speculation
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Collin237Posts: 11Joined: Thu Sep 03, 2015 4:26 pm

Post Responsible Quantum Speculation

Given that quantum mechanics on the one hand explains amazingly well various real physical phenomena, but on the other hand seems to deny reality, you'd think the world would be filled with people discussing how to reconcile quantum mechanics with the existence of the real world that exemplifies it.

Instead there seems to be a bewildering variety of proposals to make quantum theory even more unrealistic, so as to seem to bolster various claims of pseudoscience and religion. What's worse, some of these essays seem to come from the physical science community itself.

We don't know what's flawed or missing about quantum mechanics, or how to fix it, but surely by now experts in physics should have a good enough idea of what's plausible to be able to do open-minded but honest brainstorming? And surely it shouldn't even take an expert to spot the nonsense, especially when it's even advertised as such in so many words?

Is there any organization that's seriously looking for a way to make quantum theory worthy of being considered a frontier of physics, a legitimate next step in the quest started by the likes of Newton and Einstein?

If not, I think science is dead.
Thu Sep 03, 2015 5:02 pm
SpecialFrogUser avatarPosts: 827Joined: Wed Jul 16, 2014 2:13 pmLocation: Great White North Gender: Tree

Post Re: Responsible Quantum Speculation

Collin237 wrote:Given that quantum mechanics on the one hand explains amazingly well various real physical phenomena, but on the other hand seems to deny reality, you'd think the world would be filled with people discussing how to reconcile quantum mechanics with the existence of the real world that exemplifies it.

I don't see how quantum mechanics denies reality at all. What it does do is show that some of our intuitions about how reality ought to behave are wrong.

Rather than quantum mechanics denying reality, we are denying reality if we insist that it behaves in a manner inconsistent with the findings of quantum mechanics.

Collin237 wrote:Instead there seems to be a bewildering variety of proposals to make quantum theory even more unrealistic, so as to seem to bolster various claims of pseudoscience and religion. What's worse, some of these essays seem to come from the physical science community itself.

Could you give an example of what you mean? If you mean something like the "many worlds" hypothesis you might find this article interesting (even if you are not convinced by it.

Collin237 wrote:We don't know what's flawed or missing about quantum mechanics, or how to fix it, but surely by now experts in physics should have a good enough idea of what's plausible to be able to do open-minded but honest brainstorming? And surely it shouldn't even take an expert to spot the nonsense, especially when it's even advertised as such in so many words?

I'm still not sure how this is a flaw in quantum mechanics. Also, what do you mean by "nonsense"?

Collin237 wrote:Is there any organization that's seriously looking for a way to make quantum theory worthy of being considered a frontier of physics, a legitimate next step in the quest started by the likes of Newton and Einstein?

If not, I think science is dead.

I think you are somewhat overstating the importance of working out the philosophical implications of quantum mechanics.

David Mermin wrote:If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be 'Shut up and calculate!'


Also, welcome to the board. :)
"Life is nothing but an electron looking for a place to rest" -- Albert Szent-Gyrgyi
Fri Sep 04, 2015 12:20 am
australopithecusAdministratorUser avatarPosts: 4287Joined: Sun Feb 22, 2009 9:27 pmLocation: Kernow Gender: Time Lord

Post Re: Responsible Quantum Speculation

The fact snake oil salesmen use the counterintuitive nature and weirdness of QM to sell shit to the gullible isn't the fault of QM.

Is there any organization that's seriously looking for a way to make quantum theory worthy of being considered a frontier of physics, a legitimate next step in the quest started by the likes of Newton and Einstein?

If not, I think science is dead.


Quantum computing and nuclear fusion would fall under that category, and both are being heavily invested in.
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Fri Sep 04, 2015 12:16 pm
Collin237Posts: 11Joined: Thu Sep 03, 2015 4:26 pm

Post Re: Responsible Quantum Speculation

I don't see how quantum mechanics denies reality at all. What it does do is show that some of our intuitions about how reality ought to behave are wrong.

Rather than quantum mechanics denying reality, we are denying reality if we insist that it behaves in a manner inconsistent with the findings of quantum mechanics.


There's no such thing as the findings of a theory. There are only the findings of the experiments on which the theory is based. QM, which seems to be the maximum testable and verified conclusion of quantum experiments, correctly predicts and describes only their results, not the behavior that led to them. If I ask about that behavior and I'm told to "shut up", all I have left is my own amateur opinion. If, as is quite likely, I come up with something that doesn't match the experiments, then it's not my fault for denying something I haven't been told about. In terms of behavior, the findings are that no hypothesis is testable. However, there are tight constraints on what possible behaviors honestly follow from what we know about the results. If following the dictates of Popper concerning quantum experiments leads you to withhold honest knowledge from the public and let liars have free reign, then the findings are that the falsification doctrine has itself been falsified.

The purpose of science is not to remove errors, but to remove lies. If the truth is that there is a limited range of possibilities but nobody knows a way to objectively choose among them, and the lack of a unique leading hypothesis scares you into silence, then -- Popper be darned -- you've failed as a scientist.

Quantum computing and nuclear fusion would fall under that category, and both are being heavily invested in.


Nuclear fusion? Surely you jest! Fusion researchers have no regard for science. They think they can just make up things like Widom-Larson theory with no evidence.

The fact snake oil salesmen use the counterintuitive nature and weirdness of QM to sell shit to the gullible isn't the fault of QM.


I'm not faulting QM. I'm faulting the people who study QM, for not properly explaining to the public what we know and what we don't know.

Could you give an example of what you mean? If you mean something like the "many worlds" hypothesis you might find this article interesting (even if you are not convinced by it.


The problem isn't just that there are branches. It's that one of the branches agrees with empirical data and the others don't, unless the hypothesis is considered to change the definition of empiricism.

When a priest sanctifies a piece of bread, the empirical data is that it's still bread, and we have no problem accepting that it actually is still bread. If the priest says it isn't bread anymore, he's allowing the hypothesis (that it's turned into a piece of a 2000-year-old man's body) to imply that the observation (that it's still bread) is unreal. In this case we have no problem recognizing that this inference is a lie.

There is no way, except by such a dishonest leap of faith, to invalidate the claim that one branch is this universe and the other branches aren't. And if there's no physical process that can explain that distinction, it can only be ascribed to a transcendental ego. This leads directly to pseudoscience. And when the Born Rule is derived from decision theory, the assumption of ego is even more obvious.
Mon Sep 14, 2015 5:19 am
SpecialFrogUser avatarPosts: 827Joined: Wed Jul 16, 2014 2:13 pmLocation: Great White North Gender: Tree

Post Re: Responsible Quantum Speculation

Colin, I guess I don't really see your point.

I don't see anybody withholding knowledge of the limits of our understanding. There are good, accessible books out there on QM and its abuses -- Victor Stenger's book "Quantum Gods" may as well be subtitled "How Deepak Chopra is lying about physics".

What exactly do you propose scientists should be doing that they are not doing?

Basic chemistry tells us that homoeopathy is nonsense and yet some actual doctors seem to be taken in by its claims.
"Life is nothing but an electron looking for a place to rest" -- Albert Szent-Gyrgyi
Mon Sep 14, 2015 3:11 pm
Collin237Posts: 11Joined: Thu Sep 03, 2015 4:26 pm

Post Re: Responsible Quantum Speculation

Yes, of course, our understanding of QM is limited, but not nearly as limited as our knowledge. My point is that there is a lot we understand may be behind QM, without knowing how well any of those hypotheses match reality.

From the review by Yossarian, it sounds like Stenger is using QM to bolster an argument against religion. Alongside people like Chopra using QM in favor of religion, the total impression is of a palimpsest bandied about in the culture war. What's missing is an accessible exposition of the ways that QM can be developed upon as a mathematical, not emotional, philosophy. An introduction to, and acknowledgement of the worth of, the many ways to push the envelope of QM as a description of reality from a standpoint of geeky indifference to all political, cultural, and social trends. A way that the public can evaluate the various non-cultural modifications that may be provisionally plausible, to the tools of the theory, such as functional integrals, Hamiltonians, fiber bundles, etc., so as to participate in a marketplace of well-informed independently technical opinions.

As long as people like Chopra are needed, either as a friend or an enemy, they'll never stop making trouble. They can be defeated only by mathematically styled disinterest.

P.S.: Doctors believing in homeopathy? More likely they're grandstanding for artificial dignity.

That may be the problem with physicists also. They don't want to be seen as "only" technicians. I suspect that there are far more people who understand basic math and logic than it appears, due to self-censorship to appease cultural norms, fashions, gods, etc.. Scientists need to stop pandering to such affectations. They need to write clearly but not dumbly about the actual contents of their theories, especially those that depart from being well-established in a way that challenges both fashion and counter-fashion, and ask only later how well people understood them.
Last edited by Collin237 on Mon Sep 14, 2015 9:35 pm, edited 1 time in total.
Mon Sep 14, 2015 8:21 pm
SpecialFrogUser avatarPosts: 827Joined: Wed Jul 16, 2014 2:13 pmLocation: Great White North Gender: Tree

Post Re: Responsible Quantum Speculation

Collin237 wrote:Yes, of course, our understanding of QM is limited, but not nearly as limited as our knowledge. My point is that there is a lot we understand may be behind QM, without knowing how well any of those hypotheses match reality.

I'm still not really seeing your point. All of the major "interpretations" of QM match our observations of reality. People like Sean Carroll argue that "many worlds" requires the fewest assumptions but that hardly seems sufficient in this case.

Collin237 wrote:From the review by Yossarian, it sounds like Stenger is using QM to bolster an argument against religion. Alongside people like Chopra using QM in favor of religion, the total impression is of a palimpsest bandied about in the culture war.

I don't know who "Yossarian" is (apart from the Catch-22 character) but that is not an accurate representation of the book. Stenger (who was a physicist) explains why the various attempts to use QM to justify what are essentially magical claims are unsound. If a chemist similarly explained why the magical claims of homeopathy were unsound, would you see this as part of a "culture war"?

Collin237 wrote:What's missing is an accessible exposition of the ways that QM can be developed upon as a mathematical, not emotional, philosophy.

I know what the philosophy of mathematics is but I'm not sure what a "mathematical philosophy" is.
"Life is nothing but an electron looking for a place to rest" -- Albert Szent-Gyrgyi
Mon Sep 14, 2015 8:55 pm
Collin237Posts: 11Joined: Thu Sep 03, 2015 4:26 pm

Post Re: Responsible Quantum Speculation

I'm still not really seeing your point. All of the major "interpretations" of QM match our observations of reality. People like Sean Carroll argue that "many worlds" requires the fewest assumptions but that hardly seems sufficient in this case.


It's exactly this sense of "sufficiency" that I'm complaining isn't properly explained. It's possible, and arguably necessary, to make assumptions beyond the established theory while still matching observed reality, but only in very limited ways that are rarely made explicit.

If a chemist similarly explained why the magical claims of homeopathy were unsound, would you see this as part of a "culture war"?


If a chemist thought it needed any explaining at all, in a technical book about chemistry, that water mixed with nothing is the same as water with nothing added, then yes I'd think he had an axe to grind.

I know what the philosophy of mathematics is but I'm not sure what a "mathematical philosophy" is.


The articles by Philip Pearle, for example.
Mon Sep 14, 2015 10:01 pm
Dragan GlasContributorUser avatarPosts: 2959Joined: Mon Dec 14, 2009 1:55 amLocation: Ireland Gender: Male

Post Re: Responsible Quantum Speculation

Greetings,

Why do you say that a physicist or chemist debunking "quantum healing" or homoeopathy, respectively, has "an axe to grind"?

The fact is, they're simply doing what you claim you want scientists to do: explain reality, and not over-step its bounds - which is what Chopra, and his ilk, are doing.

Kindest regards,

James
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"The Word of God is the Creation we behold and it is in this Word, which no human invention can counterfeit or alter, that God speaketh universally to man."
The Age Of Reason
Tue Sep 15, 2015 8:50 am
SpecialFrogUser avatarPosts: 827Joined: Wed Jul 16, 2014 2:13 pmLocation: Great White North Gender: Tree

Post Re: Responsible Quantum Speculation

Collin, I agree with Dragan Glas. Moreover I think scientists should do more of that sort of thing and not less.

Can you give an example of the kind of Pearle article you mean? The Philip Pearle I can find has published a lot.
"Life is nothing but an electron looking for a place to rest" -- Albert Szent-Gyrgyi
Tue Sep 15, 2015 12:48 pm
Collin237Posts: 11Joined: Thu Sep 03, 2015 4:26 pm

Post Re: Responsible Quantum Speculation

Science can advance only if practiced by people skilled in innovative use of the tools of thought it's developed. Scientific thought is constrained by logic and experimental data, not by the dictates of other people.

If you just recite argumentatively why fraudsters are wrong, you don't inspire science. You inspire things like the Pope's "Laudato Si", which are facially correct but severely lacking in understanding. This will never put the fraudsters out of business; all it will do is set up a competing business whose spiel is correct as far as you've programmed it.

What's important is that people learn the overall structure of knowledge that science has found. If properly taught, then no matter how it turns through anyone's mind, it will always lead them to reject fraudsters, even if you'd disapprove of the reason why.

However, if you present a scientific theory as if you were an expert witness in court presenting an exhibit for a prosecutor, then you're misrepresenting personal understanding as communal, and intruding into the thoughts of your readers and stifling their creativity. And they'll probably fight back.

Why is this so hard for you? What part of "the truth will set you free" doesn't anyone understand anymore?!
Tue Sep 15, 2015 1:25 pm
Dragan GlasContributorUser avatarPosts: 2959Joined: Mon Dec 14, 2009 1:55 amLocation: Ireland Gender: Male

Post Re: Responsible Quantum Speculation

Greetings,

Collin237 wrote:Science can advance only if practiced by people skilled in innovative use of the tools of thought it's developed. Scientific thought is constrained by logic and experimental data, not by the dictates of other people.

If you just recite argumentatively why fraudsters are wrong, you don't inspire science. You inspire things like the Pope's "Laudato Si", which are facially correct but severely lacking in understanding. This will never put the fraudsters out of business; all it will do is set up a competing business whose spiel is correct as far as you've programmed it.

What's important is that people learn the overall structure of knowledge that science has found. If properly taught, then no matter how it turns through anyone's mind, it will always lead them to reject fraudsters, even if you'd disapprove of the reason why.

However, if you present a scientific theory as if you were an expert witness in court presenting an exhibit for a prosecutor, then you're misrepresenting personal understanding as communal, and intruding into the thoughts of your readers and stifling their creativity. And they'll probably fight back.

Why is this so hard for you? What part of "the truth will set you free" doesn't anyone understand anymore?!

With all due respect, you have a strange idea of "the truth shall set you free" if explaining something, and why fraudsters are wrong, doesn't set someone free.

You also appear to be missing the fact that there are those who've been misled already - one has first to undo this damage since they'll otherwise reject "the overall structure of knowledge that science has found". They've been told there's a creator that's responsible for everything - this makes perfect sense as a simple explanation, rather than having to think for themselves.

Kindest regards,

James
Image
"The Word of God is the Creation we behold and it is in this Word, which no human invention can counterfeit or alter, that God speaketh universally to man."
The Age Of Reason
Tue Sep 15, 2015 2:37 pm
Collin237Posts: 11Joined: Thu Sep 03, 2015 4:26 pm

Post Re: Responsible Quantum Speculation

Philip Pearle (http://cds.cern.ch/record/421060/files/0001041.pdf):
As with any modification of SQT, one expects|and hopes|for certain specially designed experiments where SQT and CSL lead to different predictions, making tests possible. For example, one such test, presently not practicable, is a two slit interference experiment with a sufficiently large bound state object. Once the two wavepackets for the object leave the slits, SQT says that their amplitudes will never change so that interference is possible at any time. CSL says that the amplitudes will fluctuate and, after a long enough wait, eventually one of the packets will become negligible in amplitude, giving no interference pattern. Such an interference experiment with e.g., 90A diameter drops of mercury over a time interval of seconds could provide such a test. However, this is a difficult experiment. For example, it is hard to prevent the two packets from being put into different angular momentum eigenstates by interaction with the environment, and then they would not interfere for this reason.


Without consulting an expert, we don't know if an argument that reasons like this is sound. But we intuit that it can be sound. Why? What distinguishes this from the things Chopra says? This intuition needs to be Socratized for the public.

There are, of course, many borderline cases. But in debating them, people who know and honestly search for sound arguments will eventually trip up the imposters, or even drive them into a fit of aporia.
Wed Sep 16, 2015 3:54 am
Collin237Posts: 11Joined: Thu Sep 03, 2015 4:26 pm

Post Re: Responsible Quantum Speculation

They've been told there's a creator that's responsible for everything - this makes perfect sense as a simple explanation, rather than having to think for themselves.


Firstly, thinking for yourself doesn't require being an atheist. Secondly, an excuse for not thinking for yourself is not necessarily a god; specifically to this thread, the Copenhagen observation process is such an excuse.

With all due respect, you have a strange idea of "the truth shall set you free" if explaining something, and why fraudsters are wrong, doesn't set someone free.


If you explain why a fraudster is wrong, then the fraudster will explain why you are wrong. It's well known that explaining, in this sense, can produce such conflicts and is therefore invalid on both sides. That's why it's rightfully mocked as "splaining".

Freedom cannot be given in battle; we should've learned that from the war in Iraq. A battle of words is no different.
Wed Sep 16, 2015 4:58 am
Dragan GlasContributorUser avatarPosts: 2959Joined: Mon Dec 14, 2009 1:55 amLocation: Ireland Gender: Male

Post Re: Responsible Quantum Speculation

Greetings,

Collin237 wrote:
They've been told there's a creator that's responsible for everything - this makes perfect sense as a simple explanation, rather than having to think for themselves.


Firstly, thinking for yourself doesn't require being an atheist. Secondly, an excuse for not thinking for yourself is not necessarily a god; specifically to this thread, the Copenhagen observation process is such an excuse.

With all due respect, you have a strange idea of "the truth shall set you free" if explaining something, and why fraudsters are wrong, doesn't set someone free.


If you explain why a fraudster is wrong, then the fraudster will explain why you are wrong. It's well known that explaining, in this sense, can produce such conflicts and is therefore invalid on both sides. That's why it's rightfully mocked as "splaining".

Freedom cannot be given in battle; we should've learned that from the war in Iraq. A battle of words is no different.

You've missed the point I was making.

In America, there are those who've sent their children to "Christian" schools where they've been taught "science" by people like Kent Hovind - who, according to his "thesis", taught science in high school for fifteen years.

Anyone familiar with his videos will know that what passes for "science" in them is confused nonsense.

To undo this takes time as they'll simply reject real science unless you undo the damage first.

You've also missed another aspect of my point when I said "explaining something, and why fraudsters are wrong" - not explaining something by explaining why fraudsters are wrong.

One is explaining science - and, en passant, why fraudsters are wrong; not just why fraudsters are wrong.

Kindest regards,

James
Image
"The Word of God is the Creation we behold and it is in this Word, which no human invention can counterfeit or alter, that God speaketh universally to man."
The Age Of Reason
Wed Sep 16, 2015 11:34 am
Collin237Posts: 11Joined: Thu Sep 03, 2015 4:26 pm

Post Re: Responsible Quantum Speculation

I agree. But that needs to be done in an educational environment and in the context of psychological intervention. It's not part of the work of the mostly isolationist ivory-tower society of the scientists that actually propose and test physical theories. And it's not at all an answer to my original post.

Furthermore, if these books are what you claim they are, they suffer from a huge PR fail. Why would anyone expect to find science in a book called "Quantum Gods: Creation, Chaos, and the Search for Cosmic Consciousness"??? :facepalm:

Anyone familiar with his videos will know that what passes for "science" in them is confused nonsense.

To undo this takes time as they'll simply reject real science unless you undo the damage first.


This doesn't make sense. Someone familiar with the videos, who knows that they're nonsense, is not damaged. People like Kent Hovind fancy themselves to be torpedo-fish, but most of their influence is just a positive-return illusion. Readers of science books deserve the respect of being considered willing and able to understand them. Those who aren't are not your problem, because how would you know who they are anyway?
Wed Sep 16, 2015 12:27 pm
he_who_is_nobodyBloggerUser avatarPosts: 3347Joined: Tue Feb 24, 2009 1:36 amLocation: Albuquerque, New Mexico Gender: Male

Post Re: Responsible Quantum Speculation

If you do not mind me asking, Collin237, but do you have the mathematical knowledge to understand what is being discussed in modern physics. I will freely admit that I do not and that is why I will defer to a consensus of experts on a subject like that. The reason I bring this up is because we recently dealt with someone on this forum that wanted to question transitional fossils and atavisms while not knowing a tibia from his asshole. Without that basic understanding of anatomy, how is one supposed to explain anything to an individual like that?

Our resident expert on physics was recently banned, but there used to be another person with equal knowledge about it that used to post here. If you would like a detailed conversation, I could send her a message and see if she would be willing to contribute to this thread. In the meantime have a read of this thread (skip everything that has to do with abelcainsbrother) and I think you might get an idea of what it actually takes to understand modern physics.
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Wed Sep 16, 2015 3:18 pm
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SpecialFrogUser avatarPosts: 827Joined: Wed Jul 16, 2014 2:13 pmLocation: Great White North Gender: Tree

Post Re: Responsible Quantum Speculation

Collin, I'm still not sure what you actually want. I've linked a good article on many worlds hypothesis and referenced a good book.

Here is a Socratic dialogue on the hidden variable hypothesis if that floats your boat.

There is a lot out there but some topics are inherently complicated.
"Life is nothing but an electron looking for a place to rest" -- Albert Szent-Gyrgyi
Wed Sep 16, 2015 4:15 pm
Dragan GlasContributorUser avatarPosts: 2959Joined: Mon Dec 14, 2009 1:55 amLocation: Ireland Gender: Male

Post Re: Responsible Quantum Speculation

Greetings,

Collin237 wrote:I agree. But that needs to be done in an educational environment and in the context of psychological intervention. It's not part of the work of the mostly isolationist ivory-tower society of the scientists that actually propose and test physical theories.

"Psychological intervention"??

You appear to be living in something of an ivory tower yourself if you think that this is how to address the issue.

Most of these people would not be found dead in an "educational environment" that teaches science - their religious beliefs and upbringing would automatically reject it.

The only way to hope to reach them is through books, magazines, TV, YouTube, etc.

Collin237 wrote:And it's not at all an answer to my original post.

It's not meant to be - you raised the issue in complaining about scientists explaining science to show why fraudsters are wrong. I attempted to addressed this.

Collin237 wrote:Furthermore, if these books are what you claim they are, they suffer from a huge PR fail. Why would anyone expect to find science in a book called "Quantum Gods: Creation, Chaos, and the Search for Cosmic Consciousness"??? :facepalm:

Why wouldn't someone interested in any of these read the book? Regardless of which side of these ideas they stand.

Why don't you read his books before you cast aspersions on them? - he's written a plethora of such for the lay-person.

The late Victor Stenger was a physicist and a university lecturer for 30+ years - who better to teach the subject to the layperson? And if scientists aren't supposed to do so - who should? Teachers - in America - who hardly seem to have a grasp of science themselves?

Collin237 wrote:
Anyone familiar with his videos will know that what passes for "science" in them is confused nonsense.

To undo this takes time as they'll simply reject real science unless you undo the damage first.

This doesn't make sense. Someone familiar with the videos, who knows that they're nonsense, is not damaged.

Again, you misunderstand.

People who've been brought up in a Christian Fundamentalist environment will lap-up Hovind's nonsense because they don't know any better.

People who know he's a charlatan and a fraud will reject his nonsense as such.

Collin237 wrote:People like Kent Hovind fancy themselves to be torpedo-fish, but most of their influence is just a positive-return illusion.

Yes - for the people who've been brought up in a Fundamentalist environment.

Collin237 wrote:Readers of science books deserve the respect of being considered willing and able to understand them.

Sure - but you still need to correct readers' misconceptions about science and reality promulgated by creationists, etc.

Collin237 wrote:Those who aren't are not your problem, because how would you know who they are anyway?

Stenger, and other authors with scientific backgrounds, are writing for those who are interested enough to find out about science and for those who might have been misled through their religious upbringing.

Again, you behave in a contrary manner.

Your original post shows you worked up about what scientists are doing - yet now say that if others aren't interested, it should be of no concern to us.

Why then are you so aerated about what others - scientists - are doing? It's their decision - not yours.

Kindest regards,

James
Image
"The Word of God is the Creation we behold and it is in this Word, which no human invention can counterfeit or alter, that God speaketh universally to man."
The Age Of Reason
Wed Sep 16, 2015 4:33 pm
Collin237Posts: 11Joined: Thu Sep 03, 2015 4:26 pm

Post Re: Responsible Quantum Speculation

If you do not mind me asking, Collin237, but do you have the mathematical knowledge to understand what is being discussed in modern physics.


I think I do have a fair amount. I would definitely like to talk to this person and learn more.
Wed Sep 16, 2015 5:09 pm
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