# Is Stephen Hawking right or not?

Discussion in 'Science & Society' started by Saint, Jun 16, 2011.

1. ### Pincho PaxtonBannedBanned

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You ignore the fact that you are the only person calling a sphere a set of calculations. I am using points to make my sphere, and they are all the scale of 6. My theory is propagated... remember? You seem to think that you can use your own words as proof at a later date of something that actually happened. Your own words are not proof of anything. I keep telling you to look up the Aether and propagation. Anything propagated doesn't use the normal maths of vectors. It's a grain structure theory.

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3. ### ReikuBannedBanned

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First, off, I don't need to qoute anyone else. Just for the plain fact that you jumped in here and yet again flung an accusation about without knowing the full story. Keep it up, in fact I beg you to. The more times you do this, the more people will begin to not even take your own sentances at face value any more. That's what happens when someone lies all the time like you do.

Secondly, it predicts the number of possible false vacua and it can refer to other universes, a multiverse if you will, but you know this and you are trying to overcomplicate things. All one needs to know is that our universe fits the laws of atleast one of the universes; there maybe more exotic universes which fit this landscape, though I highly doubt it because string theory is a load of rubbish.

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5. ### wlminexBannedBanned

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AN Post: "“ Originally Posted by wlminex
. might this structure be incorporated into string theory topology? . . . . or, perhaps how to agglomerate quarks via gluons? . ”

Do you deliberately just throw out words you don't know the meaning of or do you think you're actually forming coherent sentences?

ANS: perhaps not coherent sentences to you . . . . but, coherent 'thoughts' to me.

AN Post:
“ Originally Posted by wlminex
. . . Remember . . . It will take ALL OF US . . . . to root-out the 'true' scientific truths . . . this includes Pincho, Farsight, AN, Origin, Stonphi, AlexG, etc. . . . yes . . . and even ME! It's NOT a 'pissing' match to see who is the worthier, most educated, most intelligent, etc., etc. . . . EVERYONE has an ante in this game (and it's NOT strip-poker <--humor here)!! Re: "Civility, Please!" thread ”

AN: "If you think people like Pincho and Farsight have anything to contribute then you only demonstrate how little you grasp how science is done. When someone, such as Pincho, is deliberately dishonest then it completely removes them from contributing to anything scientific. Even if he were to occasionally say something worth listening to (which hasn't happened yet) it would be lost in the noise. That's part of the problem with exaggerating claims to the point of being ridiculous, no one will listen to you after that even if you have something worthwhile to say. "

ANS: . . . Ah, Shucks AN! . . . and I EVEN included you in my "list" . . . . !!

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7. ### AlphaNumericFully ionizedModerator

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Firstly I don't call a sphere a set of calculations. Secondly you're forgetting I've already walked you through the explanation of why something as simple as checking if two spheres intersect actually uses a lot of mathematics. Since you've forgotten, again, I'll explain it again.

You admit you use points. What are points? They are elements in a vector space. For example 1d circles are spheres in 2d. Their centres are defined by two coordinates (x,y). This requires the construction of an affine space. It requires the notion of sets and then ways of combining elements of the set in question, ie (x,y) + (a,b) = (x+a,y+b). It also requires the notion of a field and the definition of how that field acts on elements of the set, k(x,y) = (kx,ky). So we've already needed sets, arithmetic to construct a number field (and any mathematical system which can do arithmetic is sufficient complicated to fall under the remit of Godel's work, which demonstrates how far from trivial all of this is) and then upgraded them all to form an affine space.

So that's just the notion of points. Then you consider spheres, which are all those points equidistant from the central point. So you need to have a definition of distance. Thus the affine space must be upgraded to a normed space, a vector space (which is an affine space with the notion of an origin) with a norm defined on it. A norm is something which measures the length of a vector. The most familiar norm is the Euclidean norm, $||(x,y)|| = \sqrt{x^{2}+y^{2}}$. But there's infinitely many norms, such as the 1-forn $||(x,y)|| = |x|+|y|$ or the infinity-norm $||(x,y)|| = max(|x|,|y|)$ or the general p-norm $||(x,y)|| = (|x|^{p}+|y|^{p})^{\frac{1}{p}}$. Which norm you pick determines the shape of your 'spheres'. Here's a picture of the 'spheres' of the 1, 2 and infinity norms I just gave

Please Register or Log in to view the hidden image!

Clearly the way in which spheres intersect depends on their shape and thus their norm. You've assumed Euclidean structure, which is not only a massive assumption but one we actually know not to be true as general relativity uses an even more elaborate concept, that of a metric, which induces a norm on space-time, and which isn't the 2-norm everywhere.

So to even build a single sphere formally you've had to use a lot of mathematical concepts. You've made the mistake of thinking that there's little or no formal mathematics behind the stuff you might have learnt in school. That's the sort of mistake someone very unfamiliar with mathematics would make. In school you're told results without proof but that doesn't mean the use of such things isn't assuming the formal mathrmatics underneath.

So what about intersecting spheres? Well you to know if some point is close enough to another point. So you use your norm to compute the distance between the two points in question, $d(\mathbf{X},\mathbf{Y}) \equiv ||\mathbf{X}-\mathbf{Y}||_{2}$ in the Euclidean case, which will be some number in a field (not necessarily the same one the affine space was defined using, so another assumption!), typically the Reals. You consider the spheres to intersect if this number, call it distance d, is less than some amount, call it A. Except the use of < implies you're working in, at the very least, a partially ordered field. A field is not automatically a partially ordered field, it's just a set with binary operations defined on it in a particular way. To make it ordered you need to define an equivalence relation on it with particular properties. Then you end up with the ability to see if two spheres intersect.

So doing something as simple as getting a computer to construct some spheres using some coordinates and then see if they intersect is to implicitly assume all of that mathematics is valid. So your claim you do everything only assuming 1+(-1)=0 is not only wrong, it's demonstrably wrong. And now this is the second or third time I've explained it to you.

Sorry but to even define spheres you need to assume a lot of mathematics. To then have them move about, to have them propogate, involves vectors. If a point is at (x,y) and moves by an about (a,b) then it'll be at (x+a,y+b). That is a vector space structure. If you code coordinate combinations like that into your computer than you've implicitly assumed vector space properties.

Your response, aside from being hardly coherent, doesn't retort anything I've said to you (on multiple occasions). You're just showing you don't know how little you know.

8. ### AlphaNumericFully ionizedModerator

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Find me a published paper in a reputable journal.

You misused the $10^{500}$ number and you haven't provided anything but a pop science reference by someone known to have wacky ideas.

You're projecting again.

Says the guy who includes spin algebras in a book he is writing for 15 year olds!

I wasn't overcomplicating things, I was clarifying it. If I wanted to go needlessly into detail to overcomplicate things I could have explained how non-perturbative dualities in string theory actually vastly reduce that number, if you were to view them in a multiverse context, because many of them are physically equivalent. I could have explained how it's possible to apply, as it happens, spin algebras to construct huge families of such vacua all of which are equivalent. I could have gone into my own research because that's precisely what I did work in. But instead I didn't mention any of that, even to point out I've worked in string vacuum physics and Wolf hasn't. I didn't play the credentials card, I just asked if you had something viable to back up your claim. And you provided a pop science reference.

You need to realise that while you might be operating at or beyond your comfort level in discussions like this I'm not. If I wanted to overcomplicate it I'd make the stuff in our little discussion on the Dirac equation look like childs play.

I like how you simultaneously argue that my comments about the string vacua were wrong but also turn around to say nothing pertaining to it can really be trusted because you think string theory is a load of rubbish.

Now, seeing as you are currently going through a spate of watching Susskind lectures and then mangling them when you parrot them here I'll be helpful and suggest this paper by him from almost 10 years ago. It's about as layperson an overview of string cosmology as you're going to find. It explains the role possible multiple vacua play in string cosmology, including via some Penrose diagrams. To help you along I'll summarise it; within a single universe it's possible to have many different regions defined by different vacua, which have different physical properties/constants. Moving through space would move through these different regions, which are separated by rapidly changing physical properties, large domain walls. Due to particular properties of default empty de-Sitter space-time (ie empty universe with a cosmological constant which causes it to undergo accelerating expansion) such regions can 'bubble out' by the moduli running down from the unstable configuration to a different vacuum.

That is the role the landscape plays in string theory. People studying compact spaces find the mathematical structure of the moduli (how many there are, their relationships/interactions, equations of motion, constraints, physical meaning) for a given compact space. The cosmologists then simplify much of that down based on physical constraints (and often because the full equations are staggeringly huge), run the model using initial conditions/properties from observations and see how both the compact space behaves and the implications that has for the open dimensions (ie the ones we see). Inflation, power spectrum, reheating, dark energy content, Hubble constant, amount of supersymmetry and it's breaking scale. Hell you can even start tying in GUT models and extensions to the Standard Model and seeing the implications for things like the fine structure constant or the electroweak symmetry breaking scale. It's one of the few models which ties together cosmology, gravity and quantum field theory and runs from the early universe through to now and can make statements about all of those areas.

But hey, what do I know :shrug:

9. ### Pincho PaxtonBannedBanned

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That is completely wrong. You have used memorized theory. Forget all that, I have broken it down. All you need is the number 6 to do everything in your example. You have cheated, and created a mathematical formula that does everything in an add-hock way. If everything is 6, and you use the kissing problem a radius is 18, the halfway point is 0. Rebound angles are mirror particles, Time is +6, cold temperature is -6, propagation is 6, waves are 0,6,9,12,9,6,0, symmetry is 6 in 2D, 12 in 3D, dimensions are 0,3,6,12. And Chaos is 13..etc... PROPAGATION. But even better still, you never need the calculations, because you deal with 1 particle at a time, so you always use the number 6. The 18 radius in my example would be too hard for the Universe. So you see.. even simple maths skills are cheating.

Last edited: Jan 15, 2012
10. ### AlphaNumericFully ionizedModerator

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I find your choice of word interesting. 'Memorised' is usually used to imply learning something parrot fashion rather than properly understanding and seeing something in context. In that sense I didn't memorise this stuff, I learnt and understood it. Perhaps your choice of word says something about how you 'learn' anything related to science (what little you have learnt).

I'm now getting the sense you're just trolling. You've gone from +1+(-1)=0 to just the number 6? Are you attempting to see how ridiculous (and it is ridiculous, ie worthy of ridicule) a claim you can make before even people like wlminex begin to question whether you're a few sandwiches short of a picnic?

If you do anything with the number 6, be it add, subtract, divide, equate it to something, then you've assumed more than that. In fact, to even define 6 you have to assume other things. I don't even need to go into the same level of detail as my last reply to you, your claim is just that obviously flawed.

Firstly it's 'ad-hoc'. Secondly I have clearly demonstrated the opposite of ad hoc, a rigorous consideration of every assumption and then a logical construction of the relevant structures. All of the details can be found in books. As I told you once before (which you again forget) when one of the greatest pure mathematicians ever set about writing a full derivation of arithmetic from the core tautologies of logic it took 360+ pages to get to 1+1=2. That is considering everything, nothing was ad hoc.

Your method is.... well it's something you can't demonstrate and in fact is so stupid I can only assume you're deliberately trolling because the alternative is you're actually mentally impaired in some way, that you are not entirely in touch with reality.

As such I'm going to assume you're trolling and my post will be aimed at other readers who might be interested in the many ways your claims are obviously false. You obviously don't want to or are incapable of understanding even child level concepts or logic.

Kissing problem implies points and spheres in space, which assumes all the stuff I listed. You can't even define the kissing problem unless you have defined spheres and positions in a vector space, ie all the stuff I covered in my last post. And if you have notions of 18 and 0 then you have assumed basic arithmetic.

When you say "Starting with 6 I can get..." what you mean "I start with the number 6 and input it into some situation or do something to it". To do something to 6, like add or multiply etc you're assuming arithmetic. To say "I consider 6 spheres" then you assume all of that stuff about spheres. Even +1+(-1)=0 assumes arithmetic. Negative numbers are a sufficiently advanced concept many ancient cultures never developed it and you're assuming it! Even 1+1=2, so 1+1+1=3 etc assumes a lot. It requires the Peano axioms and anything that contains them is sufficiently powerful to fall under the scope of Godel's work on incompleteness. There exist simpler systems of logic which don't have Godel's work apply to them but they cannot even count!

You contradict yourself by using simple mathematics! You are doing something involving simple counting, that's mathematics. As for the claims themselves, they are so laughable you must be trolling.

11. ### ReikuBannedBanned

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Right, I am going to warn you once, as a friendly contributer to this site, I won't put up with your stalkerlike behaviour. Your attitude is a clear defense of why I would even block you if this continues, because I don't need to convince anyone you have forgotten your recent knight Hood and continued to act like the selfish and yet simultaneously childish poster you were like even before you got your new position.

I would certainly think, maybe no one else(?) that you might have became a little bit more humble over the passing few months. Instead you have revelled in the fact I have posted about physics, which you will usually try and find any good reason to refute.

I will block you, I promise, if I see another post like this trying to condescend me,

12. ### ReikuBannedBanned

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And potential universes are constructed from a maxima and minima of possibilities governed by the wave function which are the state vectors which govern the condition of your measurable. This is analagous to stating in string theory that you have some number of universes which pertain to a small quantum difference each time; this is why the Anthropic Principle is important for this understanding of string theory, not that I actually agree with it.

13. ### AlphaNumericFully ionizedModerator

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Get over yourself. You reply to plenty of threads I don't reply to and I reply to plenty of threads you're not in. This thread is about Stephen Hawking and the string landscape is something I did research in. Me having something to say about it is perfectly reasonable.

You come here and spew out a load of stuff about high level quantum field theory and you're surprised when someone who knows about quantum field theory replies? You clearly want attention but only from people who can't point out your mistakes. And when people do lay it all out for you, as my last post did your tendency is to quote large chunks of it and then just avoid responding to it. Do you admit that the vacua in string theory are not used in the same sense as a multiverse? And you failed to provide a published paper on the subject, you quoted me asking you but you didn't respond. That's typical behaviour from you, you did it multiple times in the recent Dirac and Lagrangian discussions. As you so often like to point out, others can read these exchanges and I'm sure I'm not the only one to notice your tendency to do that.

I like how you try to present it as if I'm nit picking, when some of the mistakes you've made demonstrate you have been completely dishonest about your level of knowledge. You don't know the motivation/construction of the Dirac equation, despite claiming to be knowledgeable on it. You don't know the first thing about Lagrangian mechanics, despite it being required knowledge for the Dirac equation. These aren't small problems, they are fundamental gaping holes.

I like quantum field theory and string theory. It's literally been my job. You come here and spew out nonsense and a large chunk of the time it's in those areas and you're surprised I reply? If you don't want physicists replying to your physics threads don't come to a physics forum. I don't reply to your non-physics threads, I don't even read them (I see your name on the main page in other subforums). You clearly want people to talk about the Dirac equation or Lagrangian mechanics with you so long as they don't point out error after error.

I might be abrasive with you but that's because you perpetually do this. Now you've basically admitted to having no experience with Lagrangian mechanics beyond a single Susskind video you should dial down your claims about understanding stuff which requires an understanding of Lagrangian mechanics, including quantum field theory. Of course when you don't you'll just be demonstrating dishonesty, again, and I'll have reason not to give you any benefit of the doubt (though you ran out of that years ago). Plenty of other people said this about you when you kicked up a fuss in the government forum, that if you were a little more realistic about what you do and don't know you'd be held in slightly higher regard. I have plenty of time for someone who knows little but honestly wants to learn. I have no patience at all for someone who knows little but is dishonest and tries to pretend otherwise, despite being caught in his web of lies time and again. If you grasped all of this stuff properly and had the capacity to properly accept corrections you'd be able to deal with my replies much better than you do and then we might develop a rapport. Instead you act now as you did 4 or 5 years ago and you wonder why people have no patience for your nonsense?!

Then you'll just miss my lengthy rebuttals and demonstration of your dishonesty next time you start up another thread like the Dirac equation one. Doesn't bother me in the slightest. Rather than sticking your fingers in your ears you could just answer questions honestly and show some understanding. The whole hissy fit mentality you have says a lot.

Last edited: Jan 15, 2012
14. ### universaldistressExtravagantly Introverted ...Valued Senior Member

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High AlphaNumeric

I write science fiction. And as such I am always looking out for outside-the-box thinking/directions.
Could you elaborate on the quoted sentence for me please? I would ask Reiku but after having read your last post that would be pointless.

15. ### ReikuBannedBanned

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I'd understand you'd want his opinion because he is a string theorist. Admittedly, the true definition of a Parallel universe in string theory are called D-branes. My point was that ''possible'' false vacua take on the appearance of the landscape. Each landscape is qualitatively different, so I don't see how this is any different to the idea that each universe takes on different quantum values in the many worlds interpretation. What is to say that many of these false vacua simply just purport to other physical limits and conditions that other universes are in?

There are parallel universes for instance, for those who wish to believe in them, which should in theory match every type of the possible vacua in string landscape.

As I said, he is the string theorist. I hate the theory with a passion.

16. ### ReikuBannedBanned

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The many worlds and landscape, including branes are almost never confused in physics. If the landscape and the parallel universe model's are so different, I would like to know what makes them such, because I don't see a reason.

What would be different therego, in choosing one ''branch'' (or possible vacua from a landscape) to finding the same conditions to a universe which exists in the MW/parallel universe model?

Maybe AN could enlighten us all.

17. ### ReikuBannedBanned

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However, interestingly, AN seems to admit that these vacua might purport to reality, I think he is saying not all of them would be for real

''I wasn't overcomplicating things, I was clarifying it. If I wanted to go needlessly into detail to overcomplicate things I could have explained how non-perturbative dualities in string theory actually vastly reduce that number, if you were to view them in a multiverse context.''

I'd like to know why. 10^500 is a large number indeed, but it is not as large found in parallel universes. In fact, I remember reading work not related to a string theory that all one needs is 10^100 universes in any theory... i will try and find that if you want - it was one of the early pioneers of parallel universe, probably Bryce deWitt.

I still don't see why 10^500 universe could be possible but why not all would appear. No doubt AN eludes to some mathematical reasoning. I'd like to hear it.

18. ### ReikuBannedBanned

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''You clearly want people to talk about the Dirac equation or Lagrangian mechanics with you so long as they don't point out error after error. ''

You're such a drama queen AN. You forget I had to write all that literature, write all that latex, even after you codedly pointed out to ''errors'' I still had the knowledge to calculate where the error lay. And you make it sound like I made loads of them, I made a few, and one of them was clearly a matter of how I wrote the matrix down, it wasn't a mistake as such.

And guess what folks, not only did he point an error to me, I was still smart enough to realize it was actually his error. He fantastically mixed up his vector and scalar notation then had the cheek to say it was my error. Oh the irony, don't you think! And so much for his claims saying I don't know what I am doing, yet I was still able to point out a poor error of his! LOL

19. ### AlphaNumericFully ionizedModerator

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The string landscape, as the paper by Susskind I linked to describes, allows for many different 'base' configurations of curled up dimensions in space-time. It's possible that our region of space-time has one configuration but somewhere else in the universe there's another configuration. And another, and another and another. These different configuration regions can vary in size, grow and shrink. Our current vacuum could tunnel to another vacuum state right now, right here, but it's very unlikely. The concept of different vacuum configurations isn't unique to string theory, the entire Higgs mechanism is based on a similar principle.

Here we have various constants to do with charges and masses. Elsewhere all of these things might change because they are not 'fundamental', they are just values which satisfy a bunch of more fundamental equations in string theory. Much like the Higgs field vacuum sets the masses of W and Z bosons different string vacuums can set masses of something like the electron!

In some cases different vacua look different, ie different electron masses etc but they are actually entirely equivalent. This pertains to dualities in string vacua called T, S and U dualities.

Didn't you understand the paper by Susskind?

You misrepresent what I'm saying because you do not understand. T, S and U dualities in string theory allow you to construct sets of string vacua with completely different values for things but are entirely equivalent. The simplest case is T duality. Type IIA string theory defined on a space-time with a circular dimension of radius R is entirely equivalent to a Type IIB string theory defined on a similar space-time but with radius 1/R. S duality allows you to change the coupling constants of theories. U duality.... well let's just say it's complicated.

Different vacua doesn't automatically mean different physics.

So you're throwing around the $10^{500}$ number and don't even know where it's from?

People have written computer programs which will combine equations, write text, even automatically make entire fake papers with equations and diagrams! Doesn't mean the program understands physics. Being a gloried photocopier doesn't mean you understand what you're talking about.

And you did make loads of them. Deep, essential, fundamental ones. And you've been doing it for years and years.

I was listing the things you'd gotten the tensor structure wrong of and included an extra thing in the list accidentally. You however made lengthy errors, so far as showing you didn't even understand the equations you were posting. No one would reasonable claim I don't know period is a scalar. You on the other hand I would reasonably be able to state, with plenty of evidence, do not know the material of which you speak.

Your repeated mistakes demonstrate you don't know what you're talking about. I made a single small actual error. Your mistakes are orders of magnitude worse because you don't acknowledge you don't know the stuff of which you speak.

Pretty much every post you made about Lagrangians or the Dirac equation you filled with mistakes. Some of them deep conceptuals ones about the entire motivation and origin of the Dirac equation, despite claiming you know plenty about it. Now your discussion with JamesR is basically amounting to you admitting the totality of your knowledge about Lagrangians comes from a single YouTube video. Considering you've been claiming to understand the Dirac equation for a long time you've completely contradicted yourself. Lagrangian mechanics is required knowledge for the Dirac equation, so if you don't know the first you can't grasp the second. You don't know basic matrix algebra. You can't work with spinors. You can't answer simple relevant questions for reasons which boil down to "Susskind doesn't answer it in the YouTube video I am copying this from!". There's completely different from my little slip up of including $\omega$ in a list of non-scalar objects in reference to coefficients in the Fourier transform of the Dirac equation (by the way, $\omega$ is regularly used as a component of a spinor in the Dirac equation so it's not like you're using unique notation either). It was in a post, which I'll happily link to if you wish, where I lay out, in detail, your conceptual and mathematical glaring mistakes and demonstrate a working understanding of the material. Not once have you demonstrated that with the Dirac equation or Lagrangian mechanics.

You talk about 'drama queen' but you're the guy who lies repeatedly and when he's kicked off the forum for wasting people's time comes back with sock accounts and threatens to 'cause problems'. You really need to look at yourself a little and stop projecting. Well, that and learning to use the edit button. Your post could would be 1/3 of what it is if you just learnt to compile your thoughts into single posts rather than machine gunning out 3~8 posts in a row all the time.

20. ### ReikuBannedBanned

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What paper by Susskind, have I missed something AN?

21. ### ReikuBannedBanned

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And leave the accusations and ''who makes the most mistakes'' out of this. You aren't impervious to them yourself and quite obviously capable of making silly one's yourself, despite what you say to me. Otherwise, you'd be a hypocrite.

edit

''You however made lengthy errors, ''

No I didn't. You wanna know what I did with those matrices, I copied the alpha matrix latex without changing the interior. That does not mean I made lengthly mistakes, you only made it lengthly because you made it so, with superfluous amounts of demonstrations not required. Remember when I said you made a mountain out of a molehill when I calculated the mistake for myself?

Your such a ******** drama queen it is unbelievable, I'd be surprised if no one is sick of hearing of you whining about me, like I am.

22. ### AlphaNumericFully ionizedModerator

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You don't seem to be understanding the difference between an honest slip up (ie I know frequency is a scalar) and completely misrepresenting your knowledge by essentially incorrectly copying down stuff other people say and pretending you understand it.

The error I made was a single one in an otherwise lengthy series of large posts outline, in mathematical detail, all the flaws in your posts. I spontaneously demonstrated a working understanding, you couldn't answer any question not already answered by the YouTube video.

Demonstrably false. Demonstrated false.

As I explained at length your mistakes were numerous and deep, both in terms of understanding the mathematics and understanding the concepts.

You had previously claimed to be knowledgeable in the Dirac equation and you didn't even know Dirac's original motivation.

Firstly it is you're, not your. Secondly I am not being a drama queen since I'm not making a drama out of it. I'm highlighting your dishonesty and mistakes. If you could accept correction in a mature manner our interactions would be entirely cordial. Thirdly I hardly think you're in a position to call anyone that given your love of running to the Open Government forum to complain. Not to mention your threats to cause trouble for the forum when you were banned. Hardly the actions of someone taking the moral high ground.

As for always hearing about your posts from me, I've told you plenty of time I'll stop pointing out all the problems in your posts when you stop making them. If you can demonstrate the understanding/knowledge you claim to have then I'd back off. I don't have any issues with people like Rpenner or Guest, they demonstrate they understand what they talk about. You parrot YouTube videos and can't answer simple questions. I keep giving you opportunities but you never[/] step up. And to be clear, I have no problems with people who are less familiar with a topic than me, it's your dishonesty which bugs me.

As for the paper I was referring to, I recently linked to a paper on the string landscape by Susskind in reply to a post of yours. I distinctly remember summarising its main points for you and someone else who'd asked. Didn't you read it? I can't say I'm surprised.....

23. ### brucepValued Senior Member

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Thanks for linking the Susskind paper.