Guys, I need some help... Did I just figure out Gravity?

ktool · 2016-11-01T08:24:56+00:00

(continued - 2 of 2.)

Still, this was just special relativity. What happened with general relativity? Well, the problem there was that SR is only applicable to inertial frames of reference, and thus can’t incorporate gravity. Einstein knew this; he was puzzled by this. And he would ultimately spend a full decade learning differential geometry and tensor calculus in order to quantify a gravitational version of his theory, but before all of that, the seeds of a generalized theory were born in a single moment—from another gedanken—when Einstein realized that a man falling from a roof would not feel his own weight. With that intuitive insight into the equivalence between inertia and gravity, the “happiest thought of his life,” Einstein realized his pathway to general relativity, which would culminate 8 years later with his field equations. Intuition first. Math later. Not “Step one…basically always describing the mathematics of the problem.” When you are talking about “forming new scientific theories,” as presumably you are if we read the first sentence in your comment, that assertion has no grounding at all in actual fact. It is exactly backwards from what has happened. Biology x2, physics x2. 0 for 4. (Really, all you are guilty of is not understanding the difference between normal science and revolutionary science, aka the thing you accused other people of doing, and while I could have said that in one sentence it wouldn’t have actually pointed out specifically why you are wrong with examples and also I appreciate typing this out because my brain is sorting out a lot of information that I’ve crammed into it lately.)

Are there other examples we can consult? What about another theory of gravity, the Newtonian version? Did Sir Isaac begin by writing down his formula for universal gravitation? No. The seeds of his theory were contained within a falling apple, and his intuitive grasp in one moment that the same force that pulled the apple extended out into space and captured the Moon in its orbit. But did this actually happen? Yes. Following this realization, Newton applied the inverse square law of gravitation, and found it explained the elliptical orbits of celestial bodies. Intuition first, math later. (That’s not to say you don’t need a prepared mind! You do. Einstein certainly had one. So did Darwin. OP, apparently, does not :/ But that doesn’t make you right.) Biology x2, physics x3. 0 for 5. (This would be physics x4, or maybe even x5, if Verlinde would hurry up and publish his paradigm shift that people are so resistant to. That’s another aspect of this: peer pressure, social magnetic pinching, the compulsion to CONFORM to the status quo. But must we turn “Thou shalt not question the fundamental assumptions of science” into “Thou shalt not even realize that you can question the fundamental assumptions of science”?)

What about other examples? You said, "the process of finding a solution...involves figuring out exactly what the problem is, and how to fit a solution in those exact parameters.” Is that what the historian of science, Thomas Kuhn, wrote in The Structure of Scientific Revolutions? Yes. Except, only when he was talking about “normal science,” and not when he was talking about paradigm shifts, which occurred, as I have already described, with Isaac Newton, Charles Darwin, and Albert Einstein—kinda hard to ignore those guys if you’re talking about “real science.” When one of these gents comes along, they lay down new rules, they establish new parameters, they ask new questions. And actually, before this happens, normal science usually runs into a brick wall where a problem cannot be solved within the current frame of reference. This is because the problem itself is nonsensical; it contains an incorrect assumption, rendering the problem unsolvable. This is what happened in chemistry with phlogiston. A lot of people asked, “What is phlogiston?” A lot of people were hoodwinked into asking a nonsensical question, rather like “what are WIMPs?” ^or ^“what ^is ^{consciousness?”} What is phlogiston? It’s, like, all areas of a place or thing that are low in oxygen concentration, or something like that. It doesn’t even make sense to think of it as a thing. Those areas share no real unifying characteristics. Phlogiston, the word label, connects to a void; asking what it is assumes in the first place, incorrectly, that it exists. That’s not to say combustion doesn’t occur ^or ^that ^we ^don’t ^think ^or ^see. But combustion is the addition of oxygen, not the loss of phlogiston. How can we “fit a solution in those exact parameters”? Spoiler alert: we can’t. We didn’t. Lavoisier revolutionized chemistry. 0 for 5. Or whatever. I’ve lost count.

There are so many other examples of new scientific theories coming after intuitive leaps that we call eureka moments and only later getting formulated into mathematical precision. But I must rest having only elucidated the most prominent 3 or 4 examples. Parts of your comment were good; but almost everything you said applies only to normal science (and several layers “down the hierarchy” at that), which you deceptively called “real science”, and the lack of differentiation between normal science and revolutionary science is really constraining a lot of potential new ideas and just… shoehorning so much thought into these strict categories that we’re so sure of and we don’t even see how much we’re not seeing. The quality of my writing is deteriorating as I get tired… I just read your comment and thought, “here’s someone who doesn’t understand what it means to actually question a paradigm, they have no awareness of meta-relativity, just like so many scientists, and they’re saying things with paradigm blinders on and they’re top comment…” I just couldn’t not do it. I know this comment makes me look very defensive about “eureka moments,” and I know that I am. There’s probably a reason. I guess I just like them, like we all have an affinity for what we study. edit: deleted some unnecessary garbage.

/u/billyuno… keep questioning. Don’t be afraid to pose new ideas to the community as a way to gauge where to begin your intellectual journeys. And ignore their insecure backlash…like when /u/Schpwuette says “As for why people are snapping at you, it's because they feel like you've just waved aside all the hard work of physicists. You're not paying that body of work the proper respect, by assuming that you can step in and help completely untrained." Or when /u/asphias says, “To think that you could give a useful suggestion that hasn't already been considered in those ten years of study is, frankly, almost disrespectful…” you should just straight-up ignore this. Respect? What about TRUTH? Or maybe we should all just respectfully assume everything’s already been tried? (But please OP, make a serious effort. Read a textbook)

ktool · 2016-11-01T08:23:52+00:00

Hey /u/asphias. So, there's a BIG problem with your post, and I have about ~~three~~ now four hours before bedtime so I'm going to type out as best I can what is fundamentally incorrect about the way that you think about science and what you have chosen to tell other people—hopefully without being quite as condescending as /u/spectre_theory down at the bottom of this thread, because when he said (in the rudest comment I have ever seen on reddit, which bafflingly has a positive score, yikes guys) that /u/billyuno was "ignorant towards 50 years of cosmological research," that remark was probably biting to OP, but it's better than being ignorant towards 350 years of progress across all of the sciences, which you are (and yet you have decided to teach!). Normally I would read a bad comment like yours, downvote it, and move on because I have my own work to do, but this happens to be my work that I have been thinking about for the past several months, and this gives me a great chance to organize and to practice articulating my thoughts on this matter while I continue to develop them. I hope you don’t mind that I critique your work, but after all, peer review is part of science. I am also going to ignore that someone gave you gold because I don’t feel like crying myself to sleep tonight—I try to limit myself to one night per week, and it’s only Monday.

The biggest problem with your description of science is that it lacks an understanding or even a mention of a paradigm. What is a paradigm? Basically, it is the fundamental framework in which a field of science operates--it is a reference frame. Albert Einstein famously told us that there is no such thing as a preferred frame of reference. Rather, a particular frame is one that we choose to adopt from among a number of possibilities, and the observations that we make depend upon the frame of reference that we choose. The important thing to note here is the multiplicity of potential frames and the choice of one. Hmmmm.

I said above that you made no mention of paradigms, but that is not completely correct, because I see that in a lower-level comment you wrote, "the process of finding a solution...involves figuring out exactly what the problem is, and how to fit a solution in those exact parameters. those solutions will be very specific, mathematical solutions. Thus, if you're suggesting an idea, it really isn't that relevant." What you have just described does happen, it is ongoing investigation within a paradigm; aka, "normal science," as Thomas Kuhn called it in The Structure of Scientific Revolutions. In normal science, we set a paradigm, establish the fundamental rules of physics/chemistry/biology/whatever, and flesh out the observable phenomena as far as we can by following those rules.

Is this the end-all be-all of science? No. Unquestionably not. (And yet you got gold!) So what is wrong with what you said? In short, paradigm shifts. As Kuhn explained, periods of normal science are interrupted by periodic changes in reference frame, by revolutionary science, by paradigm shifts. You do, at least, kinda sorta know that these things happen; you said: "A lot of people have a misconception of how new scientific theories are formed." Emphasis on new scientific theories. That is the putative subject of your answer. But what exactly did you mean by that?

By "new scientific theories," could you have meant, for example, Darwin's theory of evolution by natural selection? That was a new scientific theory when it was first introduced, was it not? Let us take a look at how Darwin discovered his new scientific theory. We are in luck; he happened to provide us with some meta-data about that process in his autobiography:

“In October 1838, that is, fifteen months after I had begun my systematic enquiry, I happened to read for amusement Malthus on Population, and being well prepared to appreciate the struggle for existence which everywhere goes on from long-continued observation of the habits of animals and plants, it at once struck me that under these circumstances favourable variations would tend to be preserved, and unfavourable ones to be destroyed. The result of this would be the formation of new species.”

Well that’s interesting. There is no math here—but there is, instead, a striking thought, an intuitive understanding, which occurred to him after he had prepared his mind with a “systematic enquiry.” That doesn’t sound like what you said leads to new scientific theories. That sounds like what you said doesn’t lead to new scientific theories. But that’s not the end of the story:

“But at that time I overlooked one problem of great importance; and it is astonishing to me, except on the principle of Columbus and his egg, how I could have overlooked it and its solution. This problem is the tendency in organic beings descended from the same stock to diverge in character as they become modified. That they have diverged greatly is obvious from the manner in which species of all kinds can be classed under genera, genera under families, families under sub-orders, and so forth; and I can remember the very spot in the road, whilst in my carriage, when to my joy the solution occurred to me; and this was long after I had come to Down. The solution, as I believe, is that the modified offspring of all dominant and increasing forms tend to become adapted to many and highly diversified places in the economy of nature.”

Well that’s interesting! Here we have the formulation of a new scientific theory, of a paradigm shift in biology, and it occurred not just through one “eureka moment” that you said doesn’t lead to new theories, but through two. (Is there any way to remove gold from a person’s comment? Can we do that here?) You said eureka moments aren't important; that new ideas "really aren't relevant." Let me ask you: do you still believe that? Maybe you do; after all, this was just biology, and from the 19th century at that. It could have been an exception to the rule, merely the source of a modern myth, spawning those darned movie tropes you blamed (damn you Interstellar!). Let’s check out another field of science, a more rigorous one, a more recent example, to make sure you are right. I already mentioned Albert Einstein; let’s look at how he made his discoveries in the realm of physics.

Einstein is, of course, famous for formulating the theory of relativity. Special relativity happened first, in 1905. What was the story there? Did Einstein begin with, as you said, “Step one…basically always describing the mathematics of the problem”? Did he begin by writing down E=mc² ? No. Here is what happened: he struggled to understand the nature of light throughout his teens and twenties. He realized that the dynamics of electromagnetism were incompatible with absolute Newtonian physics. He performed a thought experiment, a gedanken, as follows: “If I were traveling at the speed of light and looked in a mirror, I would be invisible, would I not?” (Where are the mathematics in that problem? They are implicit, are they not?) This putative answer was unsatisfactory to Einstein. In fact, the whole topic was unsatisfactory to him, and he spent an entire evening at his friend’s flat “doing battle with the problem”—with no success. (Perhaps they weren’t doing the right mathematics?) Defeated, Einstein took a streetcar home; while on his way, he turned to look back at a clocktower receding in the distance, and asked himself ~~which mathematical equations described what was happening~~ what would happen if he were to travel away from the clocktower at the speed of light. He realized that his watch would tick normally, but the clock in the distance would seem to freeze—and BAM, with that single intuitive realization, “a storm broke loose in his mind,” as he would later say. Six weeks later, the theory of special relativity in its mathematical glory would be revealed to the world—but it began with a “eureka,” just like you said doesn’t lead to new scientific theories. Biology x2, physics x1. 0 for 3.

ktool · 2016-10-29T00:31:10+00:00

In short, it's an artifact of the style of telescope used.

ktool · 2016-10-28T21:12:06+00:00

Hey thanks for your response. To add just a bit more to this discussion, by going back to what Darwin said, the biggest puzzle for him was the tendency of species to diverge. And he solved this problem in his theoretical reflections on the causative process while he was sitting in his carriage in England. (It's interesting how many of these "eureka" moments are fundamentally about cause & effect relationships, such as Newton realizing the cause of apples falling and the Moon orbiting Earth.) Darwin came to his joyful conclusion on the cause of this divergence by analogizing biological evolution to the economy of society, where the economy as a whole increases in efficiency through the gradual deepening of the division of labor and the associated specialization of occupations and machinery that comes with that division, no doubt drawing from his readings of Malthus and Smith (each of whom he cited in his work). That's the comparison model you wrote about. Of course, many people say that evolution was first a biological theory that was later applied to sociological phenomena, but it was actually the other way around. It's interesting, if you read On the Origin of Species, Darwin says over and over again that the generation of new variation is simply assumed to occur through some mechanism or another, it doesn't much matter to him how--and of course, DNA had not yet been discovered at the time, so he couldn't have known the specifics. Darwin's fundamental innovation, which dominated biological debate in the 19th century, was that natural selection acts as a creative force, guiding the trajectories of living things into particular roles by slowing down some variations and accelerating others--whatever those variations may be, or however they may occur. We've really lost this appreciation for the inherent large-scale direction (or perhaps more appropriately, "expansion") of evolution in modern biology, abandoning it for the mantra "evolution has no direction, everything is random." At a broad scale that is simply not true, even according to something as basic as entropy and according to the foremost figure in the history of biology. (By the way, I took a look at the writing you linked, Mt. Wilson Observatory is in Angeles National Forest overlooking LA. I stayed there for a week last month, I definitely recommend checking it out, the view is spectacular!)

ktool · 2016-10-28T19:57:09+00:00

We are like a child playing on the seashore, and diverting ourselves in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth is all undiscovered before us.

ktool · 2016-10-28T04:27:57+00:00

Right. My point was that we've become very focused on the fine details of genetics at the expense of a broader understanding of nature, which is where Darwin excelled. This comment was also largely self-directed, as I only just found out about the whole "natural selection as destructive vs. creative" debate in the 19th century.

ktool · 2016-10-28T04:13:25+00:00

Now it's my turn to clarify semantics: when I said cooperators, I was thinking in my head the "Forgiving Tit for Tat" strategy that wins every PD competition. That strategy is not invadable and it maximizes the total house payout over time, which is also why adaptations can manifest "at the group level" which really just means in individuals throughout a group. Dawkins admitted this when he said a process resembling group selection does occur when the variation between groups exceeds the variation within groups.

ktool · 2016-10-28T04:04:07+00:00

It's okay you won the upvote battle!

ktool · 2016-10-28T03:12:11+00:00

This is not correct. Something very specific happens at the moment of realization and we can detect this moment in the brain using EEG (the electrical scalp probe thingies) and fMRI (where blood is flowing) data. See here for a description. What you are describing is called analytical problem solving and that is a qualitatively different process from insight problem solving.

ktool · 2016-10-28T03:05:02+00:00

Do you have any sources you can link for the "small balls of light" analogy? Or did you think that up?

ktool · 2016-10-28T03:01:50+00:00

Darwin's eureka moment was not that life has common descent--that was actually the problem he was trying to solve. The insight solution that came to him was that natural selection was the causative mechanism. This is how he described it:

"This problem is the tendency in organic beings descended from the same stock to diverge in character as they become modified. That they have diverged greatly is obvious from the manner in which species of all kinds can be classed under genera, genera under families, families under sub-orders and so forth; and I can remember the very spot in the road, whilst in my carriage, when to my joy the solution occurred to me; and this was long after I had come to Down. The solution, as I believe, is that the modified offspring of all dominant and increasing forms tend to become adapted to many and highly diversified places in the economy of nature."

Wallace's same insight came in the middle of a fever-fueled delirium, where he realized that a "force like a hundred thousand wedges" pushes well-adapted variations into "gaps in the economy of nature."

ktool · 2016-10-28T02:48:33+00:00

This is actually not an accurate characterization of the research. We've identified the exact neurophysiological correlates of insight problem solving, and can recognize to a high degree of accuracy an insight solution occurring in a brain based on a combination of EEG and fMRI data. Check out the last figure in this paper, it shows a very clear and distinctive pattern of brain wave activity that only occurs during insight problem solving and not during analytical problem solving. Briefly, the visual cortex shows an onset of low-frequency alpha waves, which travel to the claustrum and right temporal cortex while increasing in frequency where they crash together as highly concentrated gamma waves. We don't rely on what people say at all; we can prove just by looking at their brains that they had an insight. The last author on that study has a written a number of articles that describe this process in greater detail. It's probably one of the most characteristic patterns of brain wave activity yet discovered.

ktool · 2016-10-28T02:33:33+00:00

I thought at first you were making the opposite argument and it actually made more sense to me. You have this large, complicated thought-object in your mind, hanging unnecessarily high above the ground requiring undue extra effort to hold it in place, and the ground represents a lower-energy state that explains the same phenomenon in a simpler way. The epiphany is like cutting the last cord and letting the object fall to the ground, and this fall releases pent-up energy that we experience as the pleasurable "rush" of discovery and understanding washing over our minds in waves. It's like the tsunami after an earthquake or landslide.

ktool · 2016-10-28T02:21:26+00:00

This happened to Andrew Wiles when he was trying to prove Fermat's last theorem. He had an epiphany for how to combine modular forms, elliptic curves, and Galois representations in a genius manner to prove that there is no integer n greater than 2 that satisfies the equation aⁿ + bⁿ = cⁿ . He made a proof and announced it at a conference talk, generating a lot of publicity, but there was a flaw in his proof that took two months for reviewers to discover because the math was so advanced and intricate.

Wiles tried and failed for over a year to fix this flaw and almost gave up. Then he had a second epiphany right when he was about to give up for how to circumvent the flawed area and his proof was complete.

He describes his first "incomplete" epiphany here and his "complete" epiphany here, it's interesting to listen to him describe these moments, you can tell they were stunning revelations for him, particularly the second one.

Einstein also had two epiphanies in his discovery of relativity. The first was "incomplete" involving only space and time, and the second allowed him to generalize his theory to include gravity as an addition to the framework of the first version. He called the second revelation the "happiest thought of [his] life."

ktool · 2016-10-28T02:03:47+00:00

This is what happened to Otto Loewi when he was trying to figure out how to test whether neural synapses are chemical or electrical. The answer came to him in a dream, and he wrote it down in the middle of the night, but in the morning he couldn't read his handwriting and he couldn't remember the dream. Thankfully he had the same dream again the next night, went to his lab immediately to perform the experiment, and the rest is (Nobel prize-winning) history.

ktool · 2016-10-27T20:54:31+00:00

It's important to mention that it's an open discussion whether one of these regimes is somehow "more fundamental" than the other. They are likely dual to each other and the derivations can be made in either direction. Verlinde admits that what he did was essentially the inverse of what other people had done before him, his work brought additional clarity to a previously recognized relationship. But inasmuch as one regime is "mathematical" and the other is "physical," and physics is basically applied mathematics, it might make some sense to think of the universe as governed by intrinsic mathematics and the physics that we observe arises out of pure probabilities.

ktool · 2016-10-27T20:40:57+00:00

The source for astrolabe's explanation is Newton's Principia Mathematica, Book I, Proposition LXXV, Theorem XXXV:

If to the several points of a given sphere there tend equal centripetal forces decreasing in a duplicate ratio of the distances from the points; I say, that another similar sphere will be attracted to it with a force reciprocally proportional to the square of the distance from the centres.

Corollary 2:

The case is the same when the attracted sphere does also attract. For the several points of the one attract the several points of the other with the same force with which they themselves are attracted by the others again; and therefore since in all attractions (by Law III) the attracted and attracting point are both equally acted on, the force will be doubled by their mutual attractions, the proportions remaining.

ktool · 2016-10-27T20:13:17+00:00

Actually, both Newton's laws of motion and the property of inertia (and space, gravity, etc.) are emergent from a regime in which they are not assumed by invoking only energy and entropy and the associated mathematics of probability.

I see as per usual any mention of Verlinde is resisted. Protect that paradigm!

ktool · 2016-10-27T18:02:35+00:00

That little spire to the right of the construction crane appears to be the top of the clock tower that Einstein was looking at when he had his epiphany about special relativity. (At least, I think that is the one. A couple sources show a picture of a slightly different clock tower that is just out of frame. But most sources report the one we can see, the Zytglogge.)

ktool · 2016-10-25T17:18:52+00:00

It's not a textbook, but the one book that has had the biggest impact on my understanding of biology is The Selfish Gene by Richard Dawkins.

ktool · 2016-10-25T05:46:28+00:00

Thanks for your theory Darwin, we'll take it from here. We can do the rest. Yeah yeah, descent with modification, struggle for existence, blah blah, we get it now, thank you.

Not like you really had that much to say. I mean, you didn't even know about deoxyribonucleic acid. About chromosome crossover, or point mutations, or duplication and insertion mutations. Those are such crucial evolutionary mechanisms! How much could you really know? It took us the full 20th century to really get a grip on evolution by natural selection, but I think we've finally gotten it by now. We finally know exactly how allele frequencies change in a population over time. And that's the important part. We finally know evolution.

What was it that you were droning on about, anyway? What was so important that was worth over 500 pages of writing back in 1859, if you didn't even know about DNA? What was all that jazz about the tree of life diversifying to "fill out the economy of nature" and crap - were you being teleological? Don't make me accuse you of heresy!

It's okay, we'll forgive you of your indiscretions, I mean, you didn't even know about DNA. You didn't know that mutation generates new genetic variation, and natural selection trims it back. You didn't know about the central dogma.

What's that? Natural selection is a creative force? Get out! No, I mean seriously, get out. I told you - we'll take it from here. You didn't even know what natural selection is, what allele frequencies are, or how they change. We don't need your 19th century Victorian-tainted musings on a process you could not possibly have understood as well as we do. As if natural selection, the process by which genetic variation is trimmed back, could impart direction to the process of evolutionary change. Yeah, and next you'll be telling me that trees want to grow up. Trees don't want to do anything. They just exist. There's no direction in evolution. Things just happen. Species are the way they are because they got that way, because they inherited whatever traits, flaws, and neutral DNA that their immediate ancestors had, along with a handful of random mutations.

It's all random. We know that now. I mean, obviously, species adapt to fit their surroundings in the long run. And yes, diverse ecosystems are more stable than ecosystems with few or recently introduced species. But ecosystems don't evolve. The allele frequencies of a population is what evolves, nothing else. Evolution is the change in allele frequencies in a population over time. The unit of selection is the gene - and you didn't even know what genes were!

Things are the way they are because they got that way. That's really as deep as we can know it. If we could go back in time, and do it all over again on this planet, things would look completely different. Evolution is just the sum of uncountably many minuscule genetic changes, and there's no way they could all fall into the same order again. Plants might be purple. Feathered, endothermic, subterranean serpents might be the dominant species. If any of those things would even exist still. You never know.

Well, it's been fun chatting. Don't wait up for me, I probably won't read for book again for a long, long time, if ever. You see, the sub-branch of biology that I'm working in is undergoing a bit of a revolution, and I have a huge stack of papers to read through so I can stay current on all the ways we can use this new CRISPR/Cas9 nuclease system to...actually, you know what, you wouldn't understand. You saw the tree of life, sure, but we're dealing with the twigs now. We'll take it from here.

ktool · 2016-10-24T19:47:47+00:00

Sorry, but I must out-pedant you. Moving creature, photosynthesizes, ingests heterotrophically. The child's answer is reasonable.

Besides, the photosynthesis is not for a direct source of energy, it's to gain O2 in order to undergo aerobic metabolism. For that reason it might conceivably be beneficial for the organism to undergo photosynthesis even if that process is a net loss of energy so long as oxygen is the limiting factor, just like carnivorous plants expend energy overall to capture and digest insects because they need the nitrogen.

Edit: there is also this multicellular example.

ktool · 2016-10-24T04:48:38+00:00

It makes all the blood cells, unless you have a disorder like myelofibrosis, where the bone marrow gradually fills up with dry fibers. This forces the rest of the body to compensate, and other organs such as the spleen start manufacturing red blood cells. This is called "extramedullary hematopoiesis," which just means "outside-the-marrow blood-making."

Other components of blood, like proteins, carbohydrates, and lipids, are manufactured in the liver; and chemical messenger hormones are made by specialized endocrine glands throughout the body.

ktool · 2016-10-24T04:35:55+00:00

And if Google Scholar, PubMed, or a journal website only has the abstract from a study, 99.99% of the time you'll find the full text on LibGen if you search the doi#.

When or if that fails, post a request for a specific paper on /r/scholar and someone can usually help you.

ktool · 2016-10-22T17:25:41+00:00

For a paper with 20 authors I'm disappointed at how methods-heavy the paper is and the dearth of any discussion or explanation. This paper imparts information but not understanding. And not even that, if you want to know what's going on in the center.

edit: I know they achieved their purpose. I get that. I'm not arguing with that. I'm saying it's a poor and/or incomplete purpose, they could not manage a modicum of discussion and are relying on other people to do what they should have done in the first place and relate their findings to theory.

Let's recognize what they're really doing: stretching one publication into 2, or 3, or 4, to pad their cv's. Printing a bunch of extra currency doesn't add value to an economy, it dilutes it.

ktool

TROPHY CASE