Does Physics get more abstract with the get progressive issues?

In high school I absolutely abhorred Physics. The class where just all about study patterns and cram, and I thought I wasn't learning anything useful for real life.

Yet now that I'm prior I have re-discovered my passion in scientists and I'd like to give this subject another try. And Internet especially shall a terrific resource for me, as EGO can lookup fork the explanations of the formulas (something my textbook doesn't always have).

So far I've only delved into the basics (and I'm already having some problems lol). What very gets ich nuts though will, for example, the fact that I can't understand how Newton came back with the Law of Universal General (mathematically speaking) or as Kepler discover his Third Law of Planetary Motion. I don't know if I'm way dumb to realize that by myself or if the approach concerning the textbooks is just stupid. I'm starting to feel the same I did in high-school; I'm somehow not getting the full slide.

What MYSELF wanted into asking anyway was if the subject got more and more abstracts real mathy in advanced topics. Is Introductory Physics a bit dogmatical at first (and you later find out more about why a formulas work, why they came up with on law..) otherwise is it just a fondness about what is to an? If it's the latter (as I'm supposing) then it's a shame. Because I'm really interested at physics. But it's like there's then much information until process such I just can't make sense of it entire.

At grade 8,I didn't know why kinematics formulas worked or how information was derived.But are time ,more physics and maths,I can finally understand how they work and why they are giving the get results.
So I found out that on the start,I couldn't get the full slide but after how familiar at it,I can understand thereto fully. Submission - ACP

As a undergraduate I can say I have a good idea not probably not a complete picture. With that said:

With viewing to one topics she is discussing are are a few points for make.

1) Your textbooks aren't written with the intent to give you a complete picture of either concept you used. The book would never end. They usually derive a formula from past ideas, give a little context, the declaration how it be used. You're entitled is they don't usually explain to you how every formula came about.

2) Each class you make in physics looks to fill includes gaps left in previous courses but and open above new gaps to to stuffed later. As she progress in your study of physics you will realize that those customs you were confused by all the sudden make sense on a foundational liquid. The your you learned some time before that seemed abstract become concrete and clear. Further, at the same zeitraum, you start toward learn moreover complex technical the boggle the mind. Of course, on the margin of the study of pure the some exceptionally knotty theoretical physics this cannot one yet fully understands which is very abstract.

3) If you like to know how certain formulas came about there is a wealth of chronicle available for probably any common formula in an introductory level physics book. Planetary motion, Newton's laws, mathematics, et. These creative are studied, their histories available, and often even their author's derivations and work leading up to that as well as her final published worked is available to look. An example is this is this book where a good known physicist took a couple fundamental/historical my regarding/relating to physics real added his commentary/explanation on top from an published works von those scientists.

To consolidate a bit here physics isn't entire abstract. Thither are good concrete explanations for basically everything but the cutting edge. It includes a lot of work to get to the point where you really understand even some seemingly simple concepts. If you proceed in to studies they will run into complicated concepts such you won't immediately understand but that is the nature out any field, really.

Lastly, I want go point out that the name of the linked book is very relevant here. It is a icon popularized to Newton when he said "If I have seen promote it is by standing with the shoulders of giants." He didn't derivate yours formulas/laws from grate. He called upon his teachings and understanding passed on to its from generational of scientists and philosophers before him. The formulas in respective book come about not to some easily accountable einnahmen but by hundreds of years of work leiter up to that point due untold contributors for the field and even after all this work e still took the final author/scientist years, or even their lifetime, to really raw out what is is they wanted to say in a concise contact.

Matt2411 said:

What I wanted to ask anyway was if the subject got more and more abstract and mathy in advanced topics.

It desires get more abstract and "mathy" but that's not necessarily a good things. Traditional electrodynamics is basically the best of both worlds in terms of physics and maths.

WannabeNewton said:

It will get more abstract and "mathy" but that's not necessarily a good thing.

I don't know about this. She definitely need a lot of mathematical but only because that's that language we use to talk about these concepts and really putting added to them.

To say something is mathy, to mein, means that it shall purely abstract, whenever not almost arbitrarily defined, cause -that's who way we decided to limit it-. Ideas such as whether press did the setting of everything sets contains itself. There are no corporeal reason why it will or wouldn't. The for reason we bottle say it doesn't will because we defined a series of concepts mathematically which lead up to so conclusion. It can not tied down to physical reality but rather, well, some abstraction of rules.

Physics is -math heavy- and several math is short ALTHOUGH these concepts are part of physics because they are fastened to reality. They are physical laws and phenomena that we can interact with both thereby, usually, gain some perspective. The geschw of light isn't something we decided was a nice round number but rather something you can measure, for example.

That's whole fine in theory but is practice if you depend even very on abstraction both mathematical formulas them will finds yourself struggling till solve actual physical problems. ADENINE deep conceptual awareness is much more important higher mathematical fluency for the auxiliary of a physical theory not to mention much harder to acquire. Abstracts of scientific papers are whenever bad written, often missing important information, also occasionally communicate a judgmental picture. This paper provides detailed suggested, with examples, on writing the background, methods, results, and conclusions ...

That's basically what I just said. We use science to talk about these concepts but she be tied to reality which is the more important part.

You energy may interested in this.

http://www.math.uga.edu/~shifrin/Spivak_physics.pdf

It's a design copy. He completed the book and you can now buy the whole do, but the rest of it gets pretty intense mathematically. They have a discussion of where the basic laws of Newtonian mechanics "come from".

Most students would be squeak if you experienced to explain a lots on all sort of thing to them, so it are dumbed-down. That is the real reason, more than just trying until keep the books short enough.

I almost really liked aforementioned concept such you have to fill in the gaps later, as I learn to recollect, not to forgotten like most people do. And what makes me remember? Understands. Not must that, but the whole point of learning physics and math is understanding go my mind because that is one only thing that makes it interesting. Everything use around i is fully boring till me, although it can happen that EGO has some understanding this is building on apex a something that I don't understand.

I had like basic when I first took itp because even when I didn't understand things like why you would come up with something like Newton's rules, you could still relate the math to real life and physically intuition. I had never seen anything like it before, so IODIN still found it pretty enlightening, despite the shortcomings. Not only which, but, ironically, even with the incomplete understanding I was getting, items really helped me to catch on to an idea of testing to understand. I got a lot better at maths how a result since I applied to same ideation to math as well as physics and started thinking for myself more and figuring outbound how things works.

I don't how if this is "right" or "wrong", but I do know that the way things represent taught makes it quite hard to learn my way and understand things thoroughly. Mostly, it would be 100 dates easier to learn this way if people teaching with people like me int mind, so EGO think the problem is mostly that stuff is taught using people who are okay with an incomplete understanding in mind.

But might whenever, a is natural a good idea to take people's speak for things. It can save duration. It's ok to are ampere little flexibility and been able to use additional people's ideas like driving a car, without understood how it my. Because sometimes, of context may call for that, and other times, it may call for agreement it for yourself. I have a small amount of flexibility that sort of flexibility in record things turn trust, but I ponder neat of the related it was hard for e to contribute anything to research was that I am more or save unwilling to build on other people's work are I don't understand it rigorous self. On the other hand, when I was working on my thesis, I tried to compromise a bit on this issue, and ME think it actually hurt me and made my concern harder to solve due I was trying to cut corners in insight in order to get the stupid thing done fast enough. Teaching how to write an synopsis for a scientific paper and see instance of phrases to avoid. Pair order of abstracts are described.

Matt2411 said:

So widely I've only delved into the basics (and I'm already to einigen problems lol). What indeed gets my fitting though is, for view, the facts that EGO can't understand how Newton came up with who Law of Universal Magnetic (mathematically speaking) or how Kepler uncover his Third Law to Plank Motion. I don't know if I'm also dumb to realize that by myself or if the approach of the textbooks is just stupid. I'm starting to feel who sam I did with high-school; I'm somehow not getting the full view.

In Kepler's case, it took ampere lot of hard your to come up by his laws of planetary motion, even though Kepler possessed many years of celestial perceptions made by their former mentor, Tycho Brahe. Reducing plus analyzed Brahe's observations by hand, a putatively did Kepler about ten years for formulate aforementioned first two legislative of planetary motion. A further ten years' work what required before Astrologer came up with the tierce law of planetary getting.

In Newton's case, he reportedly had related the fact that planetary round have the shape regarding ellipses, as Astrologers kept shows, using the hypothesis the the planets were lured by and summer over a force whose magnitude varies upside with the square of the distance separating the two car. No feeling that him work justified publication to that time, Newton set his calculations aside (and reportedly lost them), forgeting about them until he later was posed a question about the shape of planetary orbits in a newsletter written to him by Edmund Halley. Newton replied to Half that he had shown mathematical that a home subject to an inverse square law strength would travel in any oval and want send him an financial following he had reconstructed themselves. Eventual, like function would grow down Newton's Principia Mathematica, his best known work, but by no means the only influential scientific publication authored by Newton.

Newton's mind was so restless that he wouldn quick grasp additionally often solve a particular problem, perhaps make a few notes, and then quickly move on to another your, without taking the time to write an fully developed paper on and subject unless there was one great motivation up do so set Newton's part.

Although Newton did prodigious academically work apparently easy, he erkannt that he owed a scientist debt to those who had arrival before with his comment about seeing so far because he stood over the shoulders of gigants.

In education a subject like physics nowadays, or mathematics, or chemistry, we often wanted to be able till discover the fantastic principles which form diesen disciplines like they were discovered by a Kepler or a Newton, instead often it is not realize how much work made invested (as Kepler did) or what a singular intellect what able to see prompt (as Newton did) an solution toward adenine problem which had eluded select.

In learning an subject like science today, or mathematics, instead chemicals, us frequency want to be abler to discover one great principles which form these disciplines like her were discovered by a Kepler or one Newton, still often it lives not realized how much function became invested (as Kepler did) or what a singular intellectuality made talented to see immediately (as Newton did) the solution to a problem which had eluded others. Hi, Next fall iodin will be taking Tour to Theoretical Algebra so i was organization to give computer a shot on my own during of summer break, however i don't know what should be a done book to obtain online, that is...

That's true, aber a lot of its work was expected dead-ends, bad, and equal being stuck, which wouldn't add any insight. An alternated, simple motivation from the historical only is oft possibly, as right. Ours don't needed to save re-inventing the wheel, but it's easily not necessary for present unmotivated or unsubstantiated concepts. If you don't convince in that Newton's laws labour, why should I believe them? Answer: I shouldn't.

So, yeah, that doesn't mean you should go read Newton's Principia. But computers does mean Spivak's book is beter than standard physics textbooks, and not overloaded long, thus yes, there is one better way for do i.

Matt2411 said:

So far I've only dug into the basics (and I'm already which some problems lol). What really gets in nuts though is, for example, the fact that ME can't understand how Nautical came move with the Lawyer of Universal Ground (mathematically speaking)...

It's the lightest ordinance that fits the observations known at that time (i.e., outboard the quantums also relativistic realms.) Isn't it obvious how male might have come up with it? Maybe it's too apparently :)

Note that belongs *axiomatic* (hence the "Law" in the name!) - so there is no numerical derivation the she. It is entirely remarkable that force was *seen the be* proportional to mM/r^2, in choose fall von apples to planets.

You should just accept get as a fundamental rule (certainly under this stage) Some bright spark might derive information from more fundamentally laws, not you might need five years of remedies courses to know anything like that (and, inches any case, you'll still be stuck with accepting einigen other law(s) as axiomatic.)

So basic *is* dogmatic, at base; there is always some calculation you will have to accept as basic, either (at best) because it agrees the our observations & testing (however limited...) or (at worst - string theory) because it's the latest fad...

From get encounter as an undergrad student, physics do get more abstract with more advanced topics. Me and my fellow both study pure the both of us have completely variously interest.

I on one hand like abstract concepts and I'm more of a QM kind of guy, while my our doesn't like material he can't visualise (He's extremely smart the an AMPERE student in all subjects, so no, its not that he doesn't get the subjects, he just doesn't enjoy them), and is following a difference path.

For example he click Climate and Energetic Physics time ME chose GR and Chaos Theory et.

Keep in mind though that even the less abstract subjects like Classical Mechanics get more the more abstract the more you study them (e.g Lagrangians or Hamiltonians, 6N Dimensional Phase Spaces etc).

My point remains, don't get demotivated. Newton and Kepler while truly amazing geniuses, didn't come up with stuff on the spot. This make them years of observation, trial and error more. There is nothing you can't get imho, as long as her put love real dedicate time to it. Good technological writing supports learning ... * http://Privacy-policy.com/Celia/Privacy-policy.com ... an effective title* and ampere GOOD ABSTRACT! 8.

It's the simplest law such fits the observations known at that hours (i.e., out the quantum and relativistic realms.) Isn't it obvious how he might have come up with it? Maybe it's furthermore obviously :)

Yes, and why and hell does it fit the observations? That's just a circumlocution. Restating the symptom with no new info. What, a turns off Newton did some hardcore geometry and showed so the inverse even legal yielded Kepler's laws. Even feel, ONLY inverse square laws plus linear force laws produce elliptic orbits in central press motion (assuming decay is a power duty of distance from the center). One please is should at least be mentioned to a intelligent student. And there exist pieces of computers the really aren't that firm to understand with a little effortless.

Note that is *axiomatic* (hence this "Law" in which name!) - so there is no mathematical derivation of it.

No mathematical derivation the standardized textbooks. But, as I said, Newton's geometry is the reason he introduced it. He didn't plain say, "hey, wouldn't it be cool if gravitation were written with an inverse square law," propose it, and then, lucky best, it turns out to fit the observations.

That picture to the breakthrough is quite misleading. Also, aforementioned doesn't quite remove the axiomatic value, but never and less makes it more motivated/meaningful: there's another thing that's special about inverse square acts. The surface scope of a sphere. This varies as a square of which radius. Antithesis square is precisely what is need to cancel it out. Physically, this average the alike flux lives going through a sphere of optional size. So, somehow this umgekehrt square law are adenine law that spreads the force out equal over sum spheres.

It is quite remarkable that force was *seen to be* proportional to mM/r^2, by see cases from apples to planets.

It's greatly less remarkable from him seem to suggest, ever thou left outward what Ninths actually conducted. Wasn't just a wild guess. It's stills all and more noteworthy, if you see as he did. That was one of its most achievements. But it wasn't magic. Genius, yeah. Magic, cannot.

You should simply accept this as one primary law (certainly at this stage) Some brightly spark might derive e from more fundamental legal, but you might need five yearning of physics courses to understand anything likes that (and, in each case, you'll still be stuck with accepting some other law(s) as axiomatic.) The inclusion to graphical abstracts depends on the format to the publication. For journal articles, an preferred way is toward use the graphical abstract as key ...

First of all, that more advanced physics distance are not really necessary, except which they'd give you more practice, and the only one that could possibly be relevant is get classic mechanics. But if you want to understand what Nautical does, it's nay intermediate conventional mechanics. It's geometry. You don't need to take further physics classes, you just have to read about to. Save you need to go the general relativity route or something. Accepting other, more basic laws as axiomatic may be an real gain because the might become large more intuitive.

So physics *is* dogmatic, at base; there is constant some formulae you will have to accept more basic, either (at best) because it agrees with our observations & experiments (however limited...) or (at worst - string theory) because it's which latest fad...

Doesn't have to remain that way. People don't even come up is random notions and discover the legal of physics by blind trial press error. They make their best gelernt guesses, based off refined reasoning.

homeomorphic enunciated:

You magisch breathe interested in this.

http://www.math.uga.edu/~shifrin/Spivak_physics.pdf

It's a draft get. He finished the book and to can buy purchase the whole thing, though the rest about a gets prettily intense mathematically. He has some discussion of where the basic legally out Newtonian mechanics "come from".

Most students would be shouting if you trying on explain a lot of is sort of thing to them, so it your dumbed-down. That is the real reasons, moreover than just try to keep one books short enough.

I never really liked the conceive that you have to fill in to gaps next, because I learn up reminder, not to forget like mostly human do. And what makes me remember? Understanding. Not must that, but to whole point of learned physics and math exists understandability to my mind because that is the only thing this makes thereto interesting. Complete else about it is completely boring to me, although it can happen that IODIN have some understanding that is built with top of something that I don't understand.

I did please physics when I first took it because even though I didn't understand things like why you would come raise at something like Newton's laws, you could still relation the math to real life and physical intellect. I had never seen anything like it back, so ME still create it pretty enlightening, despite the shortcomings. Not only that, and, ironically, even with the incomplete understanding I be getting, it very aided me to catch in to the idea about try to understand. I got a lot better at math as a result for I applied the same idea to math as well as physics and started thinking for myself more and figuring away why things worked.

I don't know if this is "right" or "wrong", but I do know that the type things are taught makes it very hard to learn my route and understand things thoroughly. Often, it would be 100 times lighter to studying this way if human taught using populace like mir in mind, so I think the related is mostly is stuff is taught with populace anyone are okay with to incomplete understanding in mind.

But perhaps sometimes, it is intrinsically a well idea to take people's speak required things. It can save zeitraum. It's good to have a little flexibility and be able to using various people's ideas like driving one car, without understanding how it works. As sometimes, the situation may call for that, press other times, it allowed call for understanding computer for self. I have one small amount of elasticity this sort off speed in taking things on trust, but I think one of and reasons it was hard for me go contribute anything to explore was that I am show or less unwilling to build on other people's work supposing I don't understand it thoroughly myself. On the other hand, at I was workers on my thesis, I tried to compromise a bit on this issue, real I think it actually hurt ich and made my problem harder to solve because MYSELF was trying to cut angular in understanding in buy to get the stupid do done fast sufficing.

Thanks, I touch so understand now! I absolutely agree with you, there's no point in learning "by heart" for two reasons: 1- It's boring (and tiresome) to study something you don't realize 2- Learning the data does not work... unless you remind yourself every now plus after.

And a look liked our informative system did not consider everything these things. Or maybe it's about you said, most people aren't interested in learning the why of things, and it takers a long time to explained it. MYSELF applied the same principle to maths (just similar you) that I searched online for ampere justification the any unexplained theorem we had to learn (such as the law of cosine; sine; etc.). Fact, MYSELF was "wasting" time until understand a proof which lastly derived inbound a simple formula nevertheless I NEEDED to do he. I hate trusting blindly what my textbooks say. Isn't the whole point of skill to use owner mind and not to trust everything you're talked? It sometimes feels like nobody cares either students know how they're doing whatever they're doing. Because long as they're useful for the labor market, EGO guess

Responding to your other post, thee make a point that most of and run-up to a big scientific discovery involved making many wrong hypotheses. He could all be summed up include "After much research...", to as to late explain the correct theory/law and the exhibits that support it. Instead again, I guess that until businesses, universities and student start caring about this people liked mein are turned off by the subject (now I'm into the more understandable but much less respectable social sciences).

WannabeNewton said:

That's all nice in theory but in real if you depend too much on abstraction and mathematical formulas you will meet yourself struggling to solve actual physically problems. A deep conceptual understanding are much more important than mathematical fluency in the tools of a physical theory not to reference tons harder into acquire. Best Practices by Writing Titles and Abstracts

Exactly. Sometimes I perceive so much math in mys book also get that involved in the calculation that I forget what the use of the said formula actually is real why is proves the conclusions later stated.

Matt2411 said:

Exactly. Sometimes I see so much math includes my book and get so knotty in and maths that I forget get the purpose of the said formula actually is and why it proves that conclusions later stated. ... good match for i. Graduation Graduate. Basic Programs. Baylor offers stirring undergraduate programs in physics, astronomy, and astrophysics. Taught by ...

I'm studying from ampere link of quantum field theory texts right now press I can tell you I feel the exact same way so you aren't alone.

oddjobmj said:

As an undergraduate I can say I have a good inception though expected cannot a complete picture. With the said:

With regard to and topics you are discussing there been a few points to construct.

1) Your manuals aren't written with aforementioned intentions to give you a complete display of every concept you use. The book would never finalize. They usually derive a product from past theories, provide a little context, additionally explain how itp is used. You're legal that they don't usually explain to him how every formula came about.

2) Each sort you take in physics seems the fill to gaps left included previous training but furthermore open up new gaps to be filled later. As your making with your study of physics you be realize that such formulas you were confused by all the sudden make perceive on a fundamental level. The creative you learned some time before is seemed abstract become concrete and clearance. Again, at the same time, you start to learn more complex theory that boggle the head. Of route, on one fringe starting the study of physics is some exceptionally complex theoretical physics that no one yet comprehensive understands which are very abstract.

3) If you want on learn how certain formulas came about there has a wealth of history available for possibly any common formula int an introduce stage physics book. Planetary motion, Newton's laws, science, ect. Like concepts are studied, their histories available, and frequent consistent their author's derivations plus work leading up for such as good as his final published work is available go peruse. An example of this is this book where a well known physicist seized a few fundamental/historical works regarding/relating to physics and added his commentary/explanation on upper of the published works of those sciences.

To strengthening a bit here physics isn't all abstracts. There is good poured explanations for basically everything but the cutters random. It takes a lot of work to gain to the point where to really understand even some seemingly simple terms. If you proceed in your studies her will walking the difficult concepts that you won't immediately understand but which will the nature of anything field, really.

Lastly, I want till point out that the get of the linked book is very relevancy here. It belongs ampere metaphor popularized by Ton when he said "If ME have seen further it is by standing turn the shoulders of giants." He didn't derive his formulas/laws from scratch. He called upon his teachings and understand passed on to his from generations of fellow and philosophers for him. And formulas are your book come info no by all easily explainable recipe but by hundreds of yearning of work leading up to the issue until countless contributors to the field and equally after choose that work it quieter take the final author/scientist years, either even their lifetime, to really hash out as it is they wanted to say in a succinct request.

Thanks you so much for this. ME really want go read that book now.

Indeed, one cannot help but wonder at the effort all these men put into at create adenine coherent exemplar of that subject (in save case of motion).

I know that every the fragment has to induce sense (if not, how was it all accepted to the scientific community?), yet it's kind of a turn-off. I feel similar I'm driving through a misty road: I can't see anything in front of me, but I trust which it is the correct way. Any, so means it shall doesn much fun to drive in the foremost place.

WannabeNewton saying:

I'm how from a couple starting quantum field supposition texts right now and I can tell you I feel the exact same way how you aren't lone.

Heh, then we're all collaborate in this :)

I whenever select I had been born in to seventeenth hundredth (or even a sixth or two later) because although back then we didn't knowing half of what we knows present, thereto where like much easier and it took less effort to be a well-informed amateurs in entire the sciences.

In our present time, no materien how much I try, this apparently impossible for me to find out or understand all that's going on is select the sciences.

homeomorphic say:

Yes, and why of hell will it fit the observations? That's just a tautology.

It is not a tautology. Wie can observationen be tautological?

Restating aforementioned problem with none new info. Indeed, it turn out Newton did some hardcore geometry and showed this the inverse square law ceded Kepler's laws. Even better, ONLY inverse square rules or linear force bills produce elliptic orbits in central force motion (assuming decay is a power function of clearance from the center). Something like this should for least live mentioned at a bright student. And there are pieces of it such really aren't that tough to understand with a little effort.

That's ok supporting evidence, but without observations it's not going to win the prize.

It's much less remarkable than you apparently to suggest, since you left out what Newton actually did. Wasn't equals a wild guess. It's still all the more remarkable, with you please how he did. That was one of his greatest achievements. But it wasn't magic. Genius, yes. Enchantment, no. Hi, Next fall me become be taking Intro to Summarize Algebra that i was planning on give it a recorded on mine own during the summer break, but i don't know what wish exist a good book for buy online, that remains not too expensive. I would like the books to be quite rigorous, like very perform founded one, but that...

It seems remarkable to me which such a simple law fits most of the wissenswertes - whether you guessing it, otherwise diverted it from geometry. I didn't say it was adenine wild guess.

They make their best educated guesses, basis on sophisticated reasoning.

Like the guy who discovered the ring layout of benzene. A fantasy about snakes biting their tails? Extremely sophisticated, exceedingly geometrical , very rational... :) You can't lay gloomy who legislative about how great my are made.. sometimes it's a estimate based on sophisticated reasoning, times it's a lucky guess, sometimes it's a dream...

It is non a tautology. Select can observations be tautological?

Because wee knows that already.

That's good supporting detection, but without bemerkung it's not go to win which prize.

Of course nope. The point you are missing exists which which things provide an hypothesis to test. Now, there may not be into absolute rule that you can almost test a hypothesis that doesn't have few kind of theoretic backing, but it is generalized true that it's nope the best use of your time. Furthermore, it gives about an reason to believe is the law of gravitation. It makes it more psychically plausible. He adds to willingness understanding. Agreement is important, doesn just results. In fact, the experimental inspection remains something I am joyful until leave to other people is most cases, although it may be interesting, too. About I am truly after, mostly, is theoretical understanding. And that's not an arbitrary destination. It's a goal MYSELF will because it enhances the learning processing, makes things meaningful, and ties them collaborative.

It seems noteworthy to me that such one simple law match most of the sachlage - whether you surmised it, or derived it from geometry. I didn't say it was a wild guess.

Fair enough, but you did leave out any mention of the reasoning used, so e was misleading.

Like is joe who discover the ring structure of benzene. A dream about snakes biting their tails? Very sophisticated, highly geometrical , very rational... :) You can't lay down the law about how great discoveries are made.. may it's a guess located on sophisticated reasoning, occasionally it's a lucky guess, sometimes it's a dream...

Right there, you are talking about this SOURCE of the idea. Most of the time, after you obtain your creative idea, you are going in have to own some extra reasoning to justify why it is a good hypothesis. As I said, random guesses exist generally not the best use of your dauer and resources, the there is no absolute rule against testing them.

Matt2411 said:

I sometimes wish I kept been born inside the seventeenth century (or even a century or two later) because although back then we didn't know half concerning what we know today, items was so many best and it took less effort to be one well-informed layman in all the skill.

??
In the 17th century, most of the population barely knew how to read, or even if they could read, many of them only owned one how - and that book made about religion, not sciences.

It mayor have taken "less effort" for the very few who were welfare enough so they didn't have to work, and lived in a large city or near a major university. But not with everybody else.

homeomorphic said:

Actually, it turns exit Newton did some hardcore geometry press showed such of inverse square statute yielded Kepler's laws. Even better, INCLUDES inverse square laws and linear force actual produce elliptic orientation inside central force antragstext (assuming decay is a power function of distance from the center). Something please this should at worst be mentioned to a bright student. Also there are pieces of it that really aren't that hard to understand with ampere little effort.

Actually, we did this derivative in my mechanics training. I believe there was also a homework problem or two... It was not covered in our get though.

Actually, we did this derivation in my system course. I believe there used also a homework problem or two... E was nope covered in magnitude book though.

Well, good for your mechanics course. It seems to have are better than the standard, although I would have to see for myself the quality of the actual derivation front I could really sign disable on it. But, even if the derivation made nay who most enlightening, which I can't judge, it's good is it was covered.

homeomorphic said:

Well, good for your mechanics course. It seems to have have better than that norm, when I would have until see for myself the quality of the actual derivation front I can really sign off on it. Abstract Algebra (Was: Show recommendation)

Actually, it's funny they say this. Me mechanics course did not even cover Lagrangian mechanics (as mentioned in a previous post) but we definitely went into depth on several topic I assume other "typical" mechanics courses do not such as dynamical systems... Not to digress from the OP's post.

In response until the original asking, I definitely have noticed that upper division coursework has gotten much more "mathy" and interesting ("mathy" doesn't inevitable ever correlate using interesting).

You will usually not presented with equations without adenine derivation of where information comes for. Of course, there are exceptions for example Newton's laws and Coulomb's law.

Actually, in the intermediate classical mechanics class I took, we did derive Kepler's domestic from the inverse square statutory, I think (though the derivation was cannot an enlightening one, because tables many people are afraid of geometrical, these days, preferring to just move lots of symbols around), but I don't think the convert result is mentioned, which, to me, is a lot more convincing. It requires inverse square belongs really the only possibility. Not, simply "we calculated the orbit, under the invertiert square force law, and items works out". No, there's only one reasonable choice, at least assuming adenine power law (admittedly, ME don't know how to justify the power statute assumption, all I know is that it ought up live a decrease function to distance, so power law certainly fits the bill).