sciencenoob

stop attempting to be a know it all. all youre saying re so general and trying to make out as some sort of pro you are talking as if you could easily have solved the original X^X^X^X^X^X^X^X=2 problem prior to knowing. If one coud not mathematically solve it without the use of trial and error, and that the proof they gave is not a general one, then this means this problem here is simply a case specific solution sa ive said, the 'a' can only be between ~0.37-2.7 to work and it doesnt converge anymore to the answer a i also saw this post from the riddles forum, so its a pretty cruddy riddle, its like me telling you that A * 0 = 0 where A is any number then if i told you 0/0=? Guess what is A yea its kinda like that

nah, not good enough.. the proof works in the range of ~ 0.37 to 2.7 only hardly a proof of concept.. its a case specific proof does 10^2*10^2=10^4=10^(2+2)=10^(2*2) just becasue it works? no

sorry but thats just weak. I cant accept that. If it doesnt work, it doesnt work. Theres nothing 'case specific' about this. If what he did was correct then it should be correct for all cases. Obviously it wasnt so his method was definately wrong. again i proposed its probably cause it was the magic number to. simple example what is x^2*x^2, is the answer x^2+2 = x^4 or x^2*2 = x^4 theres only 1 right way to do it. its x^2+2

Which shows that the so called proof proposed by the OP is wrong, yet people have agreed on it. That proof only worked because it was the magic number '2'. and we know many cases where coincidental relationships and operators can be obtained that is mathematically incorrect, when dealing with the simple number 2. so his proof was not proof but merely something that seemed to be working out in his favor

bump.. look at my solution suggesting a problem in the original 'answer', that it only applies simply due to the magic of the number 2 in this situation instead of being a real answer.

Technically infinity is not a number. Only zero is a number. Infinity is a mathematical abstractation

Interesting riddle, but unfortunately I think this proof has fallacies, simply because you happen to work with the magic number '2' that it seems to work, and hence a more generalized solution following the same processes as you undertook will not yield the same conclusion. For example: let (X)^X^X^X^X^X^X^X... = A ----- (1) if (X)^(X^X^X^X^X^X^X^X...) = A Therefore using Eq(1) (X)^(Eq(1))=A Then (X)^A=A Therefore X=A^(1/A) <= is your generalized form But If you tried this with say A=4, then the iteration breaks down, where Eq(1) does not make sense in that if A=4 then X=4^0.25, then Eq(1), A=/=X^X^X^X^X^X^X... Infact, if A=4, then you will get X^X^X... = 4, given that X=4^0.25 when you have only powered it 4 additonal times, and that any more powers on top of that will start going above 4. i.e.: given your solution that X=A^(1/A), and that A=4 Then: X=4^(1/4)=4^0.25 Then X^X^X^X^X^X^X... = 4 is true only when: (4^0.25)^(4^0.25)^(4^0.25)^(4^0.25)^(4^0.25)=4 <= EXACTLY such that: (4^0.25)^(4^0.25)^(4^0.25)^(4^0.25)^(4^0.25)^(4^0.25)=7.1 Hence I think theres something wrong with this 'proof' and that it seems to work only because its a 2? Please correct me if im wrong

Of course you can & cant. In physics you can do a calculation and find out that there exists a loss of energy following a decay process and may that signifying the existance of a then unknown neutrino particle. Thats nothing you knew before, yet one had to be familar to the conservation of energy principle and the ideas surrounding quantum mechanics and 'particles'. So then it may be no because everything you know is linked in different complicated ways. And if you were to be able to find something you cannot have known then you simply could not have computed it because your language skills lies in to the picture. Really then it depends on your interpretation of what is meant by no prior link to your experience or knowledge, in which case really your question is simply a misnomer? Its unanswerable.

The problem with using a lot of mathmatical models in biology or bio-related subjects is because you start losing the objectivity of the subject. Im not saying the current curriculum and practice of biology is perfect but I think it is doing alright as it is. A lot of times, mathematical models becomes too abstract that you simply lose track of the physical interpretation of it, which is of most important when dealing with biology/medical related subjects. People will also get side tracked into trying to understand and figuring out the equations in the model more so than the actual fundamental response. Also, mathematical models will easily disencourage people away from the course simply due to its mathematical nature in which some do not like. Lets take for example the mathematical model of a pair potential, that is the lennard jones potential. Theres two ways to remember the effect of a pair potential or a bond between 2 molecules if you will. You can choose to remember that as you push 2 atoms closer the force needed gets harder, siminlar to when you try to pull it away from each other, but it is easier to pull it away until eventually you can pull the atoms apart for good. The other is to use a lennard jone's equation which has very abstract terms that people simply try to understand from a physcal interpretation, which is simply a waste of time. Its like trying to understand quantum mechanics from a physical interpreation stantpoint. So really, biology is much more effective just remembering the rules of the game, than simply remembering mathamtical models. Also even if fundamental mathamtical models were developable for biology, they are themselves not fundamental anyways. There really is no point into doing this unless you can concretely have a very good theory which will ultimately be very limited, because a lot of biological responses and topics relating to it, can either be described by existing biochemistry rules and laws, or if some magical relationship you are tyring to describe were developed, they were really the phenomenon arising from more complexed multilevel, nonlinear interactions in which case your model itself will be very limited in its applicability.

Obviously its his fault he failed his courses and has to do 6. Me by saying 'its not his choice' is referred to the other person who makes an example of how someone can choose at their own will to spread out the course requirements over a longer than normal timespan. In that case it will be their choice. But here, its not his choice because he does try to do all he can do but he cant and is thus FORCED to do 6 years. And no, it is not 'pretty common' to do engineering degrees in 5 years becomes the VAST majority of all students in any engineering program in north america will finish their degree in 4 because thats what you are surposed to do, and we are of course talking about the average to top notch bunch obviously = the bunch that will go on to get good engineering jobs without much trouble. Well the guy isnt stupid. He doesnt do shit. He locks himself in his room all day playing computer games and he sleeps at 6am and wakeups at 5, etc. He skips all his classes except labs and hands in the odd homework and studies right before the final for 24 hours straight and walks into the exam not having slept, that kind of deal. So he is not at all stupid, just incredibly incredibly lazy and a waste of his own life. But thats not the point. Employers dont know and dont care to know that! His record shows he is incompetant whether he is nor not. Ad even if employers do know, his level of laziness and bummness is NOT a good trait! The ultimate question of discussion here is how good are his chances of landing a job though? I dont know, I can imagine engineering firms being pretty tough.

you _are kidding right? Most honours bachelor degrees are 4 years. That course load is not insane, even for engineering degrees. I mean we are only taking about 5-6 courses per term versus someone doing an arts degree will have 3-4. Its not really that insane. In my point of view it is the arts students that are having an extremely relaxed time versus the very normal work load for engineering students because once you are working, we are talking 9 work hours everyday straight up for the entire week, at the minimum excluding travelling etc. And who is this 'they' anyways. But that is besides the point right. Fine, if you want to take your time and spread things out its ok, you can do it in 5 years or more as long as you arent failing courses and having a bad record. The guy i am talking about fails courses which forces him to do 6. Its not his choice.

You can't really apply for internships and expect to have a full time job of it when you dont even have your engineering degree yet. Also without an engineering degree from a known or respectable university you cant become a legal engineer professional (licensed) which means its useless. How engineering or other degrees normally work is, there are prerequisites that you must pass before you can do higher level courses. He just fails a few prerequisites every year that pulls him down a level until he is finally in his 6th year now. If he passes everything he will get his degree. Thats not the point though, he spent TWO MORE years than anybody else. On top of that his academic record is extremely scarred with really bad grades and a lot of failures in courses with extremely low grades (0GPA or 20%). I am not saying his age is a factor, but only the fact that he spent 2 more unneccesary years than what people normally spend, so this means he is wasting his time. It doesnt matter if you are 35 starting engineering degree as long as you can finish it in the normal time then you will look ok. He spent 6 years which kind of shows to employers he is incompetant

You mean apply for internship? but you cant be an engineer if you dont have an enegineering degree. if you dont goto uni its probably worse than his situation with a degree and have shit grades, at least he has the degree He is like 26 so he is basically 3 years older than anybody in his class

But who will employ him into an engineering company though? Seriously he has like a really bad record. He is extremely lazy and has really poor communication skills, like when he does presenations he chokes up pretty bad and it becomes extremely awkward because he starts getting nervous and shaking and everything, ive seen it a few times. The thing is, competant or not, it is SIX YEARS of a 4 year degree. Recruiters are known to be harsh when it comes to selection. He cant even make an interview with those grades, how can he even land the job? I dont know I feel sorry for him.

I know this guy who is currently in his 6th year at university as an undergraduate doing his bachelors in engineering. His program is surposed to be 4 years long. He has extremely low grades, with an extremely low borderline fail (literally) GPA (GPA = 2.0 or 50+%), and his academic record is also full of failed courses with courses in the 0 GPA range (20+%), with additonally certain failed courses almost every year. I have a hard time imaging him being able to find a job because most employers look at transcripts when you go straight out of university, especially so for technical engineering jobs. It is also quite impossible to talk yourself out of the fact that you are quite incompetant. Also his record will be a complete turnoff and there is no way any recruiter will even consider him on first glance. I mean i dont think he will be unemployed per se, because he can obviously get lower middle class jobs like working in a shop, restraunt, mcds, janitor,etc but other than that I dont see how he can land even a middle class to decent job. The other wierd thing is most of the people in his normal year are either done with a masters by the time he is done if he can graduate this year, or have 2 years work experience. What are you take on this?

Im afriad its not true that higher education means higher pay. Of course it does to a certain degree. I mean there is a threshold here. I am analyzing the set of data after say a minimum of a college/university degree. Of course if you are a highsdchool drop out the chances of you being middle class pay is close to nothin. Further from that then (the university degree minimum), education vs wealth has a inverse like relationship. This is especially true in the case of PhDs, as a lot of PhDs end up working in the academics and research, or are deemed overqualified for jobs, in general hence those types of jobs pay middle class pay.

I am not underappreciating any principle here nor am I questioning the validity of the energy conservation laws, so your rantings are pointless. I was pointing it out to make you aware that the conservation laws are themselves none other than a principle in itself, one that you may say can have mathematical and theoretical backup/establishments, but regardless, it is something that you would otherwise 'believe' is true in the universe, throughwhich scientists put fourth further theories and predictions based upon this principle. Likewise then, one should not exclude from the possible notion or principle, that particle dynamics and behavior at the microscopic (one would say 'quantum') level, can behaves in a deterministic and continuous manner. In fact it would be just as wrong and flawed and 'unscientific' to suggest otherwise, than to suggest that particles behave deterministically. But that is exactly why principles are quickly established in theories such that theories can be drawn, otherwise you wont have any basis to found your theory upon. Einstein's work on special and general relativity will be a waste of time, if infact the principle of relativity in itself was a flawed notion. But all of this discussion regarding scientific application of 'principles', is to carry you to the point that it is also a principle that particles may behave deterministically. If that were to be the case them, QM simply cannot be the most fundamental. But then you also dont understand, that current QM theories never have challenged or approached this principle because the current theories utilizes statistical means as a theoretical basis, but does not challenge the particle dynamics side. And since this is to be the case, then one cannot exclude the fact that there has to be a more fundamental theory, one in which can describe the particle dynamics, and one in which can also then further to it explain the findings that QM (statistics) show, experimentaly.Infact it will be bogus to suggest that QM is in itself proof that particles cannot behave deterministically and is 'random', because then it will fall into the relm of personal interpretation of QM theories, and not what the math itself is trying to explain, hence it is also unscientific (just philosophy) under your own descriptions.

Yet this proves you dont understand what I am saying or what is going on here. Do you not understand that the conservation of energy is a PRINCIPLE. We call it a law because it is so strongly substantiated in all forms of life that we can call it a law, but ultimately its a principle. Something that is the very basic foundation, perhaps abstractly controlled by natures wierd ways (which physics will never be able to __explain__ and shall never aim to anyways). But it is no doubt that if for example, conservation laws were not to be conserved then certain theories may certainly break down. I hope you do realize that Pauli looked at the problem of the missing energy, then he went on to apply a principle here to reinforce his postulate of what is the 'neutrino' now, that energy has to be conserved in life (this is a belief also!!! a good belief, yes but a belief! a principle!). Its like how the lorentz transformation is so wierd and abstract. How do you explain or understand it? Well you dont. Its a mathematical relationship, used and made and designed such that you will have the theoretical establishment of the principle of special relativity to ensure that the speed of light is (on the whole of course strictly speaking) the maximum.

Hold on a second, you are obviously the science bunch that read science textbooks, learn the modern interpretation of it (repeat: _intepretation_) without any real knowledge of the actual evolution of the theory, and perhaps the interpretation as seen through the eyes of the founders of such theory (even though they themselves may not be right, or have complete view of the theory's potential, etc). There is such thing as: 'principle', through which logical, scientific and mathematical relationships that is physics, can be successfully applied. Lets look at the numerous numerous examples. Einstein wanted to reinforce the principle of special/general relativity because he 'believed' it was true in life, that was the foundation of his theory on it. It agreed with experiments hence its now good. Wolfgang Pauli hypothesized the existance of the neutrino because of his 'belief' that the energy is surposed to be conserved. Energy conservation is a principle, a good willed belief. The neutrino was discovered later. ETC ETC So, it is no suprize that there are those in the scientific comunity (Einstein being one also!) that believes the world is deterministic and that particles infact do travel continuous, real paths. It is only because of QM's current inabilities, that such actual particle dynamics are not theorized. It doesnt make this 'belief' wrong. Maybe you just dont like the word belief and get all technical on me, and maybe i could have used a better term like the statement of a principle, etc - but like it or not ill stick to the word belief because ultimately that is what it is, it is when you can build a theory on this belief and that it agrees with experiments that it becomes science. Lets wake up a little.

The slight advent of hostility here is uncalled for. Of course there is some generalization. Obviously I was never intending to say that all who does science/engineering related professions or academics are immediately fixated into the world, to ensue a middle class at best lifestyle and pay, thats absurd. Of course in life and in job, such skills as social skills, your social network, looks, tone of voice, height, stature, race, accent, etc = all comes into play, lets not kid ourselves. For the sake of argument however we can assume those to be constant amongst everyone, and focus on the main issue of the discussion here, which is education (the level, and the type) vs wealth. Of course also, that a lot of researchers and professors and the likes in the academia choose to go into those sorts of paths very knowingly of their middle class wages as compared to more traditional commercial based routes and to assume managerial roles, but thye are willing because they like it, etc - thats great. Perhaps you just are just taking the part of selective logical thinking here. There is a reason why accountants and engineers generally dont get along (this is generally a fact, I am affraid as I have personally observed many such instances myself, through which their own education curriculums is filled with these sorts of joke like references to the fact). In any business type enviornment those are the two departments that are usually stepping on each others toes, that really is the fact of life. Engineers being engineers were generally the 'smarter' bunch in highschool and in college as well with their education curriculum very mathematical and scientific based, and when they choose to do economic courses as a electives they are also the ones that rack in the highest grades over people who officially take economics as a degree, for example and in general. Those that do pure economics or commerce type degrees, some may have lower grades than the engineering bunch, take only economics and commerce type courses and are determined to make money. The thing is engineers shadow them for too long and it is not until you get into the workplace that you can finally 'get even' with engineers (to satisfy their own insecurities, self worth, etc), thus their control of the company budget can limit the technical work that is the engineers job - without jepardizing the company's goals too of course, or they can simply play hard ball politics to make things harder. Accountants like to think that engineers dont know a thing about economics and money, and engineers like to think that accoutnants couldnt build a boat to save their lives, but thats life because everyone dispises others and think that they are the best to make themselves feel better (that is the lesson of life here). However, a sad fact is that it is true though thta taking the commercial based roles in life lead to more monetary reward than maintaining in technical side of things, such that accountants get paid more than engineers in the long run in general, plus then the accountants seemingly get 'rewarded' and seemingly wins the life long engineers vs accountants dispute. Im only using this as an example. But even in general, people not doing the technical routes (science & engineering) dont know a damned thing about those professions in general. They also dont give these professions (and its people) the respect they deserve. Nor does the social makeup, because lets face it technicall careers have middle class pay, its a fact.

To put it simply, I am a believer that the universe is deterministic. I believe that a particle has a trajectory path similar to the classical newtonian sort of way (i.e. it is continuous in spacetime). You may be able to describe things using statistics (what QM is doing) and it perhaps suffices for engineering applications, but it does not exclude from the real possibility that particles travel real deterministic paths, and hence if that were to be the case then QM simply cannot be fundamental enough. If it is true (but I dont see how one were to go about proving), the principle that particles travel discontinuously (i.e. it can exist in one point then all of a sudden decompose in spacetime and instantly spawn in another and different spacetime), then QM may then be argued to be as fundamental as it can get (perhaps, because then you may still be able to predict/document the dynamics of its movements). I dont care for the uncertainty principle that underlies QM, because that principle is simply a construct developed for the need to explain what is observed experimentally and at a theoretical level. However the uncertainly principle relates strictly applicable to QM only, the mechanism of which is perhaps explainable with more fundamental understanding.

What is your take on this issue, regarding the disparity of social and economic status (wealth) versus academic qualifications, knowledge and intelligence - in life, in general? In other words, is socialeconomic status, in general, inversely proportional to education? In particular of course, the sector of the academia relating to the sciences and technical sectors (e.g. scientists & engineering related jobs). For example, highly educated and quite possibly significantly more intelligent (dependent on personal definition thereof) PhDs dont earn nearly as much money, as compared to a much less educated and quite possibly less intelligent (in the scientific, literary, and strictly academic sense only) person, of whom simply partakes in a job that can suffice simply and merely and mostly with the input of effort alone. In the past, human civilizations relied on physical prowess in order to succeed. Without delving any deeper into that subject matter, it is safe to say that times have changed. Physical fitness, capability and strength is no longer a determining factor in one's ability to survive and be at the top of the social hierarchy. Instead, the modern society is one in which, in general, monetary wealth (a seemingly artifical and abstract system developed by humans to run their society) is the determining factor into which one's social status is determined in the social hierarchy (with limitations of this statement of course). What it means now is that the richer you are, generally the higher the socialeconomic ladder you are, and hence the more influence you have, etc (respect however is of course is another thing that weath may not gain you). However its obvious that whilst most (in general) PhDs get paid middle class wages regardless of their professional route (being a professor, a researcher, etc), that much less academically qualified individuals can strive much more easily (economically) by simply working for more mainstream commercial roles (such as being accountants, etc). I will stop here for now and let discussions role. But things to address are also to answer why this is to be the case also. Of course it may be perhaps these academics are not as fine tuned to that part of what is now the modern life (with the monetary system in place), etc. But also in general what do you think about this? Another point I want to point out is that engineers and scientists working in a company are generally paid much less and are at a much lower rank doing technical work, than a person with an MBA and good table manners that manages/oversees these technical staff. Of course it may make sense since probably those sorts of skills are what is neccesary in the economic/commercial based world we live in the modern era. But I think even more importantly is the seeming lack of respect and acknowledgment given by the public in general, towards the more academically inclined and intelligent people that does the technical work in life (such as engineering, science related research). It is easy for bank managers to trivialize the engineering/scientific career because in their point of view they get paid a good sum of money doing a very standard lower intelligence required type work (something they dont come to realize but is true, and wont ever go near to admitting) but yet they think they are better socialeconomically whilst taking everything around them for granted. It is easy for the general public to take for granted every little thing around them, without realizing that everything that deems someone's own self felt satisfaction of socialeconomic status (e.g. tangible objects such as TVs, computers, electronics, etc) are all the result of tedius work by these technical professions (engineers and scientists) that actually make it possible, and happen.

Well I have always known that einstein was famous in his attemps to discredit QM because he feels that its not deterministic enough, but its not because of einstein why people should also believe that science can be more fundamental than QM. It really should be quite obvious for people to simply accept the fact that a certain theory, whether or not they have huge invested interests in it or not (such as careers, self study dedication, etc) to understand that QM simply isn't complete in the philosophical sense. That is, statisitcs really isnt fundamental (or first principles) enough, because it fails to describe the actual manifestation and dynamics and interactions of the system itself. Of course that is not to say QM is useless because I am a strong supporter of QM for its actual usefulness and for what we can do, but at the same time I understand the limitations of QM as a fundamental theory and its incompleteness that a lot of people simply will not accept. For example, we can very well make a probability density function of a relatively hard standardized test (e.g. public exams, iq tests etc) and then be able to achieve somewhat of a normal distribution. We can then infer from this information the average test score of the population which we can then go on to say that the population is on average '____ this' smart, etc (within limitations); this works similarly to the concepts of QM. But thats not good enough in the philosophical sense of being a fundmanetal first principles description. What we will really need, is to explain perhaps the experiences of every individual taking the test, their brain network structure, how they think, etc etc, and put this in some sort of complicated matrix solution or simulation, to then obtain from this, the final observation we get from the statistics, and to even go as far as to predict what certain indibviduals in the population is capable of achieving, from the modelling alone. That will be the approach from first principles. Hence like einstein I believe in the deterministic nature of theories to be more fundamental, but unlike einstein I respect QM for its usefullness.

I can understand and have looked past the fact that QM is just abstract so we need to drop our intuitions when using QM. But I still want to try to understand the signifiance of the wave function. For example, plank has been obsessed with the signifiance of the planks constant, as have mathematicians with pi, etc. Perhaps that is naive and but though naive I think this quest is still important towards developing better intuitions about the very abstract world we live in. Nobody has explained what the wave functon is by definition though and why its use for QM works the way it does

I am not saying what I believe is significant. What I am saying is that QM is insufficient to describe the actual dynamics of the small particles, etc. The idea of first principles should be, the idea of the most fundamental description of nature, yes no matter how abstract. But using probability to describe the system isnt good enough, hence not 'first principles enouigh' because it fails to describe or explain the manifestation and phenomenas we observe, that is to explain the probability density observed as explained by QM. So future theories can certainly go further and more fundamental than what QM is currently capable of accomplishing, hence QM cant be the most fundamental description of nature.