Natural Definition and 1000 Threads

Nature, in the broadest sense, is the natural, physical, material world or universe. "Nature" can refer to the phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. Although humans are part of nature, human activity is often understood as a separate category from other natural phenomena.The word nature is borrowed from the Old French nature and is derived from the Latin word natura, or "essential qualities, innate disposition", and in ancient times, literally meant "birth". In ancient philosophy, natura is mostly used as the Latin translation of the Greek word physis (φύσις), which originally related to the intrinsic characteristics that plants, animals, and other features of the world develop of their own accord.
The concept of nature as a whole, the physical universe, is one of several expansions of the original notion; it began with certain core applications of the word φύσις by pre-Socratic philosophers (though this word had a dynamic dimension then, especially for Heraclitus), and has steadily gained currency ever since. During the advent of modern scientific method in the last several centuries, nature became the passive reality, organized and moved by divine laws. With the Industrial revolution, nature increasingly became seen as the part of reality deprived from intentional intervention: it was hence considered as sacred by some traditions (Rousseau, American transcendentalism) or a mere decorum for divine providence or human history (Hegel, Marx). However, a vitalist vision of nature, closer to the presocratic one, got reborn at the same time, especially after Charles Darwin.Within the various uses of the word today, "nature" often refers to geology and wildlife. Nature can refer to the general realm of living plants and animals, and in some cases to the processes associated with inanimate objects—the way that particular types of things exist and change of their own accord, such as the weather and geology of the Earth. It is often taken to mean the "natural environment" or wilderness—wild animals, rocks, forest, and in general those things that have not been substantially altered by human intervention, or which persist despite human intervention. For example, manufactured objects and human interaction generally are not considered part of nature, unless qualified as, for example, "human nature" or "the whole of nature". This more traditional concept of natural things that can still be found today implies a distinction between the natural and the artificial, with the artificial being understood as that which has been brought into being by a human consciousness or a human mind. Depending on the particular context, the term "natural" might also be distinguished from the unnatural or the supernatural.

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  1. B

    Logarithmic Simplification: Understanding the Natural Logarithm

    Hello, I made a mistake in the title of this thread and this question is on general logarithms; loga(aloga(x)) = loga(x) ==> aloga(x) = x Can someone enlighten me on why loga(aloga(x)) simplifies to loga(x)? Can someone prove why this is true? Futhermore, why does this imply that...
  2. S

    Time of motion, natural logarithm help

    This equation specifies displacement x in terms of motion time t (starting from rest). x = \tau g\left(t + \tau e^{-t/\tau} -\tau\right) where tau = m/b is the system time constant of a mass m suspended from a mechanical braking device with rectilinear damping constant b and g is standard...
  3. J

    Natural log fxn = negative integral?

    Homework Statement True or false? ln(1/10) = -\int dx/x The Attempt at a Solution I have no idea where to start on this one. what is dx/x ??
  4. T

    Resonance and natural frequency

    Homework Statement Ok, this is not homework, just something that's been bugging me and my tutor is unavailable(as usual) to help me. Why does increasing the mass of a system lower its natural frequency, like adding a concrete block to a washing machine. Come to think of it, I'm not even too...
  5. H

    Finding Natural Numbers n Satisfying a Congruence

    fin all natural numbers n that n\sigma (n) \equiv 2(mod\varphi(n))
  6. T

    What is the Correct Form of the Natural Logarithm Law for (ln(x))^(1/x)?

    How does (ln(x))^(1/x)=ln(x^(1/x))? A friend told me this was a true statement but could'nt prove it. If that isn't true, then how would you find the lim x->0 of (ln(x))^(1/x) using L'Hospital's Rule?
  7. T

    Is there any scientific explanation for increasingly violent natural disasters?

    Shortly after the year 2001, to now, there have been more increasingly violent earthquakes, hurricanes, tsunamis, tornadoes, etc... than in any other decade in history. I wanted to know if there is a natural, geological, and meteorological explanation for this. Not too long ago, there were Two...
  8. L

    Natural angular frequency of a bridge

    1. Consider an oscillating system of mass m and natural angular frequency omega_n. When the system is subjected to a periodic external (driving) force, whose maximum value is F_max and angular frequency is omega_d, the amplitude of the driven oscillations is A=\frac{F_{\rm...
  9. C

    Work done by expansion of liquidfied natural gas to atmosphere

    Hi All, Been try at this for a week now and I know I'm missing something. I'm too far out of university to remember how to do it, but just close enough to know that I should remember. Anyway, I have a steel can containing a mixture of liquidfied hydrocarbon gasses...
  10. M

    Is Atheism Compatible with Natural Rights?

    Is atheism incompatable with the concept of natural rights? Most (or at least some) adherents to natural rights argue that human rights come from a god, or that there is an absolute morality that is the basis of natural rights. Atheists obviously do not believe in a god and most would...
  11. N

    How can I use calculus to graph f(x)= 10(ln(ln(x))/ln(x))?

    1. Graphing Carefully: Sketch f(x)= 10(ln(ln(x))/ln(x) accurately using calculus, your calculator, or both to aid you. Make sure to include all vertical asymptotes, as well as local extrema 2. f(x)= 10(ln(ln(x))/ln(x) 3. OK. I might come across as stupid but here goes... I don't...
  12. S

    Limits involving natural exponential2

    Homework Statement lim(e-2x cosx) x-> infinity The Attempt at a Solution I thought right away that the limit would not exist because of cos x oscillating the function between + and - but the answer in the book says zero. I need help figuring out why my thinking was incorrect.
  13. S

    Limits involving natural exponential

    Homework Statement lim e3/(2-x) x->2+ The Attempt at a Solution I can't seem to get started on this one.
  14. L

    Natural Numbers: Proving Statements w/ Induction

    Hello! Question: if it is asked to prove a statement A(n_1,...,n_k) for all natural numbers n_1,...,n_k, is it actually enough to check its truth by induction on just one of the counters, say n_1?
  15. K

    Is the natural frequency the highest frequency?

    I have a theoretical question. Does a structure's natural frequency have anything to do with the highest frequency of which it can vibrate? Or can the structure vibrate in any multiple of the natural frequency (until it brakes...)?
  16. G

    Natural frequency resonance help

    I have just started to study resonance and I don't quite understand what it is. My textbook says: "All objects vibrate with a characteristic "natural frequency". When an object is forced to vibrate at its natural frequency, the amplitude of its vibration can grow very large. This effect is...
  17. N

    Prove that nCk is a natural number

    Homework Statement Prove that \binom{n}{k} is a natural number by showing that \binom{n}{k} is the number of sets of exactly k integers each chosen from 1, ..., n. Homework Equations The Attempt at a Solution I posted a similar question before...
  18. B

    Natural Log Limits: Understanding the Use of L'Hôpital's Rule

    Can someone explain to me how they get last line to work out? I am confused on how they're using natural log with limit problems. Thanks for the help! :)
  19. M

    Help with derivatives of natural logs

    Homework Statement (ln(1+e^x))^6 Homework Equations The Attempt at a Solution Honestly I haven't done this in 3 years and a friend asked me to help them with it. I'm at a bit of loss.
  20. V

    What Are the Solutions for x in (x^5)-x = 8?

    Q1) If (x^5)-x = 8 then x = e^(solve for this) not sure, x*x*x*x*x-x = 8 help please - q2) ln(3x)/x^2 dy/dx = [ ]-[ ]ln(3x) / x^3 or solve for dy/dx I get (x^2)*(dy/dx(ln(3x))) - ln(3x)*(dy/dx(x^2)) / x^2*x^2 =(x^2)*(1/x) - ln(3x)*2x / x^4 =...
  21. M

    Understanding Natural Log Problem: Taylor Series Approach

    Homework Statement y and x are both close to 1. ln(y) - ln(x) \approx (y-x)(lnx)' Can someone explain me why this is true? By the way, (lnx)' is the derivative of lnx, which is just 1/x The Attempt at a Solution I guess this is something to do with the taylor series of ln(x). I tried to...
  22. D

    Convergent/divergent with natural log

    Preparing for the math test, and cannot understand what to do for one of my practice problems: I need to find if the series is convergent or divergent, using test for divergence (divergent if limit doesn't equal 0) sigma from 1 to infinity of ln((n^2+1)/(2n^2+1)) I see that I should use...
  23. T

    Damping , resonance and natural frequency?

    When a forced oscillation is damped, it is true that the frequency at which resonance occurs decreases right? so does this mean that the natural frequency has decreased too or does it only mean that resonance does not occur at natural frequency when being damped?
  24. J

    Simple equation involving natural log

    Can anybody solve for x? 6=(36/9)ln(120/x) The answer is x=22.3 I have so far got: 6=4*ln(120)-ln(x) 6=19.15-ln(x) I think it may be incorrect
  25. M

    The Hubble Constant and Natural Unit

    Could we set the natural value Hubble constant to be 1 in some calculation of cosmology, like what we do in the natural unit?
  26. J

    Comparative GHG Emissions of Coal, Domestic Natural Gas, LNG, and SNG

    You might be interested in this paper: Jaramillo, P., W. M. Griffin, and H.S. Matthews. 2007. Comparative life-cycle air emissions of coal, domestic natural gas, LNG, and SNG for electricity generation. Environmental Science & Technology, Vol. 41, No. 17, 6290-6296 You can download it here...
  27. Spinnor

    Charge of down, up , electron; (-1/3, 2/3, -1)*3 more natural?

    Let us define the charge of the down-quark, up-quark, and electron as (-1/3, 2/3, -1)*3 or -1, 2, -3. Let momentum in some closed one dimensional space be equated with electric charge. If momentum goes as n/wavelength where n = 1,2,3,..., the down quark has a charge of -1, wavelength equal...
  28. N

    Prove by induction that nCk is always a natural number

    Homework Statement Prove by induction that \binom{n}{k} is always a natural number. Homework Equations The problem requires that we use the fact that \binom{n+1}{k}=\binom{n}{k-1}+\binom{n}{k}\tag{1} The Attempt at a Solution Well, the first part of this question requires a...
  29. P

    Solve Natural Logarithm Equation lnx+ ln(x-1) = 1

    Homework Statement lnx+ ln(x-1) = 1 solve each equation for x Homework Equations ln(e^x) = x e^lnx = x The Attempt at a Solution x + (x-1) = e^1 [==> using ln(e^x) = x] from this point on, I am stuck because I am having trouble isolating x because of the x that is in the brackets...
  30. N

    Mastering the Basics of Natural Logarithms: Simple Proof of ln(e)=1

    Homework Statement Guys how come ln(e)=1 ? How can l prove this
  31. A

    A Rotation with Translation Movement is standalone natural phenomenon.

    Please look into this site http://knol.google.com/k/alex-belov/paradox-of-classical-mechanics-2/1xmqm1l0s4ys/9# The experiment 2 animations This is animation based on classical mechnics laws http://mysite.verizon.net/vze27vxm/sim.gif This is animation based on theory of...
  32. E

    Subadditivity and Natural Logs

    Homework Statement Show that the natural logarithm is not subadditive. You could use ln(1/2+1/3)\leqln(1/2)+ln(1/3), but mathematicians view all such numerical evidence as an invalid proof. Homework Equations ln(a+b)\leqln(a)+ln(b)The Attempt at a Solution ln(1/2+1/2)\leqln(1/2)+ln(1/2) Well...
  33. G

    Natural Exponential Function Problems

    Homework Statement 10(1 + e-x)-1=3 Homework Equations The Attempt at a Solution I'm supposed to solve for x, but I don't know how to go about this. I tried dividing the 3 by the 10, but after that I don't know what to do. I believe I should use ln on both side, but that's after...
  34. E

    Matlab - ODE, find roots of the characteristic equation for the natural response

    Homework Statement I need to use MATLAB to solve these problems. http://users.bigpond.net.au/exidez/IVDP.jpg Homework Equations MATLAB The Attempt at a Solution a) R1=3.6; R2=R1; C1=33*10^-6; C2=22*10^-6; % defining the polynomial constants Vs=[R1*R2*C1*C2...
  35. L

    Natural Domain of trig functions

    Homework Statement Find all the natural domain of the function algebraically, and confirm that your result is consistent with the graph produced by your graphing utility. h(x) = 3/2-cosx Homework Equations (a) h(x) = 3/2-cosx (b)x2-1/(x+1) The Attempt at a Solution Do I need to...
  36. L

    ARE integers ordered pairs of natural numbers:

    ok. some rant about definition and semantics. integers are isomorphic ordered pairs of natural numbers (a,b) w/ equivalence relation (a,b)=(c,d) iff a+d=b+c. reals are convergent sequences of rationals, etc. in mathematics, are integers simply isomorphic to the ordered pairs of...
  37. J

    Natural Frequency Using Rayleighs Energy Method

    Hi everybody! I'm a complete newbie here, but I was hoping somebody might be able to help me out with understanding Rayleighs Energy Method and how to calculate the static deflections/natural frequencies. I am basically looking for the first and second modes/natural frequencies of a 2 mass...
  38. J

    Is the natural numbers implicit in the statement?

    In class we defined convergence as \forall\varepsilon>0\;\;\;\exists\mathrm{N}\epsilon\mathbf{N}\;\;\;\forall\mathrm{n}\geq\mathrm{N}\;\;\;\left|a_{n} \right|<\varepsilon So if a sequence {a_n} of real numbers converge to 0 if for every ε > 0 there is N s.t. |x_n| < ε for n ≥ N... Is the...
  39. E

    Natural Logarithm and Integral Operator

    Hello, Can we interchange the natural logarithm "ln" operator and the integral operator? Regards
  40. I

    Sum of series involving natural log

    Homework Statement Find the sum of the series, if it converges, of n=1 to infinity of ln(n/(n+1)) The Attempt at a Solution My intuition tells me the series converges because as n goes to infinity the series is taking the log of 1, which is 0. How to sum it though... I have no...
  41. J

    Is Singing Talent More Innate Than Other Abilities?

    than other skills? At least, that's the general impression I've seen people keep. If you see the best basketball player, it's just hard work and dedication, and people tend to think you could become one of them if you put enough effort and dedication. But if you hear someone singing...
  42. G

    Operation exists that is valid for a group limited to the natural

    What kind of operation exists that is valid for a group limited to the natural numbers?
  43. J

    Is Every Natural Number Either Even or Odd?

    Homework Statement Prove that every Natural number is either even or odd. Homework Equations Mathematical Induction Even: n = 2k where k is an integer Odd: n = 2k + 1 where k is an integer The Attempt at a Solution I think I have a relatively complete proof, however, it doesn't...
  44. T

    Are half of all natural numbers even?

    It might be a silly question but I was just wondering if this was unprovable or false... Thanks guys
  45. H

    Natural Frequency Of Space Frame & Motorcycle Frame

    Hi How do you calculate the natural frequency and vibrational response of a space frame and what is its damping characteristic? What are all the aspects to take into considerations and how do you analyse failure due to vibration? Thanx
  46. B

    Natural FrequencyWhat does the natural frequency of an object depend on?

    What does the natural frequency of an object depend on? Whenever I try to look this up, I usually read that the natural frequency depends on "intrinsic" properties or a "variety" of factors. Is the natural frequency independent for each object/is there any universal factor the natural...
  47. R

    Are Natural and Supernatural Mutually Exclusive?

    Hello I was talking with someone bout natural vs supernatural when it relates to something such as ID and one thing that seems to be a hurdle is , are they mutually exclusive or not? Is there a book or website that does a good job discussing it?
  48. T

    Definition of the natural logarithm

    I know that there is a year old thread that has just been resurrected that is slightly on this topic, but I had a question that I thought might merit a new thread. I'm working with my Calculus book here, and I'm working on the chapter called, "Logarithmic Functions from the Integral Point of...
  49. C

    Natural convection cooled enclosure

    I have a transformer in a box that is cooled using natural convection. There are louvered openings on the box to pull cool air in the bottom and let heated air out of the top. How do I determine how much heat is actually leaving the enclosure? Info that I have is the area of the enclosure, the...
  50. B

    Calculus with logs and natural logs

    im confused as to what the integrals and differentials of log and ln are. i looked up the derivative of log x and it said it was 1/x so then the integral of 1/x should be log x but i thought it was ln x im so confused! please help me just say integral of log x differential of log x...
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