What is Natural: Definition and 1000 Discussions

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. S

    Does Mapping Induced by Group Homomorphism Preserve Normal Subgroups?

    Homework Statement Let G and G' be groups. Let H and H' be normal subgroups of G and G' respectively. Let f:G->G' be a group homomorphism. Show that if f(H) is a subset of H', then there exists a natural homomorphism f*:(G/H)->(G'/H'). (Hint: This fact is used constatntly in...
  2. E

    Proving Infinitely Many Natural Numbers: Larson 4.1.6

    [SOLVED] Larson 4.1.6 Homework Statement Prove that there are infinitely many natural numbers a with the following property: The number n^4+a is not prime for any number n.Homework Equations The Attempt at a Solution I cannot even think of one such natural number a. :( I need to find some way...
  3. L

    Integration by u- substitution (involving natural logs)

    Homework Statement \int \frac{1}{1+\sqrt{2x}}dx Homework Equations u=1+\sqrt{2x} \sqrt{2x}=u-1 dx=(u-1)du The Attempt at a Solution I was able to get it down to: \int (1-\frac{1}{u})du = u-\ln{lul}}+C = 1+\sqrt{2x}-\ln{l1+\sqrt{2x}l}+C However, my book says that...
  4. F

    Limit involving natural log

    Homework Statement Find the limit of (tanx)^cosx as x-->infinity Rearrange the equation so that you can use L'Hopital's rule for the form of (infinity/infinity) The Attempt at a Solution I did ln(tanx)^cosx = cosxlntanx I know the limit of tanx as x-->infinity is pi/2 the limit of cosx as...
  5. B

    Natural Log of negative number

    I've got a simple question that's been bugging me for a while. I think I know where the problem is, I'd just like a formal mathematical reason why I can't say this: \ln{(-1)}^2 = \ln(1) = 0 That part is fine...but then: \ln{(-1)}^2 = 2 \ln(-1) = 2 (i \pi) when they should...
  6. M

    Finding the Inverse of a Function

    Homework Statement The function f is defined for x>2 by f(x)=\ln x+\ln(x-2)-\ln(x^{2}-4) a. Express f(x) in the form of (\ln\frac{x}{x+a}) b. Find an expression for f^{-1}(x) Homework Equations ..The Attempt at a Solution Well, I simplified it to: f(x)=\ln(\frac{x^{2}-2x}{x^{2}-4}) I can't...
  7. cornfall

    Exploring Natural Hydrogen: Stability and Occurrence

    Does hydrogen in its ground state occur naturally, ideally, experimentally? Is it stable? Is this like asking, "Does a center of mass occur naturally, ideally, experimentally? Is it stable?"
  8. C

    Natural Log and Inverse derivatives

    Homework Statement Let f be the function given by f(x) = ln [ x/ (x-1)] (a) What is the domain of f? (b) What is the value of the derivative of f at x = -1. (c) Write an expression for f^(-1) of x, where f^(-1) denotes the inverse function of f. The Attempt at a Solution a. x / x-1...
  9. Ivan Seeking

    News Natural disasters on the rise: What do we do?

    http://www.physorg.com/news115220493.html In this context, I think it is important to avoid debate about causes [AGW], and focus on the best means to avoid disasters and respond to the emergencies. San Diego did a fabulous job of managing the fires this year, but many homes were lost. Much...
  10. C

    Tangent lines and natural logs homework help.

    Homework Statement 1. Let f be the function defined by f(x) = -2 + ln(x^2). a) For what real numbers x is f defined b) Find the zeros of f c) Write an equation for the line tangent to the graph of f at x=1 Homework Equations The Attempt at a Solution a) all...
  11. Z

    How Is the Integral of Natural Log of x Calculated?

    can someone please explain this to me?
  12. M

    How To Fing Angular and Natural Frequencies WITH ANSYS ?

    How To Fing Angular and Natural Frequencies WITH ANSYS ?? Good Day every body, I am student in Ruhr Universität Bochum and I would like to ask please about the procedure how to find Natural and angular frequencies for a simple beam to get the idea fro it and to solve my proble. I will be...
  13. K

    How Do You Solve a Hyperbolic Function Using Natural Logs?

    Homework Statement e^x - e^-x all divided by 2 = -1 express answer in natural logs Homework Equations No equations, just properties of logs and natural logs The Attempt at a Solution First, I multiplied everything by 2 e^x - e^-x = -2 then i took the natural log of both...
  14. wolram

    Natural Gamma radiation from Earth

    http://www.sciencedaily.com/releases/2005/05/050502190314.htm ScienceDaily (May 2, 2005) — DURHAM, N.C. -- Duke University engineers have led the most detailed analyses of links between some lightning events and mysterious gamma ray emissions that emanate from Earth's own atmosphere. Their...
  15. R

    Prove that if m, n are natural, then the root

    Hi, I've encountered this exercise which I'm having a hard time proving. It goes like this: Prove that if m and n are natural, then the nth root of m is either integer or irrational. Any help would be greatly appreciated. Thanks.
  16. P

    Natural frequency of a spring(self-weight only)

    natural frequency of a spring(self-weight only) giving the length,mass, and spring constant of a spring...how do you find the resonance frequency..having been thinking about this question for so long, does anyone know how to approach this question...
  17. T

    Sums of natural numbers to p and subsequent divisibility

    So I'm taking an introductory number theory course as an undergraduate, and this particular "genre" of questions really just has me stumped. Pick a prime p such that p is odd. Now, take various sums up of natural numbers from 1 to p, and show that the results are divisible by p. For...
  18. F

    What is the derivative of ln(x^2 + y^2)?

    Homework Statement Find y' y=ln(x^2 + y^2) Homework Equations d/dx ln(u)= 1/u du/dx The Attempt at a Solution y' = [1/(x^2 + y^2)] (2x + 2y) y' = (2x+2y)/(x^2 + y^2) But my book says the answer is 2x/(x^2 + y^2 - 2y) How can that be?
  19. M

    Engineering Natural response of an RC circuit with two capacitators.

    Homework Statement I'm supposed to find the voltage v0(t) for t > 0 for the following circuit: http://img516.imageshack.us/img516/5858/circuitta7.jpg Homework Equations The first part of the excercise was to find the current io(t). I did this by using the node-voltage method to find the...
  20. M

    Find the natural domain of the function

    i have this question that i don't totally get what it wants exactly so if anyone can help me understand it correctly, thx Find the natural domain of the function algebraically,and confirm that your result is consistent with the graph produced by your graphing utility. note: set your graphing...
  21. N

    Philosophy - Natural law question

    One question which I was meant to be doing has stumped me. It is "Can the basis of natural law be located other than in social convention?". I have written "Aquinas believed the basis of natural law to be located in God’s will and the fundamental nature of humans not being corrupted." so far but...
  22. P

    Solving Natural Logarithm Equation ln(x^2 + 1 ) -3lnx=ln2

    Homework Statement ln(x^2 + 1 ) -3lnx=ln2 Solve for x. Homework Equations The Attempt at a Solution I used laws of logarithms to simplify it down to -x^2(x-1)=1 . I don't think this is the answer I'm under the impression you need x = for the answer. First I brought the 3...
  23. S

    LNG: Is 300 Pounds of LNG = 55,500 BTU's?

    Hello I'm new to the forum. I was wondering if some people can help me in trying to get some answers. I am involved in alternative fuels and it has come up where an engineer is telling me that there is 185btus/lb inside of a 100 gallon vehiculer tank. He is using a bueauro of standard empathy...
  24. F

    Quick Natural log/exp question

    A part of an example on my book goes from the following: e^(lnlnx) > e^0 to (e^lnx)^lnx > e^0 and to ln x > e^0 this last step is what threw me off--shouldn't it be x^lnx instead of ln x on the right side since they are inverse functions. Is anything being done that I have...
  25. P

    Natural Logarithm of Negative Numbers

    Well I came across this when someone asked me this question: (-2)^n = 16 I can clearly see n=4. However, he did this: ln((-2)^n) = ln(16) n*ln(-2) = ln(16) n*ln(2)+n*i*pi = ln(16) How can I show that n=4 from this?
  26. T

    Animals ability to sense impending natural disasters.

    Elephents in thailand heading to high ground before tsunami. Animals acting funny before earthquakes. Etc.
  27. B

    Natural frequency calculated theorectically and experimentally

    Homework Statement I was given a spring mass system and asked to calculate the natural frequency by theorectical analysis and by using experimental data. There was a difference between the natural frequency calculated theorectically and experimentally. I was asked to discuss the...
  28. R

    Solving for x with natural logs

    Hi Im having difficulty solving for x in this equation. 5=9ln(x+4) I have no idea where to start so i can't show u any working.
  29. J

    The Skin's Natural Protection Against Caustic Chemicals

    I didn't know where to put this since it pertains to both chemistry and biology so i put it here. One time i accedently spilt 31.45% concentrated HCl on my skin and didn't notice it right away but then i saw this fuming drop on my skin and i immediately washed it off, it never tingled, burned...
  30. G

    Natural selection needs the feeling?

    Natural selection needs the feeling?? Human(at least) has their feelings, such as anger, happiness, and depression, etc. But, is there an advantage for the survival of human being?? why natural selection choose the human being who has feelings?? I thought about this theme at last night...
  31. L

    Solve Natural Log Problem: 3^x when 2^x=3

    Problem: If 2^{x}=3, what does 3^x equal? I solved this by taking the log_{2} of both sides. However, the book's solution involves taking the natural log of both sides. Can someone show me why that would work? I don't get what the x power changes to a x term. The natural log is base 10 right?
  32. daniel_i_l

    Proving Boundedness of f(x) = (x+1)/x^2 in Natural Numbers

    Homework Statement f(x) = (x+1)/x^2 a)prove that f is bounded in N (N is the set of natural numbers so we have to prove that f(N) is a bounded set) b)find supf(N) and inff(N). c) does f have a maximum or minimum in N? Homework Equations The Attempt at a Solution First I...
  33. D

    Well-ordering of Natural Numbers

    I am trying to prove that the set of natural numbers is well-ordered using induction. I am assuming of course that the natural numbers are defined as as the smallest inductive set (of the type specified by the Axiom of Infinity) and that the usual order is defined by n<m iff n\in m. I have an...
  34. B

    How can I integrate (x-2)ln(3x) using the integration by parts formula?

    I'm having real problems integrating a natural log. The problem I have been set is (where S = integration sign) S (x - 2) Ln(3x) I'm trying to use the integration by parts rule but keep getting the wrong answer and I think it might be to do with the natural log. I have used f(x) =...
  35. G

    Derivative of Natural Log - How Does 'a' Affect the Derivative of Ln(ax)?

    If we have a function of the form Ln(ax) Is it the case that the derivative is simply 1/x no matter what the initial value of 'a' might be? Or do we take into account 'a' in some way The thing i need clarifying is this... If we have Ln(3x), the derivative is 1/x, but the integral of...
  36. S

    What causes natural electromagnetic fields?

    What event creates and sustains natural electromagnetic fields? And what do they mean when they say a photon mediates the electromagnetic field?
  37. M

    Irrational natural log integral

    Homework Statement the indefinite integral of (1+lnx)^(1/2)/(xlnx) dx Homework Equations n/a The Attempt at a Solution There aren't any x^2 in the root sign, so I don't think it can be a trig substitution. The only logical u sub I see is to let u=lnx. In that case, du=dx/x so the...
  38. P

    Intermediate algebra , Natural logarithm question

    Hello everyone, I do not understand how:: e raised to ln of x = x ? this notation might make more sense:: e^ln x=x ? Thanks for the help.
  39. Q

    Paranormal events and Natural explanations

    I'm tired of hearing people like the skeptic Michael Shermer or James Randi talk about natural explanations for supernatural events. I believe that supernatural events are natural events that we are not advanced enough to explain. These events are true and we can deduce there truthfulness...
  40. J

    Graphing Natural Numbers to Integers

    Hi, just can't get my head around how to draw these three graphs. Any help appreciated. Thanks In each case below, draw the graph of a function f that satisfies the given property. Give an example of a function f : N -> Z that is bijective/that is injective but not surjective/that is...
  41. marcus

    Universe or Multiverse? (new w/cosmic natural selection chapter)

    This is a new book from Cambridge University Press, scheduled to go on sale 30 June 2007, available now for pre-order https://www.amazon.com/dp/0521848415/?tag=pfamazon01-20 The Cambridge.org webpage for the book is here http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521848411...
  42. F

    Natural frequency of tuning fork

    Homework Statement Using a highly sensitive parabolic sound collector, Sara records the frequency of a tuning fork as it drops into the Grand Canyon. She drops the vibrating tuning fork form rest at t=0. She records a frequency of 1783.0Hz at t=8.590s. What is the natural frequency of the...
  43. P

    Proving Z is Abelian Group Under Normal Addition

    Do people usually prove that Z is an abelian group under (normal) addition or is it the definition of the natural numbers Z?
  44. K

    What's the UNIT after you take the natural log?

    I was working on an experiment for the vapor pressure of water and I have the following formula ln (p) = -L/(RT) + ln (p_o) L=heat of vaporization of water R=Molar gas constant T=temperature in Kelvins I have some data points for the pressure p in units of mm Hg, when I take the...
  45. W

    Is it true for all n, Natural number?

    Hello all, Another quick question for the number theory gurus here: Let P(n) predicate, n Natural number. Suppose that P(n) satisfies that P(1) is true, and if k in N, P(k) is true, then P(k+2) is true. Is P(n) true for ALL n in N? Why? Thanks in advace guys! -William
  46. B

    Natural Logarithm Manupulations

    Homework Statement xln(2x+1)-x+\frac{1}{2}ln(2x+1) = \frac{1}{2}(2x+1)ln(2x+1)-xHomework Equations ln(x^a) = aln(x), ln(xy) = ln(x) + ln(y), ln(\frac{x}{y}) = ln(x) - ln(y)The Attempt at a Solution I have no idea how you can go from xln(2x+1)-x+\frac{1}{2}ln(2x+1) to...
  47. D

    When should I use natural log vs common log in scientific calculations?

    Can someone explain to me when to use natural log or common log? I understand that natural log gives creates a base e and the common base 10 but i don't understand why there are 2 different ones.
  48. C

    Creativity learned or natural (born-with)

    Creativity...learned or natural (born-with) I had this conversation with some friends / coworkers today at lunch and both sides made good points. I'd like to get a view from everyone on these forums on the subject. I guess it all comes back to the big question you hear throughout management...
  49. M

    Problem with natural units in Cosmology

    Homework Statement Reading about the raditation dominated era I saw that the radiation energy density today was given by: \rho_r = \frac{\pi^2}{30} g_* T^4 = 8.09 * 10^{-34} g/cm^3 where g_*=3.36 is the degree of freedom of the radiation (equivalent) and T=2.75 K is the CBR...
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