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. T

    How could the set of natural numbers not be finite?

    The set of all possible streams of brain activity arising from all possible configurations of all possible neurons with all possible connections is finite, so if you accept that natural numbers are a creation of the human mind (brain), then don't you have to accept that the set of number is...
  2. S

    Understanding the Ordering of Complex Numbers: Why is it Difficult to Define?

    All, Could some one tell me please ,why in natural numeric system we are not allowed to move from number one to three? I mean ,is this a properties of the natural numbers to be in sequence? for instance if we count base on an imaginary numeric system which allows us to shift between numbers...
  3. P

    Calculate Natural frequency of a vibrator

    I have a construction of a vibrator (industrial use). I should be able to calculate the natural frequency, by means of Hooke's law. Since I have a physical device I already have a "real world" measurement of the Natural frequency. The problem is: How to calculate it? I have tried to do some...
  4. 4

    Natural Gas to generate hydrogen, fuel cell?

    Hi all, one last question for today - Given steam reforming of natural gas to generate hydrogen, what is the major difficulty with it with respect to most fuel cells? Thank you,
  5. T

    Finding the natural frequency of a cylinder oscillating on a circular surface

    Homework Statement Here is the problem with my 3 attempts: 1. Alright, so the first attempt, I did not take into account the rotation of the cylinder ωc so I think it is wrong. But it seems to make sense because the whole cylinder rotates about O, so if I find that energy using parallel...
  6. B

    Natural Vibration of Beam - Algebraic Query

    Folks, Just wondering what the author is doing here, given ##\displaystyle \left (\frac{2EI}{L^3} \begin {bmatrix} 6&3L\\3L&2L^2 \end {bmatrix} -\omega^2 \frac{\rho A L}{420} \begin {bmatrix} 156&22L\\22L&4L^2 \end{bmatrix} \begin {bmatrix} W\\ \theta \end {bmatrix} \right )=\begin...
  7. B

    Natural Vibration of Beam - PDE

    I am just wondering the author is doing in this calculation step. Given ##\displaystyle \rho A \frac {\partial^2 w}{\partial x^2} - \rho I \frac{\partial^4 w}{\partial t^2 \partial x^2} +\frac {\partial^2 }{\partial x^2}EI \frac {\partial^2 w}{\partial x^2}=q(x,t)## where ##w(x,t)=W(x)e^{-i...
  8. A

    Prove that the product of 2 consecutive natural numbers is even

    Homework Statement Prove that the product of two consecutive natural numbers is even. 2. The attempt at a solution Hi, I'm just starting to work with proofs by induction, I'm just wondering if this is a valid technique, and/or if I am being too verbose in my proof, thanks! Let...
  9. R

    Does Gravity Cause Hotter Water at the Top of a Tower?

    Hello, I have an interesting question about water natural convection without an external heat source. Say we have a high tower filled with water. The tower walls don’t allow any heat to escape or enter the system. There is a constant gravitational force present in a system (g-force). At the...
  10. DeusAbscondus

    MHB Natural log and trig function question

    when I differentiate: $$ln4x+sin(x)$$ I get: $$\frac{1}{x}+cos(x)$$ and Wolfgram agrees But then when i test this by calculating indefinite integral, I get: $$ln(x)+cos(x)$$ Which leaves me with three questions: 1. what happened to the 4? 2. why isn't it integrating back to (at least)...
  11. S

    Safest region on Earth from natural disasters

    Safest region on Earth from natural disasters... My question is simple but may require a complicated answer. What region on Earth is safest (note the word "safest") from natural disasters? In the United States, there are plenty of tornadoes and hurricanes, along with the threat of...
  12. M

    BA in Natural Sciences/Mathematics

    I'm looking for an online Bachelor degree that will allow me to do a Masters in Astronomy, Astrophysics, or any other physics related subject...now I do understand that the logical thing to do is a bachelor in physics however you can't study that online(nothing that I could find anyway)and...
  13. G

    Natural broadening of lithium sub-levels

    Homework Statement In the 2p state of lithium, two fine structure components are formed due to spin-orbit interaction. They produce wavelengths of 670.960nm and 670.975nm. Compare Doppler and natural broadening at 700K. The lifetime of the 2p state is 27ns and \frac{\Delta \lambda}{\lambda} ~=...
  14. J

    Natural frequency of oscillating electron

    Homework Statement a) Light of wavelength 510nm is emitted by an electron in an atom behaving as a lightly damped simple harmonic oscillator with a Q value of 3 x 107. Find the natural frequency of the system. b) Find the width of the resonance.Homework Equations The Attempt at a Solution...
  15. K

    Natural Frequencies of oscillation

    Homework Statement What are the natural frequencies (not wavelengths) of oscillation formed in a pipe that is open at both ends and a pipe open at one end and closed at the other? Homework Equations The Attempt at a Solution I don't understand this. I keep reading something about 2L and 4L.
  16. H

    Why can't an aircraft maneuver like a bird?

    In simple terms (if possible), why is an aircraft unable to achieve the manoeuvrability of a bird, eg, immediate stop, rapid acceleration, sudden change of direction? I'm guessing it relates to necessary strength and rigidity of the plane's structure, engine power/weight ratio.
  17. Y

    Natural log of a sum? (not sum of natural logs)

    Homework Statement Find the derivative of y = x^2 + x^(2x)The Attempt at a Solution By looking at the equation I think I need to use implicit differentiation + natural logs. But I can't do anything with: lny = ln(x^2 + x^(2x)) So I assume I'm wrong.. Any help??
  18. C

    The Nature of Natural Frequency

    I've been told that the natural frequency of an oscillator is the frequency an oscillator will oscillate at when left to itself. Is this referring to the frequency of an ideal oscillator subject to ONLY a restoring force. Because all REAL oscillators are subject to damping and, when left to...
  19. J

    How is the set of all natural numbers, N, denumerable?

    I know the history of how set theory came about and how Cantor showed the real numbers between (0,1) were non-denumerable. He did this by showing that they can't be put into a one-one correspondence with N (1, 2, 3...) ...So what does that really tell me? I know it tells me that the...
  20. P

    Sum of the powers of natural numbers

    Hi everyone. I have learned that: 1+2+3+...=\frac{n(n+1)}{2} 12+22+32=\frac{n(n+1)(2n+1)}{6} I want to know what the general formula of Ʃna, in which n and a are natural numbers, respect to n and a.
  21. L

    Natural Unit Confusion: M=1/L or M=T/L^2?

    If we set c=G=1, then c=1 leads to L=1/T , the G=1 means that M=L^3/T^2 and combining the two means that M=L=1/T so far so good. But say if I also want \hbar=1 this seems to imply M=T/L^2 but combining this with c=1 which gave the L=1/T now suggests that M=1/L=T . Which seems...
  22. PhizKid

    Natural force down incline plane

    Homework Statement Find the force and acceleration of the block down the inclined plane Homework Equations F = ma The Attempt at a Solution We have two unknowns in F = ma I know there is the gravitational force going straight down, and there is the normal force that is...
  23. N

    Integration of the natural log

    1. how to integrate∫ (ln x)2 /x dx Homework Equations The Attempt at a Solution
  24. G

    How Do You Differentiate y = sin(x)^x Using Natural Logs?

    Homework Statement Let y=sin(x)^x. Find dy/dx My teacher said to use Natural long to solve this. she got, step 1:ln(y)=ln(sin(x)^x)=x ln(sin(x)) step 2:y(dy/dx)=1(ln(sin(x)+x(cos(x)/sin(x) Final answer:dy/dx=((sin(x))^x)[ln(sin(x))+x(cos x/sin x) I don't understand how she...
  25. A

    MHB Proving Real Number Exists in N

    how to prove that for any real number in r (0,1) there exist a natural number n in N such that rn > 1
  26. M

    How to prove that it does not exist a natural number having the

    How to prove that it does not exist a natural number having the property that the permutation of the first digit with the last one produces a new number being 5 times bigger compared to the original one Regards
  27. M

    MATLAB Matlab code natural numbers subset

    I have array of natural numbers from 1 to n. They are divided into m groups, where m*(m-1)=n. I need all m-1 elements from first group, last m-2 elements from second group, last m-3 elements from third group...zero elements from last group. For example 5*4=20: 1,2,3,4; 5,6,7,8...
  28. QuestForInsight

    MHB Natural numbers form a poset under $ \le$

    Problem: let $\mathbb{N} = \left\{0, ~ 1, ...\right\}$ be the set of natural numbers. Prove that $(\mathbb{N},~\le)$ is a poset under the ordinary order. Solution: let $x \in\mathbb{N}$, then $x \le x$ as of course $x = x$. If also $y \in\mathbb{N}$, then $x \le y$ and $y \le x$ implies $x =...
  29. W

    Transcendental Functions Containing Natural Logs

    Homework Statement Evaluate the integrals a) y= b) y= Homework Equations The Attempt at a Solution I've tried using the Reciprocal Rule and substitution of each ln function with u to get a workable result, but haven't come anywhere near a recognizable solution. The answers...
  30. C

    Induction to demonstrate n-1 is a natural number

    The question is as follows: Using an induction argument if n > 1 is a natural number then n-1 is a natural number. P(n)=n-1 such that n-1 is a natural number Following the steps: Base case: n=2, P(2)=1 which is a natural number. We fix a natural number n and assume that P(n)=n-1 is...
  31. B

    Difference between Essential a Natural BC's

    Folks, I am looking at the Ritz method for the following problem ##\displaystyle -\frac{d^2 u}{dx^2}-u+x^2=0## for ##0<x<1## with boundary conditions ##u(0)=0## and ##\displaystyle \frac{du}{dx} |_{x=1} =1## The last derivative term, how do I know whether that is a natural or...
  32. C

    Question about natural numbers.

    Are there an \aleph_0 # of natural numbers with an \aleph_0 # of digits?
  33. Arsenic&Lace

    Testing SAT math scores; low score indicative of natural ability?

    I've actually already completed my first year of college, with quite modest results. Something which has been causing me quite a bit of psychological bother though is whether or not my SAT math score is a reflection of some kind of natural ability or intelligence, rather than a reflection of...
  34. N

    Cantilever Beam Uniform Mass Natural Freq

    Hello For my dynamics I had been going through some examples and verifying them using Staad Pro. However, I been having issues with some of the examples as some do not show the full detail of calculation description. The one example been having problem with is where you must calculate the...
  35. C

    Natural frequency, damping ratio and steady state amplitude help needed

    (1) A mass of 3.0 kg is suspended from a vertical spring and produces a static deflection of 60 mm. The system is also subjected to viscous damping of 36 N s/m. Calculate the value of the: (a) natural frequency i. In Hz ii. And rad/s (b) damping ratio...
  36. Q

    What natural phenomenon explains this glowing object.

    Many years ago I was sat playing cards with friends when I saw this strange light outside hovering just above a door handle so I went to have a look. It was about the size of a golf ball and had some resemblance to a flame but with very different properties. It was silent. It was in...
  37. T

    1. Symmetric difference; 2. Commutativity of natural numbers

    Homework Statement I have two problems that I got stuck. 1. \exists ! N\in P(X) , A\Lambda N=A, \forall A\in P(X) and for each A\in P(X), \exists ! A'\in P(X) , A\Lambda A' =N 2. Prove a+(b+c) = (a+b) +c, for positive integers a, b, cHomework Equations 1. Given sets A,B \in P(X), where P(X)...
  38. C

    What is the significance of taking derivatives in the form d ln f(x) / d ln x?

    Homework Statement What does it mean when the derivative of a function f(x) is in the form: d ln f(x) / d ln x ? Is it the logarithmic scale derivative, or something? Homework Equations d ln f(x) / d ln x The Attempt at a Solution Googling.
  39. D

    Resonant Frequency & Natural Frequency?

    Hello guys! Is it possible to convert a natural frequency to resonant frequency with maybe some kind of formula? I was given a transfer function and I was asked to draw a root locus plot and determine the resonant frequency. I know how to get the damping ratio and natural frequency and the value...
  40. Y

    Natural Frequency of Solid Spheres

    Dear Physics Forum community, I am posting here as a last resort, so any guidance/references would be much appreciated. As a small part of my project, I need to calculate the natural frequency of metallic solid spheres. All I have been able to find on the web is the Schummann Resonance...
  41. B

    Definition Of Natural Logarithm

    Hello, The definition is ln(x) = \int_1^x\frac{1}{t}dt I have read several sources regarding this, but what I can't seem to find is why it was defined this way. What is the justification for defining it this way, and how was ln (x) found to be the same as the that particular integral?
  42. L

    Integral with natural log problem

    Hello, The problem is ∫(ln x)/(x + x ln x) dx. I've done most other problems in the set, but don't know where to start with this one. Although we are just learning integration by parts, I'm not sure how this would apply. I can get to ∫u/(1+u) du Thanks for any help. Homework Statement...
  43. C

    Question about the natural numbers.

    Is the set of natural numbers the only infinite set that is not a power set of another set?
  44. R

    Does natural iron have a denser nucleous then lab made iron?

    I've heard Iron has the most condensed nucleous out of all the elements, and I asume it is due to the enormous amount of pressure in a stars core just before the end of its life. My question is if we made iron in a lab, would its nucleous be just as condensed as natural iron or would it be...
  45. S

    Quantitative modeling in social science vs natural science

    The study of social science phenomena using empirical data such as register data* are very often approached with an regression model. One of the most used approaches is a linear model where the parameters is estimated with ordinary least squares. The models of this type is often called...
  46. S

    Proving Existence of an Element in a Non-Empty Subset of Natural Numbers

    Hello all. I have been reading Halmos's Naive set theory. In chapter 12., there is an excercise problem which states I thought a lot about this but this seems like a theorem to me and is not at all trivial to prove it. I would greatly appreciate it if you can give me a hint or a clue as...
  47. R

    Natural Selection and inanimate matter

    Was the evolutionary principle of natural selection at work on the Earth before animate matter(life) emerged? Inanimate chemicals replicated before R/DNA and the first living cell. Did natural selection apply to these chemical molecules? If the answer is yes, is it just a hypothesis or has...
  48. D

    Natural Logs, adding variable exponents.

    Homework Statement e^2x * e^2 Homework Equations The Attempt at a Solution Really, I'm just a little bit confused on how I would go about adding the exponent. None of the examples in the book cover that. Is it simply e^2x+2?
  49. I

    The product of 8 consecutive natural numbers will not be a perfect square?

    I wish to show that the sum of 9 consecutive natural numbers: n(n+1)(n+2)(n+3)...(n+8) will not be a perfect square. This problem came by as a result of another problem I was doing and I'm wondering if anyone knows/has come across this already. After some searching I found that n! is not a...
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