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. A

    Calculation of different natural frequencies of a material

    Hi, As far as I know, every material has different sets of natural frequencies associated with it. For example, A simple one dimensional oscillator with stiffness "k" and mass "m" has a formula for calculating its natural frequency = 1/2pie*squareroot(k/m). I was wondering if there are...
  2. haruspex

    Insights FME in Probability - Conditionals in Natural Language - Comments

    haruspex submitted a new PF Insights post Frequently Made Errors in Probability - Conditionals in Natural Language Continue reading the Original PF Insights Post.
  3. K

    Proving combination is a natural number by induction

    Hi, I've seen on on several sites that you can prove that nCr, where r<=n, is a natural number. I'm not sure how to do this by induction. So I need help on this proof. How do I write this as a mathematical statement at the start of the induction proof? Thank you
  4. C

    MHB Partial derivatives of the natural logs

    Find the partial derivatives of the following function: Q=(1/3)logeL+(2/3)logeK Any help would be much appreciated! Below is my working out so far: \frac{\partial Q}{\partial L}= \frac{\frac{1}{3}}{L} \frac{\partial Q}{\partial K}= \frac{\frac{2}{3}}{L} Are these correct?
  5. Stoney Pete

    How to construct the natural numbers with hypersets

    I'm not a logician or mathematician but a philosopher (with dyscalculia) so please forgive me for skipping the technicalities... My question is this: Is there in the theory of non-well-founded sets (hypersets) something analogous to the set-theoretic construction of the natural numbers in ZF...
  6. A

    Problem with integration, relating natural log and arctanh

    Homework Statement The problem is actually from chemical kinetics, but my problem is solving the differential equation obtained. (dx(t))/(dt) = -j*x^2-k*x+k*a ; x is a function of t, and j,k,a are all real positive constants. Homework Equations I know this is a Ricatti type equation. But this...
  7. S

    Restricted (Natural) cubic spline - wrong equation?

    My Restricted (Natural) Cubic Spline Equation is Wrong ? I am trying to fit a restricted cubic spline (natural cubic spline) to toy data, attempting to follow Hastie, Tibshirani, Friedman 2nd ed. 5.2.1 p.144-146, Eqs 5.4 and 5.5. Data: Is basically a transposed ‘S’ shape. R-code is: n <© 100 x...
  8. A

    Vibration problem: natural frequency=resonance?

    Hi... I am leanring some knowledge about vibration. For a given vibaraiton system, for example, cantilever beam, we can perform modal anlaysis and found five natural frequency of 3, 6, 8, 10 and 20 Hz (just made up) and five corresponding vibration modes. after that we give a harmonic force on...
  9. B

    Why natural frequency conveyors are not dangerous?

    I've read that natural frequency conveyors are very efficient because the drive only compensates for the amplitude that's lost in the elastic supports. Could you please explain how is this different from working at resonant frequency which is so dangerous? P.S. What kind of analysis should I...
  10. B

    What are the features of natural frequency vibro-conveyor?

    I'm considering two types of vibrating feeders, brute force and natural frequency. Can you tell me how natural frequency conveyor works? What kind of design should I choose to transfer light materials? What If I want to use an upwards angle, how do I determine that upward going path of...
  11. Emmanuel_Euler

    Isaac Newton - The Mathematical Principles of Natural

    how can i find this book?? ( Isaac Newton - The Mathematical Principles of Natural Philosophy)
  12. S

    MHB Discover the Mysterious Natural Number with 10 Unique Digits

    I'm a natural number written with 10 different digits such that for all i∈1,...,10 the number formed by my i first digits (from left to right) is divisible by i. Who am I? Anyone got any insight? It would be much appreciated.
  13. S

    Natural log differentiation question

    Homework Statement f(x) = 1/ln (10-x) -- I would assume it to be a fairly simple equation, but I am screwing it upHomework Equations What is f'(x)?The Attempt at a Solution f'(x) = (ln (10-x))^-1 = -(ln (10-x))^-2 * -1 * 1/(10-x) -- 2 negatives cancel out = 1/(10-x) (ln(10-x))2 --...
  14. S

    Derivative of natural log function questions

    Homework Statement Hello, I had a few derivative of the natural logarithm functions questions. It seems like it should be fairly straightforward, but I am turning it into a pig’s ear.On my honor, none of these are problems on an assessment per se, however, they are not materially different than...
  15. engnrshyckh

    Finding the undamped natural frequency of 2nd order system

    the following 2nd order differential equation is given: 2y'' + 4y' +8y=8x........(1) i want to find damping ratio, undamped natural frequency, damping ratio coefficient and time constant for the above system. solution: comparimg (1) with general system equaion (veriable can be exchanged)...
  16. T

    Derivative of Natural Log: How to Solve Number 3 on Homework Assignment

    Homework Statement I posted a picture of it and my attempt it is number 3 Homework EquationsThe Attempt at a Solution I tried using log properties and I am not sure what went wrong and how to arrive at the correct answer. Mod note: Messy, disorganized image deleted.
  17. S

    How to calculate natural frequency of a circular plate

    I am trying to get used to using a Data Physics analyzer at work in order to measure the natural frequency of components of a larger project I am involved in, my method described is intentionally crude as I was trying to do this as a quick play around before diving into the real thing.. To...
  18. B0b-A

    How many elements in a hand-full of sand ?

    How many of the [ 92?] naturally occurring elements could be found in hand-full of sand ?. Including those only present at minuscule , but measurable , amounts. http://en.wikipedia.org/wiki/File:PismoBeachSand.JPG
  19. F

    Natural frequency of 3 coulomb force bound particles in EF

    Homework Statement I was given a task to model (using Matlab) 3 identical particles in external field and find spectra of lowest system energy states using gradient descend method for each particle in the system. I did a run of 500 random generated coordinates and found this distribution...
  20. T

    Natural Frequencies and Harmonics

    Homework Statement Basically, I was reading the following passage from a textbook, and I'm confused as to why they mention natural frequencies? Doesn't each harmonic have just one frequency that it oscillates at? From what I understand, the natural frequency is just the frequency an object...
  21. caffeinemachine

    MHB Natural Isomorphism b/w Dual Spaces Tensor Prod & Multilinear Form Space

    I am trying to prove the following. Let $V_1, \ldots, V_k$ be finite dimensional vector spaces over a field $F$. There is a natural isomorphism between $V_1^*\otimes\cdots\otimes V_k^*$ and $\mathcal L^k(V_1, \ldots, V_k;\ F)$. Define a map $A:V_1^*\times\cdots\times V_k^*\to \mathcal L^k(V_1...
  22. Math Amateur

    MHB What is Stoll's definition of the natural logarithm function?

    I am reading Manfred Stoll's book: Introduction to Real Analysis. I need help with Stoll's definition of the natural logarithm function (page 234 -235) The relevant section of Stoll reads as follows: In this section we read: " ... ... To prove (a), consider the function L(ax), x \gt 0. By...
  23. E

    Maximum order of essential and natural conditions

    Is there a physical explanation for why when given a differential equation with spatial derivative of spatial order 2m the maximum order of the essential (displacement) boundary condition is m, and the maximum order of the natural (force) boundary condition is 2m-1 for example, the equaiton...
  24. E

    Closed/Open Sets and Natural Numbers

    Homework Statement I am trying to understand why ℕ the set of natural numbers is considered a Closed Set. 2. Relevant definition A Set S in Rm is closed iff its complement, Sc = Rm - S is open. The Attempt at a Solution I believe I understand why it is not an Open Set: Given that it...
  25. G

    Is the natural behavior of matter to lose energy?

    Hello everyone this is my first post here. I'm sorry if my spelling is terrible. I am no physicists so I would like to ask if my thinking was going in the right direction. When I say energy I really mean electromagnetic radiation. The Earth receives it constantly from the sun but there is no...
  26. O

    Why do natural Moons revolve around planets?

    Why do Moons revolve around planets? If because of gravitational pull, why won't they clash with planets. Please help me get answer to this question!?
  27. P

    Natural Spectrum of the Universe?

    Does anyone know where I might find the natural spectrum of bodies in the universe? Something like http://upload.wikimedia.org/wikipedia/commons/2/27/Spectrum_of_Sunlight_en.svg as a sum of all known stars, black holes, pulsars, solar winds on planetary atmospheres, etc covering the entire...
  28. Charles Stark

    Natural Oscillation Frequencies

    Homework Statement Over the years, buildings have been able to be built out of lighter and lighter materials. how has this affected the natural oscillation frequencies of buildings and the problems of resonance due to passing trucks, airplanes, or by wind and other natural sources of vibration...
  29. physicsisgreat

    Units in quantum mechanical problem about 4-He

    Homework Statement Units of the problem are chosen to be such as KB = 1 and ħ = 1 so that energies are expressed in Kelvin and lengths in Å. The professor says the resulting value of ħ2 / 2 m for a 4-He atom is 6.0599278: how is that possibile? Homework Equations Natural units websites give...
  30. evinda

    MHB Each subset of the natural numbers is finite or countable

    Hello! (Smile) Proposition: Each subset of the natural numbers is finite or countable. Proof: Let $X \subset \omega$. First case: $X$ is bounded. That means that $(\exists k \in \omega)(\forall y \in X) y \leq k$. Then $X \subset k+1$ and $X$, as a subset of a finite subset, is finite ...
  31. evinda

    MHB Can Recursion Define Natural Number Addition?

    Hello! (Wave) For each pair of natural numbers $m \in \omega, n \in \omega$ we define: $$m+0=m\\m+n'=(m+n)'$$ We fix a $m$ and recursively the operation $m+n$ is defined for any $n \in \omega$. Knowing for example that $m+0=m$ we can conclude what $m+1$ means. $$m+1=m+0'=(m+0)'=m'$$ and...
  32. evinda

    MHB Prove Natural Numbers Subset Property

    Hello! (Wave) I want to prove that for any natural numbers $n,m$ it holds that: $$n \subset m \leftrightarrow n \in m \lor n=m$$ $"\Leftarrow"$: Using the sentence: "For any natural numbers $m,n$ it holds that $n \in m \rightarrow n \subset m$" if $n \in m \lor n=m$, we conclude that $n...
  33. S

    Find Natural Response of RLC Circuit: No Forcing Voltage?

    To find the natural response of a RLC circuit driven by a time-varying voltage, why do we assume that there's no forcing voltage driving the circuit even if there is one?
  34. gracy

    Natural selection and speciation

    How natural selection leads to speciation?Speciation is a process of making a new species ,right? Natural selection just select one organism from a bunch of organisms of the same species to survive ,so how does it leads to creation of a new species?For example in an area covered with snow ,white...
  35. E

    Find total length of cylinder (springs, natural frequency)

    Homework Statement A simple pressure relief device is shown in Figure Q6.1 below. It consists of a piston of mass 0.5 kg and thickness 3 cm sliding without leakage or friction into a cylinder of diameter 5 cm. The bottom section of the cylinder can be exposed to a varying source of pressure...
  36. B0b-A

    Do natural diamonds form from carbon-vapour or liquid-carbon

    What is the state of carbon just prior to it forming a diamond, deep in the Earth's crust ? Carbon vapour , or liquid carbon ?.Update: I think I've managed to answer my own question ... http://www-als.lbl.gov/images/stories/Science_Highlights/Highlights/108carbon1.png...
  37. X

    Natural numbers distributive lattice

    I need a proof that the set of natural numbers with the the relationship of divisibility form a distributive lattice with gcd as AND and lcm as OR. I know it can be shown that a AND (b OR c) >= (a AND b) OR (a AND c) for a general lattice, and that if we can show the opposite, that a AND (b OR...
  38. C

    Natural rope friction and snapping

    Ok, so there is a little discussion going on in my circle of associates at the moment regarding rope break dynamics: http://esinem.com/news/rope-friction-break-tests If you watch both videos, you can see that some ropes (usually the synthetic ones) will saw through the static bight of the...
  39. F

    Natural Light and Linear Polarizer

    Hi, In the first place I want to apologize for my bad English. In the second, I have a concept doubt, If I make natural light to go on a linear polarizer of angle 0º, the intensity, or irradiance here, It would be I0/√2 and it's Jones vector would be (1, 0) (as column). What would happen If I...
  40. PhysicsKid0123

    Natural vs normal vs resonant frequencies

    is there a difference between natural frequencies, normal frequencies, and resonant frequencies? Any subtle differences? I've seen them used at different times, and I've also seen at least two used in a single sentence implying some kind of difference. For example, "Natural Frequencies and...
  41. A

    What is the natural force of a 25kg block that is not moving?

    What is the natural force of a 25kg block that is not moving?F=ma, g=9.81m/s^2 Attempt: (25kg)*(9.81m/s^2)= 245.25kg ?
  42. emanoelvianna

    Natural deduction sets (Rules of nature deduction)

    Hello fine. I'm studying logic and great difficulties to understand its principles, and should prove some theories involving the laws of identity of sets of mathematics using the method of natural deduction, they are: a) A ∪ ∅ = A b) A ∩ ∅ = ∅ I am trying as follows, but I can not solve...
  43. Math Amateur

    MHB Proof of Infinitely Many Units of Z[sqrt n] for Eacn Non-Square Natural Number

    In John Stillwell's book: Elements of Number Theory, Exercise 6.1.3 reads as follows: ------------------------------------------------------------------------------------------------- Show that \mathbb{Z} [ \sqrt{n} has infinitely many units for any non-square natural number n...
  44. lovexmango

    What is the parametrization of the graph of ln(x)?

    Let k(x) be the curvature of y=ln(x) at x. Find the limit as x approaches to the positive infinity of k(x). At what point does the curve have maximum curvature? You're supposed to parametrize the graph of ln(x), which I found to be x(t)=(t,ln(t)). And you're not allowed to use the formula with...
  45. D

    MHB Natural frequency of a crane dropping a car

    An electromagnet weighing \(3000\) lb is at rest while holding an automobile of weight \(2000\) lb in a junkyard. The electric current is turned off, and the automobile is dropped. Assuming that the crane and the supporting cable have an equivalent spring constant of \(10000\) lb/in, find the...
  46. M

    Properties of natural log and absolute value

    Homework Statement from -lnIxI to lnI x^-1I , I try to go from -lnIxI to lnI x^-1I by using some properties. Homework Equations - lnIxI The Attempt at a Solution First I write the -lnIxI as -1*lnIxI and then I use -1 as an exponent to absolute value of x in the natural log that is ln (...
  47. D

    Natural position of a string wrapping around a cone

    I've had a problem I encountered at work some time ago and took a personal interest in. I never did end up solving it, but I've recently looked at it again. It goes like this: You have an axisymmetric part, such as a cone, and it's positioned such that its central axis is coincident and...
  48. PsychonautQQ

    Why are the results of this natural log integration seemingly inconsistent?

    Homework Statement Integrate (-m-kx)^-1 dx from a to b. The Attempt at a Solution So using the integral form I get the integral of (-m-kx)^-1 dx is (-1/k)*[ln(-m-kx)] with the bracketed expression being evaluated between a and b. (-1/k)*[ln(-m-ka) - ln(-m-kb)] My first...
  49. D

    MHB Natural frequency of a pendulum being lowered at 2m/s

    A heavy machine weighing \(9810\) N is being lowered vertically down by a winch at a uniform velocity of \(2\) m/s. The steel cable supporting the machine has a diameter of \(0.01\) m. The winch is suddenly stopped when the steel cable's length is \(20\) m. Find the period and amplitude of the...
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