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. P

    MHB Have I gone wrong in putting irrationals in one to one correspondence with natural numbers?

    Hi, New member here and have been dabbling with some aspects of George Cantor's work. I think I have found a way to put the irrationals in one to one correspondence with natural numbers but thousands of mathematicians over the years might disagree. Is there a subtle error ( or even a blatant...
  2. T

    MHB Finding Maclaurin series of a natural log function

    I need to find the Maclaurin series of this function: $$f(x) = ln(1 - x^2)$$ I know that $ln(1 + x)$ equals $$\sum_{n = 1}^{\infty}\frac{(-1)^{n - 1} x^n}{n}$$ Or, $x - \frac{x^2}{2} + \frac{x^3}{3} ...$ If I swap in $-x^2$ for x, I get: $$-x^2 + \frac{x^4}{2} - \frac{x^5}{3} +...
  3. T

    MHB Maclaurin series for natural log function

    I'm examining the Maclaurin series for $f(x) = ln(x + 1)$. It is fairly straightforward but there are a few details I'm not getting. So: $$ ln(x + 1) = \int_{}^{} \frac{1}{1 + x}\,dx$$ which equals: $A + x - \frac{x^2}{2}$ etc. or $A + \sum_{n = 1}^{\infty}(-1)^{n - 1}\frac{x^n}{n}$ I'm...
  4. karush

    MHB S6.7.1.13 natural log Integration

    $\large {S6.7.1.13}$ $\tiny\text {natural log Integration}$ $$\displaystyle \int e^{\sqrt[3]{x}} \, dx = 3\left(x^\frac{2}{3} -2\sqrt[3]{x} +2\right){e}^\sqrt[3]{x}+C \\ u=x^{1/3} \therefore 3{x}^{\frac{2}{3}} du = dx $$ $\text{not sure if this is how to start to get to a 3 term answer}...
  5. T

    MHB What is the Integral of 1 over 2 to the Natural Log of X?

    I have this integral $$\int_{}^{}\frac{1}{{2}^{lnx}} \,dx$$ I'm not sure the best way to do it. I tried u-substitution: $u = {2}^{lnx}$ and thus $u = {x}^{ln2}$, therefore $du = ln2({n}^{ln2 - 1}) dx$. However, not sure how to proceed from there.
  6. T

    MHB Derivative of function with a natural log in the exponent

    Supposing we have $f(x) = {2}^{lnx}$, how would we find $f'(x)$?
  7. T

    MHB Natural Log Inequality: True or Misunderstanding?

    I was talking to my professor and she said that $(ln n)^a < n$ for all values of $a$. Is this true or was I misunderstanding?
  8. T

    MHB Equality of natural ln function

    I have this equality: $$ (\ln\left({n}\right))^4 < {n}^{\frac{1}{4}} $$ where $ n > 1$ Can I derive a law from this such that $$ (\ln\left({n}\right))^b < {n}^{\frac{1}{b}} $$ where $n > 1$ ?
  9. Sentosa

    How can natural selection be true if disease is inherited?

    I just finishedOn the Origin of Species. It seems Darwin is saying that characteristics that make it less likely for an organism to survive will drop out over time. But other scientists tell me that cancer has a genetic link, that suicide has a genetic predisposition, etc. Many diseases have...
  10. T

    MHB Natural Log Rule: $\frac{a}{b}=-\frac{b}{a}$?

    If I have $\ln\left({a}\right) - \ln\left({b}\right)$ that would equal $\ln\left({\frac{a}{b}}\right)$ or $-(\ln\left({b}\right) - \ln\left({a}\right))$ which is also $- \ln\left({\frac{b}{a}}\right)$. So does this mean $\ln\left({\frac{a}{b}}\right)$ equals $- \ln\left({\frac{b}{a}}\right)$?
  11. T

    MHB Limit of Natural Log Sequence: How to Find It Using L'Hopital's Rule?

    I have this sequence: $${a}_{n} = \ln \left(\frac{12n + 2}{-9 + 4n}\right)$$ I need to find the limit of this sequence. How can I go about this? Do I need to apply L'Hopitals rule? I'm unsure how to simplify this expression. If I use the rule $\ln(\frac{a}{b}) = \ln a - \ln b$ I get $\infty -...
  12. ahmed tb

    Determination of the natural frequency of a Hartnell governor

    Homework Statement Homework EquationsThe Attempt at a Solution I found this solution for the nature frequency but here it does not include the Ball weight and centrifugal force in the moment balance equation about the pivot (O), it is wrong answer...is not it? I tried to solve the problem...
  13. H

    B What is the source of this intriguing natural noise diagram?

    I am trying to find the source of this diagram which came out of some old notes (not mine) I found uploaded on the web. the referencing is not clear. it seems a great diagram and I would like to find a similar one like it (or better graphics) if not the original, and some explanatory text. I...
  14. S

    Studying How important is natural talent?

    I'm a (physical) chemistry major, middle of my undergrad but I didn't really get into it until very recently. After realizing that I was missing out, I started to self study physics and chemistry earlier last month pretty seriously. I have come to the conclusion that I have no natural talent...
  15. P

    What is the term for all numbers except the natural numbers?

    Is there a term used to describe all number except the natural numbers?
  16. Liam A

    I How to create a natural vacuum

    i work at a cavern attraction and one of the parts in the speech we say is that a section of the cavern was once filled with a naturally occurring vacuum until it was punctured and destroyed. we explain in the speech that the vacuum was created when a river packed in that area with mud and clay...
  17. percussive

    Mathematical Principles of Natural Philosophy

    Is Philosophiæ Naturalis Principia Mathematica by Sir Isaac Newton, one of the top 5 Physics-Maths books of all times?
  18. anemone

    MHB Solving Equation In The Set Of Natural Numbers

    Find all the natural numbers $a$ and $b$ such that $(a^2+1)(b^2+1)+45=2(2a+1)(3b+1)$.
  19. anemone

    MHB Find solutions in natural numbers

    Find the solutions in natural numbers for the following equation: \frac{10}{x+10}+\frac{10\cdot 9}{(x+10)(x+9)}+\cdots+\frac{10\cdot 9\cdot 8 \cdots\cdot 3 \cdot 2 \cdot 1}{(x+10)(x+9)(x+8)\cdots(x+3)(x+2)(x+1)}=5
  20. S

    Finding the Dimension and Lifetime of G_F in Natural Units

    Homework Statement In natural units, the inverse lifetime of the muon is given by ##\tau^{-1}=\frac{G_{F}^{2}m^{5}}{192 \pi^{3}}##, where ##m## is the muon mass, ##106\ \text{MeV}##. What is the dimension of ##G_{F}## in natural units? Put in the factors of ##\hbar## and ##c## so that the...
  21. D

    How to find the natural frequency in ansys apdl

    Hi! I am new in ansys. I am doing rotor dynamic study of a high speed rotating shaft. the shaft comprise of two discs and at the it ends the shaft is supported by the bearing I am facing problem in modelling stage please tell me how to model the bearing and disc briefly.I am uploading the image...
  22. T

    What is the energy content of natural gas on an LNG transporter?

    My brother is working on an LNG transporter and I would like to know how much energy there is in the LNG the ship is transporting, here is the info I got : Methane ISO6974 99.8518 mole% ethane 0.0137 mole% propane 0.0000 mole% i-butane 0.0000 mole% n-butane 0.0000 mole% i-Pentane 0.0000 mole%...
  23. E

    Exploring the Diversity of Natural Electrical Circuits: A Scientific Perspective

    Hello everyone, I have a strange question. Can complete electrical circuits be found in nature? If so, can you give any examples? And what is necessarily required (besides electricity) for a complete electrical circuit to occur, naturally or unnaturally?
  24. K

    Natural SUSY-MSSM and NMSSM gluino mass bounds @LHC

    Gordon Kane states that string theory predicts 1.5 TEV Gluinos. Tommaso Dorigo No deviation is seen in gluino searches. The limit extends to 1.7 TeV, thus ruling out the region favoured by Gordon Kane in a recent paper. What's the upper limit gluino masses a 13/14 TEV can produce, and what is...
  25. Shadow-Shocker

    Any natural, non-flammable, alternative to acrylic cement?

    I am doing a project that relates to welding acrylic. I got the bottle today, and I can't use it because its flammable and has chemicals known by the state of California to cause cancer (makes you wonder why the hell they would market this crap). Are there any clean, non-flammable, and...
  26. D

    Natural units and dimensional analysis

    As far as I understand, a natural system of units is one in which the numerical values of ##c## and ##\hbar## are unity. However, they still have dimensions, indeed ##[c]=LT^{-1}## and ##[\hbar]=ML^{2}T^{-1}##. How is it the case then, that certain quantities, such as the action ##S##, can be...
  27. Junichirol

    Matlab (calculate natural frequencies using eig function)

    Homework Statement Determine the corresponding natural frequencies M = [1 0 0 0;0 1 0 0;0 0 1 0;0 0 0 1]; C = [2 0 0 0;0 0 0 0;0 0 0 0; 0 0 0 0]; K = [10 -5 0 0;-5 10 -5 0;0 -5 10 -5;0 0 -5 10]; Homework Equations A = [zeros (4) eye(4); -M/K -M/C] [V,D] = eig(A) The Attempt at a Solution just...
  28. S

    Understanding the Manipulation of Natural Logarithms

    How is it true that: Log[L+(Z^2+L^2)^(1/2)] - Log[-L+(Z^2+L^2)^(1/2)] = 2{Log[L+(Z^2+L^2)^(1/2)] - Log[Z]} ?
  29. gjonesy

    Oklo-phenomenon - is this a Natural nuclear reactor?

    I read a very interesting article about this u235 deposit found in Africa. Everything I have read about it suggest that some of the components needed for this to naturally occur can not exist without human intervention. The water involved in the nuclear reaction must be extremely pure. Even a...
  30. Sace Ver

    How did natural selection impact the size and foot structure of horses?

    Explain how natural selection might have caused the changes in each of the following: -Size of horses -Foot structure of horses I'm quite sure as to why the size of horses needed, and I'm not quite sure why the structure of the foot needed to change.
  31. C

    System Analysis - Determining Dampening and Natural Frequency

    Homework Statement Problem and work attached. It is mostly diagrams so I have just uploaded the pictures. I think what I did to determine the transfer function was correct. I'm not quite sure how to do the last section of part (a) where I need to determine the dampening, static gain, and...
  32. T

    Proof of |2^N x 2^N| = |2^N| with N the natural numbers

    Hello, At my exam I had to proof the title of this topic. I now know that it can easily be done by making a bijection between the two, but I still want to know why I didn't receive any points for my answer, or better stated, if there is still a way to proof the statement from my work. My work...
  33. Gimblestitch

    Is the IU East BA in Natural Science Worth Pursuing?

    Greetings, I see that Indiana University East offers the new titular degree with a concentration in mathematics. Is anyone in this program? Is a B. A. degree worth having? Thanks, Gimblestitch
  34. P

    Understanding the Closed Set of Natural Numbers

    Hi, How and why set of natural numbers is closed?
  35. A

    Error in Natural Frequency (Lab)

    So I just did a lab on resonant frequency, and have to find the error of the period: $$T = 2π\sqrt{m/k}$$ m and k were measured with an error of Δm and Δk. My teacher didn't explain well how to do errors, so I just want to know if I did this right. Prorogation of Error equations: $$y=x^n ⇒...
  36. astrololo

    The natural length of a spring

    Homework Statement A block is fixed on the extremity of a mobile ideal spring that is horizontal and which has the other side of it fixed (Non mobile). When the length of the spring is 50 cm, the block has a force of 5 N on the right; When the length of the spring is 80 cm, the block has a...
  37. R

    Height limitation for natural circulation thermosiphon

    Suppose I have an overhead tank that heats hot water by natural circulation via a thermosiphon (& a Heat Exchanger with some source of waste heat), is there a limitation on how tall this loop can be? e.g. Can there be an elevated tank at 30 feet with a heat exchanger at ground level that heats...
  38. S

    Simplifying natural log of complex number

    Homework Statement The problem is to sketch lines of constant u and v in the image plane for the function Log[(z+1)/(z-1)]. Homework Equations z=x+iy The Attempt at a Solution In order to do this I have to get the expression into u+iv form, so that I can read off and manipulate the u and v...
  39. J

    Proving that the natural numbers are countable, stuck.

    Homework Statement [/B] I'm working through a problem in Abott's Understanding Analysis, second edition, the statement of the problem being: "Fix a member n of the natural numbers and let An be the algebraic numbers obtained as roots of polynomials with integer coefficients that have degree n...
  40. M

    Natural Frequency: Find Equation of Motion

    Homework Statement Find the natural frequency Homework Equations On picture The Attempt at a Solution Just need help with the equation of motion.
  41. Fredrik

    Natural deduction: True iff not false

    I'm studying a book on logic, and I'm having difficulties with the book's rules of natural deduction. ##P_1,P_2,\dots## are variables that represent propositions like ##x>0##. All variables and the symbols ##\top## and ##\bot## are formulas. For all formulas ##\varphi,\psi##, the following...
  42. TomW17

    Natural frequency of a simple harmonic system

    Homework Statement Derive the natural frequency f_n of the system composed of two homogeneous circular cylinders, each of mass M, and the connecting link \text{AB} of mass m. Assume small oscillations. Homework Equations The sum of the kinetic + potential energies in an isolated system...
  43. G

    What animals are good example of natural enemy in PA setting

    I am writing story about Earth set 1000 years in future and I am looking for good example of living animals. So far I had wolves or dogs on my mind, how would they change in 1000 years?
  44. Tam Le

    Hearing which natural frequencies

    If you pluck a guitar or cello string, the string vibrates at its fundamental and harmonic frequencies. Suppose the 3rd harmonic has the greatest vibrational amplitude out of all the other rung-out natural frequencies. Do we still associate the pitch with the fundamental, or will the pitch now...
  45. A

    Natural ventilation through single opening

    Hello, I am wondering what will happen if I try to ventilate a room by natural ventilation through a single opening. In this opening there will be a ventilation grill. I already found a paper about counterflow through an open door by temperature differences...
  46. Topolfractal

    In(x) Closed Form Formula: Does It Exist?

    Does there exist a closed form formula for in(x)?
  47. Tam Le

    Natural Frequencies and Vibration Amplitudes of Object A

    Suppose a sound wave with multiple natural frequencies--a complex sound wave--strikes Object A. Some of those frequencies matches the natural frequencies of Object A. A) Will Object A vibrate at all the different frequencies or only to its natural frequencies? B) If Object A vibrates at all...
  48. Deepak K Kapur

    Why do we like natural scenery?

    Why do most of the people like natural scenery (with varying degrees, of course)? Is it in our genes? Does it serve an evolutionary purpose? Any thoughts?
  49. M

    MHB What is the origin of action at a distance forces?

    Hey! :o Action-at-a-distance forces are for example the gravity, the electromagnetic forces. They are reduced slowly in respect to the distance and are important even at distances comparable to the dimensions of the volume of the fluid. Is this correct?? (Wondering) Which is the natural...
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