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. lfdahl

    MHB Natural Numbers with Repeating Digits: Solving for Perfect Squares

    Find all natural numbers $n$, for which: \[\sqrt{1 \underbrace{4...4}_{n \: times}} \in \Bbb{N}\]
  2. H

    Natural Frequency of a rod

    does the natural frequency of a steel rod rigidly fixed will vary when it is assembled with another rod by universal joint?
  3. Math Amateur

    I The Set of Positive Integers - a Copy of the Natural Numbers

    I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ... I am currently focused on Chapter 1: Construction of the Real Numbers ... I need help/clarification with an aspect of Theorem 1.3.7 ... Theorem 1.3.7 and the start of the proof reads as follows: n the above proof we...
  4. Math Amateur

    MHB The Set of Positive Integers as a Copy of the Natural Numbers ....

    I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ... I am currently focused on Chapter 1: Construction of the Real Numbers ... I need help/clarification with an aspect of Theorem 1.3.7 ... Theorem 1.3.7 and the start of the proof reads as...
  5. Math Amateur

    Foundations Construction of the Number Systems ... Natural, Integers, etc

    At present I am trying to understand the construction of the number systems ... natural, integers, rationals and reals ... What do members of PFs think is the clearest, most detailed, most rigorous and best treatment of number systems in a textbook or in online notes ... ? NOTE: I am currently...
  6. Math Amateur

    MHB Construction of the Number Systems .... Natural, Integers, Rationals and Reals

    At present I am trying to understand the construction of the number systems ... natural, integers, rationals and reals ... What do members of MHBs think is the clearest, most detailed, most rigorous and best treatment of number systems in a textbook or in online notes ... ? NOTE: I am...
  7. Math Amateur

    MHB The Well-Ordering Principle for the Natural Numbers

    I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ... I am currently focused on Chapter 1: Construction of the Real Numbers ... I need help/clarification with an aspect of Theorem 1.2.10 ... Theorem 1.2.10 reads as follows: Towards the end (second last line) of the...
  8. Math Amateur

    I The Well-Ordering Principle for the Natural Numbers ....

    I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ... I am currently focused on Chapter 1: Construction of the Real Numbers ... I need help/clarification with an aspect of Theorem 1.2.10 ... Theorem 1.2.10 reads as follows: Towards the end (second last line) of the...
  9. Math Amateur

    MHB Addition and Multiplication of Natural Numbers - Bloch Th. 1.2.7 .... ....

    I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ... I am currently focused on Chapter 1: Construction of the Real Numbers ... I need help/clarification with an aspect of Theorem 1.2.7 (1) ... Theorem 1.2.7 reads as follows: https://www.physicsforums.com/attachments/6976...
  10. Math Amateur

    I Addition/Multiplication of Natural Numbers - Bloch Th. 1.2.7

    I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ... I am currently focused on Chapter 1: Construction of the Real Numbers ... I need help/clarification with an aspect of Theorem 1.2.7 (1) ... Theorem 1.2.7 reads as follows: In the above proof of (1) we read the...
  11. Buzz Bloom

    I Measuring distance to a galaxy using natural H20 laser

    Today's Astronomy Picture of the Day discusses a method for determining the distance to a galaxy that I had not seen before. https://apod.nasa.gov/apod/ap170707.html For a far away galaxy, the distance to M106 is well-known in part because it can be directly measured by tracking this galaxy's...
  12. davidge

    B Natural Numbers and Odd Numbers

    Given any finite set of natural numbers, it seems evident that the odd numbers form a subset of the natural numbers. But what happens "at infinity"? I mean, if we account for all infinitely many natural numbers, there would be also infinitely many odd numbers. In such case, is it still true that...
  13. BillTre

    New Concept for Zero Emission Natural Gas Power Generation

    Science mag news article on a new electrical power plant being set-up by a start-up. It burns natural gas with pure oxygen and runs turbines with CO2. It makes water rather than using it and is in theory close to competitive economically. . Sounds good to me, but I'm no engineer.
  14. K

    Natural frequency of pulley system

    Homework Statement https://www.physicsforums.com/attachments/197474 Homework Equations 3. The Attempt at a Solution [/B] ma + kx = 0 I know how to do it if the spring is in the middle of the pulley, not using energy method. by the free body diagram. But I am stuck at this. [Updated: I know...
  15. A

    I Selecting a Natural and a Real Uniformly at Random

    This work involves partitioning [ \, 0, 1 ] \, into an uncountable number of subsets, using choice to select a single element from each subset, and then defining a bijection from \mathbb{N} onto each subset using that selected element as a reference. The framework allows for proof of two...
  16. cyclogon

    B Cardinality and Natural Numbers

    Hi, I hoping someone might be kind enough to possibly tell me where I have made an error :) I'm more of a recreational maths person, lol - and I'm trying to make a scheme that 'maps' any decimal number to a natural one. The method I have come up with is a bit odd, I'm hoping it works but still...
  17. paulmdrdo1

    MHB Natural response RL circuit

    as you can see In the image I provided I have derived the equation for i(t) and v(t). On circuit A I use a passive sign convention(current flowing from positive to negative) on the inductor, hence the equation and their corresponding graph. i(t) is decaying exponentially, v(t) is decaying...
  18. paulmdrdo

    Natural response RL circuit

    as you can see In the image I provided I have derived the equation for i(t) and v(t). On circuit A I use a passive sign convention(current flowing from positive to negative) on the inductor, hence the equation and their corresponding graph. i(t) is decaying exponentially, v(t) is decaying...
  19. M

    MHB Natural Deduction: Solving Sequents [7/10]

    Hi guys, does anyone know how to complete proofs of natural deduction for these sequents? ¬ (P ˅ Q), R → P : ¬ R [7] (P & Q) → ¬ R, : R → (P → ¬ Q) [10]the {7} in brackets indicates how many lines each answer should be. I attempted both but my amount of lines were not 7 or 10 Would really...
  20. H

    Natural Frequency for torsional vibration

    I am trying to calculate natural frequency for torsional vibration of fixed fixed beam using following formula. =1/2*3.142 sqrt(K*g/mr^2) hz Where K=J*G/L and G=Modulus of rigidity g=acceleration due to gravity=386.4 in/se2 m=mass hanging on the beam at distance 'r' from the longitudenal...
  21. C

    Determine the natural frequency

    Homework Statement Determine the natural frequency in Hz of the system sketched below given the following values: Mass m=4kg Spring stiffness k=28kN/m Length a=121mm Length b=93mm Homework Equations ω=(k/m)^0.5 The Attempt at a Solution so probably I need to find m should I multiply...
  22. D

    Natural frequency of an Oscillating water column device

    Homework Statement Assuming that an OWC device is floating/moored in monochromatic waves. When there isn't air pressure distribution inside (atmospheric condition) the device behaves as an undambed body (with the oscillating chamber open to the atmosphere). When there is air pressure...
  23. M

    Exploring Natural Fission: Understanding its Role in our Universe

    If the sun and cosmic objects are powered by nuclear fusion.. why is there fission in nature via Uranium or Plutonium.. what purpose does it serve for nature since nature doesn't use it. Unless there are natural processes that uses fission or heat from slow fission (maybe heating up the earth)...
  24. R

    Unlocking the Energy Potential of Trees: A Look at Biomimicry

    A tree seed takes water and minerals(?) from the ground, carbon and oxygen(?) from the air, and heat and light(?) from the sun. When a tree dies and dries up, it can be used as firewood, a source of energy. Is there a way to capture that energy without the seed-tree scenario? i.e., but can we...
  25. L

    A Is there a natural paring between homology and cohomology?

    I am looking at the definition of the characteristic numbers from the wikipedia https://en.wikipedia.org/wiki/Characteristic_class#Characteristic_numbers "one can pair a product of characteristic classes of total degree n with the fundamental class" I am not sure how is this paring defined here...
  26. C

    Selecting a Valve for Natural Gas Flow

    Homework Statement A valve is required to regulate the flow of natural gas. Details of the gas are given in table below. It can be assumed that the pipe size and the valve size are the same [i.e. piping geometry does not have to be allowed for]. The chosen valve type is the V250 rotary ball...
  27. D

    How might I liquefy small quantities of natural gas?

    Several undergraduate and graduate students and I are building a small engine powered by Compressed Natural Gas (CNG). It is a small and straightforward affair, similar to what is found in small equipment such as chainsaws and lawn mowers. I wanted to experiment with Liquefied Natural Gas (LNG)...
  28. F

    Disproving Statement: No Natural Numbers Satisfy y^5 + 1 = (x^7-1)/(x-1)

    Homework Statement Prove that there doesn't exist natural numbers x and y such that the statement holds true. y^5 + 1 = (x^7-1)/(x-1)The Attempt at a Solution I was able to simplify the term down to y^5 / x = x^5 + (x^5-1)/(x-1) Not sure what to do with it
  29. Y

    MHB Limits with the natural logarithm

    Hello I have three limits to calculate, based on a given limits. What I know is: \[\lim_{x\rightarrow 0}\frac{ln(1+x)}{x}=1\] And based on this, I need to find (without L'Hopital rule), the following: \[\lim_{x\rightarrow 0}\frac{ln(1-x)}{x}\] \[\lim_{x\rightarrow 0}\frac{ln(1+x^{2})}{x}\]...
  30. giokrutoi

    2017 times a is a natural number

    Homework Statement find 2017 times A Homework EquationsThe Attempt at a Solution the sum of last members denominator.is 2017 multiplied by 1008 the member before it is 2015 multiplied by 1008 before it 2015 times 1007 2013 times 1007 2013 times 2016 how can i move futher
  31. Andreas C

    B How come this natural logarithm approximation works?

    I came across a guy claiming that the "best approximation" for the natural logarithm of a number is this: ln x=2^n*(x^(2^-n)-1) Oddly enough, it seems to work rather well! I don't really get why it does... I also don't know if it has a limit, I couldn't test it as I don't have access to my...
  32. Mohamed_Wael

    Determine the natural frequencies experimentally

    How can we determine the system properties (natural frequencies & damping ratio ) practically using forced vibration? One way is to measure the phase angle, using the bode plot, the exciting frequency corresponding to 90 (deg) phase shift should be the natural frequency, are there any other...
  33. E

    Engineering Find the natural response of the RLC circuit

    Homework Statement [/B] Find the natural response V1 is a squarewave Homework Equations KCL, KVL The Attempt at a Solution How would I find the natural response using differential equations? Am I doing it right? by KCL \frac{V_1-V_{in}}{R_1}+\frac{1}{L}\int_{0}^{t}V_1(t)dt +...
  34. A

    MHB Finding 3 natural numbers by the rule of Sarrus

    Here is a problem I am working on: Using the Rule of Sarrus: $$\begin{vmatrix} x & y & z \\ z & x & y \\ y & z & x \\ \end{vmatrix} =x^3+y^3+z^3-3xyz,$$ find $x, y, z$ such that $x^3+y^3+z^3-3xyz = 315.$ And here is what I have gotten so far: By row and column operations and by factoring out...
  35. M

    I What does N^2 mean in the case of natural numbers?

    What does the N^2 mean in this case? (Image below) Does it mean, for all two pairs of natural numbers, a and b? How would I represent non pair numbers, i.e. how would I write "For integers k,l, and m such that k>1, l>2, m>k+l" all in one line?
  36. F

    Maple Maple - Explicit Set Definition & Natural Number Symbol

    Hi, I would like to know if is possible define a set rule explicitly. ex.: Define the set A explicitly where ξ = ℕ and A = {x | x < 3}. The maplesoft said the (N) is a representation of Natural Numbers. f:=proc() local a,b; a:=N; b:= 3; print(a<b); end proc; when I...
  37. Thomas McGuigan

    Any thoughts on natural selection?

    I have been in a heated discussion with my acquaintance about natural selection. Anyone who thinks natural selection is a real thing any links would be helpful
  38. K

    MHB Prove that \sqrt{n+\sqrt{n}} is irrational for every natural number

    I am not sure if this is good, so I would like someone to help me a little and tell me if this is a good proof. I know how to prove that, for example, \sqrt{2} is irrational, so I tried to do something similar with this expression. So, let's assume otherwise, that \sqrt{n+\sqrt{n}} is not...
  39. N

    Proving Natural Log Proof: ln|1+σx|

    Homework Statement Prove the following statement: ln|1+\sigma x | = \frac{1}{2} ln|1-x^2| + \frac{\sigma}{2} ln| \frac{ |1+x|}{|1-x|} Homework EquationsThe Attempt at a Solution Starting from right to left would be easier: = \frac{1}{2} ln|(1+x)(1-x)| + \frac{\sigma}{2} ln| 1+x| -...
  40. L

    Separating CO2 from natural gas

    I have been given an assignment to use a specified distillation column to separate out propene from a gas. The gas consists of propene, propane, ethane and CO2. Separating out the propane has been straight forward, but ethane and especially CO2 are giving me a hard time. To make matters worse, I...
  41. B

    Natural Frequency & damping coefficient from transfer function

    Homework Statement Here is the transfer function of a buck converter I derived: What I need to do next is obtain equations for w0 and ζ. I know how to do this for equations that follow the general form: But in this case I just can't figure out exactly how to do it. How do I find a...
  42. A

    MHB Divisors of natural number n

    Hello could you help me to solve my task $n \in \Bbb{N}$ Prove that there is n which has more than 2017 divisors d that: $\sqrt{n} \le d < 1,01 * \sqrt{n}$ Thank you
  43. M

    B Natural exponential function, calculus

    So I'm trying out various practice problems and for some reason I can't get the same answer when it comes to problems involving natural exponentials. Here's the problem A type of lightbulb is labeled as having an average lifetime of 1000 hours. It's reasonable to model the probability of...
  44. ramzerimar

    Where does natural frequency comes from?

    I know everything has a natural frequency that is a intrinsic property to the body in question. For example, a string vibrating has the largest amplitudes when it's vibrating near it's natural frequency, and the same thing happens with other things too (like the Tacoma Bridge). Natural...
  45. P

    I When natural language fails to explain

    [Mentor's note: This thread started as a fork of https://www.physicsforums.com/threads/does-the-electron-really-spin-720-degrees.887917.] If you cannot translate the math to language, you are doing something very, very wrong. You are fundamentally at odds with the reality that physics is...
  46. A

    Inifinity limit with natural log

    Homework Statement Limx--> ∞ Ln(x^2-1) -Ln(2x^2+3) Homework EquationsThe Attempt at a Solution Ln(x^2-1)/(2x^2+3) Then I divided the top and bottom by x^2 so in the end I got (1/2). Is this right?
  47. M

    I Cancellation law multiplication natural numbers

    Hello everyone. I wanted to prove the following theorem, using the axioms of Peano. Let ##a,b,c \in \mathbb{N}##. If ##ac = bc##, then ##a = b##. I thought, this was a pretty straightforward proof, but I think I might be doing something wrong. Proof: Let ##G := \{c \in \mathbb{N}|## if ##a,b...
  48. K

    I 5 Higgs-like bosons -- natural supersymmetry required?

    MSSM and nMSSM require 5 higgs like bosons in addition to the 126 GEV the SM predicts. thus far LHC has not found any of them. what masses are predicted for Natural SUSY for these additional higgs and how much of a problem is it that the LHC has not found them? if natural SUSY is correct...
  49. S

    Natural units and electron mass

    I am trying to express some physical constants in natural units of ##c=1## and ##\hbar=1##. Let's start with the electron mass. In SI units, the electron mass is ##0.511 \text{MeV}/c^{2}##. I understand that in natural units, the electron mass is simply ##0.511\ \text{MeV}##. Now, is the...
  50. W

    Natural frequency of a mass spring system

    Homework Statement Homework Equations T = 2π√(m/k) mx'' + kx = 0 F = ma The Attempt at a Solution I don't honestly know where to start with this. I'm really out of my league in this class, and I'm trying my best to catch up with the things I didn't quite master in Dynamics and Physics... As...
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