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“Some things are in our control and others not. Things in our control are opinion, pursuit, desire, aversion, and, in a word, whatever are our own actions. Things not in our control are body, property, reputation, command, and, in one word, whatever are not our own actions.”

– Epictetus

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“You may be unconquerable, if you enter into no combat in which it is not in your own control to conquer.”

– Epictetus

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“But, for your part, don’t wish to be a general, or a senator, or a consul, but to be free; and the only way to this is a contempt of things not in our own control.”

– Epictetus

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“The absurd does not liberate; it binds. It does not authorize all actions. ‘Everything is permitted’ does not mean that nothing is forbidden.”
-Albert Camus

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“I may not have been sure about what really did interest me, but I was absolutely sure about what didn’t.’

-Albert Camus

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We are tiny chips inside a giant data-processing system absorbing and processing countless data bits through emails, tweets and articles.
Chips don’t have time to find out where they fit into the great scheme of things, because they are too busy answering all these emails.
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“It is quite clear to me that the religious paradise of youth, which was thus lost, was a first attempt to free myself from the chains of the ‘merely personal,’ from an existence which is dominated by wishes, hopes and primitive feelings. Out yonder there was this huge world, which exists independently of us human beings and which stands before us like a great, eternal riddle, at least partially accessible to our inspection and thinking. The contemplation of this world beckoned like a liberation….
The road to this paradise was not as comfortable and alluring as the road to the religious paradise, but it has proved itself as trustworthy, and I have never regretted having chosen it.”
-Albert Einstein

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Fundamental degrees of freedom might not be particles but extended objects: one-dimensional strings and higher dimensional branes. ……………………………………..

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Structurally symbiotic systems survive by replicating as well as waging Darwinian wars.
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All our doings are just watching.
All living organisms, including humans,  are situation-action machines driven by chemical algorithms.
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Free will  has been a very useful as well as persistent illusion that has allowed us to successfully exist and reproduce. Survivalism requires proximate causation as well as the nearest agent to an action.
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According to the ‘Bhagavad Gita’, we should stay detached from the outcome of any work since it is done through us not by us.
Free will is actually a sort of ‘which-slit experiment’ in biological disguise. We might wonder whether this useful illusion is useful since we are destined by quantum Darwinism.
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We  are not meant to do what we  love. We are meant to do what we are skilled at.

 
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We have to do what we have to give.
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Our inborn skills are our  destiny. We should unleash them.

 
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“The function of freedom is to free someone else.”
– Toni Morrison
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“You are your best thing.”

– Toni Morrison
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“I am all the things I have ever loved”.
– Toni Morrison

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A system consisting of water vapor in equilibrium with liquid water has only one degree of freedom. Either the pressure or  the temperature can only be fixed. Fixing one will automatically determine the other.

 
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A thermodynamic system is called ‘dynamic’ instead of  ‘dead’ due to its many degrees of freedom (thermal, physio/ chemical, electric, etc.)
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Degree of freedom signifies how many coordinates are required to define a state.

Zero degree of freedom means it is a fixed point/state.
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Internal Energy of a thermodynamic system can have many degrees of freedom.
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The number of degrees of freedom is the number of independent intensive variables.
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The number of degrees of freedom is  the largest number of thermodynamic parameters ( temperature , pressure, etc.) that can be varied simultaneously and arbitrarily without determining one another.
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In Gibbs phase rule (F+P= C+2), a system with C chemically independent components and P phases in equilibrium has F degrees of freedom.
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For a system consisting of one pure species the phase rule is F=3-P. If two phases are in equilibrium with each other in a one-component system, the system has one degree of freedom. The system is univariant.
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Pure water boils at 100°C if the pressure is one atmosphere. If the pressure is lower than one atmosphere, pure water will boil at a temperature below 100°C. If the pressure is higher than one atmosphere, pure water will boil at a temperature higher than 100°C.

A system consisting of water vapor in equilibrium with liquid water has only one degree of freedom. The pressure OR the temperature can be fixed. Fixing one will automatically determine the other.
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At the triple point ( 273.16 K and 612 Pa.) of H2O, ice, water, and steam are in equilibrium. According to the phase rule(F=3-P), a one component system has no degrees of freedom when three phases are in equilibrium (F=0).The system is invariant.

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The degrees of freedom is used when you have more variables than equations and the degrees of freedom is how many more variables you have than equations.

 
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Each degree of freedom lends a particular trait to a system.
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Degree of freedom of molecules is the number of independent ways in which a molecule possesses translational, rotational and/or vibratory motion without violation of the constraints.
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A Monoatomic molecule possesses only a single atom . Therefore it can have only transational movement along the three axes in free 3-D space. Thus it has degree of freedom equal to 3.

 
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Diatomic molecules can posses 3 translational(for the centre of mass of the molecule), 2 rotational (along axes perpendicular to the line joining the two atoms) and 1 vibrational motion along the line joining both . And hence a diatomic molecule possesses 6 degrees of freedom.
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For molecules with ’N’ number of atoms, degree of freedom is 3N.
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When a Monoatomic molecule is in free space it is free for motion in the 3 directions of the coordinates.

The molecule loses it’s DOF from 3 to 2 because after getting adsorbed on a surface ,now the molecule is constrained only in a two dimensional space where it can perfom motion along only X and Y axis.

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The total number of intensive variables in order to fix the state of the system is called degree of freedom.
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At the triple point of water where all the three phases of water are present that is liquid,gas and solid by Gibb’s phase rule the degree of freedom will be ZERO.

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The definition of Degrees of Freedom is same in both Thermodynamics and Mechanics.
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Each degree of freedom lends a particular trait to a system.

 
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The four laws of thermodynamics, contain deep physical and philosophical meanings.

 
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In thermodynamics,  degree of freedom tells us about the number of intensive properties required to tell the thermodynamic state of a point. So at Triple point of any pure substance its intensive properties are fixed.

 
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Intensive properties do not depend on the amount of matter.
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Iintensive properties include:

Boiling Point
Density
State of Matter
Color
Melting Point
Odor
Temperature
Refractive Index
Luster
Hardness
Ductility
Malleability
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Intensive properties identify a sample because these characteristics do not depend on the amount of sample, nor do they change according to conditions.
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Extensive properties depend on the amount of matter.
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An extensive property is additive for subsystems.

 
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Extensive properties include:

Volume
Mass
Size
Weight
Length

 
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The ratio between two extensive properties is an intensive property. For example, mass and volume are extensive properties, but their ratio (density) is an intensive property of matter.
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While extensive properties are great for describing a sample, they aren’t very helpful in identifying it because they can change according to sample size or conditions.

 
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