Hello World!

Yet another page by me, mainly driven by my urge to share perhaps the greatest personal philosophy ever, #Stoicism . I created this page because I didn't want to make StuffThatMatters page crowded with short, self-help posts etc. 

But I couldn't resist the urge to share the Stoic teachings with the world, obviously. Well, all this is due to one simple reason - writing about Stoicism (or any topic, for that matter) will help me understand the concept better, while simultaneously enabling others like me to study it occasionally. Thus, it's a win-win scenario. :)

I don't know whether this announcement counts as stuff that matters according to you, so sorry in advance. :) 

Thanks everyone. 

#Philosophy

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The Spiritual Stoic originally shared:
Hello World! 

This is a non-commercial, voluntary page driven by one sole cause - to spread the spiritual and philosophical teachings, especially those ones developed by the Stoic teachers like Epictetus, Aurelius and Seneca that we can apply to our daily lives. 

I am but one person, +Anirban Chatterjee who maintains this page as of now, and totally for the cause I mentioned. My only other incentive is to learn #Stoicism  better, by the art of what I call Stoic posting. 

Obviously, as the tagline of the page notes, Epictetus tells us to embody our philosophies, i.e live according to them, instead of discussing them, but I believe that when you write about something, and help others grasp it using simple language, your own understanding of the concept deepens. 

As such, my Stoic brothers and sisters, this post starts the journey of my Stoic posts on Google+!

Warm regards from India, 
Anirban Chatterjee 

P.S: I maintain another page, StuffThatMatters, about pretty much anything scientific that interests me. If you like, you can check it out here: http://goo.gl/iJ0AUr 

Also, my personal page remains +Anirban Chatterjee, although it will be used to host nothing other than my occasional smatterings. :)

Image credits: Pixabay.com 

#Philosophy   #spirituality   #selfimprovement  




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'A Hymn to Science' by Dr. Mark Akenside

'A Hymn to Science' by Dr. Mark Akenside 

This is a beautiful classical piece authored by the capable hands of English physician and poet Dr. Mark Akenside, who had famously turned to the path of science (medicine, to be precise) from theology. This also started a brilliant career, that saw the fusion between two great arts, science and poetry. And in this hymn, Akenside personifies science, as the great source of inspiration, intellect and passion, and yet, paradoxically, the child of them all. 

While we shouldn't, I agree, delve into blind fanboyism (without going to the depths), there's also significant need to recognize the majesty and glory of science, and not just Bah, Humbug! it off. An Aristotelian golden mean, or a Buddhist middle path between the two extremes should be the best approach, in my humble opinion. 

Hymn to Science
Dr. Mark Akenside 

Science! thou fair effusive ray
From the great source of mental Day,
Free, generous, and refin'd!
Descend with all thy treasures fraught,
Illumine each bewilder'd thought,
And bless my lab'ring mind.

But first with thy resistless light,
Disperse those phantoms from my sight,
Those mimic shades of thee;
The scholiast's learning, sophist's cant,
The visionary bigot's rant,
The monk's philosophy.

O! let thy powerful charms impart
The patient head, the candid heart,
Devoted to thy sway;
Which no weak passions e'er mislead,
Which still with dauntless steps proceed
Where Reason points the way.

Give me to learn each secret cause;
Let number's, figure's, motion's laws
Reveal'd before me stand;
These to great Nature's scenes apply,
And round the globe, and thro' the sky,
Disclose her working hand.

Next, to thy nobler search resign'd,
The busy, restless, human mind
Thro' ev'ry maze pursue;
Detect Perception where it lies,
Catch the ideas as they rise,
And all their changes view.

Say from what simple springs began
The vast, ambitious thoughts of man,
Which range beyond controul;
Which seek Eternity to trace,
Dive thro' th' infinity of space,
And strain to grasp THE WHOLE.

Her secret stores let Memory tell,
Bid Fancy quit her fairy cell,
In all her colours drest;
While prompt her sallies to controul,
Reason, the judge, recalls the soul
To Truth's severest test.

Then launch thro' Being's wide extent;
Let the fair scale, with just ascent,
And cautious steps, be trod;
And from the dead, corporeal mass,
Thro' each progressive order pass
To Instinct, Reason, GOD.

There, Science! veil thy daring eye;
Nor dive too deep, nor soar too high,
In that divine abyss;
To Faith content thy beams to lend,
Her hopes t' assure, her steps befriend,
And light her way to bliss.

Then downwards take thy flight agen,
Mix with the policies of men,
And social nature's ties:
The plan, the genius of each state,
Its interest and its pow'rs relate,
It fortunes and its rise.

Thro' private life pursue thy course,
Trace every action to its source,
And means and motives weigh:
Put tempers, passions in the scale,
Mark what degrees in each prevail,
And fix the doubtful sway.

That last, best effort of thy skill,
To form the life, and rule the will,
Propitious pow'r! impart:
Teach me to cool my passion's fires,
Make me the judge of my desires,
The master of my heart.

Raise me above the vulgar's breath,
Pursuit of fortune, fear of death,
And all in life that's mean.
Still true to reason be my plan,
Still let my action speak the man,
Thro' every various scene.

Hail! queen of manners, light of truth;
Hail! charm of age, and guide of youth;
Sweet refuge of distress:
In business, thou! exact, polite;
Thou giv'st Retirement its delight,
Prosperity its grace.

Of wealth, pow'r, freedom, thou! the cause;
Foundress of order, cities, laws,
Of arts inventress, thou!
Without thee what were human kind?
How vast their wants, their thoughts how blind!
Their joys how mean! how few!

Sun of the soul! thy beams unveil!
Let others spread the daring sail,
On Fortune's faithless sea;
While undeluded, happier I
From the vain tumult timely fly,
And sit in peace with Thee.

Image Credits: Wikimedia 

#science   #poetry  




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Visualize classical physics with Step, the best free physics simulator

Visualize classical physics with Step, the best free physics simulator 
StuffThatMatters: Open Source Software 

Step is one of the least known, but best developed software I have encountered, used and been fascinated by. A free software, free as in speech, Step is a testament to the glory of open-source, and tells us yet again, why Linux is best suited for education. 

Step is actually a simulator, that simulates the behaviour of real-world particles as per the laws of classical Newtonian mechanics. This helps us see the laws of mechanics in action, in real time. This might be a bit unfamiliar at first, especially if you haven't used a physics simulator previously, but basically it is quite similar to the particle simulators available on Android. Only, it's much, much better and feature-rich. 

What's this thing called Step? 

Step, as the KDE project page describes it, is an interactive physics simulator. However, that's a very brief description, and doesn't, in my opinion, do justice to the abilities of this fascinating piece of software. 

Step is a powerful 2-D engine that is capable of simulating the laws of physics, involving the intuitive and counter-intuitive interactions between simple particles, forces, mechanisms such as motors, springs, waves etc. It is hugely expandable, thanks to the inbuilt scripting ability, and a whole array of downloadable examples make it one of the best in its category of simulators. 

What can I do with Step? 

Step allows you to visualize the laws of physics. Mostly, we understand things like Coulomb's law of electrostatic attraction or the classical law of Newtonian gravitation etc with the use of: 

1. Math equations 

2. Static diagrams 

However, Step adds one more dimension to this process of grasping the concept, by allowing us to view the dynamism of these laws, mechanisms, actions of simple machines etc. Rather than limiting ourselves to a static approach, Step helps us get a more dynamic picture of the process, using precise mathematical computation and an adorable array of visual elements. 

An excellent use of Step, as I've discovered recently, is its ability to work with Kinetic theory. Using the particulate model of gases, Step allows us to see for ourselves, how macroscopic properties like pressure, temperature etc are related to the microscopic interactions between the constituents of these gases. It's a joy to witness the mechanism. 

The above screenshot of Step, grabbed from Wikimedia, shows the simulation of simplified gasoline system, generated using particulate model of gasoline as per the kinetic theory. 

Unique features of Step 

Other than being completely free to download, install, share, distribute, study the code of, and modify, Step packs in an array of beautiful features that make this software so adorable. The official list of features can be found here: http://ift.tt/1s5leKF

Some of notable features, that I find delightful, are as follows: 

1. Measurements: Step can be used to measure the data mined out of simulations. Various parameters, ranging from vector sum of forces to the average pressure of a compressed gas at a given condition etc can be calculated and displayed in real time using Step. 

2. Graphs: Step can automatically generate graphs of parameters against other parameters, thereby telling us more about the state of the mechanism we're simulating at any given point of time. 

3. Automatic unit conversion: Units are handled and converted automatically. To quote from the official documentation, "you can enter something like '(2 days + 3 hours) * 80 km/h' and it will be accepted as distance value"

4. Error calculation: Step helps us visualize how the final state of a system changes, even when we enter the initial parameters with error margins. 

5. Lightweight: Step, relying on the powerful UNIX philosophy, is extremely lightweight, and can run on virtually any old computer (by today's standard, at least). 

6. Downloadable examples: Other than creating and storing your own mechanisms, you can download a vast collection of freely available examples, to help you see how Step works. 

7. Flawless simulation: Simulation is not buggy at all, and can run smoothly whether you have a modern graphics card or not. 

How to install 

Officially, Step is a part of the larger KDE Education Project, a bundle of free, high-quality software for promoting the use of Linux (mainly K Desktop Environment) in education and research. As such, it's available readily for Linux-based OSes, through various repositories and package managers. 

It's also available as the source, if you're willing to study/modify/compile it from scratch, on its official website. 

For non-Linux systems, Step isn't readily available. However, Windows users can make use of KDE on Windows, which can then run Step. However, being a native Linux user, I confess that I haven't tried it practically. 

If you ask me, Step gives you an excellent reason to switch to a free software OS for education and research. You can always keep your existing Windows or Mac, and dual-boot a Linux OS like Ubuntu or OpenSuse, to harness the benefits the great open-source initiative and Free Software Movements have to offer. 

References and links 

http://ift.tt/1s5leKH (Official project page) 

http://ift.tt/1s5lf0V (Step Handbook)

#KDE   #science   #freesoftware   #physics   #linux  




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de Mere's paradox: how mathematics impacts the world more directly than we think it does

de Mere's paradox: how mathematics impacts the world more directly than we think it does
StuffThatMatters: Science & Mathematics 

Mathematics is everywhere – from simple, day-to-day calculations involving profits and losses to the complicated equations that reveal to us the profound nature of the depths of reality, in the form of quantum mechanics. However, little do we use our mathematical reasoning to make sense of this seemingly senseless world. As did Chevalier de Mere, of France, a mathematician who liked to bet in French salons and bars, for the sake of understanding the probabilities behind betting. 

Mere was quite fascinated with particularly one problem – the bet that we'd see a 6 come up when a dice is rolled 4 times, put against the bet that 2 sixes will come up when a pair of die are rolled 24 times. Naturally, Mere concluded that the probabilities of both these events were equal, on the basis of mistaken empirical probability, and he did regret his mistake. 

And interestingly, this problem also started modern probability theory. 

Initial solution

We all know that a die has 6 faces, with numbers 1-6 embedded on each side. So, when we throw a die, there are 6 possible outcomes. The probability of a 6 coming up would be: 

P ( a 6 comes up ) = number of desirable outcomes / number of possible outcomes
= 1 / 6

And similarly, when we roll 2 dice simultaneously, there are 6 x 6 possible outcomes = 36 outcomes. 

So, P ( a double-six comes up ) = 1 / 36

Now, Mere concluded that since 4 / 6 = 24 / 36, 

the probabilities of both the events are equal. However, he observed the following: 

1. When he took the first bet, i.e betting that a 6 would come up on rolling a single die for 4 times, he won most of the time, and gained money.

2. Growing confident, Mere betted that a double-six would turn up, when a pair of dice were rolled for 24 times, and he lost lots and lots of money! The more he played, the angrier he got seeing that he was losing most of the time. And this continued for a long time.

Pascal and the correct interpretation

Frustrated, de Mere contacted Pascal, who then correctly framed the problem. Let us look at it more clearly, using the same classical model of empirical probability. 

For the first scenario, we roll a single die for 4 times. Naturally, the number of possible, equiprobable (i.e equally possible) outcomes is 6 each time. Now, since the experiment is done 4 times, i.e the die is rolled 4 times, the number of equaprobable outcomes is 6 x 6 x 6 x 6 = ( 6 ) ^ 4

Now, each time, if we don't get a 6, we lose. So, the probability of getting a 6 each time is 1 / 6, but the probability of NOT GETTING a 6 is 1 – 1 / 6 = 5 / 6

When the die is rolled 4 times, the probability of not getting a 6 in the process becomes: 

( 5 / 6 ) x ( 5 / 6 ) x ( 5 / 6 ) x ( 5 / 6 ) 
= ( 5 / 6 ) ^ 4

So, the probability of winning the bet, i.e a 6 turning up in the experiment, is: 

P ( Getting a 6 ) = 1 – P ( Not getting a 6 )
= 1 - ( 5 / 6 ) ^ 4 
= 1 – 5^4 / 6^4
= 1 – 625 / 1296
= 671 / 1296 
= 0.5177 ( approximately) > 0.5 

So, P ( Getting a 6 ) > 1/2, i.e when the experiment is repeated for a large number of times, it is more probable that the bet will be won, since there's MORE THAN 50% chance that it will be won. 

The second scenario: why de Mere lost the bet 

Now, for the second scenario, for each time the pair of dice is rolled, we have 6 possible outcomes for the first die in the pair, and 6 for the second die. So, there are 6 x 6 = 36 possible combinations = 36 equiprobable outcomes. 

Now, the probability of getting a pair of sixes is 1 / 36 , and so the probability of not getting that would be: 

P ( Not getting a pair of sixes ) = 1 – 1 / 36
= 35 / 36 

And so, when the pair of dice is rolled for 24 times, we are conducting the experiment 24 times. So, the probability of not getting the desired result in 24 rolls would be: 

P ( Not getting a pair of sixes in 24 rolls ) = ( 35 / 36 ) x ( 35 / 36 ) x ... (24 times)
= ( 35 / 36 ) ^ 24
=  11419131242070580387175083160400390625 / 22452257707354557240087211123792674816
= 0.5086 (appx)

So, P ( Getting a pair of sixes in 24 rolls ) = 1 – 0.5086 
= 0.4914

Naturally, P ( Getting a pair of sixes in 24 rolls ) < 1/2, 

And so, there's less than 50% chance of winning the second bet, i.e most of the time the bet will be lost when the pair is rolled for a large number of times. 

A mathematical philosophy? 

Blaise Pascal, one of my many heroes, was also a philosopher. And his philosophy involved the use of mathematics, to make bets. Because Pascal, as we know, used to see the reality itself as a betting table. He used mathematics to justify the belief in the Christian God, famously. While that justification is rightly challenged and disputed, his use of mathematics, for solving the crises we face while taking decisions in daily life, is noteworthy. 

Pascal's philosophy involed what is known as the rational utilization of expected values, or E.Vs, to make decisions. Whenever we have to make a choice, we're virtually gambling, because our course of action is much like a bet against the unknown. And how should we place this bet? Much like de Mere's first bet, with a positive E.V (or +EV). 

That is, we should take decisions which have a greater than 50% probability of being successful. And if a decision has a -EV, i.e less than 50% chance of getting successful, then we should possibly abandon it. 

It's all a very general, very brief and very rough explanation of Pascal's philosophy, mind you, but the important thing is to realize that he managed to combine philosophy and mathematics, thus providing a more concrete reasoning behind ethical problems. 

Conclusion 

This problem, named after de Mere, is indeed a veridical paradox, as ProofWiki notes. I already used the term in my previous posts, and these are just cases in which the premise is simple to understand, but the outcome is counter-intuitive, i.e against what we'd commonly believe. 

This shows us yet another scenario of a self-evident fact, that the universe is mathematical. More philosophically speaking, the reality itself seems to prefer mathematics. Maybe the Anthropic principles will tell us why, some day. Till then, take care. 

References

http://ift.tt/1xWu9mg 

Magnificent Mistakes in Mathematics (Alfred Posamentier) 

http://ift.tt/1xWubdZ

#math   #interesting   #science   #probability  




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