How To Tell If Someone Is Truly Smart Or Just Average

Have you ever noticed how some of the worlds most successful entrepreneurs and leaders see reality in a fundamentally different way? When they talk, its almost as if theyre speaking a different language.Just look at this interview where Elon Musk describes how he understands cause and effect:I look at the future from the standpoint of probabilities.

Its like a branching stream of probabilities, and there are actions that we can take that affect those probabilities or that accelerate one thing or slow down another thing. I may introduce something new to the probability stream.Unusual, right?

One writer who interviewed Musk describes his mental process like this:Musk sees people as computers, and he sees his brain software as the most important product he owns and since there arent companies out there designing brain software, he designed his own, beta tests it every day, and makes constant updates.Musks top priority is designing the software in his brain. Have you ever heard anyone else describe their life that way?

Self-made billionaire Ray Dalio is no less weird. In his book, Principles, he describes how he sees reality: Nature is a machine. The family is a machine.

The life cycle is like a machine. Dalios company, the largest hedge fund in the world, records every conversation (meeting or phone call) inside the company and has built several custom apps that allow any employee to rate any other employee in real time. The data is then added to profiles that each employee can see and is subsequently fed into an artificial intelligence system that helps employees make better decisions.

Dalio also describes his day in much different terms than you would expect from a CEO:Im very much stepping back. Im much more likely to go to what I describe as a higher level. Theres the blizzard that everyone is normally in, and thats where theyre caught with all of these things coming at them.

And I prefer to go above the blizzard and just organize.Charlie Munger uses a cognitive bias checklist before making investment decisions to ensure he properly applies the correct mental models. Warren Buffett uses decision trees.

Jeff Bezos thinks of Amazon as being at Day One even though its been around more than 20 years.Whats going on here? Are these just the idiosyncrasies of geniuses, or do these entrepreneurs employ a way of using their brain that we too could learn from in order to become smarter, more successful, and more impactful ourselves?

How I Learned to Think Like the Worlds Best and BrightestOver the years, as Ive studied all of the above entrepreneurs, Ive also aggressively applied their teachings. Even if I didnt understand what they were saying at first, I took their advice on faith. Ive applied Ray Dalios root-cause analysis approach to our company.

Now, throughout the week, everyone on our team logs any problems theyre facing. Then, we have a weekly phone call to discuss our biggest, recurring problem and its possible root cause. Ive applied Charlie Mungers approach to mental models and collected thousands of pages of notes in order to create in-depth briefs on each model.

Ive applied Musks probabilistic thinking to major decisions by listing out all of the potential decisions I could make and then assigning a cost, potential value, and probability to each one.Ive also created an experimentation engine like Bezos and Zuckerberg, and we now perform more than 1,000 experiments each year at our company. Finally, I now follow the 5-hour rule and spend at least two hours a day on deliberate learning.

After five years of emulating the leaders I most admire, I realized something surprising was happening to my thought process. I wasnt just learning new strategies or hacks. I was learning a deeper and fundamentally different way of understanding reality like Ive accessed a hidden, secret level in the game of life.

Its thrilling to uncover deeper layers of understanding that I didnt even know existed.When I look back on my former self, I feel like Im looking at a different person altogether. As previously unsolvable problems from my past come up again, I find I can solve many of them now.

It is a great feeling to see previously insurmountable problems both personal and professional and realize I now have the tools to surmount them.Ill give you an example. In my twenties, I invested $100,000 into a business idea that never took off.

Now that I understand cognitive biases thanks to Charlie Munger I see how the pernicious sunk cost fallacy wreaked havoc upon my decision-making. Today when I consider new business ideas, instead of just imagining how great theyre going to be, I spend just as much time envisioning what could go wrong another Munger hack. I no longer have to remind myself to think this way anymore.

Ive internalized these concepts and now my mind actually works differently.I once heard a coach talk about changing a clients way of seeing the world in a way that would blow their mind. When he looked into his client eyes and could see him or her really getting it, hed say, Now, youre in my reality!

Thats how I felt. Reality somehow feels different on an aesthetic level as if Im cutting through the levels of illusion and noise we normally see and getting a more direct view. The best example I can think of is that its like wearing augmented reality glasses that constantly feed you relevant wisdom about the situation youre in.

Ultimately, what Ive learned is that billionaires dont have odd ways of talking. They, instead, are visionaries who see the world in a deeper way one that is both incredibly effective and also learnable.The Difference Between Average and Brilliant: Effective Mental ModelsMental models are to your brain as apps are to your smartphone.

-Jayme HoffmanAccording to Model Theory, we all always use mental models in our thinking. Mental models are psychological representations of real, hypothetical, or imaginary situations, according to the formal definition. Less formally, a mental model is a simplified, scaled-down version of some aspect of the world: a schematic of a particular piece of reality.

A model can be represented as a blueprint, a symbol, an idea, a formula, and in many other ways. We all unconsciously create models of how the world works, how the economy works, how politics works, how other people work, how we work, how our brains work, how our day is supposed to go, and so on.The more effective the model, the more effectively we are able to act, predict, innovate, explain, explore, and communicate.

The worse the model, the more we fall prey to costly mistakes. The difference between great thinkers and ordinary thinkers is that, for ordinary thinkers, the process of using models is unconscious and reactive. For great thinkers, it is conscious and proactive.

All of the extraordinary people mentioned above collect the most effective models across all disciplines, stress-test them, and creatively apply them to their daily lives. Mental models are so valuable that billionaire Ray Dalios only book is full of his best mental models. Charlie Mungers only book is packed full of his top mental models too.

One of the most common pieces of advice that Elon Musk gives is to think from first principles. Mental models and first principles are similar in that they each model deeper levels of reality.While most people think about knowledge just horizontally (ie across fields), these great thinkers also think about knowledge vertically in terms of depth.

Musk explains deep knowledge in a Reddit AMA, It is important to view knowledge as sort of a semantic tree make sure you understand the fundamental principles (Musk calls these first principles), i. e. the trunk and big branches, before you get into the leaves/details or there is nothing for them to hang onto.

In another interview, Musk gives an example, I tend to approach things from a physics framework. Physics teaches you to reason from first principles rather than by analogy. Physicist David Deutsch explains it even further, Its in the nature of foundations, that the foundations in one field are also the foundations of other fieldsThe way that we reach many truths is by understanding things more deeply and therefore more broadly.

Thats the nature of the concept of a foundation just as in architecture, all buildings all literally stand on the same foundation; namely the earth. All buildings stand on the same theoretical base. By understanding verticality and depth, you can see how learning mental models connects things that were previously separate and disconnected.

Just as every leaf on a tree is connected by twigs, which are connected by branches, which are connected by a tree trunk, so too are ideas connected by deeper and deeper ideas.One of the most effective and universal mental models is the 80/20 Rule: the idea that 20 percent of inputs can lead to 80 percent of outputs. This same 80/20 idea can be applied to our personal lives (productivity, diet, relationships, exercise, learning, etc.

) and our professional lives (hiring, firing, management, sales, marketing, etc). As such, you can see how the 80/20 Rule connects many disparate fields. This is what all mental models do.

To apply the 80/20 Rule, at the beginning of the day we can ask ourselves, Of all the things on my to-do list, what are the 20 percent that will create 80 percent of the results? When were searching for what to read next, we can ask ourselves, Of all the millions of books I could buy, which ones could really change my life? When considering who to spend time with, we can ask ourselves, Which handful of people in my life give me the most happiness, the most meaning, and the greatest connection?

In short, consistently using the 80/20 Rule can help us get leverage by focusing on the few things that really matter and ignoring the majority that dont.My team and I have spent dozens of hours assembling the largest list of the most useful mental models in the world (that were aware of). Weve done this by curating and combining the most useful models of other mental model collectors.

To access this spreadsheet for free, visit the download page.Mental Models Are the New AlphabetYou cant do much carpentry with your bare hands and you cant do much thinking with your bare brain. Bo Dahlbom, philosopher and computer scientistEvolution is so slow that a child born today is biologically indistinguishable from a child born 30,000 years ago.

Yet, here I am typing on a MacBook, while my ancestors spent most of their time collecting berries, throwing spears, and chipping rocks. So whats the difference between someone born 30,000 years ago and me?Tools.

Between then and now, there has been an unprecedented explosion and evolution of tools that have collectively created modern society. We all intuitively understand this. We all know that if we didnt have basic tools like fire or the plow, or more complex ones like a Macbook or car, our lives would be completely different.

Watch any post-apocalyptic TV or movie series and you can see how the world quickly falls apart when tools fail.But theres a major blindspot people have when it comes to understanding tools. Many people fail to appreciate non-physical tools tools that they cannot touch, hear, or see.

But mental tools are just as powerful and complex as physical tools. For example, consider the alphabet: the Western alphabet is a mental tool that wasnt invented until around 1100 BC (pictorial writing systems like hieroglyphics were invented much earlier). Now we take it for granted, but at the time, it was a cutting-edge tool.

Though it was adopted slowly at first only 30 percent of the population could read and write before the printing press was invented in 1440 once it began to spread, literate individuals had a huge leg up. In fact, literacy is now so important that its a national priority for all governments. That is the power of an effective mental tool.

Its by understanding the significance of the alphabet that we can understand the significance of mental models tooMental models are also fundamental and critical mental tools.Mental models represent large chunks of reality that can be combined together to create even more complex and useful supermodels. This is similar to how letters can be combined into words, which can be combined into sentences.

Mental models should be taught early in ones life, because nearly everything else builds on them.Mental models trigger higher-order thinking. This is similar to how becoming literate triggers a whole slew of higher-order thinking capabilities known as the Alphabet Effect.

As society evolves, its becoming more and more complex. There are more people, more tools, and more knowledge, all globally connected in complicated ways. Therefore, people who are able to model how this more complex reality works will be far more successful at navigating it.

Or, as Ray Dalio says in his book, Truth or, more precisely, an accurate understanding of reality is the essential foundation for any good outcome.People who are able to model how a complex business works in their minds are more likely to be successful business leaders, because they must understand the complex subtleties of finance (balance sheet, cash flow, and income statements), HR (recruiting and managing A players), product development, marketing/sales, and how they all interact with their mental models of their various stakeholders (community, customers, suppliers, employees, investors). Before an architect can build a house, he or she must first design a model of that house.

That architect must have an understanding of how the electrical, plumbing, design, materials, pricing, and so on come together to create a safe, beautiful building at the right price that the market will purchase. Someone who architects a skyscraper must have a much more complex latticework of mental models than someone who models a two-bedroom house. Furthermore, as people progress in their careers, they must evolve the amount, diversity, and quality of their mental models if they want to have higher and higher levels of success and impact:Why We Should All Become Mental Model CollectorsYou may have noticed students who just try to remember and pound back what is remembered.

Well, they fail in school and in life. Youve got to hang experience on a latticework of models in your head. Charlie Munger (self-made billionaire entrepreneur and investor)So how do you build complex, accurate mental models?

Lets me explain with a simple example: dogs. Lets hypothetically imagine for a moment that we have no idea what a dog is. Weve never seen or heard of one before.

Then, one day, we see a dog that looks like the image below on the left, and someone tells us that this is a dog. Ah, I get it, we say. Now I know what a dog is.

But if weve only seen one dog, technically we dont really know what a dog is. With just this single case example, our definition of a dog would be: a large black and brown animal with pointy ears that sits down, and sticks out its tongue. Bring out a Pomeranian dog and with only this mental model in mind, you are likely to ask What is that?

The numerous dog models on the right (the contrasting cases example) show us that dogs can come in all different colors, sizes, and shapes. At the same time, we can see the underlying element of dogness that they all share. This emergent element of dogness is a deeper mental model, and humans created the word dog to symbolize this mental model.

Using that mental model, you can identify an animal as a dog even if youve never seen a particular breed of dog before.What can we take away from this example that is relevant to our own life?Many of the worlds problems result from people overgeneralizing from simplistic models just like our hypothetical one-size-fits-all dog.

Here are three prime examples:Black/white thinking (youre either a good person or a bad person with no gray area in between)Us/Them thinking (people outside your personal religion, nationality, or belief system are the enemy).All manner of stereotypes race, gender, politics, ethnicity, etc.Over-applying models is no different than a carpenter trying to build a house with one single hammer.

All models, no matter how brilliant, are imperfect. The beauty of using multiple and diverse models is that many of the imperfections cancel each other out, allowing you to create a new emergent model that transcends all of the other models.Great thinkers improve their thinking by taking in a larger quantity of information and developing a greater diversity of models.

For example, a novice chess player might only know the name of each piece and how it moves across the board. But a grandmaster has memorized no less than 50,000 chunks (mental models) of increasing complexity including openings, closings, patterns throughout the game, and how one single move can lead to a particular result 10 moves or more down the line.Many, diverse models also lead to heightened creativity.

Nothing is truly original. Everything is derived by combining existing building blocks. Babies are created when a man and a woman have sex.

New tools are created when pre-existing tools have tool sex. New ideas are created through idea sex. In the same way, we can build more complex mental models by combining simple mental models.

For example, by understanding cause-and-effect mental models better, we can more effectively prioritize whats important for us to do now to cause something we want in the future. The larger our base of mental models, the more creative combinations we can form. The more unique our mental models are compared to other people, the more we can think in ways that they cant even fathom.

Through constant and diverse learning, we can organically build better and more varied models of reality. And those models will help us navigate the world far more effectively and creatively. Just as a blueprint is necessary for constructing a stable building, mental models of how the world works help us construct a better and more stable life.

How To Get Started With Mental ModelsEducation is not the learning of facts, but training the mind to think. -Albert EinsteinAre you convinced of the power of Mental Models? Ive learned from personal experience that it literally takes years to develop true mastery of these.

Therefore, I created two resources for you:Resource #1: Free Mental Model Course (For Newbies)If youre just learning about mental models for the first time, my free email course will help you get started. My team and I have spent dozens of hours creating it. It includes Ray Dalios and Charlie Mungers top mental models, a guide on how to create a checklist based on the best practices from medicine and aviation so that you use your mental models throughout the day, and a guide that more deeply explains what a mental model is and how to get value from one.

Sign up for the free mini-course here >>Resource #2: Mental Model Of The Month Club (For Those Who Want Mastery)If youre already are convinced of the power of mental models and want to deliberately set about mastering them, then this resource is for you. Its the program I wish Id had when I was just getting started with mental models. Heres how it works:Every month, youll master one new mental model.

Well focus on the most powerful and universal models first.Well provide you with a condensed and simple Mastery Manual (think: Cliffs Notes) to help you deeply understand the model and integrate it into your life. Each master manual includes:A 101 Overview of the mental model (why its important, how it works, its vocabulary, etc.

)An Advanced Overview that includes a more nuanced explanation.Examples of hacks you can use immediately to apply that mental model to every area of your life and career. These hacks are based on my personal experience and are crowdsourced as well.

Exercises & templates that you can use on a daily basis to integrate the lessons in the manual and achieve maximum results in your life.A Facebook community where you can meet other mental model collectors and learn from one another. To learn more about the program or to sign up, visit the Mental Model Of The Month Overview page.

If you enjoyed this story, please click the button and share to help others find it! Feel free to leave a comment below.The Mission publishes stories, videos, and podcasts that make smart people smarter.

You can subscribe to get them here. This article was written with love and care using the blockbuster mental model

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Use of Classes for Lua Extensions
The system that Supreme Commander uses is that you can subclass classes, then you define the class-specific functions and data like so:The way the code is set up, is all of the classes that have to be in C code are exposed to the lua environment for subclassing. The above method is much like your first, and i would recommend that you take it. It makes it quite usable for both programmers and modders (of which i'm both). I started out programming to this model, and while i didn't completely understand things, it worked perfectly well and made sense to meI'm asking about a very small domain. One-off extension scripts. IE, defining a new weapon for scorched earth.When providing and API for small extension I've seen two approaches.The API exposes classes that the extender then subclasses, overriding the needed methods.--# weapons/flame_missile.lua--#extender pulls in a predefined weapon base classrequire "weapon.missile"--# luabind syntax for classesclass "flame_missile" (missile)function flame_missile:__init() self.hotness 10 self:set_cost(42)endfunction flame_missile:on_hit( who ) who:take_damage(self.hotness) who:ignite()endIn the other approach the api just exposes accessors and sandboxes the script, re-executing the file with each new missile and using the globals as the instance's state.--# weapons/flame_missile.luahotness 10cost 42--# extender just knows that an on_hit function will be called--# when the missile hits something.function on_hit( who ) who:take_damage(hotness) who:ignite()endNOTE: in my example who's api is OO. I'm not interested in whether OO should be used in the extension API. I'm more interested if OO should be used to incorporate user extensions into the game.The first one feels more C-y. So I'm a little more comfortable with from a software engineering standpoint. However, one-off scripts don't need to fit together into a larger architecture. Further, they could be written by less proficient coders, so all the fancy OO might be lost on them.I really like how concise the sandbox approach is. But it's a little limiting (only one missile per file, inheriting behavior from another weapon is no longer possible. I'd really like to define my extension api like this but I'm a little wary as it's a radical departure from classic C programming style.Which method do you prefer?Have you had any bad experiences with one or the other?Is there an even better way to elegantly incorporate extensions into the game?·OTHER ANSWER:I'm asking about a very small domain. One-off extension scripts. IE, defining a new weapon for scorched earth.When providing and API for small extension I've seen two approaches.The API exposes classes that the extender then subclasses, overriding the needed methods.--# weapons/flame_missile.lua--#extender pulls in a predefined weapon base classrequire "weapon.missile"--# luabind syntax for classesclass "flame_missile" (missile)function flame_missile:__init() self.hotness 10 self:set_cost(42)endfunction flame_missile:on_hit( who ) who:take_damage(self.hotness) who:ignite()endIn the other approach the api just exposes accessors and sandboxes the script, re-executing the file with each new missile and using the globals as the instance's state.--# weapons/flame_missile.luahotness 10cost 42--# extender just knows that an on_hit function will be called--# when the missile hits something.function on_hit( who ) who:take_damage(hotness) who:ignite()endNOTE: in my example who's api is OO. I'm not interested in whether OO should be used in the extension API. I'm more interested if OO should be used to incorporate user extensions into the game.The first one feels more C-y. So I'm a little more comfortable with from a software engineering standpoint. However, one-off scripts don't need to fit together into a larger architecture. Further, they could be written by less proficient coders, so all the fancy OO might be lost on them.I really like how concise the sandbox approach is. But it's a little limiting (only one missile per file, inheriting behavior from another weapon is no longer possible. I'd really like to define my extension api like this but I'm a little wary as it's a radical departure from classic C programming style.Which method do you prefer?Have you had any bad experiences with one or the other?Is there an even better way to elegantly incorporate extensions into the game?
Definition by Recursion: Why Is the Existence Part Not (almost) Obvious?
In fact your proof is a circular argument. To prove something by induction you first have to have the something. To define something "inductively" (loose terminology) is definition by recursion.You can define a recursive function $f$ for a finite range of $ninmathbb N$, say $n le N$ by saying $f(1) e, f(2) k(e), ...... f(n) k^n-1(e)$ but why would this function exist for all values of $ninmathbb N$ ? - you can't write an infinite specification for the function. So, you have actually relied on the Theorem of Recursion (i.e. in one form, the statement you are trying to prove) when you assume the existence of $f$ for all $ninmathbb N$ (and you are then using induction to prove $f$ has the property you have assumed it to have).The longer proofs that you may have seen might in outline go as follows:(1) if $f$ exists it would be represnted as a subset of N x H, i.e. a set of ordered pairs where each $ninmathbb N$ is represented in exactly one ordered pair.(2) whatever values $f$ might take N x H contains them(3) the powerset of N x H, $mathscr P(N mathrm x H)$ contains all possible subsets of N x H(3) using specification, one can obtain a subset $mathscr D$ of $mathscr P(N mathrm x H)$ with the property that all the elements of $mathscr D$ (which are subsets of N x H) include $(1, e)$ , and if $(n, h)$ is in such an element of $mathscr D$ then so is $(n 1, k(h))$(4) The intersetion of all elements of $mathscr D$ is formed and shown to be a function and (by definition) to be recursive.(5) the function $f$ is then shown to be uniqueI saw the following statement.Let $H$ be a set, let $ein H$ and let $k:Hrightarrow H$ be a function. Then there is a unique function $f:mathbbNrightarrow H$ such that $f(1)e$, and that $fcirc skcirc f$.(where $s:mathbbNrightarrowmathbbN$ is the successor function)On the 'existence' part alone, my problem is that I can't see what the flaw is in my argument.We know $f(1)$, and if ,for some $ninmathbbN$, we are given $f(n)$ then we define $f(s(n)):k(f(n))$; so we know $ f(s(n))$ .By induction $f$ is defined on $mathbbN$.Maybe the "proof" is too informal. Some examples to illustrate may be helpful.Thanks
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Apache Always Serving First Virtual Host
As for my experience this can happen in the following situation:firstsite.com has dns 1.2.3.4 and ip in vhost 1.2.3.4 or *secondsite.com has dns 1.2.3.4 and ip in vhost is 1.2.3.5.Both 1.2.3.4 and 1.2.3.5 are ips of the problematic server and apache is listening on both ips.BUT as for the few logs and details you provided it is hard to find if this is actually the case.I have seen this asked about few times, but surprisingly no solutions worked for me:Yes, I have used "sudo a2ensite com.secondwebsite.conf"Yes, I have used "sudo /etc/init.d/apache2 reload"Yes, I have used "sudo /etc/init.d/apache2 restart"Yes, I have tried putting both virtual hosts into one file (/etc/apache2/sites-available/default), adding "NameVirtualHost *:80" on top of it and removing it from "/etc/apache2/ports.conf"Yes, I have used "sudo chmod 777 /var/www/secondwebsite"Whatever I do, secondwebsite.com keeps showing firstwebsite.com. Does anyone have any idea what might be causing this?Here is my "/etc/apache2/sites-available/default" ServerAdmin admin@gmail.com ServerName firstwebsite.com ServerAlias www.firstwebsite.com DocumentRoot /var/www Options FollowSymLinks AllowOverride None Options Indexes FollowSymLinks MultiViews AllowOverride None Order allow,deny allow from all ScriptAlias /cgi-bin/ /usr/lib/cgi-bin/ AllowOverride None Options ExecCGI -MultiViews SymLinksIfOwnerMatch Order allow,deny Allow from all ErrorLog $APACHE_LOG_DIR/error.log # Possible values include: debug, info, notice, warn, error, crit, # alert, emerg. LogLevel warn CustomLog $APACHE_LOG_DIR/access.log combined Alias /static /home/user/firstwebsite/firstwebsite/static Order allow,deny Allow from all Alias /media /home/user/firstwebsite/firstwebsite/site_media/media Order allow,deny Allow from all Order allow,deny Allow from all WSGIDaemonProcess firstwebsite WSGIProcessGroup firstwebsite WSGIScriptAlias / /home/user/firstwebsite/firstwebsite/wsgi.py My "/etc/apache2/sites-available/com.secondwebsite.conf" ServerAdmin admin@gmail.com ServerName secondwebsite.com ServerAlias www.secondwebsite.com DocumentRoot /var/www/secondwebsite/public_html ErrorLog $APACHE_LOG_DIR/secondwebsite_error.log # Possible values include: debug, info, notice, warn, error, crit, # alert, emerg. LogLevel warn CustomLog $APACHE_LOG_DIR/access.log combined My "/etc/apache2/ports.conf" # If you just change the port or add more ports here, you will likely also # have to change the VirtualHost statement in # /etc/apache2/sites-enabled/000-default # This is also true if you have upgraded from before 2.2.9-3 (i.e. from # Debian etch). See /usr/share/doc/apache2.2-common/NEWS.Debian.gz and # README.Debian.gz NameVirtualHost *:80 Listen 80 # If you add NameVirtualHost *:443 here, you will also have to change # the VirtualHost statement in /etc/apache2/sites-available/default-ssl # to # Server Name Indication for SSL named virtual hosts is currently not # supported by MSIE on Windows XP. Listen 443 Listen 443 Result of sudo /usr/sbin/apache2ctl -S VirtualHost configuration: wildcard NameVirtualHosts and _default_ servers: *:80 is a NameVirtualHost default server firstwebsite.com (/etc/apache2/sites-enabled/000-default:1) port 80 namevhost firstwebsite.com (/etc/apache2/sites-enabled/000-default:1) port 80 namevhost secondwebsite.com (/etc/apache2/sites-enabled/com.secondwebsite.conf:1) Syntax OK·OTHER ANSWER:I have seen this asked about few times, but surprisingly no solutions worked for me:Yes, I have used "sudo a2ensite com.secondwebsite.conf"Yes, I have used "sudo /etc/init.d/apache2 reload"Yes, I have used "sudo /etc/init.d/apache2 restart"Yes, I have tried putting both virtual hosts into one file (/etc/apache2/sites-available/default), adding "NameVirtualHost *:80" on top of it and removing it from "/etc/apache2/ports.conf"Yes, I have used "sudo chmod 777 /var/www/secondwebsite"Whatever I do, secondwebsite.com keeps showing firstwebsite.com. Does anyone have any idea what might be causing this?Here is my "/etc/apache2/sites-available/default" ServerAdmin admin@gmail.com ServerName firstwebsite.com ServerAlias www.firstwebsite.com DocumentRoot /var/www Options FollowSymLinks AllowOverride None Options Indexes FollowSymLinks MultiViews AllowOverride None Order allow,deny allow from all ScriptAlias /cgi-bin/ /usr/lib/cgi-bin/ AllowOverride None Options ExecCGI -MultiViews SymLinksIfOwnerMatch Order allow,deny Allow from all ErrorLog $APACHE_LOG_DIR/error.log # Possible values include: debug, info, notice, warn, error, crit, # alert, emerg. LogLevel warn CustomLog $APACHE_LOG_DIR/access.log combined Alias /static /home/user/firstwebsite/firstwebsite/static Order allow,deny Allow from all Alias /media /home/user/firstwebsite/firstwebsite/site_media/media Order allow,deny Allow from all Order allow,deny Allow from all WSGIDaemonProcess firstwebsite WSGIProcessGroup firstwebsite WSGIScriptAlias / /home/user/firstwebsite/firstwebsite/wsgi.py My "/etc/apache2/sites-available/com.secondwebsite.conf" ServerAdmin admin@gmail.com ServerName secondwebsite.com ServerAlias www.secondwebsite.com DocumentRoot /var/www/secondwebsite/public_html ErrorLog $APACHE_LOG_DIR/secondwebsite_error.log # Possible values include: debug, info, notice, warn, error, crit, # alert, emerg. LogLevel warn CustomLog $APACHE_LOG_DIR/access.log combined My "/etc/apache2/ports.conf" # If you just change the port or add more ports here, you will likely also # have to change the VirtualHost statement in # /etc/apache2/sites-enabled/000-default # This is also true if you have upgraded from before 2.2.9-3 (i.e. from # Debian etch). See /usr/share/doc/apache2.2-common/NEWS.Debian.gz and # README.Debian.gz NameVirtualHost *:80 Listen 80 # If you add NameVirtualHost *:443 here, you will also have to change # the VirtualHost statement in /etc/apache2/sites-available/default-ssl # to # Server Name Indication for SSL named virtual hosts is currently not # supported by MSIE on Windows XP. Listen 443 Listen 443 Result of sudo /usr/sbin/apache2ctl -S VirtualHost configuration: wildcard NameVirtualHosts and _default_ servers: *:80 is a NameVirtualHost default server firstwebsite.com (/etc/apache2/sites-enabled/000-default:1) port 80 namevhost firstwebsite.com (/etc/apache2/sites-enabled/000-default:1) port 80 namevhost secondwebsite.com (/etc/apache2/sites-enabled/com.secondwebsite.conf:1) Syntax OK
Viscosity of Ideal Gas From Dimensional Analysis
Your intuition is wrong on this. Consider one-dimensional steady flow, say in the $x$-direction, with a velocity gradient in the $y$-direction. Thus the particles at a given level have average velocity $$barmathbf u(u(y), 0, 0)^T,$$ and fluctuating velocities $$mathbf u'(u', v', w')^T.$$ Let's consider particles that at time $t_0$ are located at $(x,y_0)^T$, which have velocities $mathbf u(u_0u', v', w')^T.$ These particles will, on average, travel a distance of the mean free path length $l$ at that velocity, before hitting other particles. The particles will thus have migrated to a different $y$ position, where the average particle velocity will be $$barmathbf u(y)(u(y_0)(y-y_0)fracpartial upartial y, 0, 0)^T.$$ Notice that the average difference in the $x$-component of the velocity of such particles will therefore be proportional to the mean free path $l$ times an integral $I$ over the distribution of $v'$ and $w'$ velocities which does not matter here: We have $y-y_0I,l$. The mean velocity difference for such particles is therefore just $barDelta uI,l,(partial u/partial y)$.Since the mean velocity is assumed to stay constant, such particles will have their velocity adjusted to the one at their new $y$-position. Viscous forces correspond to the work required to achieve this. These forces must therefore be proportional to the velocity gradient times the mean free path length.P.S.: Also see the derivation in the Wikipedia article on viscositySummaryFrom dimensional analysis I find that the dynamic viscosity of an ideal gas must depend on its pressure $p$, density $rho$ and mean molecular free path $l$ in this way:$$mu C sqrtrho p l.quad$$Here, $Cgeq0$ is a non-dimensional constant.However, I find it counter intuitive that the dynamic viscosity, the 'internal friction', of the fluid increases with an increasing mean free path. My intuition tells me that the internal friction is low if the molecules are widely separated.Have I missed some quantity that should enter the expression?Has my derivation failed in some other way?Is my intuitive picture wrong?The derivationIn an ideal gas, molecules are interacting only through ellastic collisions. The equation of state is:$$p rho R T. quad (1)$$The variables and their units are:$p$: Pressure [kg/(m s$^2$)]$rho$: Density [kg/(m$^3$)]$R$: Specific gas constant [m$^2$/(s$^2$ K)]$T$: Temperature [K]In general, these are field variables, so $p p(mathbfx,t)$, $rho rho(mathbfx,t)$ and $T T(mathbfx,t)$. In fluid dynamics, a common assumption is that each infinitesimally small volume is in thermodynamic equilibrium, so that (1) holds at every point in the fluid. I make this assumption. I also assume that the fluid is 'Newtonian', so that the viscous stress tensor is proportional to the rate of strain. The constant of proportionality is the dynamic viscosity, $mu$, whose unit is [kg/(m s)].The dynamic viscosity is a 'material property'; it is independent of the motion of the fluid. In general, it is varying over space, so that $mu mu(mathbfx,t)$. It's value is a property of the material and depends on its thermodynamic state.It seems impossible to find how $mu$ depends on the thermodynamic state from (1). Pressure has 'almost' the correct units, but I need to multiply the pressure by some time scale $tau$ [s]. This time scale must depend on the microscopic properties of the material, and the only way I find it possible to construct it is by using the $l$ [m] the mean free path of the molecules in the fluid. The time scale contructed is:$$tau sqrtfracrhop l.quad (2)$$Using (2) I find that the dynamic viscosity must depend on $p$, $rho$ and $l$ in this way:$$mu C sqrtrho p l,quad (3)$$where $Cgeq0$ is a non-dimensional constant.·OTHER ANSWER:SummaryFrom dimensional analysis I find that the dynamic viscosity of an ideal gas must depend on its pressure $p$, density $rho$ and mean molecular free path $l$ in this way:$$mu C sqrtrho p l.quad$$Here, $Cgeq0$ is a non-dimensional constant.However, I find it counter intuitive that the dynamic viscosity, the 'internal friction', of the fluid increases with an increasing mean free path. My intuition tells me that the internal friction is low if the molecules are widely separated.Have I missed some quantity that should enter the expression?Has my derivation failed in some other way?Is my intuitive picture wrong?The derivationIn an ideal gas, molecules are interacting only through ellastic collisions. The equation of state is:$$p rho R T. quad (1)$$The variables and their units are:$p$: Pressure [kg/(m s$^2$)]$rho$: Density [kg/(m$^3$)]$R$: Specific gas constant [m$^2$/(s$^2$ K)]$T$: Temperature [K]In general, these are field variables, so $p p(mathbfx,t)$, $rho rho(mathbfx,t)$ and $T T(mathbfx,t)$. In fluid dynamics, a common assumption is that each infinitesimally small volume is in thermodynamic equilibrium, so that (1) holds at every point in the fluid. I make this assumption. I also assume that the fluid is 'Newtonian', so that the viscous stress tensor is proportional to the rate of strain. The constant of proportionality is the dynamic viscosity, $mu$, whose unit is [kg/(m s)].The dynamic viscosity is a 'material property'; it is independent of the motion of the fluid. In general, it is varying over space, so that $mu mu(mathbfx,t)$. It's value is a property of the material and depends on its thermodynamic state.It seems impossible to find how $mu$ depends on the thermodynamic state from (1). Pressure has 'almost' the correct units, but I need to multiply the pressure by some time scale $tau$ [s]. This time scale must depend on the microscopic properties of the material, and the only way I find it possible to construct it is by using the $l$ [m] the mean free path of the molecules in the fluid. The time scale contructed is:$$tau sqrtfracrhop l.quad (2)$$Using (2) I find that the dynamic viscosity must depend on $p$, $rho$ and $l$ in this way:$$mu C sqrtrho p l,quad (3)$$where $Cgeq0$ is a non-dimensional constant.
70's/80's Sci-fi TV Movie with People Exploring an Island and Being Attacked by an Extremely Large M
I think the movie is the 1977 USA/Japanese co-production The Last Dinosaur. Rankin and Bass (of Rudolph, The Red Nosed Reindeer fame) financed it. Your description of the ship matches well the Polar-Borer that takes the explorers through the Earth's crust to a prehistoric land in the Artic. Did the ship look like the one in the pictures below? The dinosaur does attack their ship at the beach and carries it away in its mouth, stranding them on the island.The Last Dinosaur is a color movie. The effects are very much in the Toho style. The T-Rex is a very unconvincing man-in-a-suit. That is why you may associate the dinosaur with Godzilla. The movie never played in movie theaters in the states. I remember watching it repeatedly on network and local television in the late '70's and early '80's. It has a largely American cast, so the lead actors speak their own lines without dubbing.Richard Boone stars as an oil tycoon (and big game hunter) who finances a scientific expedition to explore a recently discovered prehistoric land at the North Pole. A very active volcano has kept the area a tropical paradise for millennia and it is inhabited by prehistoric creatures and cave people. Both attack the expedition. Boone becomes increasingly more savage and threatens the other team members. All he wants to do is hunt and kill the last T-Rex on Earth, while the others want to recover their ship and escape. Joan Van Arc (from television's Knots Landing) plays the lead scientist.The original, un-edited cut of the movie has been released on DVD. I found two good reviews of those DVDs here and hereThe movie has a group of people who either were exploring an island or another mysterious continent. At a point in the movie, I think their ship was damaged or was thrown around by either an extremely large monster/dinosaur (or maybe even Godzilla?) I think this scene happened on land or right by water. I remember that the ship was not that fancy. I don't think that it had the look of a submarine. It almost just looked like a silver tube. Almost like a cylinder. Maybe with a cone at one end. The ship may have just have sides dented. I don't think it was destroyed and the people may have still been able to escape in the ship.I would say that the movie was made between 1950 through the 1960's. I saw it on TV in the 70's or 80's. I remember it being in color but it could have been a black and white movie with a certain hue to it to make me think it was color.
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