Serious problem of mental masturbation

Hi,
just to clear things up, yes mental masturbation is serious concept that actually exists though when I heard about it first I thought that it is just some joke or what.

Today I want to talk about YouTube, Khan Academy and what mental masturbation means.

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This topic is kind of connected to procrastination  and multitasking and I already wrote about those in previous episodes of “serious problems”.

While procrastination is simply avoiding some work that you know you are supposed to do and multitasking is doing more stuff at the same time (which decreases your overall performance) mental masturbation is doing intelectuall things that could seem on the first hand quite good but are actually either preventing you from doing real action IRL or making you think that you are just at your top productive.

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Now let me give an example.

The way I understand this concept is in watching educational YouTube videos. There are literary thousands of them, so you can spent a lot of time like that. Try to watch some video (best more) and after few days try to recall what was their content. SciShow is for example great channel for this experiment.

They release daily videos about science. Each is something like 4 minutes long and there are over 700 of them. Mental masturbation would be if I watched 10 of them and then did not remember a single thing but still thought that I was being productive by watching educational content (this is quite intuitive, if I watch so much at the same time without thinking about it I can not remember it). Actually, most people would probably agree with me and said something like “Yo man! You are doing some serious work on internet.”

Now the pitfall is of course that it is just wasted time and you do not even know it. You could say that you remember something and that is fine but you want to remember the whole video because maybe it was some high quality stuff but you just skimmed through thinking that “yeah this is great”.

The way I first noticed this was when I watched videos and then talked about them during family dinner. Sometimes I contemplated that I do not know mere minutes after it finished what it was about, though the false great feeling was still there.

This applies to lot and lot of stuff, reading too of course. I mentioned Khan Academy in the beginning. KA is a huge project that has lot of nice educational content. Like it or not, content needs to be tested and proper testing system in Khan Academy is basicly only in math sections. The other subjects you can use just as a tool for mental masturbation.

Derek Müller from Veritasium is pretty good in his physics videos. He discusses this issue in this one:

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So how can you stop mental masturbation?

1. Start taking notes from what you read, videos you watch, people you talk with
2. Talk with someone who is interested in the topic or she/he saw the video too.
3. Play it/read it it more times. Repetition of the best stuff is going to make you remember it whether you like it or not.

The last advice might seem like a waste of time but as it happens it does not need to be.

Dragallur

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65 km trip again!

Hi,
my mother told me that my post were too mathematical for her, hopefully she will like this one more :D. So about week and something back, I wrote about my summer camp where I walked 65.5 kilometers in one day. With friend I decided to repeat this and we had in plan 80 kilometers (again) though due to some things we did not finish it whole.

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Me and my friend, we started at 3:00 AM. I personally had about 3.5 hours of sleep. The trip was planned to be 80 kilometers long though in the first part which was about 32 we had a long delay.

This is the city after 32 kilometers.

We stopped at Tesco and bought some food and it was quite clear that we can not make it in time (I had to be back roughly around sunset). This was because I thought that we could do it with the speed of 5 km/h which is not much for walking but a lot when you walk for more than 12 hours. My friend went home by train than and I decided to take the shortest way to home, it took me 16 hours.

At one point we met one guy. It was in the early morning. I talked to friend who was few meters behind and I said something about 20 kilometers left to go for the northest point.
The guy asked if we think that we can walk it 😀 I had that distance almost three more times in my shoes when I returned home!

In the end I had 65.14 kilometers walked and my feet hurt a lot. Again I can just recommend you to try something like this, we also had a beautiful sunrise though my phone camera is not very good:

When we saw sunrise we had few hours behind already!

Dragallur

Limits made easy and continuity

Hi,
yesterday I wrote some basics about functions and today I will write about limits again, and when they are defined and when they are not.

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Just to remind you, we will use limits on functions. Those functions will usually be plotted on graph so it is easier to work with them. Our first function we work with will be the one below:

Some function.

If you have not seen that yet, filled dot means that the point is inside of the function and circle means that the point is not there. Now when we speak of limit and if it is defined we have to get the same results as we approach from both sides.

What do I mean by this? Limit is basicly just approaching some number very very close. Take for example x=1. At that point in the function above, y equals 5. If we wanted to take the limit it would go as follow:  

lim_x→1   f(x)                           [1]

Now if we think about it before we get the result, we know that you can approach one thing in 1st dimension in two directions. Those are in limits noted as from the negative side (-) and positive side (+).

For the limit I wrote, (lim_x→1   f(x)) from both sides we will get the normal result as if we wanted to know what the function outputs but sometimes we just can not use the limit because  it does not exist.

Such an example would be for the following limit (still working with the first function):

lim_x→2   f(x)

In this limit we are trying to approach the number two but from the graph we can see that it is strange at that point. The function jumps so we should check the limit from both sides.

lim_x→2+   f(x) = 1
lim_x→2–   f(x) = 2

Since the limits do not equal each other, the one before does not exist! We can have so called “one-sided limits” but they are not of much use as far as I know. Now we can actually create amazing definition for continous function!

Continous function is such that does not have any jumps or spaces in it.

 

 

The function on the left is discontinous. This is because on one point there is space, which means that function is not defined there.. this is problem if you want to be continous.

 

 

 

Another function is discontinous even that it is defined on all Xs. The problem lies in what I told you about, if we took the limit_x→3 f(x) = undefined
This is because from positive and negative side we will get different result.

 

Again the function is not continous. This time the  limit at 2 exists but it does not equal the value of the function.

limit_x→2 f(x) ≠ f(2)

 

 

 

 

This one on is not continous either. This is because if we approach from negative values we will get -∞ but if we approach from positive values we will get +∞. The limits do not equal so the function can not be continous.

 

From these points we can summarize what function has to have to be continous at one point.

1. Point there is defined, it is not empty circle!
2. Limit on the point exists.
3. The limit equals to the point on the function.

Or also:

1. f(a) is defined
2. lim_{x→ a} f(x) exists
3. lim_{x→ a} f(x) = f(a)

This is all from me for now, thanks to “analyzemath.com“. I did not need to create all the graphs again thanks to them.

Dragallur

[1]Sadly wordpress is not able to create some normal indexing so I will write it like this. Normally limit is noted as this:

Proper notation for limit where x approaching something is in the bottom.

Limits made easy and heart equation

Hi,
I said that I started to learn limits. Since often I write about the things I just learn I will start this series today with the very basic. (The start is actually so easy you wont even think that it is precalculus or something)

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Basicly the context for limits are functions. I have personally never learned functions on

Basic idea of function

their own and I do plan to do that but I do not think it is so important right now. You just
have to have this idea that when you have function you will give it some input and it will give out some output (kind of black box).
It is important to say that one input corresponds only to one output. You have already probably seen some graphs so it is good to say that you can plot a function.

 

The thing with outputs and inputs can be nicely illustrated on one thing: imagine a class of kids and that you measure them.

Carl – 157 cm
Ann – 152 cm
Caroline – 160 cm
… and so on

Now you will plot them on graph next to each other. In big enough class you would probably have more kids with same height.

On the left we have three example kids from one class. As is written, Ann has 152 centimeters, Susan 152 too but Jacob has 149,155 and 161 centimeters. Such class would not make a great function! The interesting thing is of course that to one height (152 cm) you can match more people (Ann and Susan), this makes sense. But you can not match one person to more heights! This is the way function works. You could just change names and heights for x and y and you would be there[1]. So if you graph some function it will never be vertical and basicly no two values will ever be above each other, when you on the other hand plot equation you can easily get graph where there are two points above each other:

Equation stolen from twitter and modified for better look.

So… what role do limits play here? As you probably already heard, limit tolds us what value will function give us when we give it input really close to some number. If you have function like

f(x)=x^2                  (f(x) is the way functions are noted, you could use other symbols)

You can ask for limit of x approaching to any real number and you would get the same as if you would calculate x to the power of 2. The real usage of limits comes when there is point where you can not get some nice value and also I think that it is defined by limits if function is continous (without jumps) or not.

I will slowly continue in the next post 😉

Dragallur

PS: some of my readers mathematicians (or anybody), if there please point out any mistakes, I am just learning this so it would be great to know my mistakes!

[1] To make it even clearer I made this extra picture:

My experience with Windows 10

Hi,
since a while back I was kind of interested in programming and computers and on the camp last two weeks there were lot of nerds to computers I decided to share my experience with Windows 10 upgrade.

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Do you remember the annoying notifications from your computer about this new operating system? Maybe you have them even now if you have not upgraded yet. My teacher on geography and computers shared with our class this link to some software that disabled these notifications. It was quite good except that I almost missed the time when Windows 10 is for free, the offer ends 28th of this month I think and I got notified just because I was on another computer.

I of course did not want to miss it because right now Windows 10 costs over 100$ which is not something I can afford. Also Microsoft promises free upgrades now and on. This makes sense, all other operating systems have it like that. At least mobile for example, not talking about Linux which is for free completely. I have heard that it would be logical to cut down the price or extend the possibility to upgrade since they want as many people as possible on the newest system. It would be quite nice if there was then just one system not 4 or 5 Windows where some are compatible to something and some are not.

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The upgrade itself went pretty smoothly though it took at least 4 hours -_-. Right now I am turning off all the various features the new OS has since I do not want to be part of sharing all my personal data right to office of Microsoft. Not that they could not see everything right now.. but the age is moving on and this is the way it is.. having too many personal things on computer may be dangerous.. the time of clouds has come and it may happen soon that we wont even have proper harddisk but everything will be somewhere else in the world.

Dragallur

PS: even that this is so called “best windows so far” it is not able to have one wallpaper for each monitor -_- 😀

Traveling faster than sound: shockwaves

Hi,
today I want to shortly explain phenomena called “shockwave”.

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You may have heard this word already used in the context of supersonic traveling. That is exactly it. Shockwave is the event, whether it is visible or not, that comes when you reach and/or cross the local speed of sound.

I say local because speed of sound changes with temperature, air density and humidity but for normal purposes it is roughly 343.2 meters per second.

When you are slower than the speed of sound the waves made by your movement do not

Circles to illustrate shockwave.

ever hit each other (without obstacle). This you can see on the left first picture. As you move through fluid [1] you create those “circles/ripples” around you and they are closer to each other in the direction you travel.

 

When you speed up to the speed of sound you will create this shockwave because suddenly all of those circles are hitting

Mach cone

everything at the same time which means that the hit is pretty hard. What you see usually is something similar to the picture on the right. This is just the condensed water in the squashed air.

I have read that it is quite dangerous to fly exactly at the speed of sound. It is not very efficient at least because the drag increases 2-3 times compared to supersonic speeds.

With sonic speed you can calculate two numbers. The first one is Mach number which is calculated as your speed divided by speed of sound. This means that Mach 1 is exactly the speed of sound. There is also something called the Mach angle which exists only in supersonic speeds. You can see it labeled as theta in the picture above. The smaller the angle is the faster you travel and the equation goes like this:

sin θ = c/v

Shockwave can also be created in space, though here that speed of sound is way higher (9,000 m/s), I already mentioned this in another post.

For more illustration you can check the video below that I made in GeoGebra:

Dragallur

Read more: 1) 2)

[1]Watch out, fluid means both liquid and gas!

Back from summer camp!

Hi,
so I returned yesterday from the summer camp where I was last two weeks I mentioned in the last post. I guess that nothing changes about my post schedule so keep tuned, maybe I will post soon something about limits since I am trying to learn those right now.

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Summer camp!
Yey! It was quite fun, lot of new people and so on. The theme was from one czech movie about girl in mill and guy who is searching for princess, though the movie is childish it was very well used by the orgs (organizators).

I can not say too much so publicly because some games are used again next year and you can go there only once a life. One of the most memorable things was the day when we woke up at 1:00 AM and hour later we went for a trip long trip. We were actually walking for quite a while. Just walking……. no I am kidding we stopped for breakfast, also we saw sunrise on the tallest mountain in Czech Republic.. then we walked, and again we walked.. we stopped because we needed to change shoes. The we walked and changed socks. And so on. This three times.. then there was storm and we had to stop on 65.5 kilometers with 2700 meters of cumulative elevation gain! It was “hard-core” trip and we did not finish it because of the storm (there was 15 km left). I would post some pictures if I had any, though you can imagine it was beautiful.

Dragallur

Leaving for 2 weeks

Hi,
yes the title says it clear. I was preparing about 2 months to have some posts that I would publish on schedule when I will be in summer camp but the only extra post I made was this one and I used it before. What this means? That until 17.7.2016 (or 18) there wont be any post from me. I am going on summer camp. Of course I wont be able to read your posts too, see at that time then 😉

Dragallur

Here are some of my favorite posts that you can read before I return! 1) 2) 3) 4)