What does “x” and “y” even mean?

Hi,
so after quite a break, I am returning with math post. It is going to be simple analytical geometry or whatever this field is called.


After teaching some people about lines, circles, circles in a hydraulic press (read: ellipse) also vectors and all sorts of shapes that you can think of[1] I bumped into a fundamental issue that my “students” missed out something important even after using it (without knowing what it really was) for a long time.

First, let’s talk points. A point on a number line is quite straightforward. Why? Because you do not need to have a lot of information to describe it. Image result for number line

Any point on the number line can be represented using only one number, one value. If you wanted to represent a line on the number line you would just need to set boundaries for the highest and lowest number, something like 3<x<5 [2]. This line would have the length of 2 and you would find it by just drawing all the numbers like 3,3.1,3.2,3.5,4,5 and all the others in between, those are all the possibilities for “x”.

Image result for grid line

Number lines start to get boring on this level so we have to step up on a grid. Here you need more information. As you can see on the map. Your city/town has two coordinates, latitude and longitude which is just a fancy name for the commonly used “x” and “y”. Here the grid is limited for x which needs to be between +180 and -180 and y between +90 and -90. With these two coordinates, you can locate any point on the Earth. The similar thing is with the commonly used grid but there, “x” and “y” do not have any boundaries[3]. But how do we write a line on the grid? Well, we could just ignore the fact that it is a grid and think about it as a number line. We just need to set “x” or “y” to some number and let it be fixed and unchanging while the other one changes and describes our infinite line (without boundaries) or just a segment (with boundaries). If “y” is constant that means that we can move only left and right and the line will be leveled. If “x” is constant we can only move and find the points on the line by moving up and down and the line will be vertical.

I will continue probably next time with lines that go different directions.

Dragallur

[1] Don’t think of too random shapes, they would be too difficult, you still have to think about “nice” shapes.

[2] Any math is really difficult to write in WordPress so what I actually meant was 3<=x<=5 which means that numbers 3 and 5 are also a possibility.

[3] Of course, Earth is a sphere and that is different geometry but it serves as a good example.

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Is consciousness an illusion?

Hi,
so apparently we have a problem. Noone knows where consciousness comes from. This is quite a big question since that is what we are, right (?) the mind.


I find this idea of consciousness very interesting, we cannot share what being mindful feels like or see that another creature is aware. We have to take it for granted from what others tell, there is no way you can tell that your friend is not just a machine, that is what I mean.

As the title suggests, I will be asking myself if consciousness is just an illusion. This might seem a bit outrageous which makes sense and I am totally open to it being wrong (which it very easily might be, see disclaimer). I think that awareness will raise as an illusion if there is enough complexity added to the system. By the system I mean of course what we perceive through our senses but also the thoughts. The thoughts might actually be the most important part, making our personality.

I am suggesting that with language and thoughts we create a fake personality, the ego which then creates a sense of existence. Through the sheer amount of information that the body receives and reacts to, arises this illusion.

Have you ever tried to notice how thoughts appear? They do so without somebody telling them anything or controlling them [1], this is why there is no one behind them but a shadow. The thoughts tell themselves that they are real but they are just a reaction to the surroundings. That is why there is no special part of the brain that cares for consciousness, it is just an emergent property of huge complexity and in the end, we truly are only robots.

Dragallur

Disclaimer: I’m not neurologist or expert on this topic, those are just my thoughts on this problem.

[1] If you think there is, think again, because those are just other thoughts.

Three year anniversary

Hi,
apparently, the three year anniversary was already yesterday though I thought that my first post became public on 21.3.2015, I guess I was living in a lie.


What now? I have been very lazy in the past weeks, not posting a lot. I am still planning to continue to write the blog, I have no doubt, definitely.

In the three years I:

Received 2 510 likes
Wrote 126 430 words in a total of 318 posts. (Harry Potter and Prisoner of Azkaban has 107 253 words.)
From my readers, I got 1 250 comments.

This is a small blog, it always was and will be in the future, I am not even really reading anybody else’s posts or trying to get more views. I just let go and write a post about once a week if I feel like it. Whoever reads it, cool, I hope that the posts help or you find them interesting at least sometimes, every like or extra view makes me happy and you are helping with that.

Dragallur

Mnemonics

Hi,
today I will write a short post about the power of mnemonics.


Those are things that help you remember something. One that I used quite a long time ago was Saturn mnemonic. I was not sure if it was Jupiter or Saturn with rings but then I realized that the letter “S” is basically just circle disconnected and changed into the shape with a single movement. One could argue that this does help because “J” could work similarly and it is not foolproof but the beauty in this is that it does not need to make sense, it is enough if it helps you remember something.

Another example would be how in 8th grade at the end of the year we had to remember (in some game) two groups of words, the key to this is for me was visual mnemonic, I simply stacked the objects on top of one another. It went like this: ruler, place, hill, plant sock and the second group was a chandelier, scissors, and map (I do not remember the next two words). The first group was extremely simple because the hill would be kind of roundish in my head, so it would nicely fit on the plate, the plant would grow on top but would be hidden by a sock, does not make sense but did its job.

From my experience, it is best to be able to create your own mnemonics connected with your life. Often they are total nonsense, some kind of absurd story. For example, this is how I remembered what in your skin is responsible for that feeling:

Pacinian corpuscules – Pa like Pascal (not my invention but Pacific as a pressure in the deep ocean would work too)
Kraus corpuscules – From Vampire Diaries, Kraus was quite a cold person (corpuscules responsible for cold)
Ruffini corpuscules – ff like fortissimo in music, fast means hot so corpuscules for heat

Sadly enough I forgot to make one for Meissner corpuscules so I didn’t do that in a test.

Now you should have the idea, I recommend the following tests to try this out or just to test your memory: https://www.humanbenchmark.com/tests/number-memory

Dragallur

Cellular automatons

Hi,
today I will write about a new thing that I just learned over the weekend. Since it is based on a competition again I will care not to post here too much so as to be fair and not to spoil it.


Cellular automatons, at least in my knowledge so far, are in a sense, computer colonies, comprising of tons of cells. In the simplest version, you have 1-dimensional automatons which means that the cells, signified by squares let’s say, are in one row, every one of them neighboring with two other.

The cell is either dead or alive. You can create rules to make them reproduce and die, when, let’s say some cell is overcrowded. If you decide that what will happen with the cell depends on the state of the cell itself and the two neighbors and the result will always be the central cell either dead or alive there are 256 options for different rules.

This is how it would look like if the rule would be that cell always reproduces to the rest of the fields that it neighbors with but dies if the two spots around are full [1]:

 

TriangleOfTruf

Not here, but it had 5000×5000 pixels. Feel free to use this picture for anything.

 

This is one of the interesting most of the 256 rules ain’t doin’ a thing but this is the rule #126 so remember that 😉

Dragallur

[1] The picture is not a line because every line of pixels is one second let’s say during which cells reproduce and die and so on, yellow means alive, purple means dead and in the beginning (top of the picture) you have only one alive.

How societies keep their members from leaving

Hi,
today I will write about societies and generally some at least partially closed groups of people that even if they seem different from each other, they share one ultimate tactic to survive.


I will start with the most common and intuitive example which is, of course, a dictatorship. For a dictator to be in reign for a long time he needs the people of the state (no ruler rules alone). Of course, they can’t be just free to leave so dictator has some simple means to keep them. Let’s say fence, it is quite effective against most folk. Also violence in general, there is this threat, if you try to leave the society you will get punished. This is simple but not perfect, there is a better way to do this and for example, democracy found that out.

I am not saying if this is good or bad, that is not the point here, what I want to illustrate is that democracy needs its people too and like in a natural selection only the strongest regimes will last [0]. Western states no longer need a brute force to keep their members from leaving because most people are from young age taught how where they live is the best [1.5], yes we have bias towards democracy, teachers in schools have bias towards democracy and there is no need to have a brute force because your family, your friends and simply your surroundings will pull you back in case you start to diverge paths with what you have been taught. Do I find this concerning? No, not really (a bit) because I am PART of the system! Which of course means that the system is doing exactly what it should do.

Those are not the only examples. Religion too, whether you like it or not. You will be looked down upon by your fellow believers if you start to question the society. The pressure on you, once again (in Western society at least), won’t be physical, rather psychical. For the system to survive it must teach it’s members that it is the best one and that it is wrong to question it, after that, it is just a cycle.

School is another example. You are forced to stay in it by everybody around you (of course we are not discussing the consequences of leaving school [1]). There are other countless examples and always the pull on oneself is stronger when more people around you are in a group that you want to leave, like let’s say if everybody in your family is religious.

Just food for thought, feel free to leave comments and proof me wrong!

Dragallur

[0] Here I am not comparing dictatorship and democracy as to which is stronger (because they both exist), rather democracy to anything you can think of that never really existed (anarchism maybe?).

[1.5] Dictator can also brainwash (a bit too strong word [1]) their people but I was thinking of let’s say communism in Czechoslovakia where my parents certainly did not think anything good about the regime.

[1] For exactly the sentence that I wrote, is this topic so nuanced. I think I should not leave school because it will worsen my life, everybody taught me to believe that, it is apparent that it might be hard for me to earn money but maybe I would be happier, who knows, but I  know I am not planning to try it.

Disclaimer: I am not an expert in whatever field this is.

 

Unrealistic radioactive decay

Hi,
today I am going to write about one of the problems that I had to solve for a physics seminar. The submissions for this series are already closed and you can look up the solutions so I know that I answered correctly to this very interesting problem.


Imagine you have two types of particles, A and B. They are radioactive, meaning they keep falling apart but in a very peculiar way, A decays into B and B decays into A. This doesn’t happen in a real world because the particles decay into something smaller, they break up, but this is a hypothetical scenario very simplified, we do not care about what is happening on the inside. The question is, what is the ratio of the particles at any point in time?

Since the answer itself and the calculation are not trivial I will mainly try to make some facts about this problem obvious and then show the answer.

There is one part that I didn’t mention in the setup. Radioactive particles do decay but there is a very important value that characterizes how fast. It is either (half-life) which tells you in what time will half of particles decay (if there is enough of them it will give the right results) or in other words when the time passes one particle has 50% chance to decay. It seems that also decay constant, which I like better, is used which is basically half-life except the larger the value is, the faster the particles will decay.

The problematic part of this exercise is that when part of the A particles decay they will increase the pile of B particles which means that more particles will decay into A and so on, this is a cycle. To get to an important point it is good to try some simple case of such decay.

Let’s say we have 200 of A particles and 100 of B and half of both will decay in 1 hour. In 1 hour:

A=200-100+50=150
B=100-50+100=150

Next hour:

A=150-75+75=150
B=150-75+75=150

It is obvious that from now on the amount won’t change. This little experiment revealed something obvious, there, first of all, no particles get lost, there is always the same amount present: A+B=constant and with a bit more experimenting it would become more apparent that there is an equilibrium between A and B meaning there is always some amount of A that when it decays it will equalize the amount that decayed from B, this equilibrium will shift depending on the length of half-life or the decay constant. From these thought experiments that reveal the behavior of this problem, we need to use some math that I will not get into here to get the result that you can try to play around with in Desmos.

Dragallur

 

Why physics and not maths

Hi,
it just so happened that it took me few weeks to finally write something. I was over the holidays on Mallorca and then I missed the last week too, oh well, today I will compare some aspects of physics and maths that I noticed and why I choose physics over math.


This is something I have realized lately during solving of physics and math problems. While math is certainly groundstone of physics the thing I dislike about math is its formalness and its need to be exact, actually, I guess the need is there because of its possibility, in the real world, not only that it is just too hard or impossible to model some situations but it is also worthless to know the answer for any number of decimal places[1]. What I really like about physics is how you can approach a problem and tell yourself:

“I can neglect this part because it won’t change the situation much.”
“I can approximate y=sin(x) close to 0 as y=x because it gives me similar values.”
“Let’s use this numerical solution for this difficult integral.”

Yeah, I love how in the real world you can approximate, though at the same time you have to keep the balance so that the solution is still useful. Math is too exact for me. I do like proofs but it has to be with balance and I need to be able to see in the world around me what I learned.

I will keep it short and end it with this meme:

Fotka uživatele Mechanically Engineered Memes for High Tensile Teens.

Dragallur

[1]Obviously a simplification.

Personal guide to melodic death metal

Hi,

It’s not like science is the trend here though the blog title could be misleading for some people but yeah, today I am not going to write about Science and Rationality. Today’s topic is quite personal and it is about the music that I listen to. I can date exactly when I started to listen to what I listen to now. It happened on 20th of June 2015 when I heard the first song from Insomnium. This one wasn’t of my taste at first and I rather liked this one.


This style of music is called melodic death metal. This is not an old genre and as it goes in metal music, it is just a subgenre, here it originates from death metal. It is also called Gothenburg metal because of the city where some of the oldest bands came from. Those are probably At the Gates, In Flames and Dark Tranquility, I do not know much about the first two especially about the first one but DT is one of my most favourite bands and particularly their newest album Atoma. Just a few days back I made a collage from the album covers, so instead of linking more of the music you can just look at this:

Albums - Copy

All this music is metal and most of it is melodic death metal.

There are some things that metal fans (also called metalheads) can be quite funny about. First of all, there is just ton of sub-genres. Whether it is progressive metal, death metal, doom metal or let’s say black metal, everybody finds their own and afterwards is extremely sensitive about its exact label. That’s where metalcore and similar come into play. That is a genre (of metal IMHO) that gets a ton of hate from the true elitist metalhead community, if I understand correctly it is because metalcore and co. are connected with the stereotypical idea that emo kids listen to the music and in some way, there is quite a difference between the bands image let’s say, one like Black Veil Brides and Amon Amarth. You can often see people arguing exactly about this on some border band where part of people dislikes it (often just because of the video) and label it metalcore, while the rest tries to defend it to stay metalhead. So yes, genres are really BIG in metal. On the picture above are probably two metalcore bands: Words of Farewell (arguably) and While She Sleeps.

To finish on some sad note as is normal in metal, what I listen to particularly has a couple of important characteristics. First of all, it is melodic as the name suggests. In MDM, there is a lot of effort put into good instrumental parts and many interprets make an instrumental song once per album and those are also listenable for non-metalheads. The second important characteristic is that it can feature growls (those are the vocals that people really hate), clean singing and even female vocals and some bands are female fronted meaning the main vocalist is female (and they often growl too, e.q. Arch Enemy). This is a quite important as when you combine these elements you can get many types of music. The third important part are lyrics, yes you normally do not understand them and yes, they are often about death, misery, sadness and such but they can have all sorts of interesting messages. I will end the post with the lyrics from Insomnium – Where the last wave broke:

How does it feel?
To welcome the new day
Not worth saving
To fall down on own imprudent acts
The wind answers quietly
Clears the black smoke far thick to see
Unfolds the true nature of man

“And this fire it burns
Consuming us all
Withered garden for posterity
Inheritance in flames”

“When the mankind moves
Rest of the life shakes
All once green turned into stone
Flesh into dust and soil
Where the last wave broke
The shores blazed red
And place once called home
Turned into hall of dead”

How does it feel?
Bite the hand that feeds you
Poison the well that waters you
Prospects made from castles of sand
Legacy in barren land

Breed, greed, bleed
Legacy in barren land
The last wave broke
Prospects made from castles of sand

Dragallur

On human nature (part 1)

Hi,

Today I was going to write about the book Brave New World and happiness but just few minutes back I settled on something else so I am not even sure what will come out in the next several minutes.


As I was going through my news feed on Facebook I noticed Phil Plait posting again. It is about another black hole merger and gravitational wave detection. This happened I think four or five times now and of course for the first time it was all over the news, everybody was talking about it (even Czech news mentioned it). I am not sure how it was like for the next time but it probably did not get such an attention… now I am not trying to say that it should have, there are other important things (like a woman under root (don’t even ask for the context)). Anyway, this time gravitational wave was detected and public could only find out through reading one tweet [1]! That is how much coverage you get for discovery in probably completely new field of physics.

I am certainly quite biased here but the point that Phil Plait made in his post and that I want to share here is how people look for new things but then quickly forget about them. It appears we live in an age where meme (meaning not only joke now) lasts for shorter and shorter time [2]. This might be caused by this “information age” or whatever we call the 21st century but I think this trend also propagates further to the need to have a new iPhone or whatever is behind schedule on being “updated”.

Maybe all of this sounds cliché and just the other day I was telling one of my teachers that the reason why man do not work with hands so much is simply because we live in different time! It reminds me of people worrying about first books then newspapers, TVs and now phones and their effect on youth (this and this XKCD will help you get the idea). And yet should we be worried about the change? How are we going to get ready for it if we leave it to itself and then it does become a problem? I could write under this picture of Black Friday: “Look at those insane people!” but maybe as things tend to be it is more complicated than that (but yeah they are probably buying useless stuff 😀 ).

Dragallur

[1] Yup that is a lie, of course it spread through the internet but it was not such a boom.

[2] I should probably put disclaimers all over the place since I have not lived very long time yet.