Associativity of equivalence 2/2 

While being structurally as simple as its conjunction version, just try to, again, focus on the right side.
((A <=> B) <=> C)

When is this true? Well, obviously if A, B and C are true. But that's not the end.
Say A and B were false, then C would need to be true, because the first equivalence would evaluate to 1.
However, if just one of A or B would be true, then C needs to be false, so the second equivalence would produce 1.

Approaching the problem from the other side, by asking when is the expression false? Leads to the same situation, just reversed.

Given the number of possible combinations and dependencies, my intuition estimated the statement is not a tautology. Like in hockey, if the puck dances too much around the net, it will eventually fall there.

But surprisingly, doing a table showed othervise. Unless I made a mistake somewhere (what I checked few times), it seems associativity really applies for equivalence. Interesting...

Associativity of equivalence 1/2 

Doing some introductory exercises into mathematical logic, one tautology has baffled my mind. Let A, B and C be arbitrary statements and <=> the symbol of equivalence. Then:
(A <=> (B <=> C)) <=> ((A <=> B) <=> C)
The law of associativity of equivalence, is a tautology.

Or not?

Usually, when figuring out whether a statement is a tautology or not, instead of brute-forcing the values, I tend to rather focus on relations between individual variables. See the dependencies, influences, and logically deduce whether they form a tautology or not.

To see why has this quite simple example picqued my interest, let's consider another law, the associativity of conjunction. Let A, B, C be arbitrary statements and & the symbol of conjunction. Then:
(A & (B & C)) <=> ((A & B) & C)
Is a tautology.

You don't really need to be a mathematical genius to see right away why is this true. Just focus on the right part, ((A & B) & C). When is this true?
Exactly when A, B and C is 1. Let any of them be 0, and the whole thing evaluates to false.
(A & (B & C)) is exactly the same case.
So it's pretty obvious both sides are equivalent.

This example is very simple, but a similar approach can be applied on more complex statements.

Except the law of associativity of equivalence.


TSFH links 

In addition to my previous series about TSFH concert in Prague, I'm posting few links for convenience.

Empire of Angels:


Never give up on your dreams:

Star sky:

All of these are official videos posted by TSFH.


Two Steps from Hell concert in Prague. When music blows both mind and soul! 4/4 

What to say as a conclusion? I'm an introvert, I live through most of things in my mind, and I even had hard times expressing emotions in the past.
Nevertheless, this concert made me not just clap, what I usually either don't do at all or just formally, but it literally took me off my seat, with clapping hands risen to the level of my face, wanting to scream from glamour. Everything completely natural, my mind and soul were literally overflowing with excitement and emotion to the point, where not even my fantasy could consume it all, so it naturally released itself to the surface.
TSFH have perfectly combined richness and epicness of their music with the dynamics of a stage, creating an unforgettable experience.

I strongly encourage readers not familiar with TSFH to give their work at least a try. You don't need to go through all mentioned compositions, Empire of Angels, Impossible, Never give up on your dreams, star sky, should give you at least a nip of what their production is about.
Despite the pieces are invaluable, you can actually find all of the mentioned (and much more!) on their Youtube channel for free.

Have a great time, live your dreams, and don't forget to rise to the sky! Whether your fantasy lives on the Earth or travels to the stars, TSFH music can be an invaluable company on all of your mind journeys.


Two Steps from Hell concert in Prague. When music blows both mind and soul! 3/4 

When the composition reached it's final ride part, that puts together individual compounds of the piece - strings, choir, flutes and electric guitars in one common massive performance, we (the audience) went completely wild, clapping like crazy, screaming, waving, jumping and whatever we could do to express our emotions.

Awesome climax, right! Except this was not one.
After the unbelievable mind-rise, we were calmed down by Little star, a beautiful, but pieceful composition that released the action of the previous song.

But we went back rather quickly.After few pieces, when we were told to never give up on our dreams, TSFH fans already knew what's coming.
Interestingly, the bulgarian text of this song, taken from Bulgarian folklore, as some of the Slavic people might have noticed, actually tells the exact opposite of the song's title and theme (the composition is called Never give up on your dreams).
However, Thomas Bergersen has nicely proven, that it's not a problem for him to outperform even spoken lyrics with the "language of music", so even though many of us likely heard the contrast, from the audience's intense reaction, the music has totally won.

After this unprecedented sensation, every next song, even though they were mostly final additions, felt like a new climax. Storm keeper, a really fancy version of Earth protectors with Electric guitars (which fit there fantastically), and extended Heart of courage prolonged the cumulated joy, making it last long after the final tone was played.


Two Steps from Hell concert in Prague. When music blows both mind and soul! 2/4 

So when I saw a TSFH concert is going to be helt in Prague, as a long-time enthusiast, I immediately knew it's going to be a big event.
However, nothing I expected and imagined could possibly have prepared me for the actual performance.

With a string orchestra, a whole ensemble of vocalists, electric guitars and loads of drums, Bergersen himself opened the concert performing on piano Empire of Angels.
They could hardly pick up a more fitting choice. This soul-touching composition embraces a mind-blowing beauty, combining the richness of instruments with the epicness of vocals, making for a mix of something that makes you rise to the sky, but at the same time feel immense power and energy wrapped inside.
Awesome demonstration of TSFH capabilities right from the start!

After the initial composition, we had a chance to hear multiple of their famous pieces like Cannon in D minor, Unbreakable or Strength of a thousand men. Everyone of them would more than deserve its own description and review, unfortunately, the space is limited, so I'm mentioning them just for reference.

When the powerful orchestra backed chorus filled the O2 universum hall with the refrain of Star sky, my amazement rised up to the level where I was sure this is the best concert I've ever witnessed.

However, as it turned out, TSFH have been merely warming up. After a 20-min break, Victory and Flight of the silver bird started to graduate the audience again.
The excitement reached a point, where merely Thomas Bergersen announcing Impossible was enough to cause large ovations.
And the composition has really turned the engines to a higher level. Combining symphony with vocals and pyrate music, this piece of art is a wonderful example of Thomas' combination skills.


Two Steps from Hell concert in Prague. When music blows both mind and soul! 1/4 

English Wikipedia lists Thomas Bergersen as an epic music composer. However, listening to his pieces, even though epic music is undoubtebly a very rich genre by nature, I've always known there is more into the story.
Thomas Bergersen is a musical arch-genius. His compositions, in my eyes, combine three major principles - complexity of classicistic symphonies (making use of the whole orchestra), really high variety of musical instruments, and an ubiquitous focus on every piece's theme.

This combination, is to my knowledge and perception, absolutely unmatched. Long time in the past, great composers like Mozart or Beethowen discovered the potential of orchestra, but what they struggled to achieve was consistency, perhaps not everyone will agree with me, but in my view, classicistic pieces quite often turn into just a soup of tones, rich in their count but lacking in terms of emotion, a bigger picture that would impress the listener and make them remember the composition.

modern symphonies suffer from a similar problem, with an additional issue that they tend to kind of forget other instruments than violin and cellos exist (and I'm saying that as a hobby violinist).

Interestingly, smaller bands and singers seem to have noticed a memorable theme and good instruments are essential for a fancy composition. Unfortunately, even though many are indeed pretty creative and achieved interesting things, it's often at the cost of complexity and even if interesting instruments are used, seeing unexpected combinations is still far rarer than I'd like.

Thomas Bergersen combines the best of all these. Combining uncombinable, mixing unmixable and capable to overwelm the listener's soul with magnificence, emotion and beauty, together with his band Two Steps from Hell, he has been producing a masterpiece after masterpiece for more than 13 years.


Eating cold food (thoughts) 

Traditionally, we are used to heat up all sorts of food stored in low temperatures before consumption. The process is so common that microwaves have become a standard equipment.
It undoubtebly has its benefits. Heat is supposed to release flavours, ease the consumption and even soften the texture in some cases.

However, in the recent weeks, I've been discovering, that cold food does not necessarily need to be bad, either. I already discovered long time ago that some kinds of pies and cakes you'd expect to eat warm, are actually better served cold.
Now, as I've been storing canned food in fridge to save up space and protect some of the more sensitive-ones from the high temperatures, I've been learning, that a similar rule applies for them. Be it beans in a tomato sauce or complete goulash soup, eating them right away seems to have its magic.

In some kind, it's similar to drinking. You can have a glass of room-temperature liquid, or even get water from the cold part of your tap, but nothing pleases the throad so much as a drink from a fridge, be it water, juice, Kofola or Coca-cola.

Eating cold canned food seems to deliver a similar refreshing experience.

I've been also experimenting with eating full cold lunches. One difficulty I see here are the differences in responses of various ingredients to cold. Some of them seem to ingest it more than others, some change texture while other don't, and some respond in a way that makes them slightly harder to eat. These differences create a variety, that seems to negatively influence the overal experience of the meal.
Therefore, I'm not decided yet, which variant is better - heated or unheated.

Since even though the flavour seems to suffer a bit in some complex meals, in one-time boxes, they still posses the ultimate advantage of cold food that also cans do.

They don't require dishes (except cutlery), that would need to be cleaned afterwards.

Also, one additional note. Privacy is definitely fine, but there is one consequence in this case. Any video you're watching/subscribing wia FreeTube won't get your activity counted, and its author won't get the revenue from the Youtube adds.
If you have a favourite youtuber or channel which is not widely known and you'd like to support it, I recommend at least considering making an exception and watch/subscribe it from the official site, the interest can motivate the author to further production.

I guess that much for this post, happy private Youtubing!


Show thread

If you don't have the development environment, that's fine as well. I'm providing myself compiled binaries, so everyone can just download and try.
You can get them from:

The server is not under my physical control, so, here are checksums:
AppImage: ffd20926991dfdc16c6bfdf4502b68979a516414b50b63c94e05349fd0cb468f
Deb: 441251944d898eeffc0f048f6d0472941b615851177a6a3ea3f983ad98af8ce2
RPM: 6a231763aa0f0573fb0a5f7559ef69b7e6e4fff53aa0be9f59804bffe7539839
Exe: c5383ca5a9a773dc3b363b4b64213430b5aebffee8c1cd6ea51dbbeaec7d80a7
Setup: bca76193024928698a3969c0a8c5ed7ea60bbfff9abc3b08b0dfe4e6c888cef1


Show thread

The changes are not yet integrated into the mainline, and that's why I'm writing here.
If you're interested, you can try out the new interface and check if I didn't forget to mention something, the developer is very responsive and serious about the issue.
You can either engage directly in the pull-request discussion:
or write your suggestions to me if you don't have a GitHub account and don't want to create one.

Now, on the topic of how to try the new version.

There are no official binaries for this as of now, since the PR was not merged yet.
If you have node.js and git installed, you can however create them yourself:

$ git clone
$ cd FreeTube
$ git switch improve-accessibility
$ npm install
$ npm run build

The binaries should be located in the build folder.


Show thread

FreeTube, a privacy focused Youtube client is getting accessibility updates 

Bored of Youtube constantly tracking you? Annoyed of the cookies banners and slow website? And the Google's more and more invasive methods of verifying age for watching videos?
FreeTube is an open-source, privacy respecting Youtube client for Linux, Mac & Windows.

Hassle-free interface, no adds, local history, subscriptions and last video position saving are just some features it provides to help you enjoy Youtube privately, without sending your data to Google.
Connecting over VPN or Tor is also supported, so you can watch completely anonymously!

Until recently, FreeTube was a great app, but with somewhat difficult accessibility making it hard to control.
Fortunately, after opening an accessibility improvements issue on the project's GitHub, one developer jumped in and did a really great job on this, making the app far better usable than it used to be.


Also note that I can't really write shortly, my last story written as a homework for my school had 12 pages despite the 1,5 limit, so... 1000 characters for a message is not quite enough for my writing style. :P

I will try to adapt, but oddities can and most likely will happen.
So if some of my posts seems... cut a bit, just check the replies, there may be a continuation.

Show thread

Hello everyone,
as I've finally got a grip of Mastodon, I think it might be a good time to introduce myself.

My name is Rastislav Kish, I'm from Slovakia. You may already know me from the forum (past member), or from various mailing lists (Orca, The vOICe, Eyes-free etc.)
Few words about myself, I'm quite hard to define. I really like exploring new things, learning new skills and especially inventing new approaches to whatever I'm currently doing, no matter how trivial the activity already is. :D
You'll often find me just turning left and right on my computer chair, with one song playing in a loop in my headphones, submerged deeply in my thoughts, imaginations, ideas etc.
After hours of dreaming, I usually express my conclusions wia coding, writing, building etc.

You can find the finished pieces of my work on various places, like my GitHub or my old website.
My most notable finished projects yet include Keyjutsu, Chinfusor, Ride and Math scanner.

A fun, happy little Mastodon/Hometown instance. Join us by the fire and have awesome discussions about things, stuff and everything in between! Please read our rules before doing that, though; applications without the password that confirms you have done so will be rejected. Admins: Talon and Mayana.