(Originally posted on Sunday, 2 October 2016)

Wow! What a cool tribute-video! My favourite actor in two of my favourite movies: The Terminator and Aliens! He was awesome in these awesome movies!

Everybody remembers these movies for the roles of Arnold Schwarzenegger and Sigourney Weaver (respectively), but the next main actor in BOTH of these movies was Michael Biehn! He was perfect in the roles of Kyle Reese and Dwayne Hicks!

PS. I prefer Aliens over The Terminator, but chronologically The Terminator was first.

## Tuesday, 31 March 2015

## Monday, 30 March 2015

## Sunday, 29 March 2015

### I saw a guy in a coffee-house today

I saw a guy in a coffee-house today. Without a phone. Without a laptop. He sat, stared through a window and drank coffee. Like a psychopath.

(Tuesday, 29 December 2015)

(Tuesday, 29 December 2015)

## Saturday, 28 March 2015

### The easiest way to tie a tie

(Originally posted on Monday, 15 August 2016)

My way of tying a tie is a rare one, but also the easiest one. My father taught me how to do it and he must had learned it during his college times, because his father (my grandfather) used to tie a tie in a different way.

The CRUCIAL thing is to start with a tie lying on your neck on the left-side!!!

I made some pictures from the point of view of a person tying a tie – I don't understand people picturing it from a different perspective.

My way of tying a tie is a rare one, but also the easiest one. My father taught me how to do it and he must had learned it during his college times, because his father (my grandfather) used to tie a tie in a different way.

The CRUCIAL thing is to start with a tie lying on your neck on the left-side!!!

I made some pictures from the point of view of a person tying a tie – I don't understand people picturing it from a different perspective.

## Friday, 27 March 2015

### The earliest sunset occurs earlier than the shortest day

The earliest sunset occurs earlier than the shortest day – this is a kind of trivia I “discovered” a few years ago and I was VERY surprised. The site below shows sunrise and sunset times and you can check it yourself.

For Washington, DC, USA the times are:

Sunrise time on December 7 is 7:13:45 am.

Sunset time on December 7 is 4:45:58 pm (the earliest sunset).

Day length on December 7 is 09:32:13.

Sunrise time on December 21 is 7:23:21 am.

Sunset time on December 21 is 4:49:41 pm.

Day length on December 21 is 09:26:20 (the shortest day).

Sunrise time on January 4 is 7:26:58 am (the latest sunrise).

Sunset time on January 4 is 4:59:35 pm.

Day length on January 4 is 09:32:37.

http://sunrise-sunset.org/search?location=washington

Here are screenshots from December 2015 and January 2016:

(Saturday, 5 December 2015)

For Washington, DC, USA the times are:

Sunrise time on December 7 is 7:13:45 am.

Sunset time on December 7 is 4:45:58 pm (the earliest sunset).

Day length on December 7 is 09:32:13.

Sunrise time on December 21 is 7:23:21 am.

Sunset time on December 21 is 4:49:41 pm.

Day length on December 21 is 09:26:20 (the shortest day).

Sunrise time on January 4 is 7:26:58 am (the latest sunrise).

Sunset time on January 4 is 4:59:35 pm.

Day length on January 4 is 09:32:37.

http://sunrise-sunset.org/search?location=washington

Here are screenshots from December 2015 and January 2016:

(Saturday, 5 December 2015)

## Thursday, 26 March 2015

### Aliens director’s cut trivia

The
theatrical version of Aliens was great on its own, but the director’s cut of
Aliens is waaay better. I was blown away when I saw what great scenes were
removed in the original release, just to make the film shorter. They removed 17
(SEVENTEEN) minutes of the film!!! And all of the removed scenes were perfectly
fitting to the story. Some of them are actually very important, like a scene
when Ellen Ripley finds out that her daughter is dead or a scene showing how (and
why) colonists found alien eggs. Those scenes make the introduction part of the
film longer, but better considering the rising tension. Some of the other removed
scenes are very fun, like Hudson’s speech or several scenes with automatic sentry
guns.

All the
actors were great in this film, especially Sigourney Weaver as Ellen Ripley, Michael
Biehn as Corporal Dwayne Hicks, Bill Paxton as Private William Hudson and Lance
Henriksen as Bishop. Newt (the little girl) was played by Carrie Henn. James
Cameron chose her, because she had no casting experience and she didn’t smile
after saying her line, unlike other girls who were auditioned for the role.
Aliens is the only film she has played in.

Do you know
that, before the filming started, actors who played Marines together went
through a military training (for two weeks), so they could play a
believable well-working unit? Do you know that a picture of Ellen Ripley’s
daughter (seen in the director’s cut) is actually a picture of Sigourney Weaver’s
mother? Do you know that Newt’s brother (seen in the director’s cut) is
actually Carrie Henn’s real brother? Do you know that one of the dropships was
named “Smart Ass” and it had a slogan: “We aim by PFM” – a shortcut form
“Pure Fucking Magic”?

There are
tons of fun trivia about Aliens, especially about its production. This film was
made in 1985-1986 in the era before digital special effects. Almost everything
seen in Aliens was filmed in a real world environment and it still looks great
today. James Cameron is praised for Titanic and Avatar, but to me his biggest
achievement as a director (and as a screenwriter as well) is the film Aliens.

There is a
great site about Aliens http://film.org.pl/fx/aliensmenu.html

where you can find almost everything about Aliens with EXAMPLES, like pictures
showing scenes which were removed in the theatrical version or pictures showing
scenes where a particular special effect was used. However, there are two
problems – this site is not in English and some of its sub-sites are show with
errors and without pictures. Fortunately a Google translation can fix those problems
and everything can be seen properly. The translation itself is not perfect, but
it is understandable in most cases. Of course you can learn all about Aliens
somewhere else, but without all those pictures.

Below are
links to Google translations of this site and all its sub-sites. They display
fine on my computer. Otherwise try pressing “stop loading” at the right moment.

Please notice
that in Polish the word “obcy” is both a singular form (“alien”) and a plural
form (“aliens”). To distinguish the first and the second film in the series in Poland the film Aliens was titled “Alien(s) – The Decisive Battle” (“Obcy – Decydujące
Starcie”). It turned out later that it was not decisive at all. :) Apparently the Google translator “knows”
about the Polish title because after translation it sometimes appear as “Aliens – Aliens”, which makes no
sense otherwise.

Production

http://translate.google.pl/translate?sl=pl&tl=en&js=n&prev=_t&hl=pl&ie=UTF-8&u=http%3A%2F%2Ffilm.org.pl%2Ffx%2Faliensr.html
Special
effects

http://translate.google.pl/translate?sl=pl&tl=en&js=n&prev=_t&hl=pl&ie=UTF-8&u=http%3A%2F%2Ffilm.org.pl%2Ffx%2Faliense.html
Director’s
cut

http://translate.google.pl/translate?sl=pl&tl=en&js=n&prev=_t&hl=pl&ie=UTF-8&u=http%3A%2F%2Ffilm.org.pl%2Fdir_cut%2Faliens.html
Introduction
and menu (logically this should be the first link)

http://translate.google.pl/translate?sl=pl&tl=en&js=n&prev=_t&hl=pl&ie=UTF-8&u=http%3A%2F%2Ffilm.org.pl%2Ffx%2Faliensmenu.html
Removed
scenes (scenes which didn’t make it even to the director’s cut)

http://translate.google.pl/translate?sl=pl&tl=en&js=n&prev=_t&hl=pl&ie=UTF-8&u=http%3A%2F%2Ffilm.org.pl%2Ffx%2Falienss.html
Evolution
of screenplay (without any pictures)

http://translate.google.pl/translate?sl=pl&tl=en&js=n&prev=_t&hl=pl&ie=UTF-8&u=http%3A%2F%2Ffilm.org.pl%2Ffx%2Faliensscr.html
Payroll

http://translate.google.pl/translate?sl=pl&tl=en&js=n&prev=_t&hl=pl&ie=UTF-8&u=http%3A%2F%2Ffilm.org.pl%2Ffx%2Faliensl.html
Here’s another site from the same main site. There’s a unique picture at the end.

(Monday, 22 July 2013)

## Wednesday, 25 March 2015

### The Big Bang Theory

The Big Bang Theory is a great sitcom series featuring a character, named Sheldon Cooper, who has Asperger Syndrome. It’s hilarious to see how he analyses everything logically, with hardly any social skills. The below fragment is also a great example of how important his habits/routines are to him.

(Saturday, 13 July 2013)

(Saturday, 13 July 2013)

## Tuesday, 24 March 2015

### My Family – my favourite sitcom ever

My Family is my favourite sitcom ever. It’s done in a very intelligent way that suits my taste perfectly.

I rarely boast about something, but here I come: I have never spent so much money for my own entertainment before – I have bought a box with 22 My Family DVDs – complete series 1-11 plus 9 Christmas specials!

The synopsis from the cover of the first DVD is quite good:

“Ben, a dentist, and Susan, the worst cook in the world, are certainly loving, caring parents, they just have a problem showing it. Ben seems to be confused as to how much time and money his kids demand from him. Susan has to juggle motherhood, a career and a husband and does not have enough time to manage everything including improving her cooking skills. Nick is always working on his next hair-brained scheme to keep him amused. Janey, like any normal teenage daughter feels that her parents are seriously embarrassing whilst Michael keeps his head in his books to get away from the noise.”

The box has one HUGE advantage – it features English subtitles! They are labelled “English for the Hard of Hearing”, but they are perfect for a person like me – English is not my native language and I have trouble understand everything by ear. While watching the DVDs I can always read the subtitles and understand everything anyway. Perfect! From what I hear by ear I must say that the subtitles are done very well – there is hardly anything omitted.

This great sitcom is rather new (was broadcasted by BBC between 2000 and 2011), but there are no good examples of it on YouTube. The ones that are on YouTube are very short and seem strange because they are taken out of context. Moreover there are NO examples with English subtitles. This is why I have created an example by myself. I did it using my mobile phone, so the quality is bad, but at least you can see how lively My Family episodes are. Enjoy!

(Sunday, 13 July 2014)

I rarely boast about something, but here I come: I have never spent so much money for my own entertainment before – I have bought a box with 22 My Family DVDs – complete series 1-11 plus 9 Christmas specials!

The synopsis from the cover of the first DVD is quite good:

“Ben, a dentist, and Susan, the worst cook in the world, are certainly loving, caring parents, they just have a problem showing it. Ben seems to be confused as to how much time and money his kids demand from him. Susan has to juggle motherhood, a career and a husband and does not have enough time to manage everything including improving her cooking skills. Nick is always working on his next hair-brained scheme to keep him amused. Janey, like any normal teenage daughter feels that her parents are seriously embarrassing whilst Michael keeps his head in his books to get away from the noise.”

The box has one HUGE advantage – it features English subtitles! They are labelled “English for the Hard of Hearing”, but they are perfect for a person like me – English is not my native language and I have trouble understand everything by ear. While watching the DVDs I can always read the subtitles and understand everything anyway. Perfect! From what I hear by ear I must say that the subtitles are done very well – there is hardly anything omitted.

This great sitcom is rather new (was broadcasted by BBC between 2000 and 2011), but there are no good examples of it on YouTube. The ones that are on YouTube are very short and seem strange because they are taken out of context. Moreover there are NO examples with English subtitles. This is why I have created an example by myself. I did it using my mobile phone, so the quality is bad, but at least you can see how lively My Family episodes are. Enjoy!

(Sunday, 13 July 2014)

## Monday, 23 March 2015

### Aliens' 30th anniversary

(Originally posted on Wednesday, 14 September 2016)

I wrote about this awesome movie here:

Aliens director’s cut trivia

This year the movie Aliens was celebrating its 30th anniversary. There are some cool articles about it:

http://screenrant.com/aliens-30-year-anniversary/

http://www.denofgeek.com/us/movies/aliens/257290/aliens-30th-anniversary-15-things-we-learned

http://www.latimes.com/entertainment/herocomplex/la-et-hc-comic-con-aliens-30th-panel-20160723-snap-story.html

http://www.usatoday.com/story/life/movies/2016/07/17/where-stars-aliens-30-years-later/86817532/

http://www.forbes.com/sites/simonthompson/2016/08/01/michael-biehn-talks-aliens-30th-anniversary-his-production-company-and-his-alien-future/#4412fb094106

There were many great actors in Aliens, but my favourite one has always been Michael Biehn. He was fantastic in Aliens! And in Terminator too! Here is a HUGE article about this actor:

https://lebeauleblog.com/2014/03/08/what-the-hell-happened-to-michael-biehn/

Some time ago I learned that he had had an alcohol problem (much later in his career than Aliens) and I was very surprised. Well, anybody can get addicted to something, but Michael Biehn? One of my favourite actors ever? Yeah, alcohol is easy to obtain and perfectly legal, so why not? I myself drink hardly any alcohol, but some of my colleagues at work are SURE that one beer a day is not a problem.

Anyway, I found a very funny anecdote about Biehn, but I doubt if it is true. It's more like a joke. I found it here:

http://www.avpgalaxy.net/forum/index.php?topic=25598.15

Quote from the user “maledoro”:

I wrote about this awesome movie here:

Aliens director’s cut trivia

This year the movie Aliens was celebrating its 30th anniversary. There are some cool articles about it:

http://screenrant.com/aliens-30-year-anniversary/

http://www.denofgeek.com/us/movies/aliens/257290/aliens-30th-anniversary-15-things-we-learned

http://www.latimes.com/entertainment/herocomplex/la-et-hc-comic-con-aliens-30th-panel-20160723-snap-story.html

http://www.usatoday.com/story/life/movies/2016/07/17/where-stars-aliens-30-years-later/86817532/

http://www.forbes.com/sites/simonthompson/2016/08/01/michael-biehn-talks-aliens-30th-anniversary-his-production-company-and-his-alien-future/#4412fb094106

There were many great actors in Aliens, but my favourite one has always been Michael Biehn. He was fantastic in Aliens! And in Terminator too! Here is a HUGE article about this actor:

https://lebeauleblog.com/2014/03/08/what-the-hell-happened-to-michael-biehn/

Some time ago I learned that he had had an alcohol problem (much later in his career than Aliens) and I was very surprised. Well, anybody can get addicted to something, but Michael Biehn? One of my favourite actors ever? Yeah, alcohol is easy to obtain and perfectly legal, so why not? I myself drink hardly any alcohol, but some of my colleagues at work are SURE that one beer a day is not a problem.

Anyway, I found a very funny anecdote about Biehn, but I doubt if it is true. It's more like a joke. I found it here:

http://www.avpgalaxy.net/forum/index.php?topic=25598.15

Quote from the user “maledoro”:

*I have a Michael Biehn story to share with you all. A few years back, my (then) girlfriend and I were walking through NYC and saw this unshaven, but well-dressed guy standing on a corner with a 40 in his hand yelling, "I was Hicks! I was Hicks!"*

My girlfriend said, "He looks like a hick...", and told her, "Wait just a sec. I think I know this guy." We walked closer, and I asked, "Sir? Are you Michael Biehn?" The guy's crazed look softened a bit and he said, "Yes, I am!"

My girlfriend asked, "You? A terrible drunk like you is Michael Biehn?" The guy looked at her and said, "Whattya mean 'terrible'? I'm one of the best drunks in this city!"

My girlfriend said, "He looks like a hick...", and told her, "Wait just a sec. I think I know this guy." We walked closer, and I asked, "Sir? Are you Michael Biehn?" The guy's crazed look softened a bit and he said, "Yes, I am!"

My girlfriend asked, "You? A terrible drunk like you is Michael Biehn?" The guy looked at her and said, "Whattya mean 'terrible'? I'm one of the best drunks in this city!"

## Sunday, 22 March 2015

### Subordinate, in the presence of the superior

(Originally posted on Friday, 16 September 2016)

Subordinate, in the presence of the superior, should have the wretched and dumb look, so that his understanding of a matter didn't embarrass the superior.

(Reputedly it's a quote from an edict issued in 1708 by Peter I the Great.)

Subordinate, in the presence of the superior, should have the wretched and dumb look, so that his understanding of a matter didn't embarrass the superior.

(Reputedly it's a quote from an edict issued in 1708 by Peter I the Great.)

## Saturday, 21 March 2015

### Ancient sites

Google
Earth has an in-built feature of rendering 3D images of some buildings or
structures, for example Egyptian Sphinx and Pyramids.

I have found such 3D structures at Machu Picchu an ancient site that I always wanted to visit.

What’s really interesting is the fact that I found there TWO separate structures. One is the well-known Machu Picchu, but the other is a structure I have never heard of. In fact this other site is even more amazing than Machu Picchu, because it is built at the very summit of a nearby mountain. Take a look.

This other structure is called Huayna Picchu or Wayna Picchu.

I found a picture of it at the site

http://www.inkas.com/tours/cuzco_machu_picchu/santillan_photos.html

Here it is (click to enlarge):

As a side note: At the same site there are pictures not only from Machu Picchu, but also from other places. There are some pictures from Cuzco showing something that is called “Incan stonework”.

It looks like this (click to enlarge):

There are some theories that claim these structures were built much earlier than Incan civilization. There are similar theories considering the age of Puma Punku, Baalbek ruins, the Sphinx and the Pyramids. If you are interested in our World's biggest archeological mysteries then check this site:

http://www.atlantisquest.com/Archeology.html

(Sunday, 20 May 2012)

## Friday, 20 March 2015

## Thursday, 19 March 2015

### 10 meter air rifle (an Olympic sport)

(Originally posted on Tuesday, 25 October 2016)

Do you remember the year 1992? Well, some of you were not even born then, yet. But I remember it – I was already a teenager then. That year is remembered mostly for the Dream Team (it was the first time that NBA players were allowed to participate in Summer Olympics), but I would like to mention one of the medals won by the Polish Olympic team. It was the first Olympic medal ever won by a Polish woman in shooting sports.

The medal was a bronze medal won by Małgorzata Książkiewicz in the discipline “50 metre rifle three positions”. Some time after that my father took me to a shooting range and for the first time in my life I shot with an air rifle (over a distance of 10 meters). It was awesome!

By the way: I shot with an air rifle because it doesn't use real bullets (unlike a 50 meter rifle) but small pellets that look like this:

Unfortunately even the “10 meter air rifle” sport was rather rare and costly then, so it didn't become my hobby. Interestingly during the next Summer Olympics (in 1996) another Polish woman (Renata Mauer) won a gold medal in this particular discipline:

In 2000 Renata Mauer (then already as Renata Mauer-Różańska) won another Olympic gold medal in shooting sports – this time in the discipline “50 metre rifle three positions”:

During the 2012 Summer Olympics another Polish woman (Sylwia Bogacka) won another medal in shooting sports (a silver medal in the discipline “10 meter air rifle”). The first picture shows her in a dress that was used by the women from the Polish Olympic team during the opening ceremony. Cool design. The third picture is my favourite one. The Chinese is happy because she won the gold medal and Sylwia Bogacka is happy because she had a fantastic last shot that helped her climb back to the second place.

There are either no Youtube videos from that events, or they can't be embedded to other sites. The only one I found that can be embedded is the transmission of the 2012 Olympic final by the Polish TV. It's not in English, but the visuals are pretty self explanatory.

Now, to the point of my post. (That was a long introduction, wasn't it?) Recently, by sheer accident I learned that there was an affordable shooting range in my home city. Remembering the fun I had when I was shooting an air rifle as a teenager, I decided to give it a try.

I took my daughter with me, but she was not able to handle an air rifle, so the guy running the shooting range gave her an air pistol and told her to study it on the counter. She did manage to hit the black area of the target a few times.

I did pretty well, considering that it was the first time I have been shooting with an air rifle in 20 years (more or less).

The guy running the shooting range allowed me to try different models of air rifles and the last one was the one that I “felt” very well. At one moment, right after a change of the target, I hit 5 times in a row very close to the centre of the target:

Do you remember the year 1992? Well, some of you were not even born then, yet. But I remember it – I was already a teenager then. That year is remembered mostly for the Dream Team (it was the first time that NBA players were allowed to participate in Summer Olympics), but I would like to mention one of the medals won by the Polish Olympic team. It was the first Olympic medal ever won by a Polish woman in shooting sports.

The medal was a bronze medal won by Małgorzata Książkiewicz in the discipline “50 metre rifle three positions”. Some time after that my father took me to a shooting range and for the first time in my life I shot with an air rifle (over a distance of 10 meters). It was awesome!

By the way: I shot with an air rifle because it doesn't use real bullets (unlike a 50 meter rifle) but small pellets that look like this:

Unfortunately even the “10 meter air rifle” sport was rather rare and costly then, so it didn't become my hobby. Interestingly during the next Summer Olympics (in 1996) another Polish woman (Renata Mauer) won a gold medal in this particular discipline:

In 2000 Renata Mauer (then already as Renata Mauer-Różańska) won another Olympic gold medal in shooting sports – this time in the discipline “50 metre rifle three positions”:

During the 2012 Summer Olympics another Polish woman (Sylwia Bogacka) won another medal in shooting sports (a silver medal in the discipline “10 meter air rifle”). The first picture shows her in a dress that was used by the women from the Polish Olympic team during the opening ceremony. Cool design. The third picture is my favourite one. The Chinese is happy because she won the gold medal and Sylwia Bogacka is happy because she had a fantastic last shot that helped her climb back to the second place.

There are either no Youtube videos from that events, or they can't be embedded to other sites. The only one I found that can be embedded is the transmission of the 2012 Olympic final by the Polish TV. It's not in English, but the visuals are pretty self explanatory.

Now, to the point of my post. (That was a long introduction, wasn't it?) Recently, by sheer accident I learned that there was an affordable shooting range in my home city. Remembering the fun I had when I was shooting an air rifle as a teenager, I decided to give it a try.

I took my daughter with me, but she was not able to handle an air rifle, so the guy running the shooting range gave her an air pistol and told her to study it on the counter. She did manage to hit the black area of the target a few times.

I did pretty well, considering that it was the first time I have been shooting with an air rifle in 20 years (more or less).

The guy running the shooting range allowed me to try different models of air rifles and the last one was the one that I “felt” very well. At one moment, right after a change of the target, I hit 5 times in a row very close to the centre of the target:

## Wednesday, 18 March 2015

### The Forever War (by Joe Haldeman) and Albert Einstein’s special theory of relativity

(Originally posted on Friday, 11 November 2016; expanded on 14 November 2016)

I am currently re-reading (once again) an awesome novel by Joe Haldeman titled “The Forever War”. I am going to review it in detail, but here I would like to mention that time dilation plays an important role in the plot of this novel. It made me ponder on the main aspects of Albert Einstein’s special theory of relativity again. Some of the things I found on the net were truly jaw-dropping and I decided to analyse this topic in detail.

This time I realised that to fully understand Albert Einstein’s special theory of relativity you have to simultaneously analyse three different things that change when travelling at speeds close to the speed of light: time, length and mass. What’s worse these three things can be seen from two different perspectives and it seems that some internet sites switch the perspectives back and forth, which is utterly confusing.

First, I have to comment on the “change of mass”. It's a concept that is a kind of simplification, but mass is something we understand by heart and this is why I use it here. The point of special theory of relativity is that anything with non-zero mass can NEVER be accelerated to the speed of light – the more the speed of a spaceship approaches the speed of light the harder it is to keep the spaceship accelerating. On the Earth (with speeds much lower that the speed of light) the acceleration is harder when a particular thing (a car for example) is heavier and this is why we can imagine that when the speed of the spaceship approaches the speed of light the spaceship is much “heavier” than normal and we need a much more powerful engine to keep it accelerating in the same way. Finally, with the speed VERY close to the speed of light, the “mass” of the spaceship would go towards infinity and we would need and infinite engine power to keep it accelerating at all. We can also look at this problem from another point of view. When we have a particular space engine and we use it at its maximum power then the more the speed of the spaceship approaches the speed of light the slower the spaceship will be accelerating (the force coming from the engine stays the same, but the mass of the spaceship gets bigger and bigger). This is the only thing that is messed up in The Forever War, but ONLY at ONE moment.

Example I (“twins”)

The most famous example of how the special theory of relativity works is the example about twins – one twin stays on the Earth and the other one travels on a spaceship and comes back after some time. The twin who was on the Earth will be older then the twin who was on the spaceship. For the sake of the example below (for the sake of easy calculations) I assume that the spaceship accelerates and decelerates “almost instantly”, which in reality is not possible. I skip the acceleration/deceleration process because otherwise I would have to use Einstein’s general theory of relativity, which would be much more complicated.

Let’s assume that the spaceship (with the moving twin) travels to a star that is exactly 1 light-year away and then comes back, so the total distance is 2 light-years, and the speed of the spaceship is 0.9 times the speed of light (0.9c). The formula for relativistic factor (Lorentz factor), which calculates the changes of time, length and mass, is this:

The relativistic factor for the assumed speed of the spaceship is 2.294. Below there are two different versions of calculations that show what exactly happens from each perspective. Lengths and masses “are different” while moving, but they “come back” to normal at the end of the journey. The time on the other hand does NOT ”come back” to normal because the time had already passed.

Example I (“twins”) – version 1 of the calculations.

Observer: the stationary twin (the twin on the Earth).

Reference point (for the speed of the moving twin): the Earth.

I.1.a. Distance of the journey (length seen in the same way): 2 light years (unchanged distance/length).

I.1.b. Length of the spaceship (length seen in a different way): normal length of the spaceship / 2.294 = 0.4359 times the normal length of spaceship (irrelevant value).

I.1.c. Time of the journey: 2 light-years / 0.9c = 2.2222 years (time on the Earth).

1d. Mass of the spaceship: normal mass of the spaceship? (there’s no way to measure the mass of the spaceship from the Earth, but it's irrelevant – anyone outside the spaceship doesn't really care about its mass).

Example I (“twins”) – version 2 of the calculations.

Observer: the moving twin (the twin on the spaceship).

Reference point (for the speed of the moving twin): the Earth.

I.2.a. Distance of the journey (length seen in a different way): 2 light years / 2.294 = 0.8718 light-years.

I.2.b. Length of the spaceship (length seen in the same way): normal length of the spaceship (unchanged length).

I.2.c. Time of the journey: 0.8718 light-years / 0.9c = 0.9687 years (time on the spaceship).

I.2.d. Mass of the spaceship: normal mass of the spaceship * 2.294 = 2.294 times the normal mass of the spaceship (more than twice as “heavy”, but still able to accelerate further in a decent way).

Example I (“twins”) – time comparison.

I.3. One day/month/year on the spaceship was equal to 2.294 days/months/years on the Earth (2.2222 years on the Earth / 0.9687 years on the spaceship).

Example I (“twins”) – interesting things to notice and explain.

4a. The LENGTHS changed for BOTH observers by the same factor, but different things changed (temporarily) for different observers. To the stationary twin it was the length of the spaceship that changed (everything else was stationary to him) and to the twin on the spaceship it was everything other than spaceship that changed (only the spaceship was stationary to him). The reference point (the real stationary point in the example) was the Earth because it was the Earth that was NOT accelerating or decelerating (except for its journey around the sun, but the solar system as a whole can be considered as a stationary point, more or less).

4b. It took 0.9687 years on the spaceship to travel a distance that the light itself travels for 2 years. How is that possible?

The problem is that both these times are given by different observers AND for different reference points. The time of 2 years is given by the observer who is watching the LIGHT from the “outside” and the time of 0.9687 years on the spaceship is given by the observer who is watching the SPACESHIP from the “inside”. As we can see in the above example for the “outside” observer the time of the journey of the spaceship is 2.2222 years on Earth, which is MORE than 2 years (the time of the journey of the light), so for the single “outside” observer everything is OK. The funny question is what time would be given from the perspective of the light itself. The answer is jaw-dropping: ZERO!!! For example if a spaceship would reach 0.99999999999999 times the speed of light (there are 14 “9”) then the relativistic factor would be 7073895.381! It means that one day/month/year on the spaceship would be equal to 7073895.381 days/months/years on the Earth! Of course it will never be possible to reach such a high speed because it would also mean that the mass of the spaceship would be 7073895.381 times the normal mass of the spaceship – there would be no way to generate enough force to accelerate such a “heavy” monster.

4c. What was the ONLY problem with Forever War?

This one fragment is dubious:

The way it is written it is clear that a 3 month journey from the spaceship perspective would mean 150,000 Earth-years. The AVERAGE relativistic factor would have to be 600,000 (150,000 years on the Earth / 0.25 years on the spaceship), but it would mean that the mass of the spaceship would be 600,000 times its normal mass. No way I could imagine an engine technology that would succeed to speed up such a “heavy” spaceship. Thankfully in other parts of the book there were no such horrendously high relativistic factors.

By the way: the relativistic factor of 600,000 is “achieved” by the speed of 0.9999999999986111c (on one of the sites given below you can find an online calculator that allows you, among other things, to do such reverse calculations in a very easy way).

4d. The twins paradox is explained by a different HISTORY of acceleration/deceleration.

The twins paradox is an example of a wrong application of the special theory of relativity. Somebody argued that from the point of view of the spaceship it was the Earth that was moving so BOTH twins should age in the same way. Some other people thought that the twins paradox is explained by the sheer acceleration/deceleration PROCESS, but it's not the case either. It's the different HISTORY of accelerations and decelerations that matters. The spaceship HAD to decelerate and accelerate to change the direction (to be able to come back to the starting point) and the Earth did not accelerate at all (except for its journey around the sun, but the solar system can be considered as an inertial system as a whole). Please notice that the accelerations and decelerations for the sake of the example were “almost instant”, but they were enough to determine which twin “was moving”. The scope of the time dilatation depends heavily on the speed of the spaceship and the length of the journey, NOT on the duration of the accelerations or decelerations alone. Below there is a fantastic visualization of the twin paradox (the Minkowski diagram of the twin paradox). The dots may be interpreted as the passing years (6 years for the travelling twin and definitely more years for the stationary twin – there are some dots missing for the stationary twin).

On a side note: I found also a fantastic visualization of an accelerating observer in special relativity:

The precise description of this “spacetime diagram” can be found here:

https://en.wikipedia.org/wiki/Minkowski_diagram

Here are some cool sites with different online calculators:

http://www.1728.org/reltivty.htm

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/ltrans.html

http://nathangeffen.webfactional.com/spacetravel/spacetravel.php

UPDATE: Example II (“three observers”)

I analysed another example of how the special theory of relativity works. One of the crucial questions is: “What would happen if 2 spaceships (A and B) were going in opposite directions at very high speeds?” I added a special twist and placed the stationery observer (the observer on the Earth) between the spaceships, which makes my example much more interesting. To make the example easier (to makes some of the calculations similar to the previous example) I assumed that each spaceship is 2 light-years away from the Earth (so they are 4 light-years away from each other) and that the speed of each spaceship is 0.9c relative to the Earth:

Example II (“three observers”) – version 1 of the calculations.

Observer: the stationary observer (the observer on the Earth).

Reference point (for ALL the speeds involved): the Earth.

II.1.a. Distance of the journey of each of the spaceships: 2 light years.

II.1.b. Length of each of the spaceship: … (irrelevant value).

II.1.c. Time of the journey: 2 light-years / 0.9c = 2.2222 years (time on the Earth).

II.1.d. Mass of the spaceship: normal mass of the spaceship? (there’s no way to measure the mass of the spaceship from the Earth, but it's irrelevant – anyone outside the spaceship doesn't really care about its mass).

Example II (“three observers”) – version 2 of the calculations (the same calculations are true for each of the spaceships).

Observer: the observer on the spaceship A (one of the moving observers).

Reference point (for ALL the speeds involved): the Earth.

II.2.0.a. Speed relative to the spaceship B: 0.994475c (this speed can actually be measured by the observer on the spaceship A, but it is NOT relative to the Earth).

The moving observer sees not only the Earth, but he also sees the other moving spaceship almost exactly in the same line as he sees the Earth (not exactly in the same line, so it is not obscured by the Earth). According to the special theory of relativity the formula for the speed addition is this:

Please notice that if the speed “u” were 0 then the sum of the speeds (“s”) would be equal to the speed “v”. In our example v=0.9c and u=0.9c, so s=0.994475c. It means that the moving observer would measure this speed relative to the other spaceship. In other words: the moving observer sees the Earth “approaching” at the speed of 0.9c and next to it he sees the other spaceship “approaching” at the speed of 0.994475c.

II.2.0.b. Speed of the other spaceship relative to the Earth: 0.994475c – 0.9c = 0.094475c (the observer on the spaceship sees this speed this way).

II.2.0.c. CALCULATED (real) speed of the other spaceship relative to the Earth: 0.9c.

If the moving observer knows the special theory of relativity he can use the above formula for the speed addition and calculate the third speed “in reverse”. It means that from the formula he would know “v” (his speed relative to the Earth) and “s” (his speed relative to the other spaceship), so he would be able to calculate “u” (the real speed of the other spaceship relative to the Earth) as being equal to 0.9c. He can't observe it directly, but he can calculate it.

II.2.0.d. Relativistic factor for the speed of 0.9c is 2.294 (we know that from the previous example).

II.2.0.e. Relativistic factor for the speed of 0.994475c is 9.526 (you can calculate it using the formula from the previous example).

II.2.a.1. Distance of the journey to the Earth: 2 light years / 2.294 = 0.8718 light-years (we know that distance from the previous example – see the point I.2.a.).

II.2.a.2.a. Distance of the journey to the other spaceship NOT relative to the Earth: 4 light-years / 9.526 = 0.4199 light-years (distance NOT relative to the Earth but to the other spaceship).

II.2.a.2.b. Distance of the journey to the other spaceship relative to the Earth: 0.4199 light-years * 2.294 = 0.9633 light-years (distance relative to the Earth).

II.2.a.3 Distance between the other spaceship and the Earth: 0.9633 light-years – 0.8718 light-years = 0.0915 light-years (distance relative to the Earth).

II.2.b. Length of each of the spaceship: … (irrelevant value).

II.2.c.1. Time of the journey to the Earth: 0.8718 light-years / 0.9c = 0.9687 years (time on the spaceship – we know that time from the previous example – see the point I.2.c.).

II.2.c.2.a. Time of the journey to the other spaceship NOT relative to the Earth: 0.4199 light-years / 0.994475c = 0.4222 years (time on the spaceship NOT relative to the Earth but to the other spaceship).

II.2.c.2.b. Time of the journey to the other spaceship relative to the Earth: 0.4222 years * 2.294 = 0.9685 years (time on the spaceship relative to the Earth).

II.2.c.3. Time of the journey of the other spaceship to the Earth: 0.0915 light-years / 0.094475c = 0.9685 (time on the spaceship relative to the Earth).

All the times of the journeys (II.2.c.1., II.2.c.2.b. and II.2.c.3.) are the same! The values 0.9687 and 0.9685 are not exactly equal because I rounded all the numbers to 3 or 4 decimal places and several steps in calculations caused this minute difference (0.0002). Anyway, it means that each journey (the spaceship A to the Earth, the spaceship A to the spaceship B and the spaceship B to the Earth) will last equally long, so all the observers will meet at the Earth at the same time – exactly as it was calculated by the stationary observer (the observer on the Earth).

II.2.d.1. Mass of the spaceship relative to the Earth: normal mass of the spaceship * 2.294 = 2.294 times the normal mass of the spaceship (more than twice as “heavy”, but still able to accelerate further in a decent way).

II.2.d.2. Mass of the spaceship relative to the other spaceship: normal mass of the spaceship * 9.526 = 9.526 times the normal mass of the spaceship (almost 10 times as “heavy” – significantly more difficult to accelerate).

Please notice that the change of mass depends on the observer AND on the reference point. The mass of the spaceship AT THE SAME TIME/PLACE seems lower (when looking at the Earth) or bigger (when looking at the other spaceship). The mass is relative too! This example “proves” that it's not really a physical change in mass, but it’s more like “it seems that the spaceships mass is higher because we can't accelerate it as well as we did at lower speeds”. The higher the OBSERVED speed the bigger the “FEELING” that the mass of the spaceship is higher.

As you can see from the above calculations you have to be very careful to use the same observer AND the same reference point for ALL the final calculations! It is very easy to mess things up by joining calculations made for different observers OR with different reference points!

Example II (“three observers”) – time comparison.

II.3. One day/month/year on the spaceship was equal to 2.294 days/months/years on the Earth (2.2222 years on the Earth / 0.9687 years on the spaceship).

The calculations can be also made for a different reference point – for example we could assume that the spaceship B is stationary and both the other spaceship A and the Earth were moving (or instead of the Earth there could be just another spaceship). It would mean that the Earth is “running away” from the spaceship A (that the Earth is going in the same direction as the spaceship A). This time the speed of the spaceship A relative to the spaceship B (0.994475c) would be the speed “v” and the speed of the spaceship A relative to the Earth (0.9c) would be the speed “s” (the sum of speeds). The speed “u” (the speed of the Earth relative to the spaceship B) would be equal to -0.9c (the negative number means that the speed is not added, but subtracted from the speed 0.994475c).

Once again: this is exactly the same example, but with the REFERENCE POINT being the spaceship B (not the Earth). Let's calculate things from the POINT OF VIEW of the spaceship A.

Example II (“three observers”) – version 3 of the calculations.

Observer: the observer on the spaceship A.

Reference point (for ALL the speeds involved): the spaceship B.

II.3.0.a. Speed relative to the Earth: 0.9c (this speed can actually be measured by the observer on the spaceship A, but it is NOT relative to the spaceship B).

II.3.0.b. Speed of the Earth relative to the spaceship B: 0.994475c – 0.9c = 0.094475c (the observer on the spaceship A sees this speed this way).

II.3.0.c. CALCULATED (real) speed of the Earth relative to the spaceship B: -0.9c (the “-“ sign determines only the direction of the movement – the same direction as the spaceship A). The observer on the spaceship A can't observe it directly, but he can calculate it.

II.3.0.d. Relativistic factor for the speed of -0.9c is 2.294 (we know that from the example I – the direction of the movement is not important).

II.3.0.e. Relativistic factor for the speed of 0.994475c is 9.526 (we know that from the example II).

II.3.a.1. Distance of the journey to the spaceship B: 4 light-years / 9.526 = 0.4199 light-years (relative to the spaceship B).

II.3.a.2.a. Distance of the journey to the Earth NOT relative to the spaceship B: 2 light-years / 2.294 = 0.8718 light-years (distance NOT relative to the spaceship B but to the Earth).

II.3.a.2.b. Distance of the journey to the Earth relative to the spaceship B: 0.8718 light-years / 2.294 = 0.3800 light-years (distance relative to the spaceship B).

II.3.a.3 Distance between the Earth and the spaceship B: light-years 0.4199 – 0.3800 light-years = 0.0399 light-years (distance relative to the spaceship B).

II.3.b. Length of each of the spaceship: … (irrelevant value).

II.3.c.1. Time of the journey to the spaceship B: 0.4199 light-years / 0.994475c = 0.4222 years (time on the spaceship A).

II.3.c.2.a. Time of the journey to the Earth NOT relative to the spaceship B: 0.8718 light-years / 0.9c = 0.9687 years (time on the spaceship A NOT relative to the spaceship B but to the Earth).

II.3.c.2.b. Time of the journey to the Earth relative to the spaceship B: 0.9687 years / 2.294 = 0.4223 years (time on the spaceship A relative to the spaceship B).

II.3.c.3. Time of the journey of the Earth to the spaceship B: 0.0399 light-years / 0.094475c = 0.4223 (time on Earth relative to the spaceship B).

All the times of the journeys (II.3.c.1., II.3.c.2.b. and II.3.c.3.) are the same! The values 0.4222 and 0.4223 are not exactly equal because I rounded all the numbers to 3 or 4 decimal places and several steps in calculations caused this minute difference (0.0001). Anyway, it means that each journey (the spaceship A to the Earth, the spaceship A to the spaceship B and the Earth to the spaceship B) will last equally long, so all the observers will be at the Earth at the same time – exactly as it was calculated with a different reference point (the Earth in the previous 2 variations of the calculations).

II.3.d.1. Mass of the spaceship relative to the Earth: normal mass of the spaceship * 2.294 = 2.294 times the normal mass of the spaceship (more than twice as “heavy”, but still able to accelerate further in a decent way).

II.3.d.2. Mass of the spaceship relative to the other spaceship: normal mass of the spaceship * 9.526 = 9.526 times the normal mass of the spaceship (almost 10 times as “heavy” – significantly more difficult to accelerate).

Example II (“three observers”) – time comparison #2 (different values for different reference points).

Before we can compare anything we have to calculate time of journey from the point of view of the spaceship B:

II.3.0. Time of the journey of the spaceship A: 4 light-years / 0.994475c = 4.0222 years (time on the spaceship B).

II.3. One day/month/year on the spaceship A was equal to 9.527 days/months/years on the spaceship B (4.0222 years on the spaceship B / 0.4222 years on the spaceship A).

We could do the calculations for the “moving Earth” because in the above example NEITHER observer accelerated, so ANY reference point was equally good. However, if we analysed a “triplets” example (all the observers are triplets – one stays on the Earth and the other 2 triplets depart the Earth in opposite directions, travel at the same speed the same distance and then come back to Earth also travelling at the same speed) then there could be only 1 correct reference point – the Earth. Only the Earth was NOT accelerating or decelerating – the other 2 triplets were accelerating and decelerating to change their direction (to be able to come back to the starting point). The Minkowski diagram of the triplets paradox would look like this:

I am currently re-reading (once again) an awesome novel by Joe Haldeman titled “The Forever War”. I am going to review it in detail, but here I would like to mention that time dilation plays an important role in the plot of this novel. It made me ponder on the main aspects of Albert Einstein’s special theory of relativity again. Some of the things I found on the net were truly jaw-dropping and I decided to analyse this topic in detail.

This time I realised that to fully understand Albert Einstein’s special theory of relativity you have to simultaneously analyse three different things that change when travelling at speeds close to the speed of light: time, length and mass. What’s worse these three things can be seen from two different perspectives and it seems that some internet sites switch the perspectives back and forth, which is utterly confusing.

First, I have to comment on the “change of mass”. It's a concept that is a kind of simplification, but mass is something we understand by heart and this is why I use it here. The point of special theory of relativity is that anything with non-zero mass can NEVER be accelerated to the speed of light – the more the speed of a spaceship approaches the speed of light the harder it is to keep the spaceship accelerating. On the Earth (with speeds much lower that the speed of light) the acceleration is harder when a particular thing (a car for example) is heavier and this is why we can imagine that when the speed of the spaceship approaches the speed of light the spaceship is much “heavier” than normal and we need a much more powerful engine to keep it accelerating in the same way. Finally, with the speed VERY close to the speed of light, the “mass” of the spaceship would go towards infinity and we would need and infinite engine power to keep it accelerating at all. We can also look at this problem from another point of view. When we have a particular space engine and we use it at its maximum power then the more the speed of the spaceship approaches the speed of light the slower the spaceship will be accelerating (the force coming from the engine stays the same, but the mass of the spaceship gets bigger and bigger). This is the only thing that is messed up in The Forever War, but ONLY at ONE moment.

Example I (“twins”)

The most famous example of how the special theory of relativity works is the example about twins – one twin stays on the Earth and the other one travels on a spaceship and comes back after some time. The twin who was on the Earth will be older then the twin who was on the spaceship. For the sake of the example below (for the sake of easy calculations) I assume that the spaceship accelerates and decelerates “almost instantly”, which in reality is not possible. I skip the acceleration/deceleration process because otherwise I would have to use Einstein’s general theory of relativity, which would be much more complicated.

Let’s assume that the spaceship (with the moving twin) travels to a star that is exactly 1 light-year away and then comes back, so the total distance is 2 light-years, and the speed of the spaceship is 0.9 times the speed of light (0.9c). The formula for relativistic factor (Lorentz factor), which calculates the changes of time, length and mass, is this:

The relativistic factor for the assumed speed of the spaceship is 2.294. Below there are two different versions of calculations that show what exactly happens from each perspective. Lengths and masses “are different” while moving, but they “come back” to normal at the end of the journey. The time on the other hand does NOT ”come back” to normal because the time had already passed.

Example I (“twins”) – version 1 of the calculations.

Observer: the stationary twin (the twin on the Earth).

Reference point (for the speed of the moving twin): the Earth.

I.1.a. Distance of the journey (length seen in the same way): 2 light years (unchanged distance/length).

I.1.b. Length of the spaceship (length seen in a different way): normal length of the spaceship / 2.294 = 0.4359 times the normal length of spaceship (irrelevant value).

I.1.c. Time of the journey: 2 light-years / 0.9c = 2.2222 years (time on the Earth).

1d. Mass of the spaceship: normal mass of the spaceship? (there’s no way to measure the mass of the spaceship from the Earth, but it's irrelevant – anyone outside the spaceship doesn't really care about its mass).

Example I (“twins”) – version 2 of the calculations.

Observer: the moving twin (the twin on the spaceship).

Reference point (for the speed of the moving twin): the Earth.

I.2.a. Distance of the journey (length seen in a different way): 2 light years / 2.294 = 0.8718 light-years.

I.2.b. Length of the spaceship (length seen in the same way): normal length of the spaceship (unchanged length).

I.2.c. Time of the journey: 0.8718 light-years / 0.9c = 0.9687 years (time on the spaceship).

I.2.d. Mass of the spaceship: normal mass of the spaceship * 2.294 = 2.294 times the normal mass of the spaceship (more than twice as “heavy”, but still able to accelerate further in a decent way).

Example I (“twins”) – time comparison.

I.3. One day/month/year on the spaceship was equal to 2.294 days/months/years on the Earth (2.2222 years on the Earth / 0.9687 years on the spaceship).

Example I (“twins”) – interesting things to notice and explain.

4a. The LENGTHS changed for BOTH observers by the same factor, but different things changed (temporarily) for different observers. To the stationary twin it was the length of the spaceship that changed (everything else was stationary to him) and to the twin on the spaceship it was everything other than spaceship that changed (only the spaceship was stationary to him). The reference point (the real stationary point in the example) was the Earth because it was the Earth that was NOT accelerating or decelerating (except for its journey around the sun, but the solar system as a whole can be considered as a stationary point, more or less).

4b. It took 0.9687 years on the spaceship to travel a distance that the light itself travels for 2 years. How is that possible?

The problem is that both these times are given by different observers AND for different reference points. The time of 2 years is given by the observer who is watching the LIGHT from the “outside” and the time of 0.9687 years on the spaceship is given by the observer who is watching the SPACESHIP from the “inside”. As we can see in the above example for the “outside” observer the time of the journey of the spaceship is 2.2222 years on Earth, which is MORE than 2 years (the time of the journey of the light), so for the single “outside” observer everything is OK. The funny question is what time would be given from the perspective of the light itself. The answer is jaw-dropping: ZERO!!! For example if a spaceship would reach 0.99999999999999 times the speed of light (there are 14 “9”) then the relativistic factor would be 7073895.381! It means that one day/month/year on the spaceship would be equal to 7073895.381 days/months/years on the Earth! Of course it will never be possible to reach such a high speed because it would also mean that the mass of the spaceship would be 7073895.381 times the normal mass of the spaceship – there would be no way to generate enough force to accelerate such a “heavy” monster.

4c. What was the ONLY problem with Forever War?

This one fragment is dubious:

*“It's not as though we'd be actually lost,” he said with a rather wicked expression. “We could zip up in the tanks, aim for Earth and blast away at full power. We'd get there in about three months, ship time.”*

“Sure,” I said. “But 150,000 years in the future.” At twenty-five gees, you get to nine-tenths the speed of light in less than a month. From then on, you're in the arms of Saint Albert.“Sure,” I said. “But 150,000 years in the future.” At twenty-five gees, you get to nine-tenths the speed of light in less than a month. From then on, you're in the arms of Saint Albert.

The way it is written it is clear that a 3 month journey from the spaceship perspective would mean 150,000 Earth-years. The AVERAGE relativistic factor would have to be 600,000 (150,000 years on the Earth / 0.25 years on the spaceship), but it would mean that the mass of the spaceship would be 600,000 times its normal mass. No way I could imagine an engine technology that would succeed to speed up such a “heavy” spaceship. Thankfully in other parts of the book there were no such horrendously high relativistic factors.

By the way: the relativistic factor of 600,000 is “achieved” by the speed of 0.9999999999986111c (on one of the sites given below you can find an online calculator that allows you, among other things, to do such reverse calculations in a very easy way).

4d. The twins paradox is explained by a different HISTORY of acceleration/deceleration.

The twins paradox is an example of a wrong application of the special theory of relativity. Somebody argued that from the point of view of the spaceship it was the Earth that was moving so BOTH twins should age in the same way. Some other people thought that the twins paradox is explained by the sheer acceleration/deceleration PROCESS, but it's not the case either. It's the different HISTORY of accelerations and decelerations that matters. The spaceship HAD to decelerate and accelerate to change the direction (to be able to come back to the starting point) and the Earth did not accelerate at all (except for its journey around the sun, but the solar system can be considered as an inertial system as a whole). Please notice that the accelerations and decelerations for the sake of the example were “almost instant”, but they were enough to determine which twin “was moving”. The scope of the time dilatation depends heavily on the speed of the spaceship and the length of the journey, NOT on the duration of the accelerations or decelerations alone. Below there is a fantastic visualization of the twin paradox (the Minkowski diagram of the twin paradox). The dots may be interpreted as the passing years (6 years for the travelling twin and definitely more years for the stationary twin – there are some dots missing for the stationary twin).

On a side note: I found also a fantastic visualization of an accelerating observer in special relativity:

The precise description of this “spacetime diagram” can be found here:

https://en.wikipedia.org/wiki/Minkowski_diagram

Here are some cool sites with different online calculators:

http://www.1728.org/reltivty.htm

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/ltrans.html

http://nathangeffen.webfactional.com/spacetravel/spacetravel.php

UPDATE: Example II (“three observers”)

I analysed another example of how the special theory of relativity works. One of the crucial questions is: “What would happen if 2 spaceships (A and B) were going in opposite directions at very high speeds?” I added a special twist and placed the stationery observer (the observer on the Earth) between the spaceships, which makes my example much more interesting. To make the example easier (to makes some of the calculations similar to the previous example) I assumed that each spaceship is 2 light-years away from the Earth (so they are 4 light-years away from each other) and that the speed of each spaceship is 0.9c relative to the Earth:

Example II (“three observers”) – version 1 of the calculations.

Observer: the stationary observer (the observer on the Earth).

Reference point (for ALL the speeds involved): the Earth.

II.1.a. Distance of the journey of each of the spaceships: 2 light years.

II.1.b. Length of each of the spaceship: … (irrelevant value).

II.1.c. Time of the journey: 2 light-years / 0.9c = 2.2222 years (time on the Earth).

II.1.d. Mass of the spaceship: normal mass of the spaceship? (there’s no way to measure the mass of the spaceship from the Earth, but it's irrelevant – anyone outside the spaceship doesn't really care about its mass).

Example II (“three observers”) – version 2 of the calculations (the same calculations are true for each of the spaceships).

Observer: the observer on the spaceship A (one of the moving observers).

Reference point (for ALL the speeds involved): the Earth.

II.2.0.a. Speed relative to the spaceship B: 0.994475c (this speed can actually be measured by the observer on the spaceship A, but it is NOT relative to the Earth).

The moving observer sees not only the Earth, but he also sees the other moving spaceship almost exactly in the same line as he sees the Earth (not exactly in the same line, so it is not obscured by the Earth). According to the special theory of relativity the formula for the speed addition is this:

Please notice that if the speed “u” were 0 then the sum of the speeds (“s”) would be equal to the speed “v”. In our example v=0.9c and u=0.9c, so s=0.994475c. It means that the moving observer would measure this speed relative to the other spaceship. In other words: the moving observer sees the Earth “approaching” at the speed of 0.9c and next to it he sees the other spaceship “approaching” at the speed of 0.994475c.

II.2.0.b. Speed of the other spaceship relative to the Earth: 0.994475c – 0.9c = 0.094475c (the observer on the spaceship sees this speed this way).

II.2.0.c. CALCULATED (real) speed of the other spaceship relative to the Earth: 0.9c.

If the moving observer knows the special theory of relativity he can use the above formula for the speed addition and calculate the third speed “in reverse”. It means that from the formula he would know “v” (his speed relative to the Earth) and “s” (his speed relative to the other spaceship), so he would be able to calculate “u” (the real speed of the other spaceship relative to the Earth) as being equal to 0.9c. He can't observe it directly, but he can calculate it.

II.2.0.d. Relativistic factor for the speed of 0.9c is 2.294 (we know that from the previous example).

II.2.0.e. Relativistic factor for the speed of 0.994475c is 9.526 (you can calculate it using the formula from the previous example).

II.2.a.1. Distance of the journey to the Earth: 2 light years / 2.294 = 0.8718 light-years (we know that distance from the previous example – see the point I.2.a.).

II.2.a.2.a. Distance of the journey to the other spaceship NOT relative to the Earth: 4 light-years / 9.526 = 0.4199 light-years (distance NOT relative to the Earth but to the other spaceship).

II.2.a.2.b. Distance of the journey to the other spaceship relative to the Earth: 0.4199 light-years * 2.294 = 0.9633 light-years (distance relative to the Earth).

II.2.a.3 Distance between the other spaceship and the Earth: 0.9633 light-years – 0.8718 light-years = 0.0915 light-years (distance relative to the Earth).

II.2.b. Length of each of the spaceship: … (irrelevant value).

II.2.c.1. Time of the journey to the Earth: 0.8718 light-years / 0.9c = 0.9687 years (time on the spaceship – we know that time from the previous example – see the point I.2.c.).

II.2.c.2.a. Time of the journey to the other spaceship NOT relative to the Earth: 0.4199 light-years / 0.994475c = 0.4222 years (time on the spaceship NOT relative to the Earth but to the other spaceship).

II.2.c.2.b. Time of the journey to the other spaceship relative to the Earth: 0.4222 years * 2.294 = 0.9685 years (time on the spaceship relative to the Earth).

II.2.c.3. Time of the journey of the other spaceship to the Earth: 0.0915 light-years / 0.094475c = 0.9685 (time on the spaceship relative to the Earth).

All the times of the journeys (II.2.c.1., II.2.c.2.b. and II.2.c.3.) are the same! The values 0.9687 and 0.9685 are not exactly equal because I rounded all the numbers to 3 or 4 decimal places and several steps in calculations caused this minute difference (0.0002). Anyway, it means that each journey (the spaceship A to the Earth, the spaceship A to the spaceship B and the spaceship B to the Earth) will last equally long, so all the observers will meet at the Earth at the same time – exactly as it was calculated by the stationary observer (the observer on the Earth).

II.2.d.1. Mass of the spaceship relative to the Earth: normal mass of the spaceship * 2.294 = 2.294 times the normal mass of the spaceship (more than twice as “heavy”, but still able to accelerate further in a decent way).

II.2.d.2. Mass of the spaceship relative to the other spaceship: normal mass of the spaceship * 9.526 = 9.526 times the normal mass of the spaceship (almost 10 times as “heavy” – significantly more difficult to accelerate).

Please notice that the change of mass depends on the observer AND on the reference point. The mass of the spaceship AT THE SAME TIME/PLACE seems lower (when looking at the Earth) or bigger (when looking at the other spaceship). The mass is relative too! This example “proves” that it's not really a physical change in mass, but it’s more like “it seems that the spaceships mass is higher because we can't accelerate it as well as we did at lower speeds”. The higher the OBSERVED speed the bigger the “FEELING” that the mass of the spaceship is higher.

As you can see from the above calculations you have to be very careful to use the same observer AND the same reference point for ALL the final calculations! It is very easy to mess things up by joining calculations made for different observers OR with different reference points!

Example II (“three observers”) – time comparison.

II.3. One day/month/year on the spaceship was equal to 2.294 days/months/years on the Earth (2.2222 years on the Earth / 0.9687 years on the spaceship).

The calculations can be also made for a different reference point – for example we could assume that the spaceship B is stationary and both the other spaceship A and the Earth were moving (or instead of the Earth there could be just another spaceship). It would mean that the Earth is “running away” from the spaceship A (that the Earth is going in the same direction as the spaceship A). This time the speed of the spaceship A relative to the spaceship B (0.994475c) would be the speed “v” and the speed of the spaceship A relative to the Earth (0.9c) would be the speed “s” (the sum of speeds). The speed “u” (the speed of the Earth relative to the spaceship B) would be equal to -0.9c (the negative number means that the speed is not added, but subtracted from the speed 0.994475c).

Once again: this is exactly the same example, but with the REFERENCE POINT being the spaceship B (not the Earth). Let's calculate things from the POINT OF VIEW of the spaceship A.

Example II (“three observers”) – version 3 of the calculations.

Observer: the observer on the spaceship A.

Reference point (for ALL the speeds involved): the spaceship B.

II.3.0.a. Speed relative to the Earth: 0.9c (this speed can actually be measured by the observer on the spaceship A, but it is NOT relative to the spaceship B).

II.3.0.b. Speed of the Earth relative to the spaceship B: 0.994475c – 0.9c = 0.094475c (the observer on the spaceship A sees this speed this way).

II.3.0.c. CALCULATED (real) speed of the Earth relative to the spaceship B: -0.9c (the “-“ sign determines only the direction of the movement – the same direction as the spaceship A). The observer on the spaceship A can't observe it directly, but he can calculate it.

II.3.0.d. Relativistic factor for the speed of -0.9c is 2.294 (we know that from the example I – the direction of the movement is not important).

II.3.0.e. Relativistic factor for the speed of 0.994475c is 9.526 (we know that from the example II).

II.3.a.1. Distance of the journey to the spaceship B: 4 light-years / 9.526 = 0.4199 light-years (relative to the spaceship B).

II.3.a.2.a. Distance of the journey to the Earth NOT relative to the spaceship B: 2 light-years / 2.294 = 0.8718 light-years (distance NOT relative to the spaceship B but to the Earth).

II.3.a.2.b. Distance of the journey to the Earth relative to the spaceship B: 0.8718 light-years / 2.294 = 0.3800 light-years (distance relative to the spaceship B).

II.3.a.3 Distance between the Earth and the spaceship B: light-years 0.4199 – 0.3800 light-years = 0.0399 light-years (distance relative to the spaceship B).

II.3.b. Length of each of the spaceship: … (irrelevant value).

II.3.c.1. Time of the journey to the spaceship B: 0.4199 light-years / 0.994475c = 0.4222 years (time on the spaceship A).

II.3.c.2.a. Time of the journey to the Earth NOT relative to the spaceship B: 0.8718 light-years / 0.9c = 0.9687 years (time on the spaceship A NOT relative to the spaceship B but to the Earth).

II.3.c.2.b. Time of the journey to the Earth relative to the spaceship B: 0.9687 years / 2.294 = 0.4223 years (time on the spaceship A relative to the spaceship B).

II.3.c.3. Time of the journey of the Earth to the spaceship B: 0.0399 light-years / 0.094475c = 0.4223 (time on Earth relative to the spaceship B).

All the times of the journeys (II.3.c.1., II.3.c.2.b. and II.3.c.3.) are the same! The values 0.4222 and 0.4223 are not exactly equal because I rounded all the numbers to 3 or 4 decimal places and several steps in calculations caused this minute difference (0.0001). Anyway, it means that each journey (the spaceship A to the Earth, the spaceship A to the spaceship B and the Earth to the spaceship B) will last equally long, so all the observers will be at the Earth at the same time – exactly as it was calculated with a different reference point (the Earth in the previous 2 variations of the calculations).

II.3.d.1. Mass of the spaceship relative to the Earth: normal mass of the spaceship * 2.294 = 2.294 times the normal mass of the spaceship (more than twice as “heavy”, but still able to accelerate further in a decent way).

II.3.d.2. Mass of the spaceship relative to the other spaceship: normal mass of the spaceship * 9.526 = 9.526 times the normal mass of the spaceship (almost 10 times as “heavy” – significantly more difficult to accelerate).

Example II (“three observers”) – time comparison #2 (different values for different reference points).

Before we can compare anything we have to calculate time of journey from the point of view of the spaceship B:

II.3.0. Time of the journey of the spaceship A: 4 light-years / 0.994475c = 4.0222 years (time on the spaceship B).

II.3. One day/month/year on the spaceship A was equal to 9.527 days/months/years on the spaceship B (4.0222 years on the spaceship B / 0.4222 years on the spaceship A).

We could do the calculations for the “moving Earth” because in the above example NEITHER observer accelerated, so ANY reference point was equally good. However, if we analysed a “triplets” example (all the observers are triplets – one stays on the Earth and the other 2 triplets depart the Earth in opposite directions, travel at the same speed the same distance and then come back to Earth also travelling at the same speed) then there could be only 1 correct reference point – the Earth. Only the Earth was NOT accelerating or decelerating – the other 2 triplets were accelerating and decelerating to change their direction (to be able to come back to the starting point). The Minkowski diagram of the triplets paradox would look like this:

## Tuesday, 17 March 2015

### Fun with a “short longboard”

(Originally posted on Saturday, 1 April 2017)

When I was a child I had a “fish skateboard”, but it was quite primitive – it wasn’t rolling well, it was rather short and it had a plastic deck. It was fun anyway, but I wished that I had a “real skateboard”. Recently my daughter has been trying to ride her scooter without using hands (it’s possible because her scooter has 2 front wheels) and it made me think that maybe I should buy a skateboard that could be used by my whole family. It would be something new and exciting for my daughter and I would finally have a “real skateboard”. And we would spend more time together too.

I picked a relatively cheap skateboard that I call a “short longboard”. It has relatively big and relatively soft wheels (like a longboard), but its size is that of a regular/conventional skateboard. It is fun to ride such a skateboard even on a dirty and rough surface (like that of a tiled pavement or a tiled road). The first movie is a good example, but I must point out that there was a very gentle slope in the first half of the “track” and the board was rolling better in that part.

The board is big enough for me and small enough for my daughter.

By the way: I bought my daughter's scooter long time ago, but she had trouble riding it when she was younger. I bought it because to me it looked like a makeshift skateboard with a stick.

The scooter is sturdy enough for me to ride it, but the deck is rather small and I have trouble to place both my feet on it. Here's a video showing how it turns:

Some of you probably wonder why my daughter (like me) wasn’t wearing a helmet. The reason is that she can actually run much faster than she can ride the board or her scooter. I don’t require that she wears a helmet while running, so I don’t do it while she is riding a skateboard or a scooter at very low speeds. Sure there are many bad things that can happen to us when we are not wearing helmets, but they can happen to us also while we are NOT riding a skateboard. Any person should generally stay alert and any person should avoid doing stupid and dangerous things. I always say to my daughter: “You may run uphill as fast as you want, but you should never run downhill.” When I say it she looks at me as if I were crazy (exactly like my wife), but she obeys this rule most of the time. I have a very good imagination and I can easily see many possible bad things that can happen then. The same rule goes for a skateboard or a scooter. Personally I would never ride a skateboard (or run downhill) on any significant slope EVEN while wearing a helmet. And I allow my daughter to ride a skateboard or a scooter only on flat ground or very gentle slope. She does wear a helmet while she is riding a bicycle.

PS. When I was recording the movies it was so chilly that people were wearing jackets and winter caps. Now, just two days later, it is so hot that people are wearing shorts. Spring has sprung!

When I was a child I had a “fish skateboard”, but it was quite primitive – it wasn’t rolling well, it was rather short and it had a plastic deck. It was fun anyway, but I wished that I had a “real skateboard”. Recently my daughter has been trying to ride her scooter without using hands (it’s possible because her scooter has 2 front wheels) and it made me think that maybe I should buy a skateboard that could be used by my whole family. It would be something new and exciting for my daughter and I would finally have a “real skateboard”. And we would spend more time together too.

I picked a relatively cheap skateboard that I call a “short longboard”. It has relatively big and relatively soft wheels (like a longboard), but its size is that of a regular/conventional skateboard. It is fun to ride such a skateboard even on a dirty and rough surface (like that of a tiled pavement or a tiled road). The first movie is a good example, but I must point out that there was a very gentle slope in the first half of the “track” and the board was rolling better in that part.

The board is big enough for me and small enough for my daughter.

By the way: I bought my daughter's scooter long time ago, but she had trouble riding it when she was younger. I bought it because to me it looked like a makeshift skateboard with a stick.

The scooter is sturdy enough for me to ride it, but the deck is rather small and I have trouble to place both my feet on it. Here's a video showing how it turns:

Some of you probably wonder why my daughter (like me) wasn’t wearing a helmet. The reason is that she can actually run much faster than she can ride the board or her scooter. I don’t require that she wears a helmet while running, so I don’t do it while she is riding a skateboard or a scooter at very low speeds. Sure there are many bad things that can happen to us when we are not wearing helmets, but they can happen to us also while we are NOT riding a skateboard. Any person should generally stay alert and any person should avoid doing stupid and dangerous things. I always say to my daughter: “You may run uphill as fast as you want, but you should never run downhill.” When I say it she looks at me as if I were crazy (exactly like my wife), but she obeys this rule most of the time. I have a very good imagination and I can easily see many possible bad things that can happen then. The same rule goes for a skateboard or a scooter. Personally I would never ride a skateboard (or run downhill) on any significant slope EVEN while wearing a helmet. And I allow my daughter to ride a skateboard or a scooter only on flat ground or very gentle slope. She does wear a helmet while she is riding a bicycle.

PS. When I was recording the movies it was so chilly that people were wearing jackets and winter caps. Now, just two days later, it is so hot that people are wearing shorts. Spring has sprung!

## Monday, 16 March 2015

### Dominant foot vs. dominant leg

(Originally posted on Saturday, 1 April 2017)

I noticed that I push a skateboard with my left leg and my daughter pushes it with her right leg. We are both right-handed and right-footed (we kick a ball with the right foot), so why is the difference in our skateboard stances? Below there is a great video with some basic longboarding tips that clearly shows how to determine which foot is your “front foot”. Well, the guy in the video uses the term “dominant foot” for a “front foot”, which is not quite the same as “dominant foot” in other contexts (for example for kicking a ball). Like in the video I pushed my daughter from the back and she moved her left foot first – the same foot she keeps first on the skateboard. I asked her to push me from the back and I moved my right foot first – the same foot I keep first on the skateboard. Interesting, isn’t it?

Actually there is a different name for each skateboard stance – regular (like my daughter’s) and goofy (like mine). Some of the sites claim that most of the people ride in regular stance and that is why it is called regular, but this site:

https://en.wikipedia.org/wiki/Footedness

clearly states that “Professionals seem to be evenly distributed between the stances”. When I look at the online pictures and videos for “longboarding” I can see that almost half of the people ride in goofy style. Personally I can’t imagine riding a board in regular stance.

If the skateboarders are more or less evenly distributed between the stances then the stances have nothing to do with the concept of “dominant foot” – most people are right handed and over 90% of right-handers are also right-footers, but only around 50% left-hander are left-footers (at least this is what Wikipedia says). So, the VAST majority of people should ride in regular stance and it is clearly not the case. So, what determines the “dominant foot as far as skateboarding is concerned”?

It seems to me that we simply push a skateboard with a LEG that is physically stronger (the “dominant LEG”) and the weaker LEG simply goes first. That is probably what our brain is used to do in our life – we may not notice which leg is stronger, but our brain surely does, so the brain makes us subconsciously prefer doing some things with our stronger leg. Like pushing a skateboard. It suits my case perfectly – my left leg is definitely stronger, even though I use my right foot to kick a ball. I used to play lots of basketball and because I am right-handed I wanted to finish my layups with my right hand, so I jumped a LOT using my left leg, making it stronger than my right leg. Walking and running require both legs, so my right leg had no chance to become dominant, even though my right foot is dominant.

If my theory is right (that we push a skateboard with our dominant – stronger LEG) then a team of right-handed basketball players should ride almost exclusively in goofy stance, like me. It would be interesting if somebody carried out such an experiment.

PS. Whenever I use the expression “my theory” my wife just rolls her eyes and prepares for the worst.

I noticed that I push a skateboard with my left leg and my daughter pushes it with her right leg. We are both right-handed and right-footed (we kick a ball with the right foot), so why is the difference in our skateboard stances? Below there is a great video with some basic longboarding tips that clearly shows how to determine which foot is your “front foot”. Well, the guy in the video uses the term “dominant foot” for a “front foot”, which is not quite the same as “dominant foot” in other contexts (for example for kicking a ball). Like in the video I pushed my daughter from the back and she moved her left foot first – the same foot she keeps first on the skateboard. I asked her to push me from the back and I moved my right foot first – the same foot I keep first on the skateboard. Interesting, isn’t it?

Actually there is a different name for each skateboard stance – regular (like my daughter’s) and goofy (like mine). Some of the sites claim that most of the people ride in regular stance and that is why it is called regular, but this site:

https://en.wikipedia.org/wiki/Footedness

clearly states that “Professionals seem to be evenly distributed between the stances”. When I look at the online pictures and videos for “longboarding” I can see that almost half of the people ride in goofy style. Personally I can’t imagine riding a board in regular stance.

If the skateboarders are more or less evenly distributed between the stances then the stances have nothing to do with the concept of “dominant foot” – most people are right handed and over 90% of right-handers are also right-footers, but only around 50% left-hander are left-footers (at least this is what Wikipedia says). So, the VAST majority of people should ride in regular stance and it is clearly not the case. So, what determines the “dominant foot as far as skateboarding is concerned”?

It seems to me that we simply push a skateboard with a LEG that is physically stronger (the “dominant LEG”) and the weaker LEG simply goes first. That is probably what our brain is used to do in our life – we may not notice which leg is stronger, but our brain surely does, so the brain makes us subconsciously prefer doing some things with our stronger leg. Like pushing a skateboard. It suits my case perfectly – my left leg is definitely stronger, even though I use my right foot to kick a ball. I used to play lots of basketball and because I am right-handed I wanted to finish my layups with my right hand, so I jumped a LOT using my left leg, making it stronger than my right leg. Walking and running require both legs, so my right leg had no chance to become dominant, even though my right foot is dominant.

If my theory is right (that we push a skateboard with our dominant – stronger LEG) then a team of right-handed basketball players should ride almost exclusively in goofy stance, like me. It would be interesting if somebody carried out such an experiment.

PS. Whenever I use the expression “my theory” my wife just rolls her eyes and prepares for the worst.

## Sunday, 15 March 2015

## Saturday, 14 March 2015

### The best of snooker

(Originally posted on Saturday, 22 April 2017)

At the end of the post there are several Youtube examples of snooker at its best.

Right now the 2017 World Snooker Championship is taking place at the Crucible Theatre in Sheffield, England. There is still over a week of play as the tournament is nearing the quarter-finals right now.

I've been a fan of snooker for a long time, even though I have never played it in the real world. I did play plenty of snooker using computer thanks to an old DOS game from 1991 – Jimmy White's 'Whirlwind' Snooker. That was an awesome game! Thanks to it I learned the rules of snooker the hard way.

Now snooker is much more known and the rules are easily available through the Internet. And when you know the rules there is no doubt that snooker is by far the best, the most sophisticated and the most difficult kind of billiards. Pool doesn't compare to snooker, to say the least.

In snooker the table is significantly bigger and the balls are smaller which makes it much harder. There are also more balls and the colour balls (balls other than red) are returned to the table after they are potted unless there are no red balls left (to legally pot a colour ball you need to pot a red ball first). A red ball is worth 1 point, yellow 2 points, green 3, brown 4, blue 5, pink 6 and black 7.

What makes snooker so fun to watch is the fact that there are many strategical aspects of this game. For example a player can lay a snooker, which means that the opponent can't target any red ball directly in a straight line. So, the opponent has to either play a curve shot (the white ball travels in a slight curve omitting an obstacle) or he (or she) has to use a table bound (or bounds) to make the white ball reach a red ball. A snooker can be laid for colour balls too, because when there are no red balls left on a table the colour balls have to be potted in a particular order: yellow, green, brown, blue, pink and black.

The most impressive plays actually don't consist in potting a ball (no matter how hard), but they consist in laying a snooker or going out of a snooker. Beautiful plays! But vastly undervalued by people who don't know much about snooker.

The first video shows awesome pots, as well as awesome snookers and awesome escapes from snookers.

In the second video Ronnie O'Sullivan (who won the World Snooker Championship 5 times – in 2001, 2004, 2008, 2012 and 2013) shows incredible control over the white ball. At the end of the video you can see 2 other former World Snooker Champions – John Parrott (in 1991) and Steve Davis (in 1981, 1983, 1984, 1987, 1988 and 1989) commenting on the game.

The third video shows some great shots by Steve Davis himself.

The fourth video shows why Jimmy White was called Whirlwind. He advanced to the World Snooker Championship Finals 6 times, but unfortunately didn't winy any of them.

The fifth video shows another great snooker player Stephen Hendry (who was the World Snooker Champion in 1990, 1992, 1993, 1994, 1995, 1996 and 1999) making a maximum break (147 points – after every red ball he potted the black ball). He made that break in 2012 when he was 43 years old! Quite an achievement, even for such a great player.

The last video shows the fastest maximum break ever, made of course by Ronnie O'Sullivan.

PS. I had never traced personal lives of snooker legends and I was saddened by what I found about some of them. I guess it is hard to be a superstar and it is even harder to be a former superstar.

At the end of the post there are several Youtube examples of snooker at its best.

Right now the 2017 World Snooker Championship is taking place at the Crucible Theatre in Sheffield, England. There is still over a week of play as the tournament is nearing the quarter-finals right now.

I've been a fan of snooker for a long time, even though I have never played it in the real world. I did play plenty of snooker using computer thanks to an old DOS game from 1991 – Jimmy White's 'Whirlwind' Snooker. That was an awesome game! Thanks to it I learned the rules of snooker the hard way.

Now snooker is much more known and the rules are easily available through the Internet. And when you know the rules there is no doubt that snooker is by far the best, the most sophisticated and the most difficult kind of billiards. Pool doesn't compare to snooker, to say the least.

In snooker the table is significantly bigger and the balls are smaller which makes it much harder. There are also more balls and the colour balls (balls other than red) are returned to the table after they are potted unless there are no red balls left (to legally pot a colour ball you need to pot a red ball first). A red ball is worth 1 point, yellow 2 points, green 3, brown 4, blue 5, pink 6 and black 7.

What makes snooker so fun to watch is the fact that there are many strategical aspects of this game. For example a player can lay a snooker, which means that the opponent can't target any red ball directly in a straight line. So, the opponent has to either play a curve shot (the white ball travels in a slight curve omitting an obstacle) or he (or she) has to use a table bound (or bounds) to make the white ball reach a red ball. A snooker can be laid for colour balls too, because when there are no red balls left on a table the colour balls have to be potted in a particular order: yellow, green, brown, blue, pink and black.

The most impressive plays actually don't consist in potting a ball (no matter how hard), but they consist in laying a snooker or going out of a snooker. Beautiful plays! But vastly undervalued by people who don't know much about snooker.

The first video shows awesome pots, as well as awesome snookers and awesome escapes from snookers.

In the second video Ronnie O'Sullivan (who won the World Snooker Championship 5 times – in 2001, 2004, 2008, 2012 and 2013) shows incredible control over the white ball. At the end of the video you can see 2 other former World Snooker Champions – John Parrott (in 1991) and Steve Davis (in 1981, 1983, 1984, 1987, 1988 and 1989) commenting on the game.

The third video shows some great shots by Steve Davis himself.

The fourth video shows why Jimmy White was called Whirlwind. He advanced to the World Snooker Championship Finals 6 times, but unfortunately didn't winy any of them.

The fifth video shows another great snooker player Stephen Hendry (who was the World Snooker Champion in 1990, 1992, 1993, 1994, 1995, 1996 and 1999) making a maximum break (147 points – after every red ball he potted the black ball). He made that break in 2012 when he was 43 years old! Quite an achievement, even for such a great player.

The last video shows the fastest maximum break ever, made of course by Ronnie O'Sullivan.

PS. I had never traced personal lives of snooker legends and I was saddened by what I found about some of them. I guess it is hard to be a superstar and it is even harder to be a former superstar.

## Friday, 13 March 2015

### Funny snooker videos

(Originally posted on Saturday, 22 April 2017)

Here are some funny snooker videos.

The first video shows that in snooker, as in any other sport, you have to be lucky sometimes.

The next video is not only funny, but it also shows (and names) many famous snooker players, including some players from the early 1980s. Cool. Unfortunately it features the uncensored version of the song “Remember the name” (I would preferred the censored one), but I had to post it anyway.

The last video shows some funny moments when even players are amused. Sometimes they are even joking themselves.

Here are some funny snooker videos.

The first video shows that in snooker, as in any other sport, you have to be lucky sometimes.

The next video is not only funny, but it also shows (and names) many famous snooker players, including some players from the early 1980s. Cool. Unfortunately it features the uncensored version of the song “Remember the name” (I would preferred the censored one), but I had to post it anyway.

The last video shows some funny moments when even players are amused. Sometimes they are even joking themselves.

## Thursday, 12 March 2015

### Beautiful flying videos

(Originally posted on Sunday, 4 June 2017)

The first three videos feature truly beautiful shots. BEAUTIFUL!

The female pilot in the second video can be briefly seen in the first video. The second video features some quotes from her interviews (I don't have time to translate them).

The third video can't be embedded and you have to watch it directly on Youtube. The flying shots start at 2:16, so I set the link to start there:

https://youtu.be/6Uc_GdEGDXY?t=2m16s

This year a local aeroclub from my home city (Zielona Góra) celebrates its 60th anniversary and yesterday there was a festival at its airport that featured, among others, numerous aerobatic displays. I went there together with my wife and our children and we watched some of the displays, including a display by the Żelazny Aerobatic Group (the word “żelazny” in Polish means the adjective “iron”).

http://en.grupazelazny.com/#o_nas

http://new.azl.pl/o-nas/?lang=en

Below there are two videos I recorded at the festival. The first one shows a short fragment of the display by the Żelazny Aerobatic Group and the second one shows a part of a display by parachutists. One of the parachutists was approaching to land so fast it was unsettling.

The first three videos feature truly beautiful shots. BEAUTIFUL!

The female pilot in the second video can be briefly seen in the first video. The second video features some quotes from her interviews (I don't have time to translate them).

The third video can't be embedded and you have to watch it directly on Youtube. The flying shots start at 2:16, so I set the link to start there:

https://youtu.be/6Uc_GdEGDXY?t=2m16s

This year a local aeroclub from my home city (Zielona Góra) celebrates its 60th anniversary and yesterday there was a festival at its airport that featured, among others, numerous aerobatic displays. I went there together with my wife and our children and we watched some of the displays, including a display by the Żelazny Aerobatic Group (the word “żelazny” in Polish means the adjective “iron”).

http://en.grupazelazny.com/#o_nas

http://new.azl.pl/o-nas/?lang=en

Below there are two videos I recorded at the festival. The first one shows a short fragment of the display by the Żelazny Aerobatic Group and the second one shows a part of a display by parachutists. One of the parachutists was approaching to land so fast it was unsettling.

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