# Does hot water freeze faster than cold?

Hi,
what is wrong with this title? Well it should sound like a nonsense, NO, of course not! Hot water freezes slower than the cold water simply because it takes some time for the water temperature to drop to the same value as the first water.

Actually you could find out that this is entirely not true and it has been a big mystery for a long time.

Of course I must add that such a water, in glass bottle for example is put into the freezer on the same place as the second bottle because if you put the hot one next to the side of the freezer, then of course it will freeze sooner.

While I did not try this experiment yet, it seems that there were already thousands of people who have done so before me and they have many hypothesis about what really happens there.

It has been actually known for years, even Aristotle pointed this out. This effect is called Mpemba effect, after the guy who wrote about it in 20th century, he discovered it when he was just a kid, with ice cream.

The graph below shows the temperatures of two water samples.

We of course must assume that this was very well conducted experiment but it works for illustration.

Now something had to happen when the water was hot. That is for sure because after about 4,000 seconds the water is same right?

Well it does not need to be, first we must know the factors that change for example how much the water holds its temperature.

Those are: its volume and its inside.

Its volume? Well 10 milliliters of water will lose their temperature almost “immediately” so this is important factor. How could it change (of course we assume that on start the volume is the same with the same water from tap)? Well water evaporates and it evaporates more quickly when it is hot. This is true the water will relly lose significant amount of its volume to have some effect. We can actually test if this is the only factor. We can close the container so it wont happen. This has been tested and even that it looked as a great hypothesis it was falsificated from what I read.

Another thing could be that when you have water and you heat it, its inside will change causing it to have different “hold” of temperature so it drops more quickly, gases dissolve better in cold liquids so there are less in the hot water.

What other factor could play here? One guy on physics stack exchange said that without the ice around the bottles everything worked perfectly fine but it seems that this is not actually the case while it could change it.

The problem here is that even if you have some process which will get it extra fast down, at one point it will be same anyway.

Another one could be convection. The top will be always hotter since the way water works. Since it loses heat primarily through surface it could lose its heat faster than we would expect because the top would be always warmer while the cold water would not be able to make such a great convection.

I came up with another solution. Even if you close the glass bottle so there is the same amount of water, the water will still evaporate and the side of the bottle will get wet with the condensated water. There will be bigger surface which will get cold while the water which condensated fell down again, cooling it by little bit. Also of course that when you put it freezer which has ice on bottom, it will melt through it and since water has higher thermal conductivity, it will get colder from the bottom.

What else? Maybe you can come up with something but I did not find the complete answer yet!

Dragallur

# Serious problem of multitasking

Hi,
when I was yesterday writing about procrastination, most of the memes I found were negatively turned towards procrastination while multitasking seems to look like a good thing to do, by most of the people on the internet.

Oh yes, I am trying to say that multitasking is really bad, but first lets define what exactly means to multitask.

So multitasking is apparent doing of several things at the same time.
I say apparent because what people actually do, is that they change their tasks very often so it seems that they are doing more things at the same time (this is exactly what computers do, switching between various tasks).

This can mean many things like: cooking and calling, emailing and eating, chatting and learning and so on, what is worse you add more and more things to do at the same time.

This takes price. Every time you switch from one task to another you must remind yourself what this task is and that takes energy so your brain eats glucose like crazy. What is even worse is that this switching between tasks releases dopamine.

Dopamine is hormone which does lot of stuff and is connected with Parkinson’s disease. This hormone is kind of good for you and your brain remembers exactly from what activity dope of dopamine was released. This is why you want to perform the task again, and again. Dopamine is stimulating your brain and this is where most of the addictions come from. So yes, what I am trying to say really is that you can get addicted to multitasking.

So what other problems are there with multitasking? Well it is energetically inefficient but also it does not let you to dive to one problem and solve it properly with your best. Sometimes multitasking can even double the time it takes to finish the task, while you still think that you are extremely efficient when multitasking.

Last thing is that when you are actually learning and playing games at the same time, the knowledge from learning, even if you learned something, may be stored in the part of brain tagged as “fun or recreation or games”. What then happens is that you are not able to properly remember those things when you are learning something similar and your brain should normally say: “Oh yeah! I know this part already!”

So my best advice, stop it now! As I said in the post about procrastination, try to learn not to be distracted by other things around and focus only on one task, the most important one.

Dragallur

1st picture

# Famous people: Galileo Galilei

Hi,
for Christmas I got some nice books and now I am reading first one which is called: 10 Physicists who transformed our understanding of reality. It seems that it is very good book and I am behind the first chapter which was about Galileo Galilei so I decided that I will write about him.

So Galileo Galilei is very famous astronomer but why? Because of Galilean moons, yes that is right and also because of his first telescope and probably even because of his conflict with church.
Galileo was born 15.2.1564.
It was time when most people thought that everything is made up of four elements and the fifth, quintessence was present in the sky. Not many people questioned those ideas. Lot of stuff was based only on thinking because it was thought that sense was easily fooled in experiment.

Galileo was born in Pisa to his father who was lute player. First he wanted to be priest but father rather wanted him to become a doctor.
Galileo had private teacher as did other mid class kids and soon he discovered that he was more curious about science than in priesthood.

He started to visit university in Pisa when he was seventeen.
There are some stories about his curiosity for all the things around, like throwing stuff from the Pisa tower or watching how pendulums swing.

For example he soon discovered that it is not true that bigger things will hit the ground first like Aristotle thought.

He left the university because his biggest concern clearly was not medicine but rather mathematics. He took some courses to become professor.

In 1595 he started to investigate the problem with tides. Nobody was able to explain them properly before because they were such a strange event, high and low tide twice a day.. geocentric model which was the only one recognized back then was not able to explain it.

This seems to be the first time that Galileo started to think about the heliocentric model first proposed by Copernicus.
Galileo wrote Kepler when he read his pro-heliocentric book. They were writing letters to each other for some time when Kepler told him that he should try to investigate stellar parallax[1].

Galileo finally did not even try because he thought that there are already people, who tried hard enough so he would not be able to measure it. It was measured for the first time in the year of 1838.

Instead of investigating stellar parallax he returned to pendulums and started to make experiments about their swing. It seemed like paradox that no matter the angle of the swing the swing will always take the same time. This was about when he discovered the first law of motion and inertia.

In geocentric model it is thought that Earth is the middle of Universe with everything rotating around it in some kind of shells. The sky is unchangeable so everything that changes must be in sub-lunary sphere[2].

It was October 1604 when supernova was seen from Earth. Galileo thought it is new star but he “knew” that the sky can not be changed so it hat do be in atmosphere where he would clearly see that parallax which I mentioned earlier.

Galileo measured its position on few places in Europe and it did not change, so clearly this model of world was wrong.

After this he constructed his best telescope with magnification of 20x. First of all he found out that the surface of Moon is not smooth as it was thought. Then finally he started to watch Jupiter.

First of all he saw three star like object around it. He thought that those are just normal stars but few days later one of them disappeared and another was visible. This was how he found Galilean moons.

It was another breakthrough since before it was thought that everything has to be orbiting Earth.
Another thing that ensured him of heliocentric model was Venus. He found out that Evening Star also goes through the cycle of “new moon” and “full moon” as Moon does. This was not possible if Venus should be orbiting Earth and at the same time rise as evening and morning star. Also he found out that when Venus is going to be in full moon it is also smaller than in new moon (it is farther away!).

The problem with these revolutionary ideas was that it was clear that church wont like to hear it.
First he only said it to Kepler but than he wrote some books.
Galileo was deeply religious man so he did not want to discredit church but rather show that there were some “small” mistakes.

Galileo thought that when he will show both sides of argument it will be perfectly fine but finally church called him for trial in Rome.
The final sentence was to put him under home arrest and that he will have to rewrite the offensive parts of the book.

I read that there is myth that when they said that he was to be at home arrest he said: “And yet it moves. (the Earth)” but as they stated in the book, he was not stupid to mutter such a thing and there is no evidence for it.

He died in January 8th 1642.

Galileo clearly was really great mind who not only explained perfectly heliocentric model but also showed the ways modern science works.

Dragallur

Galileo Galilei picture.

[1]Stellar parallax is something you see everyday and it has to do with the position of the things around you. When you are driving car the stuff close to you is moving faster than the stuff which is far away from you. It is called stellar because of the different parallax when you are looking from various point on the orbit of Earth.

[2]Sub-lunary sphere is what lies under the orbit of Moon. It is changeable while supra-lunary sphere is what is above the Moon’s orbit. It is regular and it can not be changed.

# Turn your brain into black hole

Hi,
here it goes, here it comes! Today I want to write about Graham’s number which is very interesting number and highest number which has some usage in mathematics.

Ok first of all, what is its purpose?
Imagine square where all vertices are connected. You can connect them by two colors, blue and red. You are trying to avoid one special pattern which you can see behing the mathematician Ron Graham who invented this number about which I will talk in a while. So those points can not be connected by single color the thing is that when you increase the dimension it is little harder (you already now everything about dimensions if you read my last post).
When you have 3rd dimension as you can see on the right there are 8 vertices.
This means that there are 28 lines between those dots.
Yes it is possible to avoid the special configuration. When you continue to fourth dimension you can still do it but here comes the problem. In fourth dimension there are 2^120 possible ways to color this cube. This is such a large number that no computer can solve it, in decent amount of time. Now you need to make some better way to solve it. Through some better way which I dont know mathematicians got up to 13th dimension, now they dont know maybe it is possible maybe not but the number when we are COMPLETELY sure that it is not possible is Graham’s number.

To show you how large is Graham’s number I first of all have to explain Knuth’s up-arrow notation.
3+3+3=3*3
3*3*3=3^3
3^3=3↑3=27
That’s about it when you have one arrow. It gets better when you have two:
3↑↑2=3^3=27 , easy.
3↑↑3=3^3^3=3^27=over 7 trillions$\begin{matrix} a\uparrow\uparrow b & = {\ ^{b}a} = & \underbrace{a^{a^{{}^{.\,^{.\,^{.\,^a}}}}}} & = & \underbrace{a\uparrow (a\uparrow(\dots\uparrow a))} \\ & & b\mbox{ copies of }a & & b\mbox{ copies of }a \end{matrix}$
Lets see three of them:
2↑↑↑2=2↑↑(2↑↑2)=2↑↑4=2^2^2^2=2^2^4=2^16=65536
2↑↑↑3=2↑↑(2↑↑(2↑↑2)=2↑↑65536$\begin{matrix} a\uparrow\uparrow\uparrow b= & \underbrace{a_{}\uparrow\uparrow (a\uparrow\uparrow(\dots\uparrow\uparrow a))}\\ & b\mbox{ copies of }a \end{matrix}$
Easy it continues and it gets hella huge.
So when I found out that Graham’s number needs arrow notation to be written I was like: “Easy, there will be few arrows, arrow notation is such extreme tool.”
Then after I found out how big is Graham’s number I was just like: “Oops!” You will se why.
So lets define the number g1
g1=3↑↑↑↑3
=3↑↑↑(3↑↑↑3)
=3↑↑↑(3↑↑(3↑↑3)

=3↑↑↑(3↑↑(3↑(3↑3)
=3↑↑↑(3↑↑(3↑27) i think that this is enough for ilustration.
now lets define g2=3↑↑↑↑↑↑↑…3 number of arrows equals to g1

Surprised? We are not even in beginning.
g3=3↑↑↑↑…3 number of arrows equals to g2 … so you know the process, this continues up to g64 which is Graham’s number.

Ok this is extremely large number and to remind you it is number of dimensions, which means that the combinations are even much higher, not kidding.
The Graham’s number has real meaning but I am not really able to understand so if you want to check it, somewhere in the video Ron Graham explains it. Also Numberphile has some other videos about it so check them out.
Next time I will write about Ackermann function. After that you will get this XKCD joke:
Dragallur

PS: I found lot of people trying to liken stuff to Graham’s number. Dont even try that, you wont get very close.

# Stellar classification

Hi,
what you can see on the picture is extremely cool (hot actually) even that you don´t know it yet. It is called Hertzsprung-Russell diagram and I will try to explain it with the rest of Stellar classification.

So there is first thing I have to clear out: What is Absolute magnitude?
Absolute magnitude describes how bright is star. This of course depends on the distance from which you are looking. It is called absolute because of fixed distance of 10 parsecs (around 32.6 light years). There exists also apparent magnitude which is taken from Earth´s view.

This absolute/apparent magnitude is in logarithmic scale. This means that for every point in magnitude, brightness increases by x2.512. So for 5 points, brightness increases 100 times (2.512^5=100.0226), this corresponds to what was created in ancient Greece. Also it is important to note that negative means more bright.

Absolute magnitude is Y-axis on HR diagram (it can also be luminosity) while X-axis is spectral class or sometimes surface temperature.
Spectral class corresponds with surface temperature, mass, solar radius and its rareness.
There are usually seven types but on the picture you can see nine.
Those seven are OBAFGKM. Where O type is hottest and M coolest with lowest mass.
You can use mnemonic to remember it: Oh Be A Fine Girl (Guy) Kiss Me (I really like this one :D).

And the last thing you need to know about the diagram are those roman numbers. Those are luminosity classes.
VII: those are white dwarfs.
VI: subdwarfs
V: main sequence stars
IV: subgiants
III: giants
II: bright giants
Ib: less luminous giants
Ia: luminous super giants
0: hyper giants! (those are shown on the right picture, blue line is orbit on Neptune and those stars are: blue hyper giant, yellow hg., red super giant and red hyper giant)

So now we can take our Sun and find out what we can tell about it.
Wikipedia says that spectral classification of Sun is G2V.
G: it is spectral class (girl/guy)
on the diagram it is rather on the left and you can see it is yellow.
2: means that Sun is in the upper part of G spectral class, this is only for subdividing those classes where 0 is highest and 9 lowest.
V: (it is 5) this means that Sun belongs to main sequence stars.

Now you can easily find where it stands.
Another example could be 10 Lacertae a star in the constellation of Lacertae.
O9V is its classification.
O: (Oh) you can see it is a super giant but with “only” 9 so it is rather smaller and cooler super giant.
V: again this one is lying in the main sequence so it would belong to upper left corner of diagram.

That´s about it, if you ever check for any star, this classification can be extremely helpful for you.

Dragallur

Note that there is table for spectral classes (taken from wikipedia page stellar classification):

 O B A F G K M ≥ 30,000 K blue blue ≥ 16 M☉ ≥ 6.6 R☉ ≥ 30,000 L☉ Weak ~0.00003% 10,000–30,000 K blue white deep blue white 2.1–16 M☉ 1.8–6.6 R☉ 25–30,000 L☉ Medium 0.13% 7,500–10,000 K white blue white 1.4–2.1 M☉ 1.4–1.8 R☉ 5–25 L☉ Strong 0.6% 6,000–7,500 K yellow white white 1.04–1.4 M☉ 1.15–1.4 R☉ 1.5–5 L☉ Medium 3% 5,200–6,000 K yellow yellowish white 0.8–1.04 M☉ 0.96–1.15 R☉ 0.6–1.5 L☉ Weak 7.6% 3,700–5,200 K orange pale yellow orange 0.45–0.8 M☉ 0.7–0.96 R☉ 0.08–0.6 L☉ Very weak 12.1% 2,400–3,700 K red light orange red 0.08–0.45 M☉ ≤ 0.7 R☉ ≤ 0.08 L☉ Very weak 76.45%

# Stars of our Solar System: Sun

Hi,
after few hours of study I am bringing next post, this time I am returning to where everything begun, The Sun!
So Sun is the center of our Solar System. But it is far away from the center of our galaxy as you can see on picture (it is about 27000 light years).

Sun is the brightest object on our sky with apparent magnitude -26,74 (I will definitely make post about apparent magnitude because I found it very interesting). Sun makes up of 99.8% of Solar
System´s mass so you have no way of thinking that Jupiter is big. It is 1.4 million kilometers across with mass 333,000 of Earths.

The surface temperature is 5,000°C. Surface here is the edge of what we see, or also edge of photo sphere which I will mention later on.
In the core there are temperatures about 15,000,000°C.
Sun is fusing hydrogen into helium as most stars do. Still in the core there are some more heavy elements like carbon, oxide, neon and others but only in small parts.

Every second our Sun burns 700,000,000 tuns of hydrogen which fuses into 695,000,000 tuns of helium. Those 5 millions is heat escaping the star. This is the same weight as 15 Empire State Buildings! But even more astounding is that this energy equals to 400 billions of megatons of nuclear bombs every second! That is why we feel the heat even from such a distance.

So, there are few layers. (Whole Sun is rotating but different layers in different speeds.)

Core: is the hottest part which takes up over 20% of Sun´s radius (not 20% of volume, remember, it is sphere). Here the fusion takes part.

Radiative zone: stretches to 0.7 of Sun´s radius. There are hypothesis that this zone with next zone creates magnetic field of Sun. Also here the energy is transferred by diffusion.

Convective zone: This zone is almost the rest of Sun´s volume. Here like in ocean hot gas goes up and colder down in process called convection.

Photo sphere: is the visible part of Sun. It is thousands of kilometers thick and much much colder and it has very low density (0.37% of air density on sea level).

Corona: is the outer layer of Sun. We are not really sure why but it is ridiculously hot, about 1-2 million °C even that it spreads 1-2 Sun radii from Sun´s surface. It is even less dense than photo sphere so you can not see it without telescopes blocking Sun or Sun eclipse.

For photon it can take 100-200 thousands year to escape from core because right after photon is created it collides with some particle which blasts it away with less energy so this photon is kinda lost for a long time.

Solar flares are events when charged stuff interacts with plasma. This creates eruption (last picture).
Coronal mass ejections happen when two opposite magnetic fields interact with each other throwing lot of stuff into space and some electromagnetic radiation (first picture).

Both events are connected and can occur together. In the year of 2012 we were very lucky since one coronal mass ejection appeared but thankfully missed us (this CME was so strong that it would probably cut off most of electronic circuits and we would be recovering for very long time).

This is end for today, I hope u guys liked this little bit longer post.
Dragallur

PS: I was taking information from lot of sites but I forgot to copy their URL but it was wiki, NASA and some others from first pages on google.

For more about stars, visit one of my old posts about life cycle of those balls!
And to see what kind of dwarf Sun is visit this post!

# Moons of our Solar System: Deimos

Hi,
today I will write about even smaller moon than Phobos. This time it is Deimos, again named after kid of Ares (Mars) and Aphrodite (Venus). Deimos was the god of terror/panic/dread. Radius of Deimos is 6.2 kilometers which is almost half of Phobos. This guy was also found by Asaph Hall but 6 days earlier than Phobos.

Deimos is even farther away from his father. When we would watch him from Mars´s surface we would see just a small point and in full Moon he would be bright about as Venus from our point of view, otherwise he could look like ordinary star.

On the GIF you can see Deimos hiding behind much larger Phobos. Its surface should be similar to his brother´s but instead it is much smoother which is made by “sand” which smooths everything out over time.

There are only two features named and those are craters Swift and Voltaire named after writers who speculated about moons around Mars even before anybody new they are there.

Its original is not really sure. Usually you will find that Jupiter´s gravitation threw both moons toward Mars and he caught them (this would one reason for so circular orbits of both moons) but most likely they are his kids anyway.

And again his escape velocity is 20.16km/h so if you can run 50 meters in less than 8 seconds you will be able to left him… if it would work like this.

Dragallur

If you have not read about Phobos yet, you should!

# Apollo missions: Apollo 10

Hi,
what a surprise! I am here again with Apollo missions this time with fourth manned mission.

Apollo 10 was launched in the year 1969 May 18 and 16:49:00 PM. Members of crew were three of course: from left to right Cernan, Stafford and Young.

Stafford was captain. Apollo 10 crew were unique because it was first Apollo mission where all members were already in space (Apollo 11 was second and last). Both Young and Stafford were flying for the third time while Cernan for second.

There was also back up crew if some problems occurred but Cooper and Eisele (Apollo 7) were not in favor of NASA because of some incidents on their missions so it was not planned to move them on next mission (as was usual) and they were back up crew only because NASA did not have enough experienced astronauts.

Highlight of this mission were prepared so that they had all data they needed for Apollo 11 which would two months later land on Moon. Everything they needed to do was done, the most important thing was to approach Moon as close as possible.
By one historian it is said that NASA had to give them low amount of fuel so they could not land Moon even if they wanted.

This approaching was achieved by departing a little Lunar module (called Snoopy, it is on the picture with moon) leaving only Young on the board of “Mothership” while Stafford and Cernan achieved the distance from surface of 15.6 km.

Apollo 10 orbited Moon thirty times and then after 8 days and 3 minutes and 23 seconds they splashed down in the Pacific ocean (actually mission was planned 1 minute shorter this means that they really messed it up).

One of Snoopy´s stage was left there and nobody knows where it landed (crushed) but in the year of 2011 group of amateurs started project to find it out.

Dragallur

I was taking data from these pages:
https://www.nasa.gov/mission_pages/apollo/missions/apollo10.html#.Vi5Wz7erTc

https://en.wikipedia.org/wiki/Apollo_10

# Moons of our Solar System: Phobos

Hi,
today I will write about second moon. This time it is Phobos, the bigger of the two moons of Mars.
His name comes from the son of Ares (Mars) and Aphrodite (Venus). Phobos is really strange, he orbits closer to its planet than any other moon. Every year it is closer by 2 meters so one day, about 50 million years in the future Phobos will either crush onto
Mars´s surface or he will be ripped by tidal forces so only ring will be left of him.

Phobos was found in the year of 1877 by Asaph Hall. His surface is one of the darkest of any object in our Solar System (this picture has enhanced colors). There are lot of craters and the biggest has almost the same diameter as whole Phobos. You can see it on the right of the picture and it is called Stickney crater after Asaph´s wife. Temperatures can go from -4°C to -112°C.

Phobos has too low gravity so he could not round himself, that is why he looks as potato. Escape velocity from his surface is 41km/h which means that Usain Bolt would be able to run into space on his own feet. The gravity is 0.000581 of gravity on Earth.

Phobos is small but even than he weights about  10,658,529,896,187,200 kg (or 10.6 quadrillion).

One more strange thing about him is that he is orbiting faster than Mars turns around his axis so he can be seen thrice a day rising from west and setting east.

Dragallur

PS: thanks for those who are reading my blog, I have written 50 posts already!

# Capturing territory, Facebook page

Hi,
I am here to announce that I just made a facebook page for my blog it is called Science and rationality as my wordpress.
WHY?
Because I want to extend my virtual territory and maybe collect some people from the internet.

Mostly I plan to use my facebook page for short news and links to wordpress.
I will see how it goes and if any people are “liking”.

Dragallur

Make sure to check also my twitter!