Unrealistic radioactive decay

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

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

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

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

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

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


Next hour:


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




What I think about genetic modification NOW


Coincidently just this weekend I started to read Brave New World by Aldous Huxley, because I need it for my English class. At the same time during today’s class (English conversation) we spoke about GMOs. Speaking on the topic means that I read Wikipedia page for 10-15 minutes and then I presented it in front of the class. Then we moved on to another topic and there were no comments from either the teacher or my class mates, I doubt anybody had any opinion based on anything more than impressions which is the case for me too.

The reason why I mentioned Brave New World is because it is a sci-fi about genetically modified humans. I am in the beginning of the book so it won’t have much of an effect on what I will try to do here.

So as a person who does not know much about GMO and dangers/benefits of genetic modification I want to briefly write down what I think now. After that I want to inform myself as much as possible and then write what changed and what I learned.

I think that GMO plants might be a risk but also a road that we might take eventually. I guess that there are dangers with taking DNA of one organism and putting it into some else because if I am right, we are not fully able to predict the consequences so while we are trying to get resistant corn we might also get corn that has some nasty properties that might not be visible immediately (as my mum always says, we invent something great but do not see the consequences). I assume this to be the reason why in EU it takes way more time for “new species” to be marked as safe. On the other hand, from China or USA many types of new GMO’s arrive illegally anyway. I have read that for insect resistant GMO’s you do not need so many pesticides and you generally lower the effect that the mass production has on global warming. Wikipedia also says that Greenpeace is against GMO’s but it has been criticized exactly for this.

If I ask myself about the future of all this I bet that it is the time of these technologies getting better and better and scientists making bolder and bolder changes. Once of course it might come to humans. It might be a way to treat a disease or at some point simply improve body. Now this is the point where it starts to be a bit speculative for me since I bet we might not be so far from SOME kind of human genetic modification. Because right now I think that when we compare technological and “moral” or “mind” advancement we are way ahead with the former. Therefore, I am not an advocate of immortality (when I take the point that the society is in) and also there comes all of the problems that will probably be described in the book, how people are made certain way according to certain rules which could be hazardous.


PS: All written above might be horribly wrong and that is exactly the point why I am writing it, we will see how long it will take me to learn something about genetic modification so I can bash down this post.

Peaceful dying out

today I will write about the difficulties of calculating the amount of people on Earth and demographic revolution.

For this month’s physics problems that I want to solve, I need to know how much is the number of people in the world increasing. It is just a part of the problem but necessary for the solution. One can quite easily make some simple assumptions and derive an exponential formula that is for any type of reproducing species but does not account in “human” factors. Some of those would take an effect for a population of animals or plants too of course, simply because you do not have an infinite space and other resources. Just an exponential growth would work (I think) for bacteria for example because it is simple to have enough food for LOT of them and they won’t care when they are close to each other[1].

Humanity could be assumed to increase in size in similar fashion during sometimes of its history, for example around the Industrial Revolution when mortality rapidly decreased while natality stayed the same. This did not happen across the whole globe though meaning that in most of the world we were still stagnating. In 21st century the predictions are even worse, the reason is that people in Western world are dying out, meaning we do not have enough babies. The population still increases overall but its thanks to India, Niger or other countries still in the first parts of demographical revolution, that is a part human “evolution” following the decrease and final levelling of natality and mortality. You can read more about that on Wikipedia.

Northern-Western part of the world is dying out. It is probably because people have higher education, which takes longer time and during their career they have less and less time to have and up bring babies. It is fascinating that this effect takes place even in countries with strong religion background, like Poland. I do not find it very sad though, who would think that there could be peaceful dying out?


Disclaimer: I am not a sociologist.

[1] This is actually more complicated and in a sense factually false. There are four phases to the life of bacteria colony and only the second follows what I wrote originally. In the beginning when you put bacteria into some medium, meaning place with “food”, they will start to grow individually in size. This is called the lag phase and after that follows the log phase which is an actuall explosion in the number of bacteria. Here the numbers do grow exponentionally but after they do not have anymore nutrients or there is just too much waste around they will come into a stationary phase where the population is in balance. In the end you might have the death phase but when the onset starts depends on the medium, bacteria etc. The bacteria can reach the density of several billions of cells per millilitre. That is a lot and does take some time if you start with smaller numbers but this proces CAN NOT go on forever.

Generalized bacterial growth curve showing the phases in the growth of bacterial colonies.

Generalized curve for bacteria, note that y-axis is logarithmic

Source: https://www.britannica.com/science/bacteria/Growth-of-bacterial-populations
Picture: “bacteria: bacterial growth curve”. Illustration. Encyclopædia Britannica Online. Web. 31 Oct. 2017. <https://www.britannica.com/science/bacteria?oasmId=127577>




Finally watching ISS

today I am finally going to write about my first experience watching ISS, the International Space Station. I have probably seen it before it is just that I did not realize that it is not an airplane.

ISS is a space station (biggest that humanity has) orbiting around 400 kilometers above the sea level. There is lot of interesting stuff about it but in this post, we are going to concern ourselves only with the very simple part, just seeing it.

Do not get too cocky. With naked eye, it will look like a bright star, around the magnitude of Venus at its best. It moves fast and even the best flights above your place will take maximum of about 6 minutes. From my experience, simple binoculars do not make much of a difference, though telescope could and I am yet to see how it will work out with good one, for example if I am able to track it.

Now it might not seem as much but remember, you are seeing the ISS, 150 billion $ project! The upside of it is that the station passes everyday above your place. It will always happen at sunset or sunrise, that is because the station must be sunlit but you have to be already in the shadow of Earth.

Most internet sites will recommend you the NASA webpage but it is horribly done and I will rather link to this one: http://iss.astroviewer.net/observation.php

In the case you are the type of person who uses smart phone, you can also download some app like ISS tracker.


Note: even though ISS will pass over 95% of the world population it has over every place pauses for many days. This is because the Earth is rotating under it and it takes some time before it comes to “phase” again.


Tupper’s self referential formula not so referential after all

Since the point I found about the Heart equation, which is just an equation that when you plot shows the shape of heart, I was wondering what type of pictures one could create using just math symbols. Of course, when you have function you are quite limited since there cannot be two x’s above each other. In equation, it is better since you are not limited by this but functions like logarithm or sinus are not made for drawing pictures, usually just curves. I thought that anything more complicated would be basically impossible to figure out, until I found the Tupper’s self-referential formula.

It is just completely “epic” and here is how it looks:Tupper's self referential formula plot.svg

There are two things that you might have noticed. It is a plot, that is quite simple and yeah, this formula plots itself. When I first saw I could not believe my eyes though later I found out that it is quite fake.

What you see up there is plotted function but not smoothly, rather using the mod function and bunch of rounding to get actual pixels. This is quite cool idea. You can notice one more thing, there is no number specified on the y-axis. Therefore, the function loses some of its uniqueness.

The role of this function is to convert bitmap aka picture of the size 17×106 to constant k. For this special case k is very big number, this one:

960 939 379 918 958 884 971 672 962 127 852 754 715 004 339 660 129 306 651 505 519 271 702 802 395 266 424 689 642 842 174 350 718 121 267 153 782 770 623 355 993 237 280 874 144 307 891 325 963 941 337 723 487 857 735 749 823 926 629 715 517 173 716 995 165 232 890 538 221 612 403 238 855 866 184 013 235 585 136 048 828 693 337 902 491 454 229 288 667 081 096 184 496 091 705 183 454 067 827 731 551 705 405 381 627 380 967 602 565 625 016 981 482 083 418 783 163 849 115 590 225 610 003 652 351 370 343 874 461 848 378 737 238 198 224 849 863 465 033 159 410 054 974 700 593 138 339 226 497 249 461 751 545 728 366 702 369 745 461 014 655 997 933 798 537 483 143 786 841 806 593 422 227 898 388 722 980 000 748 404 719

If you use the number in some internet program it will be reversed, so that is why the axis on the picture are reversed. Since the formula maps all possible bitmaps of the size mentioned, it is just extremely long graph containing every possible option, even itself. This is interesting in its own way though it is not anymore very “self-referential”, it is like if you would make a program creating all possibilities of 10000 characters long string. It would also contain the code itself though there is nothing special about it.

Click here to see the beginning of the graph.


Picture source: By Larske – Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=22421657


Taking closer look on Sun

today I will write about a unique mission that will go closer to the Sun than ever before (2018).

Something like 3.9 million miles will be the closest approach (should I rant about the imperial units or just convert them?). This means going through the Sun’s corona, that is the legendary region that is apparently not quite well explained, meaning, we do not know why is it hotter than the surface of the Sun, but I am no expert on that.

It is caller Parker Solar Probe, I am thinking that they named it after Matt Parker and the Parker square (anybody?). There are going to be top grade instruments on the board and these need to be carefully protected, aka. when you put 11.5 cm of carbon-composite “desk” around it, it will work.

This thing is going to be fast in its top speed, like 194 km/s, yeah that’s per second which is crazy fast. That would be less than 2 seconds to get from my home to Berlin, fun, I guess it would take some time to accelerate me to that speed (unless my life did not matter).

Another interesting thing that has an effect here and that I mentioned in other post, is that it is hard to hit the Sun since the Earth is traveling very quickly around and just because you get out of its atmosphere does not mean that you fall towards the center of its orbit. Parker Probe will use Venus to slow down to get there without such effort.



Lovely Jupiter

today I want to do a short rewrite of some posts from NASA page about things happening lately in space, simply to understand and remember them better, makes sense huh?

I have got three things, Van Allen Probes, OSIRIS-REx and Juno (I am saving that one as last since it is simply best).

Van Allen Probes are two satellites orbiting Earth in 9 hour intervals (2 000 miles per second). They celebrated their 5th year anniversary. Such a satellite must be hardened against radiation, otherwise the high energetic particles would destroy its electronics. Throughout its life, it discovered for example that there can be 3rd radiation belt around the Earth.

I already wrote about OSIRIS-Rex before. It is rare mission, first of its kind because it will optimally return samples of the asteroid Bennu back to Earth. On September 22nd, it will pass couple thousand kilometers above Earth that will speed it up so that it does not have to use so much fuel. They had to make sure that the spacecraft does not hit some other satellite that is in the Earth’s orbit, it would be quite sad if this couple hundred-million-dollar project failed even before the landing (I guess it must be in this magnitude).

If you read my blog you know about the spacecraft Juno and that it got close to Jupiter (and started the mission after the long flight). I guess I do not need to say anything when I share those (color enhanced) pictures from the eight-close approach.Juno’s Eighth Close Approach to Jupiter


Sources are just those three NASA pages.


Why do I change my mind?

I was just writing a post about Spiral dynamics and searching some resources to quote certain important bits and remind myself of things that I forgot (Spiral dynamics is a conceptual framework describing the evolution of society as well as individual). Since it is not a main stream school of thought I tried to find some criticism of it. After reading (only one) article I remembered something very interesting, why do I always change my opinion after a single piece of new evidence supporting the other side appears?

I remember very well (and I am not proud of it) how before I knew much about conspiracy theories every single piece of evidence was able to change my point of view, it got absurd after couple of times and now I have to stop and think about why is this so, why when I read about veganism let’s say (completely random), I do find why you lower your greenhouse gas emission but then in a single evidence, or even just an anecdotal saying I am back where I started. After I read exactly about the issue I go back again and again… back and forth it goes.

When I think about it I can clearly see first reason right off the back. If I do not know much about the topic before I cannot even decide what seems right and what not, I cannot simply filter out most of the crap. Also, I take an opinion after first piece of evidence and that surprises me, I could just as well hold back some time and not be surprised as much immediately. Last point is that most information, about conspiracy theory for example I take from the internet. This is very important because internet will always argue with two sides and it is just about the way that you write your question, this way you can manipulate yourself very easily (confirmation bias). In simple issues, you might find out very quickly that there are not many arguments for one side and those that exist were debunked hundreds of times.

When something is more complicated it is important to take some time.



Swap the numbers

I am reading a book from Matt Parker now. It is called “Things to make and do in the fourth dimension” and the ~200 pages that I read are quiet amazing. The author is also YouTuber and it seems that he mostly does “Standupmaths” which is cool channel. I got inspired a bit and created this game that I started to call “Swap the numbers”.

I was thinking about battery on my phone and how it is going down and that it would be interesting, if the first and second number swapped with the first after subtraction of 1,2 or 3 or more percent at a time. I wrote down bunch sequences, beginning with 100 and going down by one digit numbers.

It is not finished since I want to find a way to predict how these sequences form and I have not figured it out yet. I will give an example and then show why this game is so peculiar.

Let’s say that we subtract the number four, that is the one that I started with:

100 (subtract four) 96 (swap both digits) 69 (subtract four) 65 (and so on…) 56 52 25 21 12 8 80 76 67 63 36 32 23 19 91 87 78 74 47 43 34 30 3 -1 10 6 60 56 65 61 16 12 21 17 71 67 76 72 27 23 32 28 82 78 87 83 38 34 43 39 93 89 98 94 49 45 54 50 5 1 10 6 60 56

If you quickly go through these numbers you will find out that they repeat. When the “10” appears for the second time it starts to repeat. (I also forgot to say that if there is negative number it will act as positive on the “swap” step.) For some reason, many of these “constants” that I start with, end in lapses of “tens” meaning that after “-1” there is “10” and then that is the cycle until new “10” appears. First few numbers have the length of the cycle or lapse “36” or “12” and so far, there seems to be only “1 and 10” as constants that will pull it down to zero. (Also 100 but that is trivial and I have not checked some that could be obvious.)

I have made a program in Delphi 7 to write for me all the numbers for any given constant, that is useful but I will still have to consider the mechanism itself to start to understand it.



I have 420 likes on FB and it is completely useless

so today I reached 420 likes on my Facebook page. Page that connects directly to this blog. That is almost two times as many followers on the blog itself, after more than two years that is certainly not much but I am surprised how I got those likes on Facebook and how pointless they are anyway.


It says that I will soon reach 500 and that I should give them money so that I reach it sooner.

Since I do not post very often here, I am not preparing the posts very long time (like today), I do not get many more followers on WordPress. Most of the views come from some searches on Google and somehow people tend to be very interested in this post because it has about 7 or 8 times as much views as any other one, exactly 1,066 as of 17.7.2017. I guess most schools in USA learn about HClO4 and HClO in winter and that is why I have most views in that time of year even though it was such a long time since I wrote the post.
So, I have got 420 likes and it is completely useless. Why? Because when I share something on the page most people do not even see it on their “walls” (yes, I have an option to “market” my post for money so that more people see it which is completely absurd). Anyway 420 is a number that has something to do with cannabis and it is 42 times 10 which is nice.
420 is these numbers multiplied together: 2;2;3;5;7. Those can be accidentally also written like this:
That took me at least half an hour to come up with. The function “ceil” takes the number and rounds it up. I hope it creates the numbers correctly. Well that reminds me that you can create a game from this. I am going to do that in school. Just pick few numbers and then try to write either sequence or equation that fits it. That is actually quite endless game with lot of possibilities and variations. Maybe one could say that they will use only exponents for example though I think that it is much easier with all those other fancy functions that make the numbers “nice” like rounding up.
Well I might try another number another day.