Peaceful dying out

Hi,
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?

Dragallur

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>

 

 

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Endless games (almost)

Hi,
in this post I will write about two games that are under some conditions basically endless. If you play them normally you will win quite easily but there is version when you can play for billions of years, literally.

The one that is quite famous example is the Tower of Hanoi. In this “board” game you have three wooden rods. The first one has thin slices of wood on top of each other. The objective is to move the slices one by one on the third rod such that you lift only one piece at a time and bigger one is never on smaller one. Since these are quite simple rules you can quickly find out the best algorithm and its length. Here length means each turn of lifting piece and putting it down. The number of turns based on the number of pieces (n) is 2^n-1. This is exponential growth of course. This game is tiedwith one story about monks moving 64 of these disks. 2^64-1 = 18 446 744 073 709 551 615 which is a lot and even if you moved one disc per second you can extrapolate that this would be much longer than the age of Universe. Actually the story says that when they finish, the world will end which will apparently take some time but it is far less than what we would call the end of world like Big Freeze.

The second game might be a bit surprising at first. It is 2048. This game is played on usual 4×4 platform (it is computer game). You connect same numbers together to get bigger and bigger ones but only 2s (rarely 4s) are spawning. You need two 2s o get 4, two 4s to get 8, two 8s to get 16 and so on and you lose when you do not have anymore space. This is also exponential growth and to finish the classical game you need to make roughly 1024 moves. It can be played longer and the max you could theoretically get is 131 072 which takes about 65 536 moves. This would still be playable if you did not count in the probability of the last turns happening. Such a game would have a gameplay of several hours. On the other hand, here for example you can play on 8×8 field. This is just a derivative of the original game. Here it takes of course the same amount of moves to get to 2048 but the interesting thing is that you can go on from there. Actually, I would find it hard to believe that in serious 8×8 game anybody ever lost simply because it is so big and the biggest number that can fit there is 2^64 [1]. Half of that is the amount of moves you would have to make… here we are again at the Tower of Hanoi…

This is pretty simple, just exponential growth.[2]

Dragallur

[1] It is actually 2^65 since 4 can spawn too, but you have to be lucky.

[2] Try the game on this link if you are not sure how it works.

Finally watching ISS

Hi,
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.

Dragallur

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

Hi,
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.

Dragallur

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