Introduction To This Blog System

                                                                                                                                                                                    

Image used by permission

Postings may be later combined into a compound posting on this blog. Many of the postings concern my observations in various branches of science, but there are also many on technology, religion, economics and, general world issues.

I would really like to thank everyone who reads any of these blogs for your interest.

 

SCIENCE WRITING

 

Most of the postings on this blog are visits to various places around the world, and articles about such topics as history and religion. But much of the writing is about science. I do not write about what is already known but only if I can write something new, or at least a new way of looking at things.

 

If you would like a quick background in the science and mathematics that everyone should really know in the 21st Century, the posting "Scientific Literacy" provides this in about a hundred paragraphs. Similarly, "The Way Things Work" provides a quick background in everyday technology.

 

I am a Christian and I want to show that belief in God is not unscientific at all. I was interested in science long before I was interested in religion, and have never had any trouble believing that God created everything.

 

There are five major scientific theories, each arranged in the form of a textbook. The first four of the following five are on this blog.

 

"The Theory Of Stationary Space" is my cosmological theory of how so much revolves around time being explained by us being in four-dimensional space, with the dimension that we cannot access being perceived as time. This is my version of string theory, with matter actually being strings in four dimensions rather than particles in three dimensions. Everything is ultimately based on negative and positive electric charges, with energy being able to overcome the laws of attraction and repulsion of electric charges. No one has ever explained exactly what time is, and a myriad of explanations of other things fall right into place around it.

 

"The Flow Of Information Through The Universe" is about how so much can be explained by seeing how there is a limited amount of information, and it must be the same information that constructs the highest levels as the lowest levels. A ready example is how the orbits of planets around the sun is based on the orbitals of electrons around the nucleus, in the atoms of which the sun and planets are composed. This concept is extremely useful because, understanding this, we can study things that we cannot directly see by analyzing things that we can see because all must be built on the same information.

 

"The Theory Of Complexity" is about what information actually is, how energy and information is really the same thing, and how we see the universe as we do because of our perspective of being at a higher level of information than our inanimate surroundings.

 

"The Lowest Information Point" is about how, since information and energy is really the same thing and the universe always seeks the lowest energy state, it also always seeks the "Lowest Information Point". So much is explained by how the universe prefers equalities to inequalities and related ratios where the numerator of one ratio is also the denominator of the other. This explains so much from why dust particles are as big as they to why the planets and stars are the scale that they are.

 

"The Story Of Planet Earth", on the geology blog, is about how virtually every major feature of the earth's surface, both on land and seafloor, can be explained by lines of magma emergence from below that were affected by the landing of three Continental Asteroids. Many people believe that land originated from a past "super-continent", but there is no explanation of where it came from.

 

There are a few of what we could call "minor" theories, where there is not as much written as with the major theories. On this blog, there is "How Biology And Human Life Fits Into Cosmology". On the meteorology and biology blog, there is my theory of the nature of water, "Water Made Really Simple".

 

There are compound postings about science which are groupings of writing about a certain topic.

 

Scientific compound postings include, "Computer Science", "Atomic Science", "Measurement", "A Celebration Of The Inverse Square Law", "Our Solar System", "Mind-Bending Cosmology", "The Configuration Of The Solar System Made Really Simple", "In Appreciation Of Electrons", "The Science Of Human Society " and "Orbital And Escape Velocities And Impacts from Space".

 

Compound postings about history and the world include "The House Of Holy Wisdom, Where The Modern World Began", "Niagara Stories", "Economics", "How History Repeats Itself", "The Meaning Of Freedom", "The Western Hemisphere", "Our Language" and, "America And The Modern World Explained By Way Of Paris".

 

There are two compound postings about prophecies and the Bible. There is "The Aztec Prophecy" than, for prophecies that are directly made in the Bible there is "New Insight Into Bible Prophecy".

 

"Investigations" is the compound posting that is a collection of any posting about an investigation.

 

The rest of the postings are individual postings. For more detailed information about this blog, see the posting "Thanks To Readers". For general topics of conversation, see "Thoughts And Observations", on the world and economics blog.  

Other Blogs And Books

                                                                                                                               

Lights at night 

Here is a quick look at my other blogs before you start this one.

On this blog, you can see a list of all postings by clicking on the year or month to the right. But on the topical blogs, that is not the case. If you click on a year or month on those blogs, it will display the postings themselves, but the list on the right will still only show those postings that were added most recently.

To access a list of all postings on those blogs, it is necessary to click on the arrow in front of the year or month in question.

http://www.markmeekeconomics.blogspot.com/ is about economics, history and, general human issues.

http://www.markmeekprogress.blogspot.com/ concerns progress in technology and ideas.

http://www.markmeekearth.blogspot.com/ is my geology and global natural history blog for topics other than glaciers. My natural history blogs concerning the impact of glaciers is http://www.markmeekworld.blogspot.com/ .

http://www.markmeekniagara.blogspot.com/ is about new discoveries concerning natural history in the general area of Niagara Falls.

http://www.markmeeklife.blogspot.com/ is my observations concerning meteorology and biology.

http://www.markmeekphysics.blogspot.com/ is my blog about physics and astronomy.

http://www.markmeekcosmology.blogspot.com/ is my version of string theory that solves many unsolved mysteries about the underlying structure and beginning of the universe.

http://www.markmeekpatterns.blogspot.com/ details my work with the fundamental patterns and complexity that underlies everything in existence.

 http://www.markmeekreligion.blogspot.com/ is my religion blog.

 http://www.markmeekcreation.blogspot.com/ is proof that there must be a god.

http://www.markmeekphotos.blogspot.com/ is my travel photos of Europe.

On my photo blogs, Blogspot will not hold all of the photos in each blog in a straight line. To see all of the photos, you must click on the bottom posting listed on the right at the top of the blog after seeing all that there are in the initial showing. The last posting in the North America blog should be "Tijuana, Mexico" and the last posting in the Europe blog should be "Notre Dame Cathedral Door And Arc De Triomphe, Paris". Each photo in the photo blogs can be clicked on to enlarge it to full screen.

My autobiography is http://www.mark-meek.blogspot.com/

My books can be seen at http://www.bn.com/ http://www.amazon.com/ or, http://www.iuniverse.com/ just do an author search for "Mark Meek".   

Beijing

Beijing is an extremely old settlement but was established as the "northern capital" by the Mongol Emperor Kublai Khan. The Mongols established the Yuan Dynasty in China. It has remained the capital of China for most of the time since then, the Yuan, Ming and, Qing Dynasties, and then the modern Republic of China. 

Nationalist China, which is now Taiwan, had Nanjing and Chungking as capitals for a few years. Beijing is at the northern end of the Grand Canal, which links China north to south, Hangzhou is at the southern end.

The following scenes begin at what can be considered as the focal point of China, the portrait of Chairman Mao over the Tiananmen Gate. Mao proclaimed the creation of the People's Republic of China from here on October 1, 1949. But China itself is about five thousand years old. The first three images are from Google Street View.

The gate leads to the Imperial City, which surrounds the Forbidden City. This is the complex of palaces and pavilions that was the governing center of imperial China. The Meridian Gate, with protruding wings on either side, leads across the rectangular moat surrounding the Forbidden City.

In the following image from Google Street View, the Forbidden City is the rectangular area, enclosed by a moat and surrounded by the Imperial City. The Forbidden City is indicated by the red dot.

There are multiple scenes following. To see the scenes, after the first one, you must first click the up arrow, ^, before you can move on to the next scene by clicking the right or forward arrow, >, After clicking the up arrow, you can then hide the previews of successive scenes, if you wish.

https://www.google.com/maps/@39.90703,116.3913783,3a,75y,346.03h,94.56t/data=!3m8!1e1!3m6!1sAF1QipO4qafYoq5ctkBJ2_5p60j0suPX7OIvTNALVXCC!2e10!3e11!6shttps:%2F%2Flh5.googleusercontent.com%2Fp%2FAF1QipO4qafYoq5ctkBJ2_5p60j0suPX7OIvTNALVXCC%3Dw203-h100-k-no-pi4.0563016-ya117.05209-ro3.54362-fo100!7i5376!8i2688

To the south of the Tiananmen Gate across Chang'an Avenue, which is the main east-west axis of Beijing, is Tiananmen Square. Chang'an  is the old name of Xian, which was China's original capital city. In the satellite image from Google Earth, Tiananmen Square is the elongated rectangle indicated by the purple dot.

On this vast square is the mausoleum of Chairman Mao, the founder of modern China, and the Great Hall of the People. I can remember from childhood watching U.S. president Nixon's visit to the Great Hall of the People. This was the beginning of diplomatic relations between the U.S. and China. 

The first three images of Tiananmen Square are from Google Street View. The first image is the Monument to the People's Heroes and the Mausoleum of Chairman Mao. The third image is of the Great Hall of the People.

https://www.google.com/maps/@39.9053212,116.397587,3a,75y,104.52h,90t/data=!3m8!1e1!3m6!1sAF1QipOOG5ctXZlMi5Ju5hdoUAOQwoGzgRrPKhgE3Og!2e10!3e11!6shttps:%2F%2Flh5.googleusercontent.com%2Fp%2FAF1QipOOG5ctXZlMi5Ju5hdoUAOQwoGzgRrPKhgE3Og%3Dw203-h100-k-no-pi-3.3846793-ya106.78065-ro-1.528246-fo100!7i5472!8i2736

The following views begin in the middle of the Forbidden City. Does anyone remember when McDonald's restaurants used to be styled like a pavilion in the Forbidden City? I am sure that this is where the idea came from. The Forbidden City is where China was ruled from for about five hundred years, until the founding of the modern republic. The wide moat surrounds the rectangular Forbidden City. The first nine images are from Google Street View.

https://www.google.com/maps/@39.9174375,116.3975936,2a,75y,354.79h,90t/data=!3m7!1e1!3m5!1szWNCKS9Z-6EAAARGZ1vvFg!2e0!6shttps:%2F%2Fstreetviewpixels-pa.googleapis.com%2Fv1%2Fthumbnail%3Fpanoid%3DzWNCKS9Z-6EAAARGZ1vvFg%26cb_client%3Dmaps_sv.tactile.gps%26w%3D203%26h%3D100%26yaw%3D227.46472%26pitch%3D0%26thumbfov%3D100!7i13312!8i6656

These images are in the area of the Meridian Gate. The first three images of the Meridian Gate are from Google Street View.

https://www.google.com/maps/@39.9138998,116.3960387,2a,75y,110.09h,90t/data=!3m7!1e1!3m5!1siKAY8fyzXaEAAAREq-bSMg!2e0!6shttps:%2F%2Fstreetviewpixels-pa.googleapis.com%2Fv1%2Fthumbnail%3Fpanoid%3DiKAY8fyzXaEAAAREq-bSMg%26cb_client%3Dmaps_sv.tactile.gps%26w%3D203%26h%3D100%26yaw%3D115.48841%26pitch%3D0%26thumbfov%3D100!7i13312!8i6656

The first of the following images is looking at the way into the Forbidden City from the opposite direction, from the north looking southward. This entrance gate is the Gate of Divine Might, it is the entrance from the north just as the Tiananmen Gate, which has the portrait of Chairman Mao, is from the south. The door of the Tiananmen Gate is arched but that of the Gate of Divine Might is rectangular.

The two gates are aligned on an axis, which is the main north-south axis of Beijing. The gates within and to the Forbidden City, such as the Meridian Gate, are also aligned on this axis. In fact, that is where the Meridian Gate gets it's name. This north-south axis continues far to the north of the Forbidden City, along which are the original Bell Tower and Drum Tower. The north-south axis also continues far to the south, past Tiananmen Square.

The following views are actually taken from a hilltop. It is Jingshan Hill, on which is Jingshan Park. The Ming Dynasty, who built the Forbidden City, supplanted the Yuan Dynasty (Mongols) who had made Beijing their capital. When the moat was dug around it, they piled the dirt and stone on top of the ruins of the Yuan buildings, and that is where Jingshan Hill came from. The first two images, looking southward from Jingshan Hill to the Gate of Divine Might, are from Google Street View.

In the satellite image from Google Earth, Jingshan Hill is the dark green park area indicated by the yellow dot. Notice how the four dots, yellow, red, purple and white, form a straight line. This is the north-south axis along which Beijing is aligned.

Genghis Khan destroyed a city that had been in what is now Beijing, although some of the ruins of it can still be seen. His grandson, Kublai Khan, founded a city centered under what is now Jungshan Hill, but then the Ming Dynasty buried that and built the Forbidden City, in the early Fifteenth Century, just to the south.

https://www.google.com/maps/@39.9246609,116.3967602,3a,75y,90t/data=!3m8!1e2!3m6!1sAF1QipOj4lge6pPKQIv9KACt732kBSBFyct_eL67Vnk_!2e10!3e12!6shttps:%2F%2Flh5.googleusercontent.com%2Fp%2FAF1QipOj4lge6pPKQIv9KACt732kBSBFyct_eL67Vnk_%3Dw203-h113-k-no!7i4160!8i2336 

This is another view from Jingshan Hill, which looks over the Forbidden City.

https://www.google.com/maps/@39.9250992,116.3968433,3a,75y,127.58h,90t/data=!3m8!1e1!3m6!1sAF1QipPBfWXU_IebjnTbI2BKZwDqcdiW8HWSbe5WrStT!2e10!3e11!6shttps:%2F%2Flh5.googleusercontent.com%2Fp%2FAF1QipPBfWXU_IebjnTbI2BKZwDqcdiW8HWSbe5WrStT%3Dw203-h100-k-no-pi-0-ya135.09982-ro-0-fo100!7i7200!8i3600

The following scenes are to the south, south of Tiananmen Square, which is south of the Imperial and Forbidden Cities. The pedestrian walkway is the north-south axis continuing to the south. To the south of the Mausoleum of Chairman Mao, in Tiananmen Square, is the large gate, the Zhengyangmen Gate, and the Archery Tower, the stone building with the many small windows. The gates through both of them are aligned on this same north-south axis.

The white dot at the bottom, in the image from Google Earth, shows where the Archery Tower is located.

The first three images are from Google Street View.

https://www.google.com/maps/@39.8967831,116.3917578,3a,75y,180h,90t/data=!3m8!1e1!3m6!1sAF1QipNraHdxaXZLjOswZPCzJ-Va1JLjbF4UikdNLh8B!2e10!3e11!6shttps:%2F%2Flh5.googleusercontent.com%2Fp%2FAF1QipNraHdxaXZLjOswZPCzJ-Va1JLjbF4UikdNLh8B%3Dw203-h100-k-no-pi-0-ya265.09225-ro0-fo100!7i8704!8i4352

It might thus be said that the center of Beijing is where the main street, Chang'an Avenue, crosses this historic north-south axis through the Forbidden City, because Chang'an Avenue is the main east-west axis. This represents modern China meeting old China.

Remember that the city of Xian, which was China's original capital, is also called Chang'an. This keeping to the same cities since ancient times, but with the center of the city not necessarily in the same place, illustrates how Chinese history has operated. There might be a modern Chinese city, with a park in the city that has the ancient ruins of the original city.

Elsewhere in Beijing there is the cylindrical Temple of Heaven. Over here, about 4 km from the Forbidden City, most of the roofs are blue. The first three images are from Google Street View.

https://www.google.com/maps/@39.881832,116.4066627,3a,75y,85.95h,90t/data=!3m8!1e1!3m6!1sAF1QipOeVL-_KO5tCuMOddZSCOr51ad6I49igVhie8Wt!2e10!3e11!6shttps:%2F%2Flh5.googleusercontent.com%2Fp%2FAF1QipOeVL-_KO5tCuMOddZSCOr51ad6I49igVhie8Wt%3Dw203-h100-k-no-pi-7.1026053-ya319.80896-ro8.17181-fo100!7i3840!8i1920

It is interesting that Beijing has the Temples of the Earth, of the Moon, and of the Sun, and today China is one of the world leaders in space exploration. It became the first nation to land a spacecraft on the far side of the moon.

Beijing is a modern city too. This is some of "everyday" modern Beijing, around  Xidan. The first two images are from Google Street View.

https://www.google.com/maps/@39.9092895,116.3744405,3a,75y,100.63h,90t/data=!3m8!1e1!3m6!1sAF1QipOILrKQxU_gCg2eFz6tZrnVY8Kqna7ifDblugcO!2e10!3e11!6shttps:%2F%2Flh5.googleusercontent.com%2Fp%2FAF1QipOILrKQxU_gCg2eFz6tZrnVY8Kqna7ifDblugcO%3Dw203-h100-k-no-pi-0-ya177.75156-ro0-fo100!7i8704!8i4352

The district of Sanlitun includes the Workers' Stadium.

https://www.google.com/maps/@39.9334435,116.4550275,3a,75y,100.58h,90t/data=!3m8!1e1!3m6!1sAF1QipPcFhcgYBsjn1-muV5AkU4jN28L2iDbpbDeCQ4t!2e10!3e11!6shttps:%2F%2Flh5.googleusercontent.com%2Fp%2FAF1QipPcFhcgYBsjn1-muV5AkU4jN28L2iDbpbDeCQ4t%3Dw203-h100-k-no-pi-0-ya267.69604-ro0-fo100!7i7168!8i3584

Here is the central business district of Beijing. As you can see by the CCTV building (China Central Television) that China can be very creative with the forms of modern buildings, although Xi Jinping has made it clear that he is not an admirer of such architecture. The first of the following four images, from Google Street View, is of the CCTV building.

https://www.google.com/maps/@39.9182631,116.4608409,3a,75y,349.5h,90t/data=!3m8!1e1!3m6!1sAF1QipPCj_auKrdwcllbkAgM0ON9lMcIzKhb3wswxVXh!2e10!3e11!6shttps:%2F%2Flh5.googleusercontent.com%2Fp%2FAF1QipPCj_auKrdwcllbkAgM0ON9lMcIzKhb3wswxVXh%3Dw203-h100-k-no-pi-0-ya25.49999-ro-0-fo100!7i9728!8i4150

Finally, we come to the area of the city known as "Beijing's Silicon Valley". This is where so much of the development of information technology and artificial intelligence in the world is taking place.

https://www.google.com/maps/@39.9807786,116.3140596,3a,75y,102.91h,90t/data=!3m8!1e1!3m6!1sAF1QipNnefJCf9fKiI5mrNpICz_g2W6Ics4YENMDd2Vf!2e10!3e11!6shttps:%2F%2Flh5.googleusercontent.com%2Fp%2FAF1QipNnefJCf9fKiI5mrNpICz_g2W6Ics4YENMDd2Vf%3Dw203-h100-k-no-pi-0-ya106.64969-ro-0-fo100!7i5376!8i2688

The Story Of China

If you would like to review China's history, which goes far back into ancient times, there is a link below to "The Story Of China".

Remember that the reason for these weekly visits are to help us to understand each other. Growing up there seemed to be wars everywhere, in movies, in books, and in the news. God has given us all that we need to build a paradise on earth and this is what we do with it. Now that God has given me this vast audience I am going to all that I can to promote world peace, although I am well aware of the Apocalypse foretold in the Bible.

www.markmeeksideas.blogspot.com/2019/04/the-story-of-china.html?m=0

Apocalyptic Developments

This is in regard to the scenario described in the parallel postings "The End Of The World As We Know It" and "Inducing The Apocalypse".

The last arms control treaty is expiring and, for the first time in decades, there are no limits to countries building nuclear weapons.

The war in Ukraine has really revolved around drones, and is setting the pace for future drone warfare. All of the advances in technology and tactics are being worked out in this war. The weakness of drones is that communication with the base is necessary and this makes drones detectable. The communication between a drone and it's base can be jammed, or even hacked. The latest development in drone warfare is to attach a Starlink terminal to the drone, and communicate with it by Starlink. Starlink is a constellation of low orbit satellites that act as phone towers. But the ultimate in drone warfare is to have the drone guided by AI, choosing the target itself, so that no detectable communication with the base is necessary.

The Numerical Super Bowl

This week is America's Super Bowl. Our Super Bowl on this blog is the Numerical Super Bowl.

How about a great sports event? It is more universal than any championship game. It is zero against infinity.

Whenever we multiply zero by any number, zero always predominates.

Zero x 5 = zero

Zero x 13 = zero

Zero x 27 = zero

Whenever we multiply infinity by any number, infinity always predominates.

Infinity x 5 = infinity

Infinity x 13 = infinity

Infinity x 27 = infinity

So here is the question. What happens if we multiply zero by infinity? Does zero predominate or does infinity predominate?

Does zero x infinity = zero or does zero x infinity = infinity?

I have a feeling that the majority of people would choose zero. We are taught since early childhood that zero multiplied by anything equals zero. But I find that infinity actually has a few things going for it.

First is that while both predominate over finite numbers in multiplication, only infinity predominates in addition and subtraction. 5 + zero = 5 but 5 + infinity = infinity.

Second is the question of our inherent bias. The majority of people would probably choose zero. But are we really qualified to make an unbiased choice? We are much more familiar with zero than we are with infinity. We see zero all day in measurements and on digital clocks. We are only too familiar with zero in that it is what we have if we start with a certain amount of money and then spend that amount. In contrast infinity is a hazy and nebulous concept that has no practical meaning to most people. This familiarity gives us an unfair bias to choose zero over infinity.

Third is that, while zero multiplied by any number equals zero, infinity is such a vast number that ordinary rules do not apply. Parallel lines are defined as lines in the same geometric plane but which never meet. At least the lines never meet in the finite universe, but are defined as meeting at infinity.

Based on all of this I am going to go with infinity. Infinity is so infinitely vast that ordinary rules do not apply and even zero x infinity = infinity.

With infinity winning the Numerical Super Bowl, why don't we spend this week having a look at it?

Contemplating Infinity

I would like to do what I can to help anyone who has tried to contemplate what infinity is.

Infinity is supposedly a number, the highest number that there is. Yet, it is a realm in which numbers have absolutely no meaning. At the other end of the number line, zero is also a number.

This reveals something about numbers, to have meaning we have to be at a point on the scale of numbers where there are numbers both above and below us. If we have numbers on one side but not the other, at either zero or infinity, then numbers become meaningless. The definition of a number depends on the other numbers as a number is defined by what it is not, which is why each number requires another number both above and below it.

Numbers are themselves infinite, meaning that they continue indefinitely, they must be or else infinity could not be the supposed number that it is. That is at least the theory. But the limitation lies in ourselves. To be meaningful to us numbers must be manifested in some way, if only as figures on paper. A number has no real meaning until it is manifested. 

But that creates an impenetrable barrier between us and infinity. We could fill the whole universe with numbers on paper. But since the universe that we inhabit is finite, whatever number we could thus create would also have to be finite and so would fall short of infinity. To be infinite, a number must just be. It can never be infinite if it must be generated or manifested in any way.

Any finite number not only falls short of infinity, it must fall infinitely short of infinity. No matter what we do with finite numbers, we can never get even an iota closer to infinity. We can spend our whole lives multiplying numbers until we have a number that fills the whole universe, and we will be not a bit closer to infinity than when we started. If we could somehow get closer to it, then infinity would not be infinite. You can only make progress to a destination if it is a finite distance away. There can never be any common ground between the finite and the infinite.

In geometry, we are taught that parallel lines are sets of lines that are in the same plane but which never meet in our finite realm. They do, however, eventually meet at infinity. 

Parallel lines must meet somewhere. To claim that they do not is for the finite to reach the infinite. Parallel lines may never meet in the geometry textbook illustrations, or in the world, or in the universe. But infinity is so far, in fact infinitely far, that nothing finite like a pair of parallel lines can ever reach it. 

The most perfect pair of parallel lines that our universe can manifest must eventually meet. The parallel lines do not have to meet in the finite universe to which they belong. But for the parallel lines of a finite universe to reach infinity without meeting is to reach infinity by finite means, and we know that such a thing is impossible.

Another way to think of infinity in terms of geometry is as a perfectly straight line being an arc of an infinite circle. There cannot really be any such thing as an infinite circle because any arc of it would have to be a perfectly straight, and infinite, line. 

Defining a point as the center of an infinite circle doesn't make any sense either because it would have to cease to be the center if it was moved a finite distance in any direction and a finite number subtracted from infinity would still equal infinity. There is no such thing as an infinite circle because a circle must have a definite center and and the center could be defined as anywhere in the circle if there was an infinite circle.

Infinity actually can be expressed with finite numbers, but we must go to the opposite end of the number scale to do it. Any fraction with zero as a denominator is representative of infinity, such as 1/0, just as any fraction with zero as the numerator represents zero. 

Since zero contains nothing, one divided by zero must be infinity. An infinite number of zeros can fit into 1. If 1/0 was not tantamount to infinity, then zero would have to equal something and if it did then it wouldn't be zero. This reveals that a finite something is as far removed from zero as the finite something is removed from infinity. This is why we can only express infinity with finite numbers if one of those numbers is zero.

The opposite of the infinite is the infinitesimal. The infinitesimal is the reciprocal of infinity. Something that is infinitesimal is something that is just about zero. In fact, any finite quantity can be divided into an infinite number of infinitesimal divisions. Like the infinite, the infinitesimal can never be described with finite numbers. All finite numbers are just as meaningless with the infinitesimal as with the infinite. 

Just as the concept of infinity is used in geometry this concept of the infinitesimal is used in Calculus. On a curve of continuous change any point on the curve represents an infinitesimal section of change at a constant rate.

If we can apply numbers to something, it is neither infinitesimal nor infinite. Just as we are limited by the fact that we are composed of matter in a universe of space and matter from reaching infinity, we are also prevented from reaching the infinitesimal. An electron, a mere point particle with no discernible internal structure, is the closest we come to the infinitesimal, just as the entire universe is the closest we come to the infinite.

Upon reaching infinity, we would find that numbers have become utterly meaningless. If any number has any meaning at all, then we will have not reached infinity. Numbers are meaningless at the other end of the scale, at zero, because there is nothing to manifest numbers and numbers, or any mathematical entity, must be manifested in some way to be real. 

Zero does not mean the same thing as nothing, zero means there could potentially be something, which would be 1, but there isn't. Zero is not nothing but it is information that there is nothing. Neither would numbers make any sense at infinity, because no finite number could be manifested. 

If we have zero at one end of the number scale, and infinity at the other end, there should be some halfway point between zero and infinity. The obvious halfway point would be the number 1. This is because any number, denoted as X, that is between zero and infinity has a reciprocal, denoted as 1/X, that is between zero and 1.

The halfway point could also be considered to be the number 1/2, one half. First of all consider the time version of infinity, which is eternity. An eternal being, which has existed for eternity past and will exist for eternity future, will always be at the halfway point of it's existence. No matter how far into the past or future, the eternal being will still be at the halfway point of it's existence. A truly eternal being, meaning both past and future, can never be anywhere but at the halfway point of it's existence.

For another example of how the number 1/2 relates to eternity, consider the statistics of repetitive odds. If you play a game in which there is a 1/2 chance of winning, and you play the game twice, your odds of winning are 3/4. This is because your chance of winning the first play is 1/2. That leaves 1/2 remaining, and your chances of winning that one the second play is 1/2. So, 1/2 + 1/2 of 1/2, or 1/4, = 3/4. 

Now, suppose that we play another game in which the odds of winning are only 1/4, but we play it four times. The odds of winning become 1/4 + (3/4 x 1/4) + (1/2 x 1/4) + (1/4 x 1/4) = 10/16, or 5/8. Thus, the odds of winning are less than if we played the game of 1/2 odds twice. As the number of the odds game gets higher, for example the odds of 1/100 played 100 times, the odds of winning get progressively lower. But the odds of winning never go below 1/2, no matter how high the number. 

If the odds of winning were one in a million, but we played a million times, our odds of winning would be a shade over 1/2. When we get to infinity, and played a game in which the odds of winning were infinitesimal, or 1/infinity, but we played the game an infinite number of times, the odds of winning would be exactly 1/2. This is another way in which one-half relates to infinity as the halfway point one the number scale between zero and infinity.

What if the finite could be made infinite? It would mean that everything would have to exist. If the universe was infinite, there could be nothing which could possibly exist which did not exist somewhere, as long as the number of things that could possibly exist is finite.

There would have to be exact copies of our earth and solar system out there, in fact, an infinite number of exact copies of our earth and solar system. There would also have to be copies of the earth and solar system with every possible variation, such as solar systems with earth and Venus exchanging places and earths with Australia attached to the coast of Africa. This is because anything that could possibly exist, but with the odds against it, would effectively have an infinite number of attempts to overcome the odds.

THE ILLUSION OF INFINITY

Infinity isn't really a number. Saying that there is an infinite number of something isn't really an answer, even if it is the best answer that we can give.

Numbers are a tool that we use to describe the world and the universe around us. But it is also true that numbers are our own creation. We are more complex than the surrounding inanimate universe but we are of finite complexity and that inevitably shows up in the number system that we create. The way that it shows up is in our concept of infinity.

If we are of finite complexity and create a system of numbers that never ends, it will have to end in the nebulous concept that we call infinity. Infinity is a reflection of our finite own nature, rather than a real number.

I define complexity as the value of the denominator when something is expressed as a fraction or ratio. If we are of finite complexity ourselves then there has to be a limit to the numbers that we can effectively conceive of and measure. If numbers go on forever they must thus terminate in this concept that we call infinity.

We have developed numbers to describe the universe that we live in. But that universe is, as far as we know and as far as we can see, finite. Yet our numbers can go on forever. For that reason we have to perceive numbers as terminating in this concept of infinity.

We are of finite complexity, although more complex than our inanimate surroundings. If something was more complex than we are we would have to see it as being infinitely complex. To describe something fully with numbers we must completely understand it, such as we do with the calendar. We use words, rather than numbers, to describe what we do not completely understand. "Infinity" or "infinite" is actually a word, rather than a number.

To completely understand something it must be less complex than our brains. We can never describe something fully with numbers that is of equal or greater complexity than us. We may describe events as "random" but there is really no such thing as random. Like infinity it is a matter of our finite perspective.

Somewhere out there is a mathematical formula that completely describes us and our behavior. But to grasp it we would have to be "smarter than ourselves", which is impossible. We could not see the formula as being of any finite complexity, because then we would be on our way to grasping it. We would have to see it as being of infinite complexity, as we would anything that is more complex than we are.

So our sense of infinity is a matter of our own perspective and we have to perceive something as being infinitely complex if it should be more complex than we are.

An important issue with infinity is dimensions of space. We occupy three spatial dimensions, plus one that we perceive as time, and we see the space of the universe as infinite. But this could be just a matter of our perspective. If there were more spatial dimensions than we occupy then we would have to perceive it as greater distances. The universe may actually be very compact in space, but of an infinite number of dimensions. Since we can never perceive more dimensions than we ourselves occupy, we have to perceive the space of the universe as infinite.

If I had to guess the number of spatial dimensions in the universe, I would say an infinite number. That would actually be the lowest information state because it doesn't require specifying a number, because infinity isn't really a number. It is a lower information state for the dimensions to go on replicating indefinitely, and thus preferred, because it doesn't require specifying a number.

The Infinity Deception

Mathematics is supposed to be a tool to help us get things right. But have you ever wondered if some mathematical concepts might be helping us in some ways, but leading us astray in others, causing us to make poor decisions?

What about the concept of infinity, and it's reciprocal infinitesimal? Infinity means to be countless, to go on forever. Infinitesimal, which could be defined as the reciprocal of infinity, 1 / infinity, is not the same thing as zero but is vanishingly slight. The infinite and the infinitesimal are useful mathematical tools that have become ingrained in our thinking.

The trouble is that infinity and infinitesimal are mathematical conveniences that do not actually exist in the "real world". Everything is really finite, expressible in real numbers between the infinitesimal and the infinite. Infinity, and thus also it's reciprocal infinitesimal, are not really numbers. They are convenient to us only because of our own scale perspective on the universe.

This can lead us into error if we confuse what is really finite with being either infinite or infinitesimal.

Consider the following simple question. There is a drawer with ten gloves inside, five right and five left gloves. The gloves are well-mixed. Without looking, you reach in and take out two gloves. What are the odds that you have a matching right-left pair, and not two right or two left gloves?

Think carefully.

If you are like many people, you would have reflexively answered that there is an even chance of having a matching right-left pair of gloves, a 50% chance since there is an equal number of right and left gloves.

That would be correct if you took only one glove, an even chance that it was either right or left. But when you took the first glove, whether it be right or left, that left nine remaining gloves. Upon taking the second glove, five of the nine would have resulted in a matching right-left pair.

The odds are thus 5 / 9, which is better than even.

Only if there had been an infinite number of gloves, with each glove thus being infinitesimal, would there be a 50 / 50 chance of taking out a matching pair. The reason that the reflexive answer would get this wrong is that the set of gloves is finite but we react as if it is infinite.

An important tool of geometry is the point. A point is an infinitesimal dot that is defined only by it's location, so that we might say "From point A to point B. But, once again, such an infinitesimal point, as ingrained as it is in our thinking, is a mathematical convenience that does not actually exist. It is so easy to think in terms of the infinite and the infinitesimal but it can lead us into error.

Suppose that a spacecraft is in orbit around the center of gravity of a planet. That would be easy to describe mathematically because the center of gravity of the planet is fixed point, right?

Actually wrong. The center of mass of the planet is fixed but the center of gravity, from the perspective of the spacecraft, is not. The location of the center of gravity depends on the distance of the spacecraft from the planet.

With the spacecraft at a finite distance from the planet, the closer side of the planet has a stronger gravitational effect on the spacecraft than the further side. This means that the center of gravity of the planet, from the perspective of the spacecraft, has to be closer to the spacecraft than the planet's center of mass, and is further from the center of mass the closer the spacecraft is to the planet.

Only if the spacecraft were at an infinite distance from the planet would the center of gravity be exactly the same as the center of mass. Once again, it is easy to reflexively confuse the finite with the infinite and infinitesimal. The reason here is that the planet is not an infinitesimal point. It has a volume of it's own so that the near side is closer to the spacecraft than the further side.

Here is another question. Over the course of a year the length of day and night must even out so that each average 12 hours, right?

It is tempting to answer "yes", but if we define day as being when the sun is visible over a flat horizon then we again encounter the difference between finite and infinitesimal.

If the sun were an infinitesimal mathematical point then the answer would be "yes". But the sun has a diameter of it's own. It's angular diameter is about 1 / 2 of a degree. This means that, with the visibility of the sun being the definition of a day, day must be about four minutes longer than night.

So much about how the difference between the infinitesimal and the finite can lead us into error. What about the difference between the infinite and the finite?

In mathematics, infinity is a mystical place where parallel lines are defined as finally meeting and odds are obligated to even out. What I mean by odds "evening out" is that, if the odds of something happening on each try is 1 / 20, the results are obligated to be exactly that only if we go through an infinite number of tries.

The trouble with gambling is again that infinity is a mathematical convenience that does not actually exist. If a gambler has played a game 19 times, without a win, and it is known that the odds of winning the game are 1 / 20, then the gambler may feel "due" for a win.

Casinos must absolutely adore people who are sure that they are 'due" for a win. But in a game of pure chance, with no skill involved, the established odds are only obligated to "even out" if there is an infinite number of tries. In any finite number of tries, there is no obligation whatsoever for the odds to "even out".

Suppose that the intrinsic odds of winning at a game are 1 / 20. A gambler has played the game 19 times without a win. The gambler must thus be "due" for a win on his or her next try, right? This is commonly referred to as the "Gambler's Fallacy".

If you answered "yes" then you are the kind of person that casinos were made for. But there is no obligation for the odds to "even out" so that the twentieth try will be a win. No matter how many losses there have been in a row, the odds of winning the next one are still only 1 / 20. That is true for any finite number of tries. Only if the game were played an infinite number of times would one out of every 20 tries have to be a win.

Unfortunately, infinity is a mathematical convenience that does not really exist. But there are people in every casino who really believe that the rules of the infinite must somehow apply to the finite.

I have used gambling as a simple example. But the confusion of the finite with the infinite or it's reciprocal the infinitesimal goes far beyond gambling. Suppose that an employer is very selective of potential employees and overall only one out of every twenty applicants that are interviewed is hired.

One day the human resources manager is amazed at his good fortune. He has just interviewed three outstanding candidates in a row who clearly qualify for the job. This has been much better than interviewing for an entire day or more just to find one good candidate.

But then the human resources manager stops to think. How can this be possible? If thus far only one out of 20 candidates has qualified for the job then how can I possibly get three in a row? This is against all the odds and so I must have had poor judgement and have been too lenient with the candidates.

This is, of course, the reverse of the Gambler's Fallacy. There may well have been three qualified candidates in a row. Even if the overall odds are established as 1 / 20, there is no obligation whatsoever for those odds to "even out" in any finite set of candidates. Only in an infinite set of candidates would exactly one in 20 have to be qualified. Once again we see how confusing the infinite with the finite may lead to poor decisions.

Here is an old trick question. Don't feel bad if you get it wrong because you will have plenty of company. When we flip a coin it has an equal chance of coming up as heads, H, or tails, T. If we flip the coin 8 times, which of the following sequences are most likely to occur?

HHHHHHHH

THHTHTHT

THTTTHTH

The answer is none of them. All three sequences, and all other possible sequences, have an equal chance of coming up. In any finite sequence there is no obligation for there to be an equal number of heads and tails.

Next question. You operate a business in a city state that prints it's own currency. What would be a good way to estimate the amount of currency in circulation?

Record the serial number of every bill that comes through the business, in order of when they came through. Count how many bills pass through before the same serial number comes up again. Multiply that by two because once you have the serial number, and send the bill back into circulation, the odds exceed 50% that you will get the bill again when half the bills in circulation have passed through the business. Multiple readings taken, and then averaged together, would give a more accurate picture of the number of bills in circulation than just one reading.

But there is still the chance that a bill will come through the business and give an estimate that is well out of the scope of how much currency is actually in circulation. This is what I refer to as either a coincidence, making it seem that there is less money in circulation than there actually is, or a reverse coincidence, making it seem as if there is more money in circulation than there actually is. Only with an infinite number of such measurements would a truly accurate picture of the currency be certain.

Infinity is where parallel lines finally meet, odds even out, and there are no coincidences or reverse coincidences.