Wednesday, March 31, 2021

Wednesday, March 24, 2021

How Far Can We See From A Height? Can We See A City at 10,000 Metres?

 

Dear Captain Lim Khoy Hing

 

How Far Can We See from a Height? Can we actually see a city from a plane flying at 10,000 metres?



Before I ask my question, I have done some home-work to come out with some data first to determine visibility of a place on ground from a height, and also the distances between two locations along the curvature of the Earth. My explanation first, and my question comes last below.


The Explanation:



The distance d in miles to the true horizon on earth seen from a plane or from any height is approximately:


First Equation:

 

d = ?? (1.5 h), where h = height in feet of the eye (?? = square root)

This is a very simple formula which is applicable from most heights. Thus from an aircraft flying at 33,000 feet, then the distance to the true horizon seen by a pilot or a passenger is 222.485 miles (358 km) away.

 

Standing on a hill or tower of 100 feet high or even from an aircraft, the height (h) is much smaller than the equatorial radius (R) of the Earth of 3963.189 statute miles (6,378.135 km).


The exact formula for distance from the viewpoint to the horizon, applicable even for satellites, is:


Second Equation:

 

d = ?? (2Rh + h2), where, (?? = square root)
d = distance is also the true distance to the horizon from a height
R = Equatorial radius of the Earth (6,378,135 meters)



Applying the second equation, the horizon seen from an aircraft flying at 10 km high would also be 357.299 km (222.0154 miles) away.

 

The calculations using the above two formulae give the straight-line distance from the plane cockpit, passenger pothole, or a hill to the horizon, and NOT the distance to the horizon along the ground which would be longer for low heights such as seen from a hill.



In the second equation, both the radius (R) of the Earth, and the height (h) of the observer must be given in the same units (e.g. kilometers), but any consistent units will work.



The above two formula for d is only for the straight line of sight distance to the object of view, say the horizon.



A different relationship involves the arc length distance s along the curved surface of the Earth to the bottom of object. In this case, we apply:




The Third Equation:



l = cos-1 [r ?? (r + h)] x [2?? r ?? 360]

(?= square root)

where,

l = the distance from the observer to the horizon along the curve (Great Circle) of the planet (Earth), along the ground
r (equatorial radius of Earth) = 6,378.135 km
h (height of plane) = 10,000 metres (10 km)


(r+h) = 6388.135 km
r ?? (r+h) = 0.998 434 597
Circumference of Earth (2?? x 6378.135 km) = 40075 km
2?? r ?? 360 = 111.3194559 km
Cos-1 [r ?? (r+h)] is the angle in degree between the observer and the horizon, measured from the centre of Earth = 3.206324 degrees

 



Thus at an altitude of 10 km (33.000 ft) or 6.25 miles, the typical ceiling altitude of an jet airliner, the actual arc length (l) along the curved surface of the Earth to the bottom of an object (say a town) is 356.926 km (221.78 miles) away.

 

 

The distances along the curvature of Earth for low heights less than that of a jet plane at 10,000 meters, it would be greater than that of a direct line-of-vision. The ceiling altitude of 10 km of a jet liner is about the limit where the straight line-of-vision of a pilot to the horizon slightly exceeds the actual arc distance measured on the ground.

 

However, several calculations using varying measurements for the radius of the Earth showed that the differences were less than a kilometer provided the observer did not fly above that of a commercial jet plane.


The Limit of Comparative Distances:



At much further distances, say 150 - 300 km away as seen from a satellite, or even further out as seen by a space traveler from outer space, say from the Moon, and the extra distance due to the curvature of the Earth will become less and less significant compared to the greater and greater distances or height away from the Earth.

 

As an observer recedes into outer space, the distance to the horizon continue to increase until it far exceeds even that of the entire circumference of the Earth, let alone just a small extra arc of the curvature. The observer could be light-seconds, light-minutes, or light hours away, while the entire circumference of Earth is just only 0.133 light second round, if light could whip around the Earth.



But for low heights, such as from a small hill, a tall building, a low flying plane, or from a watch tower, the extra arc distance along the ground to the horizon would always be greater than that of a straight line vision from above.



Actually the visual horizon is slightly further away than the calculated visual horizon, due to the slight refraction of light rays due to the atmospheric density. There may be also the effect of mirage playing tricks on the eyes, lifting an invisible distant city above the horizon.



1 statute mile = 5,280 feet = 1,609 meters



Geographical Locations of Cities:



Location Longitude (E) Latitude (N)
Penang 100 0 15 50 25
Phuket 98 0 22 80 0
Kuala Lumpur 1010 41 30 9
Singapore 1030 51 10 17



Distances between Neighboring Cities:



Using the above geographical coordinates, and applying spherical trigonometry or the Haversine formula, the shortest distances along the curvature of the Earth between Malaysia and neighboring countries are:



Kuala Lumpur - Penang: 297.9 km = 185.1 statute miles = 160.8 nautical miles
Kuala Lumpur ?C Singapore: 318 km = 198 miles = 172 nautical miles
Penang - Phuket (South Thailand): 354.64 km = 220.36 miles = 191.49 nautical miles


The Question Now:



Having calculated out the distances along the Great Circle of some of the towns and cities between Malaysia, Thailand and Singapore, and we have shown that are within the theoretical distances that can be seen from an aircraft flying 10,000 metres above the ground, can we actually see Penang and Singapore from Kuala Lumpur, or Phuket above Penang from a plane flying at 10,000 meters over these areas? We presume there is no blanket of cloud cover, and that the weather is perfect with visibility up to infinity?


Frankly, I have never been able to locate where the horizon is whenever I fly. All I saw were just sheets, and sheets of thick white clouds below, and they stretched as far away as I could see. I seek your valuable experience and your expert comments.


Thank you Captain.

JB Lim
Malaysia



Hi Dr JB Lim,


Thank you for the explanation on how to calculate the visibility of an object on the ground from a particular height. Yes, pilots have been using the same formula (First Equation) to work out the line-of-sight distance, not so much to look at any particular object, but to find out the range when they could start to receive a VHF radio transmission.


You see, VHF (Very High Frequency) radio transmissions travel in a straight line and could not bend or follow the curvature of the Earth like the HF (High Frequency) transmission could.


The latest weather of a particular airport is provided by the ATIS (Aerodrome Terminal Information Service) transmitted on VHF. When I am flying at 35,000 feet, I know that at around 220 nautical miles, I would be able to receive the latest weather from the ATIS of an aerodrome.


In this sense, the formula you used to calculate the line of sight distance is useful. As to actually see a city from 220 nautical miles at 35,000 feet, it is not always possible to do so even if the visibility is up to infinity (due to traces of haze or the effect of oblique visibility).


Perhaps, at night, one may be able to see the lights of the cities on a good day when the weather is perfect, but otherwise, just like you, I would see sheets and sheets of thick white clouds below me most of the times! However, if the cities were in the range of around 100 nautical miles, I probably could see and recognize them in the horizon (crosschecking with the radar on board if needed!)

Sunday, March 21, 2021

Our Life Purpose on Earth

 

Our Life Purpose on Earth


I write this thought below in reply to a question sent to me by my former course mate Dr. Janet on her and on her colleagues’ behalf.


My answer: 


Thank you Dr. Janet for your email and long list of technical questions  

 On your first question, no, I did not get your previous email. Which email address did you use?

  I have many email addresses previously that cannot be used anymore. It is best you use the current e-mail address you sent, or WhatsApp or text message me the next time to alert me for future communications.

Yes, on your e-mail question you shared with others, I really do not know the answer Janet. For instance in question 7 you asked on your list, I have been wondering myself the purpose of our physical existence in this world

Here’s what’s I feel and can share with you

 

Our Purpose in Life:


We were born into this world, go to school, onwards to college or university, look for a job or some kind of a livelihood, get married, have a family, then we die off, leaving completely everything behind us, and let our children take over to do exactly the same aim and objective  generations after generations.


If the Creation of the Universe through the Big Bang was 13.8 billion years ago, and if our human life span at maximum last for a 100 years in comparison, then it is only (7.2 x 10-9) or 0.0,000,000,072 of this, and only 2.2 x 10-8, or 0.000,000,022 of a fraction compared the creation of Earth 4.543 billion years ago.


Another way of putting this is, if the age of the Universe at 13.8 billion years was just one day of Creation, then 100 years of our lives lasts for just 6.3 x 10-4 second (0.00063 second)

But if the age of Earth at 4.543 billion years was just one day in Creation, then 100 years of our lives last just 1.9 x 10—3  second (0.0019 sec) or 0.002 second 

 

Mankind has been doing this for a few hundred thousands of years after his existence and agricultural life in this world.

 

But what is their aim, objective and purpose for this repeated cycle in life most of us may not have not much of a clue

 

The uncanny feeling I have here is there must be some other purpose for our existence than merely to enjoy life as your colleague Prof Dr. NC Tan thinks which of course I highly disagree.


My feeling is there must be a very much higher purpose of our flickering and extremely short biological and physical existence in this world. We shall discuss this as I write on. But first, let us understand just a little bit on astronomy. Let’s begin with the size of this world of ours.


Size of this World:


I have written a tiny bit on this earlier in my blog here:


 https://scientificlogic.blogspot.com/search?q=grain+of+sand

 

But let us illustrate this in another way.

 If we take the Earth radius from its center to a point on its surface, its dimension is from a near maximum 6,378 km at the equator to a near minimum 6,357 km at the poles.

If we consider the distance from equator to pole along the circumference as 10,000 km, its radius is roughly 6,367 km, somewhat close to halfway between the minimum and maximum.

Normally for all astronomical calculations we consider the Earth’s radius as 6,371 km with 0.3% variability (+/- 10 km) for various reasons we shall not go into.

Let us now consider the size of the Sun. Its solar radius is defined as the radius to the layer in the Sun's photosphere where the optical depth which is 2/3 of its layer.

Without going into the complexities of its structure we would put the value of its radius as:

6.957 x 10^5 km or

 = 6.957 x 10 5 km = 695,700,000 metres.

 Hence its volume V is:

4/3 π r= 1.41 x 1027 cubic metres.

 The volume of Earth from her radius = 1.08 x 1021 cubic metres

 Hence, volume of Sun-Earth ratio = 1,305,000

 The Schwarzschild radius (2GM / c^2) of the Observable Universe is 13.7 billion light years or 1.3×1026 m

 (1 light year = 9.461x 1015 metres).

 Hence its Schwarzschild volume is 9.1 x 1078 cubic metres.

In other words, 8.4 x 1057 (84 followed by 56 zeros) Earths can go into the volume of the Universe while 6.45 x 1051 (645 followed by 49 zeros) Suns can enter into the Universe.


Number of Worlds:


 Now let us look at our Solar System and other stellar systems. Our Solar System has 8 planets – Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune and a number of dwarf planets including Pluto, Eris, Ceres Haumea and Makeke. Let’s put the number as 10 for convenience.  

 

Our own galaxy, the Milky Way, is a large disk-shaped barred-spiral galaxy about 30 kiloparsecs in diameter and a kiloparsec thick.

 

It contains about two hundred billion (2 x 10 11) stars and has a total mass of about six hundred billion (6 x1011) times the mass of the Sun.

 

Some estimates put the numbers of stars in our Milky Way Galaxy as 150 – 250 billion (1.5 x 10 11 – 2.5 x 10 11).

    

We do not really know how many galaxies are there in the Universe. Various estimates among different experts have been given between 100 billion – 250 billion.

 Some estimates have put the numbers as high as two trillion galaxies in the Universe. Most of the estimates were based on studies from the Hubble Space Telescope. An acceptable range is between 100 billion and 200 billion galaxies.

 Let us use just one rough estimate for the sake of easier understanding and calculation. We shall scale this down to just 200 billion stars in our Milky Way Galaxy, and equal number of 200 billion galaxies in the Universe.

Since we really do not know how many planets (exoplanets) are there in each stellar system, we need to use our Solar System as the sole example. We may roughly say instead of 8 planets, there are 10 including dwarf planets asteroids or minor planets and planetoids in other stellar systems.

 We shall for easy calculation, we shall use one out of ten planets in each stellar system that is exactly like Earth that harbors life. However in most stellar systems the picture may be entirely different

 They may have much more than 10 exoplanets or less circulating around each star, but we have no idea how many are Earth-like planets that can harbor life as we know it on Earth.

 They may even have not just one Earth-like planet, but a group or a family of them at equidistance from their star, but spaced apart among them in their star system all within what we call a habitable Goldilocks Zone where it is neither too hot, nor too cold  that can support life.  We just do not know what’s out there in such an unspeakable immensity of this Universe.

 In 1961  Frank Drake, an American astronomer and astrophysicist wrote out an equation to stimulate our thought, not just on the existence of life in an Earth-like exoplanet outside our own, but even intelligent civilizations. He wrote out his equation during the first scientific meeting in the search for extraterrestrial intelligence (SETI). But we shall not go into the equation.

 Let us presume a very modest average of just 200 billion stars in our Milky Way Galaxy and a modest average of 200 billion galaxies in the Universe, and assuming we only have one planet we call it as an exoplanet in each stellar system that has life on it similar to Earth within its Goldilocks Zone, then this works out to be:

= 4 x 10 22 (40,000,000,000,000,000,000,000) Earth-like worlds in the Universe.

 This estimate is just a very, very modest number so as to be within our human comprehension


Possibilities of Far More Beautiful Worlds:


Given this very humble estimate on the numbers of Earth-like worlds in heavens, if you were to ask me, I am very convinced there may be far, far more advanced and far more beautiful worlds out there that we have no idea.

 There may be worlds out there where there is no pain, no suffering, no illness, and where there is no death unlike us here. I really do not know because so far we have not detected the existence of any life in other planets, or do we have any acceptable definition of life or something living out of more than 100 definitions being offered.

If our sole purpose in life on Earth is merely to enjoy life in this world from birth-to death for a maximum of 100 years life-span then vanishes away into the soil from where we came as star-dusts without any more memory of past enjoyment, this to me makes completely  no sense or for any purpose.

On your question Janet on what are our requirements here. 

My answer Janet is, we are so unique and inimitable because throughout the evolution of life on Earth since the Cambrian Explosion 542 – 488 million years when most life on Earth suddenly bloomed peacefully like flowers in a field overnight, we are the only one that emerged much later who requires more than just food, and unable to live in peace with each other.

 

No other life in the open fields requires houses and large bungalows too, cars, transport, telephones, televisions, computers, or worry about the type of clothes we need to wear or the food we must or must not take …etc. down the material list. If they need shelter they will just burrow into the sand, mud, or find a hole in among the tress or live in a cave without the need for cement, concrete, bricks and steel or anything that destroys their simple habitats like we do.     

No other species of life demands any of these yet God feeds and take care of all of them including the birds in the air and the lilies in the fields until they live out their natural lives. But for humans we cannot survival without these demands. We are truly very exceptional, very unique and biologically the only animal of its kind among an estimated 10 million other life forms God created  


Spiritual Purpose:


What then is a purpose in life for us at a maximum of 100 fleeting short years is, we need to answer ourselves. There must be a much higher spiritual purpose outside our biological existence merely to breed, feed, consume, enjoy life, and die off.

 “Let us eat and drink, (and be merry) for tomorrow we die.” (Isaiah 22:13)

First of all, we have neither the knowledge, wisdom nor the vision to fathom across the physical and material dimension of this world other than eating, drinking and be merry before we die. In short we live here like a frog-in-a-well.


Spiritually Blind in a Physical World:


Without this wisdom and vision, far as I know we are the only species of life on this tiny-tiny world that is multiplying, consuming, destroying, congesting and polluting and also who fights and goes to war to kill and destroy each other for neither any biological purpose  nor spiritual gains. No other animal on Earth, an estimated 10 -12 million other species of life on this planet does the same as us. We are very unique. Most other animals fight or kill solely for food but we fight for no rhyme or reason other than to support our rights and egos.


We may be highly knowledgeable and intelligent in science, technology, in medicine, and in all other knowledge and information technology existing in this physical dimension because we currently exist in this physical world but in this dimension we are spiritually blind because the spiritual world belongs to another dimension we cannot cross over till until our spiritual body leaves our physical body.

In such a scenario the existence of spiritual worlds in heavens is blind to us as we see everything now darkly through a glass. We are the only creature of creation or from evolution on Earth that makes us so very unique, with no purpose here except our biological and physical existence.

 We are the only one of its kind as a thinking, intelligent and social animal zoologically speaking. You may be tempted to ask what then is the purpose of other life forms on this planet. You may be excused to answer all other animals and life species do not have the same thinking brain as we to be able to ask and answer this question.

 However, as far as I am guided in answering to honor and to worship our Creator I have a different answer.

 My guided thinking for the purpose of this vast diversity of life on this world is to clearly show us there are also as many other types of life and civilizations elsewhere among the estimated 40,000,000,000,000,000,000,000 Earth-like worlds in the Universe as there are life forms in this world – a credit I wish to adore and worship my Creator.

 In short, other types of life and civilizations exist throughout the immensity of heavens as much as we have the vast biodiversity in this world. That’s somehow my uncanny guided answer.


A Lesson in Bacteriology and Cancer Biology:


 In what manner is our purpose in life if we are not only in constant conflict with each other, but  multiples like cancer cells only to consume the limited resources available like petroleum, gas, coal, energy, water, given to us, and use them to construct buildings, factories, houses, cars, trains, planes to congest and pollute. 

 Our existence here is not just like cancer cells that finally kills the entire body, similar to killing all life on Earth, but similar to colonies of bacteria cultured in a Petri dish that begins with a lag phrase of no growth, then a sudden accelerated logarithmic growth rate, then stabilizes its population or colonies, before finally all die off due to depletion of nutrient (food shortage), lack of space, and accumulation of toxic waste (pollution).

 That’s exactly also the physical purpose of our existence for most people in this world as far as I can see. We are just like a colony of bacteria in a Petri dish watched by a bacteriologist outside his culture dish.

 In the laboratory of a scientist, he may have countless other empty culture plates lying around that he did not culture any bacteria on them, but among these empty culture plates he has placed many other life cultures nearby as much as we think this world is the only planet that is teeming with life while other worlds are all devoid of life. That’s what we think. Remember the figure of 40,000,000,000,000,000,000,000 or 40,000 billion, billion Earth-like worlds in the Universe or heavens in spiritual term

 On this Earth as our culture plate, not only consume, congest and pollute to destroy the entire eco-environment meant for other life species that too have the right to be here, but we also use all the resources to increase our population to construct bombs, biological weapons, missiles, rockets, guns and weapons and store them as arsenals of all sorts ready to destroy ourselves and others. This is our political purpose.

 Even for the peaceful but selfish needs our purpose is to build and destroy the natural environment, and in so doing, we are also destroying the existence of other species of life by destroying their habitats. What rights have we?

 What then is the purpose of life here when Earth is the only dwelling place we have? There must be a much higher purpose of our existence blind to most people because we are all teeming like frogs inside a well. No other life forms out of the 10 -12 million others are as destructive, exclusive, and distinctive as we.


Evolution of Life:


 Life goes into a chain of cycles. The largest and strongest of life preys on the weakest solely for food, while we have no larger and stronger predators except the most primitive and the smallest bacteria and viruses here to stay. Bacteria and viruses were the first to emerge 4,000 million years ago when the first prebiotic chemistry became possible.

Three thousand eight hundred (3,800) million years ago RNA world shown by the first chemical fossil became available as viruses, and 3,600 million years ago the first DNA protein life came into existence. We were the last to emerge, but we shall also be the first to be wiped out from the surface of this planet. As far as I understand most of us have no purpose here.

 The humble bacteria and viruses shall be the last to exist when the Sun runs out of nuclear fuel. We shall go into this later.


Emergence of Humans:


 I strongly believe the first true human created was Adam and Eve as given in Genesis.


However from the anthropological point of view as scientists see it, primitive hominids so unlike Adam and Eve may have existed about 1.8 million years ago when Homo habilis emerged out of Africa, and 1.6 million years ago Homo erectus was found in Asia, 600,000 years ago Human / Neanderthal spilt, 500,000 years ago Homo erectus use fire, and 355,000 years ago Homo heidelbergensis footprints were found, while 200,000 years ago anatomically modern human emerged, followed 250,000 – 160,000 years ago when we found the emergence of Homo sapiens. 

Since 120,000 years ago Homo language may have been possible. The earliest civilizations developed between 4000 and 3000 BCE, when the rise of agriculture and trade allowed people to have surplus food and economic stability. 

 What was the purpose of that human emergence, it is best I leave it for others to answer?   


Early Civilizations and Wars:


 The earliest civilizations developed between 4000 and 3000 BCE, when the rise of agriculture and trade allowed people to have surplus food and economic stability. 

Ever since the time of Mesopotamia, there was constant strife and war.  Even after Sargon the Great of Akkad (around 2334 - 2279 BCE) unified region under the Akkadian Empire, war was still waged, perhaps mainly against rebellions or fending off invaders. In the Early Dynastic Period of Egypt (c. 3150-c. 2613 BCE) war too started when the Pharaoh Manes of the south conquered the region of northern Egypt.

 In China too during the Zhou Dynasty battle was recorded in 1046 BCE within the Warring States Period around 476-221 BCE, and was resolved when the State of Qin defeated the other contending states in battle and unified China under the rule of Emperor Shi Huangdi around 221-210 BCE.

 Ever since all the way down the history of mankind we have been fighting and fighting against each other till the last one Iraq War and Insurgency between 2003 to 2011 beside World War II from 1939 to September 2, 1945.


Wars rained on us from Above:


 "When the Lamb broke the fourth seal, I heard the voice of the fourth living creature saying, "Come." I looked, and behold, an ashen horse; and he who sat on it had the name Death; and Hades was following with him. Authority was given to them over a fourth of the earth, to kill with sword and with famine and with pestilence and by the wild beasts of the earth"

(Revelation 6:7 -8)

 A third of the population of the earth would be killed by these four angels and the army which they lead (Rev. Rev. 9:16-18). Death will come by three means: fire, smoke, and brimstone. See commentary on Revelation 9:18.

 The trumpet judgments share a pattern of affecting one-third of what they target. In the first trumpet judgment, a third of the trees were burned up (Rev. Rev. 8:7). In the second trumpet judgment, a third of the sea became blood, a third of the creatures in the sea perish, and a third of the ships were destroyed

 (Rev. Rev. 8:8-9)

 "And the four angels who had been kept ready for this very hour and day and month and year were released to kill a third of mankind."

 (Revelation 9:15).

 

 We are the only creature on this planet that goes to war, while a Creator above is to kill us as given in some of the many biblical verses. In contrast all other creatures that live their lives peacefully are hardly attacked by pestilence and pandemic like we do. We are unique, very irreplaceable indeed.

 

Why Only Us: 

 

It is little wonder to me why the diseases and pandemics like SARS-Covid-2 and all other ancient and past plagues, famines, and pestilences befall only upon us as prescribed by an Intelligent Designer from above as given in Revelation 9:15, while the meek and humble viruses below created also by the same Intelligent Designer chose not to attack or touch any other species of life in this world?

 You need to ask both Prof Tan and Dr. Susan Lee for the reason since they claim our purpose here is just to enjoy life, when they are blind to the untold myriads of other worlds out there in this horrendous immensity of this Universe.

 If we think we are the most adapted, the most advanced form of life socially, economically, scientifically, technologically, and the strongest among all other species whom we can take advantage and for granted, why then are we so afraid of this SARS-Covid-2 virus that is the smallest and the most primitive down here that is at war with us? In truth biologically we are the weakest and least adaptable among all other life because we cannot survival without having all the material things already described

 All other animals are being attacked by larger predators only for food, but ours exclusively by a tiny- tiny virus to get rid of us is my personal answer. 

 Perhaps we are the most complicated species that needs to be periodically cut down for the benefit of all other life that too have the right to exist on Earth.


How Long More: 


 The life span of our Sun like most other stars shown in the Hertzsprung–Russell diagram has about nine or 10 billion years. The Sun is about halfway through her life's journey and is now about 4.603 billion years old. It is destroying itself at a rate of 4,000,000 metric tons every second with an energy output of 3.8 x 1026 Joules per second so as to sustain all life on Earth. So this time given to us is more than ample for us to think this over while the Sun still shines for our existence.

 If we think this thinking of mine is not for you, or good enough for you or for others, you need to ask someone else with better spiritual vision  


My Personal Answer:


But if you were to ask me what my personal purpose in life is, I will straight away tell you, I have been sustained long enough so that I can be guided by His infinite wisdom and power of His Creation for my existence to pen this article as my personal answer.

 

I shall write to you again in greater details Janet to answer your other questions as I not slept the entire night 


Thank you again for your personal communication.

  Kind regards to you and to all your elite and knowledgeable friends and colleagues out there in your chat group.

 Good Morning to you, and have a pleasant day.

lim ju boo 

 

 

 

 

 

 


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