6 Jun 2021

5th Dimension Explained - Fifth Dimension Explained - Higher Dimensions Explained

Here I'll explain the 5th dimension in detail. In this article you will understand- What we mean by a 5 dimensional space and How we can visualize the fifth dimensional space geometrically. It also answers, Why the researchers think that there must be a fifth dimension and why they needed the 5th dimension. It also covers why the fifth dimension cannot be observed directly by humans and most importantly, What is the scientific evidence for the existence of the fifth dimension?
You will also get familiar with the supernatural powers that a person living in the fifth dimension would have and the limitations of the fifth dimensional world that are not present in the dimensions higher than the 5th dimension. 

Fifth Dimension Explained (Advanced)


 

Friends now I will answer each of these questions about the 5th dimension one by one- 

What we mean by a 5 dimensional space?

As clear by the name, a five dimensional space is a space having five dimensions. But you may ask what is a dimension?
Actually Dimension of a point is defined as the minimum number of coordinates that are needed to specify that point in it.
So to represent a 5 dimensional object we need 5 coordinates.
For example to represent a straight line we need only one co-ordinate that is length, therefore it is one dimensional. To represent a surface we need 2 coordinates- length and width, so it is 2 dimensional or 2D. In the same way 3 coordinates are needed to specify a solid object these are length, width and height. Therefore it is called a 3 dimensional or 3D object.
Similarly 5 coordinates are required to represent a 5 dimensional object.

How we can represent a 5 dimensional space geometrically?

A single dot is the geometrical representation of the zeroth dimension. 0th dimension does not have any length, width or height.
Now let me tell you one important concept-
"To get the next higher dimension all we need to do is to double the number of points."
Therefore by doubling the number of points we have now two points. And this is the geometrical representation of the first dimension. By joining these two points we get a straight line which is nothing but a one dimensional object having only one dimension of length.
Now again double the number of points to get to the next higher dimension i.e. the second dimension.
Therefore In the second dimension we have four points and by joining these 4 points, we get a plane surface which is a two dimensional object. For representing a two-dimensional object two coordinates- length and width are required.
Now on doubling the number of points again we enter into the next higher dimension i.e. the 3rd dimension. Here we have 8 points. We can join the points as shown in the video to get a 3 dimensional solid object. We need three coordinates- length, width and height to represent the 3 dimensional solid object geometrically.
To go to the Fourth dimension double the number of points once again. This time we have 16 points. As you can see in the video, this 4 dimensional structure is created by joining the respective points of two, 3D structures.
Now if we double the number of points, that are present in the four dimensional structure, we get a structure of next higher dimension i.e. the 5th dimension. You can count that this five dimensional structure has 32 points. On joining these points as indicated in the article we get a 5 dimensional structure.
So friends this is the way how we can represent a five dimensional structure geometrically step by step.

Why the researchers believe in the presence of the fifth dimension and why they needed the 5th dimension?

Actually researchers wanted to develop a theory that unifies the four fundamental forces in nature which are- electromagnetism, gravity, strong and weak nuclear forces. For this they needed a five dimensional space.
In 1921, A German mathematician Theodor Kaluza and Swedish physicist Oskar Klein independently developed a theory known as the Kaluza-Klein theory. The Kaluza-Klein theory used the 5th dimension for unifying two fundamental forces in nature; gravity and electromagnetic force. But later it was found that their approaches were partially inaccurate.

Why the fifth dimension cannot be observed directly by humans?

Klein suggested that the fifth dimension would be rolled up into a tiny and compact loop and this loop is on the order of 10(-33cm).
Under this reasoning, Klein envisioned light as a disturbance caused by rippling in the higher dimension, which is just beyond the perception of humans.
To make it more simple, lets take a simple analogy-
Suppose there is a fish in a pond. When it rains, ripples are created in the water of pond because of the raindrops. But the fish present in the water can only see Shadows of ripples across the surface of the water.
Although the gravity and electromagnetic forces seem unrelated but introduction of the fifth dimension can help in finding connection between these forces.
Later, the idea of superstring theory and supergravity provided a strong support to the Kaluza-Klein Theory.
Actually according to the superstring theory, everything in this universe is made up of tiny vibrating loops, known as strings and these strings vibrate in 11 dimensions. Therefore it made the scientists believe that there are at least 11 dimensions in the universe. Hence Kaluza-Klein theory suggesting 5 dimensions of space was supported by the superstring theory.

What is the scientific evidence for the existence of the fifth dimension?

Although We cannot directly observe the fifth dimension but it is possible to record indirect evidence of existence of the 5th dimension. It has been made possible by the Large Hadron Collider (LHC). But how does it work?
When the subatomic particles collide in the Large Hadron Collider, new particles are produced including graviton.
It was found that the graviton escapes from the fourth dimension and leaks off into a 5 dimensional bulk.

What are the supernatural powers that a person living in the fifth dimension would possess?

A 5th dimensional being would have all the powers that a lower dimensional being has along with many extra capabilities.
A being of 5 dimensions would be able to control time as per his wish. He would be able to move in any direction in time - past or future.
It would be possible for him to be present at different locations simultaneously. The 5th Dimensional being would be able to choose different career paths or job at the same time.
For example he may choose the professions of a doctor, an engineer and an artist simultaneously.
Actually parallel universes exist in the five dimensional space. Therefore in 5 dimensional space you may have different self versions of yourself in parallel universes. Your different self versions would have separate timelines, so they will live their lives independently.
Lives of different versions of yourself in different universes having separate timelines will be based on cause and effect. It means it will be based on the decisions made by your self versions living in different universes.

What are limitations of the fifth dimensional world?

One major limitation of this dimension is- there are no shortcuts between the timelines. You cannot jump directly from a point on one timeline to another point on other timeline.
It means if you want to meet your self version living in another parallel universe, then you cannot meet him directly. As I have already mentioned that the 5th dimension is based on cause and effect, therefore to meet your another self version you will have to go to the point of cause in past on the timeline.
But the dimensions higher than the fifth dimension are free from this limitation. It means there are shortcuts between the timelines.

25 Mar 2021

Why Ocean Water is Blue - Why Sea Water is Blue - Why Ocean Water is Blue in Colour

Do you know, Why ocean water is blue? Many of you may think that the answer is very simple. you may say that the blue color of sea water is due to the reflection of the sky, which is of blue color but it's not like that. So let's try to find out the real reason behind it. As we all know that water has no color. The water takes the color of what is mixed into it. So has anyone mixed the blue color into our oceans? Not actually. Then why the sea water looks blue? Actually, the blue color of sea water is due to the rays coming from the sun.

Why Ocean Water is Blue Video

Perhaps you would know that the rays of the sun are white and are made up of 7 different colors. These are the seven colors that you see in the rainbow. It is also possible to separate the white light of the sun into these seven colors through a prism. The seven colors that are present in the white light are - Violet, Indigo, Blue, Green, Yellow, Orange and Red. Here you also need to know that in these 7 colors, the wavelength of purple color is the smallest and the wavelength of red color is the Largest. Pure water has the characteristic that it absorbs long wavelengths of light more in comparison to short wavelengths. This is the reason why long wavelength colors such as red, orange, yellow and green are absorbed by sea water while blue color which has smaller wavelength is not absorbed by water. This is why, the ocean water appears blue. Now you may think here that the wavelength of purple color is even smaller than the blue color, then why the color of the sea is not purple. So the reason for this is, the amount of purple color in the white light of the sun is comparatively less. Therefore, despite reflecting purple color, the sea water appears blue. You may have one more question here. You may ask, if this is the case, then pure water kept in the glass should also appear blue. Actually Pure water placed in glass is colorless. Then why does this happen. Actually the concept of wavelength that we have just seen requires excessive amount of water, as in the case of the seas. Many times you must have seen that apart from blue, sea water also shows different colors. Actually this exception is due to the excess of certain types of impurities dissolved in the water of that sea. Otherwise, sea water appears blue everywhere. So my dear friends, now you know, why the sea water looks blue.

24 Mar 2021

Why Trees are Painted White and Red

Do you know, why trees are painted white and red. Why white and red stripes on trees trunks. During the journey you must have noticed that the trees along the highway are painted in white or red stripes.
Do you know that there are many scientific reasons behind this?
Here I'll tell you 3 scientific reasons for doing this.
So let's start.

Why trees are painted white and red Video

First Reason of why trees are painted white and red

The first reason for coloring trees in white or red stripes is to make them stronger. You must have noticed cracks on the trees and many times they get infected by insects.

Second reason of why trees are painted white and red

Another important reason behind coloring trees with white or red color is their safety. Coloring the trees ensures that these trees are under the protection and supervision of the forest department. For this reason they cannot be cut. In this way, security of the trees along the highway is ensured.

Third reason of why trees are painted white and red

Now we will discuss third and the last important scientific reason behind coloring trees. Actually, when the trees along the highway are painted white or red, they can be seen from a distance. It reduces the possibility of accidents caused by hitting trees. The white color in particular provides protection from accidents at night. So, there are many scientific reasons behind coloring trees in white or red.

13 Mar 2021

Most Common Dreams and Their Meaning - Psychology About Dreams - The Interpretation of Dreams

Here you will know hidden meanings of some most common dreams. This article explains the psychology about dreams and the interpretation of dreams that people commonly see.

Here the following 5 most common dreams and their meanings have been covered:-

1. Dreams about flying 2. Dreams about taking a test (dream about failing exams) 3. Dreams about losing teeth (teeth falling out) 4. Dreams about being naked in public 5. Dreams about being chased As these are the most common dreams so you will find here also your dreams and what they actually mean. It is believed that our dreams actually reveal our unconscious mind. Our dreams represent our hidden fears, phobias, deep desires and trauma in past life or childhood. This is the reason why we see a specific type of dreams repeatedly. It can help you in understanding what's going inside your subconscious and unconscious mind that your conscious mind can not understand and what your unconscious mind wants to tell you with the help of your dreams.

Most common dreams and their interpretation Video

So let's delve deeper into the secret and fascinating world of dreams!!!

Meanings of most common dreams

Dream no. 1. Dreams about flying

Most of us have experience of flying in dreams. Dreams about flying generally have two different types of meanings. On one side such dreams may represent desire of freedom or independence but on the other side it may mean our desire to escape or flee from harsh realities of life.

Dream no. 2. Dreams about taking a test

This is a very common type of dream. Many people dream of being late for a test or failing an exam. So taking an exam in your dreams represent your underlying fear of failure. it also exposes your weaknesses and puts your capabilities to test.

Dream no. 3. Dreams about losing teeth (Teeth falling out)

Losing teeth in your dreams or teeth falling out can have different meanings. This type of dreams may indicate losing power and self protection. It may also mean that you are worried about your looks or attractiveness. It is also an indication of lack of self esteem and communication skills.

Dream no. 4. Dream about being naked in public

Have you ever been embarrassed after finding yourself naked in public in your dreams? If yes then, you are not alone who has these kinds of dreams. Actually it doesn't represent your Desire to be naked in public. According to psychologists this type of dreams may arise when you are hiding something from others and you are afraid no one knows it about you and you want to keep that secret. Dream about being naked at public places also shows your feelings of guilt and inferiority.

Dream 5. Dreams about being chased

If someone is chasing you in your dreams then it means that you are running away from your fears that you cannot face. In such dreams identity of the chaser is also important. If an animal is following you, it means that you are running away from your own feelings and fears. If some unknown person or mysterious figure is chasing you, then it may be because of some childhood trauma or painful past experiences. So these were the top 5 most common dreams and what they actually mean. You can use the interpretation of the dreams for your help as they tell you your hidden desires and fears that even you may not be aware of.

5 Mar 2021

Why Are Some People Left Handed - Why Are Some People Born Left Handed

Why are some people left-handed? Which hand would be the dominant hand is decided in the womb or after our birth? Does it has anything to do with our brain or the environment?
Do you know that around 10% of the people all over the world are left-handed and August 13 is celebrated as International Left Handers Day.

Why Are Some People Born Left Handed Video

Left-handed people are unique in themselves and there are some advantages and disadvantages of being left-handed. So let's now come to our main question, why some people are born left-handed.

Why Are Some People Left Handed 

It was previously believed that the left or right hemisphere of our brain is responsible for determining the dominant hand even before we are born. But later in a study done in 2017 it was found that it has nothing to do with the brain. Actually answer to this lies in our spinal cord. According to the research, before the brain starts controlling the body movement, it is determined in the womb whether the child would be left-handed or right-handed. Let's now understand how it happens. There is an area called motor cortex in the brain which controls arm and hand movements. This motor cortex sends Signal to the spinal cord and the signal is translated into a motion. Here it is to be noted that the motor cortex of brain and the spinal cord are not connected up until about 15 weeks of pregnancy. But the baby starts to show signals of dominant hand in the womb before 15 weeks of pregnancy. It has been observed that babies tend to suck either their right or left thumb from week 13 in the womb. It clearly indicates that the brain is not responsible for deciding left handedness or right handedness as it is not connected to the spinal cord up until 15 weeks of pregnancy. It means, the spinal cord decides the hand preference. During a study a team analyzed the gene expression in the spinal cord. The study was conducted during the 8th 12th week of pregnancy. It was found that there was significant difference between left and right handedness in the segments of the spinal cord which is responsible for controlling arm and leg movement. So it is the difference in gene expressions in the spinal cord not the brain that makes a person lefty or righty. Friends now you know why some people are left-handed. Credits and Source: https://www.businessinsider.in/science/biology/scientists-think-they-have-found-the-reason-some-people-are-left-handed-and-it-has-nothing-to-do-with-the-brain/articleshow/62368041.cms

4 Mar 2021

String Theory for Dummies - String Theory - String Theory Explained

We will discuss here- What is string theory, what are strings in string theory and how small are these strings. We will also answer, Why string theory is so important and how it has proved promising in answering the deepest questions in fundamental physics.

What are Strings in String Theory

Before the introduction of string theory, it was considered that the fundamental particles of the nature are point like particles. But according to string theory it is not true. String theory says that these fundamental particles are extremely small one dimensional objects known as strings. So strings are the smallest thing in the whole universe as everything, even the subatomic particles are made up of these one dimensional objects called strings. Graviton is a quantum mechanical particle that carries gravitational force. In string theory one of the many vibrational states of the string corresponds to the graviton.

String Theory Explained Video

What is String Theory

String theory deals with how these strings propagate through space and how do they interact with each other. According to the string theory all fundamental particles are actually tiny vibrating loops of string. Various properties of particles like mass and charge are determined by the vibrations of the one dimensional string like entities. According to researchers, the size of the string is about 10^-33 cm.

Why String Theory is Important?

Scientists hope that string theory will help in answering deepest questions related to fundamental physics. String theory has been applied to unravel mysteries of early Universe cosmology, black holes, nuclear physics and condensed matter physics. Quantum gravity is one of the deepest problems in modern physics. All the fundamental forces except gravity are described within the framework of quantum mechanics. As Albert Einstein described gravity using the general theory of relativity but the general theory of relativity is formulated within the framework of classical physics. According to Einstein's general theory of relativity, gravity is the distortion of space-time caused by the presence of matter. So a quantum theory of gravity was needed in order to reconcile general relativity with the principle of quantum mechanics. String theory can help us here. Actually string theory potentially provides a unified description of gravity and particle physics. It is a self contained mathematical model that describes all fundamental forces and forms of matter. So we can say that string theory is a candidate for a theory of everything. Now let’s get an idea about how small are the strings in string theory.

Size of Strings in String Theory

Actually a string is of the order of 10^-33. This number is so small that just by staring at this number you won’t get the idea. So let me make it simple for you with an analogy. Let’s assume an atom were magnified, to the size of the whole observable Universe, then a String would be the size of a tree!!! Now let me do one more comparison to make it more clear. This time I'll compare the size of an electron with the size of a string. So, if we increase the size of an electron equal to the size of the Earth, then a string would not be bigger than just a 3 storey building.

What Causes Fear and How to Overcome Fear in Life

What is the Purpose of Fear and why it is Necessary

There would hardly be anyone in this world who never got scared. Actually fear is the body's defense mechanism. It is the fear that keeps us in discipline and prevents us from doing wrong things. If we are not afraid of anything, then we may harm ourselves or others. Like a child is not afraid of anything. He is not afraid of heights or any creature. So we have to take care of him all the time. But as the child grows up, he also starts to feel fear.

What is Fear and how to get rid of it Video

Is the Fear Real (An Unknown Fear)

But what happens when an unknown fear always haunts you. It is important to note here that in most cases our fear is not real, it’s imaginary. You might have heard that people suffer from different types of phobias. Some are afraid of lonely places, some are afraid of crowd and some find it very difficult to face water or heights. There are thousands of kinds of phobias that people are suffering. Friends, to solve any problem, one must first know the reason for it. It means if we get to know the cause of our fear, then it will be very easy to overcome it. So here I will tell you the two root causes of fear. After knowing them you can easily overcome your fear instantly.

What Causes Fear

Two root causes of fear are-
1. Not living in the present moment
2. Your desires and attachments

1. Not living in the present moment

Whenever you feel scared, you are either afraid of thinking about the future or whatever has happened to you in the past. So fear is always in the past or future. In the present moment, there is only life, No Fear !!! Let me explain it with the help of an example. Even if you are fighting with someone, you will not be afraid. Because at that time your full focus will be on fighting. But as soon as you shift your focus from present moment to past or future and start thinking, you feel scared. You may think, what will happen to my family, what will happen to my children, if I got hurt or die in the fight. In this way, as soon as your attention is removed from your present task which is fighting, your mind gets filled with worries and fears. And when this happens, your focus is not on fighting and your chances of losing the battle are increased. Thus, only by living in the present moment, our fear is gone.
Now I will tell you about the second cause of fear.

2. Your desires and attachments

No matter what kind of fear you have, it is the result of your desires in some form or the other. If you have desire to live, then there will definitely be the fear of death. Most people will agree that the biggest fear is the fear of death. You must have seen that the person who is not afraid of dying, has nothing to lose and has no desires, can not be frightened by anything. Only a single thought that whatever is happening is temporary and one day we are going to die, will reduce your fear to a great extent. When you feel afraid, you need to notice that you must be clinging or attached to some person or object. We do not want to leave that thing or person under any circumstances. And this attachment causes our fear. If you could remove yourself from these attachments and desires somehow, you will find that you have overcome your fear at that moment.
So we have seen that if we have to overcome any kind of fear, then we have to take care of only two things. The first is to practice living only and only in the present moment without worrying about the past and future. And second, whenever you are afraid, pay attention what desires and attachments are causing it. You will get your answer.

15 Nov 2020

The Best 3D Printers to Buy for your needs

Do you want to buy a 3D Printer? Here is the guide that will help you in choosing the best 3D Printer for your specific needs. Whether you need a 3D printer for your home use, industrial production, designing, educational purpose or simply as a hobbyist, here is a 3D Printer for you.

So before buying a 3D printer, you should have a look at these top picks, so that you can select the 3D Printer that suits you best.

Disclaimer: I may earn a small commission for purchases made through the links provided on this page.


1. QIDI TECH X Plus 3D Printer


QIDI TECH X Plus 3D Printer, 3D printer, this is the best 3D printer to buy


Buy this Product from your Country's Amazon Store

(US, UK, Canada, Germany, France, India)


Who should buy it ?

It is suitable for designers, engineers, hobbyists, educational institutions and home users. Industries can use it for product development.

Brand Name

This 3D Printer is manufactured by R QIDI TECHNOLOGY. It has 6 years of manufacturing experience and develops high performance 3D printers with very high quality.

Operating System

It supports Windows & mac operating systems

Compatible Software 

It is compatible with software like Simplify3D and Cura

Color 

Available in Multi-color


Why should you choose this 3D Printer?

  • You can use 3D printer by QIDI TECH to print advanced materials such as Nylon, Carbon Fiber and PC.
  • It is possible to produce complex and giant sized models with the help of QIDI TECH 3D Printer (X Plus).
  • X plus can save the breakpoint and resume printing later
  • This 3D printer can shut-off automatically after finishing product printing job.

It offers almost all the features that a good 3D printer should have like-

  • Quiet printing 
  • Wi-Fi connection
  • Air purification
  • Break point printing and
  • One-button quick leveling


2. Dremel DigiLab 3D40 Flex 3D Printer


Dremel DigiLab 3D40 Flex 3D Printer, best 3d printer to bu, 3d printery


Buy this Product from your Country's Amazon Store 

(US, UK, Canada, Germany, France, India) 

Who should buy it?

It would be the best choice for hobbyists, beginners, teachers and students. You can use it in classroom or at your home.


Brand Name

Dremel 


Software 

It supports Dremel Digilab 3D Slicer (Included), Cura, Simplify3D, Craftware, KISSlicer, Slic3r and Repetier.


Operating System

It is compatible with Windows, MacOS, iOS and Chromebook 


Why should you choose this 3D Printer?

  • Fully enclosed housing
  • 3.5" full color touch screen
  • Flexible build plate
  • Automated 9-point leveling
  • Network friendly and cast Connectivity (with Wi-Fi, ethernet and USB connectivity.)
  • This 3D printer can print with very high accuracy of 50 micron resolution


3. Creality Ender 3 V2 3D Printer


Creality Ender 3 V2 3D Printer, 3d printer, best 3d printer to buy


Buy this Product from your Country's Amazon Store

(US, UK, Canada, Germany, France, India)


Brand Name

Tresbro


Operating System

It supports Windows XP/7/8/10, MAC


Software

It is compatible with Simplify 3d/Cura

Why should you choose this 3D Printer?

  • Technical support for 24 hours with 1 year warranty
  • Brand new user interface
  • Rotary knob added on the extruder makes filament load and feed effortless
  • No noise during printing
  • New injection tensioner
  • Carborundum glass platform
  • V-guide rail with high standard
  • Print precision of ±0.1mm


4. ANYCUBIC Photon 3D Printer


ANYCUBIC Photon 3D Printer, best 3d printer to buy, 3d printer


Buy this Product from your Country's Amazon Store

(US, UK, Canada, Germany, France, India)


Brand Name 

ANYCUBIC


Where this 3D Printer can be used (Applications)?

It can be used for jewelry and toys designing, in dental industry, miniature making, architectural design and manufacturing.


Why should you choose this 3D Printer

  • Good service and customer support
  • High quality CNC parts
  • Smart and user friendly
  • 2560x1440 2K HD masking LCD
  • Extreme precision and detail
  • Efficient and high speed printing
  • Fast slicing software (photon slicer)

5 Oct 2020

Boyle's Law - Boyle's Law Simulation - Boyle's Law Animation - Boyle's Law PhET Simulation

In this video simulation you will learn, What is Boyle's Law. Boyle's Law has been demonstrated along with the Definition of Boyle's Law. This video simulation has been created by using PhET Simulator.
Boyle's law is also known by other names like Boyle- Marriotte law or Marriotte's law. After watching the Boyle's law animation you will understand the relationship between pressure and volume of an ideal gas when temperature and number of molecules (mass) of the gas are kept constant. The concept lying behind the Boyle's law has been explained in this simulation of Boyle's law.

What is Boyle's Law (Definition of Boyle's Law)

According to Boyle's law the pressure of a given mass of an ideal gas is inversely proportional to its volume at a constant temperature.

Boyle's Law Simulation Video


Charles Law Explained here You can Play with this PhET Simulation (Boyle's Law) using the link given below- https://phet.colorado.edu/sims/html/gases-intro/latest/gases-intro_en.html Credits : PhET Interactive Simulations University of Colorado Boulder 

Charles Law - Charles's Law - Charles Law Experiment - Charles Law Simulation - Charles Law PhET

This video explains, What is Charles Law (Charles's Law or Charles' Law). This simulation video has been created by using PhET simulation. In this Charles simulation you will understand the definition of Charles's law, the formula of Charles law and also the concept of Charles law.

After watching the Charles simulation video you will understand the relation between volume and temperature in adiabatic process (relation between volume and temperature when pressure is kept constant). The concept of gas pressure has also been explained here.

Definition of Charles’ Law

At constant pressure, the volume of an ideal gas is directly proportional to the absolute temperature.

Charles Law Simulation Video



Boyle's Law Explained You can Play with this PhET Simulation (Charles Law) using the link given below- https://phet.colorado.edu/sims/html/gases-intro/latest/gases-intro_en.html Credits : PhET Interactive Simulations University of Colorado Boulder https://phet.colorado.edu

Todays Exciting deals

30 Sept 2020

Google Tricks (Google Mirror, Google Space, Askew Google, Google Gravity, Google Underwater, Voxels)

In this video you will get new Google Tricks that you may not have seen before. Here is the collection of new 9 Google Tricks that you would love. You must try all of these Amazing google tricks.

Following Google Tricks are covered in this video

1.Water Type Mr. Doob (Water Type)
2.Askew/Tilt Google
3.Google Mirror
4.Google Space
5.Voxels
6.Voxels Liquid
7.Google in 1998
8.Google Gravity and
9.Google Underwater

Google Tricks Video



Credits: Google and Mr. Doob