Calculating the number of people who have ever lived is part science and part art. No demographic data exist for more than 99% of the span of human existence.

Any estimate of the total number of people who have ever lived depends essentially on three factors: the length of time that humans are thought to have been on Earth, the average size of the population at different periods, and the number of births per 1,000 population during each of those periods. The estimate, however, does not depend on the number of deaths during any period of time.

The oldest hominins are thought to have appeared as early as 7 million B.C.E. The earliest species of the Homo genus appeared around 2 million to 1.5 million B.C.E.

Modern Homo sapiens originated in Africa, though the exact location has long been debated. Diverse groups are thought to have lived in different locations across Africa for the first two-thirds of human history.

(Table 1 displays very rough figures representing averages of an estimate of ranges given by the United Nations and other sources.) Slow population growth over the 8,000-year period—from an estimated 5 million in 8000 B.C.E. to 300 million in 1 C.E.—results in a very low growth rate of only 0.05% per year.

In all likelihood, human populations in different regions grew or declined in response to food availability, the variability of animal herds, periods of peace or hostility, and changing weather and climatic conditions.

As mothers, we love to read to our little ones. We also love it when we find books that describe how much we love our children.

Are you familiar with Dr. Kevin Leman.

However, he also has a series of children’s books that have been some of my family’s favorites. And I recently added a new one to the collection.

Therefore, the birth order theories ring true in my family. If you need to become more familiar with birth order psychology, I challenge you to study it.

Kevin Leman. First, you need to know I am the youngest child in my family.

I found the chapter about the youngest child and turned to it. To my amazement, the text called me out on my actions.

As I did, I learned so many things about myself and even more about my daughters. After becoming a fan of Dr.

I immediately bought a copy of “My Firstborn, There’s No One Like You,” “My Middle Child, There’s No One Like You,” and “My Youngest, There’s No One Like You.” As I sat and read the books to my children, they asked if I wrote them. They wondered how the author could describe their personalities so well.

My girls are now grown and having children of their own. We still have a lot of fun with the theories of birth order.

His videos about the oldest, middle, and youngest children always make us laugh. Additionally, they’ve discovered how their birth order affects them as a mom.

Likewise, understanding the psychology of birth order has made them better moms. A mother knows her children better than anyone.

These children’s books demonstrated how my children had personality traits like other firstborn, middle, and youngest children. However, they also helped each of my children appreciate their siblings’ personalities and know they have a special part to play in our family.

I was shopping on Amazon and saw “My Grandchild, There’s No One Like You.” I immediately had to buy it. Then, as I read the pages, I laughed, knowing that this book describes a grandmother’s attitude toward parenting very well.

As you do, you’ll realize there’s no one like you, Mom. Disclosure: The links above are affiliate links, meaning, at no additional cost to you, I will earn a commission if you click through and make a purchase.

Follow us for book reviews, free resources, parenting tips, and encouragement. #christianchildrensauthors #christianbooks #christianauthors #christianwritiers #christianteachers #christianchildrensbooks #childrensbookreviews #dawnstephens #dawnstephensbooks.

Quote/s of the Day – 16 December – “Month of the Immaculate Conception” – Thursday of the Third week of Advent, Readings: Isaiah 54: 1-10. Psalm30: 2 and 4-6,11-12a and 13b.

“I tell you, among those born of women,no-one is greater than John. yet the least in the kingdom of Godis greater than he.”.

“Hate what the world seeksand seek, what it avoids.”. “God’s love calls us to move beyond fear.We ask God for the courageto abandon ourselves unreservedly,so that we might be mouldedby God’s grace,even as we cannot seewhere that path may lead us.”.

In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share a birthday. The birthday paradox refers to the counterintuitive fact that only 23 people are needed for that probability to exceed 50%.

The birthday paradox is a veridical paradox: it seems wrong at first glance but is, in fact, true. While it may seem surprising that only 23 individuals are required to reach a 50% probability of a shared birthday, this result is made more intuitive by considering that the birthday comparisons will be made between every possible pair of individuals.

Real-world applications for the birthday problem include a cryptographic attack called the birthday attack, which uses this probabilistic model to reduce the complexity of finding a collision for a hash function, as well as calculating the approximate risk of a hash collision existing within the hashes of a given size of population.

The problem is generally attributed to Harold Davenport in about 1927, though he did not publish it at the time. Davenport did not claim to be its discoverer “because he could not believe that it had not been stated earlier”.

From a permutations perspective, let the event A be the probability of finding a group of 23 people without any repeated birthdays. Where the event B is the probability of finding a group of 23 people with at least two people sharing same birthday, P(B) = 1 − P(A).

for a group of 2 people, mm/dd birthday format, one possible outcome is { { 01 / 02 , 05 / 20 } , { 05 / 20 , 01 / 02 } , { 10 / 02 , 08 / 04 } ,.

} {\displaystyle \left\{\left\{01/02,05/20\right\},\left\{05/20,01/02\right\},\left\{10/02,08/04\right\},..\right\}} ) divided by the total number of birthdays with repetition and order matters, V t {\displaystyle V_{t}} , as it is the total space of outcomes from the experiment (e.g. 2 people, one possible outcome is { { 01 / 02 , 01 / 02 } , { 10 / 02 , 08 / 04 } ,.

} {\displaystyle \left\{\left\{01/02,01/02\right\},\left\{10/02,08/04\right\},..\right\}} ). Therefore V n r {\displaystyle V_{nr}} and V t {\displaystyle V_{t}} are permutations.

Another way the birthday problem can be solved is by asking for an approximate probability that in a group of n people at least two have the same birthday.

any unevenness increases this probability. The problem of a non-uniform number of births occurring during each day of the year was first addressed by Murray Klamkin in 1967.

The goal is to compute P(B), the probability that at least two people in the room have the same birthday. However, it is simpler to calculate P(A′), the probability that no two people in the room have the same birthday.

Here is the calculation of P(B) for 23 people. Let the 23 people be numbered 1 to 23.

Let these events be called Event 2, Event 3, and so on. Event 1 is the event of person 1 having a birthday, which occurs with probability 1.

Similarly, the probability of Event 3 given that Event 2 occurred is 363/365, as person 3 may have any of the birthdays not already taken by persons 1 and 2. This continues until finally the probability of Event 23 given that all preceding events occurred is 343/365.

The terms of equation (1) can be collected to arrive at:.

Evaluating equation (2) gives P(A′) ≈ 0.492703. Therefore, P(B) ≈ 1 − 0.492703 = 0.507297 (50.7297%).

This process can be generalized to a group of n people, where p(n) is the probability of at least two of the n people sharing a birthday. It is easier to first calculate the probability p(n) that all n birthdays are different.

When n ≤ 365:. where.

The equation expresses the fact that the first person has no one to share a birthday, the second person cannot have the same birthday as the first (364/365), the third cannot have the same birthday as either of the first two (363/365), and in general the nth birthday cannot be the same as any of the n − 1 preceding birthdays.

The event of at least two of the n persons having the same birthday is complementary to all n birthdays being different. Therefore, its probability p(n) is.

The Taylor series expansion of the exponential function (the constant e ≈ 2.718281828). provides a first-order approximation for ex for | x | ≪ 1 {\displaystyle |x|\ll 1} :.

Thus,. Then, replace a with non-negative integers for each term in the formula of p(n) until a = n − 1, for example, when a = 1,.

Therefore,. An even coarser approximation is given by.

According to the approximation, the same approach can be applied to any number of “people” and “days”. If rather than 365 days there are d, if there are n persons, and if n ≪ d, then using the same approach as above we achieve the result that if p(n, d) is the probability that at least two out of n people share the same birthday from a set of d available days, then:.

In a room containing n people, there are (n2) = n(n − 1)/2 pairs of people, i.e. (n2) events.

Being independent would be equivalent to picking with replacement, any pair of people in the world, not just in a room. In short 364/365 can be multiplied by itself (n2) times, which gives us.

And for the group of 23 people, the probability of sharing is. Applying the Poisson approximation for the binomial on the group of 23 people,.

The result is over 50% as previous descriptions. This approximation is the same as the one above based on the Taylor expansion that uses ex ≈ 1 + x.

A good rule of thumb which can be used for mental calculation is the relation. which can also be written as.

In these equations, m is the number of days in a year.

Which is not too far from the correct answer of 23.

This is a result of the good approximation that an event with 1/k probability will have a 1/2 chance of occurring at least once if it is repeated k ln 2 times.

Using the birthday analogy: the “hash space size” resembles the “available days”, the “probability of collision” resembles the “probability of shared birthday”, and the “required number of hashed elements” resembles the “required number of people in a group”.

For comparison, 10−18 to 10−15 is the uncorrectable bit error rate of a typical hard disk. In theory, 128-bit hash functions, such as MD5, should stay within that range until about 8.2×1011 documents, even if its possible outputs are many more.

The argument below is adapted from an argument of Paul Halmos.[nb 1]. As stated above, the probability that no two birthdays coincide is.

We chose the 11th month and 22nd day for our Emanuel Syndrome Awareness Day, to represent chromosomes 11 & 22 which are involved in Emanuel Syndrome (ES). We have been holding our annual awareness day since 2010 and use this opportunity to share photos, stories, facts and hold events to share about our amazing children and make people aware of this rare chromosome 22 disorder.

While carriers of the balanced 11q22q translocation are quite common (it is the most common recurrent balanced reciprocal translocation known in humans), Emanuel syndrome, the unbalanced version of the translocation, is considered a rare chromosome disorder.

There have been more than 275 cases reported in the scientific literature since it began to emerge as a disorder dating back to the early 70s (and some cases from the late 60s which cannot be definitively confirmed). It is estimated to occur in 1 in 110,000 live births (Ohye et.

Each year on November 22 (and in the weeks leading up to the day) we take the time to post about Emanuel Syndrome on Facebook and Instagram, tweet, share statistics, information, articles, photos, videos, stories, make the local paper, host online meetings in different time zones, hold fundraisers, have family meet-ups and marvel at the worldwide flood of “purple and blue on 11/22”.

Once upon a time, our disorder was unnamed and it was difficult for families to connect with each other. Now, we have members all over the world and we celebrate as one big family.

How can you participate and raise awareness. Share your photos and child’s bio with us and we will add you into our yearly photo blitz in the template we use that year.

From Canada to Japan – we continue to raise awareness about this rare chromosome disorder year after year. Want to learn more.

Contact us at [email protected] and we will get you set up.

Down syndrome is a condition in which a person has an extra chromosome. Chromosomes are small “packages” of genes in the body.

Typically, a baby is born with 46 chromosomes. Babies with Down syndrome have an extra copy of one of these chromosomes, chromosome 21.

This extra copy changes how the baby’s body and brain develop, which can cause both mental and physical challenges for the baby. People with Down syndrome usually have an IQ (a measure of intelligence) in the mildly-to-moderately low range and are slower to speak than other children.

Down syndrome remains the most common chromosomal condition diagnosed in the United States. Each year, about 6,000 babies born in the United States have Down syndrome.

There are three types of Down syndrome. People often can’t tell the difference between each type without looking at the chromosomes because the physical features and behaviors are similar.

A screening test can tell a woman and her healthcare provider whether her pregnancy has a lower or higher chance of having Down syndrome. Screening tests do not provide an absolute diagnosis, but they are safer for the mother and the developing baby.

Neither screening nor diagnostic tests can predict the full impact of Down syndrome on a baby. no one can predict this.

During an ultrasound, one of the things the technician looks at is the fluid behind the baby’s neck. Extra fluid in this region could indicate a genetic problem.

Rarely, screening tests can give an abnormal result even when there is nothing wrong with the baby. Sometimes, the test results are normal and yet they miss a problem that does exist.

Types of diagnostic tests include: These tests look for changes in the chromosomes that would indicate a Down syndrome diagnosis.

However, some people with Down syndrome might have one or more major birth defects or other medical problems. Some of the more common health problems among children with Down syndrome are listed below.8.

Down syndrome is a lifelong condition. Services early in life will often help babies and children with Down syndrome to improve their physical and intellectual abilities.

These services include speech, occupational, and physical therapy, and they are typically offered through early intervention programs in each state. Children with Down syndrome may also need extra help or attention in school, although many children are included in regular classes.

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currently reading A Clash of Kings by George R.R. Martin Six Crimson Cranes by Elizabeth Lim Share book reviews and ratings with Aimal (Bookshelves & Paperbacks), and even join a book club on Goodreads.

currently reading A Clash of Kings by George R.R. Martin Six Crimson Cranes by Elizabeth Lim Share book reviews and ratings with Aimal (Bookshelves & Paperbacks), and even join a book club on Goodreads.

currently reading A Clash of Kings by George R.R. Martin Six Crimson Cranes by Elizabeth Lim Share book reviews and ratings with Aimal (Bookshelves & Paperbacks), and even join a book club on Goodreads.

A Clash of Kings by George R.R. Martin.

A Clash of Kings. by George R.R.

Six Crimson Cranes by Elizabeth Lim.

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