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Essay donated by Dr. Zvi Shkedi

"3. Torah and Science: Age of the universe:
Theory & Observations; Physics,
Functions, and Differential Equations

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Theory and Observations:

Live mollusks in Hawaii had their shells dated with the carbon-14 method. The tests showed that they died 2000 years ago!

A freshly killed seal was dated at 1,300 years old!

Shells from living snails dated at 27,000 years old!

Living penguins were dated at 8,000 years old!

The oldest living coral reef is less than 4200 years old. If the earth is billions of years old, why is there not a bigger and older coral reef?

The oldest living tree in the world is about 4300 years old. If the earth is billions of years old, and life on earth started millions of years ago, why don't we find older trees?

Textbooks in astronomy state that 100,000 years are required for a star to "evolve" from a red giant to a white dwarf. Cicero in year 50 BCE described Sirius as being a red star; Seneca, approximately in year 20 AD, said Sirius was redder than Mars; Ptolemy in year 150 AD said Sirius was one of 6 red stars in the sky. Yet, today, less than 2000 years later, Sirius is a white dwarf. Where did the theory of 100,000 years come from?

In 1760, Georges-Louis Leclerc, determined that the earth is 75,000 years old. In 1831 Charles Lyell said the age of the world is 240 million years. Did the earth get 240 million years older within 71 years? Obviously it didn't. The only thing that changed was the speculative model and extrapolation used to calculate the age. In 1929 Edwin Hubble calculated the solar system to be 2 billion years old. Now the earth seemed to age at a rate of 18 million years per year.  The current theory is that the earth is 5 billion years old. That's an even faster aging rate of 38 million years per year. Is this how "time warp" in science fiction started?

The models used by scientists to calculate the age of the world keep changing frequently. There seems to be some kind of a competition among scientists - who can calculate an older age, or who can dream up a model or a theory which will yield an older age. The common aspect of all these models is extreme speculative extrapolation of current data back into a period of time for which we have no data - only assumptions, speculative theories, and a heavy dose of human imagination.

In 1959, a survey was taken of leading American scientists. Among the many questions asked was, "What is your concept of the age of the universe?" (Not just the earth, but, the entire universe).  Dr. Gerald Schroeder reports (ďAge of the Universe" January 2000) that two-thirds of the scientists gave the same answer: "There was no beginning". Aristotle and Plato said  2400 years ago that the universe is eternal. Their theory was preferred by the scientists over the first word in the Bible: "In the beginning" ("Bereshit" in Hebrew).

With the discovery of the expanding universe by Edwin Hubble, and some evidence of the "big bang" found in 1965 by Arno Penzias and Robert Wilson the world paradigm changed from a universe that was eternal to a universe that had a beginning. Scientists have made an enormous paradigm change in their understanding of the universe. They finally discovered, after more than 3000 years of research and debate, that the universe had a beginning and that the first word in the Bible is a scientifically proven truth. Now, it is only a matter of time before scientists also discover the truth of the second and third words in the Bible: "God created".

The world population in year 1000 AD was 310 million. In year 1750 AD the world population was 791 million. To avoid the impact of modern technology and medicine, we will not count the years after 1750. The world population growth from year 1000 to year 1750 gives us an average growth rate of 0.125% per year. This is a very slow rate which takes into account all the effects of wars, plagues, natural catastrophes, and negative growth periods, before the onset of modern technology and medicine.  When we extrapolate this slow growth rate backwards, we find that we have to start with 2 people in year 14100 BCE, to achieve these known world population numbers. [The mathematical equation is:  population = (starting-no.-of-people) * 1.00125 ^ (total-no.-of-years).]

Living conditions in ancient times could not be much worse than in Africa before the beginning of the 20th century. The average growth rate in Africa from year 1750 to year 1900 was 0.15%. This rate is very close, yet, larger than the 0.125% world growth rate mentioned above. In ancient times, when overall population density was lower, the growth rate was much higher than 0.15%, and definitely not lower than 0.12%. By comparison, during the 210 years that the Jews were enslaved in ancient Egypt, the average growth rate was about 5% per year.

The known growth rate in Asia between the years 1750 and 1900 was 0.42% per year. This rate is very close to the 0.45% growth rate we get if we start with the 8 biblical people who survived the Great Flood in year 2104 BCE and end with 310 million people in year 1000 AD. If we extrapolate the 0.42% rate backwards, we find that we have to start with 2 people in year  3500 BCE  to achieve the world population of 310 million in year 1000 AD.

The higher the growth rate - the shorter is the time required to achieve a known population. Obviously, the growth rate was not constant with time, but, the long-term average could not be less than 0.12%. Using this lower limit, it would be impossible for mankind to have appeared on earth earlier than 14100 BCE. The conclusion from these calculations is that mankind appeared on earth somewhere between 3500 BCE and 14100 BCE. This time range is three orders of magnitude shorter than the so-called "scientific" estimates of millions of years ago. According to the Bible, mankind appeared on earth in year 3760 BCE. This biblical date is well within the date range calculated based on the known population growth rates.

These growth numbers may not be exactly equal to the unknown numbers in ancient times. These calculations also include extrapolations which require caution when interpreting the results. However, they are infinitely better than the imaginative speculations by some biologists who claim that mankind appeared on earth millions of years ago. Did any of those biologists ever disclose a better, more accurate, mathematical model to get their "millions of years" estimate? Pulling a rabbit out of a hat is much easier to believe than the "millions of years" estimate. Did any of those biologists ever calculate the possible consequences of their "millions of years" estimate? Let's see what happens if we assume that mankind appeared on earth not millions of years ago but only 40,000 years ago.

At the lower-limit growth rate of 0.12% per year, if we were to start with 2 people  40,000 years ago, the current world population would grow to 1000 billion billions.  That's a population density of 850,000 people per square foot of earth land area.  The people on earth would have to pile up 850,000 layers high to contain all of them. Even the wildest science-fiction writers could not dream of such a large number. Even if they all perished, where are their bones, 850,000 layers high? Can anyone imagine how many more bones we would find if mankind appeared on earth millions of years ago? 150 years ago, when the imaginative theories about the beginning of mankind became popular, scientists did not have computers to calculate the consequences of these speculations. 150 years ago, scientists could also not publish their theories in the journal which is available today - "
Speculations in Science and Technology".

Today, unfortunately, the speculative theories about the age of the universe and the beginning of life have turned into an anti-religious political agenda which has nothing to do with science. If not for the anti-religious motivation, these speculations would have been long forgotten, together with so many other imaginative theories gone with the wind, like the aether, the flat earth, alchemy, and spontaneous generation of life.

As we can see from the examples above, dating early history is not a very promising branch of science.  Fiction - maybe, but science - no.

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Physics, Functions, and Differential Equations:

Now, that we have established the scientific credibility of dating early history, let's look at the subject from a different point of view, entering the world of physics, functions, and differential equations.

Let's start with a story.

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