Essay donated by Dr. Zvi Shkedi
"3. Torah and Science: Age of the universe:
Theory & Observations; Physics,
Functions, and Differential Equations
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"
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 ^
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
As we can see from the examples above, dating early history is not a
very promising branch of science. Fiction - maybe, but science - no.
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.
When I lived in California, I used to take walks along the ocean. One
day, I found a glass bottle sealed with a cork. When I opened the cork ,
a genie jumped out. The genie thanked me for releasing him from his
captivity and offered to grant me a wish. After a few moments of
pondering, I asked the genie to make me a book which is 500 years old.
The genie agreed; whispered "hocus pocus"; and the book was in my hands.
I wasn't sure whether to believe it or not. Was the book really 500
years old? On my way back home I passed near a university and went to
look for a chemistry professor to analyze the book. The professor took
the book into his lab, and, a few hours later, came out and said: "Yes,
the book is 500 years old."
When I came home, I told the whole story to my wife, not noticing that
my little son was also listening attentively. The next day I wanted to
impress my son with my new book. "Guess how old this book is?" I asked
my son. He didn't blink an eye and said: "This book is one day old." I
was shocked. " What do you mean one day old!" I screamed at him. " This
book is 500 years old. Even the professor said it is 500 years old".
"Sorry", responded my son, "if the genie made it yesterday, then it is
one day old."
So, how old is the book?
Since the genie made it yesterday, it is really only one day old. However,
to a chemist, it looks like it is 500 years old. The reason it looks so old,
is that it was made in such a way that it contains its history - it contains
chemical features and changes in the composition of the paper which would
normally take 500 years to develop. Once the history has been embedded into
the composition of the book, it is no longer possible to tell the difference
between such a book and a book which is really 500 years old.
Similarly, a fake archaeological artifact can be skillfully crafted to pass
all tests and to be pronounced authentically antique. Yet, antique it is
not. A scientist in the lab may discover that the artifact contains all the
features of a real antique. Yet, this is no evidence that it is indeed
antique. The only thing we can say with certainty is that it LOOKS antique.
Every object and every event in the physical universe can be described by a
set of mathematical functions. The most common parameters of the functions
are the three dimensions of space, and the dimension of time. We don't
always know what the functions are, but we know that the functions exist. A
unique quality of every mathematical function describing a physical object
or event is that it is continuous and can be calculated over an infinitely
wide range of parameters, regardless of whether the range is realistic or
not. So, for a car moving from Las Vegas towards Los Angeles, the function
describing the movement of the car can be calculated backwards to a location
far east of Las Vegas. Mathematically, the earlier presence of the car
somewhere between Las Vegas and New York is correct, even though the car has
never been there. When we see the car arriving in Los Angeles, it is
absolutely impossible to tell from its direction and speed, when and where
the car started its trip. Regardless of whether the car actually started in
Las Vegas, in Kansas City, or in New York, the arrival in Los Angeles will
Pierre-Simon, Marquis De Laplace (1749 - 1827) was a brilliant French
mathematician and astronomer. His work was pivotal to the development of
mathematical astronomy. Through his work with differential equations,
equations which are used by scientists to describe the characteristics of
physical systems, he discovered that the past and the future of the universe
can be calculated mathematically.
"We may regard the present state of the universe as the effect of its
past and the cause of its future. An intellect which at a certain moment
would know all forces that set nature in motion, and all positions of
all items of which nature is composed, if this intellect were also vast
enough to submit these data to analysis, it would embrace in a single
formula the movements of the greatest bodies of the universe and those
of the tiniest atom; for such an intellect nothing would be uncertain
and the future just like the past would be present before its eyes."
Obviously, this applies only to the physical universe, to the exclusion of
Godly spiritual intervention which is outside the jurisdiction of nature and
mathematics. In mathematical terms, Godly spiritual interventions would be
the equivalent of the boundaries and discontinuities described above.
Laplace did not believe in God, so he did not add the possibility of such
intervention to his mathematical discovery. Napoleon had to do it for him.
When Laplace sent to Napoleon a copy of his book about the universe,
Napoleon replied: "M. Laplace, they tell me you have written this large book
on the system of the universe, and have never even mentioned its Creator."
The past, present, and future of the universe (excluding spiritual effects)
can be described as a solution to a large set of differential equations.
Assuming we are wise enough to develop the complete set of equations, we
can, using these equations, calculate the future and calculate the past, as
long as we do not attempt to cross spiritually-induced boundaries and
discontinuities. (Don't celebrate yet - the amount of additional scientific
knowledge and computer power necessary for such calculations is millions of
times greater than what is available today.)
The physical universe is so constructed, that spiritual boundaries and
discontinuities are hidden. The origin of spiritual effects is outside the
four dimensions of physical location and time. Sefer Yetzirah (the Book of
Creation), written more than 4000 years ago, describes the universe as a
five-dimensional space. It describes the physical universe as being a
four-dimensional space of location and time and adds a fifth spiritual
dimension. (At the end of the 19th century, physicists discovered that the
physical universe is a four-dimensional space of location and time. This
discovery led to the development of Einstein's theory of relativity and to
the discovery of quantum mechanics.) All attempts to solve and extrapolate
currently known equations to calculate the past, ignore the existence of
spiritual boundaries and discontinuities and ignore the existence of the
spiritual fifth dimension. In the currently available mathematical models of
the four-dimensional physical universe, such boundaries and discontinuities
are not represented. Therefore, the calculations of the past are not
limited in range.
When we observe light rays coming from the direction of a star billions of
light years away, the only scientific facts we have are the direction from
which the light rays arrive, and the spectrum and intensity of the light.
Everything else we try to say about this light is nothing but the result of
a speculative theory - a mathematical calculation and extrapolation. The
scientific data carried by this light does not include the time or the
location where it started its journey. It is mathematically convenient to
say that the light started its journey at a far away star billions of years
ago. It looks to us as if this is when and where the light started. But, we
do not know for a fact that this is indeed the case. We don't even know for
a fact that the star exists. Just like the car arriving in Los Angeles from
the east. It is impossible to tell from the arrival direction and speed of
the car, when and where it started its journey. Similarly, it is impossible
to tell from the arrival direction and speed of the car, when and where the
car was manufactured.
To those who believe that God created the universe, what we learned so far
leads to only one possible conclusion - God created the universe with its
history. The act of creation started in the spiritual fifth dimension of the
universe. Therefore, it is not visible to scientists whose science is
confined to the first four dimensions. In exact mathematical terminology,
what is visible to scientists is the projection of the (five-dimensional)
universe into the first four dimensions. This projection is similar to the
shadow of a three-dimensional object projected on a two-dimensional screen.
When we look at the shadow, we get some information about the object, but
most of the (three dimensional) information is invisible. It is also
possible to project a shadow of a vertical pole on the ground in such a way
that the shadow looks much longer than the pole itself. If we were to
examine only the shadow, we would conclude that the pole is much longer than
it really is. Similarly, scientific research is limited to the study of the
four-dimensional projected shadow of a five-dimensional universe.
When God created the far-away stars, God also created the light rays emitted
by these stars, extending all the way to infinity. When we look at a
far-away star, we see the light rays exactly as they would have been if they
were to start their journey at this star billions of years ago, but, this is
not evidence that they actually did. Similarly, when God created the earth,
God also created fossils and other ancient-looking features. The reason God
created the universe with its history, is that the physical findings must
match the results of calculations we might want to make by solving the
equations of the universe, and extrapolating them backwards in time. If God
were to create the world without its history, there would be a mismatch
between the results of the calculations and the observed features. Such a
mismatch would be a deficiency in God's ability to create perfection.
It is important to understand that the calculation and extrapolation
backwards in time is a mathematical process. It is NOT physical evidence and
it is NOT proof that anything actually existed that far back in time. All it
means is that MATHEMATICALLY the world looks as if it existed that far back
in time. The observed features of the universe look as if they existed that
far back in time, to match the mathematical calculation. This is highlighted
by the example given above, of the car arriving in Los Angeles -
mathematically it looks as if the car started its journey in New York, even
though it actually started in Las Vegas.