Ian Ellis
One of the
hardest things for human beings to do is comprehend the difference between a number like 900 versus a number like 10 Both
numbers have the symbols '900' in them.
Thus, when someone sees a number like 10 The number
900 is just that, a number which any middle-school student can count to in a
matter of a few minutes. If a person
counted to 900, one number per second, they would count to 900 in 15 minutes. If we paid
$900 for a television set, we would see our bank account drop by $900. But how
long would it take us to count to 10 First of
all, let us look at the number 10 The number
10 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000 Each
consecutive zero in this number represents a number which is 10 times larger
than the number before it. For example, 100
is 10 times larger than 10. 1,000 is 10
times larger than 100. 10,000 is 10
times larger than 1,000. And so on. Thus, we are essentially multiplying 10, by itself, If we were
to write out a much, much smaller number (the number of atoms in the known
Universe), we would write it out: 100,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000 The number
of atoms in 10 Universes (10 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000 The number
10 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000
The above
number is 10 While we
could easily count to 900 in a few minutes, we could not count to 10 It is
absolutely critical for the reader to comprehend the difference between the
number 900 and the number 10 The point
to this discussion is when you see a number like 10
Now we will
talk about really small numbers. In this
book, a probability of 10 Obviously,
a probability of 10 While
technically, nothing is impossible, this level of probability is so rare, for
all practical purposes, a probability of this magnitude will never happen
during the age of our planet. As
mentioned above, there are about 10 How much
smaller is 10 In fact,
the probability of 10 ^{20} or:100,000,000,000,000,000,000
^{100} atoms
in this many Universes.While as
mentioned above, 10 Suppose
there was a lottery in which a 10-sided dice was rolled 100 times. In order to win this lottery you had to roll
a '1' for all 100 rolls. In other words,
you had to roll a '1' for 100 consecutive rolls, including the first roll, the
second roll, the third roll, the fourth roll, etc. It sounds
simple doesn't it? It turns out that
rolling a '1' for 100 from among 10single atom^{20} Universes, where each
Universe has 10^{80} atoms!!Each
"ticket" in this lottery represents your attempt to roll the dice 100
consecutive times where the roll is a '1' in every attempt. If you rolled something other than a '1' your
ticket immediately fails and you quit rolling the dice. Thus, if you roll a '5' on the first roll,
there is no need to make any more rolls, your ticket has failed. As another
example, suppose for one "ticket" you rolled: First
roll: a '1' Second
roll: a '1' Third roll:
a '4' You would
stop after the third roll since the third roll was not a '1'. This "ticket" failed also. In a
computer simulation of rolling dice,
Note: The
first item in the table means a '1' was not rolled in the first attempt. The second item in the table means a '1' was
rolled on the first attempt, but not the second attempt. And so on. Rolled a '1' [0] consecutive times: Count = 44,999,935,077 Rolled a '1' [1] consecutive times: Count = 4,500,063,675 Rolled a '1' [2] consecutive times: Count = 449,993,542 Rolled a '1' [3] consecutive times: Count = 45,006,419 Rolled a '1' [4] consecutive times: Count = 4,500,592 Rolled a '1' [5] consecutive times: Count = 450,545 Rolled a '1' [6] consecutive times: Count = 44,967 Rolled a '1' [7] consecutive times: Count = 4,682 Rolled a '1' [8] consecutive times: Count = 454 Rolled a '1' [9] consecutive times: Count = 43 Rolled a '1' [10] consecutive times: Count = 4 [max] In other
words, in . And this
only happened 4 times out of 10 in a row attempts.50
billionMost people
would think that it would be easy to roll 20 '1's in a row. But in 50 billion attempts, the most number
of '1's in a row was 10. Suppose you
were given this offer: "If you invest your life's savings in this lottery
(the lottery to roll 100 '1's in a row), you will be given 5,000 tickets (i.e.
5,000 attempts to win the lottery), for every second in a In other
words, we will assume this earth is 5 billion years old and you are given 5,000
tickets (i.e. attempts) every second; 24 hours a day, 365.25 days a year, for
the entire time the earth has existed!! Assuming
your life's saving were $1,000,000, would you invest your life's savings in
this lottery? Answer that question
before reading on. Let us see
your odds of winning. We will assume you
will be able to buy, 1,000,000,000,000,000,000,000
tickets in 5 billion years (actually you would be able to buy slightly less
than that). This is 10 This is
your last chance; would you spend your life's savings on these 10 To
calculate your odds of winning, we do this simple calculation: 10 But let's
suppose you didn't know the simple way to calculate your odds. The next
chart shows how to calculate your odds.
Based on 1,000,000,000,000,000,000,000
Tickets (10 "0
ct" means the first roll was not a '1' "1
ct" means the first roll was a '1', "2
ct" means the first two rolls were a '1',
0 ct
.9 9 x 10 1 ct
.09 9 x
10 2 ct
.009 9 x
10 3 ct
.0009 9 x
10 4 ct
.00009 9 x
10 5 ct
.000009 9 x
10 6 ct
.0000009 9 x
10 7 ct
.00000009 9 x
10 8 ct
.000000009 9 x
10 9 ct
.0000000009 9 x
10 10 ct .00000000009 9 x 10 11 ct .000000000009 9 x 10 12 ct .0000000000009 9 x 10 13 ct .00000000000009 9 x 10 14 ct .000000000000009 9 x 10 15 ct .0000000000000009 9 x 10 16 ct .00000000000000009 9 x 10 17 ct .000000000000000009 9 x 10 18 ct .0000000000000000009 9 x 10 19 ct .00000000000000000009 9 x 10 20 ct .000000000000000000009 9
x 10 21 ct .0000000000000000000009 9 x 10 22 ct .00000000000000000000009 9 x 10 23 ct .000000000000000000000009 9 x 10 24 ct .0000000000000000000000009 9 x 10 25 ct .00000000000000000000000009 9 x 10 ... 98 ct 9 x 10 99 ct 9
x 10 100 ct (the
only winner) 9 x 10 Even though
you own 10 Thus, even
though you get 5,000 tickets, every second, every day, every year for 5 billion
years, your chance of winning this lottery is about the same as picking the single
correct atom from among all the atoms in our Universe. Would you
spend you life's saving to enter this lottery?
Well, would you spend your life's savings on picking the correct, single
atom, from among all the atoms in our Universe?
It is effectively the same question. If you only
bought ^{20} Universes!!
Your chances would be 10^{‑100}.Hopefully
you would not buy a single ticket in this lottery. You would save a lot of time and gasoline by
simply flushing your dollar bills down the toilet. The point
to this exercise is that an event which has a probability of 10
Now let us
assume the "first living cell" of evolution had 900,000
nucleotides. How many permutations of
900,000 nucleotides are there? The
answer is 4 How much
bigger is 4 Try to
calculate it before reading on. If you said
6,000 times bigger, you would be wrong.
The correct answer is 4 Remember,
when you are dividing exponents, And this is
just the "first living cell."
Human DNA has 3,000,000,000 pairs of nucleotides!! There are 4 This is
just an introduction to the subject of permutations of nucleotides. Now let
apply the "first living cell" permutations to our probability which
is defined to be "impossible." For
example, suppose someone calculated the probability of the "first living
cell" to be 10 "first living cell" would be 10a single^{‑79}.Thus, even the
chance of a "first living cell" (which is only the very, very
beginning of evolution), is virtually impossible, even at 5,000 attempts every
second, 24 hours a day, for the age of our earth. And in the real world there would probably
only be a few hundred attempts The real
probability of the "first living cell" is not 10 ^{‑100}!!Without the
"first living cell," there is no evolution. The
"impossible" probability of 10
The
chapters on mathematics have covered a lot of concepts in a short amount of
space. If you do not feel comfortable
with these concepts, you would be advised to read these chapters again and even
get some help from a friend or relative. |