# Deductive Reasoning

The term “deductive reasoning” comes from the word “deduct”, which means to remove from a collection. For example, a tax deduction is an amount of money that one can remove from their total income, leaving a smaller income to which the tax will be applied.

Sherlock Holmes used deductive reasoning to solve many of his cases. If there were a collection of suspects, who were the only ones who could have committed the crime, then if you can prove that all but one of the suspects could NOT have committed the crime, then the one that is left is the one who committed the crime.

It turns out that the Secret of the Pulsars is discovered by deductive reasoning. If we apply this process to the binary x-ray pulsars, such as Cen X-3 and Her X-1, we can easily see how it works.

First, we must state the problem we are trying to solve:

• We have a binary system consisting of a normal star plus a neutron star in orbit around each other. The normal star is referred to as the “companion” of the neutron star.
• The question we need to answer is “Where did the neutron star come from?”.
• There are only 2 possible answers:
• Either the neutron star at an earlier time was a normal star, that through some process evolved into a neutron star.
• Or the neutron came from somewhere else and became bound in orbit around the companion star.

One preliminary point that  should be helpful as the discussion proceeds is that it is known that close binary systems, where one member is normal giant star and the other member is a neutron star, can only be in this state for approximately one million years before the giant star becomes unstable because of all the heat generated by the neutron star pulsar, and will either fly apart completely or leave white dwarf or neutron star behind, where in the latter case we would have two neutron stars. The point is that after one million years the system will no longer be a neutron star plus a giant star, but a neutron star plus “something else”.

Therefore, we may characterize a binary x-ray pulsar (1 normal star + 1 neutron star pulsar)  as follows. Because the neutron star (either because something else became the NS, or the NS came from “somewhere else”) has been with the companion star for less than 1 million years, then 2 million years ago, we can say the following about this system:

• Two million years ago, the system was originally:
• Either: 2 normal stars and one of the stars became a neutron star one million years ago.
• Or: 1 normal star two million years ago, that met up with and joined a neutron star that came from somewhere else one million years ago.

There are no other possibilities. Another example might be the following:

• A person has lived in a house for 5 years and holds a lease on the house.
• There are currently 2 people living in the house.

Only one of the two following things could have led up to this system.

• Either both people were living in the house for the whole 5 years
• Or the second person moved in later.

If we can prove that when the person holding the lease moved in 5 years ago, that person was the ONLY person living in the house, then the second bullet MUST be the one that is true.

The purpose of belaboring this point is that we must understand is that:

• Either: the Cen X-3 pulsar was originally a normal star in a binary star system, and one of the stars “evolved” and became the Cen X-3 pulsar.
• Or: the Cen X-3 pulsar was originally a neutron star floating through space and encountered a normal star, got bound up in a binary orbit, and since has become a rotating neutron star pulsar.

The NS-Capture theory is based on proving that the first possibility above IS FALSE, and therefore, the second possibiltity MUST be TRUE.