Science and Religion

There are questions about the ‘other world’ with ’life after death’ and all that is connected with them.

I remember seeing old prints, geographical maps of the world that includes hell, purgatory and heaven.

• Hell was placed deep underground
• Heaven and purgatory were high above in the skies.

Science has certainly helped in eradicating materialistic superstition in those matters.

However, this refers to a rather primitive state of mind.

There are points of greater interest. The most important contributions from science to overcome the baffiing questions

‘Who are we really? Where have I come from and where am I going?’

the gradual idealization of time.

Plato, Kant and Einstein.

In thinking of this the names of three men obtrude themselves upon us, though many others, including non-scientists, have hit on the same groove, such as St Augustine of Hippo and Boethius; the 3 are Plato, Kant and Einstein.

Plato

Plato’s long dialogues are a gratuitous quibbling on words, with no desire to define the meaning of a word.

Rather it pushes the belief that the word itself will display its content if you turn it round and round long enough.

His social and political Utopia failed. It put him into grave danger when he tried to promote it practically.

He is famous for his theory of forms (or ideas).

It is about a timeless existence or reality that goes against reason.

It was more real than our actual experience. This is but a shadow of the former, from which all experienced reality is borrowed.

How did it originate?

It was aroused by his becoming acquainted with the teaching of Parmenides and the Eleatics.

But it is equally obvious that this met in Plato with an alive congenial vein, an occurrence very much on the line of Plato’s own beautiful simile that learning by reason has the nature of remembering knowledge, previously possessed but at the time latent, rather than that of discovering entirely new verities.

However, Parmenides’ ever- lasting, ubiquitous and changeless One has in Plato’s mind turned into a much more powerful thought, the Realm of Ideas, which appeals to the imagination, though, of necessity, it remains a mystery.

But this thought sprang, as I believe, from a very real experience, namely, that he was struck with admiration and awe by the revelations in the realm of numbers and geometrical figures - as many a man was after him and the Pythagoreans were before.

He recognized and absorbed deeply into his mind the nature of these revelations, that they unfold themselves by pure logical reasoning, which makes us acquainted with true relations whose truth is not only unassailable, but is obviously there, forever; the relations held and will hold irrespective of our inquiry into them.

A mathematical truth is timeless, it does not come into being when we discover it. Yet its discovery is a very real event, it may be an emotion like a great gift from a fairy.

The 3 heights of a triangle (ABC) meet at one point (0).

(Height is the perpendicular, dropped from a ‘corner onto the side opposite to it, or onto its prolongation.)

At first sight one does not see why they should; any three lines do not, they usually form a triangle. Now draw through every corner the parallel to the opposite side, to form the bigger triangle A’ B’ C’.

It consists of 4 congruent triangles.

The 3 heights of ABC are in the bigger triangle the perpendiculars erected in the middle of its sides, their ‘symmetry lines’.

The one erected at C must contain all the points that have the same distance from A’ as from B’; the one erected at B contains all those points that have the same distance from A’ as from C’. The point where these two perpendiculars meet has therefore the same distance from all three corners A’) B’) C’, and must therefore lie also on the perpendicular erected at A because this one contains all points that have the same distance from B’ as from C’. Q.E.D.

Every integer, except I and 2, is ‘in the middle’ of two prime numbers, or is their arithmetical mean; for instance

8 == ! (5 + I I) == !(3 + 13) 17==! (3+3 1) ==!(29+ 5) ==!(23+ II) 20 ==! (I I + 29) == !(3 + 37)·

As you see, there is usually more than one solution. The theorem is called Goldbach’s and is thought to be true, though it has not been proved.

By adding the consecutive odd numbers, thus first taking just I, then I + 3 == 4, then 1 + 3 + 5 == 9, then I + 3 + 5 + 7 == 16, you always get a square number, indeed you get in this way all square numbers, always the square of the number of odd numbers you have added.

To grasp the generality of this relation one may replace in the sum the summands of every pair that is equidistant from the middle (thus: the first and the last, then the first but one and the last but one, etc.) by their arithmetic mean, which is obviously just equal to the number of summands; thus, in the last of the above examples:

4 + 4- + 4 + 4 == 4 X 4·