He produced a large notebook, and held it in a way so he could see the bend of the center page. Within the next two seconds, that center page was held straight at my face gripped only with his thumb and two longer fingers on the the top edge. The left hand side was blank; on the right was something he said he’d drawn. It was a large matrix with too many elements to count, for they were all numbers arbitrarily arranged. He let me absorb the display for a few seconds and then spoke.
“Do you see any difference at all between the elements of this matrix?”
“Yes, some are bigger and some small,” said I.
“You speak as though you were inside that matrix (chuckles). You shouldn’t see any notable differences besides the obvious fact that they are symbols differently drawn, and that is all that they are. Let me explain,…” He turned the page over revealing yet another large matrix. “…now look at this one.” This next matrix was full of the same arbitrarily arranged numbers, only interspersed with almost all of the arithmetic operators, functions, symbols known to me.
“If you think you can tell those symbols, you saw earlier, apart after seeing this matrix, you are wrong again. You still cannot.”
“But…”
“They still are the same arbitrarily arranged meaningless symbols. That figure over there (he pointed at number ‘5′) is not a ‘5′ unless I tell you it is, and also ‘figuratively’ define a ‘5′ as the number of fingers in each hand. I can point out any other symbol and have your senses register it as ‘the number of fingers in each hand’ if I haven’t yet told you that it is this one—>’5′ and not some other.”
I was suddenly reminded of a dialogue between the great private detective Sherlock Holmes and his associate Dr. Watson. “Watson, you wouldn’t hesitate one moment to tell me what’s two and two, but you will be in quite a fix were you asked to prove it to me.” There is of course no proof of that unless one is told what a ‘two’ is and how it is defined. And the mathematical system has many more anomalies like– how came a positive number when two negative numbers were multiplied or divided and not when added or subtracted? And what really is a negative number? Can something be less than nothing?
“What are you thinking?” he interrupted.
“Oh! Just something I was reminded of from a book I read. A Study in Scarlet, by Conan Doyle I think it was.”
“Ha! Seems to me that I have just about convinced you. Now, if I define each symbol here, each operator, each function, and every rule associated(created) with them to you and slowly pass it on to all of humanity, I would have them all thinking just like me. I’ll call it mathematics and we’ll have tests and examinations to separate the bright from the dull, the wise from the foolish, the mathematician from everyone else. A lie repeated often enough becomes the truth. Everyone today thinks within the mathematical system, and when Kurt Godel came up with his “Incompleteness Theorem”, the world is suddenly taken by surprise. All systems are incomplete, because a hypothesis proved correct using a system of logic can be proved wrong using the same system. Einstein once said that if his theories are not replaced in the next 100 to 150 years by theories more definite and binding, he sees no future for mankind. The reason we are now this far into the future since Newton, is simply because theories have failed, been proved wrong and have been replaced with more believable theories which are still incomplete. The next change of belief is expected out of Stephen Hawking if science magazines are to be believed.”
He stopped for what appeared to be a breather. He dug his trouser pockets looking for something; he wasn’t through yet. He soon had his left hand outstretched before my eyes. Resting on his palm was a 1:70 scaled die cast model of a popular Corvette.
“How many?” he asked.
Strangely, against my impulse to say ‘one’, I asked him to be more specific. One cannot commit to doing anything or agree wholly unless one’s own intuition allows one to. To that question, he merely smiled, put the Corvette back into his pocket, and we parted ways.
It could have been ‘one die cast toy’, ‘4 plastic wheels under a metallic superstructure’, ‘a million or more molecules’, ’several billion atoms’, ‘against the universe it amounts to nothing’…
Now, in the system of mankind, a matrix full of human life forms, are there any noticeable differences other than external appearance? Is someone bigger or smaller? What is war or religion or caste or race? Are they any different from incomplete systems of mathematical sciences and others? Can we be above these?
