“So, if we have two pears in a basket and add them to two other pears in another basket, we won’t get the equivalent of 2+2=4 equal pears, right?” Hans smiled again.
“Yes, that’s right”, she admitted, “but it does not correspond somehow with the mathematics I studied.”
“Mathematics is an idealized and correspondingly untrue reflection love, dear…” Hans was beaming. “It is a beautiful but just as much incorrect abstraction of reality…”
“Crazy stuff. I still cannot comprehend it…”
“The same goes for distances. For example, do you know how much the difference of the distances along the figure axis is between 0 and 1 and between 1 and 2?”
“Err… the distances are the same. They are both… 1…”
“No, I absolutely disagree. The distance between 0 and 1 is much greater, than between 1 and 2… accordingly that between 3 and 4 is less than that between 1 and 2, but bigger than that between 4 and 5. And so on…”
“That cannot possibly be correct”, Marcela argued.
“As I told you, it is very easy to be understood… Imagine you are poor and sick and you have no money for bread. If you have 0 dollars, you cannot buy food and will soon die. Right?”
“Well, I suppose so…”
“While if you have 1 dollar, you’ll still be alive.”
“Yeah, but no for long with food for 1 dollar.”
“True, but the difference between being alive or dead is quite substantial, as I’m sure you will agree. And it is present.”
“You convinced me” she said with a note of irony in her voice.
“It is the same with bigger numbers: the difference between having $1000 and $1 000 000 is great, but between 100 billion and 200 billion it is insignificant.” Hans took a pencil and paper and started writing. (0-1)>(1-2)>(2-3)>(3-4)…….(1million-10million)>>(10million-10 billion)>>>(10billion-100billion) etc.
“It is the same, of course, to the left of zero, with the negative numbers. The bigger the suffering is, the less it is distinguishable from the neighboring, near in measure.”
“Say again?”
“Imagine, like we said, that you are poor and sick at the point of zero. But the temperature outside is also zero and your teeth clatter with the cold. Not only that, but someone steals your trousers and you fall down to minus one on the number axis.”
“It sucks… Hungry and with no pants”, Marcela shook her head.
“It sucks, yes, but after some time your shirt is stolen too and you are sent to minus two, right?
“You are walking stark naked in the street, I get it…”
“Not until someone steals your underwear for good measure.”
“Come on, this is too much. There’s no way someone could take off the panties off your ass, Hans”, she laughed.
“We are talking just hypothetically, Marcela. Tell me, please, there is no big difference in being naked or half naked, is there? Even smaller the difference is between being naked and stark naked. In both cases you’ll die of freezing.”
“Yeah, I think so… still I don’t get it…”
“Okay, then, I’ll give you the same example as with positive numbers. If you are without a buck, it’s too bad, you are at zero level. On the other side, this is much better than beside not having anything you also owe one dollar that you borrowed from the bank the previous day to buy bread.”
“Well, that is correct…”
“But if you have two dollars and you owe two more is much worse than if you have 2 billion and you owe the bank another 2 billion, don’t you agree?” He smiled at her.
“Yes, Hans, I give up, you are right.”
“Sure, there were many mathematicians who squarely refuted Professor McDowell, because with the methods of pure mathematics the distance between 1 and 2 is exactly the same as between 2 and 3. Both are infinity.”
“Well here you lost me as a listener. Hans, you are crazy!”
“Let me write it to you.” He took again the pencil in his hand. “How many numbers can you write between 0 and +∞?”
“An infinite number.” This time she was sure.
“Correct. And how many between 0 and 1?”
“I suppose, a lot less” she mumbled not so sure any more.
“Wrong! You can also write an infinite quantity of numbers, although you wouldn’t know where to begin… Because if you start from 0.0001, you can insert between it and the zero 0.00001, and after it 0.000001 and so on till infinite number of values between whichever two numbers on the axis, no matter how close they are to each other…”
“Err… if you put it like that… when I think of it… I guess, you are right.”
“That is so, because between any two numbers there is always an infinite quantity of other numbers. And if the distance between 0 and 1 is infinite, it is equal to the distance between 1 and 2, which is also infinite, because infinities cannot be compared… they are equal. Exactly in the same way as zeroes are nothing and also cannot be compared. But the difference between being alive or dead is unimaginably more significant than the difference between being a millionaire or a billionaire… i.e. the infinity between 1 and 2 is still bigger than the infinity between 2 and 3 and so on. As you can see infinity is everywhere – in the small and in the big both.”
She sighed.
“Hans, you are right as always but I got a bit exhausted of all those figures…” Marcela was declaring retreat.
“As I said this “Theory of subjective numbers” is a lovely untruth, which, however, is a fine description of the beauty of mathematics…” The triumph of Hans was obvious.
“Right now, I personally would prefer a hot bath and a glass of Merlot… Actually, Hans, why is this theory so important and why are you telling me about it?”
“I remembered about it a short time ago, while I was working on the matter of music and the ship. It helped me understand the truth about the music. ”Hans sipped his coffee and glanced knowingly at her above the rim of the cup. “It also makes you realize that nothing here is what it seems to be.”
Ivanov pressed the red receiver on his phone.
The instructions were clear.
Nothing had to be left in the hands of the enemy. The Americans should not in any circumstances get hold of the Cube as a weapon, nor the submarine itself. It kept too many and too vital secrets or him to take a risk with hesitation and indulgence. He was obliged to take the secret weapon, only for his country to avail of, or to destroy everything.
Everything.
Even if it cost them the loss of the ship. Even if it cost him his own life. The Cube was a priority but if he could not take it only for the Russian side to keep it, destruction would follow.
He completely agreed. Not that his opinion mattered, because even if he did not approve of the orders from above, he would never question their execution.
He looked at the bag, full of explosives.
“Be careful with that!”
The Lieutenant was giving instructions to the four soldiers who carried an enormous wooden crate.
At last they reached the spot and placed it carefully on the sand at a distance of a yard from the corpse of the submarine. It was really heavy, made of thick wooden beams, reinforced with steel lining. It was designed for special loads.
“Where do we cut, Sir?”, the Sergeant asked and opened the tool box. He took out of it the helmet and the safety goggles.
He also took out the angle grinder and switched it on. He then pressed it to the metal jacket of the ship. The molten metal started throwing out an avalanche of glittering shavings.