Starship Asterisk*

owlice wrote:
104729 is the ten-thousandth prime number.

emc wrote:
I don’t know what the big deal is about numbers…

there are only ten digits for us to expound on.

• That's all our Hans had room for.

Excerpts from Chapter 23 of Oliver Sacks' The Man Who Mistook His Wife For a Hat, http://empslocal.ex.ac.uk/people/staff/ ... /twins.htm

When I first met the twins, John and Michael, in 1966 in a state hospital, they were already well known. They had been on radio and television, and made the subject of detailed scientific and popular reports ([1],[2]). They had even, I suspected, found their way into science fiction, a little 'fictionalised', but essentially as portrayed in the accounts that had been published [3].

The twins, who were then twenty-six years old, had been in institutions since the age of seven, variously diagnosed as autistic, psychotic or severely retarded. Most of the accounts concluded that, as idiots savants go, there was 'nothing much to them' -except for their remarkable 'documentary' memories of the tiniest visual details of their own experience, and their use of an unconscious, calendrical algorithm that enabled them to say at once what day of the week a date far in the past or future would fall.

...

The second time they were seated in a corner together, with a mysterious, secret smile on their faces, a smile I had never seen before, enjoying the strange pleasure and peace they now seemed to have. I crept up quietly, so as not to disturb them. They seemed to be locked in a singular, purely numerical, converse. John would say a number - a six-figure number. Michael would catch the number, nod, smile and seem to savour it. Then he, in turn, would say another six-figure number, and now it was John who received, and appreciated it richly. They looked, at first, like two connoisseurs wine-tasting, sharing rare tastes, rare appreciations. I sat still, unseen by them, mesmerised, bewildered.

...

As soon as I got home I pulled out tables of powers, factors, logarithms and primes - mementos and relics of an odd, isolated period in my own childhood, when I too was something of a number brooder, a number 'see-er', and had a peculiar passion for numbers. I already had a hunch - and now I confirmed it. All the numbers, the six figure numbers, which the twins had exchanged, were primes - i.e., numbers that could be evenly divided by no other whole number than itself or one. Had they somehow seen or possessed such a book as mine - or were they, in some unimaginable way, themselves 'seeing' primes, in somewhat the same way as they had 'seen' 111-ness or triple 37-ness? Certainly they could not be calculating them - they could calculate nothing.

I returned to the ward the next day, carrying the precious book of primes with me. I again found them closeted in their numerical communion, but this time, without saying anything, I quietly joined them. They were taken aback at first, but when I made no interruption, they resumed their 'game' of six-figure primes. After a few minutes I decided to join in, and ventured a number, an eight-figure prime. They both turned towards me, then suddenly became still, with a look of intense concentration and perhaps wonder on their faces. There was a long pause - the longest I had ever known them to make, it must have lasted a half-minute or more - and then suddenly, simultaneously, they both broke into smiles.

...

They drew apart slightly, making room for me, a new number playmate, a third in their world. Then John, who always took the lead, thought for a very long time - it must have been at least five minutes, though I dared not move, and scarcely breathed - and brought out a nine-figure number; and after a similar time his twin Michael responded with a similar one. And then I, in my turn, after a surreptitious look in my book, added my own rather dishonest contribution, a ten-figure prime I found in my book.

There was again, and for even longer, a wondering, still silence; and then John, after a prodigious internal contemplation brought out a twelve-figure number. I had no way of checking this, and could not respond, because my own book - which as far as I knew, was unique of its kind - did not go beyond ten-figure primes. But Michael was up to it, though it took him five minutes - and an hour later the twins were swapping twenty-figure primes, at least I assume this was so, for I had no way of checking it. Nor was there any easy way, in 1966, unless one had the use of a sophisticated computer. And even then, it would have been difficult, for whether one uses Eratosthenes' sieve, or any other algorithm, there is no simple method of calculating primes. There is no simple method, for primes of this order - and yet the twins were doing it.

owlice wrote:Total posts 110501

Prime, glorious prime! Hot soup, and potatoes!

Beyond wrote:x is the small version of X.

MargaritaMc wrote:The number I am considering is
125 000 000

299 195.742 • x = one astronomical unit (kilometres)

What is x?

Margarita
(Who is getting to be in command of simple mathematics...)

bystander wrote:

MargaritaMc wrote:The number I am considering is
125 000 000

299 195.742 • x = one astronomical unit (kilometres)

What is x?

Margarita
(Who is getting to be in command of simple mathematics...)

The cube root of 125,000,000 is 500.

1 AU is 149,597,870.7 km / 299,792.458 km per light-second equals 499.005 light-seconds