h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Hello Christiane,

I hope you are keeping well. Congratulations on your Reporter badge award from Lil.

Thank you for your kind comments and praise.

Was he grateful

I forgot; the other day I was for some reason drawn to thinking about simple maths, in fact determinants.

Found I forgot the definition, but luckily I found the proper definition on the internet but, my idea of a transposition is completely different and I sort of remember choosing parity differently.

Everything else still works under their definition, just can't so easily see effects of swapping rows; but as so often happens once I say that eureka.

Swapping two rows changes the parity;
so if two rows are identical

then |A|=-|A|=0

and it is easy to see that if we add a multiple of one row to another in B to get C then

|B|=|C| just use equal rows

and everything else is just too easy except

I still can't equate their idea of a transposition.

Which has caused me to become very depressed.

Curious, just last night I was mulling over something analogically similar, a comparison of the opponent process governing human sensory experience with the binary language of computers.

How the opponent process works, for example, when a visual sensor in the retina receives light in the area of the spectrum its sensitive to, it fires a neurotransmitter coding for the region of sensitivity of the receptor cell.

There are four neurotransmitters coding for actual visual sensation, white, found on the night vision rods, red, green and blue, found with the three kinds of color vision cones.

There are two other neurotransmitters involved, coding for black and yellow, which do not register actual sensation, but instead only perception originating deeper in the neural apparatus than the actual sensor cells.

When the visual sensor cell registers light in the range its sensitive to, it fires the appropriate neurotransmitter, called the 'component', then reflexively fires the 'anti-component', the opposite neurotransmitter, about a 50th second later, clearing the signal.

Black is the anti-component for white, green for red, red for green and yellow for blue with the four classes of visual sensor cells.

Its tempting to think of black and white, for example, as being analogous to the 1s and 0s of binary language, but actually they correspond to 1 and -1, the sum corresponding to zero.

Beyond vision, dualities of the character are a commonplace of the human experience and the mechanics fundamentally different from those of contemporary computer languages.

I've had a Guide article on this on my agenda for a long time and will be getting on with that.

That is interesting; I will have to resolve my problem now. Wonder if computers will see.

It's easy; the leading element in the sum is even parity, so is +1. Parity then alternates, not making sense silly statement assuming the leading element is the product of the diagonal.

Never mind; I know it but don't know how to explain it, and anyway you might already know this easy stuff.

I new it extremely well once, just goes to show how reliable memory is.

Maybe a rigorous definition of your preconception of the transposition might be interesting in its own right.

yes; but it is different. Their definition is easy to apply.

I've seen another webpage now showing what I thought it was.

So maybe they are talking about something different,but using familiar terms.

My idea of a transposition is a two lettered permutation;and any permutation can be written as an even or odd product of transpositions, but according to the webpage (1,3,2) is odd whilst ( 1,2,3) is even.

But they both look like (12)(13) and (13)(12) and even to me. But I could be all wrong.

One way to resolve it would be to assume they got it wrong and are in fact talking about parity, and parity is different to even or odd permutation.

Someone said that when you get older you lose some of three things
1. your hearing
2. your sight
3. I forget what the third thing was...oh yeah, your memory.

...or it goes like Oliver Wendell Holmes' "One Horse Shay" and everything all wears out at once...

I forgot... oh yes I saw a rule proved in Wikipedia because I don't like forgetting: Cramers rule and I couldn't understand the proof cos it was a postgraduate proof.

Took ages to find a proof I could understand and saw it was easy, trouble is it was easy and I suffer more than memory loss with age.

Russian scientists have observed cells switching off; they signal each other to commit suicide.

This is not good; but still, what can I do about it.

Anyway here is the easy proof:

http://planetmath.org/encyclopedia/ProofOfCramersRule.html

Hi dear paulh

What a lovely message from you.

well I had a brain scan four years ago, and apparently that is when I had the first stroke. Now I wonder if I have had another one ...... but as I have been doing my brain exdercises, and really working on getting my brain back into "order", I hope that I shall keep my wits about me. !

I wonder how long I have been losing my memory - I am remembering the most amazing parts of my life. Hypatia asks me if I am still writing my memoirs. I am either going to have to get a typist or get a wonderful new programme which lets one talk into a microphone and then it transfers it as script on one's computer.

But I shall have to use a magnifying glass to edit it...

Oh dear, but I am thrilled with the recall of my memory. which just shows that the brain can be repaired after a stroke. But up to now no doctor will believe me although the cardiac surgeon who first diagnosed my heart condition and two days later I was haveing a double bypass told me at the beginning of this year that he thought I would live to be a 100. My BP has gone dpwn absolutely wonderfully. But I wonder if I want to be a 100. Peutetre......

Hope you had a good weekend. I went down and visited Keith. He has made a dramatic recovery which is great.

Sincerely,

AlsoRan83
Christiane.
Monday 16th April 2012 16.40 GMT