Deck Of Cards - New Version

A bunch of students were heading on a long hike and came to a town called Bala, where they decided to rest. That evening being Wednesday, some of the students went to therapy. Those who had manuals took them out and began to discuss their life-scripts, but one student had only a deck of cards and began to lay them out. The therapist saw this and, having issues with being perfect, was cross, and said “Put away those cards and come and see me in the morning” and threw the student out of the group.

When the student returned in the morning, the therapist and his supervisor were there. “Why have you brought this student here?” said the supervisor.

“For playing cards in therapy”, said the therapist.

“I hope you have a good explanation” said the supervisor.

“I do”, said the student. “It’s like this …” and he began:

‘I have been on a long trip and during that time I have had neither my training manual, my copy of TA Theory, nor my notes from Eric Berne’s lecture series. But I have had a deck of cards which has helped me to get through the difficult times.

When I see the Ace, I remember that I’m OK. I knew that anyway.

When I see the two, I remember that every transaction takes place between two people and that there are two roles in counselling, therapist and client, and I know which one I want to be.

When I see the three, I remember the three ego-states, Parent, Adult and Child. And all the sub-states which are quite a lot more. I like the Little Professor most.

When I see the four, I think of the four life-positions in the OK Corral.

When I see the five, I think of the five drivers “be strong”, “try hard”, “please me”, “hurry up”, and “be perfect”. and the five schools of TA. Except that there are now six drivers.

When I see the six, I think of the six patterns of personality adoption identified by Stewart and Joines and the six types of social behaviour – withdrawal, ritual, activity, pastime, games, and intimacy.

When I see the seven, I remember the seven elements that make up a script and the age up to which parents give us general injunctions.

When I see the eight, I think of the eight therapeutic techniques; four are interventions and four are interpositions.

When I see the nine, I think of the nine types of complementary transaction. And some have ulterior ones.

When I see the ten, I think of the ten modes in the OK Modes Model, four effective and six ineffective. (Nancy Porter)

When I see the Jack, or Knave, I remember that I am a prince but I have been turned into a frog.

When I see the Queen, I think of my mother who as controlling parent did this by teaching me the five restrictive rules of stroking.

When I see the King, I think of Eric Berne, who developed his own theory of therapy when his application to the San Francisco Psychoanalytic Institute was turned down, and I wonder what his drivers were.

 

There are 52 cards in a deck, the number of countries which had TA Associations in 1992, so it must be true.

There are 12 picture cards, the number of script injunctions.

There are 4 suits, the number of categories of goals.

There are 13 cards in a suit, the number of people in a group session, counting the therapist.

If I add up the spots on the cards, I get 365, the number of hours it would take to learn all the theory of TA, and nearly as many as the number of games.

So you see my deck of cards is as useful for therapy and counselling as all the TA Journals and text-books put together.’

And the therapist now had enough stamps for a racket so threw him out, so the student with his awareness of himself and of phoniness went on to be a successful gestalt therapist.

Speak To Me

Nothing like going abroad to make you think about languages. And nothing like going to Holland to think about the English language.

Dutch is apparently halfway between English and German. Simple example ... "straat" is halfway between "street" and "strasse". You can read the signs above the shops (well I can tell what Wijn means anyway, lots of others).

So where did the English language come from?

French, Spanish and Italian are all obviously derived from Latin. Yet not all the same ... but when you get used to how they differ you can predict to some extent what the word will be ... verb conjugations and constructions etc. (I used to know all this stuff, not now.)

We assume this was because the Romans conquered all these places ... but the Romans conquered England. The pre-existing language was not English, but Welsh (Cornish, Celtic?). English, from the Angles, came afterwards surely? How did it supplant the Romano-British language? Why was it different from Dutch/German (Flemish)?

Expert on the history of language, someone?

Shopping

This blog hasn't had a magazine review for a while, so here's a new one. It's the Morrison's supermarket Jan/Feb issue and it's a classic.

"January is a month for looking after yourself and enjoying lots of healthy food ..." are the first words you come across in the editorial. It's not just the editor who thinks so, either.

"January is a good time to cook nutritious meals that taste great and make you feel great, too", says Aldo Zilli on page 31.

Well that's all right then. I'd like to know though which are the months when I shouldn't be looking after myself, and when it is a bad time to cook nutritious meals (or maybe just ones that don't taste great, there's a logical conjunction in there that needs analysing). Should I start on Feb 1 with a big pile of chips? (Actually you can treat yourself to some "moreish" Morrisons chocolate which is much cheaper if you buy two bars*, but I'm not sure when you're allowed to get started on that.)

We know what they mean. We didn't get the Nov/Dec issue but I bet it was all about treats for Christmas (I'd have money on the phrase "long winter nights" turning up, too, no cliche unspoken) and adverts for lots of chocolate. So having persuaded you into all that, now they can press on with ".... lose those extra festive pounds ... how do you cut back without feeling you're missing out?" (I'm back in the editorial again).

If you think I'm cynical, I'm sure I'm not the only one, the Morrisons' (and others') marketing department is there too. Oh, I beg your pardon: "Editorial opinions expressed ... are not necessarily those of Wm Morrison Supermarkets plc ..." Maybe Morrisons don't think I should look after myself in January and Jenn Cooper will get a rocket for saying so? Who can say?

While we're being healthy, Michelin-star chef Paul Rankin "tells us why he loves chip butties". Er, mixed messages? He's got a favourite ingredient .. how cheffy is that? The temptation to put extra-virgin olive oil in his butty must be overwhelming. Or not.

Now some things to put in your diary, I hope you've got plenty of space:
23-29 January is Farmhouse Breakfast Week. No you don't have to go out into some wild cottage in the country thankfully, but it's a campaign to start the day with this important meal. There's a picture of a boiled egg and French bread but otherwise I don't have a clue what a Farmhouse Breakfast is, so you'll have to go to the website www.shakeupyourwakeup.com to find out the events in your area (maybe there is a farmhouse to go to, wouldn't that be fun?) and "inspiring" breakfast ideas.

February is National Heart Month, including Wear Red day on the 25th. The British Heart Foundation is 50 so is having lots of celebrations to raise money (sic).

Bramley Apple Week starts on February 6. It's the best apple for cooking and it's grown only in Britain. I think we should stop being so mean to other countries and export them some trees.

And Feb 3 is Chinese New Year (celebrations on the 6th in Leicester Square) so there are some "healthier" recipes to celebrate. Do you think the Chinese will mind this insult to their culture? I wonder if they produce healthier Christmas dinner recipes for us and what Morrisons would think of them?

(Helpfully, all the recipes in the magazine tell you how much salt, fat etc there are in "one serving", whatever one serving is. I feel a spreadsheet and lots of graphs coming on.)

And don't forget Burns Night on January 25. Start the day with a Farmhouse Breakfast and finish with haggis, neeps and tatties and a whisky sauce (now you're talking).
And the Brighton Half-Marathon on 20 February. I think it's a bit late for me to sign up now though.

There is helpful advice too.

"Wrap rhubarb in plastic and store it in the coldest part of the fridge for up to a week." (Paul Thornton). I wonder if he means to say " ... no more than a week"? Perhaps it's the other way of looking at it.

Now one piece of advice I don't understand though. They give in five categories (energy, sugar, fat, saturated fat, and salt) a Guideline Daily Amount (GDA). This is a new one to me. Is it a recommended amount, a maximum, or a minimum? And why not call it one of these?
The sugar one is called total sugar so that one's clear but the other's aren't so-called, suggesting rather that they're what you should have or work towards - and 2500 calories for a man seems on the low side?

Why's it matter?

Back to the editorial: " .... we've included a few more indulgent recipes to treat yourself to - 30 per cent or under your GDAs". Er, but should I be making sure I get somewhere near the other 70% too? Maybe the chocolate will help me get there? Or a swift couple of pints with the lads?

There are some good things. There are some nice recipes and some for children to get them cooking too. There's very little overtly from "nutritionists" (but I think we need to look at this GDA thing and just how much fat you should have) and the keep fit advice is sensible and practical and not overdone with encouragements for vitamin pills and whatnot. I note that Zumba is an "exiting" (sic) new dance craze. Maybe everyone leaves early?

You can forgive the adverts and it's interesting where the chickens come from (and that the correct weight is 2.25 kg).

Three heaped tablespoons of cooked lentils count as one of your five a day. Geez that's a lot of lentils.

One excellent piece of advice when going shopping. Make a list and "you'll be surprised how much money you save ... you're not tempted to buy more than you really need" I wonder how much the store managers approve of that?

Oh I have to report one piece of sexism before I finish.

The tasting panel (soup this month) has 4 members - all mothers. Not even a token man, far less a balance. Maybe men are thought to be incompetent? Or maybe it's laziness. Must do bettr, Morrisons. But then there's no male customers at all pictured; I suppose some of the letters could be from men. Oh there is Scott, 15, and the packed lunches his mum makes for him.

I wonder what March and April are good months for?

*£1.19 each or 2 for £2. Er, two please!

Mathematics

Define F(N), the factor-sum of N, on integer N, as the sum of the proper factors of N. Formally F(N) = Σi, i divides N, i = 1 to N-1.

Further define Q(N), the quotient-factor of N, Q(N) = F(N)/N.

In common usage:
Q(N) = 1, N is perfect
Q(N) < 1, N is deficient
Q(N) > 1, N is abundant.

Previously existing result:
N is perfect if N = 2^n x (2^(n+1) - 1), provided (2^(n+1) - 1) is prime.
It is not known whether all perfect numbers are of this form.

Preliminary results:
If P is prime, F(P) = 1 and Q(P) = 1/P. Clearly, for e, there exists N s.t. that Q(N) < e.
Primes are maximally deficient.

If N = P^n, where P is prime, F(N) = (P^n - 1)/(P - 1), Q(N) = (N-1)/N(P-1)
For particular P, Q(P^n) tends to 1/(P-1) as n tends to infinity.
In the case P = 2, F(2^n) = 2^n - 1 and Q(2^n) tends to 1.
Integers of the form 2^n are minimally deficient.

Question: Are there other N such that F(N) = N - 1?

If N is abundant, any multiple of N is abundant with greater factor-quotient. (See following lemma; more fractions are added when a multiple is derived.) Formally, if M divides N, then Q(N) > Q(M).

Lemma
For all n, there exists N s.t. Q(N) > n. (Abundancy increases without limit.)
Proof
Q(N) is the sum of fractions of the form 1/n. Since Σ1/n diverges (well-known result), Q(N) is unbounded.

Therefore it is possible to define N is abundant-S if Q(N) >= S and assert that there exists an infinity of abundant-S numbers, whatever the value of S. For instance, 120 is abundant-2 (the smallest such).

Question: Find for each integer N, find the smallest M such that Q(M) ³ N

Further Result:
Since the sum of the odd fractions can also be shown to diverge[1], there is also an infinity of odd abundant-S numbers. The first odd abundant number is 945 and the smallest odd abundant-2 number is believed to be 1 018 976 683 725, which has Q-value 2.0107.

Define N is super-abundant if Q(N) > 1 and Q(N) > Q(n) if N > n. (Informally, a new record is set.)
The first super-abundant number is the first abundant number, 12. Q(12) = 1.33. (The record-holders that are not abundant are 2, 4 and 6.) The set of super-abundant numbers has infinitely many members. (A record-holder will be beaten by any multiple, from result above.)

Question: Find the super-abundant numbers.

[1] The proof is similar to that of the full series. Consider the series 1/3 + 1/5 + 1/7 +1/9 ... If we successively group 1, 3, 9, 27 ... terms ie 1/3 + (1/5 + 1/7 + 1/9) + (1/11 + ... + 1/27) + ... it is clear that the series is greater than 1/3 + 1/3 + 1/3 +1/3 ... and therefore diverges (slowly).

It has been necessary to replace some symbols unsupported by this font by words in the above.

Abundance

Find the next number in the sequence:

2, 4, 6, 12, 24, 60, 120 ...

I believe I know the next three but there seems to be a big gap later on so I'm doubtful whether 840 really is on it. And is there really nothing between 2520 and 27720 (assuming these are on it)? Research continues.

A slightly easier related (provably expanded?) sequence goes:
2, 4, 6, 8, 10, 12, 18, 20, 24, 30 ...

Edit: Discovered an error in the top sequence. To be updated later.