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Jan 17, 2012, 2:18:08 PM1/17/12

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Consider situations in the general form:

X disagrees with (conflicts with) Y about Z.

X and Y could be people. (Really: ideas in people.)

Or they could be ideas within one person.

One or both could be criticisms (explanations of mistakes, rather than positive ideas about what's good).

Z, by the way, might be more than one thing. X and Y can also be multi-part.

Let's consider a more specific example.

X is some idea, e.g. that I'll have pizza for dinner.

Y is a criticism of X, e.g. that I haven't got enough money to afford pizza.

So, what happens? I use an option that I have no criticism of. I get a dinner I can afford.

Now we'll add more detail to make it harder. This time, X also includes criticism of all non-X dinner plans, e.g. that they won't taste like pizza which is good.

Now I can't simply choose some other dinner which I can afford, because I have a criticism of that.

To solve this, I could refute the second part of X and change my preferences, e.g. by figuring out that something else besides pizza is good too. Or I could acquire some more money. Or adjust my budget.

There's always many ways forward that I would potentially not have any criticism of.

What if I get stuck? I want pizza, because it's delicious, but I also don't want pizza, because I'm too poor. Whatever I do I have a criticism of it. I try to think of ideas like adjusting my budget, or eating something else, but I don't see how to make them work.

There is a simple, generalized approach. I don't have to think haphazardly and hope I find an answer.

All conflicts, as we've been discussing, always raise new problems. In particular:

X disagrees with (conflicts with) Y about Z.

If we don't solve this directly, it raises the problem:

Given X disagrees with (conflicts with) Y about Z, then what should I do?

This is a new problem. And it has several positive features:

1) This technique can be repeated unlimited times. If I use the technique once then get stuck again, I can use the technique again to get unstuck.

2) In general, any solutions we think of for this new problem will not be criticized by any of the criticisms we already had in mind. This makes it relatively easy to come up with a solution we don't have any criticism of. All those criticisms we were having a hard time with are not directly relevant.

3) Every application of this technique provides an *easier problem* than we had before. So we don't just get a new problem, but also an easier one. This, combined with the ability to use the technique repeatedly, lets us make our problem situation as easy as we like.

Why do the problems get progressively easier? Because they are progressively less ambitious. They accept various things, for the moment, and ask what to do anyway, instead of trying to deal with them directly.

The new problems are also longer more targeted to dealing with the specific issue of finding a way to move forward. This additional focus, instead of just on figuring stuff out generally, makes it easier. It tends towards a minimal solution.

In the context of disagreements between persons, the problems this technique generates progressively tend towards less cooperation, which is easier. In the context of ideas within a person, it's basically the same thing but a little harder to understand.

So, that's why this is true, by Elliot:

> Premise: there is an available option that one doesn't have a criticism of (and it can be figured out fast enough even in time pressure)

Because we can get past any sticking points, in a simple way, while also reducing our problem(s) to easier problem(s) as much as necessary. (It only works the purpose of figuring out an option for how to proceed. But we only have time limits in that context.)

See also: http://fallibleideas.com/avoiding-coercion

-- Elliot Temple

http://elliottemple.com/

Jan 17, 2012, 4:41:36 PM1/17/12

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What you've described is the Socratic method. But in way simpler terms.

-- Rami

Jan 17, 2012, 4:46:43 PM1/17/12

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I don't think so. I think this is largely original (to me, Deutsch, or other people involved with TCS. Mostly me for the specific stuff in this email). Can you point out any description of the Socratic method, or essay by any Socratic advocate, which understands/covers this stuff, just more complicated?

-- Elliot Temple

http://fallibleideas.com/

Jan 17, 2012, 6:03:45 PM1/17/12

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Just one part of it. Breaking problems down into smaller parts. Each

child part is easier to tackle than its parent part.

-- Rami

Jan 17, 2012, 6:12:16 PM1/17/12

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I don't think this is very similar to the general concept of breaking problems into smaller parts. It's not a part of the original problem, it's a new problem.

And with the normal concept of breaking problems into parts, you transform one problem into two or more problems. This turns one problem into one problem. It's a different mapping.

And with breaking into parts, your goal is to solve the original problem. With this, it is not.

And with breaking into parts, you would then go through at deal with every part, one by one. But this doesn't work that way.

Jan 17, 2012, 6:18:58 PM1/17/12

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I think that means the same thing.

> And with the normal concept of breaking problems into parts, you transform one problem into two or more problems. This turns one problem into one problem. It's a different mapping.

Yes thats what I meant.

> And with breaking into parts, your goal is to solve the original problem. With this, it is not.

Yes thats different.

> And with breaking into parts, you would then go through at deal with every part, one by one. But this doesn't work that way.

Yes thats new too.

-- Rami

Jan 17, 2012, 11:12:22 PM1/17/12

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On 17 Jan 2012, at 11:03pm, Rami Rustom wrote:

> Breaking problems down into smaller parts. Each

> child part is easier to tackle than its parent part.

Just for the record: that is just one of many patterns of problem solving. Sometimes a problem is better solved by aggregating smaller problems into a larger one. This especially happens at jumps to universality, but it's common on every scale.

-- David Deutsch

Jan 18, 2012, 8:21:27 AM1/18/12

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On Jan 17, 2012 10:12 PM, "David Deutsch" <david....@qubit.org> wrote:

> On 17 Jan 2012, at 11:03pm, Rami Rustom wrote:

>

> > Breaking problems down into smaller parts. Each

> > child part is easier to tackle than its parent part.

>

> Just for the record: that is just one of many patterns of problem solving. Sometimes a problem is better solved by aggregating smaller problems into a larger one.

> On 17 Jan 2012, at 11:03pm, Rami Rustom wrote:

>

> > Breaking problems down into smaller parts. Each

> > child part is easier to tackle than its parent part.

>

> Just for the record: that is just one of many patterns of problem solving. Sometimes a problem is better solved by aggregating smaller problems into a larger one.

That makes sense but I can't come up with an example.

> This especially happens at jumps to universality,

I read this 3 times on 3 different occasions. But still confused. What

do you mean?

-- Rami

Jan 18, 2012, 12:00:06 PM1/18/12

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Universality is when a particular solution solves all of the problems

in a given domain. So, for example, the Arabic numeral system is

universal for doing addition, subtraction and multiplication with

positive integers. By contrast, tally marks are useless for doing

those things except for very small numbers. So the jump to

universality as a result of the adoption of Arabic numerals solved the

problem of how to do all of addition, subtraction and multiplication

at the same time. So it's easier to take those problems, that look

very different when expressed in terms of tally marks and invent a way

to solve them all with Arabic numerals than it is to solve them

separately.

Alan

Jan 18, 2012, 12:28:17 PM1/18/12

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Ok. But how is that an example of *Sometimes a problem is better

solved by aggregating smaller problems into a larger one*?

-- Rami

Jan 18, 2012, 12:26:24 PM1/18/12

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On Jan 18, 6:00 pm, Alan Forrester <alanmichaelforres...@googlemail.com> wrote:

> On 18 January 2012 13:21, Rami Rustom

>> <david.deut...@qubit.org> wrote:

>>> On 17 Jan 2012, at 11:03pm, Rami Rustom wrote:

>

>>>> Breaking problems down into smaller parts. Each

>>>> child part is easier to tackle than its parent part.

>

>>> Just for the record: that is just one of many patterns of problem

>>> solving. Sometimes a problem is better solved by aggregating

>>> smaller problems into a larger one.

>

>> That makes sense but I can't come up with an example.

>

>>> This especially happens at jumps to universality,

>

>> I read this 3 times on 3 different occasions. But still confused.

>

>> What do you mean?

>

> Universality is when a particular solution solves all of the

> problems

> in a given domain. So, for example, the Arabic numeral system is

> universal for doing addition, subtraction and multiplication with

> positive integers. By contrast, tally marks are useless for doing

> those things except for very small numbers.

But you can do multiplication, addition and subtraction between positive integers with tally marks.

When you add you concatenate the two strings together, when you subtract you shorten the first string by the length of the second, and when you multiply you concatenate one copy of the first string for each tally mark in the second.

There is no reason why you can't do this (in principle) with arbitrary large integers.

It is true that the Arabic system is way more efficient but even it becomes useless for sufficiently large integers.

So I'm not 100% clear what exactly is the domain where the Arabic system is universal and the tally mark system isn't.

Matjaž Leonardis

Jan 18, 2012, 1:28:09 PM1/18/12

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This is explained in BoI pp. 128-129.

Using tally marks is basically the same as counting objects. Doing arithmetic with Arabic numerals doesn't involve counting. So you can understand the properties of those operations without thinking of them in terms of counting.

Alan

Jan 18, 2012, 1:30:23 PM1/18/12

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The problem is something like: how do I write down numbers in such a way as to make it easy to read and manipulate them? Addition, multiplication and so on are just examples of operations that are easier as a result of the numbers having that property.

Alan

Jan 18, 2012, 1:53:56 PM1/18/12

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On Wed, Jan 18, 2012 at 12:30 PM, Alan Forrester

Lets see if I understand. Every time that we realize that there exists

a level of emergence, this is an example of *a problem is better

solved by aggregating smaller problems*. Is that right?

Jan 18, 2012, 2:30:17 PM1/18/12

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No. As described in pp. 108-111 of BoI, in emergence we may not be interested in the details of what the emergent behaviour emerges from. For example, when you boil a kettle you're not interested in the details of what all the water molecules are doing. You're not trying to solve the smaller problem at all so to say that you're aggregating the smaller problems is wrong.

A better example might go like this. Suppose that you want to work out how long it takes a ball to roll down an inclined plane, and you also want to work out how long it takes a brick to slide down an inclined plane, but you think of them as completely separate problems. Both of those problems might be interesting in their own right, and they can both be solved using Newtonian mechanics. So trying to solve a larger problem that contains those two problems as a special case, allows both of them to be solved.

Alan

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