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Let's say, during this step a free radical bumps into an ethene. What do you think happens, then?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,547

b happens.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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Yes, and what is the new number of ethenes and free radicals?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,547

The reaction occurs in discrete time steps, during each of which a random molecule attacks another random molecule and the result of the attack is given by the following rules:

a) Ethene attacks ethene: Nothing happens. The reaction proceeds to the next step.

b) A free radical attacks an ethene: The ethene is removed from the system. The chain length of the free radical increases by 1. The reaction proceeds to the next step.

c) A free radical of length m attacks a free radical of length n: Both radicals are removed. A new kind of molecule, called the "polymer" is formed. The polymer is of chain length m + n. The reaction proceeds to the next step.

d) A polymer attacks another polymer: Nothing happens. The reaction proceeds to the next step.

One less ethene and no change in the number of free radicals.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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Correct.

Do you now see why the probabilities will change?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,547

Yes, sometimes the reactants will be plentiful and sometimes there will be none.

What happens when there are a lot of each?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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Yes, sometimes the reactants will be plentiful and sometimes there will be none.

Correct. Let me clarify this:

Let's say there are 2 free radicals and 10 ethene molecules in the system in step i. Any two of those things react at random.

What is the probability that during this step, a will happen? (10/12)*(9/11)

What is the probability that during this step, b will happen? (2/12)*(10/11)

What is the probability that during this step, c will happen? (2/12)*(1/11)

What is the probability that during this step, d will happen? 0

Let's further assume that b happens. Now the system has 2 free radicals and 9 ethene molecules in step i+1

What is the probability that during this step, a will happen? (9/11)*(8/10)

What is the probability that during this step, b will happen? (2/11)*(9/10)

What is the probability that during this step, c will happen? (2/11)*(1/10)

What is the probability that during this step, d will happen? 0

---

Do you see how the probability changes?

Even if there are a lot of the molecules, we will assume that the spherical cow model holds.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,547

Possibly that will be enough.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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Yes.

Should I start by simulating the reaction according to the spherical cow model?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,547

I do not know the answer for spherical or ellipsoidical cows.

The changing probability is a bit like a problem I solved here just recently.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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Long/Hardwinded probability..?

Do you think the spherical cow model is a bad place to start?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,547

Long/Hardwinded probability..?

I think that was it. Only EVW has a full solution, mine is an ansatz.

Do you think the spherical cow model is a bad place to start?

For you it is fine.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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I think this is more complex.

Do you think this will agree with experimental data?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,547

That is not possible to know.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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I need a break. Talk to you later

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,547

Okay, see you later.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Primenumbers****Member**- Registered: 2013-01-22
- Posts: 127

**I think the meaning of life is to survive and have children.** Taking my theory from Darwin- "survival of the fittest". It's good to be alive right? Right. So the only reason **you** are alive is because your ancestors survived and had children. (If they hadn't done that you wouldn't be here). Therefore for your future offsprings life you must survive and have children. Therefore the purpose of life in general is to survive and have children.

**"Time not important. Only life important."*** - The Fifth Element 1997*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,547

I did not have any kids...

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Primenumbers****Member**- Registered: 2013-01-22
- Posts: 127

Neither did I. I think enjoying life is No. 1 priority, otherwise there's no point having more of a bad thing. So maybe, **the purpose of life is to enjoy it so that it's better to be alive than not.**

**"Time not important. Only life important."*** - The Fifth Element 1997*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,547

Life is such a unique experience it is hard not to get lots of enjoyment out of it. Unfortunately, some of those experiences are painful.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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Primenumbers wrote:

I think the meaning of life is to survive and have children..

I am sure all the retrovirus will agree

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**Primenumbers****Member**- Registered: 2013-01-22
- Posts: 127

I am quite lucky I am on sickness benefit so I don't have to work. I get quite a lot of enjoyment out of life really.

**"Time not important. Only life important."*** - The Fifth Element 1997*

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