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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,137

Agnishom wrote:

I always wanted to be a theoretical physicist when I was a child.

Me too!

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Did anyone in here ever dream about being a mathematician?

**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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**Relentless****Member**- Registered: 2015-12-15
- Posts: 624

I wanted to be a philosopher............

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bobbym wrote:

Did anyone in here ever dream about being a mathematician?

Yes. Although, thanks to the "careers advice" I was given at my school, I had been convinced that they either did not exist or were not worth becoming.

*Last edited by zetafunc (2015-12-27 06:02:25)*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Although I can not really argue with their conclusions the one big problem with school is that it does give a student lots of wrong ideas.

**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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**Relentless****Member**- Registered: 2015-12-15
- Posts: 624

How did you find school?

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

I liked many of my teachers but school reminded me of a jail sentence.

**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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bobbym wrote:

Did anyone in here ever dream about being a mathematician?

Me, but you don't like mathermaticians.

Here is my first model for the problem.

Assume the reaction proceeds in discrete time steps, during each of which a random molecule in the system attacks another molecule at random. Furthermore, let us assume every attack happens in the right orientation and with sufficient energy.

'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: 109,606

We need some condition that will slow down or stop the reaction and the probability this will happen. Else, the reaction will continue forever which we know does not happen.

**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 thought we already included that in the model.

**Agnishom's Spherical Cow Model for the Radical Polymerization problem**

To begin with there are n1 phenyl free radicals (a free radical with chain length 0) in the system and n2 ethene molecules.

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.

The reaction continues until the molecules in the systems undergoes no further changes, i.e, the number of free radicals in the system is 0.

*Last edited by Agnishom (2015-12-27 14:06:14)*

'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: 109,606

Is that a discrete process?

**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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The spherical cow model or reality?

'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: 109,606

This polymerization process you are trying to model.

**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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God modelled the universe like the card game Mao. There are strange rules which he refuses to disclose.

In reality, the process might be continuous. Or they might not be because space-time could be fundamentally quantized. But who knows how reality works?

The spherical cow model of the polymerization problem is discrete, though. Do you think this model is a bad place to start?

*Last edited by Agnishom (2015-12-27 16:32:47)*

'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: 109,606

Do you think this model is a bad place to start?

I do not see any probabilities provided for a,b,c, or d. To form a Markov chain we will need them.

**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 am sorry, what are a, b, c, d?

'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: 109,606

Post #260 has them.

**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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The spherical cow model picks two species from the system at each step uniformly at random.

'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: 109,606

With equal probability?

**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. But that does not mean a, b, c and d happen with equal probability.

The next does not understand.

'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: 109,606

You are right.

**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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Am I right about the probabilities or your understanding?

'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: 109,606

But that does not mean a, b, c and d happen with equal probability.

Both, what are the probabilities of a,b,c and d?

**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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It depends.

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

In the step i+1, the probabilities will change again.

'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: 109,606

Why do the probabilities change?

**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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