SERVING THE QUANTITATIVE FINANCE COMMUNITY

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Cuchulainn
Posts: 56926
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
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### Re: Philosophy of Mathematics

It was the same case, said twice.
Paul Halmos once visited our maths dept. Great mathematician.

Cuchulainn
Posts: 56926
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
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### Re: Philosophy of Mathematics

A physicist, an engineer and a mathematician were all in a hotel
sleeping when a fire broke out in their respective rooms.

The physicist woke up, saw the fire, ran over to his desk, pulled
out his CRC, and began working out all sorts of fluid dynamics
equations.  After a couple minutes, he threw down his pencil, got
a graduated cylinder out of his suitcase, and measured out a
precise amount of water.  He threw it on the fire, extinguishing
it, with not a drop wasted, and went back to sleep.

The engineer woke up, saw the fire, ran into the bathroom, turned
on the faucets full-blast, flooding out the entire apartment,
which put out the fire, and went back to sleep.

The mathematician woke up, saw the fire, ran over to his desk,
began working through theorems, lemmas, hypotheses , you -name-it,
and after a few minutes, put down his pencil triumphantly and
exclaimed, "I have *proven* that I *can* put the fire out!"
He then went back to sleep.

Collector
Posts: 3870
Joined: August 21st, 2001, 12:37 pm

### Re: Philosophy of Mathematics

Cuchulainn wrote:
A physicist, an engineer and a mathematician were all in a hotel
sleeping when a fire broke out in their respective rooms.

The physicist woke up, saw the fire, ran over to his desk, pulled
out his CRC, and began working out all sorts of fluid dynamics
equations.  After a couple minutes, he threw down his pencil, got
a graduated cylinder out of his suitcase, and measured out a
precise amount of water.  He threw it on the fire, extinguishing
it, with not a drop wasted, and went back to sleep.

The engineer woke up, saw the fire, ran into the bathroom, turned
on the faucets full-blast, flooding out the entire apartment,
which put out the fire, and went back to sleep.

The mathematician woke up, saw the fire, ran over to his desk,
began working through theorems, lemmas, hypotheses , you -name-it,
and after a few minutes, put down his pencil triumphantly and
exclaimed, "I have *proven* that I *can* put the fire out!"
He then went back to sleep.

So the proof is lost! Too bad!

snufkin
Posts: 63
Joined: January 25th, 2017, 9:05 am
Location: Cambridge

### Re: Philosophy of Mathematics

Collector wrote:
Cuchulainn wrote:
A physicist, an engineer and a mathematician were all in a hotel
sleeping when a fire broke out in their respective rooms.

The physicist ...
The engineer ...
The mathematician ... exclaimed, "I have *proven* that I *can* put the fire out!"
He then went back to sleep.

So the proof is lost! Too bad!

Hanc marginis exiguitas non caperet.
On the other hand, in my school days the joke went along the lines of,

How will physicist and mathematician solve a simple task, "Boil a kettle?" Easily: pour water, light a fire, put the kettle on fire and heat up to 100C. And now a new task, "Boil a pot filled with water?"
Physicists: light a fire, put it, heat it.
Mathematicians: pour water out of the kettle, that reduces the problem to the previous one.

Now this joke is fine, but boring. Let's see what they do if there's a house on fire? And what will they do next, when the house is not on fire, but the hay a fire extinguisher and a box of matches?

Collector
Posts: 3870
Joined: August 21st, 2001, 12:37 pm

### Re: Philosophy of Mathematics

can I use $\frac{x}{\frac{y}{0}}=\frac{x}{\infty}=$0 as part of a proof"? or will mathematicians then see a red zero? Have they got to a conclusion on division by 0?

Cuchulainn
Posts: 56926
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
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### Re: Philosophy of Mathematics

Collector wrote:
can I use $\frac{x}{\frac{y}{0}}=\frac{x}{\infty}=$0 as part of a proof"? or will mathematicians then see a red zero? Have they got to a conclusion on division by 0?

Is the article refereed? I think the referee will pick it up.What about in a footnote?

Collector
Posts: 3870
Joined: August 21st, 2001, 12:37 pm

### Re: Philosophy of Mathematics

Cuchulainn wrote:
Collector wrote:
can I use $\frac{x}{\frac{y}{0}}=\frac{x}{\infty}=$0 as part of a proof"? or will mathematicians then see a red zero? Have they got to a conclusion on division by 0?

Is the article refereed? I think the referee will pick it up.What about in a footnote?

I was able to prove it in another way, but indirectly this gives the same for my case. (the referee is father Time, mother?, yes time will always pick it up, then drop it and dissolve it.)

Cuchulainn
Posts: 56926
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
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### Re: Philosophy of Mathematics

snufkin,
is this better?

An engineer, a physicist, and a mathematician were on a train heading north, and had just crossed the border into Scotland.
• The engineer looked out of the window and said "Look! Scottish sheep are black!"
• The physicist said, "No, no. Some Scottish sheep are black."
• The mathematician looked irritated. "There is at least one field, containing at least one sheep, of which at least one side is black."
• The statistician : "It's not significant. We only know there's one black sheep"
• The computer scientist : "Oh, no! A special case!"

Hanc marginis

Collector
Posts: 3870
Joined: August 21st, 2001, 12:37 pm

### Re: Philosophy of Mathematics

If space and time at depth of reality should be quantized would then not also probabilities be quantized?

In that view I think one would get a minimum probability gap (the next probability above 0) that would be time dependent (?). (please do not introduce negative pseudo probabilities into this discussion)

This would likely not have any implications on for example finance today, but could so hypothetically in the future as the time windows for trades are getting shorter and shorter.

outrun
Posts: 4573
Joined: April 29th, 2016, 1:40 pm

### Re: Philosophy of Mathematics

Collector wrote:
If space and time at depth of reality should be quantized would then not also probabilities be quantized?

In that view I think one would get a minimum probability gap (the next probability above 0) that was time dependent? (please do not introduce negative pseudo probabilities into this discussion)

Imagine that all events / states are composites of elementary binary states.
By combining events you can construct more complicated probabilities (A and B or C happening), and variants will allow you to turns this into a categorical pdf with many categories with different probabilities. The smallest probability would probably be everything -every electron, photon- being is the state it is simultaneously?

bearish
Posts: 3681
Joined: February 3rd, 2011, 2:19 pm

### Re: Philosophy of Mathematics

Collector wrote:
If space and time at depth of reality should be quantized would then not also probabilities be quantized?

In that view I think one would get a minimum probability gap (the next probability above 0) that would be time dependent (?). (please do not introduce negative pseudo probabilities into this discussion)

This would likely not have any implications on for example finance today, but could so hypothetically in the future as the time windows for trades are getting shorter and shorter.

You may want to check in with Tom Lindstrøm at UiO. He has done extensive work on nonstandard stochastic analysis, at the heart of which lies a discrete representation of probabilities.

Cuchulainn
Posts: 56926
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

### Re: Philosophy of Mathematics

If space and time at depth of reality should be quantized would then not also probabilities be quantized?

Reasoning by analogy is tricky at best..Space and time are not reality,.they are models of reality.
What is your definition of 'probability'? What is 'quantization?'

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Re: Philosophy of Mathematics

Collector wrote:
If space and time at depth of reality should be quantized would then not also probabilities be quantized?

In that view I think one would get a minimum probability gap (the next probability above 0) that would be time dependent (?). (please do not introduce negative pseudo probabilities into this discussion)

This would likely not have any implications on for example finance today, but could so hypothetically in the future as the time windows for trades are getting shorter and shorter.
A frequentist would assert that all probabilities are rational numbers based on an integer number of in-class events out of an integer number of population events. Thus, the discrete increments would be driven by increments to the denominator and numerator.

Yet some physical stochastic systems such as https://en.wikipedia.org/wiki/Buffon%27s_needle can be shown to create transcendental values. And the central limit theorem seems to lead us to the Gaussian distribution with real-values probabilities. But do financial systems remain structurally invariant for long enough to create near-real number values of probabilities?

In the context of time and shortening trading windows, the sample size of the events over which the system follows a certain distribution would drop and the probabilities of occurrences would be M/N rational numbers.

Cuchulainn
Posts: 56926
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
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### Re: Philosophy of Mathematics

In my 4th year undergrad we did it in Banach spaces. Maybe a pointer?  So, it'e been done before?

Maybe exotic probability.

https://en.wikipedia.org/wiki/Exotic_probability

Can you write your question in maths or give a concrete case? It's a bit fuzzy.

Collector
Posts: 3870
Joined: August 21st, 2001, 12:37 pm

### Re: Philosophy of Mathematics

Can you write your question in maths or give a concrete case? It's a bit fuzzy."

you are using fuzzy logic, my question is crystal clear! Try Boolean !

anyway thanks for all the input! :+)