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complyorexplain
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### Re: Philosophy of Mathematics

the world is discrete, so sqrt 2 cannot exist physically ? it is a probability = in the head of mathematicians, and a very good approximation in the macroscopic world !!

Weyl tile
Sqrt(2) is a number, not a probability.

Collector
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### Re: Philosophy of Mathematics

the world is discrete, so sqrt 2 cannot exist physically ? it is a probability = in the head of mathematicians, and a very good approximation in the macroscopic world !!

Weyl tile
Sqrt(2) is a number, not a probability.
sure, my point was simply that sqrt 2 possibly not has an observable parallel in physical space if discrete space. My personal view is space is continuous, but what moves in it is discrete.

concerning numbers versus probability in relation to discrete observations. Assume we have a road, and we observe people crossing it during the day. Every singel day James cross the road and he is immortal. However Cathrine crosses the road 15 days a month on random days, and only once per day. The expectation for the next day is 1.5 persons crossing. The integer part represent something that will happen for "sure" 100% probability, based on some assumptions. But the fraction part represent a probability<100%. So can the fraction part of a number related to discrete events be seen as a probability?. I mean in discrete physical space if fractions do not exist as observable phenomena, would then the fraction part of the number then in many cases represent a probability?

Last edited by Collector on October 23rd, 2020, 11:46 am, edited 1 time in total.

Cuchulainn
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### Re: Philosophy of Mathematics

the world is discrete, so sqrt 2 cannot exist physically ? it is a probability = in the head of mathematicians, and a very good approximation in the macroscopic world !!

Weyl tile
Sqrt(2) is a number, not a probability.
in fact, it is an irrational number. There is no rational number $p$ satisfying $p^2 = 2$. It leads naturally to Dedekind cuts.

No way, p ~ 1.4142 cannot be a probability unless  you try to change the rules like Feynman.

Collector, I would have an open mind on square roots of (positive) probabilities.

https://arxiv.org/pdf/1603.08427.pdf
Last edited by Cuchulainn on October 23rd, 2020, 11:53 am, edited 3 times in total.
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

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Collector
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### Re: Philosophy of Mathematics

"No way, p ~ 1.4142 cannot be a probability unless  you try to change the rules like Feynman."

I disagree with F on negative probabilities, but why could we not introduce in discrete observations framework, that 5.4142 represent an expectation of for sure 5 events with 100% probability and one event with 41.42% probability?  Of course I could split it up and keep the certainty (100% probability series of events) outside and not even call them probability, as 100% probability is certain, and keep the one uncertain events separate, but this seems unnecessarily complex if I know I am dealing with only discrete observations, where only integers can be observed. I mean 5.4142 could be seen as a aggregate of probabilities in discrete space.

In discrete physical observable events would not a fraction always represent something not yet observed? So the fraction must then be a probability, why must I separate the fraction from the number to call it a probability when it is a probability and the integer parts are number of events with 100% probability, or should we call 1.4142 a aggregate probability?  (negative probabilities still not allowed, a probability >1 is then a probability aggregate). The integer parts represent the number of 100% probability events, and the fraction part represent one additional uncertain event. If working with many uncertain events then one had to do different.

Assume I only have discrete observations and I want a precise model. If the model spit out a fractional number then either the model is misspecified as a fractions not correspond to anything observable, so not testable, we can only observe integers, or the fraction is related to a probability of such an event, this we can check out.

your views and harsh critics welcome!

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### Re: Philosophy of Mathematics

Cuchulainn
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### Re: Philosophy of Mathematics

Not even wrong.

the rational numbers are the most familiar numbers: 1, -5, ½,
I see only 1 rational; the others are natural number (1) and integer (-5).
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

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Cuchulainn
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### Re: Philosophy of Mathematics

Qian Xuesen: The man the US deported - who then helped China into space

https://www.bbc.com/news/stories-54695598

From MIT Qian moved to the California Institute of Technology (Caltech), to study under one of the most influential aeronautical engineers of the day, the Hungarian émigré, Theodore von Karman. There Qian shared an office with another prominent scientist, Frank Malina, who was a key member of a small group of innovators known as the Suicide Squad.
The group had earned this nickname because of their attempts to build a rocket on campus, and because some of their experiments with volatile chemicals went badly wrong.
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

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http://www.datasim.nl

Collector
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### Re: Philosophy of Mathematics

should math be read from left to right or from right to left, or read from the direction the math makes most sense, stay inside the other existing rules?

one can easily set up nonorthodox equations that are wrong if read wrong direction, so there must be direction rules?

almost any language have rules from what side one must read for it to make sense.

platinum
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Joined: May 6th, 2009, 11:08 am

### Re: Philosophy of Mathematics

should math be read from left to right or from right to left, or read from the direction the math makes most sense, stay inside the other existing rules?

one can easily set up nonorthodox equations that are wrong if read wrong direction, so there must be direction rules?

almost any language have rules from what side one must read for it to make sense.
No doubt you are asking a deeper question, but as a start, this comes to mind about the Order of Operations:

"First, we solve any operations inside of parentheses or brackets. Second, we solve any exponents. Third, we solve all multiplication and division from left to right. Fourth, we solve all addition and subtraction from left to right."

so it is not strictly left to right no matter the operations; instead it is sequential and keeps looping back until each operation has been completed.

On texts in Chinese or Arabic, for example, it would be a very good question too though.

Cuchulainn
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### Re: Philosophy of Mathematics

Indeed, it is obvious that invention or discovery, be it in mathematics or anywhere else, takes place by combining ideas.1 Now, there is an extremely great number of such combinations, most of which are devoid of interest, while, on the contrary, very few of them can be fruitful. Which ones does our mind — I mean our conscious mind — perceive? Only the fruitful ones, or exceptionally, some which could be fruitful.
However, to find these, it has been necessary to construct the very numerous possible combinations, among which the useful ones are to be found.

"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

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trackstar
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### Re: Philosophy of Mathematics

A few resources for this thread. As part of a winter project, I'll be reading this stuff and also playing with Wolfram Alpha.

The Philosophy of Mathematics needs a laboratory.

Here are the general sources:

Stanford Encyclopedia of Philosophy - Mathematics section

Routledge Encyclopedia of Philosophy - Foundations of Mathematics

and finally:

Phil Papers - Philosophy of Mathematics Bibliography with many subtopics and follow on links.

It will take months and even years to go through all this material - but it's a great time to start as we enter year 2 of CVD-19.20.21.

Happy holidays!
The spectacle is not a collection of images, but a social relation among people, mediated by images. - Guy Debord

Cuchulainn
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### Re: Philosophy of Mathematics

The universe is vast, containing myriads of stars...likely to have planets circling around them.... The simplest living things will multiply, evolve by natural selection and become more complicated till eventually active, thinking creatures will emerge.... Yearning for fresh worlds...they should spread out all over the Galaxy. These highly exceptional and talented people could hardly overlook such a beautiful place as our Earth. – "And so," Fermi came to his overwhelming question, "if all this has been happening, they should have arrived here by now, so where are they?" – It was Leo Szilard, a man with an impish sense of humor, who supplied the perfect reply to the Fermi Paradox: "They are among us," he said, "but they call themselves Hungarians."
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

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Cuchulainn
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### Re: Philosophy of Mathematics

What's the most important

1. function
2. differential equation
3. formula (not $E = mc^2$)
4. theorem
5. Algorithm

in mathematics?
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

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http://www.datasim.nl

trackstar
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Joined: August 28th, 2008, 1:53 pm

### Re: Philosophy of Mathematics

What's the most important

1. function
2. differential equation
3. formula
4. theorem

in mathematics?
Is it important to know the context to decide?

If you are building a space ship, or trying to land on Mars, then heavier weight to 1 and 2?
If you are an AI pioneer in the mid-20th century, then more so to 3 and 4?

If we think about von Neumann, who could handle just about anything, wonder what he would say.

Also, it would be interesting to make a list - who else could cover the waterfront the way he did?
The spectacle is not a collection of images, but a social relation among people, mediated by images. - Guy Debord

Cuchulainn
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### Re: Philosophy of Mathematics

Scope is important. Start with: which of  each of 1..5 has been terribly influential, a kind of big bang.

Example of 1 $e$.
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

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http://www.datasim.nl