Do you believe in God?

[Banach-Tarski Paradox]

What culture are you from?

Several.

But primarily a mathematical culture.

 

[mikkel_the_dane]

Several.

But primarily a mathematical culture.

Okay.

 

[Banach-Tarski Paradox]

Okay.

Lewis Carol once tried to purchase a personal computer from Charles Babbage, but there were none for sale.

20 Things You Didn't Know About... Math

The equations that work for mysteries reasons, the primes with hidden patterns, and the logical statements that cannot be true or false

www.discovermagazine.com

1. The great 19th-century mathematician Carl Friedrich Gauss called his field “the queen of sciences.”
2. If math is a queen, she’s the White Queen from Alice in Wonderland, who bragged that she believed “as many as six impossible things before breakfast.” (No surprise that Lewis Carroll also wrote about plane algebraic geometry.)

Opinion | Algebra in Wonderland (Published 2010)

The other-worldly events in “Alice’s Adventures in Wonderland” can be interpreted as satire on 19th-century advances in mathematics.

www.nytimes.com

The Annotated Alice (150th Anniversary Deluxe Ed.) – Martin Gardner & Lewis Carroll / / W.W. Norton​

Mark Burstein & James Gardner - The Annotated Alice - G4G12 April 2016​

William Rowan Hamilton (Science YouTuber Collab) | A Capella Science​

 

[mikkel_the_dane]

Lewis Carol once tried to purchase a personal computer from Charles Babbage, but there were none for sale.

20 Things You Didn't Know About... Math

The equations that work for mysteries reasons, the primes with hidden patterns, and the logical statements that cannot be true or false

www.discovermagazine.com

1. The great 19th-century mathematician Carl Friedrich Gauss called his field “the queen of sciences.”
2. If math is a queen, she’s the White Queen from Alice in Wonderland, who bragged that she believed “as many as six impossible things before breakfast.” (No surprise that Lewis Carroll also wrote about plane algebraic geometry.)

Opinion | Algebra in Wonderland (Published 2010)

The other-worldly events in “Alice’s Adventures in Wonderland” can be interpreted as satire on 19th-century advances in mathematics.

www.nytimes.com

The Annotated Alice (150th Anniversary Deluxe Ed.) – Martin Gardner & Lewis Carroll / / W.W. Norton​

Mark Burstein & James Gardner - The Annotated Alice - G4G12 April 2016​

William Rowan Hamilton (Science YouTuber Collab) | A Capella Science​

Fair enough. I dont have the same relationship to math as you.
I mean good for you that your life works for you. I mean that.
But I don't personally share your view of math. That is it.

 

[Banach-Tarski Paradox]

Fair enough. I dont have the same relationship to math as you.
I mean good for you that your life works for you. I mean that.
But I don't personally share your view of math. That is it.

Neither do physicists, as Richard Feynman so loved to point out.

We believe in different things.

0.3. Clash of cultures

In the course of preparing this book I have been fortunate to have had many discussions with computer scientists, applied mathematicians, engineers, physicists, and chemists. Often the beginnings of these conversations were very stressful to all involved. I have kept these difficulties in mind, attempting to write both to geometers and researchers in other fields.

Tensor practitioners want practical results. To quote Rasmus Bro (personal communication): "Practical means that the user of a given chemical instrument in a hospital lab can push a button and right after get a result."

My goal is to initiate enough communication geometers and scientists so that such practical results will be realized. While both grouops are interested in communicating, there are language and even philosophical barriers to be overcome. The purpose of this paragraph is to is to alert geometers and scientists to some of the potential difficulties in communication.

To quote G. Folland [126] "For them (scientists), mathematics is the of manipulating symbols according to certain sophisticated rules, and the external reality to which those symbols refer lies not in an abstract universe of sets but in the real-world phenomina that they are studying."

But mathematicians, as Folland observed, are Platonists, we think that the things we are manipulating on paper have a higher existence. To quote Plato [266], "Let us take away any common instance; there are beds and tables in the world - plenty of them, are there not?"

"Yes. But there are only two ideas or forms of them - one the idea of a bed, the other of a table."

"True. And the maker of either of them makes a bed or he makes a table for our use, in accordance with the idea - that is our way of speaking in this and similar instances - but no artificer makes the ideas themselves: how could he?"

"And what of the maker of the bed? Were you not saying that he too makes, not the idea which, according to our view, is the essence of the bed, but only a particular bed?"

"Yes, I did. Then if he does not make that which exists he cannot make true existence, but only some semblence of existence; and if anyone were to say that the work of the maker of the bed, or of any other workman, has real existence, he could hardly be supposed to be speaking the truth."

The difference of cultures is particularly pronounced when discussing tensors: for some practitioners these are just multi-way arrays that one is allowed to perform certain manipulations on. For geometers these are spaces equipted with certain group actions. The emphasize the geometric aspects of tensors, geometers prefer to work invariantly: to paraphrase W. Fulton: "Don't use coordinates unless someone is holding a pickle to your head."

*Footnote: This modification of the actual quote in tribute to my first geometry teacher, Vincent Gracchi. A problem in our 9th grade geometry textbook asked us to determine if a 3-foot long rifle could be packed in a box of a certain dimensions, and Mr. Gracchi asked us all to cross out the word "rifle" and substitute the word "pickle" because he "did not like guns". A big 5q + 5q to Mr. Gracchi for introducing his students to geometry.

(pages xvii-xviii)

Tensors: Geometry and Applications

J. M. Landsberg

Graduate Studies in Mathematics (Volume 128)

American Mathematical Society

 

[mikkel_the_dane]

Neither do physicists, as Richard Feynman so loved to point out.

We believe in different things.

0.3. Clash of cultures

In the course of preparing this book I have been fortunate to have had many discussions with computer scientists, applied mathematicians, engineers, physicists, and chemists. Often the beginnings of these conversations were very stressful to all involved. I have kept these difficulties in mind, attempting to write both to geometers and researchers in other fields.

Tensor practitioners want practical results. To quote Rasmus Bro (personal communication): "Practical means that the user of a given chemical instrument in a hospital lab can push a button and right after get a result."

My goal is to initiate enough communication geometers and scientists so that such practical results will be realized. While both grouops are interested in communicating, there are language and even philosophical barriers to be overcome. The purpose of this paragraph is to is to alert geometers and scientists to some of the potential difficulties in communication.

To quote G. Folland [126] "For them (scientists), mathematics is the of manipulating symbols according to certain sophisticated rules, and the external reality to which those symbols refer lies not in an abstract universe of sets but in the real-world phenomina that they are studying."

But mathematicians, as Folland observed, are Platonists, we think that the things we are manipulating on paper have a higher existence. To quote Plato [266], "Let us take away any common instance; there are beds and tables in the world - plenty of them, are there not?"

"Yes. But there are only two ideas or forms of them - one the idea of a bed, the other of a table."

"True. And the maker of either of them makes a bed or he makes a table for our use, in accordance with the idea - that is our way of speaking in this and similar instances - but no artificer makes the ideas themselves: how could he?"

"And what of the maker of the bed? Were you not saying that he too makes, not the idea which, according to our view, is the essence of the bed, but only a particular bed?"

"Yes, I did. Then if he does not make that which exists he cannot make true existence, but only some semblence of existence; and if anyone were to say that the work of the maker of the bed, or of any other workman, has real existence, he could hardly be supposed to be speaking the truth."

The difference of cultures is particularly pronounced when discussing tensors: for some practitioners these are just multi-way arrays that one is allowed to perform certain manipulations on. For geometers these are spaces equipted with certain group actions. The emphasize the geometric aspects of tensors, geometers prefer to work invariantly: to paraphrase W. Fulton: "Don't use coordinates unless someone is holding a pickle to your head."

*Footnote: This modification of the actual quote in tribute to my first geometry teacher, Vincent Gracchi. A problem in our 9th grade geometry textbook asked us to determine if a 3-foot long rifle could be packed in a box of a certain dimensions, and Mr. Gracchi asked us all to cross out the word "rifle" and substitute the word "pickle" because he "did not like guns". A big 5q + 5q to Mr. Gracchi for introducing his students to geometry.

(pages xvii-xviii)

Tensors: Geometry and Applications

J. M. Landsberg

Graduate Studies in Mathematics (Volume 128)

American Mathematical Society

Thanks. I have all ready come across that debate before, but to me as me it is irrelevant, since I am neither of the 2.

 

[9-10ths_Penguin]

I believe in God, not because I am so smart but because I am NOT so smart. And I actually have a highish IQ but I believe that we are all in for some surprises one day. For starters, I believe in the concept laid out by so many people, that of a piece of paper with a dot on it, and that's my knowledge, as a 21st century American woman. Then draw a circle around that smaller one, and that's all the world's knowledge. Then draw a circle around THAT, and that's all the knowledge in the universe. The rest is God's knowledge.

It isn't "God's knowledge;" it's just the unknown.

Because it's the unknown, anything we say about it - including that it's "God's knowledge" is necessarily nonsense that was pulled out of someone's butt.

 

[mikkel_the_dane]

It isn't "God's knowledge;" it's just the unknown.

Because it's the unknown, anything we say about it - including that it's "God's knowledge" is necessarily nonsense that was pulled out of someone's butt.

No, not unless your declare your cognition universal, objective and independent of any bias and subjectivity.
The words as used for making sense and nonsense have no objective referents in either case.

 

[Banach-Tarski Paradox]

Thanks. I have all ready come across that debate before, but to me as me it is irrelevant, since I am neither of the 2.

You can see this cultural division here in this forum.

Only magnified, because it’s not an academic environment.

I’ve seen you have the same problems of communication with STE folks.

It’s not just the M’s who have this problem.

We just got arbitrarily grouped with the STE‘s, and those other disciplines like historiography, anthropology, music, art, dance, etc didn’t.

 

[It Aint Necessarily So]

what anyway are laws, if not order recognised and defined by an observer?

A natural law doesn't need to be discerned by a conscious agent to be a fact of nature. The earth was orbiting the sun according to mathematical laws that have since been discovered when man thought it was fixed on pillars.

it makes no sense to contemplate laws or order without addressing the part consciousness plays in the process.

Sure it does. We've done so with great success for centuries.

Perhaps the universe and the laws governing it emerged simultaneously, and while they are interdependent, their correlation is not directly causal. And perhaps in the same way, rather than consciousness having emerged from complex order, the relation between them is itself not causal but mutual.

Maybe. Now find evidence in support of such ideas. Until then, these are just idle speculations that can be disregarded. Ideas that don't predict future outcomes have little practical value. Knowledge is the collection of ideas that can do that. Other ideas are something else.

 

[YoursTrue]

Lewis Carol once tried to purchase a personal computer from Charles Babbage, but there were none for sale.

20 Things You Didn't Know About... Math

The equations that work for mysteries reasons, the primes with hidden patterns, and the logical statements that cannot be true or false

www.discovermagazine.com

1. The great 19th-century mathematician Carl Friedrich Gauss called his field “the queen of sciences.”
2. If math is a queen, she’s the White Queen from Alice in Wonderland, who bragged that she believed “as many as six impossible things before breakfast.” (No surprise that Lewis Carroll also wrote about plane algebraic geometry.)

Opinion | Algebra in Wonderland (Published 2010)

The other-worldly events in “Alice’s Adventures in Wonderland” can be interpreted as satire on 19th-century advances in mathematics.

www.nytimes.com

The Annotated Alice (150th Anniversary Deluxe Ed.) – Martin Gardner & Lewis Carroll / / W.W. Norton​

Mark Burstein & James Gardner - The Annotated Alice - G4G12 April 2016​

William Rowan Hamilton (Science YouTuber Collab) | A Capella Science​

Note: When I was in high school, I loved, loved, loved "Alice in Wonderland..." In fact, thank you for reminding me of it because I may read it again in my old-er age.

 

[YoursTrue]

A natural law doesn't need to be discerned by a conscious agent to be a fact of nature. The earth was orbiting the sun according to mathematical laws that have since been discovered when man thought it was fixed on pillars.

Sure it does. We've done so with great success for centuries.

Maybe. Now find evidence in support of such ideas. Until then, these are just idle speculations that can be disregarded. Ideas that don't predict future outcomes have little practical value. Knowledge is the collection of ideas that can do that. Other ideas are something else.

So is it that you don't think a law (natural, that is) needs to be discerned by a conscious agent to be a fact of nature. So SOME laws might not be observable by -- a "conscious agent."

 

[Polymath257]

The higher source I am referring to defies description in human terms, although I believe there are some descriptions of His being in the Bible. He sets the terms, the description and the boundaries. He does as He wills.

I don't see how that affects what I said. That 'higher source' still has properties (such as having a 'will') and those properties lead to some sort of natural law that is MORE fundamental than that source itself. Also, because 'having a will' is much more complicated than having generic properties of interaction, your theory tries to explain something simpler in terms of something more complicated.

This derails the argument leading to the hypothesis of this 'higher source' and shows it to be irrelevant to anything we want to discuss. Which, again, leads to the question of why we would assume such a thing exists. It doesn't solve the problem it was 'designed' to address and ultimately explains absolutely nothing.

 

[YoursTrue]

I don't see how that affects what I said. That 'higher source' still has properties (such as having a 'will') and those properties lead to some sort of natural law that is MORE fundamental than that source itself. Also, because 'having a will' is much more complicated than having generic properties of interaction, your theory tries to explain something simpler in terms of something more complicated.

This derails the argument leading to the hypothesis of this 'higher source' and shows it to be irrelevant to anything we want to discuss. Which, again, leads to the question of why we would assume such a thing exists. It doesn't solve the problem it was 'designed' to address and ultimately explains absolutely nothing.

The question is if I believe in God. I don't argue about it but I might state my viewpoint because belief as it stands really defies argument as far as I am concerned.

 

[Polymath257]

So the universe did not occur by accident, which was my point. We are then left with the question, Which came first, the observable universe, or the laws which appear to govern it? And what anyway are laws, if not order recognised and defined by an observer? In which case it makes no sense to contemplate laws or order without addressing the part consciousness plays in the process.

I see the properties of things to be co-existent with the things. So neither the universe nor the laws were 'first'.

I would also point out that the use of the word 'first' implies time exists and thereby the universe exists.

Third, I don't see how consciousness is relevant to there being properties (natural laws). They don't need to be 'recognized' in order to exist: things have properties, which means they interact in regular ways. Those ways *are* the natural laws. At most, consciousness is relevant to being able to *describe* those properties (natural laws). In other words, consciousness is the *result* of the action of natural laws, not the other way around (except by our local attempts to find those basic properties).

Perhaps the universe and the laws governing it emerged simultaneously, and while they are interdependent, their correlation is not directly causal. And perhaps in the same way, rather than consciousness having emerged from complex order, the relation between them is itself not causal but mutual.

So you postulate that consciousness is co-existent with the universe? That hardly seems likely given what we know about both consciousness and the universe. Instead, it seems clear that there was a LONG period of time between when the universe started and the first living things. And there was additional time between those first living things and the first *conscious* things.

 

[Polymath257]

The question is if I believe in God. I don't argue about it but I might state my viewpoint because belief as it stands really defies argument as far as I am concerned.

Fair enough. It is an assumption you make that I find no reason to make.

 

[YoursTrue]

I don't see how that affects what I said. That 'higher source' still has properties (such as having a 'will') and those properties lead to some sort of natural law that is MORE fundamental than that source itself. Also, because 'having a will' is much more complicated than having generic properties of interaction, your theory tries to explain something simpler in terms of something more complicated.

This derails the argument leading to the hypothesis of this 'higher source' and shows it to be irrelevant to anything we want to discuss. Which, again, leads to the question of why we would assume such a thing exists. It doesn't solve the problem it was 'designed' to address and ultimately explains absolutely nothing.

So in reality, the question (title of the thread) poses a yes or no answer, would you agree with that?

 

[Polymath257]

So the universe did not occur by accident, which was my point.

The word 'accident' here seems strange.

The universe did not 'come into existence'. Whenever there was time, the universe existed since time is part of the universe. So there was no time at which the universe failed to exist.

Second, the word 'accident' implies there is some intention, which seems to me to be simply false.

The way I would say it is that the universe 'simply exists'. But, in this context, the universe includes ALL space and ALL time.

 

[Polymath257]

So in reality, the question (title of the thread) poses a yes or no answer, would you agree with that?

No, for several reasons.

First, there are literally thousands of ways humans have conceptualized deities. To use the word 'God' seems to be intended to pick out one of these many viewpoints without specifying which to be used. In that way, it is horribly vague.

Second, it fails to specify which properties are relevant for said God: being the creator of the universe? being a necessary being? being a first cause? being a giver of morality? None of these is equivalent to any of the others.

So the problem becomes trying to figure out what the person asking the question means by that question. I am not a mind reader, so I don't know.

 

[Polymath257]

So is it that you don't think a law (natural, that is) needs to be discerned by a conscious agent to be a fact of nature. So SOME laws might not be observable by -- a "conscious agent."

I do not think a natural law needs to be observed by any consciousness to be a fact of nature. A rock can exist without anyone knowing it is there. The same holds for properties and thereby natural laws.

In fact, conscious beings, when attempting to describe how things work, tend to get things wrong to some degree. All *we* can do is get approximations to natural laws. That is why we need to test our ideas and determine when they fail and when they work. There is *always* the possibility we will need to modify what we have found to get a better approximation.