Mathematics/Logic

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So, as a thread hosting a discussion on this(sort of) was shut down, I thought I’d start another one, for any discussions on Logic and Mathematics.

What “is” math and/or logic?

I think that’s a sufficiently vague question to cover just about any discussion.
 
IvanKaramozov said:
So, as a thread hosting a discussion on this(sort of) was shut down, I thought I’d start another one, for any discussions on Logic and Mathematics.

What “is” math and/or logic?
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a study of certain (necessary) relationships between certain abstract objects.
 
IvanKaramozov said:
So, as a thread hosting a discussion on this(sort of) was shut down, I thought I’d start another one, for any discussions on Logic and Mathematics.

What “is” math and/or logic?

I think that’s a sufficiently vague question to cover just about any discussion.
Click to expand...
Logic, or at least deductive logic, is a set of rules for the manipulation of language, whether that be a natural language like English or a highly specialised language like mathematics.

There are a number of ways of looking at mathematics. One way is to think of it as a set of propositions which are regarded as true by definition (the axioms) along with a set of rules for making valid deductions from those axioms. That is a definition which is more likely to appeal to a pure mathematician than a physicist or the man in the street; both of whom are likely to take a more pragmatic view - “It works, who cares what it is?”

A pure mathematician once said to me that he took up mathematics because he wanted to know what made the universe work. I said that I would have gone for physics if I wanted to know that. To which the reply was, “No you wouldn’t, you would have gone for theology.” (By which he meant that the physicist eventually has to come up against a collection of “brute facts”, beyond which no further explanation is possible. In order to go beyond them you also have to go beyond the natural sciences.)
 
Mathematician,

Have you read “The Man Who Loved Only Numbers”? It is the story of Paul Erdos. Great book about the “addiction” of mathematics. The “addiction” portion is how I look at his life. Anyway, I was an Electronics Tech. by trade and enjoy the discussion of mathematics.
 
Mathematics and logic (and some would include parts of computer science, information theory, and statistics) are what are called the formal sciences

The debate whether the formal sciences are actually science or something completely different has gone on for centuries.

Formal science is distinguished from the natural and social sciences in that they are chiefly composed of theoretical symbols and rules. they are generally about the process of getting from A to B to C or teh relationship between A, B, and C and it doesn’t matter whether A, B, or C are real or true.
 
steveandersen said:
Formal science is distinguished from the natural and social sciences in that they are chiefly composed of theoretical symbols and rules. they are generally about the process of getting from A to B to C or teh relationship between A, B, and C and it doesn’t matter whether A, B, or C are real or true.
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I wouldn’t want to go quite that far. It does actually make a difference whether Pythagoras’s Theroem is true or false.
 
One of the odd things about mathematics, especially in its relation to physics, is the way in which a number like pi can pop up in all sorts of odd places. Pi is defined as the ratio of a circles circumference to its diameter, and yet it appears in the formula for the frequency of a radio wave. Now just what has the dimensions of a circle got to do with the frequency of a radio wave? It’s easy enough to do the mathematical derivation, but at the philosophical level it still seems distinctly odd.
 
mathematician said:
One of the odd things about mathematics, especially in its relation to physics, is the way in which a number like pi can pop up in all sorts of odd places. Pi is defined as the ratio of a circles circumference to its diameter, and yet it appears in the formula for the frequency of a radio wave. Now just what has the dimensions of a circle got to do with the frequency of a radio wave? It’s easy enough to do the mathematical derivation, but at the philosophical level it still seems distinctly odd.
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Since one of the primary ways to create alternating currect (AC) electricity involves rotating machinery, is should not be hard envision how the circle is involved.
 
davidv said:
Since one of the primary ways to create alternating currect (AC) electricity involves rotating machinery, is should not be hard envision how the circle is involved.
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Okay, try another one, the period of a pendulum. In any case, rotating machinery hasn’t got too much to do with a Wein Bridge Oscillator.
 
You want weird? Take a look at strange attractors, such as the Feigenbaum number. Chaos produces regularity. I ran into the effect while I was doing prey-predator interactions using the Lotka-Volterra equations, and like most people, didn’t realize that something very strange was going on.

Even more strangely, it maps nicely onto the Mandelbrot set:
http://www.chanceandchoice.com/ChanceandChoice/feigenbaum.gif

Very, very odd, to the eyes of this non-mathematician.
 
I would like to suggest math is the study of what is fair and balanced. It is related to justice and Truth. It can be extended to very complex forms but the basics are still relations, equalities, and balance.

The topic reminds me of cause and effect relationships that have a certain balance. Our fall from grace in the Garden of Eden had a certain impact. This “state” we fell into was perfectly undone in our redemption made possible by the sacrafice of Jesus.

Jesus also said “every penny will be paid in full” when discussing the effect of sin. Now, that is a nice balance sheet. Math is great! 😉
 
Logic is used to help you make a choice.

Mathematics is used to describe the choice you made.

Lets assume your car has a faulty water pump. You have the choice of a quantum mechanic or an auto mechanic and you have enough money to pay what it costs to fix it.

The auto mechanic will lift the bonnet, unbolt the faulty pump and replace it with a new one. For that he receives a sum of money and waits for his next job.

The quantum mechanic may or may not lift the bonnet. Assuming he does lift the bonnet it is because he needs to install monitoring equipment to observe the water pump after the work is done. Then he waits until the water pump decides to unbolt itself and vanish. Then when a new water pump of the right make pops into existence and attaches itself to the place on the engine where a water pump should go the car is fixed. For that you pay for the time it takes him to wait and the cost of his equipment and research.

The quantum mechanic can assure you that somewhere between now and eternity in at least one of 10^150 (that means a one with a 150 zeros) universes you have a car with a new working water pump … you just have to go and get it. If the quantum mechanic already has tenure on another project he may not lift the bonnet and decide to just tell you to take the car home and it will fix itself in some universe between now and eternity.

Logic should tell you which mechanic to use.
 
As an amateur, one who is largely self-taught in Calculus, I find this topic weird weird because I wonder what relevance what has been discussed so far has to religion or philosophy.

But carry on- it is interesting,I can follow most of it.
 
Math is a language

Logic is understanding the way things change
 
Math quantifies. Logic qualifies. And then, you come to more, and it is the question, which is dependent upon which?

All I’ve got.
 
Texas_Roofer said:
Math is a language

Logic is understanding the way things change
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Deductive logic is about how to make valid deductions given certain things which are either thought or known to be true. (Mathematics mostly.)

Inductive logic is about how to make intelligent inferences given the available data. (Physical and other sciences mostly.)
 
mathematician said:
I wouldn’t want to go quite that far. It does actually make a difference whether Pythagoras’s Theroem is true or false.
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I think it goes beyond this. If it’s true, the Pythagorean theorem is metaphysically true whether or not there ever exists a physical right triangle anywhere in the universe. This relationship is from the mind of God.

From the play Copenhagen by Michael Frayn:

Bohr: “I said wave mechanics and matrix mechanics were simply alternative tools.”

Heisenberg: “Something you’re always accusing me of. ‘If it works it works’. Never mind what it means.”

Bohr: “Of course I mind what it means.”

Heisenberg: “What it means in language.”

Bohr: “In plain language, yes.”

Heisenberg: “What something means is what it means in mathematics.”

Bohr: “You think that so long as the mathematics works out, the sense doesn’t matter.”

Heisenberg: “Mathematics IS sense! That’s what sense is!”

Good stuff.
 
Doyle_Mashern said:
I think it goes beyond this. If it’s true, the Pythagorean theorem is metaphysically true whether or not there ever exists a physical right triangle anywhere in the universe. This relationship is from the mind of God.
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I can see how it might be tempting to think of right angled triangles as things which exist in some kind of platonic realm, and perhaps in the mind of God, but even numbers themselves can be defined in a way which has nothing to do with metaphysics.
 
Looking at some of the depictions of deep space it is apparent that the matter is in strands and the voids are roughly circular. Logic indicated that if the matter was moving further out then the gravity across the voids was becoming less. Couple that with vacuum energy and surely space would distort eventually to a higher structure than 3D space on a 4D co-moving expansion.

That in a nutshell is the logic I have been asking for a little help from the science forums for so long. For my troubles I have been labeled a kook and a woo woo and asked to consider if I am sane.

There are two themes that run through my thinking, the strong one is keep going it may be important especially as the changes and surprises keep coming in the world of science. The second a dark and subtle line of thinking is that there is no one who cares enough to look at an idea and further more the world is a violent and evil unhappy place where not one person really is satisfied with their lot.

The logic has truth from both angles and is in direct opposition. Maybe Pythagorean triangles are true in the metaphysical sense only. However the mathematics for getting a triangle to determine a right for making things fit rather than just knocking bits of wood roughly together is very useful in this reality. Logic tells me that help or no help the future will happen whether we plan for it or not.
 
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