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4 = 7 - 3 is not the same as 4 = 2 + 2

Juan_Pablo
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1/14/2014 1:37:46 PM
Posted: 2 years ago
Quantitatively 4 = 7 - 3 is the same thing as 4 = 2 + 2. The total value on either side of the equal sign in either expression is 4!

However, qualitatively the two expressions are not the same! In both Number Theory and Set Theory this has philosophical importance because it demonstrates how the same numerical value can be formulated in at least two ways, which reflects unique and different functions. More formulations are also possible, up to an infinity in accordance with Set Theory.

This serves as evidence that one numerical value (or magnitude) can in theory have numerous manifestations - and it speaks directly to the issue of philosophical determinism because it shows that even though math is inherently deterministic ( 1 + 1 must equal 2 ), the total value ( 2 ) can still go on to materialize in different forms ( e.g. 3 - 1, 1/2 + 3/2 ), adding a probabilistic element to even rigid, deterministic mathematics.

I believe this characteristic about numerical values and magnitudes is the source of the natural probability found in quantum mechanics. I believe it expresses itself mechanically so it gives the electron the apparent, random "non-localized" effect attributed to it in quantum mechanics. In other words, the value the electron shares with the nucleus of the atom is conserved, so the electron is generally allowed to do a random dance without fear of violating mathematical or mechanistic rules.

Your thoughts?
Pareidolic-Dreamer
Posts: 84
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1/14/2014 3:38:06 PM
Posted: 2 years ago
At 1/14/2014 1:37:46 PM, Juan_Pablo wrote:
Quantitatively 4 = 7 - 3 is the same thing as 4 = 2 + 2. The total value on either side of the equal sign in either expression is 4!

However, qualitatively the two expressions are not the same! In both Number Theory and Set Theory this has philosophical importance because it demonstrates how the same numerical value can be formulated in at least two ways, which reflects unique and different functions. More formulations are also possible, up to an infinity in accordance with Set Theory.

This serves as evidence that one numerical value (or magnitude) can in theory have numerous manifestations - and it speaks directly to the issue of philosophical determinism because it shows that even though math is inherently deterministic ( 1 + 1 must equal 2 ), the total value ( 2 ) can still go on to materialize in different forms ( e.g. 3 - 1, 1/2 + 3/2 ), adding a probabilistic element to even rigid, deterministic mathematics.

I believe this characteristic about numerical values and magnitudes is the source of the natural probability found in quantum mechanics. I believe it expresses itself mechanically so it gives the electron the apparent, random "non-localized" effect attributed to it in quantum mechanics. In other words, the value the electron shares with the nucleus of the atom is conserved, so the electron is generally allowed to do a random dance without fear of violating mathematical or mechanistic rules.

Your thoughts?

Not really much to disagree with here. You're basically using math to confirm that there is more than one way to skin a cat.
It's an axiom. You can find some form of confirmation of all axioms in all disciplines of thought.
What amazes me, is that so few people seem to realize the true implications of this particular axiom.
Everything is possible. You only have to find a single mathematical expression that leads to 2, to know that 2 is possible. And you only have to believe that 2 is possible in order to create a mathematical expression that leads to it.
We have at our disposal all of the same tools and building materials that the universe built us with. There is no reason we could not build a universe. IF we believe.
Pareidolic-Dreamer
I see wall people.

When I argue against someone's truths, I always feel like I am arguing just as strongly against my own.
Stephen_Hawkins
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1/14/2014 4:57:55 PM
Posted: 2 years ago
They do not "go on" to materialise in different forms, as this implies temporality. They do not exist in time, but are just analytic truths. This has no effect on determinism.
Give a man a fish, he'll eat for a day. Teach him how to be Gay, he'll positively influence the GDP.

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Juan_Pablo
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1/14/2014 7:53:36 PM
Posted: 2 years ago
At 1/14/2014 4:57:55 PM, Stephen_Hawkins wrote:
They do not "go on" to materialise in different forms, as this implies temporality. They do not exist in time, but are just analytic truths. This has no effect on determinism.

Stephen, I disagree with you here. Determinism is actually established on the idea that cause and effect are inevitably, unavoidably related - and this is supported on the view that the universe is mathematical and governed by universal principals. However, the entire field of quantum mechanics is used as evidence to show that inside the atom Newtonian principles don't quite apply as they do at our scale of the universe; that is to say that in pieces the atom doesn't seem to obey all Newtonian principles, and the wave behavior of matter ( de Broglie waves ) contributes to the Newtonian break-down of cause an effect. Actually according to the de Broglie Matter-Wave theory this break down of Newtonian rigidity also exhibit with masses at our scale, but it's very small.

Quantum Mechanics already demonstrates that cause and effect ( at least with respect to qualities like momentum and position ) isn't as rigid as determinists once believed it was.

I'm offering the explanation in the first post above as a way of explaining how probability gets into the picture and why determinism appears to fail.
Juan_Pablo
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1/14/2014 8:00:39 PM
Posted: 2 years ago
Sorry.

I meant "the wave behavior of matter ( de Broglie waves) contributes to the break-down of Newtonian cause and effect" instead of

"the wave behavior of matter ( de Broglie waves ) contributes to the Newtonian break-down of cause an effect."
Stephen_Hawkins
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1/14/2014 8:41:00 PM
Posted: 2 years ago
You're not explaining in any detail, for you have not engaged with what I have said. Cause and effect are temporal. Maths is not. Therefore mathematics is not affected by any revelation made in regards to cause and effect.

You must establish that mathematics involves temporal events. Which would be explaining how definitions are temporally located (and therefore take up size as well as time, or spacetime) which is ludicrous in the extreme.
Give a man a fish, he'll eat for a day. Teach him how to be Gay, he'll positively influence the GDP.

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Juan_Pablo
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1/14/2014 9:03:26 PM
Posted: 2 years ago
At 1/14/2014 8:41:00 PM, Stephen_Hawkins wrote:
You're not explaining in any detail, for you have not engaged with what I have said. Cause and effect are temporal. Maths is not. Therefore mathematics is not affected by any revelation made in regards to cause and effect.

You must establish that mathematics involves temporal events. Which would be explaining how definitions are temporally located (and therefore take up size as well as time, or spacetime) which is ludicrous in the extreme.

No. You're not paying attention to what I'm saying. Quantum mechanics already demonstrates that some things happen indeterministically in the atomic world - but that there is a probability associated to those events. There is no firm foundation for cause and effect with many phenomena. The de Broglie matter-wave theory further reinforces this, by indicating that probability isn't just found inside the atom but also at our level at tiny, indetectable levels! That means that many things inside the atom appear to happen spontaneously - yes, over time!

I'm using Number Theory and Set Theory to explain how this can happen in an atomic system ( atomic nucleus and the adhering electrons ) to show that math isn't being violated, and that in one way determinism is still held in place.

As a system many of the physical attributes of the systems are conserved; however, various parts take on different values at different times, so as to contribute to the conservation of the whole!

I'm using this using Number Theory and Set Theory to demonstrate this roughly, by showing that even though, say, the mass + energy = 4, that 4 can still materialize in a variety of ways spontaneously without energy or anything else being contributed to the atom.

Because the value 4 is preserved, determinism remains in tact with respect to this quality of the atom, but with respect to other physical qualities ( the position of electron, it's momentum ) indeterminism becomes an unavoidable feature.

In other words the mass + energy conservation takes on many different formulations without outside influence!

I hope that helps, Stephen.
Stephen_Hawkins
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1/15/2014 6:05:57 AM
Posted: 2 years ago
At 1/14/2014 9:03:26 PM, Juan_Pablo wrote:
I'm using this using Number Theory and Set Theory to demonstrate this

Are you using maths as an analogy or as actual evidence? If the former, my only problem is that analogies don't prove anything. If the latter, then my point still stands: maths informs determinism in no meaningful way, as maths has no relationship to determinism.

The statement you made that I am engaging with, to be clear, is that "math[s] is inherently deterministic" and that "2 can go on and materialise in different forms". Both of these statements imply numbers have temporality. But neither have temporality. Therefore both statements are false.
Give a man a fish, he'll eat for a day. Teach him how to be Gay, he'll positively influence the GDP.

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Josh_b
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1/15/2014 9:20:10 AM
Posted: 2 years ago
does the ends justify the means? on paper it looks like you can get to 4 a number of ways. But in the case of 7-3 it appears as though you have 7 to begin win and suffer a significant loss in getting to 4. However in the case of 2+2 it appears as though equals are joining forces. Having four sides joined gives you a parallelogram which is 360 degrees. And 360 degrees is a complete circle. A circle is efficient, so 4 is the best number to achieve.
Scrutiny Welcome

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Juan_Pablo
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1/15/2014 3:40:28 PM
Posted: 2 years ago
At 1/15/2014 6:05:57 AM, Stephen_Hawkins wrote:
At 1/14/2014 9:03:26 PM, Juan_Pablo wrote:
I'm using this using Number Theory and Set Theory to demonstrate this

Are you using maths as an analogy or as actual evidence? If the former, my only problem is that analogies don't prove anything. If the latter, then my point still stands: maths informs determinism in no meaningful way, as maths has no relationship to determinism.

The statement you made that I am engaging with, to be clear, is that "math[s] is inherently deterministic" and that "2 can go on and materialise in different forms". Both of these statements imply numbers have temporality. But neither have temporality. Therefore both statements are false.

In Quantum Mechanics math is used ( the Schrodinger equation for example ) as actual evidence that many deterministic Newtonian principles don't apply.

I'll quote Wikipedia on the Schrodinger equation here:

"In classical mechanics, a particle has, at every moment, an exact position and an exact momentum. These values change deterministically as the particle moves according to Newton's laws. In quantum mechanics, particles do not have exactly determined properties, and when they are measured, the result is randomly drawn from a probability distribution . . . ."

"In classical physics, when a ball is rolled slowly up a large hill, it will come to a stop and roll back, because it doesn't have enough energy to get over the top of the hill to the other side. However, the Schr"dinger equation predicts that there is a small probability that the ball will get to the other side of the hill, even if it has too little energy to reach the top." [1].

That should answer your first question and your assertion that math has no relevance on determinism. It very much does; for example, let's say I have an object traveling in space at 2000 miles/hour. If the object where to continue with that velocity unimpeded for another 6 hours, determinism ( Newton's first law ) indicates that it will cover a distance of 12,000 miles in that breath of time! ( 2000 miles / hour x 6 hour / 1 = 12,000 miles after the time units are canceled. )

The example I just used shows how math can be used to convey a physical transformation in time. This should answer your concern in your second paragraph. You have to understand that what I mean by "formulation" is a function, where two or more physical states ( or properties ) of a system are addressed in terms of a quantity or magnitude. In my example in this post, I used time and speed. But in math a variety of things can be used to describe the state of a system.

[1] http://en.wikipedia.org...
Stephen_Hawkins
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1/15/2014 6:33:08 PM
Posted: 2 years ago
No, that example had no relevance to maths, but merely expressed the idea that an area of physics is dependent on other factors (whether those factors are deterministic or not has no impact on maths). State only with appeal to mathematics that either of your statements regarding mathematics are true, or withdraw those statements.
Give a man a fish, he'll eat for a day. Teach him how to be Gay, he'll positively influence the GDP.

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Juan_Pablo
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1/15/2014 8:03:09 PM
Posted: 2 years ago
At 1/15/2014 6:33:08 PM, Stephen_Hawkins wrote:
No, that example had no relevance to maths, but merely expressed the idea that an area of physics is dependent on other factors (whether those factors are deterministic or not has no impact on maths). State only with appeal to mathematics that either of your statements regarding mathematics are true, or withdraw those statements.

Stephen, I answered your questions and criticisms in the previous posts. Unless you what me to explain something in greater detail, which I'm willing to do, I think I've provided you with satisfactory answers. However, you are right to say that not all math is firmly attached to determinism, which I would agree with you and which I've already explained several times. Quantum mechanics is a mathematical framework which provides solutions to the position of the electron based on probability. This is one example of math that does not provide solitary certain answers - but answers in terms of probability.

As someone who's familiar with the complexity of language in communicating ideas, you can even say that quantum mechanics does provide deterministic solutions - but not in the Newtonian sense. Rather these solutions are expressed in terms of probability and uncertainty!
Juan_Pablo
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1/15/2014 8:06:51 PM
Posted: 2 years ago
It all depends on how you define determinism.

Though for this forum issue I define determinism in the classic philosophical sense, as pertaining to 18/19th century Newtonian mechanics.
sadolite
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1/16/2014 11:10:53 PM
Posted: 2 years ago
At 1/14/2014 1:37:46 PM, Juan_Pablo wrote:
Quantitatively 4 = 7 - 3 is the same thing as 4 = 2 + 2. The total value on either side of the equal sign in either expression is 4!

However, qualitatively the two expressions are not the same! In both Number Theory and Set Theory this has philosophical importance because it demonstrates how the same numerical value can be formulated in at least two ways, which reflects unique and different functions. More formulations are also possible, up to an infinity in accordance with Set Theory.

This serves as evidence that one numerical value (or magnitude) can in theory have numerous manifestations - and it speaks directly to the issue of philosophical determinism because it shows that even though math is inherently deterministic ( 1 + 1 must equal 2 ), the total value ( 2 ) can still go on to materialize in different forms ( e.g. 3 - 1, 1/2 + 3/2 ), adding a probabilistic element to even rigid, deterministic mathematics.

I believe this characteristic about numerical values and magnitudes is the source of the natural probability found in quantum mechanics. I believe it expresses itself mechanically so it gives the electron the apparent, random "non-localized" effect attributed to it in quantum mechanics. In other words, the value the electron shares with the nucleus of the atom is conserved, so the electron is generally allowed to do a random dance without fear of violating mathematical or mechanistic rules.

Your thoughts?

Convert the numbers to 100 dollar bills and then do the math again. If you come up with two different answers you keep the money> If the answers are the same you have to give the money away. $400 = $700 - $300 is not the same as $400 = $200 + $200
It's not your views that divide us, it's what you think my views should be that divides us.

If you think I will give up my rights and forsake social etiquette to make you "FEEL" better you are sadly mistaken

If liberal democrats would just stop shooting people gun violence would drop by 90%
sadolite
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1/16/2014 11:12:58 PM
Posted: 2 years ago
At 1/16/2014 11:10:53 PM, sadolite wrote:
At 1/14/2014 1:37:46 PM, Juan_Pablo wrote:
Quantitatively 4 = 7 - 3 is the same thing as 4 = 2 + 2. The total value on either side of the equal sign in either expression is 4!

However, qualitatively the two expressions are not the same! In both Number Theory and Set Theory this has philosophical importance because it demonstrates how the same numerical value can be formulated in at least two ways, which reflects unique and different functions. More formulations are also possible, up to an infinity in accordance with Set Theory.

This serves as evidence that one numerical value (or magnitude) can in theory have numerous manifestations - and it speaks directly to the issue of philosophical determinism because it shows that even though math is inherently deterministic ( 1 + 1 must equal 2 ), the total value ( 2 ) can still go on to materialize in different forms ( e.g. 3 - 1, 1/2 + 3/2 ), adding a probabilistic element to even rigid, deterministic mathematics.

I believe this characteristic about numerical values and magnitudes is the source of the natural probability found in quantum mechanics. I believe it expresses itself mechanically so it gives the electron the apparent, random "non-localized" effect attributed to it in quantum mechanics. In other words, the value the electron shares with the nucleus of the atom is conserved, so the electron is generally allowed to do a random dance without fear of violating mathematical or mechanistic rules.

Your thoughts? CORE Education

Convert the numbers to 100 dollar bills and then do the math again. If you come up with two different answers you keep the money> If the answers are the same you have to give the money away. $400 = $700 - $300 is not the same as $400 = $200 + $200
It's not your views that divide us, it's what you think my views should be that divides us.

If you think I will give up my rights and forsake social etiquette to make you "FEEL" better you are sadly mistaken

If liberal democrats would just stop shooting people gun violence would drop by 90%
Juan_Pablo
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1/16/2014 11:45:33 PM
Posted: 2 years ago
Sadolite, did you read my first post? I said quantitatively it's the same thing. It's not the same thing qualitatively, however.
sadolite
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1/17/2014 4:50:14 PM
Posted: 2 years ago
At 1/16/2014 11:45:33 PM, Juan_Pablo wrote:
Sadolite, did you read my first post? I said quantitatively it's the same thing. It's not the same thing qualitatively, however.

It is pointless
It's not your views that divide us, it's what you think my views should be that divides us.

If you think I will give up my rights and forsake social etiquette to make you "FEEL" better you are sadly mistaken

If liberal democrats would just stop shooting people gun violence would drop by 90%
Juan_Pablo
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1/17/2014 4:58:25 PM
Posted: 2 years ago
At 1/17/2014 4:50:14 PM, sadolite wrote:
At 1/16/2014 11:45:33 PM, Juan_Pablo wrote:
Sadolite, did you read my first post? I said quantitatively it's the same thing. It's not the same thing qualitatively, however.

It is pointless

No, I mean something significant with this. Let me give you an example.

Let's say two people have a dollar in their pocket and only a dollar. One has a dollar bill and the other has a dollar in change, which includes a quarter.

Now both of these people want a gum ball at the gum ball machine in their local store; it requires a quarter to get one. The man with the dollar bill cannot get a gum with what he has - unless he gets change.

The man with the dollar in change, which includes a quarter, can get a gum ball.

This is actually what I mean with my first post in this thread. Just because quantitatively two formulations can equal 2, not all formulations are identical! This has real merit and real consequences in the our world, as I've just shown to you with this example.

I believe this type of issue is playing a role in the weird, scientific field of quantum mechanics!
Juan_Pablo
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1/17/2014 5:17:06 PM
Posted: 2 years ago
Just because two formulations can equal 2, doesn't mean these two formulations are qualitatively the same.

Even thought both people have more than enough to purchase a gum ball, one doesn't have the right denomination to purchase one! He has to go through the extra steps of transforming his denomination into something he can use.
sadolite
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1/18/2014 3:17:15 PM
Posted: 2 years ago
At 1/17/2014 4:58:25 PM, Juan_Pablo wrote:
At 1/17/2014 4:50:14 PM, sadolite wrote:
At 1/16/2014 11:45:33 PM, Juan_Pablo wrote:
Sadolite, did you read my first post? I said quantitatively it's the same thing. It's not the same thing qualitatively, however.

It is pointless

No, I mean something significant with this. Let me give you an example.

Let's say two people have a dollar in their pocket and only a dollar. One has a dollar bill and the other has a dollar in change, which includes a quarter.

Now both of these people want a gum ball at the gum ball machine in their local store; it requires a quarter to get one. The man with the dollar bill cannot get a gum with what he has - unless he gets change.

The man with the dollar in change, which includes a quarter, can get a gum ball.

This is actually what I mean with my first post in this thread. Just because quantitatively two formulations can equal 2, not all formulations are identical! This has real merit and real consequences in the our world, as I've just shown to you with this example.

I believe this type of issue is playing a role in the weird, scientific field of quantum mechanics!

IS this what they teach in schools today? The study of the blatantly obvious.
It's not your views that divide us, it's what you think my views should be that divides us.

If you think I will give up my rights and forsake social etiquette to make you "FEEL" better you are sadly mistaken

If liberal democrats would just stop shooting people gun violence would drop by 90%
Stephen_Hawkins
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1/19/2014 8:56:14 AM
Posted: 2 years ago
Juan, let me put it simply: none of what you said has related to temporality of mathematics. When most philosophers agree that maths doesn't exist in the same way as any other object, such as atoms, then your claim that maths is temporal or occurs over time doesn't add up.

To be clear, take the example you gave of atoms. Atoms are not numbers: they are atoms. Of course, atoms exist over time. They may or may not spontaneously and indeterminstically appear or disappear (though if this is caused by an underlying feature of the physical world, this is de dicto not clear indeterminacy), but this does not relate to mathematical truisms like "4=7-3".

All problems arise when you've tried to make the scientific claims (such as that "electrons do a random dance" - which is dubious, really, due to competing hypotheses) and use an analogy to "prove" something. Proof by analogy is very common and popular (and cogent) but just inaccurate.

Some examples of analogies: "DNA is a code", or "taxation is theft" or "property is theft". These are great analogies to a point, but they are then taken as literally true, and begin to fail.

When it comes to quantum physics, there are many many many many famous ones. Shroedinger's cat is one common one, but more generally the analogous links between quantum and classical physics is the other. As such, people tend to trot about quantum physics and quantum-based "theories", the disassociation with the analogies tend to become clearer. Others like sado have pointed out other disassociations between your two points of mathematics and quantum theory.

I'd recommend to try putting your argument in formal terms (e.g. PPC arguments going premise-premise-conclusion), to highlight our misunderstanding. I can't see what your major point is though because the case breaks down at too many points for me to understand which is the major point you are trying to conclude. Is it to solely apply to mathematics, or movements of electrons, or quantum theory... and your clarifications tend to shift your conclusions to some different conclusion to your original point.
Give a man a fish, he'll eat for a day. Teach him how to be Gay, he'll positively influence the GDP.

Social Contract Theory debate: http://www.debate.org...
wrichcirw
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1/19/2014 12:02:19 PM
Posted: 2 years ago
At 1/14/2014 9:03:26 PM, Juan_Pablo wrote:
At 1/14/2014 8:41:00 PM, Stephen_Hawkins wrote:

You're not explaining in any detail, for you have not engaged with what I have said.

No. You're not paying attention to what I'm saying.

I lol'ed when I read this. =)
At 8/9/2013 9:41:24 AM, wrichcirw wrote:
If you are civil with me, I will be civil to you. If you decide to bring unreasonable animosity to bear in a reasonable discussion, then what would you expect other than to get flustered?
megaman
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1/19/2014 5:04:20 PM
Posted: 2 years ago
At 1/17/2014 5:17:06 PM, Juan_Pablo wrote:
Just because two formulations can equal 2, doesn't mean these two formulations are qualitatively the same.

Even thought both people have more than enough to purchase a gum ball, one doesn't have the right denomination to purchase one! He has to go through the extra steps of transforming his denomination into something he can use.

You have made a logical fallacy when you say that, since dollar bills and change are different qualitatively, that must mean 7-3 and 2+2 are different also in the same fashion. You have reached across the spectrum from microeconomics to concrete mathematics. You also make a very unconvincing statement when you mention how quantum mechanics and shrodinger's equation back your argument but I fail to see the logical connection.

Quantum mechanics, as you may know, concerns the wave nature of matter using Hamiltonian series and eigenvalues to demonstrate the probability of the location of a particle. This reaches into the field of abstract mathematics, and so fail to see the concrete relationship between quantum mechanics and 2+2=\7-3.

Any clarification on this?
Juan_Pablo
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1/19/2014 6:30:11 PM
Posted: 2 years ago
Megaman said: "You have made a logical fallacy when you say that, since dollar bills and change are different qualitatively, that must mean 7-3 and 2+2 are different also in the same fashion."

As functions these two mathematical expressions are very different, in spite of the fact that they reach the same value. This is what I mean by saying they differ qualitatively!

As for the connection to Quantum Mechanics, I'm only offering up this device as a possible explanation to underlying weirdness observed with particle nature in that Field. I never once stated that there definitely was a connection, only that this might explain many of the Field's mysteries. I encourage you to read the previous posts to see what I mean.

Yes, I understand the nature of Schrodinger's equation because I have used it in college classes. As I stated to Stephen Hawkins earlier, Schrodinger's equation, specifically with respect to the square of psi, gives the probability that an electron will be found at a given location. Different eigenvalues when inserted in the Schrodinger wave equation will also provide magnitudes on other qualities such as the electron's energy. The equation obviously doesn't specify the electron's position at any moment in time; it only determines the probability that the electron will be found there. Quantum Mechanical theory is abstract, in the sense that it's not a deterministic Newtonian Mechanical theory, but it does provide values that can be experimentally verified, and have been. However, the math itself does not violate any principles or theorems in the broad field of mathematics.

QM and Schrodinger's equation are therefore sturdy theories reinforced and evaluable by math. This is what makes them impressive, usable theories.
Juan_Pablo
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1/19/2014 6:37:49 PM
Posted: 2 years ago
And for those of you that are intimidated by Quantum Mechanics and Schrodinger's equation, which I admit I still occasionally feel myself, take joy in this:

Quantum Mechanics will not feed the homeless or bring about world peace.
WishfulThinking
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1/22/2014 12:30:47 AM
Posted: 2 years ago
At 1/14/2014 3:38:06 PM, Pareidolic-Dreamer wrote:
At 1/14/2014 1:37:46 PM, Juan_Pablo wrote:
Quantitatively 4 = 7 - 3 is the same thing as 4 = 2 + 2. The total value on either side of the equal sign in either expression is 4!

However, qualitatively the two expressions are not the same! In both Number Theory and Set Theory this has philosophical importance because it demonstrates how the same numerical value can be formulated in at least two ways, which reflects unique and different functions. More formulations are also possible, up to an infinity in accordance with Set Theory.

This serves as evidence that one numerical value (or magnitude) can in theory have numerous manifestations - and it speaks directly to the issue of philosophical determinism because it shows that even though math is inherently deterministic ( 1 + 1 must equal 2 ), the total value ( 2 ) can still go on to materialize in different forms ( e.g. 3 - 1, 1/2 + 3/2 ), adding a probabilistic element to even rigid, deterministic mathematics.

I believe this characteristic about numerical values and magnitudes is the source of the natural probability found in quantum mechanics. I believe it expresses itself mechanically so it gives the electron the apparent, random "non-localized" effect attributed to it in quantum mechanics. In other words, the value the electron shares with the nucleus of the atom is conserved, so the electron is generally allowed to do a random dance without fear of violating mathematical or mechanistic rules.

Your thoughts?

Not really much to disagree with here. You're basically using math to confirm that there is more than one way to skin a cat.
It's an axiom. You can find some form of confirmation of all axioms in all disciplines of thought.
What amazes me, is that so few people seem to realize the true implications of this particular axiom.
Everything is possible. You only have to find a single mathematical expression that leads to 2, to know that 2 is possible. And you only have to believe that 2 is possible in order to create a mathematical expression that leads to it.
We have at our disposal all of the same tools and building materials that the universe built us with. There is no reason we could not build a universe. IF we believe.

What you're saying is not an argument against determimism. It's an argument against not correlating cause with effect. Or at least a single effect. You're saying the end result is 4 and has multiple ways to lead to that. But that's assuming that 4 is the only piece of evidence. If you saw apples on the ground, one might assume that it came from an apple tree. It's pretty logical. Another option would be that it was thrown from the sky. The problem is there is more evidence than just that. You can see that the apple has a seed in it, which if planted would form an apple tree - in turn forming more apples. It is then safe to assume that since this process has occurred multiple times that it came from an apple tree. Not from the sky. Over your life, you would probably not have seen this process, which is much easier to be assured that if you saw the apple seed and had the knowledge that it forms a tree that it comes from a tree. You haven't seen this but it has happened. This means that it is highly likely determined. The fact that you're seeing 4 as the be all to end all is where you're misinterpreting it. 4 is not the only factor involved in the process. More, there are multiple factors, but then there's a variable which can be determined. Similarly in math this same principle applies. 2 + x = 4 can be deduced to 4 - 2 = x, which is of course 2. From multiple sources we can deduce information before it is known.
Juan_Pablo
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1/22/2014 1:23:06 AM
Posted: 2 years ago
At 1/22/2014 12:30:47 AM, WishfulThinking wrote:
At 1/14/2014 3:38:06 PM, Pareidolic-Dreamer wrote:
At 1/14/2014 1:37:46 PM, Juan_Pablo wrote:
Quantitatively 4 = 7 - 3 is the same thing as 4 = 2 + 2. The total value on either side of the equal sign in either expression is 4!

However, qualitatively the two expressions are not the same! In both Number Theory and Set Theory this has philosophical importance because it demonstrates how the same numerical value can be formulated in at least two ways, which reflects unique and different functions. More formulations are also possible, up to an infinity in accordance with Set Theory.

This serves as evidence that one numerical value (or magnitude) can in theory have numerous manifestations - and it speaks directly to the issue of philosophical determinism because it shows that even though math is inherently deterministic ( 1 + 1 must equal 2 ), the total value ( 2 ) can still go on to materialize in different forms ( e.g. 3 - 1, 1/2 + 3/2 ), adding a probabilistic element to even rigid, deterministic mathematics.

I believe this characteristic about numerical values and magnitudes is the source of the natural probability found in quantum mechanics. I believe it expresses itself mechanically so it gives the electron the apparent, random "non-localized" effect attributed to it in quantum mechanics. In other words, the value the electron shares with the nucleus of the atom is conserved, so the electron is generally allowed to do a random dance without fear of violating mathematical or mechanistic rules.

Your thoughts?

Not really much to disagree with here. You're basically using math to confirm that there is more than one way to skin a cat.
It's an axiom. You can find some form of confirmation of all axioms in all disciplines of thought.
What amazes me, is that so few people seem to realize the true implications of this particular axiom.
Everything is possible. You only have to find a single mathematical expression that leads to 2, to know that 2 is possible. And you only have to believe that 2 is possible in order to create a mathematical expression that leads to it.
We have at our disposal all of the same tools and building materials that the universe built us with. There is no reason we could not build a universe. IF we believe.

What you're saying is not an argument against determimism. It's an argument against not correlating cause with effect. Or at least a single effect. You're saying the end result is 4 and has multiple ways to lead to that. But that's assuming that 4 is the only piece of evidence. If you saw apples on the ground, one might assume that it came from an apple tree. It's pretty logical. Another option would be that it was thrown from the sky. The problem is there is more evidence than just that. You can see that the apple has a seed in it, which if planted would form an apple tree - in turn forming more apples. It is then safe to assume that since this process has occurred multiple times that it came from an apple tree. Not from the sky. Over your life, you would probably not have seen this process, which is much easier to be assured that if you saw the apple seed and had the knowledge that it forms a tree that it comes from a tree. You haven't seen this but it has happened. This means that it is highly likely determined. The fact that you're seeing 4 as the be all to end all is where you're misinterpreting it. 4 is not the only factor involved in the process. More, there are multiple factors, but then there's a variable which can be determined. Similarly in math this same principle applies. 2 + x = 4 can be deduced to 4 - 2 = x, which is of course 2. From multiple sources we can deduce information before it is known.

Interesting argument, wishful, but there are some examples in nature ( and many in the human world ) where expectation can frequently be wrong and where determinism doesn't doesn't seem to play a firm role.

For example, in the field of metereology the path that cyclones and hurricanes will take is frequently uncertain. Chaos theory plays a role, in that it's difficult to predict the exact path the storm system will take even a few hours into the future. Metereologists still can't find a model that will predict weather in a certain location a few days into the future. Human nature is another example where probability ( in place of firm determinism ) plays a dominant role. The same is true of waves crashing against the beach ( there is no pattern - something which even I was startled to discover! ). Quantum mechanics is another field where probability determines outcome instead of deterministic precepts ( Newtonian mechanics goes out the window ).

Wishful, you can think that unknown factors play a role in all of these fields, but the burden you have is that you have to demonstrate that they do, which no one yet has been able to demonstrate. Even more, you have to realize that determinism is firmly associated with Newtonian Mechanics - not quantum physics. Determinism is a 17/18th century world view, and it's lost a lot of support as new fields emerged in the 20th century that showed it doesn't always apply.

I'm not a firm determinist because I think the schema is outdated. Nature has provided us with irrefutable examples for nearly a century now where a cause can lead to one in a set of results, rather than one solitary, consistent and repeated result.
Juan_Pablo
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1/22/2014 1:34:54 AM
Posted: 2 years ago
Wishful, I also want to add something else because I think it's important for viewers to read.

There are also computer simulations out there that show firm determinism doesn't always apply even with respect to Newtonian gravity! An example has been developed where two stars of equal mass had a planet revolving around one but just in the right orbit so it could on occassion be captured by the other star. Sometimes the planet would sweep out a figure "8" orbit as it orbited both stars, sometimes it only orbited one star. There are examples even in the Newtonian Worldview where determinism breaks down, believe it or not.