Pythagoras: the triumph?

[Symphony D.]

I was sitting in my comfortable but not-too-ostentatious suburbanite dwelling, basking in self-congratulatory thoughts of my next novel idea. At that moment, some unremarkable plebeian on the obscure but still fashionable internet relay chat threw a youtube link into the agora of discourse. Disinterestedly clicking on it, i found myself at the whim of a woman's staccato voice, but that was not all...

Soon i clicked video after video but only with one concerning one of the greatest heroes in mathematics was i stopped dead cold in thought and forced to rush here posthaste to relay my findings to this esteemed body. The video in question was


Link to video.

Particularly about the one minute and thirty second mark. It recalled to mind something I had read some months prior in the regrettably named Scientific American when it could tear itself away from abusing its supposed authority. Being of the typical money-grubbing mold they have hidden most of this knowledge away from the world, but I just so happen to have preserved the issue in dark physical form, and so may quote the relevant section:

"A second alternative for the meaning of quantum field theory starts from a simple insight. Although the particle and field interpretation are traditionally considered to be radically different from each other, they have some crucial in common. Both assume that the fundamental items of the material world are persistent individual entities to which properties can be ascribed. These entities are either particles or, in the case of field theory, spacetime points. Many philosophers, including me, think this division into objects and properties may be the deep reason why the particle and field approaches both run into difficulties. We think it would be better to view properties as the one and only fundamental category."

The irascible conundrum of reconciling quantum mechanical phenomena with the cosmological principles of relativity have vexed scientists now for many decades, and in the elegance and simplicity of this solution I was thunderstruck, particularly with the way with which it dovetailed with that of the great thinker Pythagoras. This is in the same way as Zeno presaged calculus, Leucippus and Democritus the atom, and indeed how the Greek kosmos anticipates string theory itself, of course, and so it fit naturally.

Let me now turn to you and ask if you feel as i do that the contributions of this great thinker have been underplayed and that we have yet more to learn from his classical wisdom?

 

[Luckymoose]

As we all know, all problems of science and art can be answered by the Slavic master race that currently resides in Greece. I will wait for more qualified minds to speak.

 

[Borachio]

I do like Vi Hart.

As for Pythagoras, I really don't think anyone doubts his contribution. You wouldn't get anyway without a^2 +b^2 = c^2.

As for the rest of it, who knows? But I doubt his theories on reincarnation are going to turn out to be significant.

 

[Kyriakos]

I was sitting in my comfortable but not-too-ostentatious suburbanite dwelling, basking in self-congratulatory thoughts of my next novel idea.

A novel idea of yours? That alone should have told you that you are only dreaming Cool thread, bro.

 

[Symphony D.]

As for Pythagoras, I really don't think anyone doubts his contribution. You wouldn't get anyway without a^2 +b^2 = c^2.

Typical thinking, reducing a brilliant mind to so little a mathematical expression!

A novel idea of yours? That alone should have told you that you are only dreaming Cool thread, bro.

It is not the OP either so as i said, get back to topic if you must carry on.

 

[Borachio]

Ha!

You mean like this one?

e^(i pi) = -1

The simpler the formula the more elegant and important it is. Anyone can come up with complicated stuff.

e = mc^2

P = ma

 

[Symphony D.]

The simpler the formula the more elegant and important it is. Anyone can come up with complicated stuff.

Reminds me of the argument by Sarah Connor to Miles Dyson in the cult classic Terminator 2: Judgment Day that men only know how to destroy and built the h-bomb because they did now know what it is to create and feel life growing inside them. Perhaps it is more that the typical lay person only remembers simple formulas because they are lacking in attentions?

 

[Borachio]

Okaay. I'm not going to argue the point.

 

[Tahuti]

Are you going to involve some BitCoin bashing in it?

 

[Symphony D.]

Are you going to involve some BitCoin bashing in it?

Why do you troll this thread about physics with your anarcho-capitalisms? Do you want to shill for your Israel-Palestine thread more? This is no place for you if you are not concerned with the historical misrepresentation of one of the world's great thinkers!

 

[Tahuti]

Why do you troll this thread about physics with your anarcho-capitalisms?

I have very few, if any anarcho-capitalist viewpoints. However, I have a tendency to play devil's advocate for unpopular viewpoints and since you've made being against anything Libertarian part of yourself, I feel compelled to offer counterarguments, even if I may agree with your conclusions in practice.

Do you want to shill for your Israel-Palestine thread more?

The fact that you bring it up yourself in a totally unrelated thread you've opened yourself is exactly why such a thread is necessary.

This is no place for you if you are not concerned with the historical misrepresentation of one of the world's great thinkers!

Pythagoras major finding was already discovered by the Babylonians before him. Could be a nice point to include in your novel, who knows.

 

[Symphony D.]

Pythagoras major finding was already discovered by the Babylonians before him. Could be a nice point to include in your novel, who knows.

Once again this analytical reductionist viewpoint that a man's worth is in his equations, completely in ignorance of the points raised in the OP. For shame! Please cease trolling this thread.

 

[Tahuti]

Once again this analytical reductionist viewpoint that a man's worth is in his equations, completely in ignorance of the points raised in the OP.

I've never implied such. I will not claim that I'm an expert on anything Pythagoras, but I do know that he is known for a lot more than just his famed equation. Including his philosophy mentioned in the OP.

For shame! Please cease trolling this thread.

Trolling is sometimes a necessary evil. There are much worse things than trolling, like being overly obnoxious, and you are definitely guilty of that.

 

[Symphony D.]

I've never implied such. I will not claim that I'm an expert on anything Pythagoras, but I do know that he is known for a lot more than just his famed equation. Including his philosophy mentioned in the OP.

You have written off the entire premise of the thread in your post and now persist merely to pimp your own thread no one cares about and espouse the Socratic method when, although noted and appreciated, it is not even his thread, but Pythagoras'. Even in your rebuttal you refuse to engage the material. Begone, troll.

Trolling is sometimes a necessary evil. There are much worse things than trolling, like being overly obnoxious, and you are definitely guilty of that.

You don't have to read thread, troll.

 

[Tahuti]

You have written off the entire premise of the thread in your post and now persist merely to pimp your own thread no one cares about and espouse the Socratic method when, although noted and appreciated, it is not even his thread, but Pythagoras'. Even in your rebuttal you refuse to engage the material. Begone, troll.

1) I haven't written off the premise of this thread.
2) I'm not pimping my own threads, and if I were, you can ignore it. Just like you believe I should ignore it.
3) I wasn't rebutting the OP.

You don't have to read thread, troll.

Nobody has to. And perhaps, after your responses, I might just as well say that everybody SHOULD NOT read this thread. Some people may find our change of words entertaining, but I have decided not to feed the obnoxious ones any longer so I won't be attending this thread any longer. Goodbye.

 

[uppi]

isn't it the definition of properties that they apply to an object? What sense would make properties without objects? anyway, in QFT there are objects: The quantized fields. Just because we have no classic analogon for quantum fields does not mean they are no objects.

e = mc^2

P = ma

Especially when talking about QFT, the correct form is actually:

E=sqrt(m^2c^4 + p^2c^2)

Only for p=0 this reduces to E=mc^2 (and to E=pc for m=0)

 

[Borachio]

Well, quite. Even the unreduced form has an elegant simplicity, imo.

 

[Symphony D.]

isn't it the definition of properties that they apply to an object? What sense would make properties without objects? anyway, in QFT there are objects: The quantized fields. Just because we have no classic analogon for quantum fields does not mean they are no objects.)

Ah, someone actually interested in the discussion at hand! I myself am no great physicist, so I'm afraid I will have to make do with reproducing more of the immediately relevant text:

"Traditionally, people assume that properties are 'universals'—in other words, they belong to an abstract, general category. They are always possessed by particular things; they cannot exist independently. (To be sure, Plato did think of them as existing independently but only in some higher realm, not the world that exists in space and time.) For instance, when you think of red, you usually think of particular red things and not of some freely floating item called 'redness.' But you could invert this way of thinking. You can regard properties as having an existence, independently of objects that possess them. Properties may be what philosophers call "particulars"—concrete, individual entities. What we commonly call a thing may be just a bundle of properties: color, shape, consistency, and so on.

Because this conception of properties as particulars rather than universals differs from the traditional view, philosophers have introduced a new term to describe them: "tropes." It sounds a bit funny, and unfortunately the term brings inappropriate connotations with it, but it is established by now.

[...]

Applying this idea to quantum field theory, what we call an electron is in fact a bundle of various properties of tropes: three fixed, essential properties (mass, charge and spin), as well as numerous changing, nonessential properties (position and velocity). This trope conception helps to make sense of the theory. For instance, the theory predicts that elementary particles can pop in and out of existence quickly. The behavior of the vacuum in quantum field theory is particularly mind-boggling: the average value of the number of particles is zero, yet the vacuum seethes with activity. Countless processes take place all the time, involving the creation and subsequent destruction of all kinds of particles.

In a particle ontology, this activity is paradoxical. If particles are fundamental, then how can they materialize? What do they materialize out of? In the trope ontology, the situation is natural. The vacuum, though empty of particles, contains properties. A particle is what you get when those properties bundle themselves together in a certain way."

On an earlier page:

"Now the following question arises: What is the reason that we can know only the relations among things and not the things themselves? The straightforward answer is that relations are all there is. This leap makes structural realism a more radical proposition, called ontic structural realism."

This, you see, is where Pythagoras' insight was perhaps truly ahead of its time!

 

[uppi]

In a particle ontology, this activity is paradoxical. If particles are fundamental, then how can they materialize? What do they materialize out of? In the trope ontology, the situation is natural. The vacuum, though empty of particles, contains properties. A particle is what you get when those properties bundle themselves together in a certain way."

This is flawed reasoning, because it assumes that only particles can be the fundamental objects. Essentially it is a strawman argument: Particles cannot be fundamental objects, so nothing can be. It ignores the possibility (that I mentioned in my last post) that quantum fields are the fundamental objects.

I can measure the effects of the vacuum field, I can manipulate the vacuum field and particles materialize out of the vacuum field. So the vacuum field is very much an object that I can assign all these properties to that I cannot assign to particles.

 

[Symphony D.]

This is flawed reasoning, because it assumes that only particles can be the fundamental objects. Essentially it is a strawman argument: Particles cannot be fundamental objects, so nothing can be. It ignores the possibility (that I mentioned in my last post) that quantum fields are the fundamental objects.

I can measure the effects of the vacuum field, I can manipulate the vacuum field and particles materialize out of the vacuum field. So the vacuum field is very much an object that I can assign all these properties to that I cannot assign to particles.

To wit:

"For starters, the two categories blend together. Quantum field theory assigns a field to each type of elementary particle, so there is an electron field as surely as there is an electron. At the same time, the force fields are quantized rather than continuous, which gives rise to particles such as the photon. So the distinction between particles and fields appears to be artificial, and physicists often speak as if one or the other is more fundamental. [...] Even today both concepts are still in use for illustrative purposes, although most physicists would admit that the classical conceptions do not match what the theory says. If the mental images conjured up by the words 'particle' and 'field' do not match what the theory says, physicists and philosophers must figure out what to put in their place.

[...]

A classical field is like a weather map that shows the temperature in various cities. The quantum version is like a weather map that does not show you '40 degrees' but '√.' To obtain an actual temperature value, you would need to go through an extra step of applying the operator to another mathematical entity, known as a state vector, which represents the configuration of the system in question.

On some level, this peculiarity of quantum fields does not seem surprising. Quantum mechanics—the theory on which quantum field theory is based—does not traffic in determinate values either but only in probabilities. Ontologically, though, the situation seems weirder in quantum field theory because supposedly fundamental entities, the quantum fields, do not even specify any probabilities; for that they must be combined with the state vector.

The need to apply the quantum field to the state vector makes the theory very difficult to interpret, to translate into something physical you can imagine in your mind. The state vector is holistic; it describes the system as a whole and does not refer to any particular location. Its role undermines the defining feature of fields, which is that they are spread out over spacetime. A classical field lets you envision phenomena such as light as propagation of waves across space. The quantum field takes away this picture and leaves us at a loss to say how the world works.

Clearly then, the standard picture of elementary particles and mediating force fields is not a satisfactory ontology of the physical world. It is not at all clear what a particle or field even is. A common response is that particles and fields should be seen as complementary aspects of reality. But that characterization does not help, because neither of these conceptions works even in those cases where we are supposed to see one or the other aspect in purity. Fortunately, the particle and field views do not exhaust the possible ontologies for quantum field theory."