studiot

Agreed +1

One of the problems is the variability of the ocurrence of primes. Here is a comments from the beginning of du Sautoy's book.

Many jobs have indeed become obsolete. And the adjustment was for folks to take up different jobs. However this process has not been without its social pain.

The thing about fields is that they need a source and / or a sink or the go on to infinity. So if the soruce / sink is within you 'empty space' or vacuum is that space still empty ? But if it is not, then it must be external or on the boundary yet infinity has no boundary.

Actually I didn't say anything about outputs. I talked about statements which are inputs. But no, tristate logic chips do not work like that. Of course it does an the reason is embedded in a children's nursery rhyme. To rephrase it When the rain was up it was up When the rain was down it was down And when it was only halfway down it was neither down nor up. A beautiful example of second order logic, (which excludes the law of the excluded middle) unlike first order logic which you are employing (aka classical logic). It so happens that I agree with you that 'reason' exists. Reasoning is a much wider process than 'logic' or mathematics and not cecessarily causal in character. I often quote reasoning examples of how to do science without mathematics. But I'm sorry repetition does not improve veracity and 'the burden of proof' lies firmly with the promoter of a hypothesis. But you have not proven anything.

Good question. +1 Here is a rough explanation of the difference between a classical oscillator and a quantum oscillator. Consider first a classical pendulum hung up on the wall, perhaps in a clock. As it swings to and fro it has oscillatory energy. If it is not swinging but hanging stationary , it has exactly zero oscillatory energy. Of course it also has potential energy by virtue of its position in a gravitational field, but we ignore that. There are lots of other things about it we could analyse, but that is the nub of it. Just by being there it has no oscillatory energy and could hang there indefinitely where it naturally comes to rest at the lowest point of its swing or its ground state. Now consider an electron in an atom. Whatever model you choose the electron has to have oscillatory energy just to remain in the atom. This is true for particle in a box wave functions or orbiting electron particles. Beyond that both models allow for a series of increasing oscillatory energy levels. But it must have some eneregy to be in the lowest one, unlike the pendulum. This is called zero point energy. Outside the nucleus, the 'atom' is basically empty ( of material objects) space but with an electric field in it. The pendulum could equally well be in a vacuum or air. Does this help ?

What is informational symmetry please ? I had not thought about the vibration modes of a membrane in this way before, but have observed before that persistent structures appear in fluid mechanics. Indeed there are hypotheses that this is how particles appear in fields. And Professor Sean Carroll is a proponent of the version of Quantum mechanics that proposed one master field of quantum wave function for the entire universe.

I honestly don't know the answer to that. I was alluding to what is known as the old quantum theory, before the 1/2 was added. This was developed from the states of a classic harmonic oscillator (Morse curves I seem to remember) A classic oscillator not only has harmonics it has sub harmonics and a fundamental, which corresponds to the ground state. As far as I know there is no suggestion in QM of equivalent sub levels. Whilst it is possible to have a conduction current by electrons in a vacuum, again as far as I know, holes can't even exist in a vacuum, let alone conduct. The trouble is that the earlier idea of a vacuum as the absence of anything now seems to be rather oversimplistic. We should perhaps be more specific than anything.

Is that why they got the first quantum theory wrong ? Nor is that comment (though true) any reson why the ground state has to be in a vacuum.

Having carefully side stepped all my questions by addressing things I did not say how about answering the questions I did ask ? For instance I said nothing about probability. Looking more deeply now at probability, it is evident you don't undersatand some basic facts about probability. Firstly the probabilities 1 or 0 are different from all other values. Introducing a probability other than one of these two values automatically implies there must be more than one possibility. This is because the probabilities of all possibilities must add up to exactly 1 if something is to happen. We handle this by moving from individual values to what is called a probability distribution, which mathematically is a function not a value.. This may be a continuous or discrete function, with finite or infinite domain, but bounded codomain. This is different from genuine indeterminism since every possibility posseses a probability. No additional dimensions are need for this.

Where is it written that the ground state must necessarily be the vacuum state ?

Agreed repetition does not constitute proof. I have already told you twice that your understanding and statement of logic is incorrect in your definition 2. You tried incorrectly to support your definition 2 with an example from the real world. There is even a meteorological term from the real world that negates your example - virga. You offered another real world example instead, to which I can think of many real world situations that continue to negate your real world support. In purely theoretical logic it is the easiest thing in the world to create a statement which is both (or neither) true nor false at the same time. You can also make logic gate circuitry to demonstrate this. I don't see why I should reply to your questions, since you don't reply to mine. If and when you deign to reply to my questions I will tell you how to create such statements in logic.

Which may be found in the WAG's guide to the Karma Sutra 😄

Again you are incorrect.

My wife asked AI for the box office phone number of our local theatre. 😄

Yes it is possible, and in fact happened several times recently in my back garden with the unusual weather conditions lately.

Not sure there ever was a 'mother' of science or mathematics. Women were very much in the minority in years gone by. Most authorities acknowledge Aristotle as the father of science, for some of the reasons others have all ready given. As regards women Hypatia of Alexandria was probably the first, and for a long time only, female mathematician but she was not a founder as such, and died a tragic death. https://en.wikipedia.org/wiki/Hypatia Here is Aristotle encapsulated

No, c applies to a vacuum. Or are you suggesting that there is no space inside a crystal ?

First the bolded bit is not accurate. I did say in my that it is worth looking into the difference between entanglement and superposition and the connection between the two as well. I suggest a good way to do this is to study the difference between electtron spin resonance and nuclear magentic resonance spectroscopy. Both cases provide what I consider the most rock solid examples of entanglement as a result of superposition, but the Pauli exclusion principle only applies to ESR.

What I am saying with the curry and the chef is that space needs to have the qualities /characteristics/properties the users requires for his needs. But some other user may have different requirements and so will have a different meaning for 'space'. As a relativity specialist, Mordred is OK to choose space as just volume. My container and separator description allows a user to put things in and take things out of the space and not forgetting the separator function, do this in the right order or configuration at the right time.

I see my curry hasn't gained much flavour favour. 😄 Pity since no one seems to have caught my analogy. Physicists and Mathematicians have very different definitions. There are, in fact, many different spaces some real and material some abstract. So it make sense to qualify the word with additional phraseology to convey the particular description the users wishes to employ. Mordred used to say space is just volume. I like to think I can distill the essence of the idea as a container and separator. Does anyone disagree that the white space on your screen or page is real ?

So let me see the steps in your disproof of Godel. Otherwise it is just an unsupported claim.

The implications are that it would disprove Godel's Theorems. Have you achieved that ?

QM concerns material objects. I am not sure there are any non material objects subject to QM. In Mathematics we have axioms, in Physics we have principles. The fundamental principle we need here is the Principle of Least Energy. A system of material objects acts to attain minimum energy. Using this principle, mathematics can be derived to explain why fluids flow, why structures stand or fall, why hot objects cool off, why chemicals bond, why chemical reactions happen and much more. The mathematics can be used to predict what will happen (though humans do not always get if right). I said energy, but energy (which is a property of material objects) may be possessed in various ways. For a system of material objects one of these ways is configuration energy. If a system can minimise its energy by reconfiguration it will do so unless constrained in some way. It is this process which drives activity amongst sub atomic particles in a manner most readily described by QM.

This is a no then, you don't actually know what the axioms of QM are. You have stated no axioms that I can see, consequently they are all missing. But I am only looking for the main one. Einstein need two for relativity.