Theoretical probability question

[littlebabyjesus]

Surely that still means, though, it is a system of axioms and tautologous statements derived from those axioms. I don’t understand what your objection was to my characterisation of maths as being a series of tautologous statements derived logically from axioms. If you’re not saying arithmetic is axiom-free, are you saying it has statements that are neither axiomatic nor derived logically from those axioms?

What Godel's theorem tells us is that there has to be at least one axiom that is true but cannot be proved to be true within the system. To prove its truth, you would need to add another axiom. So yes, maths is a system of axioms and tautologous statements derived from those axioms (pre-Godel, Wittgenstein's point in the Tractatus was to show that all logic is tautology), but you will never have a system in which all the axioms can be fully justified logically by the system alone.

And that's where Penrose comes in with his idea that there is something outside algorithmic thinking that provides understanding. We have access to this kind of reasoning - but a purely algorithmic calculating machine such as any extant computer does not.

I would perhaps link this to Kant's ideas about analytic and synthetic propositions. Kant contended that arithmetic was purely synthetic - there is no place for experience in arithmetic propositions. But I think Godel shows that this is wrong. There is a need for experience, for an analytic proposition somewhere down the line. An analytic statement gives meanings, and it is meanings that Penrose says are missing from purely algorithmic calculation. The idea of meaning itself involves an analytic statement, I would think. How do you actually define it? There is meaning to the sensation of 'yellow' for instance, to use Jonti's example, but we can't define it: rather, we experience it, we feel it. It cannot be defined synthetically at all.

 

[Jonti]

... but you will never have a system in which all the axioms can be fully justified logically by the system alone...

Not clear what you mean by this. Axioms aren't justified by the system, they define it. Their justification is that they work to do that.

I think you meant something like "but you will never have a system in which all true theories can be fully justified logically by the system alone."?

 

[fishfinger]

I was thinking of the sensation of seeing the colour yellow. Wavelength as such has no colour.

You only see the colour yellow because an object reflects that particular frequency of light.

 

[kabbes]

You only see the colour yellow because an object reflects that particular frequency of light.

But then your brain makes sense of the wavelength. That’s why it’s an experiential phenomenon.

 

[fishfinger]

But then your brain makes sense of the wavelength. That’s why it’s an experiential phenomenon.

I was questioning Jonti 's statement that frequency has no colour - not the brains' interpretation of said frequency. I realise that there is a philosophical argument as to what is colour, but it's too much tree-falls-in-the-woods for me.

 

[kabbes]

The frequency isn’t “yellow” though. “Yellow” is an interpretation of that wavelength, not the wavelength itself. “Yellow” can only be understood by experience. Knowing the wavelength tells you nothing about what it means to see yellow.

 

[fishfinger]

Like I said: tree-falls-in-the-wood...

 

[Spymaster]

kabbes and littlebabyjesus on a theory thread together

 

[Jonti]

You only see the colour yellow because an object reflects that particular frequency of light.

I see yellow in my dreams though, and that's with the lights off and my eyes closed!

 

[fishfinger]

I see yellow in my dreams though, and that's with the lights off and my eyes closed!

Only because you have already seen yellow and have a memory of it.

 

[kabbes]

Only because you have already seen yellow and have a memory of it.

Memories aren’t wavelengths either, though.

This isn’t just abstract philosophy. Humans experience the world via a model in their heads, and that model, being a model, is not reality. We perceive stuff that isn’t there all the time, and we fail to perceive stuff that is there. Yellow is a concept — our model’s interpretation of a physical thing — not the physical thing itself.

 

[fishfinger]

Memories aren’t wavelengths either, though.

This isn’t just abstract philosophy. Humans experience the world via a model in their heads, and that model, being a model, is not reality. We perceive stuff that isn’t there all the time, and we fail to perceive stuff that is there. Yellow is a concept — our model’s interpretation of a physical thing — not the physical thing itself.

Sure, yellow is not a "thing" but it is a particular quality that can be objectively measured. Our subjective interpretation is neither here nor there.

 

[kabbes]

Sure, yellow is not a "thing" but it is a particular quality that can be objectively measured. Our subjective interpretation is neither here nor there.

No, the thing that gives rise to it can be measured. Things that give rise to pain can also be measured, but we don’t say that the cause of pain is what pain is. Yellow is a result of a measurable stimulus, not the stimulus itself.

 

[fishfinger]

No, the thing that gives rise to it can be measured. Things that give rise to pain can also be measured, but we don’t say that the cause of pain is what pain is. Yellow is a result of a measurable stimulus, not the stimulus itself.

I'm definitely struggling here. Are you saying that light acting on an object is the stimulus in this case?

 

[kabbes]

I'm definitely struggling here. Are you saying that light acting on an object is the stimulus in this case?

Yes. “Yellow” is the interaction of the stimulus with the sensory equipment and the brain that interprets it.

 

[Jonti]

Only because you have already seen yellow and have a memory of it.

One's imagination of sensations is limited to sensations one has already experienced, I agree.

What do you make of the colour green? There's a wavelength of light that looks green to us. But we get exactly the same sensation from a mixture of blue-wavelength and yellow-wavelength photons entering the eye.

 

[fishfinger]

Yes. “Yellow” is the interaction of the stimulus with the sensory equipment and the brain that interprets it.

One's imagination of sensations is limited to sensations one has already experienced, I agree.

What do you make of the colour green? There's a wavelength of light that looks green to us. But we get exactly the same sensation from a mixture of blue-wavelength and yellow-wavelength photons entering the eye.

We can leave out the brain for an objective view. We can measure and reproduce colour accurately. Our own model is immaterial.

As for yellow and blue photons reaching our eyes, I think you'll find that together they make white light.

 

[Jonti]

We can leave out the brain for an objective view. We can measure and reproduce colour accurately. Our own model is immaterial.

As for yellow and blue photons reaching our eyes, I think you'll find that together they make white light.

White light is composed of all the colours of the spectrum, not just the yellow and the blue, although a mixture of red and green light will look yellow. To make white light you can mix together equal intensities of red, green, and blue light.

Incidentally, that's how your computer monitor screen works. All you get is red, green, or blue pixels. But you don't see a chiaroscuro of red, green and blue flashes of light. What you see is an inventive interpretation based on that information.

 

[kabbes]

We can leave out the brain for an objective view. We can measure and reproduce colour accurately. Our own model is immaterial.

And what is the entirely objective measure of this accurate colour?

 

[littlebabyjesus]

I'm definitely struggling here. Are you saying that light acting on an object is the stimulus in this case?

or not. We can experience yellow without any light of the yellow wavelength present.[/QUOTE]

 

[littlebabyjesus]

We can leave out the brain for an objective view. We can measure and reproduce colour accurately. Our own model is immaterial.

As for yellow and blue photons reaching our eyes, I think you'll find that together they make white light.

If you leave out the brain you also leave out 'yellow'. You only know what the yellow wavelength range is because you've asked a person what it is. The fact that things other than light of that wavelength can produce yellow (in a synesthete perhaps the number 7 or the month of May) is a clue that yellow isn't really a wavelength of light at all.

 

[fishfinger]

White light is composed of all the colours of the spectrum, not just the yellow and the blue, although a mixture of red and green light will look yellow. To make white light you can mix together equal intensities of red, green, and blue light.

Incidentally, that's how your computer monitor screen works. All you get is red, green, or blue pixels. But you don't see a chiaroscuro of red, green and blue flashes of light. What you see is an inventive interpretation based on that information.

I know the difference between additive and subtractive colour.

And what is the entirely objective measure of this accurate colour?

We can use a spectrophotometer to measure colour objectively.

or not. We can experience yellow without any light of the yellow wavelength present.

Seeing in our mind's eye is just memory.

If you leave out the brain you also leave out 'yellow'. You only know what the yellow wavelength range is because you've asked a person what it is. The fact that things other than light of that wavelength can produce yellow (in a synesthete perhaps the number 7 or the month of May) is a clue that yellow isn't really a wavelength of light at all.

That just shows how unreliable humans are.

 

[kabbes]

View attachment 130952

We can use a spectrophotometer to measure colour objectively.

We can use it to measure wavelengths accurately. Its interpretation of that measurement is a number, not a colour.

You’ve missed the point about the additive colour, by the way, which is to do with illusion.

 

[fishfinger]

We can use it to measure wavelengths accurately. Its interpretation of that measurement is a number, not a colour.

You’ve missed the point about the additive colour, by the way, which is to do with illusion.

By illusion, do you mean the simulation of yellow produced by a colour monitor, and how the eye interprets that as the colour yellow?

 

[littlebabyjesus]

By illusion, do you mean the simulation of yellow produced by a colour monitor, and how the eye interprets that as the colour yellow?

The brain produces the quale - the experiential phenomenon - yellow.

 

[kabbes]

By illusion, do you mean the simulation of yellow produced by a colour monitor, and how the eye interprets that as the colour yellow?

If “yellow” is a specific wavelength then how comes I also see yellow by seeing a mix of two totally different wavelengths?

The answer is that yellow is not that wavelength. It is my interpretation of the wavelength as a stimulus to my senses, and I also produce the same interpretation when I am exposed to a different mix of wavelengths.

 

[littlebabyjesus]

If “yellow” is a specific wavelength then how comes I also see yellow by seeing a mix of two totally different wavelengths?

The answer is that yellow is not that wavelength. It is my interpretation of the wavelength as a stimulus to my senses, and I also produce the same interpretation when I am exposed to a different mix of wavelengths.

...or without the presence of any light of any wavelength.

Your first point is the crucial one being missed here: what we experience is our self-generated model, not some external reality. And everything we experience is generated by this model - including the subject that is doing the experiencing: our model is not just of 'the world' it is of 'me in the world'. The whole kit kaboodle.

 

[littlebabyjesus]

Not clear what you mean by this. Axioms aren't justified by the system, they define it. Their justification is that they work to do that.

I think you meant something like "but you will never have a system in which all true theories can be fully justified logically by the system alone."?

I'm going to come back to this when I have time to express what I want to say accurately. It has to do with the self-referential nature of the godel statement, but I'll have to do a worked example for it to make any sense (to me as well as anyone else!). Bear with me...

 

[littlebabyjesus]

Seeing in our mind's eye is just memory.

You can see a full reality in complete vividness down to every last detail in a hallucination - ie not in the presence of the stimuli that are normally interpreted in that way.

That just shows how unreliable humans are.

It is only in the experience of us unreliable humans that the idea 'yellow' exists at all. It is quite a triumph for us even to be able to recognise this fact, to realise that our models are just models.

 

[fishfinger]

If “yellow” is a specific wavelength then how comes I also see yellow by seeing a mix of two totally different wavelengths?

The answer is that yellow is not that wavelength. It is my interpretation of the wavelength as a stimulus to my senses, and I also produce the same interpretation when I am exposed to a different mix of wavelengths.

Because RGB monitors exploit the inherent limitations of the human eye, its inability to tell the difference between a specific wavelength of light and 2 wavelengths that are either side of that frequency and stimulate the cones in the same way. If we measure that light we will be able to differentiate between those 2 different frequencies. Again humans may have a concept of yellow that isn't tied to a particular frequency but I think this is too vague to be meaningful. Remove human interpretation and give me raw numbers, then I may then be able to make more sense of it.