Great, test concluded.
Neither option was taken, therefore the null hypothesis that you intended only to waste both our time is confirmed.
I’ll file this away, along with you having nothing to offer with regard to alleged mistakes that I have made, which I’ve repeatedly asked you to disclose in spite of all your efforts to claim I’m not interested in this, reinforcing my classification of you as a fallacious, disingenuous and slanderous thinker, compromised by your political affiliations and their routine oppositional stereotyping.
Your definition of “commitment” appears to revolve around a willingness to dishonestly debase myself before you. I’m not into prostration and self-humiliation unfortunately, nor am I denying anything except the truth of flawed and/or contradictory argument. I’m just committed to getting to the bottom of as many arguments as possible and determining their truth values - but to you, this is not commitment, the same as my interest in my mistakes not being me being interested in my mistakes. I guess this is why you feel like Trump, constantly contradicting yourself, just “saying stuff” with no justification and making impulsive claims based on popular trending prejudices.
But with that out the way, you have attempted to reignite your disagreement with the second law of thermodynamics for all cases where thermodyanmic equilibrium is not met.
This is in direct violation of your opening post on this thread, quoting James’s argument that the universe is infinitely unlikely to be homogenous.
I have no qualms with what you say James says about the universe never repeating its exact state - spacetime has un-curved to the point of curvature no longer being detectable, tending towards flatness and maximum entropy at a slower and slower rate like with the y = 1/x hyperbola, with curvature as the y axis and entropy as the x axis. Therefore it’s not expanding into anything, or into nothing, nor is it exactly finite or infinite: the dilemma disappears.
Now we’re back to before the infA nonsense you brought up and things can continue as normal, with your dilemma solved just the same as I did the first time around.
I demonstrated how to multiply sets correctly
Perhaps your refusal of relativity, and the laws of thermodynamics, extends to a refusal of arithmetic as well?
(a + b + c + … + z)ⁿ = n₁aⁿ + n₂aⁿ⁻¹b + n₂aⁿ⁻¹c + … + n₂aⁿ⁻¹z + n₃aⁿ⁻²bⁿ⁻² + n₄aⁿ⁻²bc + … + n₄aⁿ⁻²bz + n₃aⁿ⁻²cⁿ⁻² + … + n₄aⁿ⁻²cz + … + n₃aⁿ⁻²zⁿ⁻² + n₂abⁿ⁻¹ + n₄abⁿ⁻²c + … + n₄abⁿ⁻²z + n₄abcⁿ⁻² + … + n₅abcz + … + n₄abzⁿ⁻² + n₂acⁿ⁻¹ + … + n₄acⁿ⁻²z + … + n₄aczⁿ⁻² + … + n₂azⁿ⁻¹+ n₁bⁿ + n₂bⁿ⁻¹c + … + n₂bⁿ⁻¹z + n₃bⁿ⁻²cⁿ⁻² + … + n₄bⁿ⁻²cz + … + n₃bⁿ⁻²zⁿ⁻² + n₂bcⁿ⁻¹ + … + n₄bcⁿ⁻²z + … + n₄bczⁿ⁻² + … + n₂bzⁿ⁻¹ + n₁cⁿ + … + n₂cⁿ⁻¹z + … + n₃cⁿ⁻²zⁿ⁻² + … + n₂czⁿ⁻¹ + … + n₁zⁿ
but when every element a,b,c etc. is 1, and every coefficient n can be broken down into 1s added to together, n can be any value and you still get (1+1+1+…+1)
More ABCs just to prove how stupid your careless and mocking dismissals make you look, to add to demonstrations of how unfounded some of James’ basic assumptions are that you’re bringing into this thread for some reason. Those predictable , never letting you get away with lazy thinking…
To end on a positive note, I don’t subscribe to any physical existence of numbers either. Sorry, prom - however Hilbert’s Hotel is a good analogy to demonstrate the problems of infinity, so it would be good for obsrvr to refresh his memory about it.
Prom, what I mean by approaching/tending towards infinity is in the construction of their mathematical representations by using finites - these are just the standard terms that mathematicians use. I find the philosophy behind it doesn’t require Platonic Forms or anything like that. Using my philosophy, Experientialism, numbers arise from treating continuous experience as discrete experiences - as soon as you can distinguish between experiences, and judge relative similarities between experiences as the other side to that coin, you gain knowledge of a thing distinct from a similar enough thing, and using a standard signifier (starting with some value, why not call it 1) to associate with one signified thing, and a different standard signifier (why not call it 2?) when considering both similar things at the same time. Both signifiers and signifieds have real existence, with no necessary real connection beyond the utility of treating them as though they have a real connection. The rest is logical extrapolation on those humble beginnings, such as “keep adding new signifiers to associate with even more than 2 similar things at the same time”, and “why not structure the signifiers in a number system and treat them as having their own artificial precision compared to the real world of signifiers that they represent”. That doesn’t give them platonic form, but at best it’s treating them as though they had that. They’re still real signifiers in the world e.g. sounds/symbols, but its the association with their signifieds that’s “made up”: the main function of the brain being to associate real stimuli for the purposes of prediction. The normal passive associations that are “animal” are actively taken over by the conscious “creative” human mind.
The bounding of discrete experiences from continuous experience, that founds this entire process, is an exercise in defining finites. Extrapolating finites beyond this doesn’t transcend human conception as dealing in finites, the best discrete experience can do when defining real finite signifiers to associate with real finite signifieds is treat the process as though it was ongoing, and representing the outcome using finites in a finite form, but treating it as if it went on forever - and this is exactly what infinite series does. It’s amusing how skeptical obsrvr is over scientists extrapolating experimental data to things like Planck lengths, but he has no problem extrapolating entropy even further than that to infinity.
This explanation should trace the logic right back to the fundaments, which is what Experientialism is for. That way, it should be clear what infinities necessarily have to be to all humans.
We observe from experimentation that energy remains constant, and likewise no matter is gained or destroyed.
An analogy for what is happening in the universe is to drop some dyed liquid into a huge container of water, where the dyed liquid ideally has the same density as water. The dyed liquid, representing matter and energy, doesn’t go up or down, it remains constant. It does, however, swirl and eddy turbulently. The same thing would happen if the water had no bounds: the general tendency is for the dye to spread out, but the turbulence can be constructive in the same way as waveforms can constructively interfere, and isolated pockets appear to do the opposite of spreading out the dye. However these constructive interactions get less intense over time, less frequent, and more spread out, just as the rest of the dye appears to lose its colour as it dissipates into the water, which ultimately all of it does.
Entropy isn’t resetting or decreasing when the dye interferes with itself constructively.
The dye dispersing (increasing entropy) is slower when the dye is interfering with itself, same as pockets of high temperature in the universe, the entropy increases more quickly the lower this interference and the bigger difference between the dye and the water around it. Entropy increase again slows down as the differences between the dye and the water decrease, and change in entropy tends back to zero as entropy tends to infinity. This is summed up in that change in entropy equation brought up earlier in the thread.
But that’s not the whole story, you have to take the analogy away from something everyday and into the extreme conditions found in the wider universe. Under these conditions, instead of imagining whether the water has a container or not (finite or infinite), you can find the water’s volumetric dimensions themselves stretching. The water isn’t expanding into anything, the dimensions themselves are expanding. Absolute space and time is the everyday life intuition that was assumed at the time of Newtonian physics, but since Einstein and the like, better experimental evidence has shown they are not absolute, they are relative - and they observably change under conditions of extreme gravity and speeds.
A further bit of evidence for this is how visible light from stars has been red-shifted into the microwave spectrum of light by this, and due to the speed of everything moving away from everything else - as is also observed by experiment. Seeing the light from all the stars in every direction, which is red-shifted outside of the visible light spectrum is done by detecting background microwave radiation, which we do see in all directions.
All these assumed paradoxes that get people chasing invalid questions and finding invalid answers disappear if you follow what the experimental evidence shows and figure out how it all makes sense - as has already been done through things like relativity and the laws of thermodynamics.