Everything posted by Genady
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The Unreasonable Effectiveness of Mathematics in the Natural Sciences
In fact, it is overexplained. There are many different explanations, sometimes overlapping, sometimes inconsistent. My OP generated a small survey of what some members here pick as their favorite explanation. It turned out to be a subset of explanations existing "on the market."
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What does 'emergent' mean in a physics context (split from Information Paradox)
First of all, thank you for the correction. I like it. And, yes, I also think that it (something being emergent) refers to phenomenon rather than to our description of it, including all the circumstances that the said phenomenon needs in order to occur. Then, the criteria of a phenomenon being or not being emergent should not depend on how we describe it and what we know or need to know to describe it. In other words, the criteria should be about the phenomenon and not about us.
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What does 'emergent' mean in a physics context (split from Information Paradox)
Thus, there are things which are emergent as per less specific criteria but not emergent as per the more specific one.
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The Unreasonable Effectiveness of Mathematics in the Natural Sciences
Now I see where all (my) confusion in the earlier discussion came from -- I never seriously related to the word "unreasonable" and saw it just as metaphoric. In the article Wigner talks only about unexplained effectiveness.
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What does 'emergent' mean in a physics context (split from Information Paradox)
So, this criterion is different from:
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What does 'emergent' mean in a physics context (split from Information Paradox)
Does a phenomenon become 'emergent' after we find a way to describe how it emerges? If a condition for a phenomenon to be emergent is to "be described without knowing or needing from what they exactly emerge", and the evolution of a wave function is a phenomenon that is "described without knowing or needing from what they exactly emerge", how come that this phenomenon does not qualify as being emergent?
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The Unreasonable Effectiveness of Mathematics in the Natural Sciences
Do 'regularity' and 'existence and uniqueness' mean the same?
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What does 'emergent' mean in a physics context (split from Information Paradox)
Does a qualification of being 'emergent' apply to a phenomenon or to an equation describing it?
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What does 'emergent' mean in a physics context (split from Information Paradox)
Schrödinger equation describes the phenomenon of a wave function evolution without knowing or needing from what it exactly emerges. Does it make this phenomenon an emergent one?
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The Unreasonable Effectiveness of Mathematics in the Natural Sciences
Which regularity makes differential geometry effective in describing GR?
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A Riddle Or Not + Zeno's Moving Arrow
Aren't there two different concepts: one is 'probability', the other - 'probability density'?
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Corals near town
Twenty seven years ago, our Marine Park started a long-term "experiment" in coral development, albeit inadvertently. They installed concrete mooring blocks, 1m x 1m x 1m, along the town shoreline for yachts and boats to moor. Coral colonies began inhabiting the block faces. Years later, I’ve noticed that this intriguing growth is not randomly uniform but instead follows patterns, some quite puzzling. Here is one of them. There are two lines of the moorings between South and North ends of the downtown boulevard. One line consists of a dozen moorings constructed from three blocks each and is located about 50m from shore, just near the reef drop-off. Another line consists of a dozen moorings constructed from two blocks each and is located on the sand-flat, half way between the reef drop-off and the shore. I've compared exposed vertical faces of the blocks near the drop-off and those of the blocks near the shore. Where would one expect to find more corals? Wouldn’t corals prefer to grow near the reef and away from the town shoreline with all its polluted water and sewage runoff? The corals provided surprises. More coral colonies grew on the faces of the blocks close to the shore than on those close to the reef. Only 12% of the faces of the off-shore blocks are covered with live corals, like here: Twice as much, 25%, of the close-to-shore block faces are covered with live corals, like here: What is going on? Are shore effects good for the corals? Are some off-shore effects bad for them? What factors are responsible? Any ideas? Questions? More info?
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Find two 4 digit numbers that multiply to give 4^8 + 6^8 + 9^8
Step 1: 48 + 68 + 98 = 22*8 + 28*38 + 32*8 Step 1.5: = (28)2 + 28*38 + (38)2 Step 2: = (28)2 + 2*28*38 + (38)2 - 28*38 Step 2.5: = (28 + 38)2 - (24*34)2 Step 3: = (28 + 38 + 24*34)(28 + 38 - 24*34) = 8113*5521
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Quantum Made Simple - The Double Slit Experiment
Sure. The photons would change the particle's momentum, but not the observation. They would do so also if not observed.
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Quantum Made Simple - The Double Slit Experiment
Observations do not change the physical behavior of particles. They behave just the way they behave.
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Start of time ?
Thank you for the detailed answer. As a synopsis, classical GR doesn't lead to a "start of time". Quantum GR might, albeit not necessarily.
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Does space have mass ? If not, how does it accelerate ?
Shh. Nothing moves faster than light. Mass or not.
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Start of time ?
Ignoring particles and staying with geometry for now. As we go back in time, the three spatial dimensions of spacetime collapse, but the temporal dimension survives. So, at the BB the 4D spacetime geometry is replaced by 1D time geometry (there are no many choices for geometry in 1D.)
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Does space have mass ? If not, how does it accelerate ?
Einstein is not an idiot. Einstein is not, period. Just like that famous parrot: 'E's not pinin'! 'E's passed on! This parrot is no more! He has ceased to be! 'E's expired and gone to meet 'is maker! 'E's a stiff! Bereft of life, 'e rests in peace! If you hadn't nailed 'im to the perch 'e'd be pushing up the daisies! 'Is metabolic processes are now 'istory! 'E's off the twig! 'E's kicked the bucket, 'e's shuffled off 'is mortal coil, run down the curtain and joined the bleedin' choir invisible!! THIS IS AN EX-PARROT!!
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Does space have mass ? If not, how does it accelerate ?
But the second part in Dark Energy is Energy. That is what goes into that formula, Masha.
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Start of time ?
If I'm allowed to speculate here, I could imagine that in that hot dense particle soup, before Higgs and before symmetry breaking, all particles were massless. Thus, time was "frozen", like the time of a photon is.
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Does space have mass ? If not, how does it accelerate ?
Yes, space has mass. Substitute a dark energy for E in E=mc2 and you get the space mass. PS. As my math teacher used to say, "For my every question he has his every answer."
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Start of time ?
Why is it often said that "time itself started with the Big Bang"? If you take the scale factor in the Friedmann–Lemaître–Robertson–Walker metric to zero, then the spatial component goes to zero, but not the temporal one. In other words, space contracts, but nothing happens to time. Or, in the words of A. Zee, "In our current description, space is created at the Big Bang, but not time." (Zee, A. Einstein Gravity in a Nutshell: p. 787). So, any idea from where the notion of beginning of time in BB comes from?
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Find two 4 digit numbers that multiply to give 4^8 + 6^8 + 9^8
Step 1: 48 + 68 + 98 = 22*8 + 28*38 + 32*8 Step 1.5: = (28)2 + 28*38 + (38)2 Step 2: = (28)2 + 2*28*38 + (38)2 - 28*38 Step 2.5: = (28 + 38)2 - (24*34)2
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The Unreasonable Effectiveness of Mathematics in the Natural Sciences
Yes, the third one. There is one more after that. Thanks a lot. Right. Or by endlessly repeated (esp. in a pop-science) reference to "mathematical beauty".