(Today HP posted an article with this title: “Darwin Day Revelation: Evolution, Not Religion, Is the Source of Morality”.)

]]>“Thus, the name “argument from incredulity.”

I mean something specific by incredible here. I mean that,* by your own terms*, you cannot imagine a coherent, logically consistent infinite universe.

If you try, you shall contradict yourself in ways that are patently ridiculous–again, *by your own terms’ meanings*. (This, in essence, is the point which Jagjit Singh makes in the chapter where he considers these questions.)

That, I suppose, is why you’ve ignored every single question I put above seeking your clarifications of just what such an infinite universe would be like.

1) An infinite physical universe–has what? Finite or infinite matter in it?

2 ) how would one account for a single-universe event on such conditions? That is, there are no cycles, the universe either “began” at some point (your view?) or it is eternal as welll as infinite,

3 ) If the latter, then do we suppose that it has been in expansion eternally or not?

4) Does it both expand and contract? If so, how is this other than a form of cyclical universe?

5 ) In such a universe, what possible sense does it make to speak, as scientists routinely do, of the “early universe” or of “looking back into time” as their exploratory instruments take in and analyze the most distant light from the “farthest reaches of the limits of our view” ? That “time” would, it seems, be neither any earlier or any older than any other in the rest of the universe. In an eternal (i.e. infinite, how else?) universe, how can there possibly be “younger” and “older” parts of the same infinite system?

________________________

I assume that the term “infinite” applies to the fact that there are theoretically–and I gather, for you, also, not merely theoretically but in actual physical fact–an infinite number of “solutions” or values by which the function’s terms are valid–true or false?

In the case of the 1s electron, it means the wavefunction has a nonzero value for all values of r (except r=0? I forget. It may have a node of zero probability at r=0), extending out to infinity.

imagine, please that physical reality is infinite. Have you done this? Can you do this? The implications are properly incredible.

Thus, the name “argument from incredulity.” Pointing out the implications are incredible or absurd isn’t an argument against them being right. Many people find the concept of a single particle going through two holes simultaneously to be incredible, but their incredulity doesn’t change the results of the two-slit experiment. The universe may very well be incredible or absurd according to human sensibilities. Nowhere is it written that the universe’s governing laws must be ones that seem normal or sensible to humans, and that includes the humans going by the internet aliases ‘eric’ and ‘proximity1’.

]]>The product is of the form (10+1)(10^2 +1)(10^4 +1)(10^8 +1), or the product of terms [10^(2^M) +1] for M=0 to 3. In general, for M=0 to N, the product has 2^(N+1) decimal digits, each of which is 1, so their sum is also 2^(N+1). This can be proved by induction by multiplying the product for N {10^[2^(N+1) -1] + 10^[2^(N+1) -2] + … + 10 +1} by {10^[2^(N+1)] +1}.

For N=3 as in the example, there 2^4 = 16 decimal digits whose sum is 16.

]]>If I have a number where all the digits are 1 — let’s say 111 — in order to add the same number of zeroes at the end I just multiply by 1 followed by the number of digits in my number. In this case 111*1000 = 111,000. Then if I add my original number, getting 111,111, I will have multiplied by 1001. This will be true no matter the base because of the multiplication by 1s of various magnitudes. In the example the number of digits trailing the leading digit in the multipliers doubles, so the resulting sums will double each time.

BTW Jason, I love how your lead-ins always give a little hint.

]]>The problem is set up so there are no carries, so the case of carries can be left as an exercise for the reader.

So the first product is 11 * 101, or the same as 2*11, or 2+20, drop the zero, so the sum of the digits is the same as the sum of the digits of 2+2 = 4. The second product is thus 4 * 11 (we can drop the 0’s since no carries result from doing so), or 4+4 = 8. Continuing in like fashion, we get to the final answer of 32.

]]>Of course, the numbers given were just (10^x + 1) with x = 1,2,4,8,and16. Their product therefore is sum (i=0 to 31) 10^i. This, in numerical form is simply a string of 32 1’s, so the sum of the digits is 32.

]]> or even *is* very interesting, too! ;^)

“There’s three problems. First one:

(citing me) “If physical reality is finite…”

“You don’t know if it’s finite or not. None of us do.” (does)

Right, It’s a working assumption. But, imagine, please that physical reality is infinite. Have you done this? Can you do this? The implications are properly incredible. Again, I say that here the work of Jagjit Singh are very interesting. He has discussed the problems of this topic. If you can, you should try and locate his Dover texts (Great Ideas of…) and read the relevant parts.

Great Ideas of Modern Mathematics (Dover Books on Mathematics)

An infinite physical universe–has what? Finite or infinite matter in it? If finite, then the materially “occupied” part of this universe is literally “infinitely tiny”–and we occupy that part.

Second, how would one account for a single-universe event on such conditions? That is, there are no cycles, the universe either “began” at some point (your view?) or it is eternal as welll as infinite, If the latter, then do we suppose that it has been in expansion eternally or not? Does it both expand and contract? If so, how is this other than a form of cyclical universe? In such a universe, what possible sense does it make to speak, as scientists routinely do, of the “early universe” or of “looking back into time” as their exploratory instruments take in and analyze the most distant light from the “farthest reaches of the limits of our view” ? That “time” would, it seems, be neither any earlier or any older than any other in the rest of the universe. In an enternal (i.e. infinite, how else?) universe, how can there possibly be “younger” and “older” parts of the same infinite system?

]]>I havre a naive person’s question for you:

Concerning these infinite wave functions, I assume that the term “infinite” applies to the fact that there are theoretically–and I gather, for you, also, not merely theoretically but in actual physical fact–an infinite number of “solutions” or values by which the function’s terms are valid–true or false? IOW, there are an infinite number of “solutions” to the function and it closes or is said to collapse when one of these is (in whatever manner this occurs) is “determined.” Do I have that roughly correct?

]]>I see no logical escape from that conclusion though I would welcome anyone’s pointing one out to me.

Sure. There’s three problems. First one:

If physical reality is finite…

You don’t know if it’s finite or not. None of us do. So your logically inescapable argument is based on a premise that you don’t know the truth status of. This means your argument may only be valid, it is not necessarily sound.

Problem two:

functions can never produce more than the tiniest fraction of the possibilities entailed before, in nature, a function collapses in one determined state or another. To take its infinite extent seriously, we must allow and admit that, at any given determined point of the function’s closure, there reamined “an infinity of unattempted possbilities” …

Circular argument. The fact that infinite wavefunctions imply infinite possibilities that are never actualized is only a “flaw” if you start with the presumption that infinities are bad/unallowed – which is what you are trying to assert. IOW this criticism is only a criticism if you start out assuming the point you want to show. Remove the assumption/premise that infinities are bad, and your entire paragraph above becomes a non-sequitur comment rather than an argument.

…“possibilities” which, it must be admited, never had any realistic possibility to be resolved in a determined outcome.

This is empirically untrue. Every time we take data on, for example, a radioactive isotope’s half-life, we get a smooth exponential curve fully consistent with the predictions of QM. As long as we care to look, we will continue to see low probability events occurring in exactly the ratio we would expect them to occur if our math is correct. There are no boundary conditions or cut-offs that would be predicted or consistent with your notion of finite wavefunctions. Now of course we can’t observe a radioisotope for literally *forever*, and of course we have instrumentation limitations we must deal with, so like everything else in science, our conclusion is provisional and subject to being overturned should new evidence arise. But nevertheless, the best conclusion we have from the evidence we have is that you are wrong, and that low probability QM interactions do occur at exactly the frequencies predicted/consistent with current wavefunction math.