Soul Physics

just a heads up - the link to the script seems to ...

2011-12-20T04:16:50.754-05:00

just a heads up - the link to the script seems to be wrong... I ended up getting it at pitt.edu/~bwr6/misc/completion.zip

was so impressed with what you've done I thought I should let you know so you can update it for others.

keep up the great work and thanks.

The expression definitely doesn't converge for...

2011-12-18T04:21:27.696-05:00

The expression definitely doesn't converge for Re(s) <= 0, and doesn't converge for real numbers <= 1. Typically this is addressed with analytic continuation.

Locality is a tricky subject. I define it by using...

2011-11-25T18:46:20.264-05:00

Locality is a tricky subject. I define it by using clocks, relative my observations. Einstein used a definition in where he sent a light beam to a mirror, that then reflected it back to the Source&receiver, which then by splitting this two way 'communication' gave him a 'local' speed of light, relative his own clock.

That one should hold in all situations, accelerating or not, as long as you measure it the exact same way, 'locally' as I assume.

We also have NIST experiments in where they proved time dilations, due to the gravity on Earth, existing at such distances as half a meter. Assuming ideally sensitive clocks and also assuming that the shortest measure of a light 'distance' making physical sense is one Planck length in one Plank time we can get a definition of a 'frame of reference', related to 'clocks' observed relative your 'local' clock that in this case best is describe conceptually.

That also should give us a possibility to define a 'time dilation', and so discount it, to describe a 'one way speed' of radiation relative you observing, which then should be 'c' in a vacuum. Well, as I think of it :)

But as the 'frame of reference' for your 'local clock' then is one Plank length 'big' a frame of reference relative any 'clock', yours or some others, becomes a tricky definition, except in the case with the two way definition Einstein used, in where we can assume the detector to also be the 'local clock', as I think of it.

And that's sort of sad. I would have preferred a simpler way of defining 'locality', because even if using my definition you to define a 'one way' definition you then have to accept that what ever 'clock' you use locally also will be influenced by its location relative you observing it 'tick'.

All as I think of it.

Yoron.

Sorry, but this example makes no sense to me. What...

2011-11-25T18:24:41.621-05:00

Sorry, but this example makes no sense to me. What you are doing is to create a coordinate system that you then use from two separate perspectives, finding them to clash, when those happenings can't meet for any of the observers.

If there was a real possibility for you to see 'times arrow' count backwards, as you seem to assume here? Then 'time reversibility' should be possible in all accelerations. You can use gravity to show that this isn't the case.

Although all mass, according to the equivalence principle is 'gravitationally constantly uniformly accelerating' there is no such thing in SpaceTime as you observing any other 'clock', as defined by gravity, to 'tick' backwards relative your clock. So either you, or the equivalence principle, should be wrong here.

Yoron.

@Anon Thanks for the tips about the completion.zip...

2011-11-03T09:44:17.908-04:00

@Anon Thanks for the tips about the completion.zip file, I hope it works now. As for the .tm file, I suspect you might not have Textmate installed correctly. If you're sure that you do, just open the .tmCommand files with Textmate.

@Julia I'm afraid TexShop, iTexMac and the like don't have this capacity. One of the (many) reasons to switch to Textmate. Or, I suppose if you're a code hipster, you could almost certainly adapt the menu to work in emacs.

Thanks Bryan, this was quite helpful! Do you know ...

2011-11-02T23:22:57.117-04:00

Thanks Bryan, this was quite helpful! Do you know if it's possible to set up similar keystroke-shortcuts in TexShop?

also, your link to completion.zip is broken. I tri...

2011-11-02T21:49:34.170-04:00

also, your link to completion.zip is broken. I tried with a lower-case C and found it.

in the textmate installation step, when I double-c...

2011-11-02T21:47:59.851-04:00

in the textmate installation step, when I double-click the .tmComand files, I'm asked what application to use. Any ideas?

He has withdrawn his paper due to an error in page...

2011-10-31T08:51:50.645-04:00

He has withdrawn his paper due to an error in page number 29. So RH is still not proven!!!

Hmm, seem to be working for me. It's a very si...

2011-09-01T08:24:06.272-04:00

Hmm, seem to be working for me. It's a very simple applescript though; here's the text:

-- For this script to work, you must change the path /Users/YOURUSERNAME/Dropbox/Lists/@Completed.txt to the location of your completed file.

using terms from application "Quicksilver"
on process text log_text
set theDate to (do shell script "date '+%m-%d-%Y %H:%M'")
set theText to log_text
set theText to theDate & " " & theText & "
"
set thePosixFilePath to "/Users/YOURUSERNAME/Dropbox/Lists/@Completed.txt" as string
set theFilePath to POSIX file thePosixFilePath
set theFileReference to open for access theFilePath with write permission
write theText to theFileReference starting at eof
close access theFileReference
end process text

end using terms from

the script is gone. can you please check the path ...

2011-08-31T16:22:46.691-04:00

the script is gone. can you please check the path to the script.

nice

2011-07-08T14:28:08.647-04:00

nice

In simple modal logic we have a function (ie truth...

2011-05-01T01:00:18.198-04:00

In simple modal logic we have a function (ie truth table) for each world
TruthValue(PropositionalVariable, World). The nature of the truth itself is preserved in each world, we just have a lot more worlds to consider. Does not relevance logic also preserve simple truth tables = functions?

Check out Zot2Bib. It makes importing citations f...

2011-03-10T02:01:39.181-05:00

Check out Zot2Bib. It makes importing citations from Firefox to BibDesk very efficient.

http://mackerron.com/zot2bib/

The organization of your guide is great. I wish more were like it.

What about relevance logic? (I assume that the con...

2011-03-04T14:41:04.018-05:00

What about relevance logic? (I assume that the concept of truth table is misnomer in that case).

Much more accessible introduction than in wikipedi...

2011-03-04T14:37:43.740-05:00

Much more accessible introduction than in wikipedia(the real one, not simple.wikipedia.org:-)

BTW, link to pdf seems to be broken.

The only problem I have with what you say is that ...

2011-02-10T06:49:46.908-05:00

The only problem I have with what you say is that you don’t explain why the material conditional SHOULDN’T BE given a trivial or symmetric interpretation. People have difficulty accepting the material conditional interpretation of conditional statements because there are circumstances where:

I take it to be true that A,
but I take it to be false that if ~A, then B,
but “if ~A, then B” is true, if A is true, according to the material conditional interpretation.

For example, suppose I’m a Democrat, and:

I take it to be true that the Republicans will win the election
I take it to be false that if the Republicans don’t win the election, then the Democrats will increase taxes.
But “if the Republican don’t win the election, then the Democrats will increase taxes” is true, if it is true that the Republicans will win the election, according to the material conditional interpretation.
So, if we accept the material conditional interpretation, it looks like I’m holding a false belief.

http://plato.stanford.edu/entries/conditionals/

I think the answer lies in applying a possible worlds interpretation to all our conditional beliefs (indicative and subjunctive).

Nice post, Bryan. It reminds me of Einstein's ...

2010-12-24T21:29:00.562-05:00

Nice post, Bryan. It reminds me of Einstein's Galilean relativistic dream, tweeked a bit.

Imagine three cowbells, tuned to notes A, B, and C, hung a hundred feet apart in a straight line in the order A-B-C;
Einstein stands in the middle and presses a button to simultaneously send an electrical signal through three equal length electric wires to sound the bells simultaneously.
Assistant at A records the sequence ABC,
Assistant at C records the sequence CBA,
Einstein records B followed by an AC chord.
Each of these three observations is repeatable and factual, yet contradicts the other two. All three event sequences are simultaneously true!
Therefore, one must conclude that:
1) All events are relative to space-time locality
2) There are an infinite number of objectively inconsistent histories of the world, each originating in its here-now.

Steve Gabor

Penrose's CCC cosmology is either inflation or...

2010-12-20T16:42:04.692-05:00

Penrose's CCC cosmology is either inflation or gibberish- http://motls.blogspot.com/2010/11/penroses-ccc-cosmology-is-either.html

I propose to think about the “implied conditional”...

2010-12-08T23:44:46.990-05:00

I propose to think about the “implied conditional” as follows: You can’t logically label a statement false if it can be true. Thus: saying A “implies” B, or, “if A then B,” is not the same thing as saying “A causes B.” Thus, if B is true, the statement can be true. And since A does not cause B, if B is false, the statement still has the potential of being true.

Part 6: I’m sure I made all sorts of mistakes abo...

2010-10-28T11:57:02.673-04:00

Part 6:

I’m sure I made all sorts of mistakes above… Nonetheless:

In conclusion, depending on how we fill in the assumptions that aren’t filled in in the problem, A should either shoot at B, shoot at C, or shoot at neither!

Further, we can conclude that Bryan is one sick puppy… and that I’m prone to wasting my time and mental energy on figuring out why I think that a problem seems like a trick!

Part 5: But, maybe we shouldn’t have assumed that...

2010-10-28T11:56:34.507-04:00

Part 5:

But, maybe we shouldn’t have assumed that A will assume that B and C know nothing… rather, we might assume that A assumes that B and C know how good of a shot they themselves are, but that neither knows how good of a shot the other shooter is. Then A should assume that C at least will not shoot at neither even if A and B shoots at neither. But, then, who should A assume that C will shoot at in the different scenarios? Maybe that C will do so randomly? I’m not really sure. Will B being a 2/3 shooter change anything with respect to following A? I’m not really sure… let’s assume not.

If A shoots at B:

Kills B, then C kills A.
Doesn’t kill B, then B shoots at C; if B kills C, then A and B duke it out with A shooting first. If not, then C randomly kills A or B. If it is B, then A has a 1/3 shot to kill C.

If A shoots at C:

Kills C, then A and B duke it out with B shooting first.
Doesn’t kill C, then B shoots at A; if B doesn’t kill A, then C randomly kills A or B. If it is B, then A has a 1/3 shot to kill C.

If A shoots at neither:

Then B shoots at neither. Then C randomly kills A or B. If it is B, then A has a 1/3 shot to kill C.

So if A shoots at neither then A should expect to die with probability (1/2) + (1/2)(2/3) = 5/6

If A shoots at B, however, then A should expect to die with probability:

(1/3) + (2/3)(2/3)(2/3)(2/3) + (2/3)(2/3)(2/3)(1/3)(2/3)(2/3) + … +
(2/3)(1/3)(1/2) + (2/3)(1/3)(1/2)(2/3)

Which looks to be less than 5/6 (although I might be screwing this up).

If A shoots at C, however, then A should expect to die with probability:

(2/3) + (1/3)(2/3)(2/3) + (1/3)(1/3)(1/3)(2/3)(2/3) + … +
(1/3)(2/3) + (1/3)(1/3)(1/2) + (1/3)(1/3)(1/2)(2/3)

Which looks to be more than 5/6.

So A should shoot at B.

Part 4: Are there any values of X and Y in which ...

2010-10-28T11:55:55.910-04:00

Part 4:

Are there any values of X and Y in which A should not shoot neither?

Well if we are using Rule R, then yes: For whatever values are assigned, A should shoot either B or C.

What if we use Rule Q?

Well, if X was 0, then P(1) < 1/3 and P(2) < 1/3; but, that devolves into A shooting neither – if they are all utterly inept shots, then it is the same as A shooting neither.

What if X is 0.5?

Then Z is roughly 0.54… so P(1) > 1/3
And W is roughly: 0.62… so P(2) > 1/3

What if X is 0.1?

Then Z is roughly 0.08... and P(1) would be roughly 0.28….
So shooting B would be a better option than shooting neither.

And W would be roughly 0.15… so shooting B would be the best option.

But, the point of all of this was to figure out what A should think that B would do given the assumptions being made and what A does.

But, we’ve assumed that B will do what A does in the hypothetical scenario. So what A thinks B will do will depend on what A thinks the rules are and the values… And A’s thinking about C should follow suit.

So if A shoots neither, then A should think that B will think that they are using Rule R. So if A shoots, A should expect B to shoot neither… and then for C to shoot neither.

So, knowing how good of a shot they each other, but assuming that none of the others know what A knows or that A knows what A knows, should A really shoot neither?

Well, that depends on the rules. If A shoots neither, then B will shoot neither, then C will shoot neither, and so on. And if it is Rule R they are using, then A certainly dies. So A should shoot C.

And if it is Rule Q they are using, then the probability that A dies (assuming that none of them lose their shooting skills while not shooting and waiting around for one of them to die)… then A dies with probability:

1/3 + 1/3 + (1/3)(2/3)(2/3) + (1/3)(2/3)(1/3)(2/3)(2/3) + (1/3)(2/3)(1/3)(2/3)(1/3)(2/3)(2/3) + …

Or, roughly, 83%.

That isn’t very good. And it involves a lot of waiting around for people to die… and all assumes that it is Rule Q being used anyway.

So, it seems to me, that A should think that shooting neither is a lousy option, if she thinks that B and C lack her knowledge and are rational.

So, if those assumptions are correct, then A should just shoot C.

Part 3: 2. A shoots at C: A kills C with probabi...

2010-10-28T11:55:16.842-04:00

Part 3:

2. A shoots at C:

A kills C with probability X. B then shoots at A. B kills A with probability X. Otherwise B misses A with probability Y. Then A shoots at B. A kills B with probability A. Otherwise A misses B. Be then shoots at A… and so on.

Otherwise A misses C with probability Y. B then does what A did (i.e., shoot at the person right before her in line): B shoots at A. B kills A with probability X. Otherwise B misses A with probability Y. C then does what A did: C shoots at B. C kills B with probability X. A then shoots at C. A kills C with probability X. Otherwise A misses C with probability Y. C then shoots at A. C kills A with probability X. Otherwise C misses A with probability Y. A then shoots at C… and so on.

Otherwise C misses B with probability Y. A then shoots at C… and now we repeat everything from the top.
On 2, the probability that A dies (given these assumptions) is…

Well, this has two loops again. So call the probability that A dies in the first loop W. W is:

XX + XYYX + XYYYYX + XYYYYYYX + … +
YX + YYXYX + YYXYYYX + YYXYYYYYX + …

The probability that A dies is then:

W + (YYY)(W) + (YYYYYY)(W) + (YYYYYYYYY)(W) + …

3. A shoots at neither:

B then does what A does (shoots at neither). C then does what A does (shoots at neither). A then does what A does (shoots at neither)… and we now repeat everything.

At some point one of the participants dies of something. (Thirst if all they are doing is not shooting, or perhaps hunger, or some other natural cause, or….)

Now we have a rules issue!

When does it become the next person’s turn? Does the person have to indicate that they aren’t shooting in some way? (Waiving a hand, maybe?) If so, then the other two die waiting for a dead person to wave her hand. So the probability that A dies is 1. Call this Rule R.

Or does death count as giving up one’s turn? If so, then whoever is next in line when the first person dies will shoot at the other living person. And for all we know, it is equally probable that any given person will die first. So the probability that A dies would be 1/3. Call this Rule Q.

And I’m not sure how to decide the rules issue.

Part 2: But this answer makes multiple assumption...

2010-10-28T11:54:41.963-04:00

Part 2:

But this answer makes multiple assumptions that are not warranted by the question (beyond the rationality bit). What if we do not assume that A knows/believes that B and C know about their respective shooting skills? That is, what if we do not assume that A knows/believes that B or C knows how good of a shot any of the three are? What should A do given that ignorance? (And shouldn’t we assume that A is ignorant in that way given the information we are given in the question?)

Continuing to assume that A assumes that each player will behave rationally (no vengeance), the problem is pretty tricky. A needs to figure out what B will do depending on what A does, then what C will do depending on what A and B do, and so on (until one person is dead – then they all just shoot at the other person).

So, what should A think that B will do if A shoots at B and misses? If A shoots at C and misses? If A shoots at neither?

This will depend on whether A thinks that B initially thinks that A knows anything more than A thinks that B knows. Let’s assume that A does think this. Will A’s decision give B reason to change her belief about what A knows? This depends on what A should do if A has no knowledge of their respective shooting skills (and assumes similar ignorance on the part of B and C). Let’s say that A assigns the probability X to any given shot hitting the target (and assign probability Y to 1 – X). Assuming that things are as A believes:

1. A shoots at B:

A kills B with probability X. C then shoots at A. C kills A with probability X. Otherwise C misses A with probability Y. A would then shoot at C. A kills C with probability X. Otherwise A misses C with probability Y. C then shoot at A… and so on.

Otherwise A misses B with Probability Y. What should B do? Well, B should do whatever A should do in this scenario (since B is now in the same position as A). I’m a little confused by this move, but I guess that we should treat B as doing what A does… that is, as shooting at the next person in line (so for B that would be to shoot at C). (This strikes me as fishy, but I’m not sure how else to avoid the lurking regress here, so I’m going for it.) So B shoots at C. B kills C with probability X. A would then shoot at B. A kills B with probability X. Otherwise A misses B with probability Y. B then shoots at A. B kills A with probability X. Otherwise B misses A with probability Y. A then shoots at B… and so on.

Otherwise B misses C with probability Y. What should C do? Same as above, I’ll assume that C should do what A does in this scenario, that is shoot at the next person in line (so for C that would be to shoot at A). So C shoots at A. C kills A with probability X. Otherwise C misses A with probability Y. A then shoots at B again… and now we repeat everything from the top.

On 1, the probability that A dies (given these assumptions) is…

Well, this has two loops. So call the probability that A dies in the first loop Z. Z is:

XX + XYYX + XYYYYX + XYYYYYYX + … +
YXYX + YXYYYX + YXYYYYYX + … +
YYX

The probability that A dies is then:

Z + (YYY)(Z) + (YYYYYY)(Z) + (YYYYYYYYY)(Z) + …