Mathematical Obscurities in Special Relativity

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by jrich</i>
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Don't mean to get off subject, but this riddle has been used in the MB before and was similarly missolved.

Amount that salemen spent = (10 - 1) * 3 = 27
Amount that innkeeper received = (30 - 5) + 2 = 27

There is no missing dollar.

Mathematical analogies are a tricky business in that they rely somewhat on the skills of audience for proper effect, which is why I avoid them.


JR
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

You are not accusing me of not solving it correctly, are you?

The salesmen spent:

$8.33 + $8.33 + $8.34 = $25 on the room.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by jrich</i>
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by DAVID</i>
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by MarkVitrone</i>
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The last dollar disappears. <hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">30 – 3 = 27

3 x 9 = 27

The 27 results from the subtraction of 3, not the subtraction of 2.

Plus there are 2 dollars left over.

Two men wound up paying $8.33 for the room, and one wound up paying $8.34.

$8.33 + $8.33 + $8.34 = $25

$25 + $5 = $30

Their problem is to divide the $2 up 3 ways, so each will get .66666 cents.

But they can’t do that, so they settle it this way:

Two guys take .67 cents and one guy settles for .66 cents.

SR does not work because it has no “force” being placed on any of the clocks that could make them slow down.

1895 Lorentz theory works with atomic clocks because there is a “force” felt by the atoms when they are forced through fields such as gravity fields. This is generally known as the “Lorentz Force”. Einstein left out the fields and the physical “forces” in his 1905 paper, and that causes the major flaw in the paper, and so he had to add a field to the SR theory in his 1918 paper, and he had to change the mechanical clocks to atomic clocks, and that’s when he turned SR into a form of GR, and so SR literally disappeared from physics in 1918. All we have now is Lorentz theory and GR theory.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Don't mean to get off subject, but this riddle has been used in the MB before and was similarly missolved.

Amount that salemen spent = (10 - 1) * 3 = 27
Amount that innkeeper received = (30 - 5) + 2 = 27

There is no missing dollar.

Mathematical analogies are a tricky business in that they rely somewhat on the skills of audience for proper effect, which is why I avoid them.


JR
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

This is a different problem. The Innkeeper does not keep $25 + $2 since the wife gives the whole $5 back to the salesmen. The other problem resulted in a conflict because of a crooked bellman who kept $2 in his pocket.

These salesmen are given back $5 to divide into
3 so the $30 is fully accounted for without making further assumptions. The only problem they are having here is how to divide $5 equally 3 ways.

It is neat to see how a thread that starts with the Lorentz Transformation turns into Business Finance. Einstein probably forgot to extend the 4-dimensional space (x,y,z,t) with the dollar, thereby giving the 5-vector (x,y,z,t,$). []

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by 1234567890</i>
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by jrich</i>
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by DAVID</i>
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by MarkVitrone</i>
<br />
The last dollar disappears. <hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">30 – 3 = 27

3 x 9 = 27

The 27 results from the subtraction of 3, not the subtraction of 2.

Plus there are 2 dollars left over.

Two men wound up paying $8.33 for the room, and one wound up paying $8.34.

$8.33 + $8.33 + $8.34 = $25

$25 + $5 = $30

Their problem is to divide the $2 up 3 ways, so each will get .66666 cents.

But they can’t do that, so they settle it this way:

Two guys take .67 cents and one guy settles for .66 cents.

SR does not work because it has no “force” being placed on any of the clocks that could make them slow down.

1895 Lorentz theory works with atomic clocks because there is a “force” felt by the atoms when they are forced through fields such as gravity fields. This is generally known as the “Lorentz Force”. Einstein left out the fields and the physical “forces” in his 1905 paper, and that causes the major flaw in the paper, and so he had to add a field to the SR theory in his 1918 paper, and he had to change the mechanical clocks to atomic clocks, and that’s when he turned SR into a form of GR, and so SR literally disappeared from physics in 1918. All we have now is Lorentz theory and GR theory.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Don't mean to get off subject, but this riddle has been used in the MB before and was similarly missolved.

Amount that salemen spent = (10 - 1) * 3 = 27
Amount that innkeeper received = (30 - 5) + 2 = 27

There is no missing dollar.

Mathematical analogies are a tricky business in that they rely somewhat on the skills of audience for proper effect, which is why I avoid them.


JR
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

This is a different problem. The Innkeeper does not keep $25 + $2 since the wife gives the whole $5 back to the salesmen. The other problem resulted in a conflict because of a crooked bellman who kept $2 in his pocket.

These salesmen are given back $5 to divide into
3 so the $30 is fully accounted for without making further assumptions. The only problem they are having here is how to divide $5 equally 3 ways.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
The salesmen cannot divide the $5 evenly so they take $1 each and leave the $2 on the table. The question of whether one should include the $2 in the accounting of the "room charge" or as a tip is irrelevent. The Innkeeper and her husband received $27. The salesmen spent $27. I think Mark's point was that SR is a solution to a problem that was incorrectly formulated in the first place (as in the riddle) and so no amount of mathematical tweeking will make it correct.


JR

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">
The salesmen cannot divide the $5 evenly so they take $1 each and leave the $2 on the table. The question of whether one should include the $2 in the accounting of the "room charge" or as a tip is irrelevent. The Innkeeper and her husband received $27. The salesmen spent $27. I think Mark's point was that SR is a solution to a problem that was incorrectly formulated in the first place (as in the riddle) and so no amount of mathematical tweeking will make it correct.


JR
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

So you are saying that these salesmen, failing to divide $5 evelnly 3 ways, gives $2 back to
the Innkeeper's wife? If so, they've got bigger problems than the "missing dollar".

DavidS already provided the proper solution to Mark's version of the problem. The subtle difference between the two problems is the knowledge the salesmen have about the money that changed hands. In the case with the bellgirl, the salesmen thought they paid
$27 for the room since they were only given $3 back (they arrived at this conclusion by subtracting 3 from 30,
the original amount they paid). The problem then forces us to take this faulty conclusion and ad hoc the fact that the bellgirl pocketed $2 to arrive at the total amount the salesmen paid . This process
of course leads us to the false conclusion of a missing dollar ($27 + $2 = $29).

Obviously, from the omniscient viewpoint of the bellgirl, the salesmen paid $28 for
the room so that she would've arrived swiftly at the correct conclusion that
no dollar was missing- $28 + $2 = $30.

The lesson from that problem was that if you altered your assumptions in the middle of an argument, you end up inventing
a new math. Special Relativity's space-time diagram is a case
in point.

The problem as restated by Mark is different in that the salesmen were given the correct
refund so that they cannot draw the faulty conclusion that some dollar was missing
unless they just didn't know how to add.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by 1234567890</i>
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">
The salesmen cannot divide the $5 evenly so they take $1 each and leave the $2 on the table. The question of whether one should include the $2 in the accounting of the "room charge" or as a tip is irrelevent. The Innkeeper and her husband received $27. The salesmen spent $27. I think Mark's point was that SR is a solution to a problem that was incorrectly formulated in the first place (as in the riddle) and so no amount of mathematical tweeking will make it correct.


JR
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

So you are saying that these salesmen, failing to divide $5 evelnly 3 ways, gives $2 back to
the Innkeeper's wife? If so, they've got bigger problems than the "missing dollar".

DavidS already provided the proper solution to Mark's version of the problem. The subtle difference between the two problems is the knowledge the salesmen have about the money that changed hands. In the case with the bellgirl, the salesmen thought they paid
$27 for the room since they were only given $3 back (they arrived at this conclusion by subtracting 3 from 30,
the original amount they paid). The problem then forces us to use this faulty conclusion and ad hoc the fact that the bellgirl pocketed $2 to arrive at the total amount the salesmen paid . This process
of course leads us to the false conclusion of a missing dollar ($27 + $2 = $29).

Obviously, from the omniscient viewpoint of the bellgirl, the salesmen paid $28 for
the room so that she would've arrived swiftly at the correct conclusion that
no dollar was missing- $28 + $2 = $30.

The lesson from that problem was that if you altered your assumptions in the middle of an argument, you end up inventing
a new math. Special Relativity's space-time diagram is a case
in point.

The problem as restated by Mark is different in that the salesmen were given the correct
refund so that they cannot draw the faulty conclusion that some dollar was missing
unless they just didn't know how to add.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
I think you should re-read the problem, you are reading things into it that arent there. The $2 is left on the table, period. Nowhere does it say that the salesmen made any attempt to split it. Even if it is left there for all eternity and not pocketed by the innkeeper or whoever that does not change the problem. The missing dollar illusion arises from the inappropriate summing of debits and credits in the accounting of the transaction. In that, Mark's version is no different than any other.


JR