Induction and Quantum Mechanics

May28-05, 05:11 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>rof@maths.tcd.ie wrote:\n\n> Yes, but the statements "Quantum mechanics accurately describes the\n> statistics of measurement results" and "The principle of\n> induction accurately describes the statistics of measurement\n> results" both place constraints on the statistics of\n> measurement results. Probability theory, in contrast, only\n> has something to say about measurement results if one\n> introduces a model for the process generating the results.\n> That is, probability theory alone says nothing about the\n> results of experiments, but becomes applicable if one\n> introduces an extra hypothesis about the measurement\n> results.\n\nQuantum mechanics alone does not tell you anything about the results of\nexperiments either. Just as probability theory requires a distribution,\nquantum mechanics needs at least a Hamiltonian (or something equivalent,\ndepending on the formulation being used).\n\nFortunately, we seem to inhabit a world in which both QM and induction\napply, so we can use induction to figure out at least some of the\nmissing information.\n\n> Ralph Hartley <hartley@aic.nrl.navy.mil> writes:\n>>... they [QM and induction] don\'t say the *same* nontrivial thing. There are possible\n>>worlds in which induction works, but not quantum mechanics. I\'m pretty\n>>sure the reverse is true as well.\n>\n> ... It is logically\n> possible for induction to work without quantum mechanics working\n> because the principle of induction is vaguer than quantum mechanics\n> and hence weaker.\n\nFurthermore it is by induction that we discovered QM. If induction was\ndependent on QM, I\'m not sure that would make sense. In a world in which\ninduction did not work, it would be impossible to tell if QM worked or\nnot (or anything else).\n\n> Imagine what it would be like if induction didn\'t work\n> at all. Experiments would give random results, and the\n> information we would have in advance of an experiment\n> about the result would be zero. Now, suppose the\n> amount of information given by the result of the experiment\n> is I=I1 + I2, where I1 is what quantum mechanics tells us\n> and I2 is the "surprise" when we get the final result. In\n> a world where induction didn\'t work at all, we would\n> know nothing in advance about the result and so I1 would have\n> to be zero, that is, quantum mechanics would be able to\n> tell us nothing about the result.\n\nJust so. In a world in which induction does not work, QM would tell us\nnothing.\n\nLet\'s try constructing a toy world.\n\nAssume you can make a sequence of experiments. For each experiment you\nchoose an N bit number E_t, make a 1 bit "guess" G_t, and get back a one\nbit result R_t = w(E_t,t). Your goal is to be able to correctly guess as\nmany results as possible.\n\nConsider this game in which the results are produced by some process\nequivalent to a fair coin, and independent of the experiment E_t. In\nthis case you can never do better than chance. Induction doesn\'t help.\nYou can guess 1 every time, or 0, or you can flip a coin, it doesn\'t\nmatter. Your guesses will be right half the time.\n\nThis is the same regardless of how the process producing the results\nworks. It can be quantum or classical. It can even be a predetermined\nfunction of t and E_t.\n\nIn this world quantum mechanics indeed gives no information.\n\nWe can construct worlds in which induction (and/or QM) does work by\nputting restrictions on how the results are produced.\n\nFor example, we could require that the result be produced by a circuit\n(or a quantum circuit) with at most X gates, or by a program of length\nat most X. Induction will work in this world, but as X increases it will\nget harder.\n\nThese toy worlds may not be much like ours, but if one of them has a\ncertain combination of properties, then you *can* have a possible world\nwith those properties.\n\nRalph Hartley\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>rof@maths.tcd.ie wrote:

> Yes, but the statements "Quantum mechanics accurately describes the
> statistics of measurement results" and "The principle of
> induction accurately describes the statistics of measurement
> results" both place constraints on the statistics of
> measurement results. Probability theory, in contrast, only
> has something to say about measurement results if one
> introduces a model for the process generating the results.
> That is, probability theory alone says nothing about the
> results of experiments, but becomes applicable if one
> introduces an extra hypothesis about the measurement
> results.

Quantum mechanics alone does not tell you anything about the results of
experiments either. Just as probability theory requires a distribution,
quantum mechanics needs at least a Hamiltonian (or something equivalent,
depending on the formulation being used).

Fortunately, we seem to inhabit a world in which both QM and induction
apply, so we can use induction to figure out at least some of the
missing information.

> Ralph Hartley <hartley@aic.nrl.navy.mil> writes:
>>... they [QM and induction] don't say the *same* nontrivial thing. There are possible
>>worlds in which induction works, but not quantum mechanics. I'm pretty
>>sure the reverse is true as well.
>
> ... It is logically
> possible for induction to work without quantum mechanics working
> because the principle of induction is vaguer than quantum mechanics
> and hence weaker.

Furthermore it is by induction that we discovered QM. If induction was
dependent on QM, I'm not sure that would make sense. In a world in which
induction did not work, it would be impossible to tell if QM worked or
not (or anything else).

> Imagine what it would be like if induction didn't work
> at all. Experiments would give random results, and the
> information we would have in advance of an experiment
> about the result would be zero. Now, suppose the
> amount of information given by the result of the experiment
> is

where I1 is what quantum mechanics tells us
> and I2 is the "surprise" when we get the final result. In
> a world where induction didn't work at all, we would
> know nothing in advance about the result and so I1 would have
> to be zero, that is, quantum mechanics would be able to
> tell us nothing about the result.

Just so. In a world in which induction does not work, QM would tell us
nothing.

Let's try constructing a toy world.

Assume you can make a sequence of experiments. For each experiment you
choose an N bit number

make a 1 bit "guess

and get back a one
bit result

. Your goal is to be able to correctly guess as
many results as possible.

Consider this game in which the results are produced by some process
equivalent to a fair coin, and independent of the experiment

. In
this case you can never do better than chance. Induction doesn't help.
You can guess 1 every time, or 0, or you can flip a coin, it doesn't
matter. Your guesses will be right half the time.

This is the same regardless of how the process producing the results
works. It can be quantum or classical. It can even be a predetermined
function of t and

.

In this world quantum mechanics indeed gives no information.

We can construct worlds in which induction

does work by
putting restrictions on how the results are produced.

For example, we could require that the result be produced by a circuit
(or a quantum circuit) with at most X gates, or by a program of length
at most X. Induction will work in this world, but as X increases it will
get harder.

These toy worlds may not be much like ours, but if one of them has a
certain combination of properties, then you *can* have a possible world
with those properties.

Ralph Hartley

May30-05, 01:22 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In message <d755qq\\$kn9\\$1@ra.nrl.navy.mil>, Ralph Hartley\n<hartley@aic.nrl.navy.mil> writes\n>> Imagine what it would be like if induction didn\'t work\n>> at all. Experiments would give random results, and the\n>> information we would have in advance of an experiment\n>> about the result would be zero. Now, suppose the\n>> amount of information given by the result of the experiment\n>> is I=I1 + I2, where I1 is what quantum mechanics tells us\n>> and I2 is the "surprise" when we get the final result. In\n>> a world where induction didn\'t work at all, we would\n>> know nothing in advance about the result and so I1 would have\n>> to be zero, that is, quantum mechanics would be able to\n>> tell us nothing about the result.\n>\n>Just so. In a world in which induction does not work, QM would tell us\n>nothing.\n>\nInduction works as a pragmatic tool, but not as proof. But it is not\nnecessarily the case that we need induction. Einstein showed by thought\nexperiments that certain laws of relativity are necessary because of the\nway in which we go about measuring things. Likewise, as rof has pointed\nout, we do not need induction for the probabilistic part of quantum\ntheory.\n\nBut when we seek to apply simply the constraints which we can find on\nexperiment the mathematical structure becomes constrained. So\nconstrained in fact that we do not know how to satisfy it and combine\ngeneral relativity and qm. In fact we cannot even resolve all the issues\nfor a special relativistic theory.\n\nI do not believe that the physical universe can be inconsistent, and\ntherefore I believe it must be describable by a consistent mathematical\nstructure. I very much doubt that much induction will be left once we\nhave found such a mathematical structure.\n\n\nRegards\n\n--\nCharles Francis\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>In message <d755qq$kn9$1@ra.nrl.navy.mil>, Ralph Hartley
<hartley@aic.nrl.navy.mil> writes
>> Imagine what it would be like if induction didn't work
>> at all. Experiments would give random results, and the
>> information we would have in advance of an experiment
>> about the result would be zero. Now, suppose the
>> amount of information given by the result of the experiment
>> is

where I1 is what quantum mechanics tells us
>> and I2 is the "surprise" when we get the final result. In
>> a world where induction didn't work at all, we would
>> know nothing in advance about the result and so I1 would have
>> to be zero, that is, quantum mechanics would be able to
>> tell us nothing about the result.
>
>Just so. In a world in which induction does not work, QM would tell us
>nothing.
>
Induction works as a pragmatic tool, but not as proof. But it is not
necessarily the case that we need induction. Einstein showed by thought
experiments that certain laws of relativity are necessary because of the
way in which we go about measuring things. Likewise, as rof has pointed
out, we do not need induction for the probabilistic part of quantum
theory.

But when we seek to apply simply the constraints which we can find on
experiment the mathematical structure becomes constrained. So
constrained in fact that we do not know how to satisfy it and combine
general relativity and qm. In fact we cannot even resolve all the issues
for a special relativistic theory.

I do not believe that the physical universe can be inconsistent, and
therefore I believe it must be describable by a consistent mathematical
structure. I very much doubt that much induction will be left once we
have found such a mathematical structure.

Regards

--
Charles Francis

May30-05, 11:12 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Ralph Hartley <hartley@aic.nrl.navy.mil> writes:\n\n>> Imagine what it would be like if induction didn\'t work\n>> at all. Experiments would give random results, and the\n>> information we would have in advance of an experiment\n>> about the result would be zero. Now, suppose the\n>> amount of information given by the result of the experiment\n>> is I=I1 + I2, where I1 is what quantum mechanics tells us\n>> and I2 is the "surprise" when we get the final result. In\n>> a world where induction didn\'t work at all, we would\n>> know nothing in advance about the result and so I1 would have\n>> to be zero, that is, quantum mechanics would be able to\n>> tell us nothing about the result.\n\n>Just so. In a world in which induction does not work, QM would tell us\n>nothing.\n\n>Let\'s try constructing a toy world.\n\n>Assume you can make a sequence of experiments. For each experiment you\n>choose an N bit number E_t, make a 1 bit "guess" G_t, and get back a one\n>bit result R_t = w(E_t,t). Your goal is to be able to correctly guess as\n>many results as possible.\n\n>Consider this game in which the results are produced by some process\n>equivalent to a fair coin, and independent of the experiment E_t. In\n>this case you can never do better than chance. Induction doesn\'t help.\n>You can guess 1 every time, or 0, or you can flip a coin, it doesn\'t\n>matter. Your guesses will be right half the time.\n\n>This is the same regardless of how the process producing the results\n>works. It can be quantum or classical. It can even be a predetermined\n>function of t and E_t.\n\n>In this world quantum mechanics indeed gives no information.\n\nQuantum mechanics, considered as a recipe for predicting the\nreults of future measurements, works better than chance\nonly if induction works better than chance.\n\nYou didn\'t deny this, but instead hypothesised a "real world",\nwhich was invisible, but contained the "process producing\nthe results", and supposed that quantum mechanics could work\nthere, and hence still "work" even though induction didn\'t.\n\nIt was, or should have been, clear that when I was referring\nto quantum mechanics I meant the formalism which is used to\nassign probabilities to measurement results, not "what\'s\ngoing on in the real world". If the former works, meaning\nallows you to predict meaurement results better than\nchance, then induction also works.\n\nR.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Ralph Hartley <hartley@aic.nrl.navy.mil> writes:

>> Imagine what it would be like if induction didn't work
>> at all. Experiments would give random results, and the
>> information we would have in advance of an experiment
>> about the result would be zero. Now, suppose the
>> amount of information given by the result of the experiment
>> is

where I1 is what quantum mechanics tells us
>> and I2 is the "surprise" when we get the final result. In
>> a world where induction didn't work at all, we would
>> know nothing in advance about the result and so I1 would have
>> to be zero, that is, quantum mechanics would be able to
>> tell us nothing about the result.

>Just so. In a world in which induction does not work, QM would tell us
>nothing.

>Let's try constructing a toy world.

>Assume you can make a sequence of experiments. For each experiment you
>choose an N bit number

make a 1 bit "guess

and get back a one
>bit result

. Your goal is to be able to correctly guess as
>many results as possible.

>Consider this game in which the results are produced by some process
>equivalent to a fair coin, and independent of the experiment

. In
>this case you can never do better than chance. Induction doesn't help.
>You can guess 1 every time, or 0, or you can flip a coin, it doesn't
>matter. Your guesses will be right half the time.

>This is the same regardless of how the process producing the results
>works. It can be quantum or classical. It can even be a predetermined
>function of t and

.

>In this world quantum mechanics indeed gives no information.

Quantum mechanics, considered as a recipe for predicting the
reults of future measurements, works better than chance
only if induction works better than chance.

You didn't deny this, but instead hypothesised a "real world",
which was invisible, but contained the "process producing
the results", and supposed that quantum mechanics could work
there, and hence still "work" even though induction didn't.

It was, or should have been, clear that when I was referring
to quantum mechanics I meant the formalism which is used to
assign probabilities to measurement results, not "what's
going on in the real world". If the former works, meaning
allows you to predict meaurement results better than
chance, then induction also works.

R.

Jun1-05, 12:42 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n>\n> You didn\'t deny this, but instead hypothesised a "real world",\n> which was invisible, but contained the "process producing\n> the results", and supposed that quantum mechanics could work\n> there, and hence still "work" even though induction didn\'t.\n>\nThis is like watching someone bathing in quicksand right in front of the\nwarning sign! Do you have any idea of what you are doing or even of\nwhat you want? Sure, there is (A) a real universe out there made of\nsome mush substance with its built-in processes and causes. Then there\nis (B)our reality which is a total construct, which is how we experience\nthe variations this mush has to offer given the way we are built, our\nsize and the way we think. An then there is (C)our scientific analysis\nof our experience of that mush. So you see, you are a long way from\nbeing able to say what is, and what is not about that mush. So, what is\nit that you want? Do you want to understand what the universe is made of\nand how it works by itself?(It does) To that question there is a single\npossible answer and you need an ontological analysis for that. If not,\nwhat is it that you are trying to do? ????? I suggest an ontological\nanalysis of (C) in order to elucidate (A), which will come back as\nunderstanding, not experiencing. There is some good in understanding\n(you know)that we can apply to (C) and in turn physically turn into\nstuff in (A).\n\nPhilosophy is just that; standing back for a moment and asking yourself\nwhere you are and what you are trying to achieve. Good luck!.\n\nsuggestion applies to both parties.\nlebel@muontailpig.com ------- remove particle\n\nMML\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>You didn't deny this, but instead hypothesised a "real world",
> which was invisible, but contained the "process producing
> the results", and supposed that quantum mechanics could work
> there, and hence still "work" even though induction didn't.
>
This is like watching someone bathing in quicksand right in front of the
warning sign! Do you have any idea of what you are doing or even of
what you want? Sure, there is (A) a real universe out there made of
some mush substance with its built-in processes and causes. Then there
is (B)our reality which is a total construct, which is how we experience
the variations this mush has to offer given the way we are built, our
size and the way we think. An then there is (C)our scientific analysis
of our experience of that mush. So you see, you are a long way from
being able to say what is, and what is not about that mush. So, what is
it that you want? Do you want to understand what the universe is made of
and how it works by itself?(It does) To that question there is a single
possible answer and you need an ontological analysis for that. If not,
what is it that you are trying to do? ????? I suggest an ontological
analysis of (C) in order to elucidate (A), which will come back as
understanding, not experiencing. There is some good in understanding
(you know)that we can apply to (C) and in turn physically turn into
stuff in (A).

Philosophy is just that; standing back for a moment and asking yourself
where you are and what you are trying to achieve. Good luck!.

suggestion applies to both parties.
lebel@muontailpig.com ------- remove particle

MML