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FQXi FORUM

January 19, 2018

CATEGORY:
The Nature of Time Essay Contest (2008)
[back]

TOPIC: The Reasonable Ineffectiveness of Mathematics in Capturing the Nature of Time. by Dirk Vertigan [refresh]

TOPIC: The Reasonable Ineffectiveness of Mathematics in Capturing the Nature of Time. by Dirk Vertigan [refresh]

We argue that in order to avoid the timelessness of block universe models, that are manifestly inconsistent with our conscious perception of the flow of time, we should try to formulate models in which all times (all now's) cannot consistently be unified into a single well defined mathematical object incorporating all time. In other words, theorists should intentionally try to build a certain kind mathematical inconsistency into their models, in order to thwart the possibility of `blockification'.

The author is a mathematician, currently a professor at LSU.

Sorry you're late enough to the party that it looks as if you've rushed your essay. There are semi-group approaches that try to capture the direction of time in QM, for example, but I think not successfully so far.

I suggest that something of the distinction between past and future can be captured, however, merely by distinguishing between raw data and statistics of that raw data, all of which is in the past, and models which generate probability densities, expected values, correlations, etc., which legitimately try to model both the past (which must be in some sort of conformity with the statistics we have) and the future (which gives predictions of what statistics will be). Thus, ideal probability models may be as if of a block world, while the less theoretical raw data and statistics are only of the past.

Another observation is that by not explicitly including in a model the environment with which an experiment interacts, even if only marginally, one immediately fails to predict the future (or past) evolution of the system perfectly. Hence however much a model may be a block-world, the real world is not the same. Maps and territory and all that.

I guess this is only to question the normativeness of your call for us to formulate high-theory models in a time-directed way. If someone can construct a model that captures the direction of time as a fundamental principle, I would be very interested to see how it works, but it does not seem to me to be an absolute need. Some of my current approach to this can be found implicitly in my essay, posted here October 27th, where I construct an algebra of observables to be invariant under time-reversal, expecting that a direction of time will be /contingently/ expressed by states over the algebra, if such a distinction is called for when modeling a particular experiment. However I suspect that my essay is tangential to my comment here.

You almost cry out that you wish "to thwart the possibility of `blockification'". If we make limited claims for the efficacy and beauty of our models, with a proper humility, not absolute claims that our models are precisely the way the world is, a blockworld structure of our current best theories does not have to be something from which great ethical or moral principles can be derived. But perhaps I have misread your commitment to the quotation above because of my own reaction to your strong wording?

Of course I think this is an interesting issue! I have tried to formulate the above POV in response to exchanges with other essayists. Thank you.

I suggest that something of the distinction between past and future can be captured, however, merely by distinguishing between raw data and statistics of that raw data, all of which is in the past, and models which generate probability densities, expected values, correlations, etc., which legitimately try to model both the past (which must be in some sort of conformity with the statistics we have) and the future (which gives predictions of what statistics will be). Thus, ideal probability models may be as if of a block world, while the less theoretical raw data and statistics are only of the past.

Another observation is that by not explicitly including in a model the environment with which an experiment interacts, even if only marginally, one immediately fails to predict the future (or past) evolution of the system perfectly. Hence however much a model may be a block-world, the real world is not the same. Maps and territory and all that.

I guess this is only to question the normativeness of your call for us to formulate high-theory models in a time-directed way. If someone can construct a model that captures the direction of time as a fundamental principle, I would be very interested to see how it works, but it does not seem to me to be an absolute need. Some of my current approach to this can be found implicitly in my essay, posted here October 27th, where I construct an algebra of observables to be invariant under time-reversal, expecting that a direction of time will be /contingently/ expressed by states over the algebra, if such a distinction is called for when modeling a particular experiment. However I suspect that my essay is tangential to my comment here.

You almost cry out that you wish "to thwart the possibility of `blockification'". If we make limited claims for the efficacy and beauty of our models, with a proper humility, not absolute claims that our models are precisely the way the world is, a blockworld structure of our current best theories does not have to be something from which great ethical or moral principles can be derived. But perhaps I have misread your commitment to the quotation above because of my own reaction to your strong wording?

Of course I think this is an interesting issue! I have tried to formulate the above POV in response to exchanges with other essayists. Thank you.

Interesting, I will certainly read your paper- because you have me "hooked" by proposing the necessity of an inconsistency!

In my paper, I propose a solution based upon an inconsistency which has existed all along, but simply in our interpretation of complex functions, such as the complex exponential present in all signals: this includes all of Fourier analysis and the quantum mechanical wave function.

This essay contest will surely reveal *much* about reality.

In my paper, I propose a solution based upon an inconsistency which has existed all along, but simply in our interpretation of complex functions, such as the complex exponential present in all signals: this includes all of Fourier analysis and the quantum mechanical wave function.

This essay contest will surely reveal *much* about reality.

Hello Peter Morgan,

I refer to your comment of Dec.3, 16:42 GMT where you wrote

"There are semi-group approaches that try to capture the direction of time in QM, for example, but I think not successfully so far."

Did you read fqxi.org/community/forum/topic/369

Let's benefit from special mathematics for elapsed time?

If so, do you have tenable objections?

Regards,

Eckard Blumschein

I refer to your comment of Dec.3, 16:42 GMT where you wrote

"There are semi-group approaches that try to capture the direction of time in QM, for example, but I think not successfully so far."

Did you read fqxi.org/community/forum/topic/369

Let's benefit from special mathematics for elapsed time?

If so, do you have tenable objections?

Regards,

Eckard Blumschein

Hi Dirk,

You deserve credit for getting to the point.

I agree with your strategy. In the context of order that time demands, big-O + epsilon is the zeroth term in a well ordered set, if physical momentum is to be introduced. I employed such a strategy in my essay ("Time counts"). Deriving the epsilon term, rather than inserting by hand, is the mathematically interesting part.

Tom

You deserve credit for getting to the point.

I agree with your strategy. In the context of order that time demands, big-O + epsilon is the zeroth term in a well ordered set, if physical momentum is to be introduced. I employed such a strategy in my essay ("Time counts"). Deriving the epsilon term, rather than inserting by hand, is the mathematically interesting part.

Tom

Dear Professor Vertigan,

Interesting viewpoint, which, possible, may lead to an impossibility theorem.

Maybe the flow of time is just Nature’s tendency to solve its logical inconsistencies? We can view the change not only as a search for equilibrium, but for consistency. Congratulations!

Best regards,

Cristi Stoica

Flowing with a Frozen River

Interesting viewpoint, which, possible, may lead to an impossibility theorem.

Maybe the flow of time is just Nature’s tendency to solve its logical inconsistencies? We can view the change not only as a search for equilibrium, but for consistency. Congratulations!

Best regards,

Cristi Stoica

Flowing with a Frozen River

Dear mathematician Vertigan,

While physicists are ready to write themselves drunk by fabricating tortuous remedies for their weird theories and they do not even shy back from denying time, you prefer to parsimoniously indicate that they might be doomed to fail for very fundamental reasons.

This reminds me a bit of Einstein's thesis which was also very concise, just 10 pages.

However, I do not appreciate you using the notion perception. A single person relates on his subjective perception. Science is based on experience and reproducible experiments of many persons. When David Hilbert denied the objective "arrow" of time, he was therefore wrong.

Was Hilbert correct in mathematics? I consider this question justified with respect to our topic.

Could you please reveal you view concerning Hilbert's rescue of Cantor's naive set theory, the "mathematical" notion of infinity, and v. Neumann's confession in 1935: "I do not absolutely believe in Hilbert space any more"?

Curious,

Eckard Blumschein

While physicists are ready to write themselves drunk by fabricating tortuous remedies for their weird theories and they do not even shy back from denying time, you prefer to parsimoniously indicate that they might be doomed to fail for very fundamental reasons.

This reminds me a bit of Einstein's thesis which was also very concise, just 10 pages.

However, I do not appreciate you using the notion perception. A single person relates on his subjective perception. Science is based on experience and reproducible experiments of many persons. When David Hilbert denied the objective "arrow" of time, he was therefore wrong.

Was Hilbert correct in mathematics? I consider this question justified with respect to our topic.

Could you please reveal you view concerning Hilbert's rescue of Cantor's naive set theory, the "mathematical" notion of infinity, and v. Neumann's confession in 1935: "I do not absolutely believe in Hilbert space any more"?

Curious,

Eckard Blumschein

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