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As per my last question, this has less to do with cold, hard, and fast calculations and more to do with the interplay between mathematics and philosophy...but as armchair philosophers aren't as hard to come by as knowledgeable mathematicians, I'm asking this here.

Schrodinger's thought experiment about the cat came to the conclusion that the cat in the box was both alive and dead at the same time until it was actually observed, and that it was the observation of the cat that made reality collapse into only one of those outcomes (either the cat is alive, or the cat is dead, but not both.)

What I take away from that is that simply our observations can have cause/effect relationships to phenomena at the quantum level. Whether my understanding of this concept is a little too simplistic or not, I'll leave up to the opinions of those who are more knowledgeable in this matter than I.

At any rate, if such is the case, then what I'm pondering is this:

Let's assume that accurate mathematical models can be made of the inner workings of subatomic particles and their interactions. If simply by observing those particles we can change how they act, would that not mean that observation itself affects certain areas of mathematics? That certain relationships and concepts in math change based on our observance of them?

And again, just like my last question, I'm not looking for reinforcement here; I know my conclusions have to be incorrect, and I'd be interested to find out why from a mathematical point of view that's more finely honed than my own. Thanks!

Ah, I get what you guys are saying. Mathematics exists as a descriptor of objects/ideas/concepts, and nothing else...even when what it is describing is itself.

So while observation would affect objects, and perhaps to some extent ideas, observation would do absolutely nothing to the actual description of those objects and ideas, which is why mathematics wouldn't be affected.

I knew was going wrong somewhere - thanks for drawing it out, friends!

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    $\begingroup$ Before tackling with this question one has to first find answers to e.g. "Does mathematics exist as a physical entity?," so that we may think about "What happens when we observe math." Another issue is that "observing" is a very well-defined concept in quantum theory, we cannot take it literally and think about "observing a giraffe" for example. $\endgroup$
    – Lord Soth
    Apr 19, 2013 at 0:43
  • $\begingroup$ Well, for example, imagine an infinite, randomized decimal number. At any given time, we'd be able to "observe" the first chunk of it, but at some point, that number becomes "unobservable" to us, because we don't have the time/means to observe it. If we follow Schrodinger to his logical conclusion, it would seem to suggest that any digit in that number outside of our observations would actually exist as EVERY digit at the same time, until we took the time to calculate it out and observe it. $\endgroup$
    – Steve Beresh
    Apr 19, 2013 at 0:50
  • $\begingroup$ Granted, my grasp of quantum mechanics/physics is tenuous at best, so I might be unwittingly hijacking terminology all over the place here. $\endgroup$
    – Steve Beresh
    Apr 19, 2013 at 0:50
  • $\begingroup$ This might be relevant mathoverflow.net/questions/127931/age-of-stochasticity $\endgroup$
    – Baby Dragon
    Apr 19, 2013 at 2:18
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    $\begingroup$ "Observation having physical consequences" is a common misunderstanding from pop physics. It comes from the fact that in physics you typically observe or measure something by bouncing something else off of it, which has consequences. It has nothing to do with what you are cognizant of, however--we can imagine a measurement where a single photon is bounced off of an object at such an angle that it flies into interstellar space, where it will never hit anything or be observed. Nonetheless for the sake of physics that object counts as being "observed". Nothing bounces off of mathematics. $\endgroup$
    – eMansipater
    Apr 19, 2013 at 3:52

3 Answers 3

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Suppose you look at a cow and say "That cow is eating grass.' But the cow hears you, and looks up startled! It's now not eating grass.

Does any of this change what you mean by "eating grass"?

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    $\begingroup$ Zen and the art of stack exchange. $\endgroup$
    – nbubis
    Apr 19, 2013 at 1:25
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    $\begingroup$ I like cows. (I can feel moderators' fingers twitching over "off-topic" warnings.) $\endgroup$
    – not all wrong
    Apr 19, 2013 at 1:30
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    $\begingroup$ They are delicious. $\endgroup$
    – Baby Dragon
    Apr 19, 2013 at 2:15
  • $\begingroup$ You did not specify what whould be the (mathematical) effect of the observer's statement. So your counter-example (as is stated) is not to the point $\endgroup$
    – Nikos M.
    Jun 1, 2014 at 3:09
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Even if you assume we have accurate mathematical models to describe the physics of particle interactions, remember that mathematics is merely serving as a language to "model" these systems. Moreover, the act of observation should be worked into the model, as observation is a physical process (usually observing something requires shooting photons at it). In particular, the mathematical formalism of quantum mechanics basically works observers into the picture via self-adjoint operators on the Hilbert space of states of the system you are considering. On the other hand I don't know what it means to "observe mathematics", or how mathematics could be affected by observation. Remember that physics always requires making some sort of real-world measurement, while mathematics never requires making any such measurements.

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Mathematics is not a physical thing. It is based on reason, not measurement. For example, if I tell you that I have $\$5.00$ and you know you have $\$10.00$ you can deduce that we have $\$15.00$ without making a single measurement.

It is true that our daily experience guides our intuition. Mathematics captures that. Consider the case of parallel lines. We added the parallel postulate to geometry because our intuition of what happens in a plane demanded it. Even if we could do some kind of measurement in our physical world that proved that plane geometry was a figment of our imagination, everything we know about plane geometry would still be true.

Mathematics does not say what the world is made of, it is just a language for describing it.

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  • $\begingroup$ My observation of you saying that you have 5 bucks, and me hearing it is a measurement. Like wise me knowing that I have ten dollars also came from a type of measurement. $\endgroup$
    – Baby Dragon
    Apr 19, 2013 at 1:47
  • $\begingroup$ @BabyDragon These are derived quantities. Counting and measurement are different. Measurement implies precision. You cannot say something weighs exactly $10$ pounds. You can only say it weighs $10$ pounds to within a degree of precision, e.g. a tenth of an ounce. You can say you have exactly $10$ dollars because you can count them. $\endgroup$
    – John Douma
    Apr 19, 2013 at 1:58
  • $\begingroup$ I would say that the precision here is as good as you can get. $\endgroup$
    – Baby Dragon
    Apr 19, 2013 at 2:03
  • $\begingroup$ @BabyDragon A count assigns one number to one set of things. You may interpret your set of things based on some measurement, but the count is exact. For example, you may have a torn dollar bill and in some cases count it, in others not. That would affect the set of things you are counting, not the count. If you measure the same thing twice you can get different results. Therefore, a measurement is not a function. We don't reliably get one unique number for one thing in our set, even if our set is clearly defined. $\endgroup$
    – John Douma
    Apr 19, 2013 at 2:20
  • $\begingroup$ I think that we are using different notions of a measurment. en.wikipedia.org/wiki/Measure_(mathematics) $\endgroup$
    – Baby Dragon
    Apr 19, 2013 at 2:28

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