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A new Shabbat-friendly technology, KosherSwitch, uses randomly timed light pulses to create various safeks, so that flipping the switch does not hallachically count as switching the light on, even in terms of gerama. The process is explained on their website.

Different people mean different things when they say "random numbers" in mathematics and in the sciences. Asking a person to choose a random number, for example, will give rise to a distribution of numbers with certain definite biases- for instance, humans are more likely to repeat numbers. A short analysis of random number generation appears here: http://en.wikipedia.org/wiki/Random_number_generation

My question is whether anyone has written a definition of what the word "random" means in a hallachic context. I assume that a hallachic standard of randomness would be more lax than a standard of randomness in crytography, but I'm not sure just how lax. In particular, if somebody could write a computer programme to guess the pulse times with 99% accuracy, would that render KosherSwitch's patent non-Shabbat-safe?

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    Welcome to Mi Yodeya, Daniel, and thanks for bringing us your interesting question. Hope to see you around Mi Yodeya. – Scimonster Apr 14 '15 at 9:12
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    It should be noted that, regardless of the definition of randomness used, using this item for situations other than extenuating circumstances such as medical or security needs seems to be over-hyped by the company. text.rcarabbis.org/… – Yishai Apr 15 '15 at 21:04
  • @DanielMoskovich One of the best questions I've seen on this site. Yasher koach! – SAH Aug 24 '16 at 4:15
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I'd say if an average human, using an average human brain and eye, can't figure out the pattern, that's good enough.

Rabbi Asher Weiss discusses the criteria of "does an unaided human notice it?" with regards to triggering some change deep instead some semiconductor someplace that I'd never notice. He points out that I may not drag a heavy bench on shabbos that I know will dig a groove in the earth, but I am allowed to drag a lighter bench if there's reasonable doubt whether it will dig a groove. Wait!, asks Rabbi Weiss. What do you mean, reasonable doubt?! (The mass of this bench is far beyond the quantum threshold.) If you were an expert physicist and knew the exact mass, the coefficient of friction, the Young's modulus of the soil, and could calculate mgcos(θ) in your head, there would be no doubt!

The answer seems to be that we work with the average, unaided, human intellect and senses.

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    Thank you for this nice answer! It's interesting that this definition is non-multiplicative- i.e. that I can drag the lighter bench over and over and over again across the earth (e.g. with my eyes closed), until I'm humanly certain there will be a groove and with the intention to make a groove, and yet it's still permitted. – Daniel Moskovich Apr 14 '15 at 13:03
  • Thinking about this again, I'm still not sure I understand. For the bench, randomness is Bayesian- it's a measure of belief. I'm not sure whether or not there will be a groove. But for KosherLight, randomness is frequentist. I repeat the experiment many times, and I expect a certain probability distribution of outcomes. Does hallacha treat these two notions interchangeably? It's not obvious. For example, a hundred light-ish benches pulled over earth with your eyes closed. Could I ask a huge crowd to pull lots of lighter benches over the earth? – Daniel Moskovich Apr 14 '15 at 13:53
  • But I suppose that's exactly what the responsa on the website says- hallachically, all probability is interpreted in a purely Bayesian way. kosherswitch.com/live/halacha/responsa?hc_location=ufi – Daniel Moskovich Apr 14 '15 at 16:34
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    Having now read R' Gil Student's analysis and critique of the KosherSwitch, I understand now that the uncertainty in it is meant to enhance its gerama (indirect) status, and is not related to pesik reisha, the principle in the bench case. The bench case includes no indirection, so I'm pretty sure that if the intent is to make a groove, everyone would agree that it's forbidden. And according to R' Student, uncertainty makes indirection permitted only according to some authorities. – Isaac Moses Apr 15 '15 at 13:51
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    @IsaacMoses entirely correct. I'm simply saying that our definition of randomness is defined by human senses. The question of whether you can rely on randomness to allow a situation of "I want X -> I push a button -> I visibly, tangibly get X" is a different one. (Rabbi Heinemann's "Sabbath mode" oven, for instance, has a random delay from when you push the button to when the heat increases, but even then the increase is not directly visible to the naked eye.) – Shalom Apr 15 '15 at 14:28

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