I notice I am confused. I have updated my understanding of Occam’s razor numerous times in the past.
In this case I am helped by wikipedia; ” The principle states that among competing hypotheses that predict equally well, the one with the fewest assumptions should be selected. Other, more complicated solutions may ultimately prove to provide better predictions, but—in the absence of differences in predictive ability—the fewer assumptions that are made, the better.”
https://en.wikipedia.org/wiki/Occam%27s_razor
That statement would suggest that the essay is entirely not about Occham’s Razor but about “simple theories”.
Whenever I explain Occham today I try to describe. Imagine if you will; a toaster. Bread goes into the “MAGICAL BLACK TOASTER BOX”[1], and toast comes out. As a theory for how a toaster works; its fine; except that it relies on Magic and an assumption of what that is. For practical purposes, knowing that a toaster just works might be more efficient in life than the real explanation of how a toaster works, (electricity passes through coils which heat up due to electrical resistance which cause enough heat to cook a piece of bread and turn it into toasted bread[2]). However if you compare the two explanations; one doesn’t really explain how a toaster works; and the other leaves a lot less unexplained. (sure electricity is unexplained but thats a lot less than MAGIC TOASTING BOX). So Occam would suggest that [2] is more likely to be true than [1].
Does this make sense? Have I got my understanding of toasting magic and Occam correct?
I am not sure about this, but it seems to me that the electricity explanation starts to win more clearly when you do multiple experiments. (Also, “simplicity of the explanation” is in the mind, because it means the amount of information in addition to what you already know.)
If you would already know everything about laws of physics, then “magic” would be an implausible explanation; the magical toaster would require you to change your model of the world, and that would be too much work. But let’s suppose you know nothing about physics; you are just a poorly educated person with a toaster in your hands. At that moment “magic” may be a better explanation than “electricity”...
But then you do multiple experiments. What happens if you put inside a thicker or a thinner slice of bread? Something other than bread? What if you unplug the toaster? The more experiments you do, the more complicated becomes the “magic” explanation, because it must explain why the magic stops working when the toaster is unplugged, etc. (Remember, we are trying to find the simplest explanation that fits the data. A simple wrong model may perfectly fit one data point, but when you have tons of data, the complexity of your model must approach the complexity of the territory.) At some moment, it becomes easier to say “electricity” than to say “magic (which works exactly as the electricity would do)”.
I notice I am confused. I have updated my understanding of Occam’s razor numerous times in the past.
In this case I am helped by wikipedia; ” The principle states that among competing hypotheses that predict equally well, the one with the fewest assumptions should be selected. Other, more complicated solutions may ultimately prove to provide better predictions, but—in the absence of differences in predictive ability—the fewer assumptions that are made, the better.” https://en.wikipedia.org/wiki/Occam%27s_razor
That statement would suggest that the essay is entirely not about Occham’s Razor but about “simple theories”.
Whenever I explain Occham today I try to describe. Imagine if you will; a toaster. Bread goes into the “MAGICAL BLACK TOASTER BOX”[1], and toast comes out. As a theory for how a toaster works; its fine; except that it relies on Magic and an assumption of what that is. For practical purposes, knowing that a toaster just works might be more efficient in life than the real explanation of how a toaster works, (electricity passes through coils which heat up due to electrical resistance which cause enough heat to cook a piece of bread and turn it into toasted bread[2]). However if you compare the two explanations; one doesn’t really explain how a toaster works; and the other leaves a lot less unexplained. (sure electricity is unexplained but thats a lot less than MAGIC TOASTING BOX). So Occam would suggest that [2] is more likely to be true than [1].
Does this make sense? Have I got my understanding of toasting magic and Occam correct?
I am not sure about this, but it seems to me that the electricity explanation starts to win more clearly when you do multiple experiments. (Also, “simplicity of the explanation” is in the mind, because it means the amount of information in addition to what you already know.)
If you would already know everything about laws of physics, then “magic” would be an implausible explanation; the magical toaster would require you to change your model of the world, and that would be too much work. But let’s suppose you know nothing about physics; you are just a poorly educated person with a toaster in your hands. At that moment “magic” may be a better explanation than “electricity”...
But then you do multiple experiments. What happens if you put inside a thicker or a thinner slice of bread? Something other than bread? What if you unplug the toaster? The more experiments you do, the more complicated becomes the “magic” explanation, because it must explain why the magic stops working when the toaster is unplugged, etc. (Remember, we are trying to find the simplest explanation that fits the data. A simple wrong model may perfectly fit one data point, but when you have tons of data, the complexity of your model must approach the complexity of the territory.) At some moment, it becomes easier to say “electricity” than to say “magic (which works exactly as the electricity would do)”.
I am surprised I didn’t say this earlier; I would use the phrase, “most explainable” instead of the phrase, “most simple” to be more fitting to Occam.