Weber's Law - Numberphile
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All but the most impoverished in the UK live better, healthier and wealthier lives than even a Lord 100 years ago. We live longer, we have warmer homes, we have more spare time, we are healthier, we have more luxuries and amenities. Yet we don't compare ourselves to the Lord on 100 years ago. We compare our self to the guy down the street with the bigger car, the larger plasm TV and who can afford a second family holiday a year.
We are comparative by nature. Not absolute. Which is perhaps why certain economic and political ideologies fail. We don't want to be -equal- the vast majority of us strive to be, and have more. It's inbuilt. it cannot be educated away.
As we move along the X axis of our lives and innovations occur, ideologies bend our politics - and hopefully things improve, we will want want to be in the top percentile.
Like every aspect of behaviour there are some people who are exceptions and cannot understand why the majority act like they do, and perhaps wish we were all like them and strive with pure altruistic intent for a more equal world.
I would say the opposite is more true. Our advances in all aspects of life, our journey from cave dwellers to here depends, in the largest part, on those who strive for personal reasons. Create more than they need, come up with ideas they profit from in the short term but society profits from in the long term.
It wouldn't surprise me if this is also closely related to the law of pareto which seems to be inbuilt into every aspect of nature.
Date: 2022-04-09
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Comments and reviews: 9
TBot
When developing videogames, creators will often have to tweak different variables to tune the player's experience. Perhaps they need to make a character jump a little bit higher, or run a little bit faster.
However, the creators can't just playtest the game after making their tweaks, because they're too close to the project. To judge how altering these variables feels, they need to bring in playtesters who can offer unbiased feedback.
Of course, this can easily run into Weber's Law. If the creators' changes are too small or subtle, then the playtesters won't notice a difference. This lead to a particular nugget of game design wisdom: -when adjusting variables for testing, either double them or halve them-. This is the easiest way to make a difference that playtesters will notice. And if you overshoot, you can use quarters to find a comfortable middle-ground between doubling and halving.
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When developing videogames, creators will often have to tweak different variables to tune the player's experience. Perhaps they need to make a character jump a little bit higher, or run a little bit faster.
However, the creators can't just playtest the game after making their tweaks, because they're too close to the project. To judge how altering these variables feels, they need to bring in playtesters who can offer unbiased feedback.
Of course, this can easily run into Weber's Law. If the creators' changes are too small or subtle, then the playtesters won't notice a difference. This lead to a particular nugget of game design wisdom: -when adjusting variables for testing, either double them or halve them-. This is the easiest way to make a difference that playtesters will notice. And if you overshoot, you can use quarters to find a comfortable middle-ground between doubling and halving.
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Ike
It's crazy, because what you consider to be an -octave- isn't objectively an octave, it's just perceived as an octave because humans perceive frequencies logarithmically. The same difference in frequency at a low frequency (e. g. 30 hz to 60 hz) seems like a massive difference (i. e. one full octave apart) but most people cannot tell the difference between 2000 hz and 2030 hz. So music is really just an interaction of many different waveforms with overlapping frequencies, each of which has a special ratio to any other given ratio in the context of the piece. A perfect fifth, for instance, is half the distance of an octave, a perfect fourth is one third of an octave, a major third is one quarter of an octave, etc. (Although Western tuning systems don't allow these intervals to be exact due to complications with higher register notes clashing with lower ones.
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It's crazy, because what you consider to be an -octave- isn't objectively an octave, it's just perceived as an octave because humans perceive frequencies logarithmically. The same difference in frequency at a low frequency (e. g. 30 hz to 60 hz) seems like a massive difference (i. e. one full octave apart) but most people cannot tell the difference between 2000 hz and 2030 hz. So music is really just an interaction of many different waveforms with overlapping frequencies, each of which has a special ratio to any other given ratio in the context of the piece. A perfect fifth, for instance, is half the distance of an octave, a perfect fourth is one third of an octave, a major third is one quarter of an octave, etc. (Although Western tuning systems don't allow these intervals to be exact due to complications with higher register notes clashing with lower ones.
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Robert
I don't quite agree that Weber's law should apply to time perception. I think the reason for that is quite simply that, when you're a child, almost everything is new to you, whereas when you get older the portion of -been there done that- gets bigger and bigger. But no matter how old you are, whenever you're in a situation where you experience something new, time feels very different from the many everyday situations. It does for me, anyway. So I think the similarity in time perception to Weber's law is a complete coincidence for most people. But that's just my guess - maybe there's someone who's (relatively) old but still has a (relatively) large portion of new experiences and cares to reply?
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I don't quite agree that Weber's law should apply to time perception. I think the reason for that is quite simply that, when you're a child, almost everything is new to you, whereas when you get older the portion of -been there done that- gets bigger and bigger. But no matter how old you are, whenever you're in a situation where you experience something new, time feels very different from the many everyday situations. It does for me, anyway. So I think the similarity in time perception to Weber's law is a complete coincidence for most people. But that's just my guess - maybe there's someone who's (relatively) old but still has a (relatively) large portion of new experiences and cares to reply?
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Thomas
Fine detail about the prison sentences though: long sentences have more opportunities to get paroled. So you could also think of it as, -As the judge, I have seen this person's behavior in a single incident. I could put a great deal of thought into determining precisely how many months he 'needs' or 'deserves' or whatever. -Or- I can give a sentence that errs on the side of being probably too long and allow for the possibility of early parole to be decided by people who can weigh more information than just this one bad moment. -
I'm not saying that logic would excuse all sentencing discrepancies. But it should be taken into account in any complete analysis.
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Fine detail about the prison sentences though: long sentences have more opportunities to get paroled. So you could also think of it as, -As the judge, I have seen this person's behavior in a single incident. I could put a great deal of thought into determining precisely how many months he 'needs' or 'deserves' or whatever. -Or- I can give a sentence that errs on the side of being probably too long and allow for the possibility of early parole to be decided by people who can weigh more information than just this one bad moment. -
I'm not saying that logic would excuse all sentencing discrepancies. But it should be taken into account in any complete analysis.
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beeble2003
2: 55 I don't think Weber's law really is the explanation for time seeming to pass faster as you get older. The sensation of the passage of time is actually very closely related to the formation of new memories. For example, time seems to slow down when you're in danger because you're forming a lot of new memories about your experience. Conversely, that would suggest that time seems to speed up as you get older because you're experiencing fewer new things, so forming fewer new memories. Essentially, your brain is saying -I've not formed many memories in the last year, so that year can't have been very long. -
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2: 55 I don't think Weber's law really is the explanation for time seeming to pass faster as you get older. The sensation of the passage of time is actually very closely related to the formation of new memories. For example, time seems to slow down when you're in danger because you're forming a lot of new memories about your experience. Conversely, that would suggest that time seems to speed up as you get older because you're experiencing fewer new things, so forming fewer new memories. Essentially, your brain is saying -I've not formed many memories in the last year, so that year can't have been very long. -
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numberphile
To be fair, the prison sentence gaps do make some sort of sense, if you compare the idea of judging how much prison someone deserves to the idea of the precision of an instrument. A kitchen scale designed for small masses might report to the nearest gram, but a bathroom scale will report to maybe a tenth of a kg. I'm sure the larger scale COULD report to gram precision, but the larger the quantity being measured, the more uncertainty you'll have. If you're trying to assess how much prison time someone deserves, how much precision in your judgement of their crime can you really logically justify?
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To be fair, the prison sentence gaps do make some sort of sense, if you compare the idea of judging how much prison someone deserves to the idea of the precision of an instrument. A kitchen scale designed for small masses might report to the nearest gram, but a bathroom scale will report to maybe a tenth of a kg. I'm sure the larger scale COULD report to gram precision, but the larger the quantity being measured, the more uncertainty you'll have. If you're trying to assess how much prison time someone deserves, how much precision in your judgement of their crime can you really logically justify?
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Jack
I wonder if this will factor into developing more sophisticated AI? Perhaps the fact that the human brain processes things logarithmically is one fundamental factors to the manifestation of consciousness? At the very least, understanding that sensory input to the brain is generally logarithmic should help us develop sophisticated feedback sensors for prosthetic limbs. This must already be understood and used for hearing aids. I'm sure things like Neuralink will make use of this to eventually allow people to feel touch and guage the sensation weight with prosthetic arms.
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I wonder if this will factor into developing more sophisticated AI? Perhaps the fact that the human brain processes things logarithmically is one fundamental factors to the manifestation of consciousness? At the very least, understanding that sensory input to the brain is generally logarithmic should help us develop sophisticated feedback sensors for prosthetic limbs. This must already be understood and used for hearing aids. I'm sure things like Neuralink will make use of this to eventually allow people to feel touch and guage the sensation weight with prosthetic arms.
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Nuno
This holds true if and only if the -just noticeable difference- is taken as a measurement unit for -sensation-. If, on the other hand, you accept the so called Ekman's Law, the relationship between physical intensity and the magnitude of the -feeling- will follow a power function (not a logarithmic one; Steven's Law. Granted, for many things it does not really make much of a difference - but, for stuff like pain, physical exertion and electric shocks the logarythimic relation falls short of our actual sensations
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This holds true if and only if the -just noticeable difference- is taken as a measurement unit for -sensation-. If, on the other hand, you accept the so called Ekman's Law, the relationship between physical intensity and the magnitude of the -feeling- will follow a power function (not a logarithmic one; Steven's Law. Granted, for many things it does not really make much of a difference - but, for stuff like pain, physical exertion and electric shocks the logarythimic relation falls short of our actual sensations
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Adam
This is the basis behind linear progression in weight training. Each workout, try and increase the weight by a very small amount, virtually imperceptible, but because your muscles are doing more work if you keep the sets and reps equal, they adapt to the increased workload. At some point, reality and physics overrides perception, otherwise anyone could be a world class powerlifter given a few years of regular weight training and linear progression.
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This is the basis behind linear progression in weight training. Each workout, try and increase the weight by a very small amount, virtually imperceptible, but because your muscles are doing more work if you keep the sets and reps equal, they adapt to the increased workload. At some point, reality and physics overrides perception, otherwise anyone could be a world class powerlifter given a few years of regular weight training and linear progression.
reply
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