Notation for writing log has always bugged me. Like I feel like it should be more like <10>^<527> which would be the log base 10 of 527. That's not it, but something. The current notation just doesn't feel quite right.
I never understand why anyone thinks its good notation. The layout means nothing and lets you infer nothing because exponentiation isn't a 2d planar geometric operation. All the information and rules are contained in the idea "exponentials map the additive reals to the multiplicative reals".
The notation conveys no information at all, and provides no means of proving anything, and even the notation for function composition is worse.
Given the operator pow : R^2->R there are 2 possible inverses. root and log
root isn't even interesting. its just pow with the 2nd argument precomposed with reciprocal. root x b = pow x 1/b
I think it's good for explanation purposes, but not actually great as notation, especially for operations that are so common, too much room for ambiguity, especially when writing quickly.
The Triangle of power explanation of logarithms is what really got me across logs.
It wasn't until seeing the triangle and having the relationships explained that I had any clue about logarithms, up until then logs had been some archaic number that meant nothing to me.
Because of the triangle of power, I now rock up to B and B+ Trees and calculate the number of disc accesses each will require in the worst case, depending on the number of values in each block (eg, log2(n), log50(n) and log100(n))
Ironically, that notation, which I just discovered, confuses me more than anything else.
Logs clicked for me when someone online said "amongst all the definitions we have for logs, the most useful and less taught is that log() is just a power". At that exact instant, it's like if years of arcane and foreign language just disappeared in front of my eyes to leave only obviousness and poetry.
I don't understand the comment about it just being a power, but, for me, knowing that it's filling in the third vertice on the triangle with exponents at the top, and n on the other is what makes it work for me - I now know in my head when I am looking for the log of n, I am looking for the exponent that would turn the log into n.
I don't go looking for the exact log, I only look for whole numbers when I am calculating the value in my mind.
But it makes sense when I am looking for the log2 of 8 to know that the answer is "what exponent will make 2 into 8"? and that's "3"
Well, currently exponentiation has a superscript exponent to the right of the base, and logs have a subscript base to the left of the exponent. They're already very similar to your example, but they also include the word "log".
In 10 years, no trace of our current practices will remain in a recognizable form. It'll take longer than most of us think -- imagine how nonplussed Winograd and the rest of the SHRDLU-era AI gurus would have been to see how long it took to pull off the dice-matching trick in the video -- but when it does happen, it'll happen faster than we think. We're not yet at the tipping point, but it's close.
> I don't think it's _that_ widespread. Just like it's possible to lie on the stand, but people usually think twice before they do it, because _if_ they are found to have lied, they're in trouble.
I don't have data, but I suspect a LOT of people lie on the stand. This is mostly based on what I see on reality court shows and true crime type shows, so admittedly not a great sample, but I figure once something gets to trial things are going to be contentious.
> Best lesson for me - vowed never to be the person opposed to new approaches that work.
I think you'll be surprised at how hard that will be to do. The reason many people feel that way is because: (a) they've become an expert (often recognized) in the old approach. (b) They make significant money (or something else).
At the end of the day, when a new approach greatly encroaches into your way of life -- you'll likely push back. Just think about the technology that you feel you derive the most benefit from today. And then think if tomorrow someone created something marginally better at its core task, but for which you no longer reap any of the rewards.
Of course it is difficult, for precisely the reasons you indicate. It's one of those lifetime skills that you have to continuously polish, and if you fall behind it is incredibly hard to recover. But such skills are necessary for being a resilient person.
You are acting like it was obvious that machine learning was the future, but this person was just stubborn. I don't think that was necessarily the case in the early 2010s and skepticism was warranted. If you see results and ignore them, sure that is a problem. But it wasn't until ML vision results really started dominating conferences such as CVPR that it became clear. It's all a tradeoff of exploration/exploitation.
It also depends on who your parents are. My parents at my age were poor working class. We had a much smaller house (800 sq ft), used cheap cars, cheaper clothing, etc... My dad spent a lot of time fixing our cars (I don't even try), fixing plumbing issues, and we rarely ate out (and never DoorDash'ed!). I was lucky to get some quarters to go to the local arcade to play Pac Man.
My point -- even being slightly lower middle class now would feel like a good jump over my parents. That's just pointing out that comparisons to parental income is very relative.
Intelligence is likely difficult to assess during most of our evolutionary timeline. There weren't signals like attending Harvard. So physical attractiveness, providing reasonable value in health/strength/etc..., has likely evolved to be how we generate attraction.
This makes sense, although what is interesting is that what is physically attractive does change quickly. For example, chest hair as recently as the 70s was considered attractive and now less so. But how did something that seems as intrinsic as physical attractiveness could change in a generation (and so drastically).
* But how did something that seems as intrinsic as physical attractiveness could change in a generation (and so drastically)*
Influx of people with different genetics.
Even within the US in the 70's, there were subcultures where chest hair was not considered attractive. These subcultures tended to align fairly closely with certain ethnicities. Different people evolved to find different physical attributes attractive. Flat v curvy. Hairy v hairless. And on and on and on. These preferences concerted to evoke the different forms we see today.
> Even within the US in the 70's, there were subcultures where chest hair was not considered attractive. These subcultures tended to align fairly closely with certain ethnicities
Can you be more specific on the ethnicities? This seems unlikely given how pervasive the shift was, as there was not a huge ethnic genetic shift since the 70s (AFAIK).
Well, the ideal male aesthetic for black americans for instance included athletes like basketball players and the great boxers. Most of whom were hairless. Joe Frazier only had a smattering of chest hair that hardly even registered. Others from Liston to Ali to Frazier and so on might have had some peach fuzz on their chests, but it's doubtful we'd be able to see it in a photo from that era. In the 70's among that demographic you saw body hair most often in contexts where they were working hard for crossover appeal. ie - entertainment, music etc.
I'd put money on most males from that demographic being largely hairless, or having difficulty growing chest hair, even today. Despite their family lines having lived in North America in some cases as long as four or five hundred years. I'm also positive that the fact that chest hairlessness is so widespread in that demographic is a direct result of centuries of female sexual preference. Likely dating all the way back to long before they even arrived in North America. The cultural echoes probably continued the reproductive pressures selecting for that aesthetic when they arrived in North America. Even when other extrinsic reproductive pressures were brought to bear. (Slavery).
Same with other demographics that came later by the way. (Without the slavery induced reproductive pressures obviously). Reproductive pressures selected for a lack of body hair in some of those demographics. And males from those demographics probably have far less body hair at the median than males from demographics where reproductive pressures selected for more body hair.
Essentially, my bet is that chest hair or no chest hair was decided for human males long ago by ancient female sexual preference. Why females from different demographics had different preferences? Can't say. Maybe climate?
Of course I can't prove any of the last part, but climate induced reproductive pressures on genetic ancestors would be my bet as the largest indicator of whether or not males will have chest hair. Reproductive pressures like that don't just go away over night. Not even over millennia.
I get that, but what about white males? Tom Selleck and his chest hair were iconic. Guys used to wear shirts to show off their chest hair. This is gone almost completely now, not just along black men. If we limit your discussion to black men and attraction of black females I’d agree, but it seems the preferences of white females also changed.
IIRC the underlying assumption was that you should be reducing inflammation (RICE is almost all about reducing inflammation). Since then, we've learned that inflammation is a good thing, and helps things heal faster.
I'm curious now if the anti-inflammatory diets popular with dietitians and health influencers could have a negative effect when you really do want inflammation, like when fighting an infection or recovering from injury.
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