Thank you for all the effort you put into your videos, Artem. You're doing a great job taking complex topics and making them easy to visualize and to understand. In case you're looking for topic suggestions for future videos, I have a few: 1. curriculum you would follow if you had to start from scratch and wanted to teach yourself neuroscience (computational or, if you prefer, a different concentration) 2. sources of information neuroscientists should follow in order to stay current with the research in the field (e.g. journals, labs, companies, people, etc) 3. list of open problems in neuroscience Thank you again for your videos. Keep up the great work. 😊
Thank you for wonderful suggestions! Right now, I'm actually preparing the script for a video about getting started with computational neuroscience! So stay tuned ;)
@@ArtemKirsanov Can you clarify how exsctly normal.dostrobtions arise eve tally even when you have wildly extreme and different values? Is it basically just evening out?
@@leif1075 pretty much! look at height; there's a wide variance, and in any town you can find a tiny person and a giant. But overall, most people are average height, and these outliers are rare. Hence normal
Excellent video, Artem! I enjoy a lot watching your videos, they are incredibly well done and explained. I particularly liked the ones involving topology.
I can’t believe this valuable information is available on YT for free!! I just finished my a level studies and am keen on biology and neuroscience so I loved the fact I got to see a computational perspective on the brain. Makes me wonder where else can the log-normal distributions be seen in the body or what other mathematical models can be deduced in Biological systems. Keep up!
I am happy I didn't skip this video, and now I know another great channel for math and science thank you Artem great quality, and topics I am interested in
I had studied advanced mathematics in my last semester but never understand the concept of random variables and distribution with that much clarity. Amazing video with great explanation.
once wrote a spiking neural net with around a million neurons some neurons would fire almost every iteration, some every 10 iteration, and some would average once every thousands. didn't bother to plot the distribution but that could have been fun.
Its interesting because I thought the video would be able how the brain perceives information logarithmicly, but it actually shows its actually physically built logarithmicly as well.
I've been interested in brain science since I was a kid. This is definitely understandable to a 10 year old kid. Well done! More content please!! And you shud have more subscribers!!
The shape certainly makes some intuitive sense. Extremely short firing rates are more likely to be mistaken as random noise so a neuron wants to be above that limit. However, it doesn't want to be too far above it, because firing is energy-intensive and the brain is already a calorie-hungry organ. At the same time if information is encoded partially in the firing rate, then utilizing only a small subsection of possible firing rates is not information efficient, so neurons that need to be heard more often would be incentivized to use lower utilized firing rates as there is less noise in those channels. I don't know whether that explanation would necessarily result in a log-normal distribution as opposed to a low-median normal distribution, but it is interesting to see roughly the shape I was thinking emerge at the end.
Your videos have a Good dinamic and didacts and the edictions is verry harmony, its really impressive why you not have 1 million of subscribers, more one subscriber from brazil 🇧🇷
Very nice! An explanation of why the distribution of firing rates in the cortex is log-normal can be found in Roxin, Alex, et al. "On the distribution of firing rates in networks of cortical neurons." Journal of Neuroscience 31.45 (2011): 16217-16226.
i have a heavy background in audio production, and i figured this made a lot of sense given the logarithm nature of how we perceive sound, it’s cool to see that this is just inherent to our brains in general
Thank you for a great video! Very interesting topic and very nice of you to show the article to make people more likely to actually look it up for themselves. 😀👍
This is a very nice connection of logarithmic perception and biological features of humans. I wonder if there is an analogy explanation of the rule 70-30?
Helpful content, with a good lowering of entry barrier for someone uninitiated. I learned a lot. A small but important point: sum of independent random variables is not normally distributed, but mean of independent random variables is normally distributed.
Technically you're right, since the limit of the sum of the random variables diverges. However, I don't think stressing that point helps with conceptual understanding, since in practice all sums are finite, and then the sum approximately resembles the SHAPE of a normal distribution. Once you normalize it, which is what taking the mean does, you obtain a probability distribution.
Technically it's not the mean but mean times sqrt(n) where n is the number of samples taken to get the mean and under the limit that n is large. Otherwise the mean would just be a point as n becomes very large.
On a more “global” neural scale, it is well know that there is a strong (inverse) relationship between EEG power and frequency: the fast-fourier transform of EEG activity is high at low frequency (< 5 Hz) and low at high frequency (up to 100 Hz) (Buzaki, Steriadi, and others) so that a plot of log(power) vs frequency is fairly linear. Not surprising since it could be considered an “emergent” property of the neural spiking distribution you show. The slope of that relationship can be used to deduce the state of consciousness - sleep (steep negative slope) versus attentive waking (shallow negative slope). So high-frequency power shows a relative increase during waking, because (generally) there is less synchronization of neurons by thalamo-cortical inputs (e.g. during sleep).
Ok i will add ONE HUGE detail. I read a few years ago, that the brain can work in up to "10 dimentions". This means that if data is sent 1 or 2 ways at all times, the HZ should be multiplied by 2x or 1.5x. But if a crosswalk synapse can send multiple signals at once, lets say up to 5 or 10, then conditionally it can perform 5x or 10x as fast in effect, than what the hz is. So adding more specialists greatly boost the efficiency factor via that alone. To me, this explains how some days things just "click". I learned a thing asap 🤔🧐 In how it was related to what i know, or how maybe some strong synapses formed quckly 👏
Log-normal distributions are also pretty common, especially with frequency. For instance, I think that's what the black-body curve is, though I may be wrong.
i may of course be wrong, but i do not think that is related. But rather that the receptor cells themselves lose sensitivity with higher input, i don’t know anything about how those cells work, but it may possibly be due to a limited store of chemicals, like it is with visual receptors.
I'm going to engage in some rank speculation (except its not really speculation because there is *some* research I could cite). Suppose that those brain waves you're picking up aren't a single neuron at all, but actually a self perpetuating loop signal of several neurons. The longer the loop, the longer it takes for the signal to propagate back to the start, the lower the frequency. Now if you were to take a bunch of neurons connected to each other completely at random, and then count out the number of loops consisting of 2 neurons, 3 neurons, 4 neurons... n neurons, you should find that the number of loops goes down exponentially with length. Loops of length k can be made in n choose k different ways. The lower the frequency, the longer the loop, the fewer possible ways to construct it. Hence the frequencies end up with a log distribution.
Summary: the spiking frequency (aka firing rate) of neurons in the brain follow a lognormal distribution. This can be seen as a small quantity of generalizer neurons responsible for most daily neural activity (~10% of neurons do 50% of the activity) as compared to specialists neurons. (Note that this is not a binary classification but rather a continuum). One of the most promising hypotheses that explains the emergence of this distribution is that the change of size in a synaptic spine is proportional to its size.
Fascinating! But what brain region are you sampling from to see the 1 Hz to 10 Hz spread? Like your other video where sparcity amount varied by brain region, it would seem that occipital cortex might show more up to 40 Hz range. How does the fact that brain is firing at all frequencies at once reconcile with observation (using nmda antagonists) that consciousness is sometimes an all-or-none thing (either a frame is printed or it isn't at any given millisecond), and the change in frequency of these all-or-none frames is smooth, as though having inertia like the boutons' change being proportional to their currently accumulated size? Might it be the thalamo-cortical resonant circuit bringing transient coupling to a particular frequency and this chosen coupled frequency changes smoothly over time? Or, might each 'frame' of consciousness be a set of ensembles of neurons put together to make that full meaning, and each time you change the set of ensembles, you make a new frame of consciousness, and this frequency of change can vary, but has a mechanism to remain smooth (as though rate of change of frequency is itself important to stay smooth, etc., upwards in nested derivatives)?
Log normal distribution is omnipresent in nature because it is the result of feedback-born optimisation. When a snowball falls on the slope, the larger it is, the larger it will get, to a limit. The distribution of snowball sizes obeys a log normal distribution. There's a relation as well, to Poisson distribution. There was some evidence of this in social phenomena as well. When Wilfredo Pareto came up with the notion that 80% of property in Italy is owned by 20% of people, the so-called 'Pareto Principle' was merely a hint at log normal distribution. This has important consequences because if we ignore ideology, this means that wealth distribution will naturally obey a log normal distribution id the system was absolutely fair (from a functional standpoint). So inequality is intrinsic to optimal processes. This does not mean that at the shallow end of the distribution's tail, there should be less means available than needed to live... just that if we raised the threshold at the tail such that people could live comfortably, there would still be a small group of very wealthy individuals. And there's nothing in there tied to merit or morality ; it's amoral. What morality leads us to do, however, is alter the parameters of the distribution such that its "floor" is sustainable for all. Normal curves are still normal, regardless of their sigma or height. So we can alter the integral of the distribution to serve the outcomes we seek, while respecting the naturalness of the log normal distribution process. There are countless examples of this distribution in both the natural world, and in the behavioural and perceptual realms.
Ist this why our brains are so powerful, because they are based on multiplication? Compared to a computer, where the base is succession, multiplication is two steps above that in the mathematical hierarchy. Maybe an idea why computers are so limited despite their extreme calculation speed
Thanks for a good video on a good topic. I would enjoy less time on a proscriptive path of the lesson, and more time on ideas associated with any step in the chain, correlates.
Great ! I gave me some ideas for my PhD in ecology ;) Indeed, do the stability of an ecosystem relies on the number of connections or few "key connections" between organisms ? Just like brain with specialised and generalist neurons...
I would be interested to see if the weights of a self-learning computer neural net (like for OCR or object recognition) followed a log-normal distribution too, or if it's more Gaussian, or white-noise.
According to a quick google search (no academic sources), yes machine learning gradients tend to be log normal. Makes sense because the brain was the model for machine learning
Ohhh, interesting. I wonder if high iq is the result of the bulk of the slower firing neurons beign slightly faster than the average person, and it adding up a lot. Or is it something else, like the efficiency of the speciallized neural pathways. Or may be it is just neurons sending stronger signals overall. Really no idea, but very interesting indeed.
I don't like describing them as not equal. They are all equally important in the context of the brain operating at maximum capacity. If any single neuron was missing, the brain would be unable to operate at its maximum potential. They're different, that's more specific than inequal.
Question: Have anybody ever predicted anything important and completely unexpected based on only dreams, sorry thought experiences that turned out to be true after the appropriate experience became technically doable?
Oh my. Log normal distributions... This is exactly why not everyone was born to be a popstar/world leader/social media influencer, and why our society is so (toxic? Distracted? Misaligned?) For convincing them so. "Everyone go to college and generate enormous amounts of debt while competing for a narrow job market! It will be fine!"
This went too slow and didn't provide enough relations between the topics so I didn't understand the meaning or utility of these concepts and their relation to the brain.
Join Shortform for awesome book guides and get 5 days of unlimited access! shortform.com/artem
@Artem Kirsanov the text at 15:03 doesn't seem to correspond to the biorxiv paper you have linked in the description 😅
Thank you for all the effort you put into your videos, Artem. You're doing a great job taking complex topics and making them easy to visualize and to understand.
In case you're looking for topic suggestions for future videos, I have a few:
1. curriculum you would follow if you had to start from scratch and wanted to teach yourself neuroscience (computational or, if you prefer, a different concentration)
2. sources of information neuroscientists should follow in order to stay current with the research in the field (e.g. journals, labs, companies, people, etc)
3. list of open problems in neuroscience
Thank you again for your videos. Keep up the great work. 😊
Thank you for wonderful suggestions!
Right now, I'm actually preparing the script for a video about getting started with computational neuroscience! So stay tuned ;)
@@ArtemKirsanov Thank you. I look forward to it. 🙂
@@ArtemKirsanov Can you clarify how exsctly normal.dostrobtions arise eve tally even when you have wildly extreme and different values? Is it basically just evening out?
@@leif1075 pretty much! look at height; there's a wide variance, and in any town you can find a tiny person and a giant. But overall, most people are average height, and these outliers are rare. Hence normal
Great video!
Super happy to see my paper about neuron densities made it into this video 15:12 :)
wow, the RUclips algorithm is crazy
Excellent video, Artem! I enjoy a lot watching your videos, they are incredibly well done and explained. I particularly liked the ones involving topology.
I can’t believe this valuable information is available on YT for free!! I just finished my a level studies and am keen on biology and neuroscience so I loved the fact I got to see a computational perspective on the brain. Makes me wonder where else can the log-normal distributions be seen in the body or what other mathematical models can be deduced in Biological systems.
Keep up!
Wow you are such an effective communicator!!! Your insights were very clear and easy to understand
I am happy I didn't skip this video, and now I know another great channel for math and science
thank you Artem
great quality, and topics I am interested in
Your videos are fantastic for anyone interested in neuroscience!
I never studied it in depth but it's fascinating and I'm discovering it
I had studied advanced mathematics in my last semester but never understand the concept of random variables and distribution with that much clarity.
Amazing video with great explanation.
Fantastic video! Two of my interests, probability, and brain operation, in one video. Very well-done explanation. Thank you Artem!
once wrote a spiking neural net with around a million neurons
some neurons would fire almost every iteration, some every 10 iteration, and some would average once every thousands.
didn't bother to plot the distribution but that could have been fun.
Thanks! This is fascinating and useful information. You presented it so clearly, and the visuals were top notch. Really appreciate this work.
Its interesting because I thought the video would be able how the brain perceives information logarithmicly, but it actually shows its actually physically built logarithmicly as well.
I just want to probe the parts of my brain where the picture and sounds form so I can record my dreams and then play them back like a movie.
Wow man amazing videos, I wanna do research as a computational neuroscientist and your content is really what I was looking for!
I've been interested in brain science since I was a kid. This is definitely understandable to a 10 year old kid. Well done! More content please!! And you shud have more subscribers!!
damn you must be hella smart for a 10 yr old
The shape certainly makes some intuitive sense. Extremely short firing rates are more likely to be mistaken as random noise so a neuron wants to be above that limit. However, it doesn't want to be too far above it, because firing is energy-intensive and the brain is already a calorie-hungry organ. At the same time if information is encoded partially in the firing rate, then utilizing only a small subsection of possible firing rates is not information efficient, so neurons that need to be heard more often would be incentivized to use lower utilized firing rates as there is less noise in those channels. I don't know whether that explanation would necessarily result in a log-normal distribution as opposed to a low-median normal distribution, but it is interesting to see roughly the shape I was thinking emerge at the end.
Why Guys like this are so under subscribed . Wish you success
Wonderful explanation of gaussian distribution
Your videos have a Good dinamic and didacts and the edictions is verry harmony, its really impressive why you not have 1 million of subscribers, more one subscriber from brazil 🇧🇷
Brain is the most complex and fundamental part of our body - Brain
Very nice!
An explanation of why the distribution of firing rates in the cortex is log-normal can be found in Roxin, Alex, et al. "On the distribution of firing rates in networks of cortical neurons." Journal of Neuroscience 31.45 (2011): 16217-16226.
i have a heavy background in audio production, and i figured this made a lot of sense given the logarithm nature of how we perceive sound, it’s cool to see that this is just inherent to our brains in general
Thank you for a great video! Very interesting topic and very nice of you to show the article to make people more likely to actually look it up for themselves. 😀👍
High quality content here!
Very productive vid. It inspires me to be productive as well.
This is a very nice connection of logarithmic perception and biological features of humans. I wonder if there is an analogy explanation of the rule 70-30?
Helpful content, with a good lowering of entry barrier for someone uninitiated. I learned a lot. A small but important point: sum of independent random variables is not normally distributed, but mean of independent random variables is normally distributed.
Technically you're right, since the limit of the sum of the random variables diverges. However, I don't think stressing that point helps with conceptual understanding, since in practice all sums are finite, and then the sum approximately resembles the SHAPE of a normal distribution. Once you normalize it, which is what taking the mean does, you obtain a probability distribution.
Technically it's not the mean but mean times sqrt(n) where n is the number of samples taken to get the mean and under the limit that n is large. Otherwise the mean would just be a point as n becomes very large.
On a more “global” neural scale, it is well know that there is a strong (inverse) relationship between EEG power and frequency: the fast-fourier transform of EEG activity is high at low frequency (< 5 Hz) and low at high frequency (up to 100 Hz) (Buzaki, Steriadi, and others) so that a plot of log(power) vs frequency is fairly linear. Not surprising since it could be considered an “emergent” property of the neural spiking distribution you show. The slope of that relationship can be used to deduce the state of consciousness - sleep (steep negative slope) versus attentive waking (shallow negative slope). So high-frequency power shows a relative increase during waking, because (generally) there is less synchronization of neurons by thalamo-cortical inputs (e.g. during sleep).
Absolutely amazing video! Subscribed.
Thanks for the informative video
Ok i will add ONE HUGE detail. I read a few years ago, that the brain can work in up to "10 dimentions". This means that if data is sent 1 or 2 ways at all times, the HZ should be multiplied by 2x or 1.5x. But if a crosswalk synapse can send multiple signals at once, lets say up to 5 or 10, then conditionally it can perform 5x or 10x as fast in effect, than what the hz is. So adding more specialists greatly boost the efficiency factor via that alone.
To me, this explains how some days things just "click". I learned a thing asap 🤔🧐 In how it was related to what i know, or how maybe some strong synapses formed quckly 👏
Very good. Thank you.
Super cool video Artem! Keep up!
Log-normal distributions are also pretty common, especially with frequency. For instance, I think that's what the black-body curve is, though I may be wrong.
I first discovered this when my psych professor explained that we experience loudness not additionally but through log.
i may of course be wrong, but i do not think that is related.
But rather that the receptor cells themselves lose sensitivity with higher input, i don’t know anything about how those cells work, but it may possibly be due to a limited store of chemicals, like it is with visual receptors.
Wow! An amazing video! Thank you very much Artem. You have a new suscriber from Argentina 🇦🇷
1:12 woah, never seen "abstract" before in a video - nice
I thought this video was gonna be about perception like experienceing loudness in decibels and pitch in octaves.
I'm going to engage in some rank speculation (except its not really speculation because there is *some* research I could cite). Suppose that those brain waves you're picking up aren't a single neuron at all, but actually a self perpetuating loop signal of several neurons. The longer the loop, the longer it takes for the signal to propagate back to the start, the lower the frequency. Now if you were to take a bunch of neurons connected to each other completely at random, and then count out the number of loops consisting of 2 neurons, 3 neurons, 4 neurons... n neurons, you should find that the number of loops goes down exponentially with length. Loops of length k can be made in n choose k different ways. The lower the frequency, the longer the loop, the fewer possible ways to construct it. Hence the frequencies end up with a log distribution.
great effort
3:21 this video so far is more helpful than the statistics course i took
Thanks for the clear explanation, great video
Summary: the spiking frequency (aka firing rate) of neurons in the brain follow a lognormal distribution. This can be seen as a small quantity of generalizer neurons responsible for most daily neural activity (~10% of neurons do 50% of the activity) as compared to specialists neurons. (Note that this is not a binary classification but rather a continuum). One of the most promising hypotheses that explains the emergence of this distribution is that the change of size in a synaptic spine is proportional to its size.
Awesome! Can I ask how do you create these fantastic animations? Thanks!
Thanks!
You deserve subscribe
This video is fantastic
There's SEVERAL logarithmic curves involved in biochemistry. It's not a huge surprise it shows up in a resultant area of biology.
You cleared my 100 year nightmare question.
Fascinating! But what brain region are you sampling from to see the 1 Hz to 10 Hz spread? Like your other video where sparcity amount varied by brain region, it would seem that occipital cortex might show more up to 40 Hz range.
How does the fact that brain is firing at all frequencies at once reconcile with observation (using nmda antagonists) that consciousness is sometimes an all-or-none thing (either a frame is printed or it isn't at any given millisecond), and the change in frequency of these all-or-none frames is smooth, as though having inertia like the boutons' change being proportional to their currently accumulated size? Might it be the thalamo-cortical resonant circuit bringing transient coupling to a particular frequency and this chosen coupled frequency changes smoothly over time?
Or, might each 'frame' of consciousness be a set of ensembles of neurons put together to make that full meaning, and each time you change the set of ensembles, you make a new frame of consciousness, and this frequency of change can vary, but has a mechanism to remain smooth (as though rate of change of frequency is itself important to stay smooth, etc., upwards in nested derivatives)?
Great video. Human wealth is log normal distribution?
Interesting
Log normal distribution is omnipresent in nature because it is the result of feedback-born optimisation. When a snowball falls on the slope, the larger it is, the larger it will get, to a limit. The distribution of snowball sizes obeys a log normal distribution. There's a relation as well, to Poisson distribution. There was some evidence of this in social phenomena as well. When Wilfredo Pareto came up with the notion that 80% of property in Italy is owned by 20% of people, the so-called 'Pareto Principle' was merely a hint at log normal distribution. This has important consequences because if we ignore ideology, this means that wealth distribution will naturally obey a log normal distribution id the system was absolutely fair (from a functional standpoint). So inequality is intrinsic to optimal processes. This does not mean that at the shallow end of the distribution's tail, there should be less means available than needed to live... just that if we raised the threshold at the tail such that people could live comfortably, there would still be a small group of very wealthy individuals. And there's nothing in there tied to merit or morality ; it's amoral. What morality leads us to do, however, is alter the parameters of the distribution such that its "floor" is sustainable for all. Normal curves are still normal, regardless of their sigma or height. So we can alter the integral of the distribution to serve the outcomes we seek, while respecting the naturalness of the log normal distribution process. There are countless examples of this distribution in both the natural world, and in the behavioural and perceptual realms.
A very interesting video. Thank you very much
Insightful video. 👍 Keep going.
great
Ist this why our brains are so powerful, because they are based on multiplication? Compared to a computer, where the base is succession, multiplication is two steps above that in the mathematical hierarchy. Maybe an idea why computers are so limited despite their extreme calculation speed
… but in what way are neuron firing rates related as a product of “hidden” random variables? I think that part was missed.
I'm quite impressed how you present all the information, very concise and clear
It seems logarithms are intimately related to information, like Zipf’s law and such
thanks a lot for explaining so well, I wish you were my high school professor right now ahah
great video analysis
Thanks for a good video on a good topic. I would enjoy less time on a proscriptive path of the lesson, and more time on ideas associated with any step in the chain, correlates.
Great !
I gave me some ideas for my PhD in ecology ;)
Indeed, do the stability of an ecosystem relies on the number of connections or few "key connections" between organisms ?
Just like brain with specialised and generalist neurons...
Is it possible the brain is following a larger log principle universally intrinsic to infinity? Thanking you for your inspirational thinking...
So do roulette tables at casinos apply to the bell curve? Or am I overthinking it?
I would be interested to see if the weights of a self-learning computer neural net (like for OCR or object recognition) followed a log-normal distribution too, or if it's more Gaussian, or white-noise.
According to a quick google search (no academic sources), yes machine learning gradients tend to be log normal. Makes sense because the brain was the model for machine learning
Subscribed.
The log bell curve looks like 20 80 rule
Amazing video!
Ohhh, interesting.
I wonder if high iq is the result of the bulk of the slower firing neurons beign slightly faster than the average person, and it adding up a lot. Or is it something else, like the efficiency of the speciallized neural pathways. Or may be it is just neurons sending stronger signals overall.
Really no idea, but very interesting indeed.
12:49 Veritasium made a video on that. Maybe they are the identical thing
I don't like describing them as not equal. They are all equally important in the context of the brain operating at maximum capacity. If any single neuron was missing, the brain would be unable to operate at its maximum potential. They're different, that's more specific than inequal.
Nice video! Great pacing
learned a lot, ty
Name of this book is 'The Computational Brain'
So even if you flip a unfair coin, if you flip it often enough, you get a Gaussian distribution? That part confused me 😅
What was song for the outro beautiful
Please Smile in your Videos, if you love what you are doing!
내 생각엔 프랙탈의 복잡도를 넘어선 것도 매우 흔하다.다만 우리가 아직 발견하지 못했을뿐
Wow amazing work! than kyou so much! Please kepp doing this important work!
Question.. I have never seen a researcher using macbooks.. do you just do web surfing on it?
Are sypnatic weights log-normally distributed for neural networks as well?
Soooo... if wealth and power are distributed in the same way does it mean it's the most efficient way? *Scared look*
Question: Have anybody ever predicted anything important and completely unexpected based on only dreams, sorry thought experiences that turned out to be true after the appropriate experience became technically doable?
Instant Subscribe
Wow! I learned a lot thanks for the clear explanation and visuals
Thanks ;)
interesting
I guess that it would a bimodal distribution
We hear loudness logarithmically I learned
If you know the seed you can know the tree by genetics a seed has a blue print of tree
llly in every cell
Oh my. Log normal distributions... This is exactly why not everyone was born to be a popstar/world leader/social media influencer, and why our society is so (toxic? Distracted? Misaligned?) For convincing them so.
"Everyone go to college and generate enormous amounts of debt while competing for a narrow job market! It will be fine!"
Brain does Multiplications natively???? 🤯🤯🤯🤯🤯
14:41 In resume, as shown biologically, the brain learning process is exponential. 😮😮😮😮😮😮😮
technically you don't take the sum of the sample batch, you take its mean or average.
This went too slow and didn't provide enough relations between the topics so I didn't understand the meaning or utility of these concepts and their relation to the brain.
Do you produce these alone?
yep ;)
@@ArtemKirsanov Damn
Why this bro looks like young stephen hawking?
Doktor? is that you?