How To Be More Productive (Using Maths)
University of Oxford Mathematician Dr Tom Crawford explains the maths behind productivity. Use the code TOMROCKSACUMEN for 40% off a premium subscription to Acumen.
The mathematical model for productivity described in the video - "The Zenith Gradient Algorithm"- is the work of Jaheim Archibald, founder of Acumen: / jaheim-archibald
Read Jaheim's blog post on Medium about the algorithm here: / how-to-over-engineer-a...
You can find more information on the Acumen app on the website: www.acumenweb.app/
The @acumenproductivity1672 KZhead channel contains several demos: / channel
And the Acumen Discord is a great place to ask any questions you may have: / discord
The mathematical topics covered in the video include:
- Poisson distribution
- Differentiating to find the maximum of a function
- Logarithms
- Integration
- Least-squares regression
- Maximum likelihood estimation
- Partial differentiation
- Matrices
- Lagrange multipliers
- Vector calculus
Produced by Dr Tom Crawford at the University of Oxford. Tom is Public Engagement Lead at the Oxford University Department for Continuing Education: www.conted.ox.ac.uk/profiles/...
For more maths content check out Tom's website tomrocksmaths.com/
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
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Get your Tom Rocks Maths merchandise here: www.beautifulequation.com/col...
I think i'd take a different approach. I'd have both engagement and any task (or sequence of tasks) represented as separate wave forms (different colors). When flow state is reached, and a person is "in the zone", those waves should undergo constructive interference. The result would be sort of like a heart rate monitor for productivity, each "beat" displayed as the effective time being spent on a task, and the flatline in between is the time switching between 1 task and the next. Furthermore "engagement" waves are generic, if you wanted you could have even more types (mood, weather, hormones, hunger) and do things with superposition to generate the engagement value.
Great video upload now I can convince myself I'm being productive by learning maths!
In the initial minutes of the video I thought, this could be a great example in mathematical modeling. Where you take a scenario, analyze it, and quantify all the variables into an equation, or a set of related equations. Very cool 👍.
Productivity errors I had. Someone else changed the goalposts. Brexit , instead of sticking a stamp on a parcel and posting it off it now needs triplicates of every description on it , plus tariffs (where necessary along with VAT details an place/s of declared origin). Same when the Post Office when from pricing by weight alone ( and even that was bad telling others that the marginal extra weight of what we made could give very large increases of cost ) to the weight and size dimensions - then we were trying to compare what postal service would be best - not only in price but time and probanility of arriving. This was a problem for slightly bulky things we were sending out (a lot in postal tubes) regular sized stuff was easier and we used a third party for mass mailings but the odd one offs one could spend half a day packaging things working out if two smaller boxes were cheaper than one large box.
I had the same problems ngl
i cant imagine how many people are going to click on this video expecting simple arithmetic 🤣
I don't think so. This channel is for "math fans" like me and you assuming most viewers of this channel are familiar with high school+math
I would love to see something similar to this but modeling the Dunning Kruger effect to see how much time it would take to master something and be comfortable in your skills.
A number of things affect productivity - computer programs can increase it (i cut a job down from three days to half a day getting information we already had formatted and added up differently - I still had manual adjustments but they were minor). The big one I found in a repair shop environment was working out what tools to use - and where they were (every job we did was effectively bespoke as each thing coming through had been built over time slightly differently)
you should do a video trying the PUTNAM exam would be really interesting to see how you find it
professor why don’t you do daily questions like BPRP and Prime Newtons, I would love to see how you approach tough problems
niceeee, I really enjoyed it, E = 10, B = 10000
I was wondering at 8:42, when exaggerating the "effort" and the "enjoyability" why you decided to raise it to the power of 2 rather than another number - like the power of 1.5 or the power of 3? Is it just arbitrary? I have the same question at 12:00 - why is ln(E) used rather than a different base? If these values are arbitrary, how do you think we could devise a way to make it more accurate? Would we need some sort of interdisciplinary research between behavioural psychologists and mathematicians, for example? EDIT: Its 1am and I just woke up thinking about this bit (its probably obvious, I know) but maybe the powers would differ from person to person depending on their mood, how much they rely on motivation etc? It would be extremely complex to model accurately though.
I reckon the use of e seems reasonable given its appearence in so many observed number phenomena. ( I would be tempted to use rather than power 2 use power (2- (1/e)) which may be just a slightly nicer number that might fit in the observed world)
@highpath4776 hmmmm, i guess it doesn’t matter that much since we’ve made up the scale anyway
i would go so far as to say initial productivity has a linear relationship with enjoyability. just because i enjoy solving differential equations twice as much as multiplying matrices, doesn't mean i'll be 4x as productive doing it.
What is meant by time on a task? Consecutive time? Distracted time? Project length? Does the curve ever restart?? A lot that is not specified here
Neat little model, but the ultimate question is how accurate is this model given these somewhat restrictive assumptions and its simplicity? Why only one peak? For instance , looking at t in practice, one will work on something and then step away to either take a break or work on something else. When they come back, it may be difficult to orient themselves to the project. Foreseeably, they could achieve another peak relative to their start point. So this seems like better formulated as an autoregressive model. The shocks or exogenous noise are encapsulated in that c3 parameter, but that could be too limiting. There is a cost/punishment for not doing the task as well. There is an assumption that the nature of the work in the task stays constant when the effort may decay over time. Then as rms gray puts it: "There are some crucial assumptions- that the tasks are effectively endless and continuous - that you can always meaningfully put more time and work into a task, and that every incremental increase in the task's progress is equally valuable, rather than the task coming in significant chunks. There's also an assumption buried in there that there's no additional cost to interrupting a task - that you can pick up where you left off with no greater effort than it took starting in the first place. Maybe my theoretical optimum time for watching a movie is 1 hour and 45 minutes, but that doesn't mean the best use of my time would be to watch the 98 minutes of Encanto and then the first 7 minutes of Moana. And it definitely doesn't mean that I'd be better watching the 1 hour 45 minute runtime of Cats than watching Encanto and then adding the spare 7 minutes to some other task..."
how do you account for the cost/punishment of not doing the task? what about external variables, such as mood, fatigue, etc? and why is beta squared? if I enjoy one task twice as much as another, it doesn't automatically imply I'll be 4x as productive doing it. some sort of linear relationship makes more sense IMHO. you're also assuming that effort is a constant, while 90% of tasks have varying levels of effort required depending on where you are in the task. For example starting a new application from scratch requires more effort while you have to set up the environment, maybe research some things, while finishing that task, i.e. pushing some commits, requires very little effort. this is entertaining, but I suspect the actual model is much more complex than a 1-st level poisson distribution.
So, the optimum use of your time is to write about a third of an essay, finish the maths and spend an extra ten minutes checking your answers, spend over twice as long editing the video, and do almost two and a half times as much studying? There are some crucial assumptions about the nature of the tasks involved baked into the model, which don't match well with the example - that the tasks are effectively endless and continuous - that you can always meaningfully put more time and work into a task, and that every incremental increase in the task's progress is equally valuable, rather than the task coming in significant chunks. There's also an assumption buried in there that there's no additional cost to interrupting a task - that you can pick up where you left off with no greater effort than it took starting in the first place. Maybe my theoretical optimum time for watching a movie is 1 hour and 45 minutes, but that doesn't mean the best use of my time would be to watch the 98 minutes of Encanto and then the first 7 minutes of Moana. And it definitely doesn't mean that I'd be better watching the 1 hour 45 minute runtime of Cats than watching Encanto and then adding the spare 7 minutes to some other task...
Sir please make a video about trigonometry 😢
Please do this for me 🙏 Kate likes to walk down moving escalators and she takes one step at a time. When she walks down at a rate of 2 steps per second, she reaches the bottom from the top after 18 steps. When she is exhausted, she will walk down at a rate of 1 step per second and she will reach the bottom from the top after 12 steps. Find the time- taken for her to reach the bottom from the top if she just stands on the escalator.
When Kate walks at 2 steps per second, she takes 18 steps to reach the bottom. So, the time taken = number of steps / rate of walking = 18 steps / 2 steps per second = 9 seconds. When Kate walks at 1 step per second, she takes 12 steps to reach the bottom. So, the time taken = number of steps / rate of walking = 12 steps / 1 step per second = 12 seconds. Now, let's find the speed of the escalator. We know that the escalator moves 18 steps in 9 seconds when Kate walks down at 2 steps per second, which means the escalator moves at 2 steps per second. So, when Kate stands still, the escalator moves at 2 steps per second. Kate needs to cover the same distance as when she walked down at 1 step per second, which took her 12 seconds. Thus, the time taken for her to reach the bottom from the top if she just stands on the escalator is 12 seconds.
@@nicholashung7871 the answer is wrong
@@AsGangIII 18 seconds
😊😊😊
كيف
Who old are you sir ?
That's a very elegant and cool model. However, it totally ignores the possible synergies and antisynergies between the tasks. This means that the order you do the tasks in matters as well
I am an idiot who always fail at math in my mind, can you please recommend 5 books that can take me from high school mathematics to Oxford level mathematics, please i have week understanding in trigonometry and calculus and my mind can't imagine the questions that i am solving, like a slave i am memorizing equations without knowing how it works😢😢😢😢 I am getting straight A s but i am not satisfied
Bro u are not an idiot🤦♂️ just search for a video on KZhead explaining the equation you need. And understand why the equation exists. Don't beat yourself up dawg.
@@Chakamatics the problem is i have straight A in all my maths exams but i can't do a different type math questions other than teachers gave me or have same logic i can't come up with solutions without following what teachers spoon feeded me 🥲
do not memorize, understand the material.
Yeah, take it easy, bro. It takes time to become good at anything, math is certainly no exception, just accept it. I was somewhat mediocre at math when I was in high school, but things clicked into place little by little, as I was studying physics and other topics that rely a lot on applied math. Only time will give you a deeper understanding and good intuition. Here are a few modest pieces of advice I wish I heard at the time: 1) I would not recommend solving exercises like there's no tomorrow. A recent study showed (can't remember the exact source right now), that doing exercises is only profitable to people who are already somewhat accustomed to a topic, but may in fact discourage newbies. Reading solutions to exercises is a more fruitful approach for beginners. This implies that if you're going to buy a textbook, get one with detailed solutions to the exercises. 2) Learn how to learn. A math book is not to be read linearly like a novel, there's a method to it, plenty of people explain it on youtube better than I would. 3) Motivate new concepts. Teachers often do a terrible job motivating stuff, and you end up questioning why the f you're learning something "you won't need". Maybe just read the relevant part on wiki that explains why something is useful, where it is used, and why it is done this way. 4) Visualize. Use tools to actually see what you're working with, plot your functions (there are interactive tools online like desmos for instance), draw things, maybe have a white board on your wall. Some youtube vids have wonderful animations that can help you get a grasp, seeing things unfolding over time is tremendous help. Channels like 3blue1brown do exactly that. Heck, I even had that one project where *hearing* my data was more helpful than seeing a spectrum to detect a particular change of regime. Mobilize your senses, we make the most sense out of information that spreads over multiple perceptual modalities. Also, write things by hand, a lot. 5) Accept that forgetting is part of the learning process. We all forget, we all have to google the most basic sh*t from time to time to reactivate those neural pathways. 6) There are often multiple ways to arrive at a result, and multiple valid points of view on a given concept. The more diverse your approaches to appreciate something, the more profound your understanding gets. 7) If you can't solve a problem, maybe there is a simpler version of the problem that you can find a solution to, and this will give you insights for the more difficult one. Start simple and also learn to split a complex problem into multiple simple ones. Rely on what you know. 8) Have a hobby which makes use of what you learn in math. Maybe learn a programming language (like Python) and write code that actually solves a real world problem. I'm doing indie game development for example, and I can tell you that I'm using trigonometry, calculus, linear algebra and graphs all the time. Any subdomain of engineering would do, electronics is nice too as far as applied maths go. 9) Social skills do make a difference. Talk with people who are good at math, nerds can be cool dudes to have a chat with. Having a mentor helps tremendously. Collaborate with a friend to solve problems, having a little back and forth is stimulating. Verbal expression is key. When you think you understand something, try to teach it to someone else. You really understand something once you're able to explain it in simple terms. Explaining something to someone will also make it easier to remember. 10) Have fun. That's the most important part. Math is a game, and there's no point in playing a game you don't enjoy.
I did a few things (and I have forgotten more than I knew - my O levels in the 1970s would have been Oxford level stuff in the 1700s !) One was to re-write the question from a book parsed into a format I could understand (so a bit more space in it and using the maths notation around the narrative words). I also re-wrote the textbook/s I had been allocated and re wrote my notes after lectures, getting things in twice made it easier for me to follow what I was trying to do , though that does take time.
How come when I call beta “beater” ppl look at me weird, but Tom does it and nobody bats an eye…
IIt's complicated
Isn't this ignoring factors like a structured work environment or breaks the day before/current breaks?? I don't like the idea that "you guys" know the most important variables and us peasants can only hope to be modeled... very economists-esque.. The second can be collapsed into enjoyability, but other can't
Referring to yourself with your title is super dumb.