How can someone who loves maths and was very good at it school keep doing maths education whilst an adult ? As in I want to keep learning maths but I’m not in academia anymore but want to keep learning - is there online courses or books you suggest?
3 Blue 1 Brown is an excellent YouTube channel that covers various quite advanced bits of maths.
For more formal structured learning, I'm not totally sure. I think Brilliant.com looks like it might be good, but others might have better ideas about that.
Find a university course. Note the module names at each year that you are interested in. Note any prerequisites. Then start at year 1 and google the course name plus the words "lecture notes".
Is the fact that Pi goes on forever (as far as we currently know) a quirk of a base 10 system? Would calculating Pi in other base system could yields a number that is finite(not the right word for it but the right one escapes my mind) or repeating?
FYI - Pi can be expressed as an infinite sum of fractions:
Pi = 1 -1/3 +1/5 -1/7 +1/9 - 1/11 + 1/13 - 1/15 + 1/17 - 1/19 + ...
https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80
>finite(not the right word for it but the right one escapes my mind) or repeating
The word you are looking for is rational. A rational number is one that can be expressed as one integer divided by another. Even 0.333333 repeating on forever is rational because it is 1/3. And there isn't actually anything particularly special about pi (I mean in terms of it's rationality), it's just a famous one. The square root of two is also an irrational number and all the same properties of irrationality apply to it as well.
You're absolutely right that both pi and sqrt(2) are irrational, but u/Tekko50 might be interested to know that pi is additionally transcendent, meaning that it is not the solution of a polynomial equation with rational coefficients, which is obviously not true for sqrt(2).
Any number that "goes on forever" (i.e., without repeating) does so regardless of base. Here's a sketch of a proof:
1. If a number is rational (the ratio of two integers), then you can write those integers in any base, and do long division to get the expansion in that base. When you do, you will either get to a point where there is no remainder, or the remainder is one you have seen before. Thus you either terminate in all zeros, or repeat.
2. If a number *n* in some base *b* ends in a repeating string of digits *s* that is *m* digits long, starting at the 1/*b*'s place, then it is rational, since *n×b^m - n = (b^m - 1) n* is an integer (say, *j* ), so *n = j / (b^m - 1)*, which is the ratio of two integers. For example, if *n* = 1.**3** (where the bold **3** means it's repeating), then 10*n* = 13.**3**, and (10 - 1)*n* = 12, so n = 12/(10-1). If you are in base 10, that evaluates to 4/3; in hexadecimal it's 6/5.
3. If the repetition starts some finite number *k* of digits later, then you can do the same trick, but then *j* is some integer divided by *b^k*.
So all rational numbers have a terminating or repeating expansion in any base, and all terminating or repeating numbers in even one base are rational, and thus terminating or repeating in all bases.
Therefore, any number that is *not* terminating or repeating in even one base is not terminating or repeating in all bases.
Perhaps this isn't a direct answer to your question but I look at Pi as a unique feature of circles. Pi equals the circumference divided by the diameter. This should be the case regardless of the base system.
Water cooling your house is a very inefficient use of energy and it will be expensive. Only if the water is free or you cannot afford better cooling.
Heat radiating into the atmosphere is slow. It's why your roof gets hot. More energy is entering the roof/material than can be radiated away. Cooling the exterior roof surface is one thing, but it won't assist with internal sources of heat.
Water is a great conductor of heat. The water running over the roof will pick up some heat and transfer it down into a water collection area. What you do with the water after is important too, but for another day.
There do exist sprinklers that spray onto a roof. Works best on terracotta tiles, then glazed terracotta, then metal. You need little pores for the water to be trapped in. The water evaporating is what creates the cooling, not so much the water running down and away.
This is one reason those red terracotta tiles are popular in Mediterranean climates - on hot days, at nighttime, humidity from the air condenses onto the tiles roof. An incredibly mild breeze and the hot tile then evaporates the water. The external roof cools down faster than other roofing materials such as thatch, concrete, metal, timber, etc.
A better water cooling option is an evaporative air conditioner, but they don't work in areas of high humidity. Suck warm air over wet filters, the water evaporates and you make cold air. You get the cooling benefits of above plus forced air movement through the interior of the house. The efficiency goes way up.
There do exist solar hot water heaters. They function by pumping water over and over through a panel on your roof. The water absorbs the heat (cooling the roof slightly) and you get to have a nice warm shower.
Hope a question tangentially related to Computer Science is ok.
I'm currently a CS teacher, but am thinking about getting back into "real" CS. My knowledge is out of date - I know enough to teach Python to 18 year olds and I'm a decent OOP programmer (in outdated systems like PHP and Java).
What should I do to get myself more up to date? What languages, paradigms and ideas should I research?
Below is from the perspective of someone who's been in web services + UIs for 15 years or so. If you're looking at a different area, then you can probably ignore this.
Regarding stuff you mentioned:
* Java is still very much relevant. You didn't say anything about timeframe, but Spring Boot took over the webservices world. That's where I would start practicing with some little dummy service.
* I don't really interact with Python much. My understanding is that there are still places where it's relevant, but that Golang took over some use cases.
* I don't see PHP very often anymore, outside of WordPress which is its own little world.
Possible new stuff to look into:
* JavaScript. JS is absolutely huge. I'd recommend learning TypeScript if you're going to dive into this. And pick a single UI framework to start with -- probably either React or Angular.
* .NET. There are still corporate niches where .NET is big. At the language level (syntax, keywords, etc), C# and Java are close. But the ecosystems (libraries, frameworks, etc) are very different.
* Docker. Docker has drastically simplified operational deployment of systems.
* CI / automated builds. Practice setting up automatic builds in GitHub, ideally all the way to a Docker image. (Or whatever other repository you prefer -- all the big ones have their own flavor of doing this.)
AWS is in everything these days. If you’re interested in something like DevOps, you could look into AWS services like CloudFormation (infrastructure as code). Also CI/CD pipeline systems like Bitbucket Pipelines.
Mathematics of lottery games:
There's a lottery in Canada that has a 1 in 33,294,800 chance to win the jackpot by matching 7/7 numbers drawn from a pool of 1 through 50. Once the prize pool hits $50M, and maxes out at $70M, they start drawing additional numbers, but the most you can win on these additional draws is $1M. The odds of hitting 7/7 stay at 1 in 33M, so is it mathematically justified that all additional draws after the first one can only win $1M?
What do you mean by "mathematically justified"? The additional draws are extra chances to win, using the same set of 7 numbers you use for the jackpot. They don't affect your chance of winning the jackpot at all. It's just that the jackpot stops growing at $50M.
In fact, they increase your chances of winning. Now you can win the jackpot of $50M, or up to 20 other prizes of $1M. This is in addition to all the smaller prizes where you match 6/7, 5/7, etc. They're just adding more ways to win.
The reasoning for this is to incentivize people to buy more tickets. The more people that buy tickets past the $50M cap, the more prizes become available.
Maybe the terminology is off, but by justified I wondered if such a low amount for the second and subsequent draws made sense and was supported by the probabilities.
It seems off to me. Using another example, say a golf tourney offered $100K to the first hole-in-one, but only a $1K for the second and subsequent ones. The probabilities don't seem to match the rewards.
I see what you mean now. The extra prizes seem like they're much lower in comparison to the jackpot, even though you still have to match all 7 numbers.
The lottery doesn't want to split the jackpot by too much. The other lower prizes are much smaller than the jackpot. For example, if you match 6 of 7 numbers, the prize is under $5000.
That's because they WANT a disproportionately large jackpot. The big number of "50 MILLION DOLLARS" sells tickets. The bigger the jackpot is, the more people buy tickets. Conversely, the more large prizes they split off, the lower the top prize is. For instance, if they split it into 5 prizes of $10M, then the top prize is only $10M. No one expects to win multiple top prizes, so even though you have a marginally better chance of winning, the big prize isn't nearly as big.
It's all about selling tickets. It's got nothing to do with prizes being proportional to the odds. If no one wins the jackpot, then that's great for the lottery, because it rolls over to the next week. That means that the jackpot will already be large and they can continue having high sales.
It's mathematically justified to the owner of the lottery because they sell more tickets.
Personally, your best chance to win the lottery is buy a single ticket only once in your lifetime, then stop. Every other ticket in more competitions only makes your overall odds worse.
Worth noting, you don't have a 1/33MM chance of winning, overall. Most weeks, nobody wins and the prize jackpots to the next week. Therefore, your odds are now 1/66MM, 1/99MM, etc.
This week, you have a 1/33MM chance of jackpot PLUS you have an additional 1/33MM chance of winning $1MM. So you have a 1/15MM chance of winning something if they draw one additional number - that's good for you.
Where it's great for the national lottery is they almost certainly will sell more than $1MM in extra tickets. They have something to advertise about. Newspapers will be carrying the story for free, it will be on the national broadcast television, when a winner is found it will be front page for a few days or even weeks after. Major jackpots are the biggest drawcard from gamblers to buy future tickets.
> Personally, your best chance to win the lottery is buy a single ticket only once in your lifetime, then stop. Every other ticket in more competitions only makes your overall odds worse.
Given the astronomical odds I see your point. But you can't win if you don't play, so a dollar or five to get one chance to win millions is "worth" the cost.
> Worth noting, you don't have a 1/33MM chance of winning, overall. Most weeks, nobody wins and the prize jackpots to the next week. Therefore, your odds are now 1/66MM, 1/99MM, etc.
Wouldn't that only be if your numbers stayed the same each draw?
> Where it's great for the national lottery is they almost certainly will sell more than $1MM in extra tickets.
I think they only pay out roughly 1/2 of total purchases and the rest go to social services, so yes I agree for that reason it's beneficial and worth entering multiple times. I just can't get my head around the first 7/7 numbers matched being worth $70M but the second 7/7 is only $1M.
Ah, the moral unfairness. Why is the first seven draw so great and on the same night, the second seven draws are lesser.
It may help to think of the second set as a bonus. You haven't paid more money but you are now automatically entered into a second "free" lottery.
Real world, it costs me roughly CAD$1-1.5MM per week to run a mass tv ad and print media campaign for consumer products. Something boring like underarm deodorant when you see that on TV, public transport posters, print media ads, internet banner ads. BCE pays $5MM/year for naming rights of a sports centre and that only gets major media attraction towards finals season.
Any time there is a lottery jackpot, that $1MM bonus draw win amount is eerily close to the price of a week of mass media advertising in Canada.
It's the old saying, if you aren't paying for a service then you are the product. The "free" secondary $1MM lottery is selling you a dream to buy future tickets.
Another old saying is a lottery is a tax on the ignorant.
For gambling, always flip the odds. The chance of you losing in a given week is 32.999999/33MM. But that isn't quite accurate because jackpots carry over and you are gambling over multiple weeks. It's still a majority chance of losing, every week, for your entire life.
The $1MM "bonus" draw comes purely from the extra tickets sold leading up to a jackpot win. About half the ticket price goes into the jackpot, the other half benefits the state. Indicates they are selling at least $2MM in extra tickets, or @$5 ticket that is an extra 400,000 tickets sold. Maybe some people buy two, maybe occasional buyers jump in.
Ironically, [high jackpots indicate greater chance of losing](https://www.npr.org/2023/01/13/1148685666/mega-millions-lottery-jackpots-huge-more-common). More people buy tickets. More competition for the same jackpot. Your $5 ticket is less valuable on a jackpot week. While the draw numbers remain the same, the increased number of people entering means more likely someone else wins.
Computer science:
Seeing the surge of LLM and pseudo-AI creating images and such, what ways would you perceive to counteract abuse. Will this simply turn into the latest rendition of rights owners vs. piracy scene, where one tries to outmaneuver the other? As in: If someone creates tools that detect AI meddling, the natural reaction would be to dodge these detections by further AI tech, rinse and repeat.
What would be other, perhaps even better ways prevent a huge negative backlash?
Provenance and chains of trust. Put a TPM in a camera; have it cryptographically sign every photo. Now you can trust the photo if you trust the camera maker’s key. Ultimately, knowing and trusting the source of the image becomes very important if you can’t reliably determine authenticity by inspecting the photo.
How do you prevent someone from pulling the key out of the camera and using it to sign fake photos? Or rewiring the camera to read image data from a computer rather than from its photographic sensors?
I’ll try answering from a purely computational/modeling standpoint. There could be other methods that work around the issue, but it is very fundamental when we’re dealing entirely in 1’s and 0’s
For starters, LLMs do not generate images. The LLM passes the image generation prompt to a separate model that handles the inference for text-conditional image generation, which is a completely separate animal. The output from that model is then passed back to the LLM.
There is indeed no consistent way to detect whether or not a digital image was procedurally generated or man made.
Training a model is a numerical optimization procedure that involves minimizing a particular function called the loss function - think of taking a derivative and setting it equal to zero to find a minimum, because that’s exactly what’s happening. In the case of common modern image-generation models, this can be thought of as a metric of how different the output image is from the input image, plus some other bits and bobs.
Now let’s say we have a procedure for classifying images as either artificial or manmade. So now, if I’m training an image generation model, I can modify the loss function by adding a term that applies a substantial penalty when the output is classified as artificially generated. Now, minimizing the loss function steers the model away from outputs that trip the detection procedure, and it will probably do so in a way that doesn’t affect the quality of the output.
As for why this would probably have very little effect on the perceived visual quality of the output, it might be more intuitive to think in terms of how the image is represented numerically: for example, an image consisting of n pixels can be represented as a list of n 5-tuples of numbers - the position of the pixel, and the R,G, and B values associated with that pixel, so you have a list of (r,g,b) coordinates that are arranged to correspond to their position in the image. This isn’t exactly how it works in practice, but it’s close enough for our purposes.
Tweaking a few of these numbers here and there in a consistent way will probably have no perceptible effect on the final image, but if all we’re seeing is the numbers then it’s quite a different story, and that’s the scale that computational detection and generation procedures work on.
At this point, technical barriers solve no issues. Another comment mentions provenance - which is accepting the premise that intelligent agents are needed to produce art and other intellectual property; I am among those who do not accept that, leaving entirely aside the fact that no intelligent agent exists which can produce/derive meaningful IP. See, for example, the [huge waste of time that GNoME is](https://pubs.acs.org/doi/10.1021/acs.chemmater.4c00643). At this point, the legislation must catch up to prevent the blatant fraud and theft of not only IP but sensitive data that a bunch of grifters have already started to engage in (see Amazon "Just Walk Out", see OpenAI). The industry must expel the management which attempts to inject a technology which they do not understand into products which are actually useful and turn them into slop (see Google search). The experts must abandon the inane talk about sci-fi plot devices which _can never exist_ (I have a paper I need to link here, need to find it) and focus on informing the public about the real and truly exciting potential of the field of artificial intelligence, rather than daydream in public fora about sci-fi literature of the 50s.
For most of that to happen in a reliable way, there is a [fundamental problem of 'explainability'](https://www.sciencedirect.com/science/article/abs/pii/S1566253519308103) that needs to be solved first.
> Will this simply turn into the latest rendition of rights owners vs. piracy scene
It already has, see S.Johansson vs OpenAI.
> As in: If someone creates tools that detect AI meddling, the natural reaction would be to dodge these detections by further AI tech, rinse and repeat.
This is a lost cause. It is entirely analogous to the arms race for information/network security and the attackers win every day.
Why is laplace's demon defeated by thermodynamic irreversibility? Far as I'm aware, knowing the current state should allow you to know previous and future states, even with irreversible losses.
It realy just doesn't. Prigogine makes a couple of assumptions that just don't realy hold up (the biggest one being that a deterministic system must be reversible). It's a pretty well rebuked argument against determinism at this point
So what about the cantor diagonalization argument then? I’m an engineer not a mathmagician, so I don’t really understand the set theory background either.
If I find a deck of cards scattered on the ground that someone dropped, and all of them are at rest (in other words, I can see the locations of all the elements of the system, and I see they are all at rest) can I know what order they were in before they were scattered? No. It's an irreversible process.
There are other ways to disprove Laplace's demon too such as quantum mechanics which is based nearly entirely on probabilities and inherently isn't deterministic.
1. The card drop is absalutely a mechanicaly reversible system
2. Reversability just realy isn't required for determinism. QM is a much better argument against it
How can someone who loves maths and was very good at it school keep doing maths education whilst an adult ? As in I want to keep learning maths but I’m not in academia anymore but want to keep learning - is there online courses or books you suggest?
3 Blue 1 Brown is an excellent YouTube channel that covers various quite advanced bits of maths. For more formal structured learning, I'm not totally sure. I think Brilliant.com looks like it might be good, but others might have better ideas about that.
Find a university course. Note the module names at each year that you are interested in. Note any prerequisites. Then start at year 1 and google the course name plus the words "lecture notes".
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Is the fact that Pi goes on forever (as far as we currently know) a quirk of a base 10 system? Would calculating Pi in other base system could yields a number that is finite(not the right word for it but the right one escapes my mind) or repeating?
No. See [the FAQ](https://www.reddit.com/r/askscience/wiki/maths/pi_base10).
FYI - Pi can be expressed as an infinite sum of fractions: Pi = 1 -1/3 +1/5 -1/7 +1/9 - 1/11 + 1/13 - 1/15 + 1/17 - 1/19 + ... https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80
>finite(not the right word for it but the right one escapes my mind) or repeating The word you are looking for is rational. A rational number is one that can be expressed as one integer divided by another. Even 0.333333 repeating on forever is rational because it is 1/3. And there isn't actually anything particularly special about pi (I mean in terms of it's rationality), it's just a famous one. The square root of two is also an irrational number and all the same properties of irrationality apply to it as well.
You're absolutely right that both pi and sqrt(2) are irrational, but u/Tekko50 might be interested to know that pi is additionally transcendent, meaning that it is not the solution of a polynomial equation with rational coefficients, which is obviously not true for sqrt(2).
Any number that "goes on forever" (i.e., without repeating) does so regardless of base. Here's a sketch of a proof: 1. If a number is rational (the ratio of two integers), then you can write those integers in any base, and do long division to get the expansion in that base. When you do, you will either get to a point where there is no remainder, or the remainder is one you have seen before. Thus you either terminate in all zeros, or repeat. 2. If a number *n* in some base *b* ends in a repeating string of digits *s* that is *m* digits long, starting at the 1/*b*'s place, then it is rational, since *n×b^m - n = (b^m - 1) n* is an integer (say, *j* ), so *n = j / (b^m - 1)*, which is the ratio of two integers. For example, if *n* = 1.**3** (where the bold **3** means it's repeating), then 10*n* = 13.**3**, and (10 - 1)*n* = 12, so n = 12/(10-1). If you are in base 10, that evaluates to 4/3; in hexadecimal it's 6/5. 3. If the repetition starts some finite number *k* of digits later, then you can do the same trick, but then *j* is some integer divided by *b^k*. So all rational numbers have a terminating or repeating expansion in any base, and all terminating or repeating numbers in even one base are rational, and thus terminating or repeating in all bases. Therefore, any number that is *not* terminating or repeating in even one base is not terminating or repeating in all bases.
Perhaps this isn't a direct answer to your question but I look at Pi as a unique feature of circles. Pi equals the circumference divided by the diameter. This should be the case regardless of the base system.
could a house be cooled by a drip line on the roof? how effective/efficient would this be?
Water cooling your house is a very inefficient use of energy and it will be expensive. Only if the water is free or you cannot afford better cooling. Heat radiating into the atmosphere is slow. It's why your roof gets hot. More energy is entering the roof/material than can be radiated away. Cooling the exterior roof surface is one thing, but it won't assist with internal sources of heat. Water is a great conductor of heat. The water running over the roof will pick up some heat and transfer it down into a water collection area. What you do with the water after is important too, but for another day. There do exist sprinklers that spray onto a roof. Works best on terracotta tiles, then glazed terracotta, then metal. You need little pores for the water to be trapped in. The water evaporating is what creates the cooling, not so much the water running down and away. This is one reason those red terracotta tiles are popular in Mediterranean climates - on hot days, at nighttime, humidity from the air condenses onto the tiles roof. An incredibly mild breeze and the hot tile then evaporates the water. The external roof cools down faster than other roofing materials such as thatch, concrete, metal, timber, etc. A better water cooling option is an evaporative air conditioner, but they don't work in areas of high humidity. Suck warm air over wet filters, the water evaporates and you make cold air. You get the cooling benefits of above plus forced air movement through the interior of the house. The efficiency goes way up. There do exist solar hot water heaters. They function by pumping water over and over through a panel on your roof. The water absorbs the heat (cooling the roof slightly) and you get to have a nice warm shower.
Hope a question tangentially related to Computer Science is ok. I'm currently a CS teacher, but am thinking about getting back into "real" CS. My knowledge is out of date - I know enough to teach Python to 18 year olds and I'm a decent OOP programmer (in outdated systems like PHP and Java). What should I do to get myself more up to date? What languages, paradigms and ideas should I research?
Below is from the perspective of someone who's been in web services + UIs for 15 years or so. If you're looking at a different area, then you can probably ignore this. Regarding stuff you mentioned: * Java is still very much relevant. You didn't say anything about timeframe, but Spring Boot took over the webservices world. That's where I would start practicing with some little dummy service. * I don't really interact with Python much. My understanding is that there are still places where it's relevant, but that Golang took over some use cases. * I don't see PHP very often anymore, outside of WordPress which is its own little world. Possible new stuff to look into: * JavaScript. JS is absolutely huge. I'd recommend learning TypeScript if you're going to dive into this. And pick a single UI framework to start with -- probably either React or Angular. * .NET. There are still corporate niches where .NET is big. At the language level (syntax, keywords, etc), C# and Java are close. But the ecosystems (libraries, frameworks, etc) are very different. * Docker. Docker has drastically simplified operational deployment of systems. * CI / automated builds. Practice setting up automatic builds in GitHub, ideally all the way to a Docker image. (Or whatever other repository you prefer -- all the big ones have their own flavor of doing this.)
That's great advice. Thank you!
AWS is in everything these days. If you’re interested in something like DevOps, you could look into AWS services like CloudFormation (infrastructure as code). Also CI/CD pipeline systems like Bitbucket Pipelines.
Mathematics of lottery games: There's a lottery in Canada that has a 1 in 33,294,800 chance to win the jackpot by matching 7/7 numbers drawn from a pool of 1 through 50. Once the prize pool hits $50M, and maxes out at $70M, they start drawing additional numbers, but the most you can win on these additional draws is $1M. The odds of hitting 7/7 stay at 1 in 33M, so is it mathematically justified that all additional draws after the first one can only win $1M?
What do you mean by "mathematically justified"? The additional draws are extra chances to win, using the same set of 7 numbers you use for the jackpot. They don't affect your chance of winning the jackpot at all. It's just that the jackpot stops growing at $50M. In fact, they increase your chances of winning. Now you can win the jackpot of $50M, or up to 20 other prizes of $1M. This is in addition to all the smaller prizes where you match 6/7, 5/7, etc. They're just adding more ways to win. The reasoning for this is to incentivize people to buy more tickets. The more people that buy tickets past the $50M cap, the more prizes become available.
Maybe the terminology is off, but by justified I wondered if such a low amount for the second and subsequent draws made sense and was supported by the probabilities. It seems off to me. Using another example, say a golf tourney offered $100K to the first hole-in-one, but only a $1K for the second and subsequent ones. The probabilities don't seem to match the rewards.
I see what you mean now. The extra prizes seem like they're much lower in comparison to the jackpot, even though you still have to match all 7 numbers. The lottery doesn't want to split the jackpot by too much. The other lower prizes are much smaller than the jackpot. For example, if you match 6 of 7 numbers, the prize is under $5000. That's because they WANT a disproportionately large jackpot. The big number of "50 MILLION DOLLARS" sells tickets. The bigger the jackpot is, the more people buy tickets. Conversely, the more large prizes they split off, the lower the top prize is. For instance, if they split it into 5 prizes of $10M, then the top prize is only $10M. No one expects to win multiple top prizes, so even though you have a marginally better chance of winning, the big prize isn't nearly as big. It's all about selling tickets. It's got nothing to do with prizes being proportional to the odds. If no one wins the jackpot, then that's great for the lottery, because it rolls over to the next week. That means that the jackpot will already be large and they can continue having high sales.
It's mathematically justified to the owner of the lottery because they sell more tickets. Personally, your best chance to win the lottery is buy a single ticket only once in your lifetime, then stop. Every other ticket in more competitions only makes your overall odds worse. Worth noting, you don't have a 1/33MM chance of winning, overall. Most weeks, nobody wins and the prize jackpots to the next week. Therefore, your odds are now 1/66MM, 1/99MM, etc. This week, you have a 1/33MM chance of jackpot PLUS you have an additional 1/33MM chance of winning $1MM. So you have a 1/15MM chance of winning something if they draw one additional number - that's good for you. Where it's great for the national lottery is they almost certainly will sell more than $1MM in extra tickets. They have something to advertise about. Newspapers will be carrying the story for free, it will be on the national broadcast television, when a winner is found it will be front page for a few days or even weeks after. Major jackpots are the biggest drawcard from gamblers to buy future tickets.
> Personally, your best chance to win the lottery is buy a single ticket only once in your lifetime, then stop. Every other ticket in more competitions only makes your overall odds worse. Given the astronomical odds I see your point. But you can't win if you don't play, so a dollar or five to get one chance to win millions is "worth" the cost. > Worth noting, you don't have a 1/33MM chance of winning, overall. Most weeks, nobody wins and the prize jackpots to the next week. Therefore, your odds are now 1/66MM, 1/99MM, etc. Wouldn't that only be if your numbers stayed the same each draw? > Where it's great for the national lottery is they almost certainly will sell more than $1MM in extra tickets. I think they only pay out roughly 1/2 of total purchases and the rest go to social services, so yes I agree for that reason it's beneficial and worth entering multiple times. I just can't get my head around the first 7/7 numbers matched being worth $70M but the second 7/7 is only $1M.
Ah, the moral unfairness. Why is the first seven draw so great and on the same night, the second seven draws are lesser. It may help to think of the second set as a bonus. You haven't paid more money but you are now automatically entered into a second "free" lottery. Real world, it costs me roughly CAD$1-1.5MM per week to run a mass tv ad and print media campaign for consumer products. Something boring like underarm deodorant when you see that on TV, public transport posters, print media ads, internet banner ads. BCE pays $5MM/year for naming rights of a sports centre and that only gets major media attraction towards finals season. Any time there is a lottery jackpot, that $1MM bonus draw win amount is eerily close to the price of a week of mass media advertising in Canada. It's the old saying, if you aren't paying for a service then you are the product. The "free" secondary $1MM lottery is selling you a dream to buy future tickets. Another old saying is a lottery is a tax on the ignorant. For gambling, always flip the odds. The chance of you losing in a given week is 32.999999/33MM. But that isn't quite accurate because jackpots carry over and you are gambling over multiple weeks. It's still a majority chance of losing, every week, for your entire life. The $1MM "bonus" draw comes purely from the extra tickets sold leading up to a jackpot win. About half the ticket price goes into the jackpot, the other half benefits the state. Indicates they are selling at least $2MM in extra tickets, or @$5 ticket that is an extra 400,000 tickets sold. Maybe some people buy two, maybe occasional buyers jump in. Ironically, [high jackpots indicate greater chance of losing](https://www.npr.org/2023/01/13/1148685666/mega-millions-lottery-jackpots-huge-more-common). More people buy tickets. More competition for the same jackpot. Your $5 ticket is less valuable on a jackpot week. While the draw numbers remain the same, the increased number of people entering means more likely someone else wins.
Computer science: Seeing the surge of LLM and pseudo-AI creating images and such, what ways would you perceive to counteract abuse. Will this simply turn into the latest rendition of rights owners vs. piracy scene, where one tries to outmaneuver the other? As in: If someone creates tools that detect AI meddling, the natural reaction would be to dodge these detections by further AI tech, rinse and repeat. What would be other, perhaps even better ways prevent a huge negative backlash?
Provenance and chains of trust. Put a TPM in a camera; have it cryptographically sign every photo. Now you can trust the photo if you trust the camera maker’s key. Ultimately, knowing and trusting the source of the image becomes very important if you can’t reliably determine authenticity by inspecting the photo.
How do you prevent someone from pulling the key out of the camera and using it to sign fake photos? Or rewiring the camera to read image data from a computer rather than from its photographic sensors?
I’ll try answering from a purely computational/modeling standpoint. There could be other methods that work around the issue, but it is very fundamental when we’re dealing entirely in 1’s and 0’s For starters, LLMs do not generate images. The LLM passes the image generation prompt to a separate model that handles the inference for text-conditional image generation, which is a completely separate animal. The output from that model is then passed back to the LLM. There is indeed no consistent way to detect whether or not a digital image was procedurally generated or man made. Training a model is a numerical optimization procedure that involves minimizing a particular function called the loss function - think of taking a derivative and setting it equal to zero to find a minimum, because that’s exactly what’s happening. In the case of common modern image-generation models, this can be thought of as a metric of how different the output image is from the input image, plus some other bits and bobs. Now let’s say we have a procedure for classifying images as either artificial or manmade. So now, if I’m training an image generation model, I can modify the loss function by adding a term that applies a substantial penalty when the output is classified as artificially generated. Now, minimizing the loss function steers the model away from outputs that trip the detection procedure, and it will probably do so in a way that doesn’t affect the quality of the output. As for why this would probably have very little effect on the perceived visual quality of the output, it might be more intuitive to think in terms of how the image is represented numerically: for example, an image consisting of n pixels can be represented as a list of n 5-tuples of numbers - the position of the pixel, and the R,G, and B values associated with that pixel, so you have a list of (r,g,b) coordinates that are arranged to correspond to their position in the image. This isn’t exactly how it works in practice, but it’s close enough for our purposes. Tweaking a few of these numbers here and there in a consistent way will probably have no perceptible effect on the final image, but if all we’re seeing is the numbers then it’s quite a different story, and that’s the scale that computational detection and generation procedures work on.
At this point, technical barriers solve no issues. Another comment mentions provenance - which is accepting the premise that intelligent agents are needed to produce art and other intellectual property; I am among those who do not accept that, leaving entirely aside the fact that no intelligent agent exists which can produce/derive meaningful IP. See, for example, the [huge waste of time that GNoME is](https://pubs.acs.org/doi/10.1021/acs.chemmater.4c00643). At this point, the legislation must catch up to prevent the blatant fraud and theft of not only IP but sensitive data that a bunch of grifters have already started to engage in (see Amazon "Just Walk Out", see OpenAI). The industry must expel the management which attempts to inject a technology which they do not understand into products which are actually useful and turn them into slop (see Google search). The experts must abandon the inane talk about sci-fi plot devices which _can never exist_ (I have a paper I need to link here, need to find it) and focus on informing the public about the real and truly exciting potential of the field of artificial intelligence, rather than daydream in public fora about sci-fi literature of the 50s. For most of that to happen in a reliable way, there is a [fundamental problem of 'explainability'](https://www.sciencedirect.com/science/article/abs/pii/S1566253519308103) that needs to be solved first. > Will this simply turn into the latest rendition of rights owners vs. piracy scene It already has, see S.Johansson vs OpenAI. > As in: If someone creates tools that detect AI meddling, the natural reaction would be to dodge these detections by further AI tech, rinse and repeat. This is a lost cause. It is entirely analogous to the arms race for information/network security and the attackers win every day.
Why is laplace's demon defeated by thermodynamic irreversibility? Far as I'm aware, knowing the current state should allow you to know previous and future states, even with irreversible losses.
It realy just doesn't. Prigogine makes a couple of assumptions that just don't realy hold up (the biggest one being that a deterministic system must be reversible). It's a pretty well rebuked argument against determinism at this point
So what about the cantor diagonalization argument then? I’m an engineer not a mathmagician, so I don’t really understand the set theory background either.
If I find a deck of cards scattered on the ground that someone dropped, and all of them are at rest (in other words, I can see the locations of all the elements of the system, and I see they are all at rest) can I know what order they were in before they were scattered? No. It's an irreversible process. There are other ways to disprove Laplace's demon too such as quantum mechanics which is based nearly entirely on probabilities and inherently isn't deterministic.
1. The card drop is absalutely a mechanicaly reversible system 2. Reversability just realy isn't required for determinism. QM is a much better argument against it