I have always wondered why setting goals is advantageous. Instead of saying “I want to lose 10 pounds this month” why not just attempt to lose as much weight as possible? An empty argument about this is that “but then if I did lose more than 10 pounds I wouldn’t feel satisfied since I didn’t break a goal I set myself”. This is quite bizarre thinking. Goals make you happy because of the effect they have on the universe. You’re happy because you lost weight not because you achieved a goal. But there is a small amount of truth to this. I found finally understood the nature of goals.

Goals are self fulfilling prophecies. As you achieve more goals the power of goals as self fulfilling prophecies increases. This is because your confidence in them increases and in the realm of mind, your expectation of achieving a goal increases the probability that you will succeed in that goal. That’s the nature of it.

So therefore it would be a bad idea to often set yourself goals that you can never achieve, such as losing 100 pounds in a month. Because this means that the moment you set the goal you have a strong belief that you won’t complete this goal because you’ve never completed any of your previous goals.

This is why setting realistic goals is beneficial to you. Setting goals which are too easy is a waste of time. You want to be at the point where setting the goal makes the difference between achieving it or not. You would’ve lost 1 pound in a month without setting yourself that goal, making the process of setting such a goal wasteful. You need to be setting goals that you wouldn’t have achieved without setting that goal.

With this new understanding of goals it surprisingly does make sense to be happy that you completed a goal because it gives you more power over your decisions. Your belief in goals increases as a result of finishing a goal therefore goals you set in the future will have a greater probability of success.

Optimizing the goals you set for yourself is key. I recommend setting goals which you think have a 50% chance of success to maximize your growth. The further you stray from 50% the less influence you have over whether it is completed or not. If you think your chance of success is 99% then it doesn’t really matter what you do, you’re going to succeed anyway. If your chance of success is 1% then it doesn’t really matter what you do, you’re going to fail anyway.

With this new understanding of goals, I began to value them a lot more. I started to build a program to visualize goals. The basic idea is for it to visualize the probability that you succeed for a range of goals by analyzing goals you input in the past along with the record of if that goal was completed. It uses the information in a very strict way. It can only work with goals that are time based such as “jog for 30 hours in the next 2 weeks” or “spend 40 hours per week learning to program”.

Here is an image of the program.


This graph visualizes 2 goals, one was successful and the other was not. The goals shown were the following:

8 hours work in 24 hours: Success

12 hours in 24 hours: Failure

Before I go further explaining what is shown, I need to explain the logical deductions about the ability of this person to work using the information from a single goal. Here are the simple deductions:

If a person does x hours of work in y hours he must therefore be able to do x hours of work in z hours where z >= y. This is fairly intuitive – it wouldn’t make any sense for a person to not be able to do the same amount of work given more time.

If a person does x hours of work in y hours, he must therefore be able to do Minimum(0, x-z) hours work in y-z hours where z <= y. This one’s slightly harder to grasp. The basic idea is to think about the worst case scenario of how a worker might complete his work and then work for that. Perhaps there is a worker who always waits 16 hours before starting his goal. If he set a goal to do 8 hours work in 24 hours, he would succeed. But this deduction also means he can do 7 hours work in 23 hours, 6 hours work in 22 hours and so on.

These logical deductions can basically never be wrong without weird assumptions (such as a person being able to do more work with a smaller time limit). It could be true that a person is motivated more when there’s less time left but if you’re given more time then you’re inevitably going to end up with a small amount of time left at some point.

Back to the graph. Here it is again with the goals annotated.


It could be that a work does do more work given less time, but that isn’t calculated by the algorithm. It just assigns it an unknown value for that amount of time.

If the areas overlap, they mix colors. If green overlaps red it becomes yellow.



This is how the graph looks once I’ve added the goal 14 hours work in 20 hours, success. The old success goal has been totally eclipsed (because the new goal does more work in less time) and there has been some overlap creating a yellow area to represent a 50% chance of success. In reality the edge would never go straight from 50% to 100% it would be a gradient but this will be shown wen the user has completed many goals so it becomes a gradient. Trying to do it using an algorithm would result in incorrect values – it’s impossible to know just how the transition from 0% success to 100% success will be. There’s not enough data to do this (and there never will be) without potentially creating bias. By bias I mean some users could look better than other users even though they’re just as capable overall as a result of how the algorithm might change their results.

I’m still working on this, it’s a growing project. The hardest part is trying to get goals to work together. Setting goals of different types is quite tricky since one goal may be more important than another. The basic problem is that if you set two different goal types in the same period, it makes it look worse than if you just did one of those goals alone since you’d have more time to do it (since you wouldn’t spend any time on a goal you didn’t set) but it would show up on the graph the same. This is why I haven’t yet fully figured out how to use multiple goals together.

I suspect the solution is for the user to input their idea ratio of goals in. For every 2 hours of programming, do 1 hour of jogging and such. And I suspect the ideal ratio of people will change according to how much time they have. If its only 20 hour in the next week all of that should be sleep (sleeping is a goal – you aim to sleep when you go to bed) – it would be crazy to try to have less sleep than this.


The Inadequacy of the RGB system

Pixel is a poorly defined term. It can mean both a hardware pixel, something that your monitor is made up of, or it can mean software pixels, what a bitmap is made up of. Wikipedia starts out with admitting this in its first sentence “In digital imaging, a pixel, or pel, is a physical point in a raster image, or the smallest addressable element in a display device”. The article should be split into software pixel and hardware pixel to avoid confusion.

In this blog post I will be referring only to hardware pixels and how the software ought to calculate them.

The RGB system that is universal is fundamentally flawed for one reason: it doesn’t allow you to state brightness. Suppose that a new monitor is invented that allows it to be arbitrarily bright – it could be as bright as the sun if you told it to be. With the RGB system it would be impossible to have any reasonable way to control a monitor. How should one tell this monitor to show red? giving ig 255,0,0 and it showing a normal red colour would mean that it could show no reds brighter than this and hence the sun could never be displayed as being brighter than red paint since 255 is the limit of the RGB system.

Here’s how it should work: specify the wavelength of the colour you want to use and then the intensity (in lumens) of the light for the pixel to emit. You can now emit all colours at any intensity level. The monitor’s drivers would calculate how to turn a wavelength into an intensity for each of the red, green and blue sub pixels. All visible wavelengths of light can be composed from red green and blue.

Mathematically speaking, the RGB system would be the same as the wavelength system except that there is a cap on how bright a pixel can be.

Most monitors allow you to change their brightness and contrast amongst other things. I think this is bad, it’s a symptom of a larger problem. This should never be necessary. The way its like this is because we haven’t yet come up with a good way of dealing with how the human eye changes in different scenarios.

If you have just been in a pitch black room and the monitor lights up, it will appear very bright. If you’ve just been outside on a very sunny day, the monitor would appear very dim and you may even struggle to read it. If I am a GUI designer I can’t possible account for this effect because there is no input that tells me about the state the user’s eyes are in. The reason the monitor would appear dark isn’t due to the brain not yet adapting to the image, its due to the eye’s sphincter restricting the magnitude of light hitting the retina. If there was a camera pointing at the users eyes this problem could be accounted for and solved easily with some nifty mathematical calculations to keep the amount of photons hitting the eye at a constant rate regardless of the size of my aperture.

One problem with my proposed system is that some monitors wouldn’t be able to display some brightnesses like the sun. Resolving this issue would not be simple. Mapping the brightnesses from the data to the range that the monitor could display isn’t trivial. Should it just set all brightnesses beyond that which can be displayed as the brightest it can display, or should it affect how the other brightnesses are displayed. For example, if it can only display 10 lumens and the brightest in the video about to be displayed is 20 lumes, it could divide all brightnesses by 2 to sustain a relative level.

But the biggest problems with systems like this is latency. It would depend on the camera detecting the size of the eyes aperture very quickly and calculating it very quickly. It’s not often that you see systems that take input in the real world analyse dynamic data quickly. It takes programming talent to make systems like this work, not processer power.

So in summary, I have proposed a new system for how monitors could work.

Programming Puzzle: Unbiased Selection Algorithms

Programming Challenge: Unbiased Results

There is a set of sets of characters. Your task is to produce an algorithm which outputs a set of characters by taking exactly one random character from each of the sets of characters with probability 1/(total possible outputs). There is one rule. Once you select a character from a set, that character can’t be selected all remaining sets. For example with
{{A, B, C} {A,B}} if you choose A from the first set, the legal choices from the second set becomes {B} – choosing A would result in a collision and this is not legal. It is assumed that there is always a solution – you never have to worry about there being no possible solutions (so you will not encounter sets such as {{A},{A}}).
The potential combinations are {A,B},{B,A},{C,A},{C,B}. (note that {B,C} and similar is not possible since C is not in the 2nd set (output is in the same order as the sets are in))
You must make an algorithm which can pick these potential outputs with equal probability.
A naive and incorrect solution works as follows:

0. create an empty set for the output
1. start at the first set of characters
2. generate a random number from 0 inclusive to the cardinality of the set of characters exclusive.
3. Select that character and append it to the output set.
4. remove that character from the remaining sets which have not yet had a character picked from them
5. if the cardinality of the output set is the same as the cardinality of the set of sets, terminate. Else, iterate to the next set of characters and go to step 2

The problem of this is obvious. The order of the sets affects the probability of producing certain outputs and makes it wrong. If the order is {A,B}{A,B,C}, the probabilities of each permutation are as follows

A B 1/2 * 1/2
A C 1/2 * 1/2
B A 1/2 * 1/2
B C 1/2 * 1/2

But if the order is {A,B,C},{A,B} the probabilities of output is

A B 1/3 * 1
B A 1/3 * 1
C A 1/3 * 1/2
C B 1/3 * 1/2

as you can see, they don’t all have the same probability of output. this is an error. What is the solution to this problem?

General Intelligence Does Not Exist

There is a specific case of the use of the word general that is entirely inapprpriate – intelligenece. The problem is that we don’t know and possible it may be impossible to know what constitutes as general intelligence. We do not the significance of what we don’t know.

To assert that an entity has general intelligence would require you to know everything. It’s sort of like how you need to know the entire Earth’s surface area before you can say that someone has explored most of it.

Artificial Intelligence has many people in it working together towards a “General Intelligence”. What they are really doing is moving towards human-like intelligence. This term is a much more accurate description of what they are working towards.

The strange thing about intelligence is that you can not understand all the thoughts of an entity smarter than yourself. This means that a human could never intentionally create an AI greater than themselves. It would require some kind of randomness to create the AI. If you keep generating AI by means of simply producing random code, eventually, you will produce something more intelligent than yourself.

Ants are smarter than humans when it comes to working in large crowds. Humans often crush themselves to death in large crowds. It’s very surprising to say the least that ants behave more intelligently than humans. They have almost no brain compared to us. We can build fusion reactors and smash particles into each other at the speed of light but the tasks that ants accomplish every day are too much for us.

Swarm intelligence is an intelligence we lack. When we’re being crushed to death by people running away from a fire in a crowded building, people scream. This makes it hard. I’ve never really understood this response, screaming achieves nothing other than making it more difficult for those around you to communicate. If you were in isolation screaming does make sense. Anyway, the simple rules that ants have triumph over our neocortex. It reminds me of cellular automata in which simple rules can create complex beautiful behavior.

I strongly advise against using the phrase “general intelligence” again. Use human-like intelligence instead. Perhaps it will turn out that there’s a huge space of problems that we cannot comprehend that are parts of everyday life. That we’re not even aware of. I sometimes get the idea that, perhaps just as we can only view a small part of the visible spectrum (and the non-visible spectrum does have profound consequences on our body) perhaps our mind can only ‘see’ a very small space of problems.


Information Visualization Isn’t Easy

Knowing how to best represent a set of quantitative information is not easy. I strongly recommend a quick read of the Wikipedia entry on Misleading Graphs and if you want to read a whole book try The Visual Display of Quantitative Information by Edward R. Tufte. Instead of remphasizing the need for displaying information in the simplest way possible, I’m going to give examples of how not to display information. Sometimes the errors are only small. But those errors will always be notiable, they affect how people interpret the information. First up, WordPress’s graphs


The problem here is that when the view count is 0 the colour is grey – it should just be a lighter shade of yellow. The sudden shift from 1 as yellow to grey as 0 suggests there is a fundamental difference between 1 and 0. There isn’t, as I explained in my my https://emphatious.wordpress.com/2012/10/12/zero/. Wikipedia correctly uses a colour to show a semantic difference. White is used to represent the fact that there is no information available in the following graph.Image

However, this graph isn’t without its own problems. Can you figure out what the problem is? It’s incredibly difficult to realize the problem as it is a very deep one. Think about colours.

The most obvious problem is that the graph does not use a gradient. groups of GDP are lumped together for no reason. There should be no groups. instead of $800-$1600 being one colours, $900 should be a little more red than $850, $950 a bit more red than $900 and so on. They are essentially rounding figured for no reason. If you had a graph showing $11.53 million profit in Q1 and $12.42 million profit in Q2, would you round them? Rounding them serves no purpose. All it does is reduce accuracy… nothing is improved.

There is a much more subtle assumption made by this graph. It might not be wrong but it isn’t explained. The assumption is that the utility of money increases logarithmically. Look at the groups, they increase logarithmically.

The designers of the graph took it upon themselves to change how the information is shown. Instead of something that’s 10x the size quantitatively being 10x brighter or bigger (10x more intense in some way represented visually) on the graphic, they’ve made it log_10 times brighter. That’s an arbitrary operation done without justification. I do expect that if I were to ask the designer of the graphic why he did this, he would reply with the unforgivable line
“because if it weren’t like that, it’d be hardest to tell the difference between countries with low income. For example, almost all of Africa would be very similar in colour”.
If your goal is to let everyone know the exact GDP of countries, use a table not a graphic.

It is not a dilemma that people would see only a small difference in the colours of African countries because there is only a small difference in the GDP of African countries.

One last puzzle. Can you spot what’s wrong with this graph?


The problem is that again they’ve grouped things together when not necessary. But more importantly, look at the way the “Barely Dem” and “Barely GOP” are coloured. They are different to the others in that their centers are not coloured. This destroys the semantic meaning of the colours of the graph. It was originally that the colour represents the strength of the likelihood but not the colour AND how much white is in the center also represents it, adding complexity without adding any information.

One last error in this graph is that they have changed the size of Alaska. This is only confusing. The graph is being totally warped by the designer who felt that the shape of Alaska was awkward to work with.This makes the graph now entirely subjective. The designer could’ve also changed the shape of all other states – the integrity of the graphic is entirely destroyed by this decision.