Archive for: November, 2013

The Birthday Paradox

Nov 18 2013 Published by under probability

To me, the thing that makes probability fun is that the results are frequently surprising. We've got very strong instincts about how we expect numbers to work. But when you do anything that involves a lot of computations with big numbers, our intuition goes out the window - nothing works the way we expect it to. A great example of that is something called the birthday paradox.

Suppose you've got a classroom full of people. What's the probability that there are two people with the same birthday? Intuitively, most people expect that it's pretty unlikely. It seems like it shouldn't be likely - 365 possible birthdays, and 20 or 30 people in a classroom? Very little chance, right?

Let's look at it, and figure out how to compute the probability.

Interesting probability problems are all about finding out how to put things together. You're looking at things where there are huge numbers of possible outcomes, and you want to determine the odds of a specific class of outcomes. Finding the solutions is all about figuring out how to structure the problem.

A great example of this is something called the birthday paradox. This is a problem with a somewhat surprising outcome. It's also a problem where finding the right way to structure the problem is has a dramatic result.

Here's the problem: you've got a group of 30 people. What's the probability that two people out of that group of thirty have the same birthday?

We'll look at it with some simplifying assumptions. We'll ignore leap year - so we've got 365 possible birthdays. We'll assume that all birthdays are equally likely - no variation for weekdays/weekends, no variation for seasons, and no holidays, etc. Just 365 equally probable days.

How big is the space? That is, how many different ways are there to assign birthdays to 30 people? It's 36530 or something in the vicinity of 7.4*1076.

To start off, we'll reverse the problem. It's easier to structure the problem if we try to ask "What's the probability that no two people share a birthday". If P(B) is the probability that no two people share a birthday, then 1-P(B) is the probability that at least two people share a birthday.

So let's look at a couple of easy cases. Suppose we've got two people? What's the odds that they've got the same birthday? 1 in 365: there are 3652 possible pairs of birthdays; there are 365 possible pairs. So there's a probability of 365/3652 that the two people have the same birthday. For just two people, it's pretty easy. In the reverse form, there's a 364/365 chance that the two people have different birthdays.

What about 3 people? It's the probability of the first two having different birthdays, and the probability of the third person having a different birthday that either of those first two. There are 365 possible birthdays for the third person, and 363 possible days that don't overlay with the first two. So for N people, the probability of having distinct birthdays is \(1 times (1 - 1/365) times (1 - 2/365) times dots (1 - (n/365))\).

At this point, we've got a nice recursive definition. Let's say that \(f(N)\) is the probability of \(N\) people having distinct birthdays. Then:

  1. For 2 people, the probability of distinct birthdays is 364/365. (\(f(2) = frac{364}{365}\))
  2. For N>2 people, the probability of distinct birthdays is
    \(frac{365-(N-1)}{365} times f(n-1)\).

Convert that to a closed form, and you get: \(f(n) = frac{365!}{(365-(n-1))!365^n}\). For 30 people, that's
\(frac{365!}{(365-29)!*365^{30}}\). Work it out, and that's
0.29 - so the probability of everyone having distinct
birthdays is 29% - which means that the probability of at least
two people in a group of 30 having the same birthday is 71%!

You can see why our intuitions are so bad? We're talking about something where one factor in the computation is the factorial of 365!

Let's look a bit further: how many people do you need to have, before there's a 50% chance of 2 people sharing a birthday? Use the formulae we wrote up above, and it turns out to be 23. Here's the numbers - remember that this is the reverse probability, the probability of all birthdays being distinct.

1 1
2 0.997260273973
3 0.991795834115
4 0.983644087533
5 0.9728644263
6 0.959537516351
7 0.943764296904
8 0.925664707648
9 0.905376166111
10 0.883051822289
11 0.858858621678
12 0.832975211162
13 0.805589724768
14 0.776897487995
15 0.747098680236
16 0.716395994747
17 0.684992334703
18 0.653088582128
19 0.620881473968
20 0.588561616419
21 0.556311664835
22 0.524304692337
23 0.492702765676
24 0.461655742085
25 0.431300296031
26 0.401759179864
27 0.373140717737
28 0.345538527658
29 0.319031462522
30 0.293683757281
31 0.269545366271
32 0.24665247215
33 0.225028145824
34 0.20468313538
35 0.185616761125
36 0.16781789362
37 0.151265991784
38 0.135932178918
39 0.121780335633
40 0.108768190182
41 0.0968483885183
42 0.0859695284381
43 0.0760771443439
44 0.0671146314486
45 0.0590241005342
46 0.0517471566327
47 0.0452255971667
48 0.0394020271206
49 0.0342203906773
50 0.029626420422

With just 23 people, there's a greater than 50% chance that two people will have the same birthday. By the time you get to just 50 people, there's a greater than 97% chance that two people have the same birthday!

As an amusing aside, the first time I saw this problem worked through was in an undergraduate discrete probability theory class, with 37 people in the class, and no duplicate birthdays!

Now - remember at the beginning, I said that the trick to working probability problems is all about how you formulate the problem. There's a much, much better way to formulate this.

Think of the assignment of birthdays as a function from people to birthdays: \(f: P rightarrow B\). The number of ways of assigning birthdays to people is the size of the set of functions from people to birthdays. How many possible functions are there? \(| B | ^{| P |}\). \(| B |\) is the number of days in the year - 365, and \(| P |\) is the number of people in the group.

The set of assignments to unique birthdays is the number of injective functions. (An injective function is a function where \(f(x) = f(y) Leftrightarrow x = y\).) How many injective functions are there? \(frac{| B |!}{(| B | - | P |)!}\).

The probability of all birthdays being unique is the size of the set of injective functions divided by the size of the set of all assignments: \(frac{frac{| B |!}{(| B | - | P |)!}}{ | B | ^{| P |} } = frac{365!}{365^Ptimes (365 - P)!}\).

So we've got the exact same result - but it's a whole lot easier in term of the discrete functions!

21 responses so far

The Elegance of Uncertainty

Nov 15 2013 Published by under Good Math, Good Physics

I was recently reading yet another botched explanation of Heisenberg's uncertainty principle, and it ticked me off. It wasn't a particularly interesting one, so I'm not going disassemble it in detail. What it did was the usual crackpot quantum dance: Heisenberg said that quantum means observers affect the universe, therefore our thoughts can control the universe. Blah blah blah.

It's not worth getting into the cranky details. But it inspired me to actually take some time and try to explain what uncertainty really means. Heisenberg's uncertainty principle is fascinating. It's an extremely simple concept, and yet when you realize what it means, it's the most mind-blowingly strange thing that you've ever heard.

One of the beautiful things about it is that you can take the math of uncertainty and reduce it to one simple equation. It says that given any object or particle, the following equation is always true:

\[sigma_x sigma_p ge hbar\]

Where:

  • \(sigma_x\) is a measurement of the amount of uncertainty
    about the position of the particle;
  • \(sigma_p\) is the uncertainty about the momentum of the particle; and
  • \(hbar\) is a fundamental constant, called the reduced Plank's constant, which is roughly \(1.05457173 times 10^{-34}frac{m^2 kg}{s}\).

That last constant deserves a bit of extra explanation. Plank's constant describes the fundamental granularity of the universe. We perceive the world as being smooth. When we look at the distance between two objects, we can divide it in half, and in half again, and in half again. It seems like we should be able to do that forever. Mathematically we can, but physically we can't! Eventually, we get to a point where where is no way to subdivide distance anymore. We hit the grain-size of the universe. The same goes for time: we can look at what happens in a second, or a millisecond, or a nanosecond. But eventually, it gets down to a point where you can't divide time anymore! Planck's constant essentially defines that smallest unit of time or space.

Back to that beautiful equation: what uncertainty says is that the product of the uncertainty about the position of a particle and the uncertainty about the momentum of a particle must be at least a certain minimum.

Here's where people go wrong. They take that to mean that our ability to measure the position and momentum of a particle is uncertain - that the problem is in the process of measurement. But no: it's talking about a fundamental uncertainty. This is what makes it an incredibly crazy idea. It's not just talking about our inability to measure something: it's talking about the fundamental true uncertainty of the particle in the universe because of the quantum structure of the universe.

Let's talk about an example. Look out the window. See the sunlight? It's produced by fusion in the sun. But fusion should be impossible. Without uncertainty, the sun could not exist. We could not exist.

Why should it be impossible for fusion to happen in the sun? Because it's nowhere near dense or hot enough.

There are two forces that you need to consider in the process of nuclear fusion. There's the electromagnetic force, and there's the strong nuclear force.

The electromagnetic force, we're all familiar with. Like charges repel, different charges attract. The nucleus of an atom has a positive charge - so nuclei repel each other.

The nuclear force we're less familiar with. The protons in a nucleus repel each other - they've still got like charges! But there's another force - the strong nuclear force - that holds the nucleus together. The strong nuclear force is incredibly strong at extremely short distances, but it diminishes much, much faster than electromagnetism. So if you can get a proton close enough to the nucleus of an atom for the strong force to outweigh the electromagnetic, then that proton will stick to the nucleus, and you've got fusion!

The problem with fusion is that it takes a lot of energy to get two hydrogen nuclei close enough to each other for that strong force to kick in. In fact, it turns out that hydrogen nuclei in the sun are nowhere close to energetic enough to overcome the electromagnetic repulsion - not by multiple orders of magnitude!

But this is where uncertainty comes in to play. The core of the sun is a dense soup of other hydrogen atoms. They can't move around very much without the other atoms around them moving. That means that their momentum is very constrained - \(sigma_p\) is very small, because there's just not much possible variation in how fast it's moving. But the product of \(sigma_p\) and \(sigma_x\) have to be greater than \(hbar\), which means that \(sigma_x\) needs to be pretty large to compensate for the certainty about the momentum.

If \(sigma_x\) is large, that means that the particle's position is not very constrained at all. It's not just that we can't tell exactly where it is, but it's position is fundamentally fuzzy. It doesn't have a precise position!

That uncertainty about the position allows a strange thing to happen. The fuzziness of position of a hydrogen nucleus is large enough that it overlaps with the the nucleus of another atom - and bang, they fuse.

This is an insane idea. A hydrogen nucleus doesn't get pushed into a collision with another hydrogen nucleus. It randomly appears in a collided state, because it's position wasn't really fixed. The two nuclei that fused didn't move: they simply didn't have a precise position!

So where does this uncertainty come from? It's part of the hard-to-comprehend world of quantum physics. Particles aren't really particles. They're waves. But they're not really waves. They're particles. They're both, and they're neither. They're something in between, or they're both at the same time. But they're not the precise things that we think of. They're inherently fuzzy probabilistic things. That's the source uncertainty: at macroscopic scales, they behave as if they're particles. But they aren't really. So the properties that associate with particles just don't work. An electron doesn't have an exact position and velocity. It has a haze of probability space where it could be. The uncertainty equation describes that haze - the inherent uncertainty that's caused by the real particle/wave duality of the things we call particles.

29 responses so far

This one's for you, Larry! The Quadrature BLINK Kickstarter

Nov 14 2013 Published by under Bad Physics

After yesterday's post about the return of vortex math, one of my coworkers tweeted the following at me:

Larry's a nice guy, even if he did give me grief at my new-hire orientation. So I decided to take a look. At oh my, what a treasure he found! It's a self-proclaimed genius with a wonderful theory of everything. And he's running a kickstarter campaign to raise money to publish it. So it's a lovely example of profound crackpottery, with a new variant of the buy my book gambit!

To be honest, I'm a bit uncertain about this. At times, it seems like the guy is dead serious; at other times, it seems like it's an elaborate prank. I'm going to pretend that it's completely serious, because that will make this post more fun.

So, what exactly is this theory of everything? I don't know for sure. He's dropping hints, but he's not going to tell us the details of the theory until enough people buy his book! But he's happy to give us some hints, starting with an explanation of what's wrong with physics, and why a guy with absolutely no background in physics or math is the right person to revolutionize physics! He'll explain it to us in nine brief points!

First: Let me ask you a question. Since the inclusion of Relativity and Dirac’s Statistical Model, why has Physics been at loose ends to unify the field? Everyone has tried and failed, and for this reason so many have pointed out: what we don’t need, is another TOE, Theory of Everything. So if I was a Physicist, my theory would probably just be one of these… a failed TOE based on the previous literature.

But why do these theories fail? One thing for sure is that in academia every new ideas stems from previously accepted ideas, with a little tweak here or there. In the main, TOEs in Physics have this in common, and they all have failed. What does this tell you?

See, those physicists, they're all just trying the same stuff, and they all failed, therefore they'll never succeed.

When I look at modern physics, I see some truly amazing things. To pull out one particularly prominent example from this year, we've got the higgs boson. He'll sneer at the higgs boson a bit later, but that was truly astonishing: decades ago, based on a deep understanding of the standard model of particle physics, a group of physicists worked out a theory of what mass was and how it worked. They used that to make a concrete prediction about how their theory could tested. It was untestable at the time, because the kind of equipment needed to perform the experiment didn't exist, and couldn't exist with current technology. 50 years later, after technology advanced, their prediction was confirmed.

That's pretty god-damnned amazing if you ask me.

Based on the arguments from our little friend, a decade ago, you could have waved your hands around, and said that physicists had tried to create theories about why things had mass, and they'd failed. Therefore, obviously, no theory of mass was going to come from physics, and if you wanted to understand the universe, you'd have to turn to non-physicists.

On to point two!

Second: the underlying assumptions in Physics must be wrong, or somehow grossly mis-specified.

That's it. That's the entire point. No attempt to actually support that argument. How do we know that the underlying assumptions in physics must be wrong? Because he says so. Period.

Third: Who can challenge the old paradigm of Physics, only Copernicus? Physicists these days cannot because they are too inured of their own system of beliefs and methodologies. Once a PhD is set in place, Lateral Thinking, or “thinking outside the box,” becomes almost impossible due to departmental “silo thinking.” Not that physicists aren’t smart – some are genius, but like everyone in the academic world they are focused on publishing, getting research grants, teaching and other administrative duties. This leaves little time for creative thinking, most of that went into the PhD. And a PhD will not be accepted unless a candidate is ready and willing to fall down the “departmental silo.” This has a name: Catch 22.

It's the "good old boys" argument. See, all those physicists are just doing what their advisors tell them to; once they've got their PhD, they're just producing more PhDs, enforcing the same bogus rules that their advisors inflicted on them. Not a single physicist in the entire world is willing to buck this! Not one single physicist in the world is willing to take the chance of going down as one of the greatest scientific minds in history by bucking the conventional wisdom.

Except, of course, there are plenty of people doing that. For an example, right off the top of my head, we've got the string theorists. Sure, they get lots of justifiable criticism. But they've worked out a theory that does seem to describe many things about the universe. It's not testable with present technology, and it's not clear that it will ever be testable with any kind of technology. But according to Bretholt's argument, the string theorists shouldn't exist. They're bucking the conventional model, and they're getting absolutely hammered for it by many of their colleagues - but they're still going ahead and working on it, because they believe that they're on to something important.

Fourth: There is not much new theory-making going on in Physics since its practitioners believe their Standard Model is almost complete: just a few more billion dollars in research and all the colors of the Higgs God Particle may be sorted, and possibly we may even glimpse the Higgs Field itself. But this is sort of like hunting down terrorists: if you are in control of defining what a terrorist is, then you will never be out of a job or be without a budget. This has a name too: Self-Fulfilling Prophesy. The brutal truth…

Right, there's not much new theory-making going on in physics. No one is working on string theory. There's no one coming up with theories about dark matter or dark energy. There's no one trying to develop a theory of quantum gravity. No one ever does any of this stuff, because there's no new theory-making going on.

Of course, he hand-waves one of the most fantastic theory-confirmations from physics. The higgs got lots of press, and lots of people like to hand-wave about it and overstate what it means. ("It's the god particle!") But even stripped down to its bare minimum, it's an incredible discovery, and for a jackass like this to wave his hands and pretend that it's meaningless and we need to stop wasting time on stuff like the LHC and listen to him: I just don't even know the right words to describe the kind of disgust it inspires in me.

Fifth: Who then can mount such a paradigm-breaking project? Someone like me, prey tell! But birds like me just don’t sit around the cage and get fat, we fly to the highest vantage point, and see things for what they are! We have a name as well: Free Thinkers. We are exactly what your mother warned you of… There’s a long list of us include Socrates, Christ, Buddha, Taoist Masters, Tibetan Masters, Mohammed, Copernicus, Newton, Maxwell, Gödel, Hesse, Jung, Tesla, Planck… All are Free Thinkers, confident enough in their own knowledge and wisdom that they are willing to risk upsetting the applecart! We soar so humanity can peer beyond its petty day to day and discover itself.

There's two things that really annoy me about this paragraph. First of all, there's the arrogance. This schmuck hasn't done anything yet, but he sees fit to announce that he's up there with Newton, Maxwell, etc.

Second, there's the mushing together of scientists and religious figures. Look, I'm a religious jew. I don't have anything against respecting theology, theologians, or religious authorities. But science is different. Religion is about subjective experience. Even if you believe profoundly in, say, Buddhism, you can't just go through the motions of what Buddha supposedly did and get exactly the same result. There's no objective, repeatable way of testing it. Science is all about the hard work of repeatable, objective experimentation.

He continues point 5:

This chain might have included Einstein and Dirac had they not made three fatal mistakes in Free Thinking: They let their mathematical machine dictate what was true rather than using mathematics only to confirm their observations, they got fooled by their own anthropomorphic assumptions, and then they rooted these assumptions into their mathematical methods. This derailed the last two generations of scientific thinking.

Here's where he strays into the real territory of this blog.

Crackpots love to rag on mathematics. They can't understand it, and they want to believe that they're the real geniuses, so the math must be there to confuse things!

Scientists don't use math to be obscure. Learning math to do science isn't some sort of hazing ritual. The use of math isn't about making science impenetrable to people who aren't part of the club. Math is there because it's essential. Math gives precision to science.

Back to the Higgs boson for a second. The people who proposed the Higgs didn't just say "There's a field that gives things mass". They described what the field was, how they thought it worked, how it interacted with the rest of physics. The only way to do that is with math. Natural language is both too imprecise, and too verbose to be useful for the critical details of scientific theories.

Let me give one example from my own field. When I was in grad school, there was a new system of computer network communication protocols under design, called OSI. OSI was complex, but it had a beauty to its complexity. It carefully divided the way that computer networks and the applications that run on them work into seven layers. Each layer only needed to depend on the details of the layer beneath it. When you contrast it against TCP/IP, it was remarkable. TCP/IP, the protocol that we still use today, is remarkably ad-hoc, and downright sloppy at times.

But we're still using TCP/IP today. Why?

Because OSI was specified in english. After years of specification, several companies and universities implemented OSI network stacks. When they connected them together, what happened? It didn't work. No two of the reference implementations could talk to each other. Each of them was perfectly conformant with the specification. But the specification was imprecise. To a human reader, it seemed precise. Hell, I read some of those specifications (I worked on a specification system, and read all of specs for layers 3 and 4), and I was absolutely convinced that they were precise. But english isn't a good language for precision. It turned out that what we all believed was perfectly precise specification actually had numerous gaps.

There's still a lot of debate about why the OSI effort failed so badly. My take, having been in the thick of it is that this was the root cause: after all the work of building the reference implementations, they realized that their specifications needed to go back to the drawing board, and get the ambiguities fixed - and the world outside of the OSI community wasn't willing to wait. TCP/IP, for all of its flaws, had a perfectly precise specification: the one, single, official reference implementation. It might have been ugly code, it might have been painful to try to figure out what it meant - but it was absolutely precise: whatever that code did was right.

That's the point of math in science: it gives you that kind of unambiguous precision. Without precision, there's no point to science.

Sixth: What happens to Relativity when the assumptions of Lorentz’ space-time is removed? Under these assumptions, the speed of light limits the speed of moving bodies. The Lorentz Transformation was designed specifically to set this speed limit, but there is no factual evidence to back it up. At first, the transformation assumed that there would be length and time dilations and a weight increase when travelling at sub-light speeds. But after the First Misguided Generation ended in the mid 70’s, the weight change idea was discarded as untenable. It was quietly removed because it implied that a body propagating at or near the speed of light would become infinitely massive and turn into a black hole. Thus, the body would swallow itself up and disappear!

Whoops… bad assumption!

The space contraction idea was left intact because it was imperative to Hilbert’s rendition of the space-time geodesic that he devised for Einstein in 1915. Hilbert was the best mathematician of his day, if not ever! He concocted the mathematical behemoth called General Relativity to encapsulate Einstein's famous insight that gravitation was equivalent to an accelerating frame. Now, not only was length assumed to contract, but space was assumed to warp and gravitation was assumed to be an accelerating frame, though no factual evidence exists to back up these assumptions!

Whoops… 3 bad assumptions in a row!

This is an interestingly bizarre argument.

Relativity predicts a change in mass (not weight!) as velocity increases. That prediction has not changed. It has been confirmed, repeatedly, by numerous experiments. The entire reasoning here is based on the unsupported assertion that relativistic changes in mass have been discarded as incorrect. But that couldn't be farther from the truth!

Similarly, he's asserting that the space-warping effects of gravity - one of the fundamental parts of general relativity - is incorrect, again without the slightest support.

This is going to seem like a side-track, but bear with me:

When I came in to my office this morning, I took out my phone and used foursquare to check in. How did that work? Well, my phone received signals from a collection of satellites, and based on the tiny differences in data contained in those signals, it was able to pinpoint my location to precisely the corner of 43 street and Madison avenue, outside of Grand Central Terminal in Manhattan.

To be able to pinpoint my location that precisely, it ultimately relies on clocks in the satellites. Those clocks are in orbit, moving very rapidly, and in a different position in earths gravity well. Space-time is less warped at their elevation than it is here on earth. Relativity predicts that based on that fact, the clocks in those satellites must move at a different rate than clocks here on earth. In order to get precise positions, those clocks need to be adjusted to keep time with the receivers on the surface of the earth.

If relativity - with its interconnected predictions of changes in mass, time, and the warp of space-time - didn't work, then the corrections made by the GPS satellites wouldn't be needed. And yet, they are.

There are numerous other examples of this. We've observed relativistic effects in many different ways, in many different experiments. Despite what Mr. Bretholt asserts, none of this has been disproven or discarded.

Seventh: Many, many, many scientists disagree with Relativity for these reasons and others, but Physics keeps it as a mainstream idea. It has been violated over and over again in various space programs, and is rarely used in the aerospace industry when serious results are expected. Physics would like to correct Relativity because it doesn’t jive with the Quantum Standard Model, but they can’t conceive how to fix it.

In Quadrature Theory the problem with Relativity is obvious and easily solved. The problem is that the origin and nature of space is not known, nor is the origin and nature of time or gravitation. Einstein did not prove anything about gravitation, norhas anyone since. The “accelerating frame” conjecture is for the convenience of mathematics and sheds no light on the nature of gravitation itself. Quantum Chromo Dynamics, QCD, hypothesizes the “graviton” on the basis of similarly convenient mathematics. Many scientists disagree with such “force carrier” propositions: they are all but silenced by the trends in Physics publishing, however. The “graviton” is, nevertheless, a mathematical fiction similar to Higgs Boson.

Whoops… a couple more bad assumptions, but where did they come from?

Are there any serious scientists who disagree with relativity? Mr. Bretholt doesn't actually name any. I can't think of any credible ones. Certainly pretty much all physicists agree that there's a problem because both relativity and quantum physics both appear to be correct, but they're not really compatible. It's a major area of research. But that's a different thing from saying that scientists "disagree" with or reject relativity. Relativity has passed every experimental test that anyone has been able to devise.

Of course, it's completely true that Einstein didn't prove anything about gravity. Science doesn't deal with proof. Science devises models based on observations. It tries to find the best predictive model of the universe that it can, based on repeated observation. Science can disprove things, by showing that they don't match our observations of reality, but it can't prove that a theory is correct. So we can never be sure that our model is correct - just that it does a good job of making predictions that match further observations. Relativity could be completely, entirely, 100% wrong. But given everything we know now, it's the best predictive theory we have, and nothing we've been able to do can disprove it.

Ok, I've gone on long enough. If you want to see his last couple of points, go ahead and follow the link to his "article". After all of this, we still haven't gotten to anything about what his supposed new theory actually says, and I want to get to just a little bit of that. He's not telling us much - he wants money to print his book! - but what little he says is on his kickstarter page.

So let me introduce that modification: it’s called Quadrature, or Q. Quadrature arose from Awareness as the original separation of Awareness from itself. This may sound strangely familiar; I elaborate at length about it in BLINK. The Theory of Quadrature develops Q as the Central Generating Principle that creates the Universe step by step. After a total of 12 applications of Quadrature, it folds back on itself like a snake biting its tail. Due to this inevitable closure, the Universe is complete, replete with life, energy and matter, both dark and light. As a necessary consequence of this single Generating Principle, everything in the Universe is ultimately connected through ascending levels of Awareness.

The majesty and mystery of Awareness and its manifestation remains, but this vision puts us inside as co-creative participants. I think you will agree that this is highly desirable from a metaphysical point of view. Quadrature is the mechanism that science has been looking for to unify these two points of view. Q has been foreshadowed in many ways in both physics and metaphysics. As developed in BLINK, Quadrature Theory can serve as a Theory of Everything.

Pretty typical grandiose crackpottery. This looks an awful lot like a variation of Langan's CTMU. It's all about awareness! And there's a simple "mathematical" construct called "quadrature" that makes it all work. Of course, I can't tell you what quadrature is. No, you need to pay me! Give me money! And then I'll deign to explain it to you.

To make a long story short, Quadrature Theory supports four essential claims that undermine Relativity, Quantum Mechanics, and Cosmology while placing these disciplines back on a more secure foundation once their erroneous assumptions have been removed. These are:

  1. The origin of space and its nature arise from Quadrature. Space is shown to be strictly rectilinear; space cannot warp under any conditions.
  2. The origin of the Tempic Field and its nature arise from Quadrature. This field facilitates all types of energetic interaction and varies throughout space. The idea of time arises solely from transactions underwritten by the Tempic Field. Therefore, time as we know it here on Earth is a local anomaly, which uniquely affects all interactions including the speed of light. “C,” in fact, is a velocity, and is variable in both speed and direction depending on the gradient of the Tempic Field. Thus, “C” varies drastically off-planet!
  3. Spin is a fundamental operation in space that constitutes the only absolute measurement. Its density throughout space is non-linear and it generates a variable Tempic Field within spinning systems such as atoms, or galaxies. This built-in “time” serves to hold the atom together eternally, and has many other consequences for Quantum Mechanics and Cosmology.
  4. Gravity is also a ringer in physics. Nothing of the fundamental origin of gravity is known, though we know how to use it quite well. Given the consequence of Spin, gravity can be traced to forms that have closed Tempic Fields. The skew electric component of spinning systems will align to create an aggregated, polarized, directional field: gravity.

Pop science, of course, loves to talk about black holes, worm holes, time warps and all manner of the ridiculous in physics. There is much more fascinating stuff than this in my book, and it is completely consistent with what is observable in the Universe. For example, I propose the actual purpose of the black hole and why every galaxy has one. At any rate, perhaps you now have an inkling of why Quadrature Theory is a Revolution Waiting to Happen!

Pure babble, stringing together words in nonsensical ways. As my mantra goes: the worst math is no math. Here he's arguing that rigorous, well-tested mathematical models are incorrect - because vague reasons.

14 responses so far

Vortex Math Returns!

Nov 12 2013 Published by under Bad Physics

Cranks never give up. That's something that I've learned in my time writing this blog. It doesn't matter how stupid an idea is. It doesn't matter how obviously wrong, how profoundly ridiculous. No matter what, cranks will continue to push their ridiculous ideas.

One way that this manifests is the comments on old posts never quite die. Years after I initially write a post, I still have people coming back and trying to share "new evidence" for their crankery. George Shollenberger, the hydrino cranks, the Brown's gas cranks, the CTMU cranks, they've all come back years after a post with more of the same-old, same-old. Most of the time, I just ignore it. There's nothing to be gained in just rehashing the same old nonsense. It's certainly not going to convince the cranks, and it's not going to be interesting to my less insane readers. But every once in a while, something comes along in those comments, something that's actually new and amusing comes along. Today I've got an example of that for you: one of the proponents of Markus Rodin's "Vortex Math" has returned to tell us the great news!

I have linked Vortex Based Mathematics with Physics and can prove most physics using vortex based mathematics. I am writing an article call "Temporal Physics of Vortex Based Mathematics" here: http://www.vortexspace.org

This is a lovely thing, even without needing to actually look at his article. Just start at the very first line! He claims that he can "prove most of physics".

Science doesn't do proof.

What science does is make observations, and then based on those observations produce models of the universe. Then, using that model, it makes predictions, and compares those predictions with further observations. By doing that over and over again, we get better and better models of how the universe works. Science is never sure about anything - because all it can do is check how well the model works. It's always possible that any model doesn't describe how things actually work. But it gives us a good approximation, in a way that allows us to understand how things work. Or, not quite how things work, but how we can affect the world by our actions. Our model might not capture what's really happening - but it's got predictive power.

To give an example of this: our model of the universe says that the earth orbits the sun, which is orbits the galactic core, which is moving through the universe. It's possible that this is wrong. You can propose an alternative model in which the earth is the stationary center of the universe, and everything moves around it. As a model, it's not very attractive, because to make it fit our observations, it requires a huge amount of complexity - it's a far, far more complex model than our standard one, and it's much harder to use to make accurate predictions. But it can be made to work, just as well as our standard one. It's possible that that's how the universe actually works. I don't think any reasonable person actually believes that the universe works that way, but it's possible that our entire model is wrong. Science can't prove that our model is correct. It can just show that it's the simplest model that matches our observations.

But Mr. Calhoun claims that he can prove physics. That claim shows that he has no idea of what science is, or what science means. And if he doesn't understand something that simple, why should we trust him to understand any more?

Ah, but when we take a look at some of his writings... it's a lovely pile of rubbish. Remember the mantra of this blog? The worst math is no math. Mr. Calhoun's writing is a splendid example of this. He claims to be doing science, math, and mathematical proofs - but when you actually look at his writing, there's not a spec of genuine math to be found!

Let's start with a really quick reminder of what vortex math is. Take the sequence of doubling in natural numbers in base-10. 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, .... If, for each of those numbers, you sum the digits until you get a single digit result, you get: 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, ... It turns into a repeated sequence, 1, 2, 4, 8, 7, 5, over and over again. You can do the same thing in the reverse direction, by halving: 1, 0.5, 0.25, 0.125, 0.0625, 0.03125, 0.015625, 0.0078125, where the digits sum to 1, 5, 7, 8, 4, 2, 1, 5, ...

According to Rodin, this demonstrates something profound. This is the heart of Vortex mathematics: this cycle in the numbers shows that there's some kind of energy flow that is fundamental to the universe, based on this kind of repeating sequence.

So, how does Mr. Calhoun use this? He thinks that he can connect it to black holes and white holes:

Do not forget that we already learned that black holes suck in matter while "compressing" it; and, on the other side of the black hole is a white hole that then takes the same matter and spits it back out while "de-compressing" the matter. The "magnetic warp" video on Youtube shows the same torus shape Marko had illustrated in his "vortex based mathematics" video [see below]:

You can clearly see the vortex in the center of the torus magnets. This is made possible using two Ferrofluid Hele-Shaw Cells [Hele-Shaw effect]. Here are a few links about using ferrofluid hele-shaw cell to view magnetic fields:

http://en.wikipedia.org/wiki/Hele-Shaw_flow

http://www2.warwick.ac.uk/fac/cross_fac/iatl/ejournal/issues/volume2issue1/snyder/

Here is a quote from a Youtube user about the magnets:

"Walter Rawls, a? scientist who did a great deal of research with Albert Roy Davis, said that he believes at the center of every magnet there is a miniature black hole."

I have not verified the above statement about Walter Rawls as of yet. However, the above images prove beyond doubt Marko's torus universe mathematical geometry. Now lets take a look at Marko's designs:

The pictures look kind-of-like this silly torus thing that Rodin likes to draw: therefore they prove beyond doubt that Rodin's rubbish is correct! Wow, now that's a mathematical proof!

It gets worse from there.

The next section is "The Physics of Time".

If you looked at the Youtube videos of the true motion of the Earth through space you now know that we are literally falling into a black hole that is at the center of the galaxy. The motion of the Earth; all of the rotation and revolution, all of that together is caused by space-time. Time is acually the rate and pattern of the motion of matter as it moves through space. It is the fourth dimension. you have probably heard this if you have studied Einstien theories: "As an object moves faster the rate of its motion [or time] slows down". Sounds like an oxymoron doesn't it? Well it not so strange once you understand how the fabric of space-time relates to Vortex Based Mathematics.

Motion of the Earth

The planet Earth rotates approx every twenty-four hours. It makes a complete 360o rotation every twenty-four hours. That amount of time is the frequency of the rate of rotation.

Looking down from the north pole of the Earth, you will see that if we divide the sphere into 36 equal parts the sunrise would have to pass through all of the degrees of the sphere in order to make a complete cycle:

Remember the Earth is a "giant magnet" that is spinning. The electromagnetic field of this "giant magnet" is moving out of the north pole [which is really at the geographic south pole] and going to the south pole [which again is really at the geographic north pole]. This electromagnetic field is moving or spinning [see youtube video at top] according to a frequency or cycle.

I don't know if you realize this, but matter can be compressed or expanded without it being destroyed. A black hole does not de-molecularize matter then in passing to the white hole reassemble it again. Nothing that is demolecularized can naturally be put back together again. If an object is destroyed then is it destroyed; there is no reassembly. Matter can be however, compressed and decompressed. As you probably know and have heard this before there is an huge amount of distance between the atoms in your body. Like the giant void of space and much like the distances between planets in our solar system; the atomic matter in our bodies is just as similar in the amount of space between each atom.

What fills the spaces between each atom? Well, Its space-time. It is the fabric of the inertia ether that all matter in space moves through. Spacetime or what I call "etherspace" is what I have come to realize as "the space in between the spaces". This "etherspace" can be compressed and then decompressed. Etherspace can enable all of the matter in your body to be greatly compressed without your body being destroyed; and at the same time functioning as it normally should. The ether space then allows your body to be decompressed again; all the while functioning as it should.

It is the movement of spacetime or "ether space" that is causing the rotation and revolving of the planet we live on. It is also responsible for the motions of all of the bodies in space.

Magnets will, whether great or small, act as engines for etherspace. They pull in etherspace at the south pole and also pump out etherspace at the north pole of the magnet. All magnets do this; the great planet earth all the way to the little magnet that sticks to your refridgerator door. Vortex based mathematics prove all of this. I will show you.

As I stated earlier the Earth is a giant magnet and if we apply the Vortex Based Mathematics to the 10o degree spacings of this "giant magnet" lets see what happens. Now we are going to see the de-compression of space-time eminatiing from the true north pole of the giant magnet of the Earth. Let's deploy a doubling circuit to the spacings of the planet. We will start at 0o and go all the way to 360o .

Calhoun certainly shows that he's a worthy inheritor of the mantle of Rodin. Rodin's entire rubbish is really based on taking a fun property of our particular base-10 numerical notation, and without any good reason, believing that it must be a profound fundamental property of the universe. Calhoun takes two arbitrary things: the 360 degree conventional angle measurement, and the 24 hour day, and likewise, without any good reason, without even any argument, believes that they are fundamental properties of the universe.

Where does the 24 hour day come from? I did a bit of research, and there are a couple of possible arguments. It appears to date back to the old empire of Egypt. The argument that I found most convincing is based on how the Egyptians counted on their hands. They did a lot of things in base-12, because using your thumb to point out the joints of the fingers on your hand, you can count to 12. The origin of our base-10 is based on using fingers to count; base-12 is similar, but based on a slightly different way of counting on your fingers. Using base-12, they decided to describe time in terms of counting periods of light and darkness: 12 bright periods, 12 dark ones. There's nothing scientific or fundamental about it: it's an arbitrary way of measuring time. The Greeks adopted it from the Egyptians; the Romans adopted it from the Greeks; and we adopted it from the Romans. There is no fundamental reason why it is the one true correct way of measuring time.

Similarly, the 360 degree system of angular measure is not the least bit fundamental. It dates back to the Babylonians. In writing, the Babylonions used a base-60 system, instead of our base-10. In their explorations of geometry, they observed that if you inscribed a hexagon inside of a circle, each of the segments of the hexagon was the same length as the radius of the circle. So they measured an angle in terms of which segment of the inscribed hexagon it crossed. Within those sig segments, they divided them into sixty sections, because what else would people who use base-60 use? And then to subdivide those, they used 60 again. The 360 degree system is a random historical accident, not a profound truth.

I don't want to get too far off track (or too farther off track), but: In fact, when you're talking about angles, there is a fundamental measurement, called a radian. Whenever you do math using angles, you end up needing to introduce a conversion factor which converts your angle into radians.

Anyway - this rubbish about the 24 hour day and 360 degree circle are what passes for math in Calhoun's world. This is as close to math or to correctness that Calhoun gets.

What's even worse is his babble about black holes and white holes.

Both black and white holes are theoretical predictions of relativity. The math involved is not simple: it's based on Einstein's field equations from general relativity:

\[ R_{munu} - frac{1}{2}g_{munu}R + g_{mueta}Lambda = frac{8pi G}{c^4}T_{munu}\]

In this equation, the subscripted variables are all symmetric 4x4 tensors. Black and white holes are "solutions" to particular configurations of those tensors. This is not elementary math, not by a long-shot. But if you want to really talk about black and white holes, this is how you do it.

Translating from the math into prose is always a problem, because the prose is far less precise, and it's inevitably misleading. No matter how well you think you understand based on the prose, you don't understand the concept, because you haven't been told enough, in a precise enough way, to actually understand it.

That said, the closest I can come is the following.

We'll start with black holes. Black holes are much easier to understand: put enough mass into a small enough area of space, and you wind up with a boundary line, called the event horizon, where anything that crosses that boundary, no matter what - even massless stuff like light - can never escape. We believe, based on careful analysis, that we've observed black holes in our universe. (Or rather, we've seen evidence that they exist; you can't actually see a black hole; but you can see its effects.) We call a black hole a singularity, because nothing beyond the event horizon is visible - it looks like a hole in space. But it isn't: it's got a mass, which we can measure. Matter goes in to a black hole, and crosses the event horizon. We can no longer see the matter. We can't observe what happens to it once it crosses the horizon. But we know it's still there, because we can observe the mass of the hole, and it increases as matter enters.

(It was pointed out to me on twitter that my explanation of the singularity is wrong. See what happens when you try to explain mathematical stuff non-mathematically?)

White holes are a much harder idea. We've never seen one. In fact, we don't really think that they can exist in our universe. In concept, they're the opposite of a black hole: they are a region with a boundary than nothing can ever cross. In a black hole, you can't cross the boundary an escape; in a white hole, once something crosses the boundary, it can't ever re-enter. White holes only exist in a strange conceptual case, called an eternal black hole - that is, a black hole that has been there forever, which was never formed by gravitational collapse.

There are some folks who've written speculative work based on the solutions to the white hole field equations that suggest that our universe is the result of a white hole, inside of the event horizon of a black hole in an enclosing universe. But in this solution, the white hole exists for an infinitely small period of time: all of the matter in it ejects into a new space-time realm in an instant. There's no actual evidence for this, beyond the fact that it's an interesting way of interpreting a solution to the field equations.

All of this is a long-winded way of saying that when it comes to black holes, Calhoun is talking out his ass. A black hole is not one end of a tunnel that leads to a white hole. If you actually do the math, that doesn't work. A black hole does not "compress" matter and pass it to a white hole which decompresses it. A black hole is just a huge clump of very dense matter; when something crosses the event horizon of a black hole, it just becomes part of that clump of matter.

His babble about magnetism is similar: we've got some very elegant field equations, called Maxwell's equations, which describe how magnetism and electric fields work. It's beautiful, if complex, mathematics. And they most definitely do not describe a magnet as something that "pumps eitherspace from the south pole to the north pole".

There's no proof here. And there's no math here. There's nothing here but the midnight pot-fueled ramblings of a not particularly bright sci-fi fan, who took some wonderful stories, and believed that they were based on something true.

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