I realized that there's a big difference between deciding to leave and knowing where to go.

So apparently I was bored so I wrote a program in C that numerically simulates time evolution of the Schrödinger equation and a wave packet tunneling through a potential barrier. Nothing unusual, but to make it a bit harder, I decided that I will also write my own basic functions such as exponential function, square root and sine using nothing but standard additions, subtractions and multiplication. I also didn't replicate any known algorithm (at least not intentionally), but instead just improvised something (inefficient).

Gif compression is a bit funny, but you get the point. Simulation done by a C program, data plotted in matlab.

// #include <math.h>
#include <stdio.h>

#define PI 3.14159265358979323846264338327950288419716939937508

struct mycomplex {
  double real;
  double imag;
};

/* e^x is a function that grows at a rate proportional to its value */
/* really inefficient, but there's a more efficient one with taylor series below */
double r_exp(double x) {
  double r = 1;
  if(x>0)
    for(double y=0; y<x; y+=0.000002)
      r = r + r*0.000002;
  if(x<0)
    for(double y=0; y>x; y-=0.000002)
      r = r - r*0.000002;
  return r;
}

/* my routine for natural logarithm as inverse of e^x similarly to sqrt */
double my_log(double x) {
  double low = 0;
  double high = x;
  double neg = 1;
  if(x<1) {
    x = 1/x;
    high = x;
    neg = -1;
  }
  double value = (low + high)/2;

  for(int i=0; i<30; i++) {
    if(r_exp(value) < x)
      low = value;
    else
      high = value;
    value = (low + high)/2;
  }
  return neg*value;
}

/* x^y */

double my_pow(double x, double y) {
  return r_exp(y*my_log(x));
}

/* abs(x) */
double my_abs(double x) {
  if(x<0)
    return -x;
  else
    return x;
}

/* my routine for sqrt */
double my_sqrt(double x) {
  double low = 1;
  double high = x;
  double root = (low + high)/2;
  if(x<1) {
    low = x;
    high = 1;
  }
  for(int i=0; i<30; i++) {
    if(root*root < x)
      low = root;
    else
      high = root;
    root = (low + high)/2;
  }
  return root;
}

/*
double my_sqrt(double x) {
  return my_pow(x, 0.5);
}
*/

/* function for taking a modulo for floating point numbers */
double my_fmod(double in, double n) {
  if(in<0)
    n = -n;
  while(in>n)
    in += n;
  return in;
}

/* my routine for sine */
double my_sin(double a) {
  double l = 0, x0 = 0, y0 = 1, x = 0, y = 1, neg = 1.0;

  /* utilize symmetries to only calculate quarter */
  while(a<0) {
    a = a + 2*PI;
  }
  a = my_fmod(a, 2*PI);
  if(a>PI) {
    neg = -neg;
    a = 2*PI-a;
  }
  if(a>PI/2)
    a = PI-a;

  /* integrate perimeter length until it corresponds to given angle */
  while(l<a) {
    x = x + 0.000005;
    y = my_sqrt(1-x*x);
    l = l + my_sqrt((x-x0)*(x-x0)+(y-y0)*(y-y0));
    x0 = x;
    y0 = y;
  }

  return neg*x;
}

/* integrate the perimeter length until x/y corresponds to r */
double my_atan(double r) {
  double l = 0, x0 = 0, y0 = 1, x = 0, y = 1;
  while(x/y<r) {
    x = x + 0.000002;
    y = my_sqrt(1-x*x);
    l = l + my_sqrt((x-x0)*(x-x0)+(y-y0)*(y-y0));
    x0 = x;
    y0 = y;
  }
  return l;
}

/* my routine for multiplying two complex numbers */
struct mycomplex my_mul(struct mycomplex a, struct mycomplex b) {
  struct mycomplex out;

  out.real = a.real * b.real - a.imag * b.imag;
  out.imag = a.imag * b.real + a.real * b.imag;

  return out;
}

/* my routine for taking exp(z), where z is complex valued vector */
struct mycomplex my_exp(double real, double imag) {
  struct mycomplex out;

  out.real = r_exp(real)*my_sin(imag+PI/2);
  out.imag = r_exp(real)*my_sin(imag);

  return out;
}

/* my routine for constructing linear real valued vector */
my_linspace(double a, double b, int n, double out[]) {
  double df = (b-a)/(n-1);
  double f = a;
  for(int i=0; i<n; i++) {
    out[i] = f;
    f = f + df;
  }
}

main() {
  double k[800];
  struct mycomplex diff2[800];
  struct mycomplex tmp;
  struct mycomplex tmpb;
  struct mycomplex psi[800];
  struct mycomplex potential[800];

  /* just for testing of accuracy */
  /*
  printf("my_sqrt(2)=%f sqrt(2)=%f\n", my_sqrt(2), sqrt(2));
  printf("my_sin(pi/4)=%f sin(pi/4)=%f\n", my_sin(PI/4), sin(PI/4));
  printf("4*my_atan(1)=%f 4*atan(1)=%f\n", 4*my_atan(1), 4*atan(1));
  printf("my_exp(1)=%f exp(1)=%f\n", r_exp(1), exp(1));
  printf("my_exp(-1)=%f exp(-1)=%f\n", r_exp(-1), exp(-1));
  exit(0);
  */

  /* prepare a potential barrier */
  for(int i=0; i<800; i++) {
    potential[i].real = 0;
    potential[i].imag = 0;
  }
  for(int i=390; i<410; i++)
    potential[i].real = 0.05;

  my_linspace(0, 50, 800, &k);

  /* prepare initial wave function */
  for(int i=0; i<800; i++) {
    psi[i].real = r_exp(-0.07*(k[i]-12)*(k[i]-12));
    tmp = my_exp(0, -900*k[i]);
    psi[i] = my_mul(psi[i], tmp);
    psi[i].real = psi[i].real/8.7;
    psi[i].imag = psi[i].imag/8.7;
    // printf("%f\n", i/800.0);
  }

  /* evolve */
  for(int t=0; t<2000000; t++) {
    diff2[0].real = 0;
    diff2[0].imag = 0;
    for(int i=1; i<799; i++) {
      diff2[i].real = (psi[i+1].real-psi[i].real)-(psi[i].real-psi[i-1].real);
      diff2[i].imag = (psi[i+1].imag-psi[i].imag)-(psi[i].imag-psi[i-1].imag);
    }
    diff2[799].real = 0;
    diff2[799].imag = 0;
    for(int i=0; i<800; i++) {
      tmp = my_mul(potential[i], psi[i]);
      tmpb.real = diff2[i].real - tmp.real;
      tmpb.imag = diff2[i].imag - tmp.imag;
      tmp.real = 0;
      tmp.imag = 0.001;
      tmp = my_mul(tmp, tmpb);
      psi[i].real = psi[i].real + tmp.real;
      psi[i].imag = psi[i].imag + tmp.imag;
    }
    if(t%1000==1) {
      for(int i=0; i<800; i++)
printf("%f, %f\n", psi[i].real, psi[i].imag);
    }
  }
}

--

Actually, you only need complex valued exponential function and some iterative inversions to calculate pretty much anything (normal).

--
#include <math.h>
#include <stdio.h>
#include <complex.h>

#define PI 3.14159265358979323846264338327950288419716939937508

/* iteratively invert a growing function with a and b as limits */
double inv(double (*f)(), double x, double a, double b) {
  for(int i=0; i<20; i++)
    if(f((a+b)/2)<x) a = (a+b)/2;
    else b = (a+b)/2;
  return (a+b)/2;
}

/* integrate from definition: e^z = de^z/dz, z^0 = 1 */
double complex my_exp(double complex z) {
  double complex v = 1;

  for(double a=0; a<1; a+=1/1e5)
    v = v + v*(z/1e5);
  return v;
}

/* more efficient (taylor series), less intuitive e^z */
double complex alt_exp(double complex z) {
  double complex v = 1, w = 1;
  for(int k=1; k<20; k++)
    v += (w*=z/k);
  return v;

}

double real_my_exp(double x) { return creal(my_exp(x)); }

double my_log(double x) {
  if(x<1) return -my_log(1/x);
  return invert(real_my_exp, x, 0, x);
}

double my_sq(double x) { return x*x; }

double my_sqrt(double x) {
  if(x>1) return invert(my_sq, x, 1, x);
  return invert(my_sq, x, x, 1);
}

double my_sin(double x) { return cimag(my_exp(I*x)); }
double my_cos(double x) { return creal(my_exp(I*x)); }
double my_tan(double x) { return my_sin(x)/my_cos(x); }
double my_cot(double x) { return my_cos(x)/my_sin(x); }
double my_pow(double x, double y) { return creal(my_exp(y*my_log(x))); }
double my_sinh(double x) { return (creal(my_exp(x))-creal(my_exp(-x)))/2; }
double my_cosh(double x) { return (creal(my_exp(x))+creal(my_exp(-x)))/2; }
double my_tanh(double x) { return my_sinh(x)/my_cosh(x); }
double my_coth(double x) { return my_cosh(x)/my_sinh(x); }
double my_log10(double x) { return my_log(x)/my_log(10); }

double my_atan(double x) {
  if(x<0) return -my_atan(-x);
  return invert(my_tan, x, 0, 1.6); /* 1.6 is just some value above pi/2 */
}

double my_asin(double x) { return my_atan(x/my_sqrt(1-x*x)); }
double my_acos(double x) { return 2*my_atan(1)-my_atan(x/my_sqrt(1-x*x)); }

/* alternative sin by integration of perimeter until y corresponds to a*/
double alt_sin(double a) {
  double c, x = 1, y = 0, xn = 1, yn = 0, l = 0, dl;

  /* utilize symmetries */
  while(a<0) a = a + 2*PI;
  while(a>2*PI) a = a - 2*PI;
  if(a>PI) return -alt_sin(2*PI-a);
  if(a>PI/2) return alt_sin(PI-a);

  /* integrate the perimeter length */
  while(l<a) {
    x = x - 1e-5;
    y = sqrt(1-x*x);
    dl = sqrt((x-xn)*(x-xn)+(y-yn)*(y-yn));
    l = l + dl;
    xn = x;
    yn = y;
  }
  return y;

}

/* alternative atan by integrating the perimeter length until x/y corresponds to v */
double alt_atan(double v) {
  double l = 0, x0 = 0, y0 = 1, x = 0, y = 1;
  if(v<0) return -alt_atan(-v);
  while(x/y<v) {
    x = x + 1e-5;
    y = sqrt(1-x*x);
    l = l + sqrt((x-x0)*(x-x0)+(y-y0)*(y-y0));
    x0 = x;
    y0 = y;
  }
  return l;
}

/* discrete Fourier transform: F(w) = sum(f(t)e^(-iwt)) */
int dft(double complex *a, double complex *b, int n) {
  for(int m=0; m<n; m++) {
    b[m] = 0;
    for(int t=0; t<n; t++) /* w = 2*PI*m/n */
      b[m] = b[m] + a[t]*cexp(-I*2*PI*m*t/n); /* (a+bi)*(c+di) */
  }
}

/* more efficient, less intuitive Fourier transform */
int fft(double complex a[], double complex b[], int n, int step) {
  double complex t;
  if(step==1) for(int i=0; i<n; i++) b[i] = a[i];
  if(step<n) {
    fft(b, a, n, step * 2);
    fft(b + step, a + step, n, step * 2);
    for(int i=0; i<n; i+=2*step) {
      t = cexp(-I*PI*i/n)*a[i+step];
      b[i/2] = a[i]+t;
      b[(i+n)/2] = a[i]-t;
    }
  }
} /* notice that this fft alters the input vector */

int main() {
  double complex a[] = {1, 2, -1, 4};
  double complex b[4];

  printf("Function  \tMy        \tC       \tAlt\n");
  printf("exp(1)    \t%f\t%f\t%f\n", creal(my_exp(1)), exp(1), creal(alt_exp(1)));
  printf("exp(-1)   \t%f\t%f\t%f\n", creal(my_exp(-1)), exp(-1), creal(alt_exp(-1)));
  printf("sqrt(2)   \t%f\t%f\n", my_sqrt(2), sqrt(2));
  printf("sqrt(0.5) \t%f\t%f\n", my_sqrt(0.5), sqrt(0.5));
  printf("log(2)    \t%f\t%f\n", my_log(2), log(2));
  printf("log(0.5)  \t%f\t%f\n", my_log(0.5), log(0.5));
  printf("atan(1)   \t%f\t%f\t%f\n", my_atan(1), atan(1), alt_atan(1));
  printf("atan(-1)  \t%f\t%f\t%f\n", my_atan(-1), atan(-1), alt_atan(-1));
  printf("\n");

  dft(a, b, 4);
  printf("Discrete Fourier Transform of 1 2 -1 4\n");
  for(int i=0; i<4; i++)
    printf("%f\t%f\n", creal(b[i]), cimag(b[i]));
  printf("\n");

  printf("Fast Fourier Transform of 1 2 -1 4\n");
  fft(a, b, 4, 1);
  for(int i=0; i<4; i++)
    printf("%f\t%f\n", creal(b[i]), cimag(b[i]));
}

Being present is being connected to All Things.

If the many worlds interpretation of quantum mechanics is in fact true then the universe is deterministic, but we are faced with an interesting philosophical question of identity. Since all possible outcomes exist simultaneously, it's not surprising we find ourselves asking and existing as the question must be asked by those who exist, can and do ask it, wherever and whenever. However, why exactly does our life as an individual take this particular path instead of some other? For physics they're all equal. Futhermore, if time doesn't truly exist, why/how do we experience present and flow of time?

True free will cannot exist in a deterministic universe and therefore our path cannot be determined by one. If there existed no subjective experience of specific consciousness then the question would perhaps vanish. From purely physical point of view, I suppose there doesn't have to be anything special about every possible past, present and future existing simultaneously, but from the point of view of our consciousness, it's deeply mysterious. It may of course be that in some way consciousness is just an illusion and there is nothing special about this particular experience. Though, the illusion does appear to be extremely convincing.

--

Occasionally one runs into discussions about the simulation argument according to which we almost certainly live in a simulation because if simulations are possible and run then there are going to be very large amounts of them. While this is certainly somewhat entertaining argument, there isn't particularly much one can deduce from it. Whether we are in a simulation or not tells us nothing about where these simulations ultimately originate from and also doesn't tell us anything about our place in the hierarchy of the simulations (for example how deep we are from the fundamental underlying universe), unless of course we can somehow acquire empirical knowledge concerning them.

Quinine in tonic water converting 405nm (violet) laser light into 450nm (blue) by fluorescence. Diluting tonic water down to a single quinine molecule should allow antibunching to be observed by a detector capable of resolving single photons on timescales less than fluorescence lifetime of 20ns. Only a single photon from a single emitter on average within fluorescence lifetime can be emitted regardless of the number of photons in the exiting laser pulse.

Also, what might be worth considering is that at least in this particular universe (or simulation) all systems whether they be simulations or not, appear to interact with their environment to some extent and it is in fact impossible to create a perfectly isolated systems. This is why for example row hammer exploit [https://en.wikipedia.org/wiki/Row_hammer] is possible. Therefore no simulation is fundamentally any different from just a weakly coupled system in the most fundamental underlying universe. In certain sense creatures living in a simulation are then nothing more than caged animals born in captivity. Not that different from what we are now (as we are also caged by at least the limits of our current physical bodies and consciousness). Of course no particular reason why this couldn't change in the end.

What ought to be done?

What we are forced to ask every now and then is, what do we truly want?

This question kind of contains all meaningful questions concerning morality, ethics, right and wrong and in general all conceivable oughts. Even when we ask if we have the right to decide this for some other species, we're simply asking what we truly want - what kind of rights we wish to grant the other species. It's all on us whether we want it or not.

Of course we also have to ask ourselves more specific questions like what we want as a group or as a species and at the same time what we want as individuals, but these are simply extension of the "other species". These are the only meaningful prescriptive questions. Even if you're a religious person, the situation doesn't change very much. Your deity might act as an additional source of prescription to you and you might think you have access to their prescription as a description, but I posit that you are still faced with the exact same questions as the rest of us who don't believe. You need to ask yourself how you wish to value your supposed deity's prescription and determine what, if any, describes your deity's prescription most accurately. It's all on you. Even the methods are exactly the same, your very own reason and judgement.

What is the origin of their will and motivation ultimately? Why they feel thighs ought to be one way instead of the other? My limited understanding is that our motivation is a result of natural selection, history of our species, our personal histories and partly because of the history of our societies. However, going back even further, it would appear that these are simply arbitrary coincidences, some of which have served our species well in the battle for survival, some less so.

These are arbitrary preferences. Generally people prefer to continue to exist and avoid suffering for example, but what is generally considered moral varies from group to group and the extent that it doesn't vary, appears to be mostly simply due to our biological similarity.

Knowing this does not limit us from acknowledging the consequences, for example, we understand it is likely in our interest to grant certain degree of equality to other people, given we don't know how our own lives are going to evolve. We might be the other people one day. It's like gambling, but for a rational person, it's not really gambling, it's investing. It could fail, but it's still better to play the stock market than it is to play the lottery.

Unavoidable conflicts between dissimilar groups are perfectly expected, but luckily most groups are at least somewhat rational and optimize by compromising. However, it is conceivable that conflicts that cannot be solved by negotiation might emerge. These are normally called wars and the worst ones are about survival and extermination rather than anything that could be reasoned.

Once we've determined what we want as a species, we only need to figure out how to best approach that goal. There basically exists only a single method to answer these question for us - science. Science is nothing more than a name for the rational process of fishing out the best model out of all the possible descriptions out there by any means imaginable. Science gives us a description of the universe including its inhabitants - us, and tells us how to best achieve our goals and what outcomes to expect given specific choices. It doesn't tell us what we ought to do. That task is left for us.

Every decision has consequences, typically both good and bad, often unavoidable. There are many ways to make a decision, none of which are necessarily any better than the other. We can aim for least suffering, most pleasure, least boredom, maximized fairness, longest life, maximum number of lives, maximum knowledge, maximum safety, etc. Many of these are mutually exclusive. Most pleasure could mean most suffering. Longest life could mean most boring life. Least suffering almost certainly means minimum number of lives. We can expect negative consequences due to our decisions as well as positive, there will almost certainly always be some of both. Maximizing the number of people is not going to maximize the quality of life for an individual, it might not even maximize the total sum of happiness. Not to mention it probably won't maximize the long term total sum considering all the generations to come who will have to live a life of scarcity when resources have been depleted by the previous generations. Some alternatives are obviously excluded, like maximum suffering. Although, it's not entirely clear we know how to do this either, because what is bad for the humanity now, might be good for the humanity later if we manage to save the planet and its resources for times when they can be more efficiently used. Economic growth tends towards faster depletion and increased rate of destruction. Diseases limit the number of people and save the environment. None of these alternatives are trivially good or bad. Never the less, to deny the nature of this answer, not to mention the existence of these questions and knowledge concerning them is to deny the truth and to deny who we are. We know that doing one thing now will favor some and hurt some others. Not deciding has its own consequences as well. That is the nature of the game. We shouldn't just ignore it.

The barrier has begun to yield

The following papers might have tremendous implications for astronomy as they imply telescopes far beyond our current ones can be built without making them any larger. In other words, they've beaten the diffraction limit, even for incoherent astronomical light sources.

In case you're unfamiliar with the diffraction limit, for telescopes it says that the ultimate limit for angular resolution is a function of the used wavelength and diameter of the used focusing element. For a microscope their resolution is a function of the wavelength and the index of refraction. That's why astronomical telescopes tend to be huge and microfabrication uses shorter wavelengths.

We already knew superlenses existed, but they were mostly limited to near field. Spatial-mode demultiplexing on the other hand can be utilized to beat the diffraction limit in the far field as well. While not entirely surprising, it's not everyday news. I can't wait to buy a telescope that allows me to see the footprints on the moon (likely not going to happen anytime soon).

This method has some similarities to Fourier transforms in a way that is decomposes the spatial modes of the electromagnetic field into orthogonal components that not only carry information about the amplitude, but phase as well.

Here's an unrelated figure.

Subdiffraction incoherent optical imaging via spatial-mode demultiplexing

https://arxiv.org/pdf/1608.03211v1.pdf

"The seemingly infinite enhancement offered by SPADE does not imply unlimited resolution for finite photon numbers. Provided that enough photons can be collected, however, the giant improvements over direct imaging should still be useful."


Far-field linear optical super-resolution via heterodyne detection in a higher-order local oscillator mode

https://arxiv.org/pdf/1606.02662v2.pdf

"If our technique is used with state-of-the art microscopes, precision on nanometer scales can be expected."

Achieving the ultimate optical resolution

https://doi.org/10.1364/OPTICA.3.001144

"Our results stress that diffraction resolution limits are not a fundamental constraint but, instead, the consequence of traditional imaging techniques discarding the phase information."

What can be shown, cannot be said.

When something is "known for certain" and we cannot doubt it, then we cannot truly speak of knowledge. An experience is something like this, it is rather like a simple reaction, an unavoidable brain state dictated by a thin causal chain, a quale (plural: qualia) if you will. Being our brain state, an essential part of what we are, we by definition cannot doubt its existence any more than we can doubt our own existence. This causal chain is what allows us and in fact forces us to be conscious and experience things, but knowledge is something more complicated.

Being unique to our particular brain states and history, it should not be a big surprise that qualia can never be communicated to others. We are all individuals and live unique lives, and this forbids anyone from truly knowing what it is to be some other individual. We can only communicate our experiences to others by assuming a degree of similarity, but you can never truly tell a blind person what it is like to see and you shouldn't expect to. After all, the causal chain leading to the experience of vision cannot be the same for the blind person as it is for the one seeing. Simply telling the physical facts does not reproduce this causal chain and therefore cannot lead to the same brain states.

So experience is an integral brain state to the existence of our consciousness, but existence of that state does not represent the nature of reality or fundamental truth underlying all of existence in any obvious way besides perhaps simply by existing. Qualia alone tells you nothing about the underlying reality. Like an apple falling from the tree, it has no particular meaning before meaning is assigned to it by a consciousness for example by using complicated correlations and words like apple, fall, tree and such that point to some interpretation, model, history, reoccurring experience and most of the time the ability to share these experiences to certain degree with other similar creatures of our kind.

Experience cannot be said to be primary or secondary representation of truth without interpreting the experience, and immediately when an interpretation is made, a claim is made. Something is said using some kind of language and the claim becomes subject to doubt. By building beliefs which are consistent with each other, i.e. increasing coherence, we are building knowledge.

All knowledge is uncertain, if it isn't uncertain, it isn't knowledge - only a reaction. We can never be sure of what the fundamental nature of the universe is simply based on our experience, but this does not prevent us from playing the game by building coherence. This has undeniable utility and allows us to experience a life much more diverse than that of a mere reacting puppet, even if we fundamentally still are only some kind of puppets of the "second degree", without true free will, but at least we're no longer simple puppets of the "first degree".

--

It is suggested that quantum entanglement emerges from the holographic principle stating that all of the information of a region (bulk bits) can be described by the bits on its boundary surface. There are redundancy and information loss in the bulk bits that lead to the nonlocal correlation among the bulk bits. Quantum field theory overestimates the independent degrees of freedom in the bulk.

https://arxiv.org/pdf/1109.3542v1.pdf

Quantum bomb

This is an experiment in which we wish to detect the presence of a bomb B without detonating it. However, the bomb will automatically detonate even if only a single photon hits it. One might intuitively think such detection is impossible, because in order to see something, one needs to shine light at it. However, turns out this is in fact possible and here's how.

A polarised photon is injected into the device and it experiences a rotation of A degrees by the rotator each time it passes through. It is passed through N times such that N*A = 90 degrees before being ejected. After the rotator the light is split into horizontally and vertically polarised components by a polarising beam splitter (PBS). The bomb is placed in the path of the weaker signal and the signals are combined with another PBS afterwards. The photon will remain polarised in the original orientation only if there was a bomb that prevented polarisation from being rotated. The probability of setting off the bomb is sin(A)^(2N) which approaches 0 as N approaches infinity and A approaches 0.

This outcome is a consequence of the fact that insignificantly small amount of light lost in one of the arms will prevent a large amount of light from rotating over a large number of circulations which would detonate the bomb. This works simply due to the fact that the lost light compared to the total in each rotation is insignificant compared to the rotation. While the polarisation is rotated by A, it's not difficult to see that loss becomes insignificant respect to A as A becomes small. Never the less, it is the elimination of this small signal which prevents the rotation from accumulating and consequently makes detection without large interaction possible. It is also closely related to quantum Zeno effect.

Rotation by 1 degree

This works even with a classical signal if the detector simply consists of light level detector which is set off when some threshold is exceeded. The only quantum mechanical aspect of this is that it will work with a single photon as well, implying that the photon didn't simply take one path or the other, but actually took both. One might also say that its wavefunction collapsed into one single polarisation each round because of the presense of the bomb. The experiment would seem to imply that these extremely small subphoton amplitudes are in some sense real even though one can only detect single photons.

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This paper [http://arxiv.org/pdf/1609.04050.pdf] seems to be of the opinion that the universe is discrete and finite. I'm sure some people find it pleasing.

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It is suggested that quantum entanglement emerges from the holographic principle stating that all of the information of a region (bulk bits) can be described by the bits on its boundary surface. There are redundancy and information loss in the bulk bits that lead to the nonlocal correlation among the bulk bits. Quantum field theory overestimates the independent degrees of freedom in the bulk. [https://arxiv.org/pdf/1109.3542v1.pdf]

Tripping balls

US states I've been to
1. Washington
2. Oregon
3. California
4. Nevada
5. Arizona
6. Colorado
7. Texas
8. Idaho
9. Montana
10. Wyoming
11. Utah
12. Wisconsin
13. Illinois
14. Indiana
15. Michigan
16. Ohio
17. Pennsylvania
18. New York
19. Virginia
20. North Carolina
21. South Carolina
22. Georgia
23. Florida
24. Tennessee
25. Kentucky
26. New Jersey
27. Maryland
28. Connecticut
29. Massachusetts
30. Vermont
31. New Hampshire
32. West Virginia
33. Delaware
34. Rhode Island

States I've not been to
1. New Mexico
2. North Dakota
3. South Dakota
4. Nebraska
5. Kansas
6. Oklahoma
7. Minnesota
8. Iowa
9. Missouri
10. Arkansas
11. Louisiana
12. Mississippi
13. Alabama
14. Hawaii
15. Alaska
16. Maine

I guess I will have to visit the remaining ones at some point, just to complete the list. And why not complete the list of Canadian provinces as well, though Nunavut might be a bit challenging.

Though, next of the previously unvisited locations I was thinking I might visit India, Nepal, China, Japan, Thailand, Vietnam, Australia, New Zealand, Israel, Argentina, Chile, Yukon, Alaska, Hawaii and then perhaps Africa in some way. Brazil, Peru, Korea and Russia might be worth visiting at some point as well. Not necessarily in any particular order. Of these locations I'm thinking Japan, Australia, New Zealand, Yukon, Alaska and Hawaii might be decent enough to visit alone, but I'm thinking other location might be nicer to visit with some company.

Some Nietzsche quotes, just for the sport of it...

“I mistrust all systematizers and avoid them. the will to a system is a lack of integrity.”

"Two great European narcotics, alcohol and Christianity."

"You have your way. I have my way. As for the right way, the correct way, and the only way, it does not exist."

"Faith: not wanting to know what the truth is."

"A thinker sees his own actions as experiments and questions--as attempts to find out something. Success and failure are for him answers above all."

"Today as always, men fall into two groups: slaves and free men. Whoever does not have two-thirds of his day for himself, is a slave, whatever he may be: a statesman, a businessman, an official, or a scholar."

"They muddy the water, to make it seem deep."

"Is life not a thousand times too short for us to bore ourselves?"

"I know of no better life purpose than to perish in attempting the great and the impossible."

"It is my ambition to say in ten sentences what others say in a whole book."

"To live is to suffer, to survive is to find some meaning in the suffering."

"Convictions are more dangerous foes of truth than lies."

"My solitude doesn’t depend on the presence or absence of people; on the contrary, I hate who steals my solitude without, in exchange, offering me true company."

"A thought comes when it will, not when I will."

"He who climbs upon the highest mountains laughs at all tragedies, real or imaginary."

"Many are stubborn in pursuit of the path they have chosen. Few in pursuit of the goal."

"One loves ultimately one's desires, not the thing desired."

"Most people are far too much occupied with themselves to be malicious."

"The vanity of others runs counter to our taste only when it runs counter to our vanity."

"Character is determined more by the lack of certain experiences than by those one has had."

"We would not let ourselves be burned to death for our opinions: we are not sure enough of them for that."

"Every word is a prejudice."

Sometimes it's almost scary how much I have in common with this guy.