Mushroom season is well under way and this weekend in the Middlesex Fells I came across the largest patch of ‘Chicken of the Woods’ mushroom (Laetiporus sulphureus). See below:
This lovely mushroom is apparently edible but I didn’t take any to try. Regretting that now. It should be cooked and even them there are some adverse reactions reported. Mostly stomach upset. It is not dangerous or deadly. It should also be eaten when young. This specimen was very fresh. Here is a closeup:
It was still very thick and wet and had not been attacked by bugs or deer yet (both of which will happily eat it – and I have seen deer in the area, although infrequently).
All in all it was a lovely walk that morning. Fresh cool summer air – and I was out before the flying bugs got annoying. When leaving the area I spotted another patch on the back side of the tree:
These two patches to the right were younger and probably still developing. All in all a great day out there. I’ve developed an interest in getting there early in the mornings when there are less people and everything is just fresher before the heat of the day disturbs everything.
We recently had some warm weather often extremely frigid conditions between Christmas 2017 and the first week and a half of 2018. Well, it warmed up to about 13 °C / 55 °F on Saturday so I hit up the Middlesex Fells with the dog.
Over Christmas I’ve been reading more and more about fungus and mushrooms and I really wanted to go to a few locations where I had seen mushrooms during the summer and autumn season last year. So the first place I went was a silver birch tree very close to the east side of Bellevue Pond on South Border Rd, Medford, MA, USA. I had seen these really curious white balls on this live tree in early September and at the time I really didn’t know what they were. They certainly looked fungal/mushroomy but I was expecting to see a more typical mushroom shape and was surprised that if this was a mushroom that it could push through the bark. See the images below:
Fast forward to now and after significant snow melt, the same tree looks like this:
Cool, they did turn into a more typical ‘mushroom’ shape. After some web searches and reference mushroom books I identified this mushroom as the birch polypore (Fomitopsis betulina). One of the lobes/caps had fallen off and was on the ground nearby so I picked it up and flipped it over.
You can see the underside doesn’t have gills but pores. The margin (edge) of the cap rolls over and under the underside, exactly matching the birch polypore description. (I took this sample home!) Below is a closeup on the cap that formed at the bottom of the tree – it was still attached.
It turns out this mushroom is edible but doesn’t taste very good. I didn’t eat this one. It contains a number of compounds that are suppose to be good at killing some intestinal worms and has anti-bacterial and anti-inflammatory properties. Well, research continues.
Another fungus I encountered was as an odd looking jelly-like mushroom. See below:
I wasn’t even sure this thing was a fungus. Some research showed that, yeap it is! And a well known fungus that comes out this time on year (deep winter). Its the amber jelly roll or willow rain (Exidia recisa). Apparently it is edible but does not have an interesting taste, nor is it fowl or bitter.
I have many more photos from last Summer and I may get into some more identifications of those as well. It is amazing how many different kinds of mushrooms are out there, even in the dead of winter.
So Solar Eclipse 2017 has come and gone. I managed to be outside for it – only partial here in Boston unfortunately. I put together a nice little shoebox viewer, which worked quite well. It was virtually impossible to get a good photo of it though, so no pictures. I was up Wright Tower in the Middlesex Fells where lots of others were out with a multitude of various ‘devices’ to see the partial eclipse.
So while I didn’t get a good shot of the sun being blocked, I did come home and hit up a web site with a series of satellite images of the US as the eclipse moved over the country. Below is a gif of the transit:
You can see the sun slowly rising over the western part of the country followed by a dimming of the light over Washington State and Oregon. The white splotch is presumably from the total darkness of the total eclipse area.
Most interesting is watching the speckled ‘cloud’, which looks like rising humidity as the day progresses, around the gulf of Mexico – Texas coast to Florida and up into Arkansas and Tennessee. When the totality of darkness moves through the area, this cloud disappears for a while, only to reform when it passes. Pretty cool effect!
Today I went on a nice little walk in the woods, just me and dog – like I do most weekends. Our favourite haunt is the Middlesex Fells, situated in the northern suburbs area of Boston. We’ve been going for about a year, so I have seen all seasons in the park/forest and know most of the trails quite well.
Oddly enough there is one area where I always seem to get a little lost. Not lost – lost. Just disorientated. In my own head I call this region the ‘Fells Triangle’ because I seem to lose all sense of orientation. Coincidently, this area also contains the site of an old silver mine. I’ve been looking for this mine and it turns out I’ve been looking in the complete wrong area for some time. The map of the area contains references to the old mine with a hill named for it and a path. In the picture below you can see in red the area I’ve been looking.
But it turns out it is located much closer to the reservoir, in the area circled in green. (I originally screwed this up and circled the area in blue – this is the wrong area and more proof this part of the Fells is weird and deserves its name as ‘The Fells Triangle’.) This green area is also where I always seen to get confused about where I am.
The mine is clearly labeled by the park with a sign up on a nearby tree. See below:
The flat depression in the center of this picture is actually a concrete slab that covers what used to be a huge hole dug out of the ground. Historic reports describe how workers used explosives to carve the mine but very little silver if any was ever found. I also recall reading how the miners used lots of water and since the location of the mine is closer to the reservoir waters, this all makes a lot more sense. There are also a number of concrete poles that are erected around it and look like they once carried planks of wood designed to keep people and/or animals out. The concrete slab is square and now well covered by nature’s debris and time:
I can only imagine how they managed to place this here. The concrete is reinforced with steel bars, which can be seen in a small hole that is in the center of the slab. The hole looks like it has been dug out by curious hikers who wanted to see into the remains of the mine:
There seems to be water at the bottom. I dropped some sticks into the hole and after a considerable time I heard it splash. I would estimate the depth to be more than 10 meters or the height of a three story building.
What possessed people to think there was silver here? Or anything of use? When I hit the ‘net’ looking for information on the Silver Mine I could find very little information. Now I’ve found it its tempting to hit google again and see what more I can find out. The whole thing just seems like an odd enterprise.
On the way there and back there was a number of wild flowers out. This time of year is great for hiking. The weather is starting to cool off, and like today the humidity can drop down quite a bit here in New England. But the summer flowers persist and look so much better in the less harsh light this time of year. I’ll post some pictures below. I have no idea what these flowers are or what the plant name is. I’ll try and figure it out and edit this post.
If you know more about the mine in the Middlesex Fells or the names of these flowers, feel free to drop me a line.
Following on from my last post, I’ve been trying to read the voltage values that are generated from the random number generator I put together. I was initially using an arduino unit so I could control the voltage output down to below 1 volt. Ultimately I want to read the values with an ESP8266 unit running micropython so I can upload the values to an internet based data logger and the ESP8266 is only 1 volt tolerant on its analog-to-digital pin. So, the voltage has to be controlled and I didn’t mind blowing up one of my arduinos (which are 5 volt tolerant). The voltage divider is now composed of a 10k resistor from positive rail to analog out and a 1k resistor from analog out to ground.
The ardunio was giving me readings up to about 180 unit out of 1024 which gives about 180/1024 * 5V = 0.8789 volts… nice and safe.
Reading these voltages with the ESP8266 gave some interesting results. The code to do this was very simple:
from machine import ADC
import timeadc = ADC(0)# create ADC object on ADC pinfor i in range(1000000):print(adc.read(), end=',')time.sleep_ms(10)
This reads a voltage every 10 milliseconds from the analog pin and reports one million of them. It took about 2.8 hours and the output was redirected to a file of type csv with this command on my mac:
ampy --port /dev/tty.SLAB_USBtoUART run readanalog.py > avalanche_noise.csv
I then analyzed this data in python using the jupyter web interface. A histogram plot of the values looks like this:
The values range from 135 to 674 with a mean of ~292.6. This distribution is obviously skewed too so it’s not gaussian distributed – maybe Poisson? But the most striking thing is the lines of empty space (no blue) – is this a plotting problem or are certain values skipped during the reads? Well lets zoom in around the top of the distribution.
So its true, some values are just never recorded. Its hard to believe the voltages from the circuit would do this. Also, its clear from the numbers that every 12th value is skipped. I think this must be an error in the way micropython reads the register so I’ll probably post this somewhere in the micropython forums and see if this is true or if I’m just doing something wrong.
Next I tried to fit this distribution to a gaussian curve. It failed. Here is the python code:
import math
import numpy as np
import matplotlib.pyplot as plt
import scipy as scipy
import scipy.stats as stats
from scipy.optimize import curve_fit
from scipy.misc import factorial
from scipy.stats import norm
%matplotlib inline # needed for plotting in jupyter
data_p = data # not really needed
fig = plt.figure(figsize=(20, 8))
entries, bin_edges, patches = plt.hist(data_p, bins=(int(np.amax(data_p)-np.amin(data_p))), range=[np.amin(data_p),np.amax(data_p)], normed=True)
bin_middles = 0.5*(bin_edges[1:] + bin_edges[:-1])
# poisson function, parameter lamb is the fit parameter
def gauss(x, *p):
A, mu, sigma = p
return A*np.exp(-(x-mu)**2/(2.*sigma**2))
# fit with curve_fit
p0 = [1., 260., 30.] # initial guesses for height, mean and SD
parameters, cov_matrix = curve_fit(gauss, bin_middles, entries, p0 = p0)
print parameters # print results
print np.sqrt(np.diag(cov_matrix)) # print errors of fit
# plot poisson-deviation with fitted parameter
x_plot = np.linspace(0, np.amax(data_p), 1000)
plt.plot(x_plot, gauss(x_plot, *parameters), 'r-', lw=4)
plt.show()
One way I like to think of the Poisson distribution and Poisson processes is as follows. They arise from discrete events that must always have a positive value – this is not true for Gaussian distributions. So, in our circuit, current (electrons) flow or do not flow. When they flow, a discrete (integer) number of them flow. There is a lower limit on the number that can jump the gap. That number is zero. The gaussian distribution is the limit of a binomial distribution as the number of events goes to infinity. The binomial distribution is based on the idea that an event either happens or does not. (N.B. this is different from the Poisson case because in that case, events either happen 1 or more times or do not happen). If we accumulate binomial events, there is no limit to how many ‘yes’ or ‘no’ events can happen so some of the distribution must extend as far as the number of events recorded – for gaussian this limit goes to infinity and negative infinity. The Poisson distribution doesn’t act this way. If we try and model the Poisson distribution as an infinite binomial distribution we quickly realize that while we can get an infinite number of ‘zero value’ events as well (with low probability) there is more than one other alternative. So the distribution must take into account these many possible values which stretches the distribution in the positive direction while there is a still a hard limit at zero. We can shift the Poisson distribution so ‘N’ zero-value trials will be plotted at ‘-N’ (like we would for a binomial distribution) but on the positive size, the curve would extend past ‘+N’ because some of those trials can have a value of more than 1.
Well my thought was that the numbers I’m reading don’t match the number of electrons actually flowing. This signal is amplified by the transistors and then quantized, not in nature, but by the ADC converter in the ESP8266. My hope is that this signal is proportional to the number of electrons that flowed during signal acquisition. But this signal is not the same as the number of electrons which will be behaving as a Poisson process. But the recorded numbers should be proportional to the number of electrons. So if we divide these values by some constant, can we get the fit to work, and at what optimal division factor.
Long story short, if I divide the 1000000 million points by 23.9 I get an optimal fit in terms of the error reported for the fitted parameter. That parameter, which is the mean value, is ~6.558336. Does this mean, that on average 6.5 electrons pass through the transistor while the ESP8266 is taking an ADC measurement? I think it might be! Here is the fit:
If I take these same numbers and try and fit a Gaussian curve, it doesn’t do as well.
Conclusions? The electrons that flow across the junction in reverse bias are behaving as a Poisson process as expected. The distribution is not flat. I’ve seen some discussion on the net where people seem to assume this would be the case. It does seem to be random! One of the next steps is to convert these numbers to a flat distribution or at least make it generate a binary sequence. It seems to be that XORing or Von Neumann filtering will not do a good job of removing the biasing that the Poisson distribution will introduce.
The notion of randomness has consistently intrigued me, so I have always wanted to build a random number generator and play with it. Just how easy is it to generate truly random numbers as opposed to pseudo-random numbers? First of all, pseudo-random numbers are based on an algorithm so computationally they are easy to generate but also easy to copy or determine the nature of the sequence. They also ‘repeat’ their pattern eventually, even if the repeat cycle might be very large. No, no, no. I want to generate random numbers from an unpredictable natural source such as radioactive decay, cosmic rays, radio noise or ‘avalanche noise’ (hint: not the noise of snow falling down a mountain).
The Source:
In short, avalanche noise is the noisy current flow when a diode is reverse biased (voltage applied the wrong way), once that voltage is high enough to make electrons jump over the semiconductor gap the wrong way. The nifty thing is transistors have these diode junctions and so current can flow, for example, from the base to the emitter in an NPN transistor once it is reverse biased with high enough voltage. So what many circuits do to generate random noise is set up a transistor in this way, and then amplifying the current that flows, which for ‘quantum energy gap’ reasons is noisy.
An Example Circuit:
Browsing the net I came across Rob Seward’s attempts at doing this and set up his circuit since I had all the components on hand. The circuit is below:
This is my understanding of this circuit: Here, Q1 is reverse biased with 12 V of EMF via the 4.7k resistor. Q2 is forward biased and so it should conduct with a small voltage drop (~0.9 V) across its base to emitter junction so the reverse bias in Q1 is actually ~11.1 volts through the 4.7k resistor. This should be enough to jump the gap as outlined in this great summary of this phenomenon by Giorgio Vazzana. If current randomly jumps the gap in Q1, this current will flow into the base of Q2 where it will be amplified by a common emitter setup and passed into the 0.1 uF capacitor. These spikes in current will pass through the capacitor and into the base of Q3, which is highly biased by the 1.5M resistor. I think whats going on here is this transistor is set up to be a switch – this high bias turns the collector to emitter current essentially off, so any current that flows into its base will turn it on. Thus a voltage appears at its collector (its also in common emitter mode). This voltage is divided by the two resistors of 10k and 4.7k and presented as an analog out signal.
I put this together and applied the analog out and a ground to some earbuds I had lying around. Faint noise!
I quickly wired up an arduino to take sample measurements of the voltage via an analogRead(). The values were peaking out at around 260 out of 1023 where 1023 would be a voltage of 5V. So Im seeing peak voltage here of about 1.25V. Ultimately I want to read these voltages with an ESP8266 unit or a raspberry pi which can only safely sample an analog voltage of 1V so I needed to play with the voltage divider. I’m not entirely sure why this works but I replaced the 10k resistor with a 22k resistor and the 4.7k resistor with a 10k resistor, which in turn dropped the analog reads to maximum reads of about 110 – or a little over half a volt. This is nice and safe.
The code I used for the arduino is here:
/*
Read analog signal on pin A0
*/
const int analogInPin = A0; // Analog pin that noise is fed at
int sensorValue = 0; // Inital sensor value
int low = 30; // Set a low value to be surpassed
int high = 40; // Set a high value to be surpassed
void setup() {
// initialize serial communications at 9600 bps:
Serial.begin(9600);
}
void loop() {
// read the analog in value:
sensorValue = analogRead(analogInPin);
// if value is higher than ever recorded, lets note it
if (sensorValue > high) {
Serial.print("high: ");
Serial.println(sensorValue);
high = sensorValue;
}
// if value is lower than ever recorded, lets note it
if (sensorValue < low) {
Serial.print("low: ");
Serial.println(sensorValue);
low = sensorValue;
}
// wait 2 milliseconds before the next read
// thats 500 samples per second
delay(2);
}
Whats next:
The next step before making an extensive set of analog reads is to add an OP amp so I can drive a speaker and listen to the noise out loud and make some recordings for here. Until then…
The recent flare up between rapper B.o.B and Neil DeGrasse Tyson over earth curvature has been interesting to watch. A nice summary can be found here (NPR link). B.o.B asserts not only that the earth is flat but that there is also a NASA coverup. It’s not clear why there would be a coverup.
So lets unpack this a bit. The tweet below is what set off the whole thing:
First, lets explain why our perceptions can be mistaken. B.o.B asks, “Where is the curve?”. Well it is right in front of his eyes but over a distance of 16 miles it is not perceptible. Sixteen miles is only about 0.064 % of the earths circumference (if you believe it has a circumference) which means there are over 1500 more of these distances in the great circle that includes these two cities. Now, imagine you cut a pie or an orange 1500 times, pull out a single slice and looked at its edge. How much evidence of the original curve do you think you will see? This is a classic mistake where we think we are seeing everything we need to see. And ‘seeing is believing’. ‘Our eyes are never mistaken’. This is wrong. And there is a litany of optical illusions on line that can demonstrate this. A classic is the straight lines that look bent.
It’s a different phenomenon but it illustrates the problem.
Another tweet B.o.B put out appears to be a from a list of reasons why the earth is flat. No doubt from a very trusted online source.
This contains a lie and demonstrates that the earth is curved, all in one poorly thought out argument. To begin, you can’t see Polaris 20 degrees South. But thanks for using a curved metric (what does 20 degrees mean if the earth is flat?) to prove the earth is not curved. Polaris is about 2 degrees off the Northern Pole so Polaris is visible from the Southern Hemisphere so long as you are very close to the equator and not too far south into the Southern Hemisphere. Any further south than Nairobi in Kenya and it does indeed never rise above the horizon.
So I guess Barak Obama never saw it either until he moved to the US. Yes, that is how dumb this all sounds.
Now lets get personal. I know all this about Polaris because I was born and grew up in the Southern Hemisphere. I never saw Polaris until one day I moved to the US. One of the first things I did was go out at night and look up at the night sky and look for all the constellations I had been told about but could never see. Heh, maybe I had been lied to. Think of it from my perspective. Time and again, we of the Southern Hemisphere are told how to find north by using the Pole Star and how to find it using the ‘Big Dipper’ (North American media is strong – it’s not called the big dipper anywhere else). What utter crap! There is no Big Dipper, no Pole Star! From my 33 Degrees South location, none of this is visible. But I could see the Southern Cross and the Magellanic Clouds, neither of which can be seen from most of the Northern Hemisphere and certainly not Atlanta (just saying).
These things are real, but you have probably never seen them for two reasons. 1) You probably have never heard about them and 2) You are probably from the Northern Hemisphere (see first reason) and the earth beneath you makes you point in the wrong direction to see it… because the earth is round. Just like it is impossible to see the Pole Star from the Southern Hemisphere. This is how I knew for sure the earth was curved – not that I ever doubted it but it was amazing to have it demonstrated. It was mind blowing and humbling. The Pole star was there, but my Southern Cross was gone. It hadn’t just been moved further down in the sky (like if the earth of flat)… it was gone!
So this is the fundamental problem. Our perspective can be so limiting some times its hard to think outside it. It’s easier to accept our small world view and assume a conspiracy of lies:
These two patches to the right were younger and probably still developing. All in all a great day out there. I’ve developed an interest in getting there early in the mornings when there are less people and everything is just fresher before the heat of the day disturbs everything.
