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(Big Think)   We didn't discover the "smoking gun" evidence for the Big Bang until the mid-1960s. We could have done it much earlier just by looking at the TV static on channel 03   (bigthink.com) divider line
    More: Weird, Redshift, Cosmic microwave background radiation, Big Bang, Universe, Galaxy, Physical cosmology, primeval abundances of the light elements, General relativity  
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974 clicks; posted to STEM » on 11 Aug 2022 at 10:20 AM (7 weeks ago)   |   Favorite    |   share:  Share on Twitter share via Email Share on Facebook



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2022-08-11 8:49:32 AM  
Yes
That's another thing they used to teach in school
 
2022-08-11 9:28:00 AM  

cretinbob: Yes
That's another thing they used to teach in school


I went to school in the 70s and 80s and never heard of it.  Cool find subby.
 
2022-08-11 10:17:46 AM  

enry: cretinbob: Yes
That's another thing they used to teach in school

I went to school in the 70s and 80s and never heard of it.  Cool find subby.


Really?
I can see that, since we didn't go to the same school.
 
2022-08-11 10:32:34 AM  
I thought it was on channel 02...
Look out your window, I can see his light
If we can sparkle, he may land tonight
Don't tell your poppa or he'll get us locked up in fright
 
2022-08-11 10:37:17 AM  
(canned laughter)
 
TWX
2022-08-11 10:37:49 AM  
That static makes a great seed for random number generation.
 
2022-08-11 10:44:55 AM  
That information was shared in the original Cosmos series.
 
2022-08-11 10:52:45 AM  
"... channel 03..."

hmmmm...

channel 3...

3 = э = z

The B-52's were right! The answer is on Channel Z!
 
2022-08-11 10:53:20 AM  
I used to turn it to channel 3 to see scrambled porn.
Talk about a big bang.
 
2022-08-11 10:56:37 AM  
OK, Ethan, help me out here.  Below is TV channel 03 from 60 to 66 MHz at a 10 MHz sample rate through an SDRPlay brand RSP1A SDR receiver.  Screencap taken just now.

What am I looking at?  Where's the CBR ?

Fark user imageView Full Size
 
2022-08-11 10:59:08 AM  
Weren't there some stations that broadcast on channel 3? That's why the RF modulator on old video game consoles let you switch between 3 and 4.
 
2022-08-11 11:01:59 AM  
They're hee-ere
 
2022-08-11 11:03:32 AM  

Olympic Trolling Judge: Weren't there some stations that broadcast on channel 3? That's why the RF modulator on old video game consoles let you switch between 3 and 4.


Yes -- NBC broadcast on three in the greater philly area.
 
2022-08-11 11:11:40 AM  

SansNeural: OK, Ethan, help me out here.  Below is TV channel 03 from 60 to 66 MHz at a 10 MHz sample rate through an SDRPlay brand RSP1A SDR receiver.  Screencap taken just now.

What am I looking at?  Where's the CBR ?

[Fark user image 850x388]


Buried in the noise. To see it, you'd need to get rid of all the other noise sources - weather, electrical appliances nearby, radio noise from the Sun, cosmic rays, etc.

In other words, you can't discover it with a TV. You can discover it with a very large antenna well shielded against noise in the sky, and this was how it was discovered, because when the Big Ear antenna at OSU detected it, they spent months trying to track down where that noise was coming from, and after they had accounted for everything they could tell could be there in that amount, they realized it wasn't noise - it was signal, and they had the first antenna able to reject enough other noise to see it.

Also, it looks like in the distance you have something broadcasting on channel 3, judging by the wide band noise bump on the lower half of the waterfall. Too distant to capture a useful signal. Wikipedia has a list of channels still on VHF 3 (all brodcasting digital now) if one of them is sort of close to you that may be what that is.

https://en.wikipedia.org/wiki/Channel_3_digital_TV_stations_in_the_United_States
 
2022-08-11 11:11:58 AM  
E. Siegel: "In a world where experts tell you over and over "don't try this at home," this is one lost technology we shouldn't forget."

Yeah, yeah.  We have new technology that is, arguably, in easier reach to most people than an old, analog TV.  Your article and "Someday, you'll be the last one who remembers" makes it seem like a last chance thing.  But no, we have much more appropriate receivers and ability to apply software to pull out or suppress any known signals...

OK, I did a little research myself.  Some folks have already used SDR to detect cosmic background radiation at 78 MHz (old TV channel 5, the "hydrogen line 1.4 GHz red-shifted to a center around 78 MHz).

DO NOT click their link for "the paper"... its domain now points to spam/crap.
 
2022-08-11 11:17:10 AM  
Decades old news is so exciting. That part of the static is from the big bang has been a staple of pop science seemingly forever.
 
2022-08-11 11:17:57 AM  

I hereby demand that I be given a Fark account: Buried in the noise. To see it, you'd need to get rid of all the other noise sources


Yeah, I read the article and was being deliberately obtuse to poke at TFA.  I usually find his articles interesting at the very least, though I often can't follow them well.  This time it's a topic I'm at least fairly familiar with (the RF, not the CBR part, me holding an Amateur Extra license and an SDR zealot).

The issue I take with it is he's glossed over any useful HOWTO details and made it seem like an old TV is the only way this magic can be seen - and it's a LAST CHANCE!
 
2022-08-11 11:20:42 AM  
Only thing I ever used Channel 3 for was connecting the cable box.  Those were the days.

Fark user imageView Full Size


Fark user imageView Full Size
 
2022-08-11 11:23:53 AM  

Olympic Trolling Judge: Weren't there some stations that broadcast on channel 3? That's why the RF modulator on old video game consoles let you switch between 3 and 4.


Yes. I call BS on the "channel 3 bit". The story of Penzias finding the CBR is true. He was working for Bell Labs and got the Nobel for his discovery.

Channel 3 had the Hartford station (WFSB) on it when I was in college in the 70s. And Channel 2 was WGBH, a Boston station. I don't think there was ever a situation where you had both channel 2 and channel 3 transmitters active, so one of those channels was usually vacant. Along with a whole lot of other VHF channels (I think we usually had 3-5 of the 11 available channels in use.

A TV set isn't sensitive enough to pick up the CBR. Penzias was using a microwave receiver anyway.
 
2022-08-11 11:27:24 AM  
 
2022-08-11 11:36:05 AM  

enry: cretinbob: Yes
That's another thing they used to teach in school

I went to school in the 70s and 80s and never heard of it.  Cool find subby.


In school at the same time.  Learned about this one afternoon from Mr. Wizard.
 
2022-08-11 11:47:33 AM  

Flowery Twats: Olympic Trolling Judge: Weren't there some stations that broadcast on channel 3? That's why the RF modulator on old video game consoles let you switch between 3 and 4.

Yes. I call BS on the "channel 3 bit". The story of Penzias finding the CBR is true. He was working for Bell Labs and got the Nobel for his discovery.

Channel 3 had the Hartford station (WFSB) on it when I was in college in the 70s. And Channel 2 was WGBH, a Boston station. I don't think there was ever a situation where you had both channel 2 and channel 3 transmitters active, so one of those channels was usually vacant. Along with a whole lot of other VHF channels (I think we usually had 3-5 of the 11 available channels in use.

A TV set isn't sensitive enough to pick up the CBR. Penzias was using a microwave receiver anyway.


The CBR is natively microwave. It's the redshifted (frequency lowered because of apparent/relative receding motion) stuff that shows up in the tens of MHz region and not just at "TV channel 3".  A/the primary CBR frequency is the "hydrogen line" at ~1.4 GHz.  Generally when looking for CBR you're looking for that either at its native frequency or red-shifted on account of relative motion or just universal expansion in general.

That CBR redshift down to all-over-the-farking-place is something Siegel didn't mention and, by talking only about TV channel 3, implies there's something magic around 63 MHz.  There isn't.
 
2022-08-11 11:54:18 AM  

MrBonestripper: enry: cretinbob: Yes
That's another thing they used to teach in school

I went to school in the 70s and 80s and never heard of it.  Cool find subby.

In school at the same time.  Learned about this one afternoon from Mr. Wizard.


In school at the same time.  Didn't have a TV.  Had an Encyclopedia Britannica set from the '60s though.  If there was a hydrogen line in there, I didn't find it :|
 
2022-08-11 12:00:00 PM  
"The unique prediction of the Big Bang model is that there would be a leftover glow of radiation permeating the entire Universe in all directions"
If i understood correctly, it surrounds us and penetrates us; it binds the galaxy together.
lol.
 
2022-08-11 12:03:03 PM  
Omg i thought for a second that the tv had a little puritan hat on.
 
DVD
2022-08-11 12:16:51 PM  
Fark user imageView Full Size


They're heeerrre....
 
2022-08-11 12:19:00 PM  
When my old man was getting his teaching degree in the '70s (in his 40s), he got an A from his physics prof (that didn't understand electronics) by removing the crt from a tv chassis, tuning it to something (I can't remember) that gave an occasional chirp and claiming he was "tracking Sputnik".

He also told another prof, to his face, that he was glad that the "university's standards have improved" when he pointed out that the paper he plagiarized got an A in a previous year, but was worth a D when he handed in the same paper, with corrections.

It sounds like he's a "work smart not hard" kinda guy, but he just didn't suffer fools
 
2022-08-11 12:20:22 PM  

SansNeural: DO NOT click their link for "the paper"... its domain now points to spam/crap.


Would an old link on archive.org be safe to click on?
 
2022-08-11 12:22:28 PM  

Flowery Twats: ...And Channel 2 was WGBH


I can't look at those letters without hearing an analog synth riff in my head
 
2022-08-11 12:27:13 PM  

SansNeural: Flowery Twats: Olympic Trolling Judge: Weren't there some stations that broadcast on channel 3? That's why the RF modulator on old video game consoles let you switch between 3 and 4.

Yes. I call BS on the "channel 3 bit". The story of Penzias finding the CBR is true. He was working for Bell Labs and got the Nobel for his discovery.

Channel 3 had the Hartford station (WFSB) on it when I was in college in the 70s. And Channel 2 was WGBH, a Boston station. I don't think there was ever a situation where you had both channel 2 and channel 3 transmitters active, so one of those channels was usually vacant. Along with a whole lot of other VHF channels (I think we usually had 3-5 of the 11 available channels in use.

A TV set isn't sensitive enough to pick up the CBR. Penzias was using a microwave receiver anyway.

The CBR is natively microwave. It's the redshifted (frequency lowered because of apparent/relative receding motion) stuff that shows up in the tens of MHz region and not just at "TV channel 3".  A/the primary CBR frequency is the "hydrogen line" at ~1.4 GHz.  Generally when looking for CBR you're looking for that either at its native frequency or red-shifted on account of relative motion or just universal expansion in general.

That CBR redshift down to all-over-the-farking-place is something Siegel didn't mention and, by talking only about TV channel 3, implies there's something magic around 63 MHz.  There isn't.


There is - the CBR is very close to the blackbody radiation from a body at 3K. It's not a distinct frequency, it's a curve. The peak of the curve is in the microwave band (which is why it's also called the CMB, the Cosmic Microwave Background) but there are definitely detectable emissions at 60Mhz, if your receiver is sensitive enough and other sources of radiation at 60MHz aren't swamping out the very weak signal. Of course, it's much easier to see if you're receiving at much higher frequencies, but the peak emission is at 160.4GHz, and it was detected by a telescope working near 2.4GHz.

Aside: I was confused. It wasn't the Big Ear that found it (the Big Ear was the Wow! signal) it was the Holmdel Horn Antenna, which was built by Bell Labs as part of Project Echo, the first telecommunications satellite.
 
2022-08-11 12:29:16 PM  

ZMugg: "... channel 03..."

hmmmm...

channel 3...

3 = э = z

The B-52's were right! The answer is on Channel Z!


Username denotes a snifter of expertise.
 
2022-08-11 12:32:47 PM  

phaseolus: Flowery Twats: ...And Channel 2 was WGBH

I can't look at those letters without hearing an analog synth riff in my head


Have an earworm

WGBH Boston TV Logo
Youtube EUWygGsyCyY
 
2022-08-11 12:41:35 PM  
When it came to old black and white TVs, I thought the big bang was the sound you heard after smacking the TV in order to get the picture to stop jumping.
 
2022-08-11 12:53:09 PM  

SansNeural: OK, Ethan, help me out here.  Below is TV channel 03 from 60 to 66 MHz at a 10 MHz sample rate through an SDRPlay brand RSP1A SDR receiver.  Screencap taken just now.

What am I looking at?  Where's the CBR ?

[Fark user image 850x388]


The CBR is a thermal (black-body) spectrum, peaking at about 100 GHz (much longer wavelength than warm objects, like the earth, which peaks in IR, or sun, which peaks in visible).  Channel 2 (in the US) is 54-60 MHz, and channel 3 is 60-66 MHz. At those frequencies, the CBR is down around 50 or 60 dB from its peak, but it's there. However, at those frequencies, galactic noise and atmospherics each contribute about 100,000 K of noise, and the earth contributes 290 K, so you have to calibrate and subtract those out to see the 2.7 K CBR. It's there, but not easy to see.

In your plot, it's probably not there unless you have a lot of dynamic range and a really low-noise front end. I think you'd need at least 24-bit samples, or it will be below the quantization noise of your sampler. It's also probably well outside the dynamic range of a TV set, so although it's technically there, it's not resolvable under the other noise sources.

Strictly speaking, the atmospherics and galactic noise are not thermal, but they are diffuse and broadband, and radio astronomers like to characterize all broadband noise sources by temperature, even when they're not a black-body spectrum. The Sun and Jupiter also radiate a lot at 54-66 MHz, but they're point sources, so their contribution probably isn't large unless you have a high gain antenna pointing at them.

For terrestrial observations, there's a nice window around 1-10 GHz where galactic and atmospheric noise fall off and atmospheric absorption and photon shot noise hasn't picked up. Penzias and Wilson were listening at 4.08 GHz, so they were in a good spot. They also had a high-gain antenna, so they were avoiding most of the 290 K earth radiation (about 0.1 K did sneak in via back lobes.) They measured 6.7 K, of which 3.5 K couldn't be accounted for with known contributors. Subsequent measurements at other frequencies (e.g. Roll and Wilkinson at c. 10 GHz) established the slope of the curve, which got us the generally accepted value of 2.7 K.

Above the atmosphere, higher frequencies are a better choice, COBE uses 31, 53 and 90 GHz, and also far IR (on the other side of the peak.)

/source: Radio Astronomy, 2nd edition, John D. Kraus (my copy is well-worn, and has a permanent bookmark in the section on radio sky sources, I need to know this stuff to earn my keep.)
//TLDR: it's there, but you won't learn anything about the CBR staring at static on a TV screen.
 
2022-08-11 1:01:13 PM  

SansNeural: OK, Ethan, help me out here.  Below is TV channel 03 from 60 to 66 MHz at a 10 MHz sample rate through an SDRPlay brand RSP1A SDR receiver.  Screencap taken just now.

What am I looking at?  Where's the CBR ?

[Fark user image 850x388]


Ethan's article is kind of misleading and buries the lede which seems to be a pattern with his articles. The CBR only 1% of the signal and it's drowned out by terrestrial radio signals and solar radiation. Buried in the article:

If you wanted to perform the ultimate experiment imaginable, you could power a rabbit-ear-style television set on the far side of the Moon, where it would be shielded from 100% of Earth's radio signals. Additionally, for the half of the time the Moon experienced night, it would be shielded from the full complement of the Sun's radiation as well. When you turned that television on and set it to channel 03, you'd still see a snow-like signal that simply won't quit, even in the absence of any transmitted signals.

So all you have to do is take your SDR or an old TV to the far side of the moon at night and you'll be able to pick it up.
 
2022-08-11 1:04:34 PM  

I hereby demand that I be given a Fark account: There is - the CBR is very close to the blackbody radiation from a body at 3K. It's not a distinct frequency, it's a curve. The peak of the curve is in the microwave band (which is why it's also called the CMB, the Cosmic Microwave Background) but there are definitely detectable emissions at 60Mhz, if your receiver is sensitive enough and other sources of radiation at 60MHz aren't swamping out the very weak signal. Of course, it's much easier to see if you're receiving at much higher frequencies, but the peak emission is at 160.4GHz, and it was detected by a telescope working near 2.4GHz.

Aside: I was confused. It wasn't the Big Ear that found it (the Big Ear was the Wow! signal) it was the Holmdel Horn Antenna, which was built by Bell Labs as part of Project Echo, the first telecommunications satellite.


But the point about the red-shift is important. The BB didn't start at a point. The universe was a really big hot mass of gases at the beginning. So big (billions of LY across) that the red-shifting between the opposite edges of the newly birthed universe would smear frequencies across a wide chunk of spectrum.
 
2022-08-11 1:04:53 PM  

SansNeural: The CBR is natively microwave. It's the redshifted (frequency lowered because of apparent/relative receding motion) stuff that shows up in the tens of MHz region and not just at "TV channel 3".  A/the primary CBR frequency is the "hydrogen line" at ~1.4 GHz.  Generally when looking for CBR you're looking for that either at its native frequency or red-shifted on account of relative motion or just universal expansion in general.

That CBR redshift down to all-over-the-farking-place is something Siegel didn't mention and, by talking only about TV channel 3, implies there's something magic around 63 MHz.  There isn't.


I don't know if Ethan's right, but you didn't do much better.

1. CMB is blackbody radiation, you won't find hydrogen lines in it.  Hydrogen lines come from a different kind of radiation.

2. The microwave frequency is what we get after redshift.  CMB is not "natively microwave", when it was originally emitted the peak was visible light (3000 K).  And the redshifting isn't "all over the place", it's the same amount no matter what.

3. The radiation itself could be said to be "all over the place": blackbody radiation is not a single frequency but covers a whole range of frequencies.  But the peak of the CMB radiation is at about 160 GHz, which is around 1-10 thousand times the frequency of television signals (which are are in the MHz range).  So the strength of the CMB in television frequency range is very, very low, definitely not 1% of the noise.

Giving Ethan the benefit of the doubt, I suspect that Channel 3 (the old analog channel 3, probably not the much narrower digital channel 3) has a tuning frequency that might pick up a stray harmonic of the peak CMB frequency.  It would not be a lot (only 1% of background noise, apparently) but I'd guess that a harmonic of the CMB peak is much stronger than the CMB at that frequency.  And I suppose he singled it out Channel 3 because it's the channel with the strongest effect.
 
2022-08-11 1:15:09 PM  

I hereby demand that I be given a Fark account: Aside: I was confused. It wasn't the Big Ear that found it (the Big Ear was the Wow! signal) it was the Holmdel Horn Antenna, which was built by Bell Labs as part of Project Echo, the first telecommunications satellite.


When I worked there, Big Ear ran a differential feed (we called it a Dicke switch, but it wasn't quite the same as the scheme Dicke invented.) The effect was to subtract out the background (CBR as well as some other noise sources) in order to better resolve discrete sources.
There might have been some  CBR observation before my time (it went through a lot of receiver changes in 35 years), but our mesh spacing was only good up to about 2.6 GHz, not ideal for CBR measurement. We also had more directivity than would be ideal for observing a diffuse source.
 
2022-08-11 1:15:16 PM  

Rage Against the Thorazine: If you wanted to perform the ultimate experiment imaginable, you could power a rabbit-ear-style television set on the far side of the Moon, where it would be shielded from 100% of Earth's radio signals. Additionally, for the half of the time the Moon experienced night, it would be shielded from the full complement of the Sun's radiation as well. When you turned that television on and set it to channel 03, you'd still see a snow-like signal that simply won't quit, even in the absence of any transmitted signals.

So all you have to do is take your SDR or an old TV to the far side of the moon at night and you'll be able to pick it up.


Bah, you'd see snow even in a deep cave that CMB can't penetrate.  Television (and most RF communication equipment in general) works by isolating and amplifying frequencies, and no matter how weak the signal is, it gets amplified to around the same relative strength.  (This is because the radio waves are a carrier signal, not the signal itself.)  If there are no stray radio waves to pick up, there is still noise in the electonics themselves.
 
2022-08-11 1:19:01 PM  
Penzias and Wilson won the Nobel for finding something they weren't looking for.  It took some Princeton guys to explain what it was.  They were looking for the CBR, as it had been predicted in the 1940s  Bell labs had the bigger antenna and found it first.
 
jbc [TotalFark]
2022-08-11 1:26:53 PM  
atariage.comView Full Size


Well I'll be damned. He's right.
 
2022-08-11 1:40:46 PM  
Nods approvingly
Cyanotic "Static Screens"
Youtube lRG0Y3j4Rgk
 
2022-08-11 2:27:49 PM  
no such thing as the big bang, it's just guano.
 
2022-08-11 5:01:38 PM  

MrBonestripper: enry: cretinbob: Yes
That's another thing they used to teach in school

I went to school in the 70s and 80s and never heard of it.  Cool find subby.

In school at the same time.  Learned about this one afternoon from Mr. Wizard.


I don't remember where I learned it, But I did watch a lot of TV static. There are patterns if pay close attention. I probably figured it out during a demonstration of a Crook's tube or similar CRT.
I was as weird a kid as I am an adult.
 
2022-08-11 5:46:39 PM  

Flowery Twats: https://en.wikipedia.org/wiki/Arno_Allan_Penzias


came to post that
or this
https://en.wikipedia.org/wiki/Robert_Woodrow_Wilson
 
2022-08-11 6:46:35 PM  
I forgot to mention -- Katie Mack's excellent book The End of Everythinghas a wonderful retelling of the whole Penzias and Wilson discovery, and the happy accidents surrounding how all the pieces finally dropped into place.
 
2022-08-11 7:28:58 PM  

I hereby demand that I be given a Fark account: SansNeural:

Erick Von Tutri IV:
Rage Against the Thorazine:
aerojockey:


Thanks for all the good input, Farkers.  Like I said, I grok the RF but not really the rest.
 
2022-08-11 7:44:47 PM  
The fact that you have to turn your TV to channel 3 to see the evidence of the universe's creation proves we're living in a simulated video game.
 
2022-08-11 8:26:46 PM  

aerojockey: SansNeural: The CBR is natively microwave. It's the redshifted (frequency lowered because of apparent/relative receding motion) stuff that shows up in the tens of MHz region and not just at "TV channel 3".  A/the primary CBR frequency is the "hydrogen line" at ~1.4 GHz.  Generally when looking for CBR you're looking for that either at its native frequency or red-shifted on account of relative motion or just universal expansion in general.

That CBR redshift down to all-over-the-farking-place is something Siegel didn't mention and, by talking only about TV channel 3, implies there's something magic around 63 MHz.  There isn't.

I don't know if Ethan's right, but you didn't do much better.

1. CMB is blackbody radiation, you won't find hydrogen lines in it.  Hydrogen lines come from a different kind of radiation.

2. The microwave frequency is what we get after redshift.  CMB is not "natively microwave", when it was originally emitted the peak was visible light (3000 K).  And the redshifting isn't "all over the place", it's the same amount no matter what.

3. The radiation itself could be said to be "all over the place": blackbody radiation is not a single frequency but covers a whole range of frequencies.  But the peak of the CMB radiation is at about 160 GHz, which is around 1-10 thousand times the frequency of television signals (which are are in the MHz range).  So the strength of the CMB in television frequency range is very, very low, definitely not 1% of the noise.

Giving Ethan the benefit of the doubt, I suspect that Channel 3 (the old analog channel 3, probably not the much narrower digital channel 3) has a tuning frequency that might pick up a stray harmonic of the peak CMB frequency.  It would not be a lot (only 1% of background noise, apparently) but I'd guess that a harmonic of the CMB peak is much stronger than the CMB at that frequency.  And I suppose he singled it out Channel 3 because it's the channel with the strongest effect.


60MHz (channel 3) isn't any kind of a harmonic of 160GHz.  To be a harmonic, it needs to be higher in frequency and a multiple of the fundamental. And the graph in TFA shows not a lot of energy at 60MHz. There's no peak there that I can see. So the channel 3 stuff is pure garbage. The "snow" you see on a vacant channel is mostly thermal noise from the cheap front end of your receiver, which doesn't need to be that sensitive to detect a multi kW TV broadcast. if I were being very generous, I would say the author was trying to give an example that people could relate to, but he's about 20 years too late and it's BS anyway.
 
2022-08-12 1:18:43 AM  

Flowery Twats: To be a harmonic, it needs to be higher in frequency and a multiple of the fundamental. And the graph in TFA shows not a lot of energy at 60MH


There are other possibilities, for example it could match or be a multiple of the ratio between carrier frequency and some major frequency in the signal.  If that were the case, that wouldn't appear on the blackbody spectrum chart, the idea is you're picking up something due to resonance somewhere in the system.  Yes, that would still mean most of the snow is from other sources of noise, Ethan only claimed CMB was 1%.  Channel 3 is not exactly 60 MHz BTW, in fact it's a range ("band" if you will).

I don't know, it probably is bullshjt.  Like I said, I was giving Ethan benefit of the doubt.
 
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