For the discussion of math. Duh.

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quarkcosh1
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As was pointed out to you in the first reply to this thread, you were previously asked to just start one new thread for your musings about the mathematical coincidences where one number is kinda near another. So, this shall be that thread. Do not start another. - gmalivuk

http://en.wikipedia.org/wiki/Monster_gr ... _structure

The = means approximately equal. I was looking at the subgroups of the monster group and 11 appears 6 times which seems kind of high since numbers slightly lower than it don't appear as many times. The best explanation I can think of as to why that is is because pi^3 - e^3 = 11 but I can't explain this connection any more deeply than this.

firesoul31
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### Re: pi^3 - e^3 = 11 and the monster group subgroup structure

I don't know enough about math to answer this, but 1) Why are you assuming there's some special reason for this?
2) Pi^3 - e^3 is not exactly equal to eleven, so why would that be the equation?

Not everything in math is intrinsically linked to some other number.

Also...

gmalivuk wrote:Like scratch123, who is probably the same person, I'm going to go ahead and lock most of these threads. If you insist on starting new discussions about random patterns you think you see between unrelated numbers, quarkcosh1, you can start one thread for all of them.

quarkcosh1
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### Re: pi^3 - e^3 = 11 and the monster group subgroup structure

firesoul31 wrote:I don't know enough about math to answer this, but 1) Why are you assuming there's some special reason for this?
2) Pi^3 - e^3 is not exactly equal to eleven, so why would that be the equation?

Not everything in math is intrinsically linked to some other number.

Also...

[quote=gmalivuk]Like scratch123, who is probably the same person, I'm going to go ahead and lock most of these threads. If you insist on starting new discussions about random patterns you think you see between unrelated numbers, quarkcosh1, you can start one thread for all of them.
[/quote]

gmalivuk is known for being incredibly biased so quoting him is pointless. There is even another topic on this board not made by me that compares the square root of 1/3 to another math constant. Also approximation is a perfectly legitimate area of math but sadly many people seem to be unaware how often it is used.

WibblyWobbly
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### Re: pi^3 - e^3 = 11 and the monster group subgroup structure

But don't forget firesoul31's point (2): pi3 - e3 = 10.9207... by my calculator. Definitely not exact, and really not even close enough to suggest anything more than a "huh" response. You get nearly the same level of accuracy from the assertion that pi2 = 10, but that's also not very interesting, IMO. Approximation is useful, as you say, but largely because approximations allow us to do mental math a little faster, not because approximations underlie some greater connections between the numbers. So, if you're saying just that it's a fair approximation, I'll say "sure, for some reason that you need to calculate pi3 - e3 in your head." Other than that, you're going to have to offer something more.

quarkcosh1
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### Re: pi^3 - e^3 = 11 and the monster group subgroup structure

WibblyWobbly wrote:But don't forget firesoul31's point (2): pi3 - e3 = 10.9207... by my calculator. Definitely not exact, and really not even close enough to suggest anything more than a "huh" response. You get nearly the same level of accuracy from the assertion that pi2 = 10, but that's also not very interesting, IMO. Approximation is useful, as you say, but largely because approximations allow us to do mental math a little faster, not because approximations underlie some greater connections between the numbers. So, if you're saying just that it's a fair approximation, I'll say "sure, for some reason that you need to calculate pi3 - e3 in your head." Other than that, you're going to have to offer something more.

The reason these numbers are interesting is because pi^3 = 31.00 while e^3 = 20.0 . Getting this close to an integer after only cubing the numbers is surprising.

WibblyWobbly
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### Re: pi^3 - e^3 = 11 and the monster group subgroup structure

quarkcosh1 wrote:
WibblyWobbly wrote:But don't forget firesoul31's point (2): pi3 - e3 = 10.9207... by my calculator. Definitely not exact, and really not even close enough to suggest anything more than a "huh" response. You get nearly the same level of accuracy from the assertion that pi2 = 10, but that's also not very interesting, IMO. Approximation is useful, as you say, but largely because approximations allow us to do mental math a little faster, not because approximations underlie some greater connections between the numbers. So, if you're saying just that it's a fair approximation, I'll say "sure, for some reason that you need to calculate pi3 - e3 in your head." Other than that, you're going to have to offer something more.

The reason these numbers are interesting is because pi^3 = 31.00 while e^3 = 20.0 . Getting this close to an integer after only cubing the numbers is surprising.

Why?

Edit: more to the point, perhaps, why is it surprising that you get "this close to an integer after only cubing the numbers"? Is there some some reason that low exponents are to be desired? Would higher exponents actually be more likely to be close to integers? (Also, e3 is closer to 20.1, but perhaps that depends on how you define "close to an integer", which you seem to be doing arbitrarily based on what you want to be interesting). I mean, again, depending on your definition of "close", pi2 is pretty close to 10, and I only had to use one constant and square it to get there.
Last edited by WibblyWobbly on Thu Feb 13, 2014 11:52 pm UTC, edited 1 time in total.

brenok
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### Re: pi^3 - e^3 = 11 and the monster group subgroup structure

quarkcosh1 wrote:
WibblyWobbly wrote:But don't forget firesoul31's point (2): pi3 - e3 = 10.9207... by my calculator. Definitely not exact, and really not even close enough to suggest anything more than a "huh" response. You get nearly the same level of accuracy from the assertion that pi2 = 10, but that's also not very interesting, IMO. Approximation is useful, as you say, but largely because approximations allow us to do mental math a little faster, not because approximations underlie some greater connections between the numbers. So, if you're saying just that it's a fair approximation, I'll say "sure, for some reason that you need to calculate pi3 - e3 in your head." Other than that, you're going to have to offer something more.

The reason these numbers are interesting is because pi^3 = 31.00 while e^3 = 20.0 . Getting this close to an integer after only cubing the numbers is surprising.

Pi^3 is 31.01 and e^3 is 20.1
And why is it surprising exactly?

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### Re: pi^3 - e^3 = 11 and the monster group subgroup structure

quarkcosh1 wrote:
firesoul31 wrote:I don't know enough about math to answer this, but 1) Why are you assuming there's some special reason for this?
2) Pi^3 - e^3 is not exactly equal to eleven, so why would that be the equation?

Not everything in math is intrinsically linked to some other number.

Also...

[quote=gmalivuk]Like scratch123, who is probably the same person, I'm going to go ahead and lock most of these threads. If you insist on starting new discussions about random patterns you think you see between unrelated numbers, quarkcosh1, you can start one thread for all of them.

gmalivuk is known for being incredibly biased so quoting him is pointless. There is even another topic on this board not made by me that compares the square root of 1/3 to another math constant. Also approximation is a perfectly legitimate area of math but sadly many people seem to be unaware how often it is used.

Approximation is relevant for many things, but not for connecting random things. Do you know what is exactly 11? 3^3-4^2=11.
Does it mean anything, no. Does your approximation mean more because it contains pi and e? Well let's put it this way: did you have any real reason for choosing e and pi in that specific configuration?

Also it matters little what you think of gmalivuk, since he can just do what he said he will do no matter whether you consider him biased or not. Making the quote quite relevant. Edit: And looking up at the first post the red text is already there.
Last edited by PeteP on Fri Feb 14, 2014 12:03 am UTC, edited 4 times in total.

gmalivuk
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### Re: quarkcosh1's math coincidences threat

I'm not biased against approximations or the noticing of interesting coincidences. I'm biased against people who insist on posting new threads for every random coincidence they notice where one number isn't even a very good approximation for another. And most importantly, I am biased against people who point out such coincidences and then refuse to accept anyone's argument that it is, in fact, just a coincidence.

The sqrt(3) thread was started by someone without a history of starting similar threads, and who indicated, with the quotes around "why", an understanding that there may not be any important underlying reason for the coincidence.

quarkcosh1: as I edited into the first post of this thread, you are no longer welcome to start any more new threads about this. If you notice another numerical coincidence, post it here and see what people have to say about it.
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quarkcosh1
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### Re: pi^3 - e^3 = 11 and the monster group subgroup structure

WibblyWobbly wrote:
quarkcosh1 wrote:
WibblyWobbly wrote:But don't forget firesoul31's point (2): pi3 - e3 = 10.9207... by my calculator. Definitely not exact, and really not even close enough to suggest anything more than a "huh" response. You get nearly the same level of accuracy from the assertion that pi2 = 10, but that's also not very interesting, IMO. Approximation is useful, as you say, but largely because approximations allow us to do mental math a little faster, not because approximations underlie some greater connections between the numbers. So, if you're saying just that it's a fair approximation, I'll say "sure, for some reason that you need to calculate pi3 - e3 in your head." Other than that, you're going to have to offer something more.

The reason these numbers are interesting is because pi^3 = 31.00 while e^3 = 20.0 . Getting this close to an integer after only cubing the numbers is surprising.

Why?

Edit: more to the point, perhaps, why is it surprising that you get "this close to an integer after only cubing the numbers"? Is there some some reason that low exponents are to be desired? Would higher exponents actually be more likely to be close to integers? (Also, e3 is closer to 20.1, but perhaps that depends on how you define "close to an integer", which you seem to be doing arbitrarily based on what you want to be interesting). I mean, again, depending on your definition of "close", pi2 is pretty close to 10, and I only had to use one constant and square it to get there.

http://en.wikipedia.org/wiki/Mathematical_beauty

This is why low exponents are important. The most relevant part of that link is the low assumptions part. Since you can generate 3 by only applying the successor function a few times you don't have to assume much computational power exists.

gmalivuk
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### Re: quarkcosh1's math coincidences thread

But you *can't* get pi or e by only applying a few simple functions. You *do* need a lot of computational power to get those numbers, so why is it suddenly important to keep things simple when you get to the exponents?
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quarkcosh1
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### Re: quarkcosh1's math coincidences thread

gmalivuk wrote:But you *can't* get pi or e by only applying a few simple functions. You *do* need a lot of computational power to get those numbers, so why is it suddenly important to keep things simple when you get to the exponents?

pi and e can be generated simply in a geometric context. Also pi and e have so many connections to the rest of math that its hard not to generate them when analyzing a variety of math concepts.

Dopefish
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### Re: quarkcosh1's math coincidences thread

I'm mostly going to try to not be involved in this, but as a reader, I'm not terribly ok with the use of = to mean approximately equal, particularly with the sorts of comparisons you're inclined to make. I know you put a warning so that's better than nothing, but it could get confusing if you ever stumble across an actual equality.

I'd rather see something like ~= be used which is similarly easy to type and doesn't need any unicode shenanigans or tex stuff, and should be clearer from context what you mean.

DavCrav
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### Re: quarkcosh1's math coincidences thread

The = means approximately equal. I was looking at the subgroups of the monster group and 11 appears 6 times which seems kind of high since numbers slightly lower than it don't appear as many times. The best explanation I can think of as to why that is is because pi^3 - e^3 = 11 but I can't explain this connection any more deeply than this.

1) I only count 5. (You cannot have 2^{2+11+22}.(M_{24} × S_3) as that's a 2^11, not 11.) You think things like M_{11} "have an 11 in them"?)

2) What? If you want to try an explanation, it could include the fact that the normalizer of the Sylow 11-subgroup is complex reflection (it's G_{16} IIRC) and so the automizer structure matches up for simple groups.

3) The maximal subgroups of the Monster each exist for certain reasons, but 11 isn't one of them. For example, there are many more than this number of copies of PSL_2(2)=S_3, but they aren't maximal, so you don't see them on this list.

gmalivuk
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### Re: quarkcosh1's math coincidences thread

DavCrav wrote:
The = means approximately equal. I was looking at the subgroups of the monster group and 11 appears 6 times which seems kind of high since numbers slightly lower than it don't appear as many times. The best explanation I can think of as to why that is is because pi^3 - e^3 = 11 but I can't explain this connection any more deeply than this.

1) I only count 5. (You cannot have 2^{2+11+22}.(M_{24} × S_3) as that's a 2^11, not 11.) You think things like M_{11} "have an 11 in them"?)

2) What? If you want to try an explanation, it could include the fact that the normalizer of the Sylow 11-subgroup is complex reflection (it's G_{16} IIRC) and so the automizer structure matches up for simple groups.

3) The maximal subgroups of the Monster each exist for certain reasons, but 11 isn't one of them. For example, there are many more than this number of copies of PSL_2(2)=S_3, but they aren't maximal, so you don't see them on this list.
I'd suggest that before delving into details like this, try to determine whether quarkcosh knows anything whatsoever about the Monster group apart from the frequency with which certain numbers show up in that Wikipedia list.
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DavCrav
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### Re: quarkcosh1's math coincidences thread

gmalivuk wrote:I'd suggest that before delving into details like this, try to determine whether quarkcosh knows anything whatsoever about the Monster group apart from the frequency with which certain numbers show up in that Wikipedia list.

Just because someone is stringing together meaningless concepts without any understanding of them doesn't mean they don't get an (meaning one) answer. The next one will cost him at my standard rate as a professional group theorist. And it was just timely because I'm classifying maximal subgroups of simple groups right now.

fishfry
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### Re: quarkcosh1's math coincidences thread

DavCrav wrote:The next one will cost him at my standard rate as a professional group theorist.

Doctor, I'm not feeling very amenable lately. My wife think I'm a monster. She refuses to conjugate with me. I stopped commuting by car and now I cycle. I'm having an identity crisis. Am I normal? If she splits I'll need representation. I used to be a smooth operator, and that's no Lie!

philoctetes
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### Re: quarkcosh1's math coincidences thread

Bravo, fishfry!

PsiSquared
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### Re: quarkcosh1's math coincidences thread

quarkcosh1 wrote:
gmalivuk wrote:But you *can't* get pi or e by only applying a few simple functions. You *do* need a lot of computational power to get those numbers, so why is it suddenly important to keep things simple when you get to the exponents?

pi and e can be generated simply in a geometric context. Also pi and e have so many connections to the rest of math that its hard not to generate them when analyzing a variety of math concepts.

I am not aware of any geometric construction of e.

At any rate, if you're looking for ways to generate the number 11 from basic building blocks, there are far simpler and more elegant ways to do it.

For example: 11 = 23+3 = 32+2 (which is a beautiful coincidence on its own IMO)

Besides, why not simply deal with the number 11 itself? I think "11" is far simpler than your cumbersome "pi^3-e^3" (which doesn't even give the right answer, as 10.92... is not equal to 11).

quarkcosh1
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### I am looking for a certain type of 2 LED's

I am doing a little experiment and I am looking for 2 LED's that emit a certain frequency of light (a different frequency for each LED). The exact frequency in hz or nm doesn't matter much (I would prefer to use visible light or IR though) but the ratio between these 2 frequencies has to equal one of the following numbers:

2.38 since cosh^2(1) = 2.38
1.38 since sinh^2(1)
0.30 since log(2)
1.41 since sqrt(2)

I am hoping that by getting photons that have these frequency ratios to interact I can get something interesting to happen. The problem is I am having trouble finding LED's that correspond to these ratios so I need help finding them.

Sizik
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### Re: I am looking for a certain type of 2 LED's

If you want precise frequencies, you probably want to go with lasers instead of LEDs.

quarkcosh1 wrote:0.30 since log(2)

That is the base-10 log. If there was anything to be found in this endeavor, it would at least be using the natural log.
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### Re: I am looking for a certain type of 2 LED's

What exactly do you expect to happen and how exactly do you plan to make them "interact"? Also, LED spectral lines are not extremely narrow.
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VrookLamar
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### Re: I am looking for a certain type of 2 LED's

1.38 since sinh^2(1)
1.41 since sqrt(2)

That's a pretty amazing coincidence you found, sqrt(2) = sinh^2(1).

quarkcosh1
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### Re: I am looking for a certain type of 2 LED's

YpsilonOmega wrote:What exactly do you expect to happen and how exactly do you plan to make them "interact"? Also, LED spectral lines are not extremely narrow.

So if I touch the 2 leds together none of the photons will interact? I know photons don't usually interact but I remember reading that photons at high enough energy can sometimes create quarks and electrons. I am not saying this will happen here but I at least hope to see something.

Sizik wrote:If you want precise frequencies, you probably want to go with lasers instead of LEDs.

quarkcosh1 wrote:0.30 since log(2)

That is the base-10 log. If there was anything to be found in this endeavor, it would at least be using the natural log.

I was wondering why google and wolfram alpha were giving me different results for log(2) so I guess it is because one of them uses log 10. I am still interested in that number though since it can be derived from the fine structure constant as shown here: http://en.wikipedia.org/wiki/Fine-struc ... Definition. I guess I could try lasers instead and I did look at some of those as well but I was still having trouble finding the frequency ratio I wanted.

Dopefish
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### Re: I am looking for a certain type of 2 LED's

Is there any particular reasoning on which of the two in the ratio is on the top or the bottom?

One of your ratios is less than 1, so it's not a matter of just consistently putting the higher frequency one in the numerator.

quarkcosh1
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### Re: I am looking for a certain type of 2 LED's

Dopefish wrote:Is there any particular reasoning on which of the two in the ratio is on the top or the bottom?

One of your ratios is less than 1, so it's not a matter of just consistently putting the higher frequency one in the numerator.

I considered writing out the inverse of log10(2) but decided against it because I would just have to invert it again to show how it was related to the fine structure constant.

gmalivuk
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### Re: quarkcosh1's math coincidences thread

I put this in your math coincidences thread, because that seems to underlie whatever you're trying to do here.

Here is some description of how photons interact, but I can't imagine how you're going to get anything special from the random ratios you've picked here.
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cjameshuff
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### Re: I am looking for a certain type of 2 LED's

quarkcosh1 wrote:I am doing a little experiment and I am looking for 2 LED's that emit a certain frequency of light (a different frequency for each LED). The exact frequency in hz or nm doesn't matter much (I would prefer to use visible light or IR though) but the ratio between these 2 frequencies has to equal one of the following numbers:

2.38 since cosh^2(1) = 2.38
1.38 since sinh^2(1)
0.30 since log(2)
1.41 since sqrt(2)

I am hoping that by getting photons that have these frequency ratios to interact I can get something interesting to happen. The problem is I am having trouble finding LED's that correspond to these ratios so I need help finding them.

Sunlight contains all those ratios.

Forest Goose
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### Re: I am looking for a certain type of 2 LED's

quarkcosh1 wrote:I am doing a little experiment and I am looking for 2 LED's that emit a certain frequency of light (a different frequency for each LED). The exact frequency in hz or nm doesn't matter much (I would prefer to use visible light or IR though) but the ratio between these 2 frequencies has to equal one of the following numbers:

2.38 since cosh^2(1) = 2.38
1.38 since sinh^2(1)
0.30 since log(2)
1.41 since sqrt(2)

I am hoping that by getting photons that have these frequency ratios to interact I can get something interesting to happen. The problem is I am having trouble finding LED's that correspond to these ratios so I need help finding them.

I don't exactly understand what you're proposing here:

Is there some reaction that you are expecting?
Is there some reason you expect something specifically at these values?

Unless there is some theoretical reason to expect to find something novel, this seems entirely random and pointless - if there is a reason, then, obviously, that doesn't apply, but it just seems arbitrary without further explanation.
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D.B.
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### Re: quarkcosh1's math coincidences thread

But full marks for actually looking at making an empirical test for your theory.

quarkcosh1
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### Re: quarkcosh1's math coincidences thread

gmalivuk wrote:I put this in your math coincidences thread, because that seems to underlie whatever you're trying to do here.

Here is some description of how photons interact, but I can't imagine how you're going to get anything special from the random ratios you've picked here.

No it doesn't. I am trying to do an experiment not point out coincidences since those coincidences have been already posted before. If I didn't post their mathematical representation people would be asking me what was so special about those numbers in order to justify doing an experiment about them. You can't just say I am not allowed to discuss certain numbers because they happened to be used in another topic that had to do with coincidences. I really can't believe your reasoning is this bad but you are always finding ways to surprise me. You are seriously the worst mod on the internet.

I have been thinking that maybe having 2 photons interact isn't the best idea but I still want to do something with electricity and ratios. Maybe I could do the ratios between 2 charges but I am not sure what type of equipment I would need for that. If you have any other ideas involving electricity and ratios feel free to post them.

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### Re: quarkcosh1's math coincidences thread

What do you mean by "experiment?" Is there a thing you are trying to test?
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### Re: quarkcosh1's math coincidences thread

doogly wrote:What do you mean by "experiment?" Is there a thing you are trying to test?

quarkcosh1 wrote:I am hoping that by getting photons that have these frequency ratios to interact I can get something interesting to happen. The problem is I am having trouble finding LED's that correspond to these ratios so I need help finding them.

I'm putting my money on tachyon generation.